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Inference of emission rate using the inverse-dispersion method for the multi-source problem
Abstract
The inverse-dispersion method (IDM) has been widely used to infer the emission rate of a spatially homogeneous and well-defined source (referred to as the single-source problem). To infer the emission rate of a spatially heterogeneous source (referred to as the multi-source problem), a large number of downwind concentration measurements usually need to be conducted. In this paper, with the evapotranspiration (ET) data obtained in a field-scale experiment, we evaluated the feasibility and accuracy of IDM for multi-source strength inference with only two downwind concentration measurements. Field ET in this experiment exhibited typical multi-source characteristics due to sequential irrigation plot by plot. Under such conditions, large errors existed in the ET estimation via conventional methods, such as the gradient method. This heterogeneous ET was inferred by IDM with two assumptions: (1) the magnitude of the plot ET decays exponentially with the date after irrigation, having a characteristic decay timescale τ; (2) the daily variation pattern of ET obeys normal distribution with an expectation μ and a standard deviation σ. The accuracy of the inferred ET was validated by the measured water vapor fluxes via eddy covariance system. Then, sensitivity analysis on τ and σ was conducted. We found that only σ had an obvious effect on the accuracy of the ET inference. Moreover, our analysis showed that it was better to make accurate measurements on the upwind concentration, which was essential to the reliability of the implementation of IDM.
... Therefore, estimation of the NH 3 emission is challenged by the heterogeneous sources in the field-scale: temporal and spatial variations of NH 3 emissions. For such heterogeneous emissions, a method similar to Huo et al. (2014) was employed, which is based on the principle of the inverse dispersion method (IDM). They inferred the heterogeneous cropland evapotranspiration of the same experiment via IDM with two-level downwind water vapor measurements. ...
... Our experiment was conducted in a representative farmland in the North China Plain (37 32 0 04 00 N, 115 54 0 51 00 E, 16 m a.s.l.) in Guangchuan town, Hebei province. Huo et al. (2014) described the study site in detail. Fig. 1 presents the illustrations of the study area. ...
... The method on NH 3 emission rate estimation is similar to that of Huo et al. (2014), who established and examined an IDM with twolevel concentrations to estimate the heterogeneous evapotranspiration for the same experiment. It is more complex for the estimation of NH 3 emissions compared to that of evapotranspiration, since the heterogeneity of NH 3 emissions was formed due to not only the inconsistent fertilization dates but also different types of fertilizer used. ...
A field-scale experiment was conducted in the spring of 2012 at a winter wheat cropland, aiming to
quantify ammonia (NH3) emissions from surface fertilization under realistic cultivation conditions. Since
the fertilization lasted about 20 days for hundreds of divided plots and three types of fertilizers were
used (i.e., urea, ammonium sulfate and compound nitrogen-phosphorous-potassium fertilizer), the
heterogeneity was one of the significant characteristics of the cropland NH3 emissions during the
experiment, which is a great challenge for the classical micrometeorological methods to calculate NH3
fluxes. Based on continuous measurements of NH3 concentrations at two heights (2.5 m and 8 m) and
detailed records of the fertilization plot by plot, an inverse dispersion method was employed to derive
the heterogeneous NH3 emissions and the corresponding emission factors (EFs). The EFs derived from
this experiment for urea, ammonium sulfate and compound fertilizer were 12.0% ± 3.1%, 8.5% ± 1.6% and
4.5% ± 1.7%, respectively. The EF of urea we obtained was lower than most of other domestic measurements
and those used in the NH3 emission inventories in China. Measurements on EFs of ammonium
sulfate and compound fertilizer are not available in China. However, the EFs of ammonium sulfate and
compound fertilizer we obtained were comparable to those used in NH3 emission inventories of China.
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... The bLS method has been usually used to predict emission rates from a single source [20,26]. Implementing the bLS method to measure multiple source emissions is more complicated than single-source emissions when a gas concentration sensor can simultaneously detect gas concentrations from several sources [27][28][29][30][31][32][33]. For multi-source emissions measurements, the minimum requirement in the bLS model is that the number of concentration sensors (n) must be at least equal to emission sources (m) (i.e., n ≥ m) [27,29]. ...
... Most studies of multi-source emissions have focused on optimizing sensor-source geometry to improve flux calculations [27][28][29][30][31][32]. Few studies have investigated the effect of advection from adjacent fields on emission estimations [33][34][35][36]. As a result, the criteria used for quality assurance of the single-source bLS emission estimations cannot be directly applied for multi-source emission estimations. ...
Nitrous oxide (N2O) emissions from agricultural soil are substantially influenced by nitrogen (N) and field management practices. While routinely soil chambers have been used to measure emissions from small plots, measuring field-scale emissions with micrometeorological methods has been limited. This study implemented a backward Lagrangian stochastic (bLS) technique to simultaneously and near-continuously measure N2O emissions from four adjacent fields of approximately 1 ha each. A scanning open-path Fourier-transform infrared spectrometer (OP-FTIR), edge-of-field gas sampling and measurement, locally measured turbulence, and bLS emissions modeling were integrated to measure N2O emissions from four adjacent fields of maize production using different management in 2015. The maize N management treatments consisted of 220 kg NH3-N ha−1 applied either as one application in the fall after harvest or spring before planting or split between fall after harvest and spring before planting. The field preparation treatments evaluated were no-till (NT) and chisel plow (ChP). This study showed that the OP-FTIR plus bLS method had a minimum detection limit (MDL) of ±1.2 µg m−2 s−1 (3σ) for multi-source flux measurements. The average N2O emission of the four treatments ranged from 0.1 to 2.3 µg m−2 s−1 over the study period of 01 May to 11 June after the spring fertilizer application. The management of the full-N rate applied in the fall led to higher N2O emissions than the split-N rates applied in the fall and spring. Based on the same N application, the ChP practice tended to increase N2O emissions compared with NT. Advection of N2O from adjacent fields influenced the estimated emissions; uncertainty (1σ) in emissions was 0.5 ± 0.3 µg m−2 s−1 if the field of interest received a clean measured upwind background air, but increased to 1.1 ± 0.5 µg m−2 s−1 if all upwind sources were advecting N2O over the field of interest. Moreover, higher short-period emission rates (e.g., half-hour) were observed in this study by a factor of 1.5~7 than other micrometeorological studies measuring N2O-N loss from the N-fertilized cereal cropping system. This increment was attributed to the increase in N fertilizer input and soil temperature during the measurement. We concluded that this method could make near-continuous “simultaneous” flux comparisons between treatments, but further studies are needed to address the discrepancies in the presented values with other comparable N2O flux studies.
... For acquiring up-to-date EFs that could reflect NH 3 volatilization from synthetic fertilizer application in present Chinese agricultural practice, we measured NH 3 EF by using micrometeorological method for a whole year in a typical farmland in the North China Plain and an inverse dispersion model was also used to derive the ammonia EFs (Huo et al., 2014(Huo et al., , 2015. The in situ results could represent better than those used in Huang et al. (2012) which were derived from studies in early years. ...
Ammonia (NH3) can interact in the atmosphere with other trace chemical
species, which can lead to detrimental environmental consequences, such as
the formation of fine particulates and ultimately global climate change.
China is a major agricultural country, and livestock numbers and nitrogen
fertilizer use have increased drastically since 1978, following the rapid
economic and industrial development experienced by the country. In this
study, comprehensive NH3 emissions inventories were compiled for China
for 1980–2012. In a previous study, we parameterized emissions factors
(EFs) considering ambient temperature, soil acidity, and the method and rate
of fertilizer application. In this study, we refined these EFs by adding the
effects of wind speed and new data from field experiments of NH3 flux
in cropland in northern China. We found that total NH3 emissions in
China increased from 5.9 to 11.1 Tg from 1980 to 1996, and then decreased to
9.7 Tg in 2012. The two major contributors were livestock manure and
synthetic fertilizer application, which contributed 80–90 % of the total
emissions. Emissions from livestock manure rose from 2.86 Tg (1980) to 6.16 Tg (2005), and then decreased to 5.0 Tg (2012); beef cattle were the largest
source followed by laying hens and pigs. The remarkable downward trend in
livestock emissions that occurred in 2007 was attributed to a decrease in
the numbers of various livestock animals, including beef cattle, goats, and
sheep. Meanwhile, emissions from synthetic fertilizer ranged from 2.1 Tg
(1980) to 4.7 Tg (1996), and then declined to 2.8 Tg (2012). Urea and
ammonium bicarbonate (ABC) dominated this category of emissions, and a
decline in ABC application led to the decrease in emissions that took place
from the mid-1990s onwards. High emissions were concentrated in eastern and
southwestern China. Seasonally, peak NH3 emissions occurred in spring
and summer. The inventories had a monthly temporal resolution and a spatial
resolution of 1000 m, and thus are suitable for global and regional
air-quality modeling.
... For acquiring up-to-date EFs that could reflect NH 3 volatilization from synthetic fertilizer application in present Chinese agricultural practice, we measured NH 3 EF by using micrometeorological method for a whole year in a typical farmland in the North China Plain and an inverse dispersion model was also used to derive the ammonia EFs (Huo et al., 2014(Huo et al., , 2015. The in situ results could represent better than those used in Huang et al. (2012) which were derived from studies in early years. ...
Ammonia (NH3) can interact in the atmosphere with other trace chemical species, which can lead to detrimental environmental consequences, such as the formation of fine particulates and ultimately global climate change. China is a major agricultural country, and livestock numbers and nitrogen fertilizer use have increased drastically since 1978, following the rapid economic and industrial development experienced by the country. In this study, comprehensive NH3 emissions inventories were compiled for China for 1980–2012. In a previous study, we parameterized emissions factors (EFs) considering ambient temperature, soil acidity, and the method and rate of fertilizer application. In this study, we refined these EFs by adding the effects of wind speed and new data from field experiments of NH3 flux in cropland in northern China. We found that total NH3 emissions in China increased from 5.9 to 11.2 Tg from 1980 to 1996, and then decreased to 9.5 Tg in 2012. The two major contributors were livestock manure and synthetic fertilizer application, which contributed 80–90 % of the total emissions. Emissions from livestock manure rose from 2.87 Tg (1980) to 6.17 Tg (2005), and then decreased to 5.0 Tg (2012); beef cattle were the largest source followed by laying hens and pigs. The remarkable downward trend in livestock emissions that occurred in 2007 was attributed to a decrease in the numbers of various livestock animals, including beef cattle, goats, and sheep. Meanwhile, emissions from synthetic fertilizer ranged from 2.1 Tg (1980) to 4.7 Tg (1996), and then declined to 2.8 Tg (2012). Urea and ammonium bicarbonate (ABC) dominated this category of emissions, and a decline in ABC application led to the decrease in emissions that took place from the mid-1990s onwards. High emissions were concentrated in eastern and southwestern China. Seasonally, peak NH3 emissions occurred in spring and summer. The inventories had a monthly temporal resolution and a spatial resolution of 1000 m, and thus are suitable for global and regional air-quality modeling.
... We prescribed diurnal profiles of industrial, transportation, residential, and power plant emissions following . Hourly variations in NH 3 emissions were derived from measurements in Huo et al. (2014). In addition, biomass burning was classified into three subclasses: forest and grass fires, field burning of crop residues, and biofuel combustion. ...
The direct radiative effect (DRE) of multiple aerosol species [sulfate, nitrate, ammonium, black carbon (BC), organic carbon (OC), and mineral aerosol] and their spatiotemporal variations over China were investigated using a fully coupled meteorology-chemistry model [Weather Research and Forecasting (WRF) Model coupled with Chemistry (WRF-Chem)] for the entire year of 2006. This study made modifications to improve the model performance, including updating land surface parameters, improving the calculation of transition-metal-catalyzed oxidation of SO2, and adding heterogeneous reactions between mineral dust aerosol and acid gases. The modified model generally reproduced the magnitude, seasonal pattern, and spatial distribution of the measured meteorological conditions, concentrations of PM10 and its components, and aerosol optical depth (AOD), although some low biases existed in modeled aerosol concentrations. A diagnostic iteration method was used to estimate the overall DRE of aerosols and contributions from different components. At the land surface, the incident net radiation flux was reduced by 10.2 W m-2 over China. Aerosols significantly warmed the atmosphere with the national mean DRE of +10.8 W m-2. BC was the leading radiative heating component (+8.7 W m-2), followed by mineral aerosol (+1.1W m-2). At the top of the atmosphere (TOA), BC introduced the largest radiative perturbation (+4.5W m-2), followed by sulfate (-1.4W m-2). The overall perturbation of aerosols on radiation transfer is quite small over China, demonstrating the counterbalancing effect between scattering and adsorbing aerosols. AerosolDREat theTOAhad distinct seasonality, generally with a summer maximum and winter minimum, mainly determined by mass loadings, hygroscopic growth, and incident radiation flux.
... The inputs of this model include mean wind speed, wind direction, standard deviation of the lateral wind component, friction velocity, surface roughness, and Obukhov length (Cai et al. 2008). The evapotranspiration strength of each plot at each time of the day during the experiment was inferred by Huo et al. (2013) via the inverse dispersion method. In their study, the accuracy of the inferred evapotranspiration was examined by the eddy covariance measurements. ...
Based on the micrometeorological measurements at a heterogeneous farmland in the North China Plain, this study focused on the effects of surface source/sink distributions on the flux-gradient similarity theory in the unstable surface layer. Firstly, the quality of the micrometeorological measurements was evaluated by the analysis of the surface energy balance closure and the integral turbulence characteristics. In general, a 22 % deficit of energy balance was found at this site, with the sum of sensible and latent heat being smaller than the available energy. The normalized standard deviations of turbulent quantities behaved in accordance with Monin-Obukhov similarity theory. However, slight departures from the classical formulations might be caused by the surface heterogeneity. Then, the applicability of flux-gradient similarity over the heterogeneous surface was examined. The observed normalized wind gradients agreed with the classical universal function established over homogeneous surface. However, due to the effects of surface source/sink distributions, the observed normalized humidity and temperature gradients deviated from the classical universal functions. Our study shows that the classical universal functions, when adjusted by a coefficient considering the effects of surface heterogeneity, can be utilized to estimate fluxes via gradient method even though over the heterogeneous surface. This adjustment coefficient was found to decrease linearly from unity with the increase of the absolute value of the vertical flux divergence.
Based on the turbulent observations during April 30 and May 10 2012, this work investigated statistical characteristics of atmospheric turbulent and water, heat, carbon dioxide (CO2) and methane (CH4) transport in North China. The empirical coefficient used to calculate the flux of CH4 in the Relaxed Eddy Accumulation (REA) method was simulated. The results show that in unstable conditions, the normalized standard deviations of temperature, humidity, CO2 and CH4 are related to z/L following the "-1/3 power law". The ratios between horizontal transport and vertical transport of heat, water vapor and CO2 are related to z/L, but CH4 has no similar relationship. Sensible heat flux is quite low while latent heat flux is relatively high. CO2 flux is slightly above zero during nighttime and below zero during daytime, indicating that the observed area is a carbon sink. CH4 flux is mainly below zero, indicating that the observed area is a methane sink. The values of the empirical coefficients used to calculate the flux of CO2 and CH4 in REA method are 0. 61 and 0. 30, respectively.
Deposition of atmospheric ammonia (NH3) to semi-natural ecosystems leads to serious adverse effects, such as acidification and eutrophication. A step in quantifying such effects is the measurement of NH3 fluxes over semi-natural and agricultural land. However, measurement of NH3 fluxes over vegetation in the vicinity of strong NH3 sources is challenging, since NH3 emissions are highly heterogeneous. Indeed, under such conditions, local advection errors may alter the measured fluxes. In this study, local advection errors (DeltaFz,adv) were estimated over a 14 ha grassland field, which was successively cut and fertilised, as part of the GRAMINAE integrated Braunschweig experiment. The magnitude of DeltaFz,adv was determined up to 810 m downwind from farm buildings emitting between 6.2 and 9.9 kg NH3 day-1. The GRAMINAE experiment provided a unique opportunity to compare two methods of estimating DeltaFz,adv: one inference method based on measurements of horizontal concentration gradients, and one based on inverse dispersion modelling with a two-dimensional model. Two sources of local advection were clearly identified: the farm NH3 emissions leading to positive DeltaFz,adv ("bias towards emissions") and field NH3 emissions, which led to a negative DeltaFz,adv ("bias towards deposition"). The local advection flux from the farm was in the range 0 to 27 ng NH3 m-2 s-1 at 610 m from the farm, whereas DeltaFz,adv due to field emission was proportional to the local flux, and ranged between -209 and 13 ng NH3 m-2 s-1. The local advection flux DeltaFz,adv was either positive or negative depending on the magnitude of these two contributions. The modelled and inferred advection errors agreed well. The inferred advection errors, relative to the vertical flux at 1 m height, were 52% on average, before the field was cut, and less than 2.1% when the field was fertilised. The variability of the advection errors in response to changes in micrometeorological conditions is also studied. The limits of the 2-D modelling approach are discussed.
The gas emission rate Q from an artificial 36-m2 surface area source was inferred from line-average concen- tration CL measured by an open-path laser situated up to 100 m downwind. Using a backward Lagrangian stochastic (bLS) model, a theoretical CL/Q relationship was established for each experimental trial by simulating an ensemble of fluid-element paths arriving in the laser beam under the prevailing micrometeorological conditions. The diagnosed emission rates (QbLS) were satisfactory for trials done when Monin-Obukhov similarity theory gave a good description of the surface layer, but were poor during periods of extreme atmospheric stability ( | L | # 2 m) and transition periods in stratification. With such periods eliminated, the average value of the 15-min ratios QbLS/Q over n 5 77 fifteen-minute trials spanning 6 days was 1.02. Individual 15-min estimates, however, exhibited sizable variability about the true rate, with the standard deviation in QbLS/Q being sQ/Q 5 0.36. This variability is lessened (sQ/Q 5 0.22, n 5 46) if one excludes cases in which the detecting laser path lay above or immediately downwind from the source—a circumstance in which the laser path lies at the edge of the gas plume.
At a cropland and a grassland site field scale ammonia (NH3) emissions from slurry application were determined simultaneously by two approaches based on (i) eddy covariance (EC) flux measurements using high temperature Chemical Ionisation Mass Spectrometry (HT-CIMS) and on (ii) backward Lagrangian Stochastic (bLS) dispersion modelling using concentration measurements by three optical open path Fourier Transform Infrared (FTIR) systems. Slurry was spread on the fields in sequential tracks over a period of one to two hours. In order to calculate field emissions, measured EC/HT-CIMS fluxes were combined with flux footprint analysis of individual slurry spreading tracks to parameterise the NH3 volatilisation with a bi-exponential time dependence. Accordingly, track-resolved concentration footprints for the FTIR measurements were calculated using bLS. A consistency test with concentrations measured by impingers showed very low systematic deviations for the EC/HT-CIMS results (
In order to examine methodologies to quantify methane emissions from small surface sources, methane emissions from a ground level grid (3m×3m) were estimated using a simplified micrometeorological mass difference (MMD) and an inverse dispersion technique (backward Lagrangian Stochastic model, bLS). Results indicated that the MMD and bLS techniques both provided accurate ensemble recoveries of 1.01 (σQMMD/Q=0.06) and 1.03 (σQbLS/Q=0.16), respectively. It was shown that in order to obtain accurate MMD estimates one must account for the turbulent component of the horizontal flux. This requires instantaneous measurements of wind speed and methane concentrations. Without this component (which is not typically measured), the MMD calculations overestimated the actual emissions by about 12% under very unstable conditions, 10% under moderately unstable conditions, and 7 and 8% under slightly unstable and near neutral conditions. Dispersion model simulations corroborated the overestimation with atmospheric stabilities and also indicated that this value varies with the distance between the source and the laser path. This study demonstrated that the MMD and the bLS techniques are both suitable for quantifying gas emissions from small area sources but the number of sensors required for the bLS technique is considerably less than for the MMD technique.
The performance of two inverse dispersion models to quantify ammonia (NH3) fluxes has been evaluated. Ammonia emissions from cattle slurry spreading have been estimated following two different application techniques in northern Italy: (i) surface spreading with incorporation after 24 h and (ii) injection into the soil. Passive diffusion samplers were used to measure atmospheric ammonia concentrations at the treated fields and at background sites. A sonic anemometer was used to characterise the atmospehric turbulence and provided the necessary inputs for the inverse models. Two inverse dispersion models were then employed: FIDES, based on the Philip (1959) analytical solution of the advection–diffusion equation and WindTrax, a Lagrangian stochastic dispersion model. Both models were parameterised with friction velocity, Obukhov length and roughness as input. WindTrax was also alternatively used with wind components statistics from the sonic anemometer. The two models agreed well in estimating ammonia emissions under neutral conditions but diverged under stable and unstable conditions because of different parameterisation of the diffusivity profile. The maximum difference between the two models was less than 32%. The uncertainty associated with the concentration measurements with the passive samplers, was lower than 11%. The direct injection of slurry into the soil was the most effective method for reducing N loss from slurry application, resulting in an emission of 2% of the total ammoniacal nitrogen (TAN) applied when surface application resulted in losses of 5.4% of TAN.
The surface energy balance in an irrigated urban park in suburban Sacramento, CA is observed. Three sites extend from the edge of the park to its centre, along a transect which is aligned with the prevailing wind. Direct measurements of the fluxes of net radiation, soil heat flux and evaporation are made at each site and the convective sensible heat is found by residual. Strong advective effects on evaporation are observed, especially in the afternoon and evening. The driving forces for this are the differences in surface and air temperature, and humidity, between the cool, wet park and its warmer, drier built-up surroundings. The control of the surroundings on park evaporation is demonstrated by comparing values with those from synchronous observations in the surrounding suburbs and at an irrigated sod farm just outside the city. Greatest evaporative enhancement is observed at the upwind edge. Throughout the afternoon evaporation considerably exceeds the net radiation. This is interpreted to be due to the microscale leading-edge effect which appears to be restricted to a fetch of about 20 m. Further into the park evaporation also exceeds the net radiation in the afternoon due to the oasis effect. At all sites the sensible heat flux density in the afternoon is negative. Daily and daytime total evaporation from the park is more than 300% that from the integrated suburban area, and more than 130% that from the irrigated rural grass site. The unlimited water supply and the high temperatures of the park allow it to behave like a wet leaf in that its surface temperature seems to be ‘thermostatically’ controlled—it never rises more than a few degrees above that of the park air and for much of the day is cooler than the park air. Copyright © 2000 Royal Meteorological Society
1] Tower-based measurements of mass and energy exchanges at the end of the growing season in central Botswana were used to evaluate functional relationships commonly applied to predict water and carbon fluxes between savanna landscapes and the atmosphere. Following a large rainfall event, daily evapotranspiration (ET daily) exhibited an exponential decay consistent with a derived analytical expression based on critical and wilting-point soil moisture limits for savanna vegetation native to the study region. A piecewise linear soil moisture limitation function provided good estimates of ET daily as a function of potential evapotranspiration and soil moisture (R 2 = 0.92). Comparison of a soil moisture mass balance with measured ET daily indicated deeper root water uptake at a site with more woody vegetation compared with a grass-dominated site. Linear correlation (R 2 = 0.90) of daytime CO 2 flux and evapotranspiration supported a constant water use efficiency to estimate carbon fluxes from water fluxes. Daytime and nighttime CO 2 fluxes responded similarly to soil drying, enabling estimation of total daily CO 2 flux from ET daily . These experimental results support a simple model of savanna land-atmosphere exchange over interstorm periods. INDEX TERMS: 1818 Hydrology: Evapotranspiration; 3322 Meteorology and Atmospheric Dynamics: Land/atmosphere interactions; 1866 Hydrology: Soil moisture; 1878 Hydrology: Water/energy interactions; KEYWORDS: African savanna, evapotranspiration, land-atmosphere exchange, soil moisture, water and carbon flux, water limitation Citation: Williams, C. A., and J. D. Albertson (2004), Soil moisture controls on canopy-scale water and carbon fluxes in an African savanna, Water Resour. Res., 40, W09302, doi:10.1029/2004WR003208.
We propose an analytical model for the so-called footprint of scalar fluxes in the atmospheric boundary layer. It is the generalization of formulations already given in the literature, which allows to account for thermal stability. Our model is only marginally more complicated than these, and it is therefore simple enough to be applicable for a routine footprint analysis within long-term measurements. The mathematical framework of our model is a stationary gradient diffusion formulation with height-independent crosswind dispersion. It uses the solution of the resulting two-dimensional advection – diffusion equation for power law profiles of the mean wind velocity and the eddy diffusivity. To find the adjoint Monin–Obukhov similarity profile, we propose two different approaches, a purely analytical one and a simplenumerical error minimalization.
Inverse-dispersion calculations can be used to infer atmospheric emission rates through a combination of downwind gas concentrations
and dispersion model predictions. With multiple concentration sensors downwind of a compound source (whose component positions
are known) it is possible to calculate the component emissions. With this in mind, a field experiment was conducted to examine
the feasibility of such multi-source inferences, using four synthetic area sources and eight concentration sensors arranged
in different configurations. Multi-source problems tend to be mathematically ill-conditioned, as expressed by the condition
number κ. In our most successful configuration (average κ = 4.2) the total emissions from all sources were deduced to within 10% on average, while component emissions were deduced
to within 50%. In our least successful configuration (average κ = 91) the total emissions were calculated to within only 50%, and component calculations were highly inaccurate. Our study
indicates that the most accurate multi-source inferences will occur if each sensor is influenced by only a single source.
A “progressive” layout is the next best: one sensor is positioned to “see” only one source, the next sensor is placed to see
the first source and another, a third sensor is placed to see the previous two plus a third, and so on. When it is not possible
to isolate any sources κ is large and the accuracy of a multi-source inference is doubtful.
A method for calculating the dispersion of plumes in the atmospheric boundary layer is presented. The method is easy to use on a routine basis. The inputs to the method are fundamental meteorological parameters, which act as distinct scaling parameters for the turbulence. The atmospheric boundary layer is divided into a number of regimes. For each scaling regime we suggest models for the dispersion in the vertical direction. The models directly give the crosswind-integrated concentrations at the ground, xy, for nonbuoyant releases from a continuous point source. Generally the vertical concentration profile is proposed to be other than Gaussian. The lateral concentration profile is always assumed to be Gaussian, and models for determining the lateral spread σy are proposed. The method is limited to horizontally homogeneous conditions and travel distances less than 10km. The method is evaluated against independent tracer experiments over land. The overall agreement between measurements and predictions is very good and better than that found with the traditional Gaussian plume model.
We use an inverse–dispersion technique to diagnose gas emissions (ammonia) from a swine farm. A backward Lagrangian stochastic (bLS) model gives the emission-concentration relationship, so that downwind gas concentration establishes emissions. The bLS model takes as input the average wind velocity and direction, surface roughness, and atmospheric stability. Despite ignoring wind complexity and assuming a simplified source configuration in the model calculations, we argue that with concentration and wind measured sufficiently far from the farm the errors can be relatively small. An important part of our analysis was identifying periods likely to give erroneous results. The resulting emission calculations (6.5 and 16 g animal−1 day−1 in March and July, respectively) are plausible in the light of comparative figures.
The sensitivity of evapotranspiration (ET) to soil moisture storage plays an important role in the land-atmosphere system. Yet little is known about its magnitude, or its dependence on vegetation, soil, and/or climate characteristics. Here we relate the sensitivity to the timescale of ET decay in absence of rainfall, and show that it can thus be derived from time series of ET alone. We analyze ET observations from 15 vegetated sites covering a range of climates conditions, yielding timescales of 15-35 days. Longer timescales (weaker ET sensitivity) are found in regions with seasonal droughts, or at sites with woody vegetation. We compare observed values with output of different land surface models (LSMs) from the Second Global Soil Wetness Project, revealing large inter-model differences and significant differences with observations. Our methodology can lead to improved representation of soil moisture effects on ET in LSMs.
Deposition of atmospheric ammonia (NH<sub>3</sub>) to semi-natural ecosystems leads to serious adverse effects, such as acidification and eutrophication. A step in quantifying such effects is the measurement of NH<sub>3</sub> fluxes over semi-natural and agricultural land. However, measurement of NH<sub>3</sub> fluxes over vegetation in the vicinity of strong NH<sub>3</sub> sources is challenging, since NH<sub>3</sub> emissions are highly heterogeneous. Indeed, under such conditions, local advection errors may alter the measured fluxes. In this study, local advection errors (Δ F <sub>z,adv</sub>) were estimated over a 14 ha grassland field, which was successively cut and fertilised, as part of the GRAMINAE integrated Braunschweig experiment. The magnitude of Δ F <sub>z,adv</sub> was determined up to 810 m downwind from farm buildings emitting between 6.2 and 9.9 kg NH<sub>3</sub> day<sup>−1</sup>. The GRAMINAE experiment provided a unique opportunity to compare two methods of estimating Δ F <sub>z,adv</sub>: one inference method based on measurements of horizontal concentration gradients, and one based on inverse dispersion modelling with a two-dimensional model.
Two sources of local advection were clearly identified: the farm NH<sub>3</sub> emissions leading to positive Δ F <sub>z,adv</sub> ("bias towards emissions") and field NH<sub>3</sub> emissions, which led to a negative Δ F <sub>z,adv</sub> ("bias towards deposition"). The local advection flux from the farm was in the range 0 to 27 ng NH<sub>3</sub> m<sup>−2</sup> s<sup>−1</sup> at 610 m from the farm, whereas Δ F <sub>z,adv</sub> due to field emission was proportional to the local flux, and ranged between −209 and 13 ng NH<sub>3</sub> m<sup>−2</sup> s<sup>−1</sup>. The local advection flux Δ F <sub>z,adv</sub> was either positive or negative depending on the magnitude of these two contributions. The modelled and inferred advection errors agreed well. The inferred advection errors, relative to the vertical flux at 1 m height, were 52% on average, before the field was cut, and less than 2.1% when the field was fertilised. The variability of the advection errors in response to changes in micrometeorological conditions is also studied. The limits of the 2-D modelling approach are discussed.
Manure storage tanks and animals in barns are important agricultural sources of methane. To examine the possibility of using an inverse dispersion technique based on a backward Lagrangian Stochastic (bLS) model to quantify methane (CH4) emissions from multiple on-farm sources, a series of tests were carried out with four possible source configurations and three controlled area sources. The simulated configurations were: (C1) three spatially separate ground-level sources, (C2) three spatially separate sources with wind-flow disturbance, (C3) three adjacent ground-level sources to simulate a group of adjacent sources with different emission rates, and (C4) a configuration with a ground level and two elevated sources. For multiple ground-level sources without flow obstructions (C1 and C3), we can use the condition number (K, the ratio of the uncertainty in the calculated emission rate to the uncertainty in the predicted ratio of concentration to emission rate) to evaluate the applicability of this inverse dispersion technique and a preliminary threshold of K <10 is recommended. For multiple sources with wind disturbance (C2) or an even more complex configuration including ground level and elevated sources (C4), a low kappa is not sufficient to provide reasonable discrete and total emission rates. The effect of flow obstructions can be neglected as long as the distance between the source and the measurement location is greater than approximately 10 times the height of the flow obstructions. This study shows that the bLS model has the potential to provide accurate discrete emission rates from multiple on-farm emissions of gases provided that certain conditions are met.
Estimates of enteric methane (CH4) emissions from ruminants are typically measured by confining animals in large chambers, using head hoods or masks, or by a ratiometric technique involving sampling respired air of the animal. These techniques are not appropriate to evaluate large-scale farm emissions and the variability between farms that may be partly attributed to different farm management. This study describes the application of an inverse-dispersion technique to calculate farm emissions in a controlled tracer-release experiment. Our study was conducted at a commercial dairy farm in southern Alberta, Canada (total of 321 cattle, including 152 lactating dairy cows). Sulfur hexafluoride (SF6) and CH4 were released from 10 outlet locations (barn and open pens) using mass-flow controllers. A Lagrangian stochastic (LS) dispersion model was then used to infer farm emissions from downwind gas concentrations. Concentrations of SF6 and CH4 were measured by gas chromatography analysis and open path lasers, respectively. Wind statistics were measured with a three-dimensional sonic anemometer. Comparing the inferred emissions with the known release rate showed we recovered 86% of the released CH4 and 100% of the released SF6. The location of the concentration observations downwind of the farm was critically important to the success of this technique.
The footprint of a turbulent flux measurement defines its spatial context. With the onset of long-term flux measurement sites over forests and other inherently inhomogeneous areas, and the development of the FLUXNET program, the need for flux footprint estimations has grown dramatically. This paper provides an overview of existing footprint modeling approaches in the critical light of hindsight and discusses their respective strengths and weaknesses. The second main objective of this paper is to establish a formal connection between micrometeorological measurements of scalar fluxes and their mass conservation equation, in a surface-vegetation-atmosphere volume. An important focus is to identify the limitations of the footprint concept and to point out situations where the application of footprint models may lead to erroneous conclusions, as much as to demonstrate its utility and power where warranted. Finally, a perspective on the current state-of-the-art of footprint modeling is offered, with a list of challenges and suggestions for future directions.
Based on the micrometeorological measurements at a heterogeneous farmland in the North China Plain, this study focused on the effects of surface source/sink distributions on the flux-gradient similarity theory in the unstable surface layer. Firstly, the quality of the micrometeorological measurements was evaluated by the analysis of the surface energy balance closure and the integral turbulence characteristics. In general, a 22 % deficit of energy balance was found at this site, with the sum of sensible and latent heat being smaller than the available energy. The normalized standard deviations of turbulent quantities behaved in accordance with Monin-Obukhov similarity theory. However, slight departures from the classical formulations might be caused by the surface heterogeneity. Then, the applicability of flux-gradient similarity over the heterogeneous surface was examined. The observed normalized wind gradients agreed with the classical universal function established over homogeneous surface. However, due to the effects of surface source/sink distributions, the observed normalized humidity and temperature gradients deviated from the classical universal functions. Our study shows that the classical universal functions, when adjusted by a coefficient considering the effects of surface heterogeneity, can be utilized to estimate fluxes via gradient method even though over the heterogeneous surface. This adjustment coefficient was found to decrease linearly from unity with the increase of the absolute value of the vertical flux divergence.
Ammonia (NH3) emissions were measured during summer from a circular area of short pasture on a slightly acid stony sandy loam soil, treated with 156 cattle urine patches of realistic size and a nitrogen (N) content of 15 g N each. Horizontal fluxes of NH3 were sampled at five heights in the centre of the treated circle. Three micrometeorological methods were used to derive the NH3 emission rate from these horizontal fluxes: the mass-budget (MB) method, the backward-Lagrangian stochastic (BLS) method, and the ZINST (height, z, independent of stability) method. Soil temperature was measured and soil samples were taken from within selected urine patches to provide pH, ammoniacal-N (NHx-N) and moisture contents as input parameters for a volatilisation model. The model describes a chain of three processes: the phase equilibrium between aqueous NHx in the soil solution and gaseous NH3 at the liquid-air interface (within the soil pores), the diffusion of gaseous NH3 in the soil layer, and the diffusion of gaseous NH3 in the atmospheric surface layer between ground and sampling height. The two diffusion processes are parameterised by resistances as functions of soil and wind flow parameters, respectively.
`Backward' Lagrangian stochastic models calculate an ensemble of fluid element (particle) trajectories that are distinguished by each passing through an observation point. As shown, they can be faster and more flexible in calculating short-range turbulent dispersion from surface area sources than `forward' models, which simulate trajectories emanating from a source. Using a backward model, one may catalog a set of `touchdown' points (where trajectories reflect off the ground) and vertical touchdown velocities w0 of particles `on their way to' a sensor location. It is then trivial to deduce the average concentration resulting from a surface source using the touchdown catalog: by summing the reciprocal of w0 for touchdowns occurring within the source boundary. An advantage of this methodology is that while forward model trajectories are linked to a specific source, backward trajectories have no such dependence. In horizontally homogeneous flow, a `library' of touchdown catalogs (for representative surface roughnesses and atmospheric stabilities) would allow concentration (at a given height) to be rapidly calculated at any location from any uniform surface source.A `well-mixed' backward model is exploited to calculate the touchdown points of particles passing over a small plot on their way to an observation tower and it is shown how to use those data to estimate the plot emission rate from a single measurement of average concentration, wind speed, and wind direction on the tower. The method was evaluated using 36 field experiments. Predicted emission rates using the backward method agreed well with mass balance estimates.
To improve the interpretation of the results from NH3-volatilization experiments, the cumulative loss rates for different treatments were fitted to a simple logistic equation. This equation is a function: Y = a(1 - e-ct)i, with Y the cumulative N loss (%). The first derivative of this function represents the daily volatilization rate and is Y′ = acie-ct(1 - e-ct)i-1. Important parameters such as the total cumulative loss (a), and the maximum (Rm) and average (Ra) volatilization rates can easily be calculated. In the case of urea applications, an estimation can be made of the time it takes to hydrolyze all applied urea (th). This parameter also corresponds to the lag phase of the cumulative volatilization curve. Parameter i determines the position of the point of inflection of the curve. For values of i between 0 and 1, volatilization rates cannot be adequately calculated. This can be encountered if the initial volatilization rate is very high, e.g., after ammonium sulphate application upon calcareous soils. In this case, volatilization rates will be estimated by fitting the results to a modified logistic equation in which i = 1. This value of i is most common for NH4NO3 application. The best applicability of the logistic equation is with i values >1. These values are typical for the shape of cumulative volatilization curves obtained on application of urea-containing fertilizers. Possible applications of the logistic equation are illustrated by some experimental results.
In reference to previously observed concentrations of methane released from a source enclosed by a windbreak, this paper examines a refined "inverse dispersion" approach for estimating the rate of emission Q from a small ground-level source, when the surface-layer winds near that source are highly disturbed. The inverse dispersion method under investigation is based on simulation of turbulent trajectories between sources and detectors, using a Lagrangian stochastic (LS) model. At issue is whether it is advantageous to recognize the flow as being disturbed and use a computed approximation to that disturbed flow to drive a fully three-dimensional LS model (3D-LS), or whether it suffices to ignore flow disturbance and adopt an LS model attuned to the horizontally homogeneous upwind flow (MO-LS, as Monin-Obukhov similarity theory describes the vertical inhomogeneity). It is demonstrated that both approaches estimate the source strength to within a factor of 2 of the true value, irrespectively of the location of the concentration measurement, and moreover that both approaches estimate the source strength correctly (to within the experimental uncertainty), when based on concentrations measured far away from the immediate influence of obstacles in the flow. However, if the concentration detector is positioned close to the flow-disturbing obstacles, then inverse dispersion based on 3D-LS provides a better estimate of source strength than does MO-LS.
We apply a backward-Lagrangian stochastic (BLS) model to determine methane (CH4) emission rates from a herd of dairy cows freely grazing pasture within a fenced paddock. We assess how model characteristics and measurement errors of the input variables contribute to the error of the emission rate. This error is of order 20%. We find a scattered but systematic trend for the predicted CH4 source strengths to increase with the ratio of concentration detector height to source–detector distance, z/r, by around 20% across a 20-fold range of data for z/r. We then compare the CH4 source strengths from BLS to those from two other micrometeorological techniques. Compared to the flux-gradient technique (FG), there is little bias (slope of linear regression 0.98) but large scatter (squared correlation coefficient, R2, of 0.53). We believe this high degree of scatter is largely due to the deficiencies of FG. By contrast, comparison of BLS to the integrated horizontal flux technique (IHF) yields a larger bias (regression slope 1.09) but much better correlation (R2=0.80). When we express the z/r dependence of the BLS source strength by the excess relative to IHF source strength, we find that BLS source strengths vary from about 10% higher than IHF, for z/r≈0.005, up to about 35% higher, for z/r≈0.12. We compare the z/r dependence of the BLS results to the dependence of the turbulent Schmidt number on z/r as we determined earlier from analysis of field measurements. We find the results from the BLS model are less sensitive to the implicit choice of the Schmidt number than expected. We conclude that BLS is useful to corroborate IHF (since it requires no additional measurements), or as a viable alternative when technical requirements for IHF are too demanding and a slightly larger error in CH4 emission rate is acceptable.
A relatively simple scheme is presented for estimating vertical diffusion from continuous sources near the ground. The description is given in terms of well defined surface layer parameters: the surface roughness length z0 the Obukhov stability length L and the friction velocity . The effect of source height is considered. A comparison with observations is made; calculated values compare favorably with experimental data.
This paper presents and evaluates an inverse model for estimating ammonia emission from agricultural land. The method is based on an analytical model derived from the advection-diffusion equation, assuming power law profiles for wind speed and diffusivity. A three-dimensional model and a two-dimensional model are evaluated. The hypotheses of flux-driven or concentration-driven emissions are also tested. The model is evaluated against three datasets covering a range of ammonia fluxes, field geometry/size and measurement techniques. The sensitivity and the uncertainty of the method is also evaluated with a MonteCarlo approach, as well as based on existing datasets. Finally, the capability of the method to work with time-integrated concentrations (e.g. using diffusive concentration samplers) is also evaluated. The inverse model gives estimations of the ammonia emissions within a few per cent of the measurements. Moreover, the method is mainly sensitive to the concentration, the friction velocity and the thermal stratification of the atmosphere. The two-dimensional approaches give similar results to the three-dimensional one, provided the field is large enough. The concentration-driven hypothesis is similar to the flux-driven hypothesis for a fetch greater than approximately 20 m. The results are discussed in comparison with the previous approaches: the Theoretical Profile Shape (TPS or Zinst approach) and the backward Lagrangian Stochastic model (BLS).
Multi-source emission rates inferred from measured concentrations using numerical dispersion models are often extremely sensitive to measurement and model error, rendering them unusable. This sensitivity to error is quantified by the condition number of the matrix of model-derived coefficients relating source strengths to concentrations. Using a dispersion model, we examine the dependence of this condition number on source–sensor geometry, atmospheric conditions, and the amount of concentration data included in the solution. Optimal sensor arrangements are those that measure source emissions (and background concentration, if it is unknown) as independently from each other as possible under the expected range of wind directions and atmospheric stabilities. Although including more concentration measurements can improve the emission inferences, the benefit is highly contingent upon sensor placement. A set of recommendations to minimize sensitivity to error is presented. This includes arranging sensors so that each detects emissions from as few sources as possible; keeping sensors separated, both horizontally and vertically, to benefit from asymmetries in source distribution and surface layer structure; using more measurements in a given calculation, either by adding more sensors or by incorporating data from different times; and using dispersion models to assess condition number and guide sensor placement before and during a field study.
Ammonia (NH3) emission from land application of manure is typically measured using the integrated horizontal flux (IHF) micrometeorological method. However, there are some situations in which alternative techniques (such as an inverse dispersion modelling technique) might be preferable, for example when measuring from large or irregularly shaped source areas. In this study, an inverse dispersion technique using the backward Lagrangian stochastic (bLS) model, with 2 different experimental configurations, was compared with the Integrated Horizontal Flux method (i.e. IHF), which was used as reference technique. Pig slurry was surface-applied at 125 kg N ha(-1) to bare soil on a large plot (80 x 125 m). Cumulative emissions were 19.3, 21.2 and 18.4 kg N ha(-1) from the IHF and the bLS technique (experimental configurations I and II), respectively. Mean flux within each sampling period as estimated by the two techniques compared extremely well, with a slope not significantly different from 1 and r(2) of 0.99. Although limited in extent, this dataset agree with a previous study in demonstrating the use of the bLS technique with longer period time-averaged concentration measurements. (C) 2009 Elsevier Ltd. All rights reserved.
The MODDAS-2D model (MOdel of Dispersion and Deposition of Ammonia over the Short-range in two dimensions) is presented. This stationary model couples a two-dimensional Lagrangian stochastic model for short-range dispersion, with a leaf-scale bi-directional exchange model for ammonia (NH3), which includes cuticular uptake and a stomatal compensation point. The coupling is obtained by splitting the upward and downward components of the flux, which can be generalized for any trace gas, and hence provides a way of simply incorporating bi-directional exchanges in existing deposition velocity models. The leaf boundary-layer resistance is parametrized to account for mixed convection in the canopy, and the model incorporates a stability correction for the Lagrangian time-scale for vertical velocity, which tends to increase the Lagrangian time-scale in very stable conditions compared with usual parametrizations. The model is validated against three datasets, where concentrations of atmospheric NH3 were measured at several distances from a line source. Two datasets are over grassland and one is over maize, giving a range of canopy structure. The model correctly simulates the concentration in one situation, but consistently overestimates it at further distances or underestimates it at small distances in the two other situations. It is argued that these discrepancies are mainly due to the lack of length of one of the line sources and non-aligned winds. Analysis shows that the surface exchange parameters and the turbulent mixing at the source level are the predominant factors controlling short-range deposition of NH3. Copyright © 2006 Royal Meteorological Society
Results from an experiment measuring methane emissions from a herd of cattle are used to investigate the performance of a backward-Lagrangian stochastic model (distributed under the name WindTrax). The availability of simultaneous mass-budget measurements of the emission rate, together with a unique setup geometry, allow to compare modelled and measured normalised concentration profiles and horizontal flux profiles with five sensor heights, z, and for four horizontal source-sensor distances, x. Simulated emission rates differ typically by 10-20% to those obtained from the mass-budget measurements, which is in agreement with previous tests of the accuracy of WindTrax. Thus, the idealisation of a herd of animals as a homogeneous area source at ground level does not seriously affect the model's applicability to infer emission rates. The profile comparison suggests that WindTrax may overestimate the speed of vertical dispersion. As a consequence, for this experiment an ideal z/. x ratio exists where the modelled emission rate is unbiased. Its value is about 0.080 in unstable and 0.067 in stable stratification. Using concentration measurements taken above or below this z/. x threshold leads to emission rates that are slightly under- or overestimated, respectively. Simultaneous measurements with an open-path methane laser are compatible with this finding. Possible causes of the apparent overestimate of vertical dispersion rates are discussed, leading to the cautious suggestion that it may stem from the choices for the Kolmogorov constant and/or the normalised dissipation rate in the model, which reflects gaps in our understanding of the atmospheric surface layer. It is argued that this notion does not contradict the earlier results from a number of controlled tracer-release experiments that had been designed to test WindTrax.
1] To understand the coupled water and energy cycles in semiarid environments, we measured temporal fluctuations of evapotranspiration (ET) and identified key sources of the observed variability. Flux measurements are made using the Bowen ratio method, accompanied by measurements of soil moisture and radiation. We present data from semiarid grassland and shrubland sites, situated within 2 km of each other in New Mexico. The study includes three summer monsoon seasons. Midday available energy (Q a) is higher at the grassland than at the shrubland by 20% or 70 W m À2 because of differences in net radiation (R n) and soil heat flux (G). At both sites, midday evaporative fraction and daily ET are strongly correlated with surface soil moisture (q 0 – 5cm) but poorly correlated with water content at greater depths or averaged throughout the entire root zone. The sensitivity of EF to q 0 – 5cm is 30% lower at the grassland site. The differences in Q a and EF cancel, yielding similar time series of ET at the two sites. Decreases in q 0 – 5cm , ET, and EF following rainfall events are rapid: exponential time constants are less than 3 days. With the exception of the largest storms, infiltration following rainfall events only wets the top 10 cm of soil. Therefore the surface soil layer is the primary reservoir for water storage and source for ET during the monsoon season, suggesting that direct evaporation is a large component of ET. Given these results, predicting ET based on root zone–averaged soil moisture is inappropriate in the semiarid environments studied here.
Ammonia losses following urea fertilization of maize and winter wheat were determined in field trials carried out at Fengqiu Experimental Station in the North China Plain in 1998 and 1999. Four experiments were carried out using two simplified micrometeorological integrated horizontal flux methods [IHF(L) and IHF(S)], a chamber method (calibrated Drger-Tube Method DTM) and the 15N-balance method using 15N-labeled urea. The IHF(L) was taken as the reference method. Both IHF methods showed good agreement in one experiment only, while the IHF(S) overestimated as well as underestimated cumulative ammonia losses compared to IHF(L) in the other experiments (deviation ranged from 12.5% to 64% based on cumulative ammonia losses). Regression analysis of the fluxes showed that in particular different sensitivities of the samplers to wind speed accounted for the discrepancies observed. The IHF(L) and the DTM flux curves were very similar in three experiments, while the values obtained with DTM considerably deviated from IHF(L) results in one experiment. A comparison with apparent fertilizer-N losses determined by the 15N-labeling approach showed that ammonia volatilization was the major pathway of fertilizer-N loss in this study.
A field study of surface-air exchange of carbon, water, and energy was conducted at a mid-latitude, mixed forest on non-flat terrain to investigate how to best interpret biological signals from the eddy flux data that may be subject to advective influences. It is shown that during periods of Southwest winds (sector with mild topography), the eddy fluxes are well-behaved in terms of energy balance closure, the existence of a constant flux layer, consistency with chamber observations and the expected abiotic controls on the fluxes. Advective influences are evident during periods with wind from a steep (15%) slope to the Northeast of the tower. These influences appear more severe on CO2 flux, particularly in stable air, than on the energy fluxes. Large positive flux of CO2 (> 23 μmol m-2 s-1) occurs frequently at night. The annual sum of the carbon flux is positive, but the issue about whether the forest is a source of atmospheric carbon remains inconclusive.
Attempts are made to assess vertical advectionusing the data collected on a single tower. Over the Southwestsector, vertical advection makes a statistically significant but small contribution to the 30-min energy imbalance and CO2 flux variations. Contributions by horizontal advection may be larger but cannot be verified directly by the current experimental method.
Previous results of non-dimensional wind and temperature profiles as functions of ( = z/L) show systematic deviations between different experiments. These discrepancies are generally believed not to reflect real differences but rather instrumental shortcomings. In particular, it is clear that flow distortion has not been adequately treated in most previous experiments. In the present paper, results are presented from a surface-layer field experiment where great care was taken to remove any effects from this kind of error and also to minimize other measuring errors. Data from about 90 30-min runs with turbulence measurements at three levels (3, 6, and 14 m) and simultaneous profile data have been analysed to yield information on flux-gradient relationships for wind and temperature.The flux measurements themselves show that the fluxes of momentum and sensible heat are constant within 7% on average for the entire 14 m layer in daytime conditions and when the stratification is slightly stable. For more stable conditions, the flux starts to decrease systematically somewhere in the layer 6 to 14 m. From a large body of data for near-neutral conditions ( 0.1), values are derived for von Krmn's constant: 0.40 0.01 and for
h
at neutrally, 0.95 0.04. The range of uncertainty indicated here is meant to include statistical uncertainty as well as the effect of possible systematic errors.Data for
m
and
h
for an extended stability range (1 > > – 3) are presented. Several formulas for
m
and
h
appearing in the literature have been used in a comparative study. But first all the formulas have been modified in accordance with the following assumptions: = 0.40 and (
h
) = 0 = 0.95; deviations from this result in the various studies are due to incomplete correction for flow distortion. After new corrections are introduced, the various formulas were compared with the present measurements and with each other. It is found that after this modification, the most generally used formulas for
m
and
h
for unstable conditions, i.e., those of Businger et al. (1971) and Dyer (1974) agree with each other to within 10% and with the present data. For stable conditions, the various formulas still disagree to some extent. The conclusion in relation to the present data is not as clear as for the unstable runs, because of increased scatter. It is, however, found that the modified curve of Businger et al. (1971) for
h
fits the data well, whereas for
m
, Dyer's (1974) curve appears to give slightly better agreement.
The spatial resolution of meteorological observations of scalars (such as concentrations or temperature) and scalar fluxes (e.g., water-vapour flux, sensible heat flux) above inhomogeneous surfaces is in general not known. It is determined by the surface area of influence orsource area of the sensor, which for sensors of quantities that are subject to turbulent diffusion, depends on the flow and turbulence conditions.
Functions describing the relationship between the spatial distribution of surface sources (or sinks) and a measured signal at height in the surface layer have been termed thefootprint function or thesource weight function. In this paper, the source area of levelP is defined as the integral of the source weight function over the smallest possible domain comprising the fractionP of the total surface influence reflected in the measured signal. Source area models for scalar concentration and for passive scalar fluxes are presented. The results of the models are presented as characteristic dimensions of theP=50% source areas (i.e., the area responsible for 50% of the surface influence): the maximum source location (i.e., the upwind distance of the surface element with the maximum-weight influence), the near and the far end of the source area, and its maximal lateral extension. These numerical model results are related directly to non-dimensional surface-layer scaling variables by a non-linear least squares method in a parameterized model which provides a user-friendly estimate of the surface area responsible for measured concentrations or fluxes. The source area models presented here allow conclusions to be made about the spatial representativeness and the localness (these terms are defined in the text) of flux and concentration measurements.
We ran a Lagrangian stochastic (LS) dispersion model in both forward-in-time and backward-in-time ways to derive footprints.
Three Eulerian analytical footprint models were compared with this Lagrangian model for a wide atmospheric stability range.
Despite some differences among the three analytical footprint models, their results generally agreed. Results from the forward
LS simulations agreed well with the analytical solutions for both concentration footprints and flux footprints, if turbulent
parameters were properly prescribed. Quantitative equivalence between the forward and backward Lagrangian footprint estimates
was demonstrated. However, concentration footprint derived by backward LS simulation can be seriously contaminated by numerical
errors. A ‘test-adjustment’ scheme treating the temporal integration, and a ‘buffer’ layer treating the surface reflection
of the LS particles eliminate numerical errors. Forward LS simulations or the flux footprint estimates were quite insensitive
to these errors.
Using the eddy covariance technique, three years (October 2005–September 2008) of water and energy flux measurements were obtained for a winter wheat/summer maize rotation cropland in the North China Plain. This region is critical for food production in China, and is prone to significant water shortages and drought. Seasonal and interannual variability in evapotranspiration (ET) were examined in terms of relevant controlling factors. The annual ET was 595 and 609 mm in the periods of 2005–2006 and 2006–2007, respectively. The average seasonal ET in the wheat and maize field was 401 and 212 mm, respectively. Seasonal variability in ET was primarily explained by the variations in equilibrium evaporation (ETeq) and canopy conductance (Gs). Daily evapotranspiration ranged from 1.0 to 7.8 mm day−1 during the wheat season and reached up to 5.1 mm day−1 during the maize season. The maximum midday average Gs was 32 mm s−1 for wheat and 17 mm s−1 for maize. During the rapid growth stages, the average midday LE/Rn (LE is latent heat flux, Rn is net radiation) was 83% for wheat and 57% for maize, indicating a higher water consumption for wheat than for maize. On an annual basis, latent heat flux accounted for about 59% of the net radiation, suggesting that more energy is partitioned into evapotranspiration in this agroecosystem site. Regional irrigation promoted sensible heat advection from the surrounding drier surface during the wheat seasons. Monthly ET totals enhanced by sensible heat advection accounted for 27% of the ETeq during the rapid growing season of wheat.
Presented are the results of a field trial designed to test the accuracy of a backward Lagrangian stochastic (bLS) model. The accuracy of the bLS model was determined by comparing estimated CH4 emission rates (QbLS) to measured CH4 emission rates (Q) for four different experimental set-up. Releases of CH4 (99% purity) were made from a ground level grid (3 m × 3 m), as well as an elevated grid (1 m × 3 m) that was suspended 1.2 m above the surface. The bLS model was used to obtain emission estimates using concentration measurements and turbulence data obtained from an open-path laser and a three-dimensional sonic anemometer, respectively. The comparisons suggest that the bLS model can be used effectively in an agricultural setting provided the surface layer is homogeneous and the atmosphere can be described by Monin-Obukhov similarity theory. Under ideal conditions the average value of QbLS/Q was found to be 1.06 with a standard deviation (σbLS) = 0.16 and a standard error . Obstructions upwind of the concentration and wind sensors were determined to have little impact on the estimated emissions provided the distance between the sensors and the obstructions was at least 25 times the height of the obstruction. For an elevated source (z = 1.2 m) the average value of QbLS/Q over a homogenous terrain was 0.99, with σbLS = 0.20 and . The accuracy of the model varied with the sampling height, zm, suggesting that an ideal measurement height that is insensitive to atmospheric stability might exist.
An inverse-dispersion technique is used to calculate ammonia (NH3) gas emissions from a cattle feedlot. The technique relies on a simple backward Lagrangian stochastic (bLS) dispersion model to relate atmospheric NH3 concentration to the emission rate QbLS. Because the wind and the source configuration are complicated, the optimal implementation of the technique is unclear. Two categorically different measurement locations (for concentration and winds) are considered: within the feedlot and downwind. The in-feedlot location proved superior, giving a nearly continuous QbLS timeseries. We found average emissions of 0.15 kg NH3 animal−1 day−1 in both 2004 and 2005, representing a loss of 63% (2004) or 65% (2005) of the dietary nitrogen in the animal feed. Downwind measurement locations were less useful for several reasons: a narrow range of useable wind directions; ambiguity in the choice of wind statistics to use in the calculations; low NH3 concentrations; and downwind deposition of NH3. When addressing a large source (like a feedlot) that modifies the ambient wind flow, we recommend in-source measurements for use in inverse-dispersion applications.
Source distributions for heat, water vapour, CO2 and CH4 within a rice canopy were derived using measured concentration profiles, a prescribed turbulence field and an inverse Lagrangian analysis of turbulent dispersion of scalars in plant canopies. Measurements were made during IREX96, an international rice experiment in Okayama, Japan. Results for the cumulative fluxes of heat, water vapour and CH4 at the canopy top were satisfactory once their respective concentration profiles were smoothed using simple analytic functions. According to the inverse analysis, water vapour was emitted relatively uniformly by each of five equi-spaced layers within the canopy, whereas sensible heat fluxes were small (<100 W m⁻²) and of either sign. Methane fluxes were predicted to be emitted most strongly in the lower 50% of the canopy, as expected from the distribution of micropores along leaves and leaf sheaths, the major pathway for CH4 loss from the soil–crop system. No smoothing was required for CO2 concentration profiles and the inverse analysis provided close correspondence between the turning point in the concentration profile is the changeover from respiration by the soil/paddy water and lower canopy to net photosynthesis by the upper canopy. These results could only be obtained by including both the near- and far-field contributions of sources to the total concentration profile. Neglect of the near-field contribution in the inverse analysis led to spurious source distributions.
Accurately determining methane emission factors of dairy herd in China is imperative because of China's large population of dairy cattle. An inverse dispersion technique in conjunction with open-path lasers was used to quantify methane emissions from a dairy feedlot during the fall and winter seasons in 2009-2010. The methane emissions had a significant diurnal pattern during both periods with three emission peaks corresponding to the feeding schedule. A 10% greater emission rate in the fall season was obtained most likely by the higher methane emission from manure during that period. An annual methane emission rate of 109±6.7 kg CH4 yr(-1) characterized with a methane emission intensity of 32.3±1.59 L CH4 L(-1) of milk and a methane conversion factor (Ym) of 7.3±0.38% for mature cattle was obtained, indicating the high methane emission intensity and low milk productivity in Northern China.
The determination of atmospheric emission rates from multiple sources using inversion (regularized least-squares or best-fit technique) is known to be very susceptible to measurement and model errors in the problem, rendering the solution unusable. In this paper, a new perspective is offered for this problem: namely, it is argued that the problem should be addressed as one of inference rather than inversion. Towards this objective, Bayesian probability theory is used to estimate the emission rates from multiple sources. The posterior probability distribution for the emission rates is derived, accounting fully for the measurement errors in the concentration data and the model errors in the dispersion model used to interpret the data. The Bayesian inferential methodology for emission rate recovery is validated against real dispersion data, obtained from a field experiment involving various source-sensor geometries (scenarios) consisting of four synthetic area sources and eight concentration sensors. The recovery of discrete emission rates from three different scenarios obtained using Bayesian inference and singular value decomposition inversion are compared and contrasted.
Observed timescales of evapotranspiration response to soil moisture Simple estimates for vertical diffusion from sources near ground
- A J Teuling
- S I Seneviratne
- C Williams
- P A Troch
Teuling, A.J., Seneviratne, S.I., Williams, C., Troch, P.A., 2006. Observed timescales of evapotranspiration response to soil moisture. Geophys. Res. Lett., 33. van Ulden, A.P., 1978. Simple estimates for vertical diffusion from sources near ground. Atmos. Environ. 12, 2125–2129.