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Deep Convective Adjustment of Temperature and Moisture
Abstract
Simple process models and complex climate models are remarkably sensitive to the timescale of convective adjustment (τ), but this parameter remains poorly constrained and understood. This study uses the linear-range slope of a semi-empirical relationship between precipitation and a lower-free tropospheric buoyancy measure ( B L ). The B L measure is a function of layer-averaged moist enthalpy in the boundary layer (150 hPa thick layer above surface), and temperature and moisture in the lower-free troposphere (boundary layer top to 500 hPa). Sensitivity parameters with units of time quantify the B L response to its component perturbations. In moist enthalpy units, B L is more sensitive to temperature than equivalent moisture perturbations. However, column-integrated moist static energy conservation ensures that temperature and moisture are equally altered during the adjustment process. Multiple adjusted states with different temperature-moisture combinations exist; the B L sensitivity parameters govern the relationship between adjusted states, and also combine to yield a timescale of convective adjustment ~ 2 hours. This value is comparable to τ values used in cumulus parameterization closures. Disparities in previously reported values of τ are attributed to the neglect of the temperature contribution to precipitation, and to averaging operations that include data from both precipitating and non-precipitating regimes. A stochastic model of tropical convection demonstrates how either averaging operations or neglected environmental influences on precipitation can yield τ estimates longer than the true τ value built into the model. The analysis here culminates in construction of a precipitation closure with both moisture and temperature adjustment (q-T closure), suitable for use in both linearized and non-linear, intermediate-complexity models.
... We formulate a linear scheme for the convective process based on the separate contributions of the PBL and the free troposphere, as suggested by Zhang (2002), whose scheme resulted in better MJO simulation in a GCM (Zhang and Mu 2005). First, the convective heat source and moisture sink are related to the free-tropospheric moisture anomaly with a convective adjustment timescale τc of 12-18 hours (Bretherton et al. 2004;Adames and Kim 2016;Rushley et al. 2018;Ahmed et al. 2020). Vertical profiles of the convective heat source and moisture sink terms are determined by combinations of both the vertical gradients of the dry static energy and moisture of the basic state, respectively, and the standardized vertical motion analytically derived from the slow moist mode solution reported by Neelin and Yu (1994) that approximates the first baroclinic vertical structure in the tropics. ...
... File generated with AMS Word template 2.0 timescale τb is a few hours based on the typical lifetime of shallow mesoscale convective systems in the tropics (Houze Jr. 2004;Betts and Miller 1993). This time scale needs additional theoretical support to improve further (e.g., Ahmed et al. 2020). Note that this part is not essential for simulating the internal variability (Section 4c) but is more important for calculating the steady response to SST forcing. ...
... In contrast, the period is still 68 days even when the timescale τb = 240 hours, indicating that the impact of the convective heating associated with PBL moisture on the propagation mechanism is secondary (τb=6h, τb=13h, and τb=240h; see also, noLSCτb=240h). Tuning these adjustment time scales based on theory (e.g., Ahmed et al. 2020) is interesting to simulate the propagating mode more realistically. Note that the result is insensitive to the convective efficiency (noCeff), which reduces precipitation under a dry basic state. ...
Tropical intraseasonal variability (ISV) is dominated by the Madden–Julian oscillation (MJO), and its spatiotemporal characteristics vary with the Indo-Pacific warm-pool background on seasonal and longer timescales. Previous works have suggested ISV dynamics in various frameworks, whereas a unifying view remains challenging. Motivated by the recent advance in moisture mode theory, we revisit the ISV as a leading moisture mode modulated by varying background states derived from a reanalysis, using a moist linear baroclinic model (mLBM) improved with a simple convective scheme relating convective precipitation to tropospheric and boundary-layer moisture anomalies and simple cloud–radiative feedback representations. Under a boreal winter background state, this mLBM yielded a large-scale but local eastward-propagating mode with a phase speed of 3–5 m/s over the warm-pool region, resembling the MJO. Background lower-tropospheric winds and thermodynamic fields are important in determining the growth rate and periodicity of the leading mode, whose stability depends on cloud–radiative feedback and background state variations. We further demonstrate why the MJO is locally contained in the Indo-Pacific warm-pool region. The local thermal/moisture condition and Walker circulation greatly enhance its instability, but outside this region, this mode is heavily damped. Thus, the expansion/contraction of this warm-pool condition may enhance/reduce its instability and expand/reduce its domain of activity. Prescribing El Niño background causes eastward displacement of the wintertime ISV activity, reminiscent of the observed MJO modulations by El Niño. Under a summer background state, the eastward-propagating leading mode resembles the boreal summer ISV but biased, requiring further model improvements.
... This sensitivity is well captured if the convection is treated as an entraining plume whose buoyancy is determined by the thermodynamic properties of the boundary layer and the overlying free troposphere (Brown and Zhang 1997;Ahmed and Neelin 2018;Schiro and Neelin 2019a;Wolding et al. 2022). Application of this plume buoyancy framework to observations and reanalysis reveals that rainfall increases steeply and quasi linearly after some critical buoyancy value is exceeded Ahmed et al. 2020;Adames et al. 2021). While this linear relationship has been used to parameterize convection in simple models of tropical motions (Ahmed et al. 2020(Ahmed et al. , 2021Adames et al. 2021;Ahmed 2021), we still lack an explanation for it that is based on first principles. ...
... Application of this plume buoyancy framework to observations and reanalysis reveals that rainfall increases steeply and quasi linearly after some critical buoyancy value is exceeded Ahmed et al. 2020;Adames et al. 2021). While this linear relationship has been used to parameterize convection in simple models of tropical motions (Ahmed et al. 2020(Ahmed et al. , 2021Adames et al. 2021;Ahmed 2021), we still lack an explanation for it that is based on first principles. It is well-known that tropical precipitation is directly related to large-scale vertical motions via the weak temperature gradient approximation (Sobel and Bretherton 2000;Sobel et al. 2001). ...
... If we scale the convective available potential energy (CAPE = ∫ ) of the cloud cluster as H we obtain a value of 100 J kg −1 . Thus, the buoyancy and CAPE are small in these clusters, consistent with both observations and with quasi-equilibrium thinking (Emanuel et al. 1994;Singh and O'Gorman 2013;Ahmed and Neelin 2018;Ahmed et al. 2020;Adames et al. 2021). Note that the CAPE we 1The parameter should vary in space since it depends on the the vertical mass flux of small-scale updrafts and downdrafts. ...
The "damped gravity wave" (DGW) approximation occurs when convective momentum dissipation is balanced by the pressure gradient force of convectively forced gravity waves. While this balance has been used to parameterize large-scale lifting in limited-domain models of tropical deep convection, its applicability to observed phenomena has not been carefully examined. A scale analysis indicates that DGW balance can occur in tropical cloud clusters occurring in low shear environments, with horizontal scales of ~ 100 km or greater and timescales of a day. The DGW balance is then used to explain three well-known properties of tropical deep convection. First, DGW balance implies that the average mesoscale vertical velocity in cloud clusters will be closer to first baroclinic, with second baroclinic motions contributing a smaller fraction of the total ascent. The first baroclinic mode is dominant because gravity waves and momentum diffusion induce a nonlocal velocity response to buoyancy, making ascent over regions of negative buoyancy possible. Second, a combination of the weak temperature gradient (WTG) and DGW balances yields a form of convective quasi-equilibrium, with adjustment timescales comparable to those previously estimated. Third, the use of WTG-DGW approximations in an entraining plume model reproduces the empirical precipitation-buoyancy relationship from Ahmed and Neelin. The sensitivity of precipitation to mean CAPE is interpreted as a small excursion from the zero buoyancy approximation where the undilute buoyancy and dilution by entrainment nearly, but not completely, cancel. Overall, these results support viewing cloud clusters as a coupling between deep convection and gravity waves.
... CC BY 4.0 License. temperature anomaly θ ′ eB (Ahmed et al., 2020): ...
... (1) depends positively on θ ′ eB because it increases undilute plume buoyancy, and depends positively on q ′ L through its effect on entrainment (the entrainment of moister free-tropospheric air is less efficient at reducing the buoyancy of ensembles of convective plumes). The negative dependence on T ′ L arises through its combined effect on undilute buoyancy (a colder lower-free-troposphere yields higher convective available potential energy) 65 and on the subsaturation of the free troposphere (Ahmed et al., 2020). ...
... The theoretical sensitivity estimate depends on the definition of the lower-tropospheric 280 layer used to define T ′ L and q ′ L . There is uncertainty in the definition of its lower edge (the boundary layer top) and its upper boundary has been chosen somewhat arbitrarily here and in past related work (Nicolas and Boos, 2022;Ahmed et al., 2020). ...
Some of the rainiest regions on Earth lie upstream of tropical mountains, where the interaction of prevailing winds with orography produces frequent precipitating convection. Yet, the response of tropical orographic precipitation to the large-scale wind and temperature variations induced by anthropogenic climate change remains largely unconstrained. Here, we quantify the sensitivity of tropical orographic precipitation to background cross-slope wind using theory, idealized simulations, and observations. We build on a recently developed theoretical framework that predicts enhanced seasonal-mean convective precipitation in response to cooling and moistening of the lower free-troposphere by stationary orographic gravity waves. Using this framework and convection-permitting simulations, we show that higher cross-slope wind speeds deepen the penetration of the cool and moist gravity wave perturbation upstream of orography, resulting in a mean rainfall increase of 20–30 % per m s−1 increase in cross-slope wind speed. Additionally, we show that orographic precipitation in five tropical regions exhibits a similar dependence on changes in cross-slope wind at both seasonal and daily timescales. Given next-century changes in large-scale winds around tropical orography projected by global climate models, this strong scaling rate implies wind-induced changes in some of Earth's rainiest regions that are comparable with any produced directly by increases in global mean temperature and humidity.
... Considerations of entrainment/dilution of CAPE have led to more realistic representations of convective processes in models (Zhang 2009); lack of entrainment can render models unable to reproduce convective variability across subdaily to interannual timescales (Tokioka et al. 1988;Neale et al. 2008;Del Genio and Wu 2010;Kim et al. 2012). More recently, measures of LFT buoyancy have expanded on the relationship between the entrainment process and precipitation Ahmed et al. 2020;Adames et al. 2021;Ahmed and Neelin 2021a;Wolding et al. 2020Wolding et al. , 2022. Specifically, observed mass flux profiles and vertical velocities imply substantial entrainment of environmental air through the lower free troposphere (Kumar et al. 2015;Giangrande et al. 2016;Schiro et al. 2018). ...
... Convective adjustment is employed as a closure in several convective schemes (Manabe and Strickler 1964;Manabe et al. 1965;Betts 1986;Betts and Miller 1986;Keil et al. 2014) and is generalized as convective quasi-equilibrium (e.g., Arakawa and Schubert 1974;Emanuel et al. 1994). The adjustment process is assumed to happen instantaneously or with a finite adjustment timescale (Moorthi and Suarez 1992;Zhang and McFarlane 1995;Bechtold et al. 2008;Ahmed et al. 2020). ...
... The leading order (small buoyancy) approximation can be used to estimate radiative-convective equilibrium temperature and moisture profiles (Singh and O'Gorman 2013;Zhou and Xie 2019) and provides a method for consistently treating departures from zero buoyancy associated with raining events (e.g. Ahmed et al. 2020). In section 7, we derive the "pseudo-entrainment" diagnostic, an estimate of entrainment undergone by a bulk plume through the LFT, by applying the small buoyancy approximation to thermodynamic profiles of the environment. ...
Conditional instability and the buoyancy of plumes drive moist convection but have a variety of representations in model convective schemes. Vertical thermodynamic structure information from Atmospheric Radiation Measurement (ARM) sites and reanalysis (ERA5), satellite-derived precipitation (TRMM3b42), and diagnostics relevant for plume buoyancy are used to assess climate models. Previous work has shown that CMIP6 models represent moist convective processes more accurately than their CMIP5 counterparts. However, certain biases in convective onset remain pervasive among generations of CMIP modeling efforts. We diagnose these biases in a cohort of nine CMIP6 models with sub-daily output, assessing conditional instability in profiles of equivalent potential temperature θ e and saturation equivalent potential temperature θ es in comparison to a plume model with different mixing assumptions. Most models capture qualitative aspects of the θ es vertical structure, including a substantial decrease with height in the lower free troposphere associated with the entrainment of subsaturated air. We define a “pseudo-entrainment” diagnostic that combines subsaturation and a θ es measure of conditional instability similar to what entrainment would produce under the small-buoyancy approximation. This captures the trade-off between larger θ es lapse rates (entrainment of dry air) and small subsaturation (permits positive buoyancy despite high entrainment). This pseudo-entrainment diagnostic is also a reasonable indicator of the critical value of integrated buoyancy for precipitation onset. Models with poor θ e / θ es structure (those using variants of the Tiedtke Scheme) or low entrainment runs of CAM5, and models with low subsaturation, such as NASA-GISS, lie outside the observational range in this diagnostic.
... In this study, we will examine the role that temperature and moisture may have in the convective coupling and thermodynamics of AEWs and PEWs. To understand the convective coupling we will make use of the plume buoyancy framework developed by Ahmed and Neelin (2018) and expanded upon by Ahmed et al. (2020) and Adames et al. (2021). We will also implement the scale analysis framework of Adames et al. (2019) and Adames (2022) to understand the relative importance of temperature and moisture in the thermodynamic evolution of these waves. ...
... In this study, we make use of the plume buoyancy framework developed by Ahmed and Neelin (2018) and extended upon by Ahmed et al. (2020) and Adames et al. (2021) to diagnose PEW and AEW-related rainfall. The main variables are shown in Table 1. ...
... where is the latent heat of vaporization, * is the saturation specific humidity, is the specific heat of dry air at constant pressure, is the gas constant of water vapor, and is the temperature. Ahmed et al. (2020) showed that precipitation increases quasi-linearly once the LFT averaged value of ( ) exceeds a critical value. They parameterized this pickup curve in their model using a ramp function. ...
The thermodynamic processes associated with convection in Tropical African and Northeastern Pacific Easterly Waves (AEWs and PEWs, respectively) are examined on the basis of Empirical Orthogonal Functions (EOFs) and a plume-buoyancy framework. Linear regression analysis reveals the relationship between temperature, moisture, buoyancy, and precipitation in EWs. Plume buoyancy is found to be highly correlated with rainfall in both AEWs and PEWs, and a near 1:1 relationship is found between a buoyancy-based diagnostic of rainfall and rainfall rates from ERA5. Close inspection of the contribution of moisture and temperature to plume buoyancy reveals that temperature and moisture contribute roughly equally to the buoyancy in AEWs, while moisture dominates the distribution of buoyancy in PEWs. A scale analysis is performed in order to understand the relative amplitudes of temperature and moisture in easterly waves. It is found that the smaller contribution of temperature to the thermodynamics of PEWs relative to AEWs is related to their slower propagation speed, which allows PEWs to more robustly adjust to weak temperature gradient (WTG) balance. The consistency of the buoyancy analysis and the scale analysis indicates that PEWs are moisture modes: waves in which water vapor plays a dominant role in their thermodynamics. AEWs, on the other hand, are mixed waves in which temperature and moisture play similar roles in their thermodynamics. 2
... Specifically, we use QE theory to describe the statistical average effect of mountains on time-mean convective precipitation, rather than formulating a theory of event-wise convective triggering by orographic ascent. While early QE theories employed CAPE-based convective closures, we leverage recent developments that incorporate observed relationships between precipitation and lower-tropospheric temperature and humidity (Derbyshire et al. 2004;Raymond et al. 2015;Ahmed et al. 2020). We discuss further details and possible caveats, such as whether Eulerian or Lagrangian time scales are relevant for evaluating the validity of QE, later in the context of results from our idealized model. ...
... Its aim is to account for the main features of time-mean precipitation around the ridge (peak value, spatial extent of upstream enhancement, rain shadow length), as a function of large-scale flow characteristics and ridge shape. The theory is based loosely on the Quasiequilibrium Tropical Circulation Model (QTCM) of Neelin and Zeng (2000), but employs the moisturetemperature ( − ) convective parameterization proposed by Ahmed et al. (2020). This closure was derived from the empirical relationship between precipitation and lowerfree-tropospheric buoyancy and parameterizes precipitation as a response to both temperature and moisture perturbations, with different sensitivities. ...
... In addition to these orographically induced thermodynamic variations, we will show that the solution depends on the convective adjustment time scales and on an advective length scale, with the latter being the product of the background wind speed with a time scale for relaxation to radiative-4 AMS JOURNAL NAME convective equilibrium (RCE). The mountain wave may also modify the tropospheric static stability and wind shear, but we focus on lower-tropospheric temperature and moisture anomalies because these have been found to exert a strong control on deep convection (Derbyshire et al. 2004;Raymond et al. 2015;Ahmed et al. 2020). ...
Spatial patterns of tropical rainfall are strongly influenced by mountains. Although theories for precipitation induced by convectively stable upslope ascent exist for the midlatitudes, these do not represent the interaction of moist convection with orographic forcing. Here, we present a theory for convective precipitation produced by the mechanical interaction of a tropical ridge with a basic state horizontal wind. Deviations from this basic state are represented as the sum of a 'dry' perturbation, due to the stationary orographic gravity wave, and a 'moist' perturbation that carries the convective response. The moist component dynamics are subject to the weak temperature gradient approximation; they are forced by the dry mode's influence on lower-tropospheric moisture and temperature. Analytical solutions provide estimates of the precipitation profile, including peak precipitation, upstream extent, and rain shadow extent. The theory can be used with several degrees of complexity depending on the technique used to compute the dry mode, which can be drawn from linear mountain wave theory or full numerical simulations. To evaluate the theory, we use a set of convection-permitting simulations with a flow-perpendicular ridge in a long channel. The theory makes a good prediction for the cross-slope precipitation profile, indicating that the organization of convective rain by orography can be quantitatively understood by considering the effect of stationary orographic gravity waves on a lower-tropospheric convective quasiequilibrium state.
... The terms τ t and τ q can be defined as a measure of the sensitivity of precipitation to temperature and moisture fluctuations. The values of τ t and τ q in Equation 5 are estimated as in Ahmed et al. (2020), where precipitation can be related to moisture and temperature by using a multiple linear regression model as follows, ...
... For the Indo-Pacific warm pool region, we obtain an average value of the convective sensitivities τ t and τ q of about 12.5 and 24.3 hr. These values are longer than those used in Ahmed et al. (2021) because using time-filtered data always yields larger adjustment times since precipitating and non-precipitating times are convolved (Ahmed et al., 2020). Similar values are obtained outside the warm pool except near the prime meridian, where both τ q and τ t increase by nearly a factor of 3. ...
Plain Language Summary
The Madden‐Julian Oscillation is one of the most important phenomena that occur at the subseasonal to seasonal timescale and is a source of weather predictability at this timescale. Despite its importance, many features of Madden‐Julian Oscillation (MJO) remain elusive, and many theories have been proposed to understand its behavior. Arguably, the most recent popular MJO theory is the moisture mode theory. The theory posits that moisture governs the evolution of the MJO. Here, we show that this theory is applicable only over the Indian Ocean, where MJO's small zonal scale and slow propagation allow moisture modes to exist at the scale of the MJO. Elsewhere, temperature fluctuations in the MJO become as important as moisture, a feature that is inconsistent with the moisture mode theory.
... The precipitation onset determines the most probable thermodynamic phase space for precipitating points 57-59 , thereby governing the mean state. The B L measure is a function of lower-tropospheric measures of subsaturation and convective instability (see Methods); a consequence is that the B L threshold is attained in stable environments when convection's moisture sensitivity is small but in unstable environments if the moisture sensitivity is large 60 . This behavior is confirmed using CAM5.3 sub-daily output (Fig. 8c-d) in which weak entrainment (Fig. 8c) permits convective onset in a more stable troposphere, compared to a case with strong entrainment (Fig. 8d). ...
... This quantity is then multiplied by 340 K to be expressed in units of K. Similarly, subsaturation is computed as the difference between θ * eL and the lower free tropospheric equivalent temperature (θ eL ), and then normalized by θ * eL . This quantity is then also multiplied by 340 K to be expressed in units of K. Detailed derivations of these quantities are available in 55,60 . ...
Among models participating in the Coupled Model Intercomparison Project phase 6 (CMIP6), here we show that the magnitude of the tropical low cloud feedback, which contributes considerably to uncertainty in estimates of climate sensitivity, is intimately linked to tropical deep convection and its effects on the tropical atmospheric overturning circulation. First, a reduction in tropical ascent area and an increased frequency of heavy precipitation result in high cloud reduction and upper-tropospheric drying, which increases longwave cooling and reduces subsidence weakening, favoring low cloud reduction (Radiation-Subsidence Pathway). Second, increased longwave cooling decreases tropospheric stability, which also reduces subsidence weakening and low cloudiness (Stability-Subsidence Pathway). In summary, greater high cloud reduction and upper-tropospheric drying (negative longwave feedback) lead to a more positive cloud feedback among CMIP6 models by contributing to a greater reduction in low cloudiness (positive shortwave feedback). Varying strengths of the two pathways contribute considerably to the intermodel spread in climate sensitivity. The magnitude of the tropical low cloud feedback, which contributes considerably to uncertainty in estimates of climate sensitivity, is closely linked to tropical deep convection and its effects on the tropical atmospheric overturning circulation.
... More analysis with real-data forecasts compared against observations are needed to clarify this point. buoyancy (B L ) (Ahmed et al., 2020). SF, also known as column relative humidity, is the ratio of precipitable water vapor to saturated precipitable water vapor. ...
... , Π is the Exner function, g is gravity, subscript L represents lower-tropospheric layer (500-850 hPa), subscript B represents the boundary layer (850-1,000 hPa), and w L and w B are weighting functions set as 0.52 and 0.48 (Ahmed et al., 2020). ...
This study investigates the effects of resolved deep convection on tropical rainfall and its multi‐scale variability. A series of aquaplanet simulations are analyzed using the Model for Prediction Across Scales‐Atmosphere with horizontal cell spacings from 120 to 3 km. The 3‐km experiment uses a novel configuration with 3‐km cell spacing between 20°S and 20°N and 15‐km cell spacing poleward of 30°N/S. A comparison of those experiments shows that resolved deep convection yields a narrower, stronger, and more equatorward intertropical convergence zone, which is supported by stronger nonlinear horizontal momentum advection in the boundary layer. There is also twice as much tropical rainfall variance in the experiment with resolved deep convection than in the experiments with parameterized convection. All experiments show comparable precipitation variance associated with Kelvin waves; however, the experiment with resolved deep convection shows higher precipitation variance associated with westward propagating systems. Resolved deep convection also yields at least two orders of magnitude more frequent heavy rainfall rates (>2 mm hr⁻¹) than the experiments with parameterized convection. A comparison of organized precipitation systems demonstrates that tropical convection organizes into linear systems that are associated with stronger and deeper cold pools and upgradient convective momentum fluxes when convection is resolved. In contrast, parameterized convection results in more circular systems, weaker cold pools, and downgradient convective momentum fluxes. These results suggest that simulations with parameterized convection are missing an important feedback loop between the mean state, convective organization, and meridional gradients of moisture and momentum.
... By considering the effect of convective entrainment, these relationships were framed in terms of the buoyancy of a hypothetical cloud that mixes with its environment by Ahmed and Neelin (2018). The authors used the observed precipitation-buoyancy relationship to motivate a model for the adjustment of temperature and moisture within the troposphere, finding a relationship between stability and humidity similar to that described by the ZBP model above (Ahmed et al., 2020). ...
Our conceptual understanding of the tropical thermal structure is based on two complementary idealisations: one stemming from convective quasi‐equilibrium (QE) and the other being the weak temperature gradient (WTG) approximation. Through QE, moist convection provides a vertical control on the thermal structure, while, under WTG, wave dynamics are assumed to provide a non‐local horizontal control. While it is clear that moist convection plays an important role in setting the tropical mean stability through QE, the extent to which QE implies a local constraint on stability or whether the requirement for WTG effectively inhibits the influence of local conditions on stability remains debated. Here we hypothesise that a strong local vertical control of the thermal structure would imply a relationship between humidity and stability in the troposphere, as convection within moister regions would be less affected by entrainment of surrounding air. We utilise a combination of ERA5 reanalysis and observational data to examine the relationship between stability and local humidity across the Tropics. The results are compared with a prediction based upon a specific realisation of the theory of QE that incorporates entrainment through a simple plume model. We discover that, in convective regions, wave dynamics do not eliminate the effect of local conditions on stability, and that the resulting relationship between stability and humidity can be approximated well by the entraining plume model. Since QE is not applicable in the absence of convection, in non‐convective regions the WTG, and possibly other factors, acts to set stability in the region. These results may help us understand the controls on horizontal density gradients in the tropical troposphere and the associated overturning circulations.
... The relative contribution of the boundary-layer instability and LFT dryness to convective buoyancy depends on the weighting w of LFT environmental air typically entrained by convecting plumes. Observations suggest that both the boundary layer and LFT contribute nearly equally to the properties of a convective plume 44,46,49 , yielding approximately equal weighting 47 of the instability and dryness measures, that is, w ≈ 1 in equation (1). Climate models with slightly different entrainment could have slightly different values of w, but the overall effects would be similar. ...
Moist heatwaves in the tropics and subtropics pose substantial risks to society, yet the dynamics governing their intensity are not fully understood. The onset of deep convection arising from hot, moist near-surface air has been thought to limit the magnitude of moist heatwaves. Here we use reanalysis data, output from the Coupled Model Intercomparison Project Phase 6 and model entrainment perturbation experiments to show that entrainment of unsaturated air in the lower-free troposphere (roughly 1–3 km above the surface) limits deep convection, thereby allowing much higher near-surface moist heat. Regions with large-scale subsidence and a dry lower-free troposphere, such as coastal areas adjacent to hot and arid land, are thus particularly susceptible to moist heatwaves. Even in convective regions such as the northern Indian Plain, Southeast Asia and interior South America, the lower-free tropospheric dryness strongly affects the maximum surface wet-bulb temperature. As the climate warms, the dryness (relative to saturation) of the lower-free tropospheric air increases and this allows for a larger increase of extreme moist heat, further elevating the likelihood of moist heatwaves.
... The Convective Quasi-Equilibrium (CQE) theory, first introduced by Arakawa and Schubert (1974), posits that convective energy within cumulus ensemble remains in statistical equilibrium, balanced between large-scale replenishment and cloud-scale consumption. Intrinsic to the equilibrium, moist convection actively steers vertical temperature perturbations toward specific reference profiles, a principle embedded in various moist convective adjustments (Ahmed et al., 2020;Betts, 1973;Betts & Miller, 1986;Kuo, 1974;Manabe et al., 1965) and parameterizations (Chikira & Sugiyama, 2010;Frierson, 2007;Moorthi & Suarez, 1992;Randall & Pan, 1993;T. Wu, 2012;G. ...
Plain Language Summary
Convective Quasi‐Equilibrium (CQE) is a concept in atmospheric science that explains a state where the influence of deep convection (cumulonimbus clouds) and large‐scale atmospheric forces is balanced, causing certain thermodynamic properties to adjust toward specific reference profiles. Previous studies have focused on how temperature changes relate to the CQE structure but in specific regions or sites while this study aims areas near deep convection—supposedly the source of CQE constraints. Using a unique framework with data from multiple satellites, we track the evolution of temperature patterns near deep convection and find temperatures near deep convection with extreme rainfall are adjusted toward the CQE structure rapidly within 3 hr of maximum rainfall. However, only the deep convection with top 7% extreme rainfall can effectively affect nearby temperature pattern beyond 1°, with the top 1% influencing up to an 9° radius. These findings highlight the dominant impact of a small fraction of deep convection, particularly those with extreme rainfall, on nearby temperature perturbation patterns.
... − ⟨ ⟩ DIBcrit., disorg. (Peters and Neelin 2006;Neelin et al. 2009;Ahmed et al. 2020). Mesoscale convective organization is poorly represented in many current weather and climate models. ...
An energy budget combining atmospheric moist static energy (MSE) and upper ocean heat content (OHC) is used to examine the processes impacting day-to-day convective variability in the tropical Indian and western Pacific oceans. Feedbacks arising from atmospheric and oceanic transport processes, surface fluxes, and radiation drive the cyclical amplification and decay of convection around suppressed and enhanced convective equilibrium states, referred to as shallow and deep convective discharge-recharge (D-R) cycles respectively. The shallow convective D-R cycle is characterized by alternating enhancements of shallow cumulus and stratocumulus, often in the presence of extensive cirrus clouds. The deep convective D-R cycle is characterized by sequential increases in shallow cumulus, congestus, narrow deep precipitation, wide deep precipitation, a mix of detached anvil and alto-stratus and alto-cumulus, and once again shallow cumulus cloud types. Transitions from the shallow to deep D-R cycle are favored by a positive “column process” feedback, while discharge of convective instability and OHC by mesoscale convective systems (MCSs) contributes to transitions from the deep to shallow D-R cycle. Variability in the processes impacting MSE is comparable in magnitude to, but considerably more balanced than, variability in the processes impacting OHC. Variations in the quantity of atmosphere-ocean coupled static energy (MSE+OHC) result primarily from atmospheric and oceanic transport processes, but are mainly realized as changes in OHC. MCSs are unique in their ability to rapidly discharge both lower tropospheric convective instability and OHC.
... where is a convective moisture relaxation timescale. While the relationship between and is nonlinear (Bretherton et al. 2004;Ahmed and Neelin 2018;Ahmed et al. 2020;Emanuel 2019), using this linear form will significantly simplify the interpretation of the results of this study. ...
Interactions between large-scale waves and the Hadley Cell are examined using a linear two-layer model on an f-plane. A linear meridional moisture gradient determines the strength of the idealized Hadley Cell. The trade winds are in thermal wind balance with a weak temperature gradient (WTG). The mean meridional moisture gradient is unstable to synoptic-scale (horizontal scale of ∼1000 km) moisture modes that are advected westward by the trade winds, reminiscent of oceanic tropical depression-like waves. Meridional moisture advection causes the moisture modes to grow from “moisture-vortex instability” (MVI), resulting in a poleward eddy moisture flux that flattens the zonal-mean meridional moisture gradient, thereby weakening the Hadley Cell. The amplification of waves at the expense of the zonal-mean meridional moisture gradient implies a downscale latent energy cascade. The eddy moisture flux is opposed by a regeneration of the meridional moisture gradient by the Hadley Cell. These Hadley Cell-moisture mode interactions are reminiscent of quasi-geostrophic interactions, except that wave activity is due to column moisture variance rather than potential vorticity variance. The interactions can result in predator-prey cycles in moisture mode activity and Hadley Cell strength that are akin to ITCZ breakdown. It is proposed that moisture modes are the tropical analog to midlatitude baroclinic waves. MVI is analogous to baroclinic instability, stirring latent energy in the same way that dry baroclinic eddies stir sensible heat. These results indicate that moisture modes stabilize the Hadley Cell, and may be as important as the latter in global energy transport.
... Generally, deterministic schemes "fire-off" when a deterministic condition is satisfied (Suhas and Zhang 2014;Rio et al. 2019), while stochastic schemes fire-off with "some" probability. The main impediment is the necessity to carefully constraint this "firing-off" probability observationally, for which process-oriented diagnostics, as advocated by Rio et al. (2019), relating precipitation to measures of buoyancy (Neelin et al. 2008;Khouider et al. 2010;Kuo et al. 2018;Schiro et al. 2016Schiro et al. , 2018Ahmed and Neelin 2018;Ahmed et al. 2020;Serrano-Vincenti et al. 2020) are a starting point. ...
The performance of GCMs in simulating daily precipitation probability distributions are investigated by comparing 35 CMIP6 models against observational datasets (TRMM-3B42 and GPCP). In these observational datasets, PDFs on wet days follow a power-law range for low and moderate intensities below a characteristic precipitation cutoff-scale. Beyond the cutoff-scale, the probability drops much faster, hence controlling the size of extremes in a given climate. In the satellite products analyzed, PDFs have no interior peak. Contributions to the first and second moments tend to be single-peaked, implying a single dominant precipitation scale— the relationship to the cutoff scale and log-precipitation coordinate and normalization of frequency density are outlined. Key metrics investigated include the fraction of wet days, PDF power-law exponent, cutoff-scale, shape of probability distributions and number of probability peaks. The simulated power-law exponent and cutoff-scale generally fall within observational bounds, although these bounds are large; GPCP systematically display smaller exponent and cutoff-scale than TRMM-3B42. Most models simulate a more complex PDF shape than these observational datasets, with both PDFs and contributions exhibiting additional peaks in many regions. In most of these instances, one peak can be attributed to large-scale precipitation and the other to convective precipitation. Similar to previous CMIP phases, most models also rain too often and too lightly. These differences in wet-day fraction and PDF shape occur primarily over oceans and may relate to deterministic scales in precipitation parameterizations. It is argued that stochastic parameterizations may contribute to simplifying simulated distributions.
... The use of B L provides a framework to understand the sensitivity of precipitation to changes in its thermodynamic environment. Following Ahmed et al. (2020), we can decompose B L into two terms: ...
Purpose of Review:
Review our current understanding of how precipitation is related to its thermodynamic environment, i.e., the water vapor and temperature in the surroundings, and implications for changes in extremes in a warmer climate.
Recent Findings:
Multiple research threads have i) sought empirical relationships that govern onset of strong convective precipitation, or that might identify how precipitation extremes scale with changes in temperature; ii) examined how such extremes change with water vapor in global and regional climate models under warming scenarios; iii) identified fundamental processes that set the characteristic shapes of precipitation distributions.
Summary:
While water vapor increases tend to be governed by the Clausius-Clapeyron relationship to temperature, precipitation extreme changes are more complex and can increase more rapidly, particularly in the tropics. Progress may be aided by bringing separate research threads together and by casting theory in terms of a full explanation of the precipitation probability distribution.
... While examples of the above metrics have been reported in recent literature (e.g., Klingaman et al. 2017;Ahmed et al. 2020;Feng et al. 2021a), they are deemed exploratory partly because they have not been widely used or implemented in standard metrics and diagnostics packages and partly because they allow deeper exploration of precipitation characteristics and associated processes. Some of these diagnostics and metrics require variables besides precipitation to evaluate relationships with environmental conditions, or to track weather features, so their data requirements go beyond the baseline precipitation metrics already implemented in widely used metrics and diagnostics packages (Pendergrass et al. 2020). ...
Precipitation sustains life and supports human activities, making its prediction one of the most societally relevant challenges in weather and climate modeling. Limitations in modeling precipitation underscore the need for diagnostics and metrics to evaluate precipitation in simulations and predictions. While routine use of basic metrics is important for documenting model skill, more sophisticated diagnostics and metrics aimed at connecting model biases to their sources and revealing precipitation characteristics relevant to how model precipitation is used are critical for improving models and their uses. This paper illustrates examples of exploratory diagnostics and metrics including: (1) spatiotemporal characteristics such as diurnal variability, probability of extremes, duration of dry spells, spectral characteristics, and spatiotemporal coherence of precipitation; (2) process-oriented metrics based on the rainfall-moisture coupling and temperature-water vapor environments of precipitation; and (3) phenomena-based metrics focusing on precipitation associated with weather phenomena including low pressure systems, mesoscale convective systems, frontal systems, and atmospheric rivers. Together, these diagnostics and metrics delineate the multifaceted and multiscale nature of precipitation, its relations with the environments, and its generation mechanisms. The metrics are applied to historical simulations from the Coupled Model Intercomparison Project Phase 5 and Phase 6. Models exhibit diverse skill as measured by the suite of metrics, with very few models consistently ranked as top or bottom performers compared to other models in multiple metrics. Analysis of model skill across metrics and models suggests possible relationships among subsets of metrics, motivating the need for more systematic analysis to understand model biases for informing model development.
... where q NS = q(p NS ) is the near-surface specific humidity. This rescaling is inspired by recently introduced lower-tropospheric buoyancy measures (72,73), but with an extension to the full troposphere (74). While Eq 9 does not explicitly include entrainment effects, the mapping ofT buoyancy (p) andq RH (p) to heating and moisture sink will implicitly include these. ...
Data-driven algorithms, in particular neural networks, can emulate the effects of unresolved processes in coarse-resolution climate models when trained on high-resolution simulation data; however, they often make large generalization errors when evaluated in conditions they were not trained on. Here, we propose to physically rescale the inputs and outputs of machine learning algorithms to help them generalize to unseen climates. Applied to offline parameterizations of subgrid-scale thermodynamics in three distinct climate models, we show that rescaled or "climate-invariant" neural networks make accurate predictions in test climates that are 4K and 8K warmer than their training climates. Additionally, "climate-invariant" neural nets facilitate generalization between Aquaplanet and Earth-like simulations. Through visualization and attribution methods, we show that compared to standard machine learning models, "climate-invariant" algorithms learn more local and robust relations between storm-scale convection, radiation, and their synoptic thermodynamic environment. Overall, these results suggest that explicitly incorporating physical knowledge into data-driven models of Earth system processes can improve their consistency and ability to generalize across climate regimes.
... As observed in previous studies, the temperature shows maximum amplitude near the surface. A secondary peak is located in the lower free troposphere (;500-850 hPa), where tropical rainfall is highly influenced by fluctuations in temperature (e.g., Haertel and Kiladis 2004;Ahmed et al. 2020). Finally, a third peak is located near the tropopause. ...
The dynamical and thermodynamical features of Amazonian 2-day westward-propagating inertia-gravity waves (WIG) are examined. On the basis of a linear regression analysis of satellite brightness temperature and data from the 2014-15 Observations and Modeling of the Green Ocean Amazon (GoAmazon) field campaign, it is shown that Amazonian WIG waves exhibit structure and propagation characteristics consistent with the n = 1 WIG waves from shallow water theory. These WIG waves exhibit a pronounced seasonality, with peak activity occurring from March to May and a minimum occurring from June to September. Evidence is shown that mesoscale convective systems over the Amazon are frequently organized in 2-day WIG waves. Results suggest that many of the Amazonian WIG waves come from pre-existing 2-day waves over the Atlantic, which slow down when coupled with the deeper, more intense convection over tropical South America. In contrast to WIG waves that occur over the ocean, Amazonian 2-day WIG waves exhibit a pronounced signature in surface temperature, moisture, and heat fluxes.
... Following Ahmed et al. (2020) and Adames et al. (2021), a lower-tropospheric averaged buoyancy measure B L is defined as: ...
Plain Language Summary
Climate models have difficulties in capturing accurate rainfall statistics. A primary reason is that they disagree on how sensitive rainfall ought to be to atmospheric moisture, when compared to near‐surface warmth. For simplicity, let us call this the moisture‐temperature sensitivity of rainfall. We know what this looks like from observations. We present a new method to compare the moisture‐temperature sensitivity in climate models to observations. We apply this method to check how well the state‐of‐the‐art climate models perform. We find that in about half the models, rainfall has close to the right moisture‐temperature sensitivity. This is good news. In earlier generations, climate model rainfall has not been sensitive enough to moisture. However, rainfall in some models is over‐sensitive to moisture. We perform experiments with a climate model to examine why. Our experiments highlight two possible reasons: (a) the clouds in these models may not act fast enough to remove excess moisture from the air or (b) the model may have been tuned to make clouds more sensitive to moisture but has overshot the mark. This experiment is presented as a proof of concept for how a model developer would use our moisture‐temperature sensitivity tool to improve their model.
... Two physical processes are thought to explain the coupling between free tropospheric water vapor and precipitation. First, rising cumulus clouds in the tropics tend to lose buoyancy as they entrain air from the surrounding environment, and dry environments are more effective at diluting the updraft than moist environments [61][62][63]. Another explanation is based on the observation that MSE tends to remain fixed within the tropical boundary layer, which forms the basis of a concept known as boundary-layer quasi-equilibrium (BLQE) [64,65]. ...
Purpose of Review
Our understanding of the Madden-Julian Oscillation (MJO) and other tropical motion systems has significantly improved in recent years. This article reviews the contribution of moisture mode theory to this progress.
Recent Findings
Two realizations have contributed significantly to our understanding of the MJO: (1) Free tropospheric water vapor plays an important role in the occurrence and organization of tropical deep convection. (2) The latent heat released in convection is quickly transported around the tropics by gravity waves, the physical mechanism underpinning the weak temperature gradient (WTG) approximation. Simple models of the tropics that include (1) and (2) revealed the existence of moisture modes, waves in which water vapor plays a dominant role in their evolution. It was soon recognized that the MJO exhibits properties of moisture modes. The ensuing development and application of the so-called moisture mode theory of the MJO have led to the recognition that horizontal and vertical moisture advections are central to the propagation of the MJO, and that cloud-radiative heating is at least partially responsible for its maintenance. Moisture mode theory has also been applied to understand the MJO’s seasonality, Maritime Continent transit, and response to increasing CO2. Recent work suggests that moisture mode theory can be extended beyond the MJO in order to explain the observed diversity of tropical motion systems.
Summary
A mounting body of evidence indicates that the MJO has properties of moisture modes. Extension of the theory beyond the MJO may help us further understand the processes that drive large-scale tropical circulations.
Two robust peaks in the diurnal evolution of orographically-locked precipitation are simulated in large-eddy simulations with an idealized ocean-plain-mountain topography. The ensemble experiment design is guided by sounding statistics from summertime afternoon thunderstorms in Taiwan to obtain realistic variability of free-tropospheric moisture associated with the intensity of the summertime subtropical high. The convection in the first peak is directly modulated by convective available potential energy, while the convection in the second peak is associated with low-level moist static energy (MSE) transport by the island-scale (40-km) local circulation, producing more extreme rainfall. When the initial free troposphere is drier, the convection in the second peak is strengthened. Both the environmental adjustments by the first peak and local circulation development contribute to the sensitivity of the second peak to free-tropospheric moisture. This work highlights the critical roles of convection-environment interaction and upstream MSE supply in enhancing extreme diurnal precipitation over complex topography.
In real-world observations, long-lived tropical mesoscale convective clusters (TMCCs) often exhibit quasi-periodic oscillations. Previous studies have suggested that these oscillations can be induced by external forcings. However, many idealized simulations provided evidence that TMCCs can display quasi-periodic behavior even without external forcings. Through this study, it is demonstrated that all TMCCs possess an inherent internal oscillation, and the physics behind is a convectively coupled inertia-gravity oscillation. When deep convection within a TMCC decays, the stratiform heating within the system triggers an inertia-gravity oscillation. This oscillation induces upward motion at lower levels of the disturbance, which facilitates the recovery of low-level buoyancy and initiates new convection. Notably, in this oscillation, diabatic heating serves not only as a consequence of the preceding oscillation but also as the source for the subsequent oscillation. The internal oscillation acts as a fundamental component in the life cycle of long-lived TMCCs, providing clearer physical intuition for understanding the variation of TMCCs in real-world scenarios.
The shallow‐water analogue models for the tropical atmosphere are examined from a formulational point of view. The normal‐mode approach provides a formal procedure to reduce the primitive equation system to a shallow‐water analogue, although approaches based on vertical integrals of the primitive equation system may be more intuitively appealing. Under a general framework of the latter, classical models by Gill (1980, https://doi.org/10.1256/smsqj.44904) and Lindzen and Nigam (1987, 2.0.co;2>https://doi.org/10.1175/1520‐0469(1987)044<2418:otross>2.0.co;2) are derived in a deductive manner, by elucidating their limitations, implications, as well physical processes assumed. Major advantage of shallow‐water analogue models is that after a vertical integral, the determination of convective heating rate simply reduces to that of a precipitation rate. Consequently, the question of representing convection also almost reduces to that of precipitation. This fact leads to confusions in literature about distinction between large‐scale precipitation and subgrid‐scale convection. This framework further supports a popular notion of the moisture as a key variable for describing convection. By reviewing the existing formulations, it is shown that convection can be parameterized without moisture under the limit of the parcel‐environment quasi‐equilibrium.
Projecting climate change is a generalization problem: We extrapolate the recent past using physical models across past, present, and future climates. Current climate models require representations of processes that occur at scales smaller than model grid size, which have been the main source of model projection uncertainty. Recent machine learning (ML) algorithms hold promise to improve such process representations but tend to extrapolate poorly to climate regimes that they were not trained on. To get the best of the physical and statistical worlds, we propose a framework, termed “climate-invariant” ML, incorporating knowledge of climate processes into ML algorithms, and show that it can maintain high offline accuracy across a wide range of climate conditions and configurations in three distinct atmospheric models. Our results suggest that explicitly incorporating physical knowledge into data-driven models of Earth system processes can improve their consistency, data efficiency, and generalizability across climate regimes.
Convective Quasi-Equilibrium (CQE) is often adopted as a useful closure assumption to summarize the effects of unresolved convection on large-scale thermodynamics, while existing efforts to observationally validate CQE largely rely on specific spatial domains or sites rather than the source of CQE constraints—deep convection. This study employs a Lagrangian framework to investigate leading temperature perturbation patterns near deep convection, of which the centers are located by use of an ensemble of satellite measurements. Temperature perturbations near deep convection with high peak precipitation are rapidly adjusted towards the CQE structure within the two hours centered on peak precipitation. The top 1% precipitating deep convection constrains the neighboring free-tropospheric leading perturbations up to 8 degrees. Notable CQE validity beyond a 1-degree radius is observed when peak precipitation exceeds the 95th percentile. These findings suggest that only a small fraction of deep convection with extreme precipitation shapes tropical free-tropospheric temperature patterns dominantly.
Mechanical forcing by orography affects precipitating convection across many tropical regions, but controls on the intensity and horizontal extent of the orographic precipitation peak and rain shadow remain poorly understood. A recent theory explains this control of precipitation as arising from modulation of lower-tropospheric temperature and moisture by orographic mechanical forcing, setting the distribution of convective rainfall by controlling parcel buoyancy. Using satellite and reanalysis data, we evaluate this theory by investigating spatiotemporal precipitation variations in six mountainous tropical regions spanning South and Southeast Asia, and the Maritime Continent. We show that a strong relationship holds in these regions between daily precipitation and a measure of convective plume buoyancy. This measure depends on boundary layer thermodynamic properties and lower-free-tropospheric moisture and temperature. Consistent with the theory, temporal variations in lower-free-tropospheric temperature are primarily modulated by orographic mechanical lifting through changes in cross-slope wind speed. However, winds directed along background horizontal moisture gradients also influence lower-tropospheric moisture variations in some regions. The buoyancy measure is also shown to explain many aspects of the spatial patterns of precipitation. Finally, we present a linear model with two horizontal dimensions that combines mountain wave dynamics with a linearized closure exploiting the relationship between precipitation and plume buoyancy. In some regions, this model skillfully captures the spatial structure and intensity of rainfall; it underestimates rainfall in regions where time-mean ascent in large-scale convergence zones shapes lower-tropospheric humidity. Overall, these results provide new understanding of fundamental processes controlling subseasonal and spatial variations in tropical orographic precipitation.
Interactions between large-scale waves and the Hadley cell are examined using a linear two-layer model on an f plane. A linear meridional moisture gradient determines the strength of the idealized Hadley cell. The trade winds are in thermal wind balance with a weak temperature gradient (WTG). The mean meridional moisture gradient is unstable to synoptic-scale (horizontal scale of ∼1000 km) moisture modes that are advected westward by the trade winds, reminiscent of oceanic tropical depression–like waves. Meridional moisture advection causes the moisture modes to grow from “moisture-vortex instability” (MVI), resulting in a poleward eddy moisture flux that flattens the zonal-mean meridional moisture gradient, thereby weakening the Hadley cell. The amplification of waves at the expense of the zonal-mean meridional moisture gradient implies a downscale latent energy cascade. The eddy moisture flux is opposed by a regeneration of the meridional moisture gradient by the Hadley cell. These Hadley cell–moisture mode interactions are reminiscent of quasigeostrophic interactions, except that wave activity is due to column moisture variance rather than potential vorticity variance. The interactions can result in predator–prey cycles in moisture mode activity and Hadley cell strength that are akin to ITCZ breakdown. It is proposed that moisture modes are the tropical analog to midlatitude baroclinic waves. MVI is analogous to baroclinic instability, stirring latent energy in the same way that dry baroclinic eddies stir sensible heat. These results indicate that moisture modes stabilize the Hadley cell and may be as important as the latter in global energy transport.
Significance Statement
The tropics are characterized by steady circulations such as the Hadley cell as well as a menagerie of tropical weather systems. Despite progress in our understanding of both, little is known about how the mean circulations and the weather systems interact with one another. Here we show that tropical waves can grow by extracting moisture from the Hadley cell, thereby weakening it. They also transport moisture to higher latitudes. Our results challenge the notion that the Hadley cell is the sole transporter of energy out of the tropics and instead favor a view where tropical waves are also essential for the global energy balance. They dry the humid regions and moisten the drier regions via stirring.
An idealized large-eddy simulation of a tropical marine cloud population was performed. At any time, it contained hundreds of clouds, and updraft width in shallow convection emerging from a subcloud layer appeared to be an important indicator of whether specific convective elements deepened. In an environment with 80%–90% relative humidity below the 0°C level, updrafts that penetrated the 0°C level were larger at and above cloud base, which occurred at the lifting condensation level near 600 m. Parcels rising in these updrafts appeared to emerge from boundary layer eddies that averaged ∼200 m wider than those in clouds that only reached 1.5–3 km height. The deeply ascending parcels (growers) possessed statistically similar values of effective buoyancy below the level of free convection (LFC) as parcels that began to ascend in a cloud but stopped before reaching 3000 m (nongrowers). The growers also experienced less dilution above the LFC. Nongrowers were characterized by negative effective buoyancy and rapid deceleration above the LFC, while growers continued to accelerate well above the LFC. Growers occurred in areas with a greater magnitude of background convergence (or weaker divergence) in the subcloud layer, especially between 300 m and cloud base, but whether the convergence actually led to eddy widening is unclear.
Significance Statement
Cumulonimbus clouds are responsible for many extreme weather phenomena and are important contributors to Earth’s energy balance. However, the processes leading to the growth of individual clouds are not completely understood nor well-represented in weather prediction models. We find that the clouds containing updrafts that start out wider at early stages of their life cycles grow taller, possibly because they are protected more from drier air outside the cloud than narrow clouds. In addition, this work shows how the initial width of clouds might be related to convergence in the lowest part of the atmosphere, at heights where clouds initially develop. However, meteorologists must be careful not to overinterpret these results because numerical simulations inherently include assumptions that may not reflect reality. This reinforces the need to also observe processes occurring at the scales of individual clouds.
Idealized simulations of tropical, marine convection depict shallow, nonprecipitating cumuli located beneath the 0°C level transitioning into cumulonimbi that reach up to 12 km and higher. The timing of the transition was only weakly related to environmental stability, and 13 of the 15 simulations run with 5 different lapse-rate profiles had rain develop at nearly the same time after model start. The key quantity that apparently controlled deep convective formation was vertical acceleration inside cloudy updrafts between cloud base and the 0°C level. Below a critical value of updraft vertical acceleration, little rainfall occurred. Just as the domain-mean updraft acceleration reached the critical value, the first convection quickly grew to past 12 km altitude. Then, as acceleration increased above the critical value, rain rate averaged in the model domain increased quickly over about a 3-h-long period. The specific value of the critical updraft acceleration depended on how updrafts were defined and in what layer the acceleration was averaged; however, regardless of how criticality was defined, a robust relationship between domain-mean updraft vertical acceleration and rain rate occurred. Positive acceleration of updrafts below the 0°C level was present below 2.75 km and was largest in the 500 m above cloud base. However, the maximum difference between updraft and environmental temperatures occurred between 2 and 3 km. The domain-mean Archimedean buoyancy of updrafts relative to some reference state was a poor predictor for domain-mean rain rate. The exact value of the critical updraft acceleration likely depends on numerous other factors that were not investigated.
Significance Statement
A numerical model is utilized to investigate potential thermodynamic and dynamic quantities related to the growth of cumulus clouds into cumulonimbus clouds over tropical oceans when the atmosphere is sufficiently moist to support rainfall. Archimedean buoyancy alone cannot be used to predict rain rate reliably. Instead the total buoyancy not relative to an arbitrary reference state must be considered. The simulated relationship between total vertical acceleration in updrafts and rain rate was robust. While the processes that control the vertical acceleration remain unclear, our results highlight the importance of observing processes that occur on spatial scales of tens of meters and temporal scales of a few minutes.
Tropical areas with mean upward motion—and as such the zonal-mean intertropical convergence zone (ITCZ)—are projected to contract under global warming. To understand this process, a simple model based on dry static energy and moisture equations is introduced for zonally symmetric overturning driven by sea surface temperature (SST). Processes governing ascent area fraction and zonal mean precipitation are examined for insight into Atmospheric Model Intercomparison Project (AMIP) simulations. Bulk parameters governing radiative feedbacks and moist static energy transport in the simple model are estimated from the AMIP ensemble. Uniform warming in the simple model produces ascent area contraction and precipitation intensification—similar to observations and climate models. Contributing effects include stronger water vapor radiative feedbacks, weaker cloud-radiative feedbacks, stronger convection-circulation feedbacks, and greater poleward moisture export. The simple model identifies parameters consequential for the inter-AMIP-model spread; an ensemble generated by perturbing parameters governing shortwave water vapor feedbacks and gross moist stability changes under warming tracks inter-AMIP-model variations with a correlation coefficient ∼0.46. The simple model also predicts the multimodel mean changes in tropical ascent area and precipitation with reasonable accuracy. Furthermore, the simple model reproduces relationships among ascent area precipitation, ascent strength, and ascent area fraction observed in AMIP models. A substantial portion of the inter-AMIP-model spread is traced to the spread in how moist static energy and vertical velocity profiles change under warming, which in turn impact the gross moist stability in deep convective regions—highlighting the need for observational constraints on these quantities.
Significance Statement
A large rainband straddles Earth’s tropics. Most, but not all, climate models predict that this rainband will shrink under global warming; a few models predict an expansion of the rainband. To mitigate some of this uncertainty among climate models, we build a simpler model that only contains the essential physics of rainband narrowing. We find several interconnected processes that are important. For climate models, the most important process is the efficiency with which clouds move heat and humidity out of rainy regions. This efficiency varies among climate models and appears to be a primary reason for why climate models do not agree on the rate of rainband narrowing.
African easterly waves (AEWs) exert significant influence on local and downstream high impact weather including tropical cyclone (TC) genesis over the Atlantic. Accurate representation of AEWs in climate and weather prediction models therefore is necessary for skillful predictions. In this study, we examine simulated AEWs, including their evolution, vertical structure, and linkage to tropical cyclone genesis, in the NASA Goddard Earth Observing System Model, Version 5 (GEOS-5) atmospheric global climate model. Identified by the leading empirical orthogonal function mode of time-filtered precipitation, the observed westward propagating AEWs along the southern track over the Atlantic are largely captured in GEOS5, but with a slower phase speed and significantly weaker amplitude downstream off the West Africa coast. The weak downstream development of AEWs in GEOS5 is accompanied by much reduced TC genesis over the main development region. Further analyses suggest that the slow westward propagation and weaker AEW amplitude downstream can be ascribed to a weak African easterly jet, while overestimated negative (positive) meridional potential vorticity (PV) gradients to the north (south) of 10°N in GEOS5. The greatly overestimated positive meridional PV gradient to the south of 10°N is expected to generate strong horizontal stretching in the AEW wave pattern in the model, which hinders organization of convection and its feedback to sustain the AEW development. Persistent and vigorous AEW precipitation in the Guinea Highlands of the West Africa coast could also be responsible for reduced westward propagation of AEWs in the model.
This study examines thermodynamic-convection coupling in observations and re-analyses, and attempts to establish process level benchmarks needed to guide model development. Thermodynamic profiles obtained from the NOAA Integrated Global Radiosonde Archive, COSMIC-1 GPS radio occultations, and several reanalyses are examined alongside Tropical Rain-fall Measuring Mission precipitation estimates. Cyclical increases and decreases in a bulk measure of lower tropospheric convective instability are shown to be coupled to the cyclical amplification and decay of convection. This cyclical flow emerges from conditional-mean analysis in a thermodynamic space comprised of two components: a measure of “undiluted” instability which neglects lower free tropospheric (LFT) entrainment, and a measure of the reduction of instability by LFT entrainment. The observational and reanalysis products examined share the following qualitatively robust characterization of these convective cycles: increases in undiluted instability tend to occur when the LFT is less saturated, are followed by increases in LFT saturation and precipitation rate, which are then followed by decreases in undiluted instability. Shallow, convective and stratiform precipitation are coupled to these cycles in a manner consistent with meteorological expectations. In situ and satellite observations differ systematically from reanalyses in their depictions of lower tropospheric temperature and moisture variations throughout these convective cycles. When using reanalysis thermodynamic fields, these systematic differences cause variations in lower free tropospheric saturation deficit to appear less influential in determining the strength of convection than is suggested by observations. Disagreements amongst reanalyses, as well as between reanalyses and observations, pose significant challenges to process level assessments of thermodynamic-convection coupling.
Plain Language Summary
Recent studies have shown that water vapor plays a crucial role in the occurrence and organization of tropical rainfall, leading to the existence of moisture modes. Such waves do not exist in the dry theory of tropical waves. While this acknowledgment has significantly advanced our understanding of tropical meteorology, most studies on how moisture and the large‐scale circulation couple have been focused on the equatorial eastern hemisphere. In this study, we examine the features of a westward‐propagating signal that has received relatively little attention. On the basis of several objective criteria, we show that this wave has properties consistent with moisture modes. We show evidence that this is the case by investigating the thermodynamic budget of this wave, which is shown to be consistent with the budget of a theoretical moisture mode. Our results underscore the importance of water vapor in the governing dynamics of tropical waves, and the need to move away from dry theory as a basis to understand convectively coupled tropical motions.
Linearized wave solutions on the equatorial beta-plane are examined in the presence of a background meridional moisture gradient. Of interest is a slow, eastward propagating n = 1 mode that is unstable at planetary scales and only exists for a small range of zonal wavenumbers (≲ 6). The mode dispersion curve appears as an eastward extension of the westward propagating equatorial Rossby wave solution. This mode is therefore termed the eastward propagating equatorial Rossby wave (ERW). The zonal wavenumber 2 ERW horizontal structure consists of a low-level equatorial convergence center flanked by quadrupole off-equatorial gyres, and resembles the horizontal structure of the observed MJO. An analytic, leading order dispersion relationship for the ERW shows that meridional moisture advection imparts eastward propagation, and that the smallness of a gross moist stability like parameter contributes to the slow phase speed. The ERW is unstable near planetary scales when low-level easterlies moisten the column. This moistening could come from either zonal moisture advection or surface fluxes or a combination thereof. When westerlies instead moisten the column, the ERW is damped and the westward propagating long Rossby wave is unstable. The ERW does not exist when the meridional moisture gradient is too weak. A moist static energy budget analysis shows that the ERW scale selection is partly due to finite timescale convective adjustment and less effective zonal wind-induced moistening at smaller scales. Similarities in the phase speed, preferred scale and horizontal structure suggest that the ERW is a beta-plane analog of the MJO.
Over most tropical land areas, the annual peak in precipitation occurs during summer, associated with the local monsoon circulation. However, in some coastal regions in the tropics the bulk of annual precipitation occurs in autumn, after the low-level summer monsoon westerlies have abated. Examples include the Nordeste region of Brazil, southeastern India and Sri Lanka, and coastal Tanzania. Unlike equatorial regions, they receive little rainfall during local spring. Such regions are present along the eastern coasts of nearly all continents, suggesting that they comprise a coherent yet previously unrecognized global phenomenon.
In this study, we identify eight tropical locations that experience an “autumn monsoon” and show that this unusual seasonal cycle is generated by similar mechanisms in all of these. When these regions receive their peak rainfall, they lie poleward of the ITCZ in easterly low-level winds. The spatial structure of precipitation in these regions can be explained by their placement to the east of mountain ranges that organize moist convection on their windward sides. However, orographic forcing alone cannot explain their unique seasonal cycle: despite similarities in wind direction, surface humidity, and sea surface temperatures (SSTs) between autumn and spring, these regions receive significantly more rainfall in autumn than in spring. We show that this is due to differences in the large-scale atmospheric stability between the equinoctial seasons, which can be captured by a relative SST metric and is influenced by SSTs in the remote eastern upwelling zones of the Pacific and Atlantic Oceans.
A convectively coupled equatorial Kelvin wave (CCKW) was observed over the equatorial Indian Ocean in early November 2011 during the DYNAMO field campaign. This study examines the structure of the CCKW event using two simulations made using the MPAS model: one with 3-km grid spacing without convective parameterization and another with a 15-km grid and parameterized convection.
Both simulations qualitatively capture the observed structure of the CCKW, including its vertical tilt and progression of cloud/precipitation structures. The two simulations, however, differ substantially in the amplitude of the CCKW-associated precipitation. While the 3-km run realistically captures the observed modulation of precipitation by the CCKW, the 15-km simulation severely underestimates its magnitude. To understand the difference between the two MPAS simulations regarding wave-convection coupling within the CCKW, the relationship of precipitation with convective inhibition, saturation fraction, and surface turbulent fluxes is investigated. Results show that the 15-km simulation underestimates the magnitude of the CCKW precipitation peak in association with its unrealistically linear relationship between moisture and precipitation. Precipitation, both in observations and the 3-km run, is predominantly controlled by saturation fraction and this relationship is exponential. In contrast, the parameterized convection in the 15-km run is overly sensitive to convective inhibition and not sensitive enough to environmental moisture. The implications of these results on CCKW theories are discussed.
A linear two-layer model is used to elucidate the role of prognostic moisture on quasi-geostrophic (QG) motions in the presence of a mean thermal wind ( ). Solutions to the basic equations reveal two instabilities that can explain the growth of moist QG systems. The well-documented baroclinic instability is characterized by growth at the synoptic scale (horizontal scale of ~1000 km) and systems that grow from this instability tilt against the shear. Moisture-vortex instability —an instability that occurs when moisture and lower-tropospheric vorticity exhibit an in-phase component— exists only when moisture is prognostic. The instability is also strongest at the synoptic scale, but systems that grow from it exhibit a vertically-stacked structure. When moisture is prognostic and is easterly, baroclinic instability exhibits a pronounced weakening while moisture vortex instability is amplified. The strengthening of moisture-vortex instability at the expense of baroclinic instability is due to the baroclinic ( ) component of the lower-tropospheric flow. In westward-propagating systems, lower-tropospheric westerlies associated with an easterly advect anomalous moisture and the associated convection towards the low-level vortex. The advected convection causes the vertical structure of the wave to shift away from one that favors baroclinic instability to one that favors moisture-vortex instability. On the other hand, a westerly reinforces the phasing between moisture and vorticity necessary for baroclinic instability to occur. Based on these results, it is hypothesized that moisture-vortex instability is an important instability in humid regions of easterly such as the South Asian and west African monsoons.
Convective Quasi-equilibrium (QE) and weak temperature gradient (WTG) balances are frequently employed to study the tropical atmosphere. This study uses linearized equatorial beta-plane solutions to examine the relevant regimes for these balances. Wave solutions are characterized by moisture-temperature ratio (q-T ratio), and dominant thermodynamic balances. An empirically-constrained precipitation closure assigns different sensitivities of convection to temperature (εt) and moisture (εq). Longwave equatorial Kelvin and Rossby waves tend toward the QE balance with q-T ratios of εt : εq, which can be ~ 1-3. Departures from strict QE, essential to both precipitation and wave dynamics, grow with wavenumber. The propagating QE modes have reduced phase speeds due to the effective gross moist stability (meff) with a further reduction when εt > 0. Moisture modes obeying the WTG balance, and with large q-T ratios (> 10) emerge in the shortwave regime; these modes exist with both Kelvin and Rossby wave meridional structures. In the v = 0 case, long propagating gravity waves are absent and only emerge beyond a cutoff wavenumber. Two bifurcations in the wave solutions are identified and used to locate the spatial scales for QE-WTG transition and gravity wave emergence. These scales are governed by the competition between the convection and gravity wave adjustment times, and are modulated by meff. Near-zero values of meff shift the QE-WTG transition wavenumber toward zero. Continuous transitions replace the bifurcations when meff <0 or moisture advection/WISHE mechanisms are included, but the wavenumber-dependent QE and WTG balances remain qualitatively unaltered. Rapidly decaying convective/gravity-wave modes adjust to the slowly evolving QE/WTG state in the longwave/shortwave regimes, respectively.
Observations have shown that tropical convection is influenced by fluctuations in temperature and moisture in the lower free-troposphere (LFT, 600–850 hPa), as well as moist enthalpy (ME) fluctuations beneath the 850 hPa level, referred to as the deep boundary layer (DBL, 850–1000 hPa). A framework is developed that consolidates these three quantities within the context of the buoyancy of an entraining plume. A “plume buoyancy equation” is derived based on a relaxed version of the weak-temperature gradient (WTG) approximation. Analysis of this equation using quantities derived from the Dynamics of the Madden-Julian Oscillation (DYNAMO) sounding array data reveals that processes occurring within the DBL and the LFT contribute nearly equally to the evolution of plume buoyancy, indicating that processes that occur in both layers are critical to the evolution of tropical convection. Adiabatic motions play an important role in the evolution of buoyancy both at the daily and longer timescales and are comparable in magnitude to horizontal moisture advection and vertical moist static energy advection by convection. The plume buoyancy equation may explain convective coupling at short timescales in both temperature and moisture fluctuations and can be used to complement the commonly-used moist static energy budget, which emphasizes the slower evolution of the convective envelope in tropical motion systems.
The probability distribution of daily precipitation intensities, especially the probability of extremes, impacts a wide range of applications. In most regions this distribution decays slowly with size at first, approximately as a power law with exponent between 0 and −1, and then more sharply, for values larger than a characteristic cutoff scale. This cutoff is important because it limits the probability of extreme daily precipitation occurrences in current climate. There is a long history of representing daily precipitation using a Gamma distribution—here we present theory for how daily precipitation distributions get their shape. Processes shaping daily precipitation distributions can be separated into non-precipitating and precipitating regime effects, the former partially controlling how many times in a day it rains, and the latter set by single-storm accumulations. Using previously developed theory for precipitation accumulation distributions—which follow a sharper power law range (exponent < −1) with a physically derived cutoff for large sizes—analytical expressions for daily precipitation distribution power law exponent and cutoff are calculated as a function of key physical parameters. Precipitating and non-precipitating regime processes both contribute to reducing the power-law range exponent for the daily precipitation distribution relative to the fundamental exponent set by accumulations. The daily precipitation distribution cutoff is set by the precipitating regime and scales with moisture availability, with important consequences for future distribution shifts under global warming. Similar results extend to different averaging periods, providing insight into how the precipitation intensity distribution evolves as a function of both underlying physical climate conditions and averaging time.
We seek to use ARM MJO Investigation Experiment (AMIE)-DYNAMO field campaign observations to significantly constrain height-resolved estimates of the parameterization-relevant, causal sensitivity of convective heating Q to water vapor q. In field data, Q profiles are detected via Doppler radar wind divergence D while balloon soundings give q. Univariate regressions of D on q summarize the information from a 10-layer time–pressure series from Gan Island (0°, 90°E) as a 10 × 10 matrix. Despite the right shape and units, this is not the desired causal quantity because observations reflect confounding effects of additional q-correlated casual mechanisms. We seek to use this matrix to adjudicate among candidate estimates of the desired causal quantity: Kuang’s matrix [Formula: see text] of the linear responses of a cyclic convection-permitting model (CCPM) at equilibrium. Transforming [Formula: see text] to more observation-comparable forms by accounting for observed autocorrelations, the comparisons are still poor, because (we hypothesize) larger-scale vertical velocity, forbidden by CCPM methodology, is another confounding cause that must be permitted to covary with q. By embedding [Formula: see text] and modified candidates in an idealized GCM, and treating its outputs as virtual field campaign data, we find that observations favor a factor of 2 (rather than 0 or 1) to small-domain [Formula: see text]’s free-tropospheric causal q sensitivity of about 25% rain-rate increment over 3 subsequent hours per +1 g kg ⁻¹ q impulse in a 100-hPa layer. Doubling this sensitivity lies partway toward Kuang’s [Formula: see text] for a long domain that organizes convection into squall lines, a weak but sign-consistent hint of a detectable parameterization-relevant (causal) role for convective organization in nature. Caveats and implications for field campaign proposers are discussed.
It is an open question whether an integrated measure of buoyancy can yield a strong relation to precipitation across tropical land and ocean, across the seasonal and diurnal cycles, and for varying degrees of convective organization. Building on previous work, entraining plume buoyancy calculations reveal that differences in convective onset as a function of column water vapor (CWV) over land and ocean, as well as seasonally and diurnally over land, are largely due to variability in the contribution of lower-tropospheric humidity to the total column moisture. Over land, the relationship between deep convection and lower-freetropospheric moisture is robust across all seasons and times of day, whereas the relation to boundary layer moisture is robust for the daytime only. Using S-band radar, these transition statistics are examined separately for mesoscale and smaller-scale convection. The probability of observing mesoscale convective systems sharply increases as a function of lower-free-tropospheric humidity. The consistency of this with buoyancybased parameterization is examined for several mixing formulations. Mixing corresponding to deep inflow of environmental air into a plume that grows with height, which incorporates nearly equal weighting of boundary layer and free-tropospheric air, yields buoyancies consistent with the observed onset of deep convection across the seasonal and diurnal cycles in the Amazon. Furthermore, it provides relationships that are as strong or stronger for mesoscale-organized convection as for smaller-scale convection.
Previous studies have documented that deep convection responds more strongly to above-the-cloud-base temperature perturbations in the lower troposphere than to those in the upper troposphere, a behavior that is important to the dynamics of large-scale moist flows, such as convectively coupled waves. A number of factors may contribute to this differing sensitivity, including differences in buoyancy, vertical velocity, and/or liquid water content in cloud updrafts in the lower versus upper troposphere. Quantifying the contributions from these factors can help to guide the development of convective parameterization schemes. We tackle this issue by tracking Lagrangian particles embedded in cloud-resolving simulations within a linear response framework. The results show that both the differences in updraft buoyancy and vertical velocity play a significant role, with the vertical velocity being the more important, and the effect of liquid water content is only secondary compared to the other two factors. These results indicate that cloud updraft vertical velocities need to be correctly modeled in convective parameterization schemes in order to properly account for the differing convective sensitivities to temperature perturbations at different heights of the free troposphere.
Precipitation accumulations, integrated over precipitation events in hourly data, are examined from 1979 to 2013 over the contiguous United States during the “warm" season (May‐October). As expected from theory, accumulation distributions have a characteristic shape, with an approximate power law decrease with event size followed by an exponential drop at a characteristic cutoff scale sL for each location. This cutoff is a predictor of the highest accumulation percentiles, and of a similarly defined daily precipitation cutoff PL. Comparing 1997‐2013 and 1979‐1995 periods, there are significant regional increases in sL in several regions. This yields distribution changes that are weighted disproportionately toward extreme accumulations. In the Northeast for example, risk ratio (conditioned on occurrence) for accumulations larger than 109mm increases by a factor of 2‐4 (5th‐95th). These changes in risk ratio as a function of size, and connection to underlying theory, have counterparts in the observed daily precipitation trends.
Significance
Representations of strongly precipitating deep-convective systems in climate models are among the most important factors in their simulation. Parameterizations of these motions face the dual challenge of unclear pathways to including mesoscale organization and high sensitivity of convection to approximations of turbulent entrainment of environmental air. Ill-constrained entrainment processes can even affect global average climate sensitivity under global warming. Multiinstrument observations from the Department of Energy GoAmazon2014/5 field campaign suggest that an alternative formulation from radar-derived dominant updraft structure yields a strong relationship of precipitation to buoyancy in both mesoscale and smaller-scale convective systems. This simultaneously provides a key step toward representing the influence of mesoscale convection in climate models and sidesteps a problematic dependence on traditional entrainment rates.
In Part II of this two-part paper, documentation is provided of key aspects of a version of the AM4.0/LM4.0 atmosphere/land model that will serve as a base for a new set of climate and Earth system models (CM4 and ESM4) under development at NOAA's Geophysical Fluid Dynamics Laboratory (GFDL). The quality of the simulation in AMIP (Atmospheric Model Intercomparison Project) mode has been provided in Part I. Part II provides documentation of key components and some sensitivities to choices of model formulation and values of parameters, highlighting the convection parameterization and orographic gravity wave drag. The approach taken to tune the model's clouds to observations is a particular focal point. Care is taken to describe the extent to which aerosol effective forcing and Cess sensitivity have been tuned through the model development process, both of which are relevant to the ability of the model to simulate the evolution of temperatures over the last century when coupled to an ocean model.
A stochastic prognostic framework for modeling the population dynamics of convective clouds and representing them in climate models is proposed. The framework follows the nonequilibrium statistical mechanical approach to constructing a master equation for representing the evolution of the number of convective cells of a specific size and their associated cloud-base mass flux, given a large-scale forcing. In this framework, referred to as STOchastic framework for Modeling Population dynamics of convective clouds (STOMP), the evolution of convective cell size is predicted from three key characteristics of convective cells: (i) the probability of growth, (ii) the probability of decay, and (iii) the cloud-base mass flux. STOMP models are constructed and evaluated against CPOL radar observations at Darwin and convection permitting model (CPM) simulations. Multiple models are constructed under various assumptions regarding these three key parameters and the realisms of these models are evaluated. It is shown that in a model where convective plumes prefer to aggregate spatially and the cloud-base mass flux is a nonlinear function of convective cell area, the mass flux manifests a recharge-discharge behavior under steady forcing. Such a model also produces observed behavior of convective cell populations and CPM simulated cloud-base mass flux variability under diurnally varying forcing. In addition to its use in developing understanding of convection processes and the controls on convective cell size distributions, this modeling framework is also designed to serve as a nonequilibrium closure formulations for spectral mass flux parameterizations.
In the tropics, rainfall is coupled with atmospheric dynamics in ways that are not fully understood, and often different mechanisms are proposed to underlie different modes of variability. Here it is shown that a unified model with a simple form can produce many different modes of variability. In particular, this includes the Madden-Julian Oscillation and convectively coupled equatorial waves. The model predicts the length scales, time scales, structures, and spatiotemporal variability of these modes reasonably well for a simple model. Furthermore, the model produces a background spectrum of rainfall that resembles spatiotemporal red noise and is only weakly coupled with wave dynamics. The full spectrum is also shown to be shaped by antiresonance, whereby rainfall oscillations are prevented from occurring at the oscillation frequencies of dry waves. To produce all of these aspects simultaneously, a key factor is differing roles of lower and middle tropospheric water vapor.
The intraseasonal oscillations and in particular the MJO have been and still remain a “holy grail” of today's atmospheric science research. Why does the MJO propagate eastward? What makes it unstable? What is the scaling for the MJO, i.e. why does it prefer long wavelengths or planetary wavenumbers 1-3? What is the westward moving component of the intraseasonal oscillation? Though linear WISHE has long been discounted as a plausible model for intraseasonal oscillations and the MJO, the version we have developed explains many of the observed features of those phenomena, in particular, the preference for large zonal scale. In this model version the moisture budget and the increase of precipitation with tropospheric humidity lead to a “moisture mode”. The destabilization of the large scale moisture mode occurs via WISHE only and there is no need to postulate large-scale radiatively induced instability or negative effective gross moist stability. Our WISHE-moisture theory leads to a large scale unstable eastward propagating mode in n=-1 case and a large scale unstable westward propagating mode in n=1 case. We suggest that the n=-1 case might be connected to the MJO and the observed westward moving disturbance to the observed equatorial Rossby mode.
Despite its widespread influences on the atmosphere, the Madden-Julian oscillation (MJO) remains poorly represented in state-of-the-art general circulation models (GCMs). Motivated by recent findings that the horizontal advection of the mean low-tropospheric moist static energy or moisture by MJO winds plays a crucial role in the eastward propagation of the MJO, we investigate the relationship between lower-tropospheric moisture patterns over the Indo-Pacific and MJO eastward propagation in a suite of 23 GCM simulations. Model capability of reproducing the observed November–April mean lower-tropospheric moisture pattern over the Indo-Pacific, especially near the Maritime Continent (MC), is highly correlated with model skill in simulating MJO eastward propagation. In GCMs with difficulty capturing realistic MJO propagation, the amplitude of the mean low-level moisture over the MC is greatly underestimated, leading to weak horizontal moisture gradients and thus discrepancies in moisture advection, significantly affecting MJO propagation. This study suggests that the mean lower-tropospheric moisture pattern over the MC can serve as an important diagnostic metric for MJO propagation in climate models.
Significance
Large accumulations of rainfall over a precipitation event can impact human infrastructure. Unlike precipitation intensity distributions, probability distributions for accumulations at first drop slowly with increasing size. At a certain size—the cutoff scale—the behavior regime changes, and the probabilities drop rapidly. In current climate, every region is protected from excessively large accumulations by this cutoff scale, and human activities are adapted to this. An analysis of how accumulations will change under global warming gives a natural physical interpretation for the atmospheric processes producing this cutoff, but, more importantly, yields a prediction that this cutoff scale will extend in a warmer climate, leading to vastly disproportionate increases in the probabilities of the very largest events.
A branch-run perturbed-physics ensemble in the Community Earth System Model estimates impacts of parameters in the deep convection scheme on current hydroclimate and on end-of-century precipitation change projections under global warming. Regional precipitation change patterns prove highly sensitive to these parameters, especially in the tropics with local changes exceeding 3 mm/d, comparable to the magnitude of the predicted change and to differences in global warming predictions among the Coupled Model Intercomparison Project phase 5 models. This sensitivity is distributed nonlinearly across the feasible parameter range, notably in the low-entrainment range of the parameter for turbulent entrainment in the deep convection scheme. This suggests that a useful target for parameter sensitivity studies is to identify such disproportionately sensitive “dangerous ranges.” The low-entrainment range is used to illustrate the reduction in global warming regional precipitation sensitivity that could occur if this dangerous range can be excluded based on evidence from current climate.
A cloud resolving model in spectral weak temperature gradient mode is used to explore systematically the response of mean convective rainfall to variations tropical environmental conditions. A very large fraction of the variance in modeled rainfall is explained by three variables, the surface moist entropy flux, the instability index (a measure of low to midlevel moist convective instability), and the saturation fraction (a kind of column-averaged relative humidity). The results of these calculations are compared with the inferred rainfall from 37 case studies of convection over the tropical west Pacific, the tropical Atlantic, and the Caribbean, as well as in the NCEP FNL analysis and the ERA-Interim reanalysis. The model shows significant predictive skill in all of these cases. However, it consistently overpredicts precipitation by about a factor of three, due possibly to simplifications made in the model. These calculations also show that the saturation fraction is not a predictor of rainfall in the case of strong convection. Instead, saturation fraction covaries with the precipitation as a result of a moisture quasi-equilibrium process.
This paper presents a conceptual picture of balanced tropical tropospheric dynamics inspired by recent observations. The most important factor differentiating the tropics from middle and higher latitudes is the absence of baroclinic instability; upward motion occurs primarily via deep convective processes. Thus, convection forms an integral part of large-scale tropical motions. Since convection itself is small-scale and chaotic in detail, predictability lies in uncovering the hidden hands that guide the average behavior of convection. Two appear, balanced dynamics and thermodynamic constraints. Contrary to conventional expectations, balanced dynamics plays a crucial role in the tropical atmosphere. However, due to the smallness of the Coriolis parameter there, non-linear balance is more important in the tropics than at higher latitudes. Three thermodynamic constraints appear to play an important role in governing the average behavior of convection outside of the cores of tropical storms. First, convection is subject to control via a lower tropospheric buoyancy quasi-equilibrium process, wherein destabilization of the lower troposphere by non-convective processes is balanced by convective stabilization. Second, the production of precipitation is extraordinarily sensitive to the saturation fraction of the troposphere. Third, “moisture quasi-equilibrium” governs the saturation fraction, with moister atmospheres being associated with smaller moist convective instability. The moist convective instability is governed by the balanced thermodynamic response to the pattern of potential vorticity, which in turn is slowly modified by con-vective and radiative heating. The intricate dance between these dynamic and thermodynamic processes leads to complex behavior of the tropical atmosphere in ways that we are just beginning to understand. This article is protected by copyright. All rights reserved.
As part of an international intercomparison project, a set of single-column models (SCMs) and cloud-resolving models (CRMs) are run under the weak-temperature gradient (WTG) method and the damped gravity wave (DGW) method. For each model, the implementation of the WTG or DGW method involves a simulated column which is coupled to a reference state defined with profiles obtained from the same model in radiative-convective equilibrium. The simulated column has the same surface conditions as the reference state and is initialized with profiles from the reference state. We performed systematic comparison of the behavior of different models under a consistent implementation of the WTG method and the DGW method and systematic comparison of the WTG and DGW methods in models with different physics and numerics. CRMs and SCMs produce a variety of behaviors under both WTG and DGW methods. Some of the models reproduce the reference state while others sustain a large-scale circulation which results in either substantially lower or higher precipitation compared to the value of the reference state. CRMs show a fairly linear relationship between precipitation and circulation strength. SCMs display a wider range of behaviors than CRMs. Some SCMs under the WTG method produce zero precipitation. Within an individual SCM, a DGW simulation and a corresponding WTG simulation can produce different signed circulation. When initialized with a dry troposphere, DGW simulations always result in a precipitating equilibrium state. The greatest sensitivities to the initial moisture conditions occur for multiple stable equilibria in some WTG simulations, corresponding to either a dry equilibrium state when initialized as dry or a precipitating equilibrium state when initialized as moist. Multiple equilibria are seen in more WTG simulations for higher SST. In some models, the existence of multiple equilibria is sensitive to some parameters in the WTG calculations.
Many convective parameterization schemes define a convective adjustment time scale t as the time allowed for dissipation of convective available potential energy (CAPE). The Kain-Fritsch scheme defines t based on an estimate of the advective time period for deep convective clouds within a grid cell, with limits of 1800 and 3600 s, based on practical cloud-lifetime considerations. In simulations from the Weather Research and Forecasting (WRF) Model using 12-km grid spacing, the value of t often defaults to the lower limit, resulting in relatively rapid thermodynamics adjustments and high precipitation rates. Herein, a new computation for t in the Kain-Fritsch scheme is implemented based on the depth of the buoyant layer and the convective velocity scale. This new t formulation is applied using 12-and 36-km model grid spacing in conjunction with a previous modification that takes into account the radiation effects of parameterized convective clouds. The dynamically computed convective adjustment time scale is shown to reduce the precipitation bias by approximately 15% while also providing improved simulations of inland rainfall from tropical storms.
This paper investigates stochastic models whose dynamics switch depending on the state/regime of the system. Such models have been called " hybrid switching diffusions " and exhibit " sliding dynamics " with noise. Here the aim is an application to models of rainfall, convection, and water vapor, where two states/regimes are considered: precipitation and non-precipitation. Regime changes are modeled with a " trigger function, " and four trigger models are considered: deterministic triggers (i.e. Heaviside function) or stochastic triggers (finite-state Markov jump process), with either a single threshold for regime transitions or two distinct thresholds (allowing for hysteresis). These triggers are idealizations of those used in convective parameterizations of global climate models, and they are investigated here in a model for a single atmospheric column. Two types of results are presented here. First, exact statistics are presented for all four models, and a comparison indicates how the trigger choice influences rainfall statistics. For example, it is shown that the average rainfall is identical for all four triggers, whereas extreme rainfall events are more likely with the stochastic trigger. Second, the stochastic triggers are shown to converge to the deterministic triggers in the limit of fast transition rates. The convergence is shown using formal asymptotics on the Master-Fokker-Planck equations, where the limit is an interesting Fokker-Planck system with Dirac delta coupling terms. Furthermore, the convergence is proved in the mean-square sense for pathwise solutions.
Convectively coupled Kelvin waves (CCKW) are analysed using a cloud-resolving model to gain a better understanding of the mechanisms that initiate and drive these waves. We compare the modelled precipitation and vertical structure of a convectively coupled Kelvin wave to the mechanisms that control precipitation over warm tropical oceans: convective inhibition (CIN), saturation fraction, atmospheric stability and surface moist entropy fluxes. Our results show that the primary onset mechanism for precipitation associated with CCKW is CIN associated with a decrease in the threshold moist entropy. Saturation fraction and atmospheric instability exhibit a time lag in comparison with the rainfall evolution and are, therefore, not primary controls in the onset of these waves. The modelled CCKW evolve by starting with congestus convection, develop into deep convection and decay with the stratiform convection. The results from the presented model agree with observations and linearised models.
Convective interaction with dynamics (CID) dictates the structure and behavior of the eigenmodes of the tropical atmosphere under moist convective adjustment (MCA) when the convective adjustment time scale, τc, is much smaller than dynamical time scales, as examined analytically in Part I. Here, the modes are reexamined numerically to include the effects of finite τc, again for a primitive equation model with the Betts-Miller MCA parameterization. The numerical results at planetary scales are consistent with the analytical approach, with two well-separated classes of vertical modes: one subset evolves at the cumulus time scale, while the other subset evolves at a time scale set by the large-scale dynamics. All modes are stable for homogeneous basic states in the presence of simple mechanical damping effects. Thus, there is no CISK at any scale under MCA. However, the finite τc effect has the property of selectively damping the smallest scales while certain vertical modes at planetary scales decay only slowly. This planetary scale selection contrasts to many linear CISK studies, which tend to select the smallest scale.
The Madden–Julian mode, which resembles the observed tropical intraseasonal oscillation, is found as a single vertical mode arising through Kelvin wave-CID. When the evaporation-wind feedback is included, this slowly decaying MJ mode is selectively destabilized at wavenumber one or two, consistent with the observations in the tropics. Stochastic forcing by nonresolved mesoscale processes can also potentially account for the existence of large-scale tropical variance. When the stochastic forcing occurs in the thermodynamic equation, the propagating deep-convective mode at planetary scales is the most strongly excited. Kinematic forcing excites slowly decaying kinematically dominated modes but cannot account for the characteristics of observed Madden-Julian variance.
The exponential increase in precipitation with increasing column saturation fraction (CSF) is used to investigate the role of moisture in convective coupling. This simple empirical relationship between precipitation and CSF is shown to capture nearly all MJO related variability in TRMM precipitation, ~ 80% of equatorial Rossby wave related variability, and ~ 75% of east Pacific easterly wave related variability. In contrast, this empirical relationship only captures roughly half of TRMM precipitation variability associated with Kelvin waves, African easterly waves, and mixed Rossby gravity waves, suggesting coupling mechanisms other than moisture are playing leading roles in these phenomena. These latter phenomena have strong adiabatically forced vertical motions which could reduce static stability and convective inhibition while simultaneously moistening, creating a more favorable convective environment. Cross-spectra of precipitation and column integrated dry static energy show enhanced coherence and an out-of-phase relationship in the Kelvin wave, mixed Rossby gravity wave, and eastward inertio-gravity wave bands, supporting this narrative. The cooperative modulation of precipitation by moisture and temperature anomalies is shown to shorten the convective adjustment timescale (i.e. timescale by which moisture and precipitation are relaxed towards their “background” state) of these phenomena. Speeding the removal of moisture anomalies relative to that of temperature anomalies may allow the latter to assume a more important role in driving moist static energy fluctuations, helping promote the gravity wave character of these phenomena.
The moist deep tropics are typically separated from the drier subtropics by a sharp horizontal gradient of moisture. The physical nature of this tropical margin is investigated by using A-Train satellite observations to reconstruct its composite mean quasi-meridional thermodynamic structure and processes. The margin is defined here as the most poleward position of a specified column water vapor (CWV) threshold along a satellite track. Multiple CWV thresholds are selected from 35 mm to 60 mm, bracketing the global tropics histogram minimum value of 48 mm. For all margin thresholds, CWV increases equatorward from the subtropics and eventually asymptotes to 48 mm far on the tropical side, apparently as a coincidence of composite averaging since values of 48 mm are infrequent as noted above. For all margin thresholds, precipitation peaks on the tropical side and then asymptotes equatorward to 85 W m ⁻² , equal to the evaporation asymptote. For the 48 mm threshold, total diabatic forcing of the air column (radiative heating plus surface latent and sensible heat fluxes) changes sign from positive on the tropical side to negative in the subtropics, with the main contrast in radiative heating, owing principally to the longwave effect of high clouds. An analytic two-vertical-mode model of equatorward-flowing air columns is fitted from the observations, to elucidate the processes in a Lagrangian column transition. The model captures key features of the composite, and suggests that a key process in the abrupt moistening at the margin is bottom-heavy ascent growing upward beneath the deep subtropical subsidence.
Observations and theory of convectively coupled equatorial waves suggest that they can be categorized into two distinct groups. Moisture modes are waves whose thermodynamics are governed by moisture fluctuations. The thermodynamics of the gravity wave group, on the other hand, are rooted in buoyancy (temperature) fluctuations. On the basis of scale analysis, it is found that a simple nondimensional parameter—akin to the Rossby number—can explain the processes that lead to the existence of these two groups. This parameter, defined as N mode , indicates that moisture modes arise when anomalous convection lasts sufficiently long so that dry gravity waves eliminate the temperature anomalies in the convective region, satisfying weak temperature gradient (WTG) balance. This process causes moisture anomalies to dominate the distribution of moist enthalpy (or moist static energy), and hence the evolution of the wave. Conversely, convectively coupled gravity waves arise when anomalous convection eliminates the moisture anomalies more rapidly than dry gravity waves can adjust the troposphere toward WTG balance, causing temperature to govern the moist enthalpy distribution and evolution. Spectral analysis of reanalysis data indicates that slowly propagating waves ( c p ~ 3 m s ⁻¹ ) are likely to be moisture modes while fast waves ( c p ~ 30 m s ⁻¹ ) exhibit gravity wave behavior, with “mixed moisture–gravity” waves existing in between. While these findings are obtained from a highly idealized framework, it is hypothesized that they can be extended to understand simulations of convectively coupled waves in GCMs and the thermodynamics of more complex phenomena.
Radar and rawinsonde data from four ground-based observing stations in the tropical Indo-Pacific warm pool were used to identify possible associations of environmental state variables and their vertical profiles with radar-derived rain rate inside a mesoscale radar domain when the column-integrated relative humidity (CRH) exceeds 80%. At CRH exceeding 80%, a wide range—from near 0 to ~50 mm day ⁻¹ —in rain rate is observed; therefore, tropospheric moisture was a necessary but insufficient condition for deep convection. This study seeks to identify possible factors that inhibit rainfall when the atmosphere is sufficiently moist to support large precipitation rates. The domain-mean rain rate was highly sensitive to the areal coverage of intense, convective rainfall that occurs. There were two fundamentally different instances in which convective area was low. One was when the radar domain is primarily occupied by weakly precipitating, stratiform echoes. The other was when the radar domain contained almost no precipitating echoes of any type. While the former was dependent upon the stage of the convective life cycle seen by radar, the latter was probably dependent upon the convective environment. Areal coverage of convective echoes was largely determined by the number of individual convective echoes rather than their sizes, so changes in the clear-air environment of updrafts might have governed how many updrafts grew into deep cumulonimbi. The most likely environmental influence on convective rainfall identified using rawinsonde data was 900–700-hPa lapse rate; however, processes occurring on spatial scales smaller than a radar domain were probably also important but not investigated.
Precipitation clusters are contiguous raining regions characterized by a precipitation threshold, size, and the total rainfall contained within—termed the cluster power. Tropical observations suggest that the probability distributions of both cluster size and power contain a power-law range (with slope ~ −1.5) bounded by a large-event “cutoff.” Events with values beyond the cutoff signify large, powerful clusters and represent extreme events. A two-dimensional stochastic model is introduced to reproduce the observed cluster distributions, including the slope and the cutoff. The model is equipped with coupled moisture and weak temperature gradient (WTG) energy equations, empirically motivated precipitation parameterization, temporally persistent noise, and lateral mixing processes, all of which collectively shape the model cluster distributions. Moisture–radiative feedbacks aid clustering, but excessively strong feedbacks push the model into a self-aggregating regime. The power-law slope is stable in a realistic parameter range. The cutoff is sensitive to multiple model parameters including the stochastic forcing amplitude, the threshold moisture value that triggers precipitation, and the lateral mixing efficiency. Among the candidates for simple analogs of precipitation clustering, percolation models are ruled out as unsatisfactory, but the stochastic branching process proves useful in formulating a neighbor probability metric. This metric measures the average number of nearest neighbors that a precipitating entity can spawn per time interval and captures the cutoff parameter sensitivity for both cluster size and power. The results here suggest that the clustering tendency and the horizontal scale limiting large tropical precipitating systems arise from aggregate effects of multiple moist processes, which are encapsulated in the neighbor probability metric.
Tropical convection that occurs on large-enough space and time scales may evolve in response to large-scale balanced circulations. In this scenario, large-scale midtropospheric vorticity anomalies modify the atmospheric stability by virtue of thermal wind gradient balance. The convective vertical mass flux and the moisture profile adjust to changes in atmospheric stability that affect moisture and entropy transport. We hypothesize that the convection observed during the 2011 DYNAMO field campaign evolves in response to balanced dynamics. Strong relationships between midtropospheric vorticity and atmospheric stability confirm the relationship between the dynamic and the thermodynamic environments, while robust relationships between the atmospheric stability, the vertical mass flux, and the saturation fraction provide evidence of moisture adjustment. These results are important because the part of convection that occurs as a response to balanced dynamics is potentially predictable. Furthermore, the diagnostics used in this work provide a simple framework for model evaluation, and suggest that one way to improve simulations of large-scale organized deep tropical convection in global models is to adequately capture the relationship between the dynamic and thermodynamic environments in convective parameterizations.
The atmospheric component of Energy Exascale Earth System Model version 1 has included many new features in the physics parameterizations compared to its predecessors. Potential complex nonlinear interactions among the new features create a significant challenge for understanding the model behaviors and parameter tuning. Using the one-at-a-time method, the benefit of tuning one parameter may offset the benefit of tuning another parameter, or improvement in one target variable may lead to degradation in another target variable. To better understand the Energy Exascale Earth System Model version 1 model behaviors and physics, we conducted a large number of short simulations (three days) in which 18 parameters carefully selected from parameterizations of deep convection, shallow convection, and cloud macrophysics and microphysics were perturbed simultaneously using the Latin hypercube sampling method. From the perturbed parameter ensemble simulations and use of different skill score functions, we identified the most sensitive parameters, quantified how the model responds to changes of the parameters for both global mean and spatial distribution, and estimated the maximum likelihood of model parameter space for a number of important fidelity metrics. Comparison of the parametric sensitivity using simulations of two different lengths suggests that perturbed parameter ensemble using short simulations has some bearing on understanding parametric sensitivity of longer simulations. Results from this analysis provide a more comprehensive picture of the Energy Exascale Earth System Model version 1 behavior. The difficulty in reducing biases in multiple variables simultaneously highlights the need of characterizing model structural uncertainty (so-called embedded errors) to inform future development efforts.
South Asian monsoon low pressure systems, referred to as synoptic-scale monsoonal disturbances (SMDs), are convectively coupled cyclonic disturbances that are responsible for up to half of the total monsoon rainfall. In spite of their importance, the mechanisms that lead to the growth of these systems have remained elusive. It has long been thought that SMDs grow because of a variant of baroclinic instability that includes the effects of convection. Recent work, however, has shown that this framework is inconsistent with the observed structure and dynamics of SMDs. Here, we present an alternative framework that may explain the growth of SMDs and may also be applicable to other modes of tropical variability. Moisture is prognostic and is coupled to precipitation through a simplified Betts-Miller scheme. Interactions between moisture and potential vorticity (PV) in the presence of a moist static energy gradient can be understood in terms of a "gross" PV (qG) equation. The qG summarizes the dynamics of SMDs and reveals the relative role that moist and dry dynamics play in these disturbances, which is largely determined by the gross moist stability. Linear solutions to the coupled PV and moisture equations reveal Rossby-like modes that grow because of a moisture vortex instability. Meridional temperature and moisture advection to the west of the PV maximum moisten and destabilize the column, which results in enhanced convection and SMD intensification through vortex stretching. This instability occurs only if the moistening is in the direction of propagation of the SMD and is strongest at the synoptic scale.
Convective transition statistics, which describe the relation between column-integrated water vapor (CWV) and precipitation, are compiled over tropical oceans using satellite and ARM site measurements to quantify the temperature and resolution dependence of the precipitation-CWV relation at fast time scales relevant to convection. At these time scales, and for precipitation especially, uncertainties associated with observational systems must be addressed by examining features with a variety of instrumentation and identifying robust behaviors versus instrument sensitivity at high rain rates. Here the sharp pickup in precipitation as CWV exceeds a certain critical threshold is found to be insensitive to spatial resolution, with convective onset occurring at higher CWV but at lower column relative humidity as bulk tropospheric temperature increases. Mean tropospheric temperature profiles conditioned on precipitation show vertically coherent structure across a wide range of temperature, reaffirming the use of a bulk temperature measure in defining the convective transition statistics. The joint probability distribution of CWV and precipitation develops a peak probability at low precipitation forCWVabove critical, with rapidly decreasing probability of high precipitation below and near critical, and exhibits systematic changes under spatial averaging. The precipitation pickup withCWVis reasonably insensitive to time averaging up to several hours but is smoothed at daily time scales. This work demonstrates that CWV relative to critical serves as an effective predictor of precipitation with only minor geographic variations in the tropics, quantifies precipitation-related statistics subject to different spatial-temporal resolution, and provides a baseline for model comparison to apply these statistics as observational constraints on precipitation processes.
The tropical precipitation-moisture relationship, characterized by rapid increases in precipitation for modest increases in moisture, is conceptually recast in a framework relevant to plume buoyancy and conditional instability in the tropics. The working hypothesis in this framework links the rapid onset of precipitation to integrated buoyancy in the lower troposphere. An analytical expression that relates the buoyancy of an entraining plume to the vertical thermodynamic structure is derived. The natural variables in this framework are saturation and subsaturation equivalent potential temperatures, which capture the leading-order temperature and moisture variations, respectively. The use of layer averages simplifies the analytical and subsequent numerical treatment. Three distinct layers, the boundary layer, the lower free troposphere, and the midtroposphere, adequately capture the vertical variations in the thermodynamic structure. The influence of each environmental layer on the plume is assumed to occur via lateral entrainment, corresponding to an assumed mass-flux profile. The fractional contribution of each layer to the midlevel plume buoyancy (i.e., the layer weight) is estimated from TRMM 3B42 precipitation and ERAInterim thermodynamic profiles. The layer weights are used to ''reverse engineer'' a deep-inflow mass-flux profile that is nominally descriptive of the tropical atmosphere through the onset of deep convection. The layer weights-which are nearly the same for each of the layers-constitute an environmental influence function and are also used to compute a free-tropospheric integrated buoyancy measure. This measure is shown to be an effective predictor of onset in conditionally averaged precipitation across the global tropics- over both land and ocean.
Bretherton et al. (2004) used the Special Sensor Microwave Imager (SSM/I) version 5 product to derive an exponential curve that describes the relationship between precipitation and column relative humidity (CRH) over the tropical oceans. The curve, which features a precipitation pickup at a CRH of about 0.75 and a rapid increase of precipitation with CRH after the pickup, has been widely used in the studies of the tropical atmosphere. This study re-examines the moisture-precipitation relationship by using the version 7 SSM/I data, in which several biases in the previous version are corrected, and evaluates the relationship in the Coupled Model Intercomparison Project phase 5 (CMIP5) models. In the revised exponential curve derived using the updated satellite data, the precipitation pick-up occurs at a higher CRH (~0.8), and precipitation increases more slowly with CRH than in the previous curve. In most CMIP5 models, the precipitation pickup is too early due to the common model bias of overestimated (underestimated) precipitation in the dry (wet) regime.
The impact of the seasonal mean background state on the physical processes responsible for better Madden-Julian Oscillation (MJO) propagation and prediction was investigated using 20-year ECMWF reforecast datasets. While the reforecast captures the MJO propagating signal in the circulation field, the OLR and column-integrated moist static energy (MSE) anomalies show a weaker signal than the reanalysis when the MJO detours and propagates in the southern Maritime Continent (MC). By comparing individual MSE budget terms, it is found that the predicted positive MSE tendency to the east of the MJO convection center is weaker than the reanalysis due to the weaker horizontal MSE advection. The dry bias in the seasonal mean lower tropospheric moisture is a key factor that weakens the horizontal MSE advection, and thus deteriorates the MJO propagation in the reforecasts. Therefore, improvements in the mean state could further extend the MJO prediction and associated subseasonal weather phenomena over the globe.
This paper complements Part 1 in which cloud processes of aggregated convection are examined in a large-domain radiative convective equilibrium simulation in order to uncover those responsible for a consistently observed, abrupt increase in mean precipitation at a column relative humidity value of approximately 77%. In Part 2, the focus is on how the transition is affected independently by total moisture above and below the base of the melting layer. When mean precipitation rates are examined as simultaneous functions of these two moisture layers, four distinct behaviors are observed. These four behaviors suggest unique, yet familiar, physical regimes in which (i) little rain is produced by infrequent clouds, (ii) shallow convection produces increasing warm rain with increasing low-level moisture, (iii) deep convection produces progressively heavier rain above the transition point with increasing total moisture, and (iv) deep stratiform cloud produces increasingly intense precipitation from melting for increasing upper level moisture. The independent thresholds separating regimes in upper and lower layer humidity are shown to result in the value of total column humidity at which a transition between clear air and deep convection, and therefore a pickup in precipitation, is possible. All four regimes force atmospheric columns toward the pickup value at 77% column humidity, but each does so through a unique set of physical processes. Layer moisture and microphysical budgets are analyzed and contrasted with column budgets.
A survey of published results indicates that a column relative humidity near 77% is consistently observed to separate raining and nonraining columns in a time and space mean in the tropics, but why this approximate value of humidity should initiate such a statistical state transition is not readily apparent. An investigation is conducted of the submesoscale cloud processes that link column relative humidity to this abrupt pickup in heavy precipitation and of the magnitude of humidity at which this transition occurs. A cloud system resolving model in radiative convective equilibrium is used. Precipitation statistics from this simulation indicate a switch in mean precipitation state at 77% relative humidity with infrequent heavy rainfall at lower humidity. These statistics are broadly insensitive to spatial scaling. Low-level cloud fraction and convergent flux of moisture are shown to be sensitive to column humidity near 77%, while upper level cloud fraction is markedly less sensitive. Mean updraft mass flux increases with increasing humidity but only at values of humidity well above the pickup. Both warm rain processes and melting are shown to depend strongly on column humidity near the pickup but in different circumstances. No single process is determined to result in a pickup in precipitation. It is suggested that column humidity temporally leads precipitation and therefore causes its intensity.
Column moisture and moist static energy (MSE) budgets have become common tools in the study of the processes responsible for the maintenance and evolution of the MJO. While many studies have shown that precipitation is spatially correlated with column moisture, these budgets do not directly describe the MJO-related precipitation anomalies. Other spatially varying fields may also play a role in determining the horizontal distribution of anomalous precipitation. In this study, an empirical precipitation anomaly field is derived that depends on three variables in addition to column moisture. These are the low-frequency distribution of precipitation, the low-frequency column saturation water vapor, and the sensitivity of precipitation to changes in column relative humidity. The addition of these fields improve upon moisture/MSE budgets by confining these anomalies to the climatologically rainy areas of the tropics, where MJO activity is strongest. The derived field adequately describes the MJO-related precipitation anomalies, comparing favorably with TRMM precipitation data.
Furthermore, a “precipitation budget” is presented that emphasizes moist processes over the regions where precipitation is most sensitive to free tropospheric moisture. It is found that moistening from vertical moisture advection in association with regions of shallow ascent plays a central role in the propagation of the MJO. The overall contribution from this process is comparable to the contribution from horizontal moisture advection to propagation. Consistent with previous studies, it is found that vertical advection arising from longwave radiative heating maintains the intraseasonal precipitation anomalies against drying by horizontal moisture advection.
The authors study the interaction of large-scale waves with deep convection in nonrotating mesoscale model simulations, without mean vertical shear, under idealized boundary conditions (doubly periodic, fixed uniform sea surface temperature). Radiative cooling is fixed, so radiative–convective feedbacks are not considered. The model is initialized with random thermal perturbations near the surface and then run for 16 days to a state of approximate radiative-convective equilibrium. At this point, a wave-like heating is imposed for one day in order to create a wave. The heating is uniform in the meridional direction, sinusoidal with a wavelength equal to the domain size (4500 km) in the zonal direction, and has a roughly “first baroclinic mode” structure in the vertical. After this single day of forcing, the heating is turned off and the wave is allowed to evolve freely for seven more days. A range of forcing phase speeds and amplitudes are used, but two simulations are presented in detail. One has a flow-relative forcing phase speed of 55 m s −1 and the other of zero, and both have maximum forcing amplitude of 10 K d −1 . Both of these forcings produce waves which are initially rapidly damped, but then settle in to quasi-steadily propagating, coherent configurations which are weakly decaying or neutral. The authors focus on this latter period. The faster forcing produces a convectively coupled gravity wave qualitatively similar to those predicted by strict quasi-equilibrium (SQE) theory, but whose interaction with convection is weaker than that theory predicts. The adiabatic cooling is considerably larger than the diabatic heating, and consequently the phase speed is roughly 30m s −1 rather than the 10−15m s −1 typically predicted by SQE for waves of this vertical structure. Sensitivity studies show that this wave, when propagating eastward against a mean westward flow, is destabilized by linear evaporation-wind feedback. The slower forcing produces a wave which is stationary in the mean flow frame and does not have the structure of a gravity wave. This wave has a much larger signal in the moisture field than does the faster wave, and much closer cancellation between adiabatic cooling and diabatic heating. This wave appears similar to ones appearing in some recent theoretical studies and cloud-resolving simulations. DOI: 10.1034/j.1600-0870.2003.201421.x
In this study, we show that the well-documented exponential increase in the precipitation-water vapor (P-r) curve over tropical oceans also applies to tropical land, but that the land curve starts its exponential increase at smaller values of column moisture than over ocean. We demonstrate that daytime surface heating contributes to this characteristic shape of the land P-r curves. There is also significant geographical variation in the shape of the P-r curve within land and ocean regions, with the Amazon, the Maritime Continent and the eastern edges of oceans as distinct outliers. We further show that convective and stratiform rain intensities exhibit a pickup that is separate from the corresponding rain areas in the tropical P-r curve while shallow convective rain has a yet another pickup. These variations of the P-r curve characteristics likely represent geographical variations of environmental controls on storm life cycle.
Temporal precipitation autocorrelations drop slower than exponentially at long lags, and there is a range from tens to thousands of minutes where it is relevant to ask if a scale-free process might underlie the long autocorrelations. A simple stochastic model in which precipitation appears as variable-length spikes provides a reasonable prototype for this behavior. In both observations and the model, separating the component of the autocorrelation within wet events from the interevent contribution suggests long autocorrelation behavior is primarily associated with the latter. When precipitation spikes are short compared to dry events, a true power law is obtained with analytical exponent −0.5 and precipitation autocorrelation is determined by dry-spell model parameters. In more realistic cases, wet-spell termination is also important. Although a variety of apparent power law exponents can be obtained for different parameters, the fundamental long-lag process appears to be that of the interevent correlation.
Despite its pronounced impacts on weather extremes worldwide, the Madden-Julian Oscillation (MJO) remains poorly represented in climate models. Here, we present findings that point to some necessary ingredients to produce a strong MJO amplitude in a large set of model simulations from a recent model inter-comparison project. While surface flux and radiative heating anomalies are considered important for amplifying the MJO, their strength per unit MJO precipitation anomaly is found to be negatively correlated to MJO amplitude across these multi-model simulations. However, model MJO amplitude is found to be closely tied to a model's convective moisture adjustment time-scale, a measure of how rapidly precipitation must increase to remove excess column water vapor, or alternately the efficiency of surface precipitation generation per unit column water vapor anomaly. These findings provide critical insights into key model processes for the MJO, and pinpoint a direction for improved model representation of the MJO.
Significance
Previous studies have argued that monsoons, which are continental-scale atmospheric circulations that deliver water to billions of people, will abruptly shut down when aerosol emissions, land use change, or greenhouse gas concentrations reach a critical threshold. Here it is shown that the theory used to predict such “tipping points” omits a dominant term in the equations of motion, and that both a corrected theory and an ensemble of global climate model simulations exhibit no abrupt shift in monsoon strength in response to large changes in various forcings. Therefore, although monsoons are expected to change in response to anthropogenic forcings, there is no reason to expect an abrupt shift into a dry regime in the next century or two.
We reexamine the well known empirical relationship between area-averaged surface precipitation (P) and the column moisture content (r) using ground radar and satellite observations, with an emphasis on the convective and stratiform rainfall classifications. The rapid rise in P above critical r (rc) or the "pickup" is more pronounced for stratiform rainfall on hourly and less time scales while convective rainfall, displays only a weak pickup above rc. After partitioning the area-averaged rainfall into conditional rain rates and rain area, we find that the nonlinearity in the P-r curve can be almost entirely explained by the nonlinear increase in rain area, especially in stratiform regions. These findings have implications for the representation of organized convective cloud systems in global circulation models.
A linear wave theory for the Madden-Julian oscillation (MJO), previously developed by Sobel and Maloney, is extended upon in this study. In this treatment, column moisture is the only prognostic variable and the horizontal wind is diagnosed as the forced Kelvin and Rossby wave responses to an equatorial heat source/sink. Unlike the original framework, the meridional and vertical structure of the basic equations is treated explicitly, and values of several key model parameters are adjusted, based on observations. A dispersion relation is derived that adequately describes the MJO's signal in the wavenumber-frequency spectrum and defines the MJO as a dispersive equatorial moist wave with a westward group velocity. On the basis of linear regression analysis of satellite and reanalysis data, it is estimated that the MJO's group velocity is ~40% as large as its phase speed. This dispersion is the result of the anomalous winds in the wave modulating the mean distribution of moisture such that the moisture anomaly propagates eastward while wave energy propagates westward. The moist wave grows through feedbacks involving moisture, clouds, and radiation and is damped by the advection of moisture associated with the Rossby wave. Additionally, a zonal wavenumber dependence is found in cloud-radiation feedbacks that cause growth to be strongest at planetary scales. These results suggest that this wavenumber dependence arises from the nonlocal nature of cloud-radiation feedbacks; that is, anomalous convection spreads upper-level clouds and reduces radiative cooling over an extensive area surrounding the anomalous precipitation.
The authors analyze composite structures of tropical convectively coupled Kelvin waves (CCKWs) in terms of the theory of Raymond and Fuchs using radiosonde data, 3D analysis and reanalysis model output, and annual integrations with the ECMWF model on the full planet and on an aquaplanet. Precipitation anomalies are estimated using the NOAA interpolated OLR and TRMM 3B42 datasets, as well as using model OLR and rainfall diagnostics. Derived variables from these datasets are used to examine assumptions of the theory. Large-scale characteristics of wave phenomena are robust in all datasets and models where Kelvin wave variance is large. Indices from the theory representing column moisture and convective inhibition are also robust. The results suggest that the CCKW is highly dependent on convective inhibition, while column moisture does not play an important role.
Prototype models are presented for time series statistics of precipitation and column water vapor. In these models, precipitation events begin when the water vapor reaches a threshold value and end when it reaches a slightly lower threshold value, as motivated by recent observational and modeling studies. Using a stochastic forcing to parameterize moisture sources and sinks, this dynamics of reaching a threshold is a first-passage-time problem that can be solved analytically. Exact statistics are presented for precipitation event sizes and durations, for which the model predicts a probability density function (pdf) with a power law with exponent -3/2. The range of power-law scaling extends from a characteristic small-event size to a characteristic large-event size, both of which are given explicitly in terms of the precipitation rate and water vapor variability. Outside this range, exponential scaling of event-size probability is shown. Furthermore, other statistics can be computed analytically, including cloud fraction, the pdf of water vapor, and the conditional mean and variance of precipitation (conditioned on the water vapor value). These statistics are compared with observational data for the transition to strong convection; the stochastic prototype captures a set of properties originally analyzed by analogy to critical phenomena. In a second prototype model, precipitation is further partitioned into deep convective and stratiform episodes. Additional exact statistics are presented, including stratiform rain fraction and cloud fractions, that suggest that even very simple temporal transition rules (for stratiform rain continuing after convective rain) can capture aspects of the role of stratiform precipitation in observed precipitation statistics.
The two leading principal components of the daily 850- minus 150-hPa global velocity potential in the Interim European Centre for Medium-Range Weather Forecasts (ECMWF) Re-Analysis (ERA-Interim) (1979-2011) data are used as time-varying Madden-Julian oscillation (MJO) indices. Regression maps and meridional cross sections based on these indices are used to document the structure and evolution of the zonal wind (u) and geopotential height (Z) anomalies in the MJO cycle. The data are daily, and they are not separated by season. At upper-tropospheric levels the MJO signature is dominated by eastward-propagating planetary wave packets consisting of equatorial Kelvin waves flanked by Rossby waves centered along 28 degrees N/S, for which the westerly jet streams serve as waveguides. At lower-tropospheric levels the pattern more closely resembles the response to a pulsating heat source over the Maritime Continent, where the Andes block the eastward-propagating Kelvin wave pulse. The contrasting upper- and lower-tropospheric patterns are made up of the same building blocks: a deep, baroclinic modal structure with a node at the 400-hPa level, which dominates the tropical signature, and a barotropic residual field consisting mainly of extratropical wave trains oriented along great circles. The extratropical wave trains emanate from the flanking Rossby waves in the baroclinic modal structure. The strongest of them, which resembles the Pacific-North America (PNA) pattern, extracts kinetic energy from the climatological-mean flow in the jet exit region. At other longitudes the jet stream seems to act as a barrier to the poleward propagation of MJO-related wave activity.
[1] Convective available potential energy (CAPE) is shown to increase rapidly with warming in simulations of radiative-convective equilibrium over a wide range of surface temperatures. The increase in CAPE implies a systematic deviation of the thermal stratification from moist adiabatic that is non-negligible at high temperatures. However, cloud buoyancy remains much smaller than what CAPE would imply because entrainment is more effective in reducing buoyancy in warmer atmospheres. An entraining plume model in the limit of zero cloud buoyancy is shown to reproduce the increase in CAPE with warming if the entrainment rate is held fixed and increases in the vertical extent of convection are taken into account. These model results together with radiosonde observations are used to support a conceptual model in which entrainment plays a role in determining the thermal stratification of the tropical atmosphere.
Motivated by observations of the mean state of tropical precipitable water (PW), a moist, first baroclinic mode, shallow-water system on an equatorial β-plane with a background saturation profile that depends on latitude and longitude is studied. In the presence of a latitudinal moisture gradient, linear analysis of the non-rotating problem reveals large-scale, symmetric, eastward and westward propagating unstable modes. The introduction of a zonal moisture gradient breaks the east–west symmetry of the unstable modes. The effects of rotation are then included by numerically solving the resulting eigenvalue problem on an equatorial β-plane. With a purely meridional moisture gradient, the system supports large-scale, low-frequency, eastward and westward moving neutral modes. Some of the similarities, and some of the discrepancies of these modes with intraseasonal tropical waves are pointed out. Finally, a zonal moisture gradient in the presence of rotation renders some of the aforementioned neutral modes unstable. In particular, according to observations of large-scale, low-frequency tropical variability, it is seen that regions where the background saturation profile increases (decreases) to the east favour eastward (westward) moving moist modes. Copyright © 2010 Royal Meteorological Society
Recent studies have pushed forward the idea that congestus clouds, through their moistening of the atmosphere, could promote deep convection. On the other hand, older studies have tended to relate convective initiation to the large-scale forcing. These two views are here contrasted by performing a time-scale analysis. The analysis combines ship observations, large-eddy simulations, and 1 month of brightness temperature measurements with a focus on the tropical Atlantic and adjacent land areas.
The time-scale analysis suggests that previous work may have overstated the importance of congestus moistening in the preconditioning of deep convection. It is found that cumuli congestus transition very rapidly to deep convection, in 2 h over land and 4 h over ocean. This is much faster than the time needed (10 h and longer) by congestus clouds to sufficiently moisten the atmosphere. Moreover, the majority of congestus clouds seem unable to grow into cumulonimbus and the probability of transition does not increase with increasing congestus lifetime (i.e., more moistening). Finally, the presence of cumuli congestus over a given region generally does not enhance the likelihood for deep convection development, either with respect to other regions or to clear-sky conditions. Hence, the results do not support the view of an atmosphere slowly deepening by local moistening, but rather, they may be interpreted as reminiscent of an atmosphere marked by violent and sudden outbursts of convection forced by dynamical effects. This also implies that moisture convergence is more important than local surface fluxes to trigger deep convection over a certain region.
The authors discuss modifications to a simple linear model of intraseasonal moisture modes. Wind-evaporation feedbacks were shown in an earlier study to induce westward propagation in an eastward mean low-level flow in this model. Here additional processes, which provide effective sources of moist static energy to the disturbances and which also depend on the low-level wind, are considered. Several processes can act as positive sources in perturbation easterlies: zonal advection (if the mean zonal moisture gradient is eastward), modulation of synoptic eddy drying by the MJO-scale wind perturbations, and frictional convergence. If the sum of these is stronger than the wind-evaporation feedback-as observations suggest may be the case, though with considerable uncertainty-the model produces unstable modes that propagate weakly eastward relative to the mean flow. With a small amount of horizontal diffusion or other scale-selective damping, the growth rate is greatest at the largest horizontal scales and decreases monotonically with wavenumber.