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Understanding the spatiotemporal variability of tropical orographic rainfall1
using convective plume buoyancy2
Quentin Nicolasaand William R. Boosa,b
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aDepartment of Earth and Planetary Science, University of California, Berkeley, California
bClimate and Ecosystem Sciences Division, Lawrence Berkeley National Laboratory, Berkeley,
California
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Corresponding author: Quentin Nicolas, qnicolas@berkeley.edu7
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This Work has been accepted to Journal of Climate. The AMS does not guarantee that the copy provided here is an
accurate copy of the Version of Record (VoR).
ABSTRACT: Mechanical forcing by orography affects precipitating convection across many trop-
ical 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 precip-
itation 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 precip-
itation 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 pre-
cipitation 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 di-
rected 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 dimen-
sions 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.
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1. Introduction29
Mountains shape rainfall distributions in many of Earth’s tropical land regions, modifying the30
thermodynamic environment by interacting with large-scale winds or altering surface fluxes. With31
over 2.5 billion people living in mountainous areas and another 2 billion in lowland areas depending32
on mountain water resources (Viviroli et al. 2020), orographic precipitation is currently the main33
water source for over 55% of the world’s population, with a majority of that fraction located in34
the tropics. It is also the main source of energy for hydropower, which is the primary resource for35
renewable electricity generation globally, and a potential cause of dam failures when occurring in36
excess (Li et al. 2022).37
Orographic rainfall features large spatial gradients, with vastly different hydrological conditions38
upwind and downwind of ridges. In the tropics, strong precipitation gradients are widely observed39
along local orography in South and Southeast Asia, the Maritime Continent, and the northern and40
central Andes (Fig. 1). The spatial structure of orographic precipitation has been studied in various41
regions across the tropics, with examples including the Ethiopian Highlands (Van den Hende et al.42
2021), the Andes (Espinoza et al. 2015), the Western Ghats (e.g., Tawde and Singh 2015) and43
the Arakan Yoma range of Myanmar (e.g., Shige et al. 2017). The qualitative picture behind this44
spatial organization is widely known: mountains force low-level ascent on their upwind flanks,45
which, with sufficient moisture, drives condensation and precipitation (Smith 1979; Roe 2005).46
The subsiding downstream flow, conversely, is warm and dry. Yet this paradigm, which assumes47
layer-wise ascent and saturation, is unlikely to be quantitatively accurate in tropical regions where48
most rainfall stems from convection (Kirshbaum et al. 2018) and where even simple questions, such49
as what sets the upstream extent of orographic rainfall enhancement, have been debated (Smith50
and Lin 1983; Grossman and Durran 1984). This study aims to address this issue and related open51
questions (such as controls on rain shadow extent and the amplitude of rainfall maxima), taking52
several tropical regions as examples.53
In midlatitudes, column-integrated water vapor transport (IVT) has been proposed as a dom-57
inant control on orographic precipitation (Sawyer 1956; Smith 2019). Indeed, in the idealized58
picture of forced ascent over an orographic barrier, IVT modulates the condensation rate over the59
upwind slopes. Additionally, stronger IVT typically results in a smaller nondimensional mountain60
height (through both stronger winds and a smaller effective static stability), causing flow to ascend61
3
120°W 80°W 40°W 0°W 40°E 80°E 120°E 160°E
10°S
0°
10°N
20°N
TRMM PR/GPM DPR July mean precipitation
10 m s−1
120°W 80°W 40°W 0°W 40°E 80°E 120°E 160°E
10°S
0°
10°N
20°N
TRMM PR/GPM DPR November mean precipitation
0
5
10
15
20
mm day−1
Fig. 1. TRMM PR and GPM DPR near-surface precipitation, 500 m surface height level (thin brown contours),
and ERA5 wind vectors 100 m above the surface averaged over July (top) and November (bottom) from 2001 to
2020. See section 2 for details on the data products.
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rather than detour around mountains (Smith 1989; Kirshbaum and Smith 2008). Other controls62
on midlatitude orographic precipitation include mountain slope and temperature-mediated micro-63
physical effects (Kirshbaum and Smith 2008). The spatial organization of orographic precipitation64
in convectively stable flows has been understood through the influence of topography on vertical65
velocities in saturated flows, with a contribution from the downwind advection of hydrometeors66
(Smith and Barstad 2004, hereafter SB04).67
Orographic precipitation generally occurs in association with various types of disturbances, from68
frontal systems in midlatitude winter to deep convective systems in parts of the tropics (Houze69
2012). We illustrate these in Fig. 2, which shows instantaneous radar reflectivity from the70
Global Precipitation Measurement (GPM) Ku-band radar (Seto et al. 2021) for two cases. The71
first illustrates a winter frontal system over coastal mountains of British Columbia and features72
a horizontally wide, vertically shallow signal with a sloping bright band (visible between 30073
and 550 km at 2 km altitude in the vertical cross-section), characteristic of frontal ascent. In74
contrast, the Western Ghats case, during the summer monsoon, features smaller scale, stronger75
echoes reaching deeper heights (up to 10 km; note that summertime convection in and upstream76
of the Western Ghats is shallower than in the rest of the tropics, see Kumar and Bhat 2017).77
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Fig. 2. Near-surface radar reflectivity from the Ku-band GPM radar (top) and vertical cross-section of corrected
Ku-band reflectivity (bottom) for two overpasses : February 11th , 2015 (GPM orbit No. 005434) over the coast
range of British Columbia (left) and June 19th, 2014 (GPM orbit No. 001735) over the Western Ghats (right).
The black lines on the top panels show the location of the cross-sections on the bottom panels, with the L and R
marks corresponding to the left/right of the cross-sections. This figure was produced using the DRpy software
package (Chase and Syed 2022).
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While wide radar echoes are also observed in the tropics, such as in mesoscale convective systems78
(Houze et al. 2015), such systems reach deeper heights than winter midlatitude storms (because the79
tropical troposphere is nearly moist neutrally stable (Xu and Emanuel 1989), while midlatitudes80
are more stably stratified, preventing convection embedded in midaltitude cyclones from reaching81
deep heights).82
Tropical orographic precipitation has a more even temporal distribution than surrounding conti-89
nental or oceanic precipitation (Van den Hende et al. 2021; Espinoza et al. 2015; Sobel et al. 2011).90
Nevertheless, intraseasonal and interannual variability in orographic rainfall seems to be influ-91
enced by the classical tropical modes that regulate moist convection. Examples include the boreal92
summer intraseasonal oscillation (BSISO, Shige et al. 2017; Hunt et al. 2021), the Madden-Julian93
Oscillation (MJO, Bagtasa 2020) and large-scale interannual modes such as the El Ni˜
no-Southern94
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Oscillation and the Indian Ocean Dipole (Yen et al. 2011; Revadekar et al. 2018; Lyon et al. 2006;95
Smith et al. 2013). Hence, any successful theory for tropical orographic precipitation needs to96
address the question of how mountains interact with moist convection.97
Boundary-layer moist static energy and free-tropospheric temperature regulate moist convection98
by influencing column stability. Observations and simulations have shown that free-tropospheric99
water vapor also exerts a strong control on precipitation, consistent with the idea that entrainment100
of free-tropospheric air modulates plume buoyancy (e.g., Derbyshire et al. 2004). Tropical rainfall101
is thus jointly influenced by free-tropospheric temperature and moisture, and interacts with slower,102
balanced dynamics to eliminate positive perturbations in these quantities—a behavior termed103
lower-tropospheric quasi-equilibrium (QE, e.g., Raymond et al. 2015). The prominent role of lower-104
tropospheric moisture has been confirmed in observations of orographic convection at low latitudes105
(Hunt et al. 2021; Nelson et al. 2022). Beyond the lower-tropospheric thermodynamic environment,106
factors such as the wind profile—especially vertical wind shear, which one could expect to be107
important in the presence of mountain waves—should affect moist convective development (see,108
e.g., Robe and Emanuel 2001; Anber et al. 2014; Peters et al. 2022a,b). We do not consider such109
factors here.110
Ahmed et al. (2020) cast the observed dependence of tropical convection on the lower-111
tropospheric thermodynamic environment into a simple buoyancy-based framework. Precipitation112
is strongly controlled by a measure of plume buoyancy that takes into account the influences of113
instability and entrainment, and depends on boundary layer equivalent potential temperature as114
well as lower-free-tropospheric temperature and moisture. We recently posited (Nicolas and Boos115
2022, hereafter NB22) that mechanically forced orographic convection can be understood in this116
framework, with stationary mountain waves disturbing lower-free-tropospheric thermodynamics,117
in turn affecting precipitation. We developed a linear model for the spatial distribution of rainfall,118
combining orographic gravity wave dynamics with the linearized QE closure of Ahmed et al.119
(2020). That model assumes a simple background state that has horizontally uniform temperature120
and moisture profiles, with horizontally and vertically uniform wind. At first order, the temperature121
and moisture perturbations are dictated by vertical displacement in a mountain wave, which is in122
turn controlled by the topographic shape, cross-slope wind, and static stability. The normalized123
gross moist stability (e.g., Raymond et al. 2009) appears as a second-order control, because it mod-124
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ulates convective moisture relaxation. One goal of the present work is to evaluate to what extent125
this framework (extended to two horizontal dimensions) can explain observed spatial patterns of126
orographic tropical rainfall.127
More generally, this study explores the physical drivers behind the temporal variations and128
spatial structure of orographic precipitation around six tropical mountain regions: the Western129
Ghats (India), the western coast of Myanmar (Arakan Yoma mountain range), the eastern coast130
of Vietnam (Annam Range), the Malay peninsula, the Philippines, and the island of New Britain131
(Papua New Guinea). We justify the use of a lower-tropospheric buoyancy measure in quantifying132
daily orographic precipitation variability and explore the dominant controls on its components—133
both within the boundary layer and the lower-free-troposphere. We then explore to what extent134
time-averages of this buoyancy measure account for observed spatial patterns of rainfall, and test135
the QE-based linear theory of NB22 against observations.136
2. Data137
Two precipitation products are used. Seasonal averages (used in sections 1, 3, and 6) are obtained138
from monthly averages of near-surface precipitation rates from the Tropical Rainfall Measuring139
Mission Ku-band precipitation radar (TRMM PR 3A25, Tropical Rainfall Measuring Mission140
2021) for the 01/2001–03/2014 period and the Global Precipitation Measurement dual-frequency141
precipitation radar (GPM 3DPR, Iguchi and Meneghini 2021) for the 04/2014–12/2020 period,142
both on a 0.25◦grid. In section 4, where we require daily resolution, we use the IMERG V06B143
precipitation dataset (Huffman et al. 2019), which combines satellite-based infrared and passive144
microwave measurements with rain gauge data to provide hourly estimates at 0.1◦resolution.145
IMERG is known to suffer from biases in regions of complex topography relative to rain gauge146
measurements, but these biases are reduced when considering spatial averages (Pradhan et al.147
2022). We use daily precipitation averages at large spatial scales, and the regions over which we148
average consist of 45%–80% ocean points, where confidence in IMERG retrievals is higher.149
We evaluate the thermodynamic environment and horizontal winds from the ERA5 reanalysis150
(Hersbach et al. 2018), which provides hourly data at 0.25◦resolution. Johnston et al. (2021)151
showed that moisture soundings from ERA5 had excellent agreement with satellite-based radio152
occultation retrievals in the tropics and subtropics. Proper evaluation of ERA5 lower-tropospheric153
7
temperature is lacking; we note that Hersbach et al. (2020) showed improved 850 hPa temperature154
estimates (when compared to radiosondes) over ERA-Interim, especially in the past two decades.155
Unless otherwise specified, we use topography from the ETOPO1 global relief model (National156
Geophysical Data Center 2011; Amante and Eakins 2008), at 60 arc-second resolution.157
3. Selecting regions of mechanically forced tropical orographic rainfall158
To illustrate the physical drivers of tropical orographic precipitation, we select six regions in159
South Asia and the Maritime Continent. We focus on mechanically forced convection, a regime in160
which orographic forcing is felt through the forced uplift of impinging flow, by opposition to ther-161
mal forcing, where the diurnal cycle of heating over sloped terrain drives low-level convergence.162
The wind speed threshold marking the transition from thermal to mechanical forcing depends on163
various factors including static stability 𝑁and mountain height ℎ𝑚. One quantity often used to164
characterize orographic flows is the nondimensional mountain height1,𝑀=𝑁 ℎ𝑚/𝑈, where 𝑈is165
the cross-slope wind speed. Flows with 𝑀 < 1 tend to cross topography (rather than being blocked166
upstream), which may prevent the development of thermally forced circulations (Kirshbaum et al.167
2018). For moderately high mountains (500–1000 m) in the tropics, various studies have suggested168
that mechanical forcing dominates above about 5 m s−1(Nugent et al. 2014; Wang and Sobel 2017).169
Accordingly, we selected six regions with a mean upstream wind (during the local rainy season)170
higher than 5 m s−1and a visible orographic rain band. This sample is not an exhaustive represen-171
tation of tropical orographic rainfall, although we think it is quite representative of mechanically172
forced cases. These regions are outlined in Fig. 1, with close-up views of their topography and173
seasonal-mean rainfall and wind in Fig. 3. The rainfall maps have some visible noise because they174
are only based on TRMM and GPM radar overpasses, which have sparse temporal coverage.175
For each region, we analyze data over a 20-year period (2001–2020) during the local rainiest176
season (which also corresponds to a mechanically forced regime), defined below for each specific177
case. Two regions (Vietnam and the Philippines) experience a second rainfall peak in boreal178
summer on the other side of their mountain ranges, associated with reversed winds during the179
summer monsoon (see Fig. 1). Because the winds are not as strong then, the dominance of180
mechanical forcing cannot be clearly established, and we did not include these secondary rainy181
seasons in our analysis. In section 4, we analyze daily data averaged over the orographic rain bands;182
1𝑀is also the inverse of a Froude number.
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Table 1. Key information about the regions studied. Here and in later tables, PNG refers to Papua New Guinea.
Region name Rainy season
considered in this study
Nondimensional
mountain height
Western Ghats June-August 0.8
Myanmar June-August 0.8
Vietnam October-November 1
Malaysia November-December 0.5
Philippines November-December 0.3
PNG June-August 0.4
these rain bands are defined manually using rectangular boxes and outlined in red in Figure 3. We183
summarize key information about each region in Table 1, and describe these in detail hereafter.184
Three of these regions have their rainiest season in boreal summer (June-August). The Western185
Ghats, a mountain range on the west coast of peninsular India, form a kilometer-high barrier to186
the southwesterly monsoon flow. With 𝑀≃0.8 (measuring wind speed 500 km upstream of the187
coast and 100 m above the surface to avoid influences from surface friction and flow deceleration188
by topography), the Ghats fall within a clear mechanically forced regime, as attested by the small189
diurnal cycle of rainfall there (Shige et al. 2017). The dynamics of orographic precipitation in the190
Western Ghats have been the subject of several modeling studies (Smith and Lin 1983; Grossman191
and Durran 1984; Ogura and Yoshizaki 1988; Xie et al. 2006; Oouchi et al. 2009; Sijikumar et al.192
2013; Zhang and Smith 2018). These studies confirm that the presence of orography is crucial193
in producing the observed rain band, and (expectedly) that latent heating cannot be neglected194
in describing the orographic flow. Past literature has also discussed the location of the rainfall195
maximum upstream of the Western Ghats. While some studies initially suggested that it occurred196
upstream of the coastline (e.g., Xie et al. 2006), Shige et al. (2017) determined that it was positioned197
over the western slopes of the Ghats (consistent with Fig. 3).198
The Arakan Yoma mountain range, located along the coast of Myanmar, also interacts with199
the Asian summer monsoon (Oouchi et al. 2009; Wu et al. 2018). With maximum seasonal-200
mean precipitation values exceeding 30 mm day−1upstream of the range, it is responsible for201
the strongest rain band (in terms of mean precipitation rate) on Earth in boreal summer. This202
precipitation maximum is located along the coast (see Fig. 3 and Shige et al. 2017). Compared203
to the Western Ghats, convection is deeper and of wider scale upstream of Myanmar, a fact that204
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Shrestha et al. (2015) associated with differences in lower tropospheric humidity. 𝑀has a similar205
value around 0.8 there.206
The island of New Britain, in Papua New Guinea (hereafter PNG), is our third region of interest207
in boreal summer. The mountains are of modest height there (300 m when averaging across the208
island, although individual peaks exceed 2 km), but a strong precipitation band reaching 25 mm209
day−1lies upstream of the island. Winds speeds around 8–9 m s−1yield a nondimensional mountain210
height 𝑀≃0.4. Orographic rainfall in PNG has been the focus of a few studies (e.g., Biasutti et al.211
2012; Smith et al. 2013).212
The remaining three regions are associated with boreal autumn rainfall. The coast of Vietnam,213
east of the Annam range, receives most of its rainfall in October and November (Chen et al. 2012;214
Ramesh et al. 2021), with an onshore cross-slope wind of 8–9 m s−1during this season (𝑀=1).215
The eastern coast of the Philippines experiences a late autumn precipitation peak (November–216
December) with a similar wind speed and 𝑀=0.3 (Chang et al. 2005; Robertson et al. 2011).217
Finally, the eastern half of the Malay Peninsula also receives most of its rainfall in November and218
December (Chen et al. 2013), similarly associated with mechanical orographic forcing (𝑀=0.5).219
4. Controls on daily variations of orographic rainfall225
In the tropics, mechanically forced orographic rainfall is subject to less temporal variability than226
rainfall over surrounding land and ocean. In particular, it has a weak diurnal cycle, as noted by227
Shige et al. (2017) in the Western Ghats and in Myanmar (see also Aoki and Shige 2024). This228
can be understood as resulting from daytime heating of the boundary layer being limited by the229
ventilation resulting from strong wind (e.g., Nugent et al. 2014). The distribution of daily rainfall230
within regions where mechanical forcing dominates is also more uniform, with less contribution231
from extreme days. This was noted by Espinoza et al. (2015) in the Central Andes and is confirmed232
for regions studied here (Table 2). Nevertheless, these regions still show substantial subseasonal233
rainfall variations. The goal of this section is to determine the factors governing these temporal234
variations of daily-mean precipitation.235
10
65°E 70°E 75°E 80°E
10°N
15°N
20°N
Western Ghats
(Jun-Aug
)
85°E 90°E 95°E 100°E
10°N
15°N
20°N
Myanmar (Jun-Aug)
100°E 105°E 110°E 115°E
10°N
15°N
20°N
25°N Vietnam (Oct-Nov)
100°E 105°E 110°E
0°
5°N
10°N
15°N Malaysia (Nov-Dec)
120°E 125°E 130°E 135°E
5°N
10°N
15°N
20°N
Philippines (Nov-Dec)
10 m s
−1
145°E 150°E 155°E 160°E
15°S
10°S
5°S
0° PNG (Jun
-Aug
)
0
5
10
15
20
mm day−1
Fig. 3. TRMM PR and GPM DPR near-surface precipitation, 500 m surface height level (thin brown contours),
and ERA5 wind vectors 100 m above the surface in six tropical regions, averaged over each region’s rainiest
season (see text) from 2001 to 2020. The red dashed boxes outline the orographic rain bands, which are analyzed
in section 4. The blue dashed boxes define the regions over which cross-slope IVT is averaged in Fig. 5. Here
and in later figures, PNG refers to Papua New Guinea.
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221
222
223
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Table 2. Percentage of seasonal rainfall contributed by the rainiest days (defined as days and locations where
rainfall is above the 90th percentile), in the whole region and within the orographic rain band, for each region
studied. The rain bands are defined by the red dashed rectangles in Fig. 3.
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237
238
Region name Whole region Orographic rain band
Western Ghats 74 53
Myanmar 59 43
Vietnam 80 73
Malaysia 63 61
Philippines 76 66
PNG 70 55
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a. Dynamic and thermodynamic predictors of daily rainfall variations239
The canonical picture of orographic rainfall highlights the importance of the cross-slope vapor240
transport in governing rain rates (Smith 2019). In a saturated atmosphere ascending with velocity241
𝑤, the column-integrated condensation rate is242
𝐶=−∫∞
0
𝑤𝑑(𝜌𝑞sat)
𝑑𝑧 𝑑𝑧. (1)
The water vapor density can be approximated as decreasing exponentially with 𝑧, with a scale height243
𝐻sat. If udenotes the surface horizontal wind and ℎthe surface height, then 𝑤(𝑧=0)=u· ∇ℎ. In244
the simplest approximation where 𝑤is vertically uniform, then245
𝐶=∫∞
0
(u· ∇ℎ)𝜌𝑞sat
𝐻sat
𝑑𝑧 ≃IVT · ∇ℎ
𝐻sat
,(2)
where IVT denotes the vertically integrated water vapor transport. Setting precipitation equal to253
the product of 𝐶with a precipitation efficiency, one sees that in this so-called upslope model,254
it is proportional to the cross-slope IVT. This model has several shortcomings, including the255
assumption of a saturated atmosphere and the oversimplified vertical velocity parameterization.256
Nevertheless, it skillfully characterizes temporal rainfall variations in some midlatitude mountain257
ranges, as illustrated for the British Columbia coastal range in Fig. 4; despite some scatter, daily258
precipitation rates in winter are decently described by a linear relationship with cross-slope IVT259
(hereafter IVT⊥). Although the vertically uniform ascent model for vertical velocity (𝑤=u· ∇ℎ)260
is crude, it captures the simple fact that vertical velocities in convectively stable orographic flows261
are controlled by cross-slope wind. Deviations from this simple picture, including effects of262
stratification, wind shear, and the specific dynamics of various types of weather systems, yield the263
scatter.264
In the tropics, where convective ascent is more important, one might expect other factors than273
cross-barrier winds to modulate ascent rates. Still, Bagtasa (2020) suggested that enhanced cross-274
slope winds in the Philippines associated with certain phases of the MJO favored rainfall in late275
autumn. Similarly, Shige et al. (2017) showed that rainfall in the Western Ghats and the Arakan276
Yoma range of Myanmar was in phase with the southwesterly wind strength modulated by the277
BSISO. This suggests that cross-slope winds, and perhaps cross-slope IVT, still are important278
12
−400 −200 0 200 400 600
IVT
⟂
(kg m−1 s−1)
0
20
40
60
80
Precipitation (mm da −1)
British Columbia coast range
R
2 = 0.68
10 m s−1 0 5 10 15 20 25
Precip. (mm da −1)
5 10 15 20 25
Count
Fig. 4. Joint distributions of daily cross-slope IVT and precipitation in the coast range of British Columbia.
Precipitation is averaged over the orographic rain band (red box in the inset). Cross-slope IVT (defined as its
northeastward component) is averaged immediately upstream of the precipitation maximum (blue dashed box
in the inset). The black dashed line shows the best linear fit. The red dots represent conditionally averaged
precipitation over bins of width 80 kg m−1s−1, with error bars representing a 95% confidence interval obtained by
bootstrapping. The inset shows climatological rain (IMERG) and 100 m wind (ERA5) averaged over November-
January.
246
247
248
249
250
251
252
controls on orographic precipitation at low latitudes. Figure 5 (first and third columns) shows the279
joint distributions of IVT⊥and precipitation, as well as precipitation conditionally averaged on280
IVT⊥2. While a positive relationship remains, it does not hold as strongly as in the midlatitude281
winter case shown in Fig. 4, with numerous dry days associated with strong IVT⊥. Therefore, we282
attempt to find another variable to characterize temporal variations in tropical orographic rainfall,283
starting with thermodynamic metrics that have been associated with convective rainfall.284
The question of what environmental factors set convective precipitation rates is at the heart of285
any theory of tropical atmospheric dynamics. The QE hypothesis (e.g., Emanuel et al. 1994) states286
that convection acts to deplete anomalies in convective available potential energy (CAPE). This287
description predicts the effect moist convection has on its environment, consuming instability and288
setting vertical temperature profiles close to moist adiabats. However, it alone does not provide289
2Throughout this manuscript, conditionally averaging A on B means averaging A over days where B is in a given range of values. Where
relevant, the ranges of values are defined in the figure captions.
13
Fig. 5. Joint distributions of daily cross-slope IVT and precipitation (first and third columns, green colors)
and 𝐵𝐿and precipitation (second and fourth columns, red colors). 𝐵𝐿and precipitation are averaged spatially
over the rain band regions (red boxes in Fig. 3). IVT is averaged right upstream of the rain band regions (blue
boxes in Fig. 3). The cross-slope direction is defined as 70◦(Ghats), 60◦(Myanmar), 240◦(Vietnam), 225◦
(Malaysia), 225◦(Philippines), and 320◦(PNG). Linear fits (for the IVT-precipitation relation) and exponential
fits (for the 𝐵𝐿-precipitation relation) are shown as dashed lines, with the associated coefficients of determination
in the legend. The black dots represent conditionally averaged precipitation over bins of width 80 kg m−1s−1(for
IVT) and 0.03 m s−2(for 𝐵𝐿), with error bars representing a 95% confidence interval obtained by bootstrapping.
265
266
267
268
269
270
271
272
information on convective intensity or precipitation rates, given environmental conditions. One290
further development stems from the observed exponential dependence of precipitation rates on291
column moisture content (e.g., Bretherton et al. 2004). The physical roots of this dependence lie292
in the effect that entrainment of free-tropospheric air has on plume buoyancy.293
14
Seeking a unified measure that would characterize rainfall across the tropics, Ahmed and Neelin294
(2018) derived an expression for a lower-tropospheric averaged plume buoyancy, that only depends295
on environmental temperature and moisture profiles. Dividing the lower atmosphere in two layers,296
a boundary layer (subscript 𝐵) and a lower-free-troposphere3(subscript 𝐿), this expression reads297
(Ahmed et al. 2020)298
𝐵𝐿=𝑔𝛼𝐵
𝜃𝑒𝐵 −𝜃∗
𝑒𝐿
𝜃∗
𝑒𝐿
−𝛼𝐿
𝜃∗
𝑒𝐿 −𝜃𝑒 𝐿
𝜃∗
𝑒𝐿 ,(3)
where 𝑔is the acceleration of gravity, 𝜃𝑒is equivalent potential temperature (and 𝜃∗
𝑒its saturated299
value), and subscripts denote averages taken over respective layers. The weights 𝛼𝐵and 𝛼𝐿=1−𝛼𝐵
300
depend on the thickness of each layer and the assumed mass flux profile of the plume. We use301
𝛼𝐵=0.52 (as in Ahmed et al. 2020). The first term in (3) is a CAPE-like term, wherein the302
difference between boundary layer 𝜃𝑒and lower-free-tropospheric 𝜃∗
𝑒provides a measure of moist303
convective instability. The second term describes subsaturation of the lower free troposphere,304
and quantifies the efficiency of entrainment at reducing buoyancy by drying the plume (hence the305
negative sign in front of it).306
When conditionally averaged on 𝐵𝐿(at O(10 km) and hourly scale), precipitation is near-zero316
for negative values and strongly increases above zero buoyancy, a behavior reminiscent of its expo-317
nential dependence on column moisture. The strength of this precipitation-buoyancy relationship318
lies in its universality, as it holds over all tropical oceans, and, with slight modifications, over319
tropical land (Ahmed et al. 2020). Using conditional averages reduces the scatter in precipitation320
rates associated with a given value of 𝐵𝐿. This spread can be due to both stochasticity or ignored321
physical effects, e.g., higher-order dependencies on the vertical structure of environmental temper-322
ature and moisture, or wind shear effects. Figure 5 (second and fourth columns), shows the joint323
distribution of precipitation and 𝐵𝐿for each region, using daily-mean data spatially averaged over324
the rain bands (red boxes in Figure 3). Spatially averaging the nonlinear rainfall-𝐵𝐿relationship325
is expected to smooth out the sharp increase around zero buoyancy; hence, we show exponential326
fits (rather than ramp fits of the form max(0, 𝑎𝐵𝐿+𝑏)) with the joint distributions. We also show327
conditional averages at various 𝐵𝐿values. 𝐵𝐿is more skillful than IVT⊥at capturing daily rainfall328
3Here, the boundary layer is defined as between the surface and 900 hPa, and the lower-free-troposphere between 900 hPa and 600 hPa. We chose
these definitions (over using a fixed-depth boundary layer and variable-depth lower free troposphere) so that lower-free-tropospheric averages are
not affected by surface elevation changes. Points where the surface pressure is lower than 900 hPa are masked out of all analyses. These represent a
small fraction of each domain, and can be visualized as the white shaded regions in Figure 11. The analyses are robust to the exact definition of the
boundary layer top: changing it to 875 or 925 hPa does not significantly affect any of the results presented. Moreover, daily variations in boundary
layer height (as determined by ERA5) are modest in the rain bands analyzed in Figs. 5-10, with standard deviations lower than 15 hPa.
15
variations in all regions except perhaps Myanmar, where the range of 𝐵𝐿is narrower than in other329
regions (during the summer monsoon, the coast of Myanmar is in a precipitating state most of the330
time). It is notable that 𝐵𝐿characterizes rainfall with similar accuracy in regions that have different331
convective vertical structures (Kumar and Bhat 2017; Shige and Kummerow 2016). This indicates332
that 𝐵𝐿is not only suitable to quantify rainfall from deep convection, but that it is also an adequate333
measure in regions where precipitation tops frequently lie around 4 to 6 km. We next decompose334
variations in 𝐵𝐿into contributions from its components to understand the origins of precipitation335
variability in tropical orographic regions.336
𝐵𝐿is a function of three variables: 𝜃𝑒 𝐵 ,𝜃𝑒 𝐿 , and 𝜃∗
𝑒𝐿 (eqn. 3). Alternatively, following Ahmed337
et al. (2020), it can be viewed as a function of 𝜃𝑒𝐵 ,𝑇𝐿and 𝑞𝐿, where 𝑇is temperature and 𝑞338
denotes specific humidity, hereafter in temperature units (i.e. multiplied by the ratio of the latent339
heat of vaporization of water 𝐿𝑣to the heat capacity of air at constant pressure 𝑐𝑝). In this340
description, plume buoyancy is affected by boundary layer 𝜃𝑒(which affects lower-tropospheric341
stability), lower-free-tropospheric temperature (affecting both stability and lower-free-tropospheric342
subsaturation) and lower-free-tropospheric moisture (affecting only the subsaturation component).343
To evaluate the sensitivity of 𝐵𝐿to each component, we linearize its expression:344
𝛿𝐵𝐿=𝜕 𝐵𝐿
𝜕𝜃𝑒 𝐵
𝛿𝜃𝑒𝐵 +𝜕𝐵𝐿
𝜕𝑇𝐿
𝛿𝑇𝐿+𝜕𝐵𝐿
𝜕𝑞𝐿
𝛿𝑞 𝐿(4)
where 𝛿denotes a deviation from a time-average, 𝜕𝐵𝐿/𝜕𝜃𝑒𝐵 =𝑔𝛼𝐵/𝜃∗
𝑒𝐿 , and the expressions for345
𝜕𝐵𝐿/𝜕𝑇𝐿and 𝜕𝐵𝐿/𝜕𝑞𝐿are given in Ahmed et al. (2020) (these expressions were derived from a346
simplified version of 𝐵𝐿that is very close to the one employed here). Here, we use fixed values of347
𝜕𝐵𝐿/𝜕𝜃𝑒 𝐵 =0.014, 𝜕 𝐵𝐿/𝜕𝑇𝐿=−0.058, and 𝜕 𝐵𝐿/𝜕 𝑞 𝐿=0.014, which have little dependence on348
the specific base state considered.349
Figure 6 examines the contribution of each term on the right-hand-side of (4) to variations in350
𝐵𝐿, over the Western Ghats and PNG. For example, to estimate the contribution of 𝜃𝑒 𝐵 variations351
to 𝐵𝐿variations, we fix 𝑇𝐿and 𝑞𝐿and estimate the 𝐵𝐿perturbations that would have occurred352
if only 𝜃𝑒𝐵 had varied, i.e. (𝜕 𝐵𝐿/𝜕𝜃𝑒𝐵 )𝛿𝜃𝑒𝐵 . We regress 𝛿𝐵𝐿on this measure and show the353
joint distribution of both quantities (top panels), then repeat the same analysis with (𝜕𝐵𝐿/𝜕𝑇𝐿)𝛿𝑇𝐿
354
(middle panels) and (𝜕 𝐵𝐿/𝜕 𝑞 𝐿)𝛿𝑞𝐿(bottom panels). It is apparent from these univariate linear355
regressions that 𝑞𝐿dominates 𝐵𝐿variations in both regions. This is true even though 𝐵𝐿is356
16
∂
BL
∂
θeB δθeB
(m s−2)
-0.4
-0.2
0.0
0.2
δBL
(m s
−2)
Western Ghats
R2 = 0.00
∂
BL
∂
TLδTL
(m s−2)
-0.4
-0.2
0.0
0.2
δBL
(m s
−2)
R2 = 0.28
-0.4 -0.2 0.0 0.2
∂
BL
∂
qLδqL
(m s
−2)
-0.4
-0.2
0.0
0.2
δBL
(m s
−2)
R2 = 0.64
∂
BL
∂
θeB δθeB
(m s−2)
PNG
R2 = 0.33
∂
BL
∂
TLδTL
(m s−2)
R2 = 0.00
-0.2 0.0 0.2
∂
BL
∂
qLδqL
(m s
−2)
-0.4
R2 = 0.82
5 10 15 20 25 30
Count
Fig. 6. Joint distributions of buoyancy anomalies 𝛿𝐵𝐿and their contribution from 𝜃𝑒 𝐵 anomalies (first row), 𝑇𝐿
anomalies (second row), and 𝑞𝐿anomalies (third row), for two regions illustrating different regimes: the Western
Ghats (left) and PNG (right). For each plot, 𝛿𝐵𝐿is also regressed on the individual contribution (𝜕 𝐵 𝐿/𝜕𝑉 )𝛿𝑉
where 𝑉=𝜃𝑒𝐵 , 𝑇𝐿, or 𝑞𝐿. Black dashed lines show the best fit linear regression.
307
308
309
310
four times more sensitive to 𝑇𝐿(|𝜕𝐵𝐿/𝜕𝑇𝐿| ≃ 4𝜕𝐵𝐿/𝜕𝑞𝐿). Indeed, variations of 𝑞𝐿are less357
constrained than those of 𝑇𝐿: lower-free-tropospheric temperature anomalies are quickly smoothed358
in the tropics by gravity waves, resulting in a state of weak temperature gradients (e.g., Sobel359
et al. 2001). Over the Western Ghats, 𝑇𝐿variations still account for 28% of the variance in 𝐵𝐿,360
while 𝜃𝑒𝐵 variations do not correlate with 𝐵𝐿. In PNG, the converse picture holds. Figure 7361
shows the coefficients of determination (𝑅2) of the regression lines that appear in Fig. 6, extended362
to all regions. In addition, we perform bivariate linear regressions of 𝛿𝐵𝐿against 𝜃𝑒𝐵 and 𝑇𝐿,363
17
Western Ghats
Myanmar
Vietnam
Malaysia
Philippines
PNG
0.0
0.2
0.4
0.6
0.8
1.0
R
2
θeB
θeB
&
TL
TL
θeB
&
qL
qL
TL
&
qL
Fig. 7. Coefficients of determination (𝑅2) from linear regressions of 𝛿𝐵𝐿against its individual contributions
from 𝜃𝑒𝐵 ,𝑇𝐿, and 𝑞𝐿anomalies (see Fig. 6), as well as joint contributions from pairs of these variables. Note
that despite differences in the univariate 𝑅2s across regions (with 𝜃𝑒 𝐵 anomalies accounting for more variance
in 𝐵𝐿than 𝑇𝐿anomalies in a univariate sense), the (𝑇𝐿,𝑞𝐿) pair explains the highest fraction of variance in 𝛿𝐵𝐿
in all regions.
311
312
313
314
315
𝜃𝑒𝐵 and 𝑞𝐿, and 𝑇𝐿and 𝑞𝐿(we omit 𝜕𝐵𝐿/𝜕𝜃 𝑒 𝐵 and other prefactors as these only change the364
regression coefficients, and not the 𝑅2). From the univariate regressions alone, there seem to be365
two types of behavior: one where buoyancy variations are controlled by lower-free-tropospheric366
thermodynamic quantities (the Western Ghats and Myanmar), and the other where boundary layer367
𝜃𝑒and lower-free-tropospheric moisture set these variations (Vietnam, Malaysia, the Philippines,368
and PNG). However, the bivariate regressions show that in all regions, 𝑇𝐿and 𝑞𝐿account together369
for the highest fraction (over 85%) of the variance in 𝐵𝐿. Consistently, the rest of this section370
focuses primarily on the factors governing 𝑇𝐿and 𝑞𝐿variations.371
An important caveat is that the three variables that control variations in lower tropospheric372
buoyancy 𝐵𝐿are not independent of each other. In QE theory, convection rapidly reduces CAPE373
variations, tying free-tropospheric saturation equivalent potential temperature 𝜃∗
𝑒to subcloud layer374
equivalent potential temperature 𝜃𝑒𝐵 . Thus, one expects 𝜃𝑒𝐵 and 𝑇𝐿to exhibit substantial corre-375
lation. Indeed, correlation coefficients between daily 𝜃𝑒𝐵 and 𝑇𝐿averaged over the orographic376
precipitation bands vary between 0.7 and 0.9 in all regions. However, this relationship only indi-377
cates that 𝜃𝑒𝐵 and 𝜃∗
𝑒𝐿 covary, and does not provide insight on 𝐵𝐿variations because 𝐵𝐿depends378
on 𝜃𝑒𝐵 −𝜃∗
𝑒𝐿 , as in (3). Additionally, turbulent exchange between the subcloud layer and the lower379
18
Table 3. Correlations between daily precipitation (P) and the three quantities affecting plume buoyancy (𝜃𝑒𝐵,
𝑇𝐿and 𝑞𝐿), and between daily SST and boundary layer equivalent potential temperature 𝜃𝑒𝐵. Precipitation, 𝜃𝑒𝐵 ,
𝑇𝐿and 𝑞𝐿are averaged over the red boxes in Fig. 3, and SST is averaged over the ocean part of each box.
389
390
391
Region name P - 𝜃𝑒𝐵 P - 𝑇𝐿P - 𝑞𝐿SST-𝜃𝑒𝐵
Western Ghats 0.19 -0.15 0.56 0.80
Myanmar 0.16 -0.18 0.30 0.53
Vietnam 0.23 0.03 0.53 0.61
Malaysia 0.17 -0.18 0.51 0.69
Philippines 0.12 -0.06 0.50 0.56
PNG 0.15 -0.15 0.51 0.60
free troposphere produces smaller correlations (0.3–0.6) between daily 𝜃𝑒𝐵 and 𝑞𝐿variations. 𝑇𝐿
380
and 𝑞𝐿are essentially uncorrelated across all regions.381
To link this analysis back to precipitation variations, we compute correlations between daily382
values of rainfall and each of 𝜃𝑒𝐵,𝑇𝐿, and 𝑞𝐿upstream of each of the mountain ranges studied383
(Table 3). These correlations are only a crude measure of the association of each component384
with precipitation, given that the precipitation-buoyancy relationship is expected to be nonlinear.385
Nevertheless, a few of the observations made above hold: 𝑞𝐿has the strongest association with386
precipitation, 𝑇𝐿anomalies are negatively associated with precipitation (recall that 𝜕𝐵𝐿/𝜕𝑇𝐿<0),387
and 𝜃𝑒𝐵 has a weak positive association with rainfall.388
b. Controls on daily 𝜃𝑒𝐵 variations392
In this work, the boundary layer extends between the 900 hPa level and the surface—which393
loosely corresponds to the subcloud layer. Boundary layer 𝜃𝑒, or equivalently subcloud entropy, is394
set by exchanges with the surface and the lower free troposphere, with a small contribution from395
radiative cooling (Emanuel et al. 1994). Entropy exchanges at the top of the boundary layer are396
twofold: one contribution being in the form of quasi-continuous turbulent mixing across the top of397
the layer, the other one arising from penetrative convective downdrafts. Over ocean, sea-surface398
temperature (SST) is often the dominant quantity affecting subcloud entropy (e.g., Lindzen and399
Nigam 1987). Because the orographic rain bands of interest in this section are in close proximity400
to the sea, one might expect SSTs to exert a strong control on 𝜃𝑒𝐵 . We verify this fact in Table 3:401
19
65°E 70°E 75°E 80°E
10°N
15°N
20°N
Western
Ghats
85 E 90 E 95 E 100 E
10 N
15 N
20 N
Myanmar
100 E 105 E 110 E 115 E
10 N
15 N
20 N
25 N Vietnam
100 E 105 E 110 E
0
5 N
10 N
15 N Malaysia
120 E 125 E 130 E 135 E
5 N
10 N
15 N
20 N
Philippines
5 m s−1K−1
145 E 150 E 155 E 160 E
15 S
10 S
5 S
0 PNG
284
285
286
287
288
289
K
Fig. 8. Boundary layer horizontal wind regressed on lower-free-tropospheric temperature (𝑇𝐿, averaged in
the dashed boxes). The result is multiplied by −1 so that upslope flow is associated with negative temperature
perturbations. The color shading shows seasonal-mean 𝑇𝐿. Arrows are masked where neither the 𝑢wind
regression nor the 𝑣wind regression satisfy the false discovery rate criterion (Wilks 2016) with 𝛼=0.01.
408
409
410
411
SST strongly correlates with 𝜃𝑒𝐵 at the daily scale, with correlation coefficients between 0.5 and402
0.8 in all regions.403
Other factors such as surface wind speed variations or convective downdrafts contribute to404
variations in 𝜃𝑒𝐵 on shorter timescales than SST changes. Because there is no clear influence of405
orographic mechanical forcing on any of these factors, we do not delve deeper into this topic.406
c. Controls on daily lower-free-tropospheric temperature variations407
Topographically forced gravity waves carry temperature perturbations. In the canonical picture412
of mechanical orographic forcing, a mountain of height ℎ𝑚is placed in a stratified atmosphere (with413
buoyancy frequency 𝑁) with a uniform background horizontal wind 𝑈. When the nondimensional414
mountain height 𝑁 ℎ 𝑚/𝑈≲1, the flow ascends over the mountain, creating (by adiabatic cooling)415
a cold anomaly in the lower-free-troposphere upstream. The stronger the wind, the deeper the416
20
ascent region, hence the colder the anomaly. In the case of an idealized ridge of height 1 km, the417
sensitivity of the temperature perturbation to the impinging wind is (see Appendix)418
𝜕𝑇′
𝐿
𝜕𝑈 ≃ −0.2 K/(m s−1).(5)
We now seek to verify whether 𝑇𝐿variations in our regions have patterns that are consistent with419
this picture. Figure 8 shows time-mean 𝑇𝐿maps in all six regions. Cold anomalies (of around420
0.5 K) are visible in each region’s rain band, indicated by poleward (in the Western Ghats and421
Myanmar) or equatorward (in Vietnam, the Philippines and PNG) excursions of isotherms upstream422
of and above the topography. These anomalies are consistent with the idea of upstream cooling423
by orographic lifting in the mean state. To study temporal variations in the strength of this cool424
anomaly, we average 𝑇𝐿upstream of each mountain range to obtain daily timeseries. Because the425
mountains are of modest height in each region, we expect mountain waves to be dominantly affected426
by winds in the lowermost kilometer of the troposphere. We thus average horizontal winds within427
the boundary layer and regress them on the 𝑇𝐿timeseries at each location. The resulting wind428
vectors are multiplied by −1 so that onshore cross-slope flow corresponds to negative temperature429
perturbations, and shown in Fig. 8. If our simple estimate (5) were to hold, regressed winds would430
have a magnitude around 5 m s−1K−1for a 1 km-high mountain.431
The wind regressions are directed onshore and cross-slope in each region, which is again consis-435
tent with the idea that 𝑇𝐿is modulated by the strength of stationary mountain waves. Furthermore,436
the magnitude of the regression vectors upstream of each region (except Myanmar) is around 2–5 m437
s−1K−1, consistent with (5). It is apparent from Fig. 8 (especially in the Philippines, Vietnam, and438
PNG) that cold anomalies are also associated with up-temperature-gradient winds: background439
temperature gradients are not everywhere small in these tropical regions, and accordingly cooling440
can happen through horizontal advection.441
d. Controls on daily lower-free-tropospheric moisture variations442
Given the dominant control 𝑞𝐿exerts on lower tropospheric buoyancy (Fig. 6), understanding443
drivers of its temporal changes is key to understanding rainfall variations. In the same way444
they bear temperature anomalies, mountain waves carry moisture perturbations through vertical445
displacements in a background profile of specific humidity. Rising air upstream of a mountain446
21
65°E 70°E 75°E 80°E
10°N
15°N
20°N
Western
Ghats
85 E 90 E 95 E 100 E
10 N
15 N
20 N
Myanmar
100 E 105 E 110 E 115 E
10 N
15 N
20 N
25 N Vietnam
100 E 105 E 110 E
0
5 N
10 N
15 N Malaysia
120 E 125 E 130 E 135 E
5 N
10 N
15 N
20 N
Philippines
1 m s−1K−1
145 E 150 E 155 E 160 E
15 S
10 S
5 S
0 PNG
19
20
21
22
23
24
25
26
27
28
K
Fig. 9. Boundary layer horizontal wind regressed on lower-free-tropospheric moisture (𝑞𝐿, averaged in the
dashed boxes, in temperature units). The color shading shows seasonal-mean 𝑞𝐿. Arrows are masked using the
same criterion as in Fig. 8.
432
433
434
moistens the lower-free-troposphere, while downstream subsidence dries it. The magnitude of this447
effect is estimated using linear mountain wave theory in the Appendix. In this idealized picture,448
the sensitivity of the upstream moisture perturbation to the cross-slope wind is449
𝜕𝑞′
𝐿
𝜕𝑈 ≃0.5 K/(m s−1).(6)
Once again, this effect neglects any convective response: mountain-induced 𝑇𝐿and 𝑞𝐿perturbations450
result in enhanced convection, which, in turn, dries the troposphere. A framework to understand451
the response of convection to thermodynamic perturbations in a mountain wave is presented in452
section 6. Solving for 𝑞′
𝐿in this framework reduces the sensitivity in (6) by about half.453
In the absence of horizontal gradients in the background moisture profile, 𝑞𝐿perturbations454
would be dominantly due to the time-mean ascent perturbation imposed by the terrain, which455
is well described by stationary mountain waves for a mechanically forced regime (NB22). In456
22
Earth’s tropics however, water vapor is far from horizontally homogeneous. This is apparent in457
Fig. 9, where color shading represents the time-mean 𝑞𝐿in each region: horizontal moisture458
gradients are much stronger than 𝑇𝐿gradients. Although the impact of orography on the mean 𝑞𝐿
459
distribution is less apparent compared to 𝑇𝐿(because of the stronger background 𝑞𝐿variations),460
it seems to be associated with moisture contours deviating southward in Myanmar and northward461
in the Philippines (corresponding to positive anomalies); a local maximum is also present over462
PNG. Given the background horizontal moisture gradients and the moisture perturbations around463
orography in Fig. 9, one might expect variations in 𝑞𝐿to be influenced by both winds along the464
background moisture gradient and winds across orographic slopes.465
The vectors in Fig. 9 show horizontal winds regressed on upstream-averaged 𝑞𝐿. In the Western466
Ghats and Myanmar, moist perturbations are mostly associated with cross-slope winds, following467
the theoretical picture of mechanical forcing. The magnitude of the regressions (1–2 m s−1K−1) is468
somewhat smaller than expected from (6); one would expect 2–4 m s−1K−1when accounting for469
the correction due to convective feedback (see above). The fact that both negative 𝑇𝐿and positive470
𝑞𝐿perturbations—hence positive 𝐵𝐿perturbations—are favored by cross-slope winds in the Ghats471
and Myanmar explains why IVT⊥characterizes precipitation better there than in other regions472
(Fig. 5).473
In Vietnam, Malaysia, and the Philippines, regressed winds have little cross-slope flow compo-474
nent: they are mostly directed down mean moisture gradients. In these regions, moistening of the475
lower free troposphere thus seems to be more effectively attained through large-scale horizontal476
moisture advection than mechanical forcing of upslope flow. This result contrasts with the intu-477
itive view that mechanically forced orographic precipitation and accompanying lower-tropospheric478
humidity variations are mostly controlled by forced ascent, i.e. by the strength of upslope flow.479
It shows that, despite its importance in setting the time-mean rainfall pattern, orographic forcing480
might be less important than large-scale horizontal moisture advection in setting the daily vari-481
ability of precipitation in these regions. Such control of precipitation by large-scale advection of482
moisture in the midtroposphere was noted over the Arabian sea during the summer monsoon (Hunt483
et al. 2021), and in northern Australia during its monsoon season (Xie et al. 2010).484
The regression pattern in PNG is neither cross-slope nor down-moisture-gradient. Indeed, the485
orographic rain band of PNG corresponds to a local maximum in lower-tropospheric specific486
23
65°E 70°E 75°E 80°E
10°N
15°N
20°N
Western Ghats
85°E 90°E 95°E 100°E
10°N
15°N
20°N
Myanmar
100°E 105°E 110°E 115°E
10°N
15°N
20°N
25°N Vietnam
100°E 105°E 110°E
0°
5°N
10°N
15°N Malaysia
120°E 125°E 130°E 135°E
5°N
10°N
15°N
20°N
Phili ines
145°E 150°E 155°E 160°E
15°S
10°S
5°S
0°
0.2 m s−1(mm/day)−1
PNG
0.0
0.4
0.8
1.2
1.6
nondimensional
Fig. 10. Boundary layer horizontal wind regressed on precipitation averaged in the dashed boxes. The color
shading shows precipitation regressed on this same index. Masked arrows and white shading indicate that the
regressions do not satisfy the false discovery rate criterion with 𝛼=0.01.
496
497
498
humidity. Although we do not have a precise explanation for this pattern of wind anomalies, one487
may speculate that it is associated with large-scale upward motion in the South Pacific convergence488
zone (SPCZ), where PNG is located.489
We note that moistening of the lower troposphere is not solely controlled by horizontal winds, and490
that any source of uplift, such as convectively coupled waves or cyclonic disturbances, will affect491
𝑞𝐿. In this section we focused on horizontal wind control because horizontal winds dictate the492
strength of uplift in stationary mountain waves, and are consequently a primary factor modulating493
the effect of orography on 𝑞𝐿variations.494
e. Controls on daily precipitation variations495
To verify whether the same factors that govern lower-free-tropospheric temperature and moisture499
control rainfall variations, we now regress horizontal wind on daily upstream precipitation in each500
region (Fig. 10; upstream precipitation is defined as an average over the same boxes we previously501
24
used to define the rain bands). Enhanced rainfall is associated with some amount of upslope502
flow in all regions, confirming the importance of orographic mechanical forcing in influencing503
precipitation variability there. Deviations from pure upslope flow (especially in Vietnam, Malaysia,504
the Philippines and PNG) are consistent with the wind patterns that accompany 𝑞𝐿variations (see505
Fig. 9), i.e. down-moisture gradient winds. This confirms the joint control of orographic lifting506
and large-scale moisture advection on orographic precipitation variability in the tropics.507
Color shading in Fig. 10 shows precipitation regressed on this same upwind precipitation index.508
The existence of areas of weak positive association with the upwind rain index that are much509
wider than the orography indicate that orographic rainfall is partially controlled by large-scale,510
“background” precipitation variations. The stronger regression coefficients localized close to511
and preferentially upstream of the orography suggests the existence of an orographic mode of512
precipitation variability in each region. Patterns of positive association extend several hundred513
kilometers upstream of the regions used to define the rainfall index, as expected given the far-514
reaching influence of mechanical forcing upstream of a ridge (NB22).515
5. Spatial distribution of buoyancy around orography516
Strong spatial gradients are an ubiquitous characteristic of orographic rainfall. All regions in519
Fig. 3 exhibit a windward rainfall peak and a leeward rain shadow less than 200 km apart, with520
seasonal-mean precipitation rates varying from more than 15 mm day−1to less than 5 mm day−1
521
on short distances. The buoyancy framework presented in section 4 naturally applies on short522
(hourly to daily) temporal scales, as buoyancy anomalies are consumed in a few hours (Ahmed523
et al. 2020). Here, we explore its potential to explain precipitation patterns on much longer time524
scales. Specifically, we explore whether seasonal-mean spatial features of orographic precipitation525
follow the spatial distribution of time-averaged buoyancy 𝐵𝐿.526
The precipitation-𝐵𝐿relationship was initially introduced as a nonlinear statistical relationship527
holding at short spatial and small temporal scales (Ahmed and Neelin 2018). It is statistical in528
the sense that a single value of 𝐵𝐿corresponds to a range of precipitation rates—the relationship529
appears when conditionally averaging precipitation. Taking time averages is thus favorable in that530
it eliminates the underlying stochasticity. However, averaging over a nonlinear relationship may531
yield a non-unique mapping between time-mean precipitation 𝑃and time-mean buoyancy 𝐵𝐿.532
25
65°E 70°E 75°E 80°E
10°N
15°N
20°N
Western
Ghats
85 E 90 E 95 E 100 E
10 N
15 N
20 N
Myanmar
100 E 105 E 110 E 115 E
10 N
15 N
20 N
25 N Vietnam
100 E 105 E 110 E
0
5 N
10 N
15 N Malaysia
120 E 125 E 130 E 135 E
5 N
10 N
15 N
20 N
Philippines
145 E 150 E 155 E 160 E
15 S
10 S
5 S
0 PNG
−0.19
−0.17
−0.15
−0.13
−0.11
−0.09
−0.07
−0.05
m s−2
Fig. 11. Maps of seasonal-mean plume buoyancy 𝐵𝐿. The 500 m topography contour is shown in magenta.
White shading represents undefined 𝐵𝐿values, wherever the surface pressure is lower than 900 hPa.
517
518
For example, it appears from Fig. 5 that the orographic rain band upstream of Myanmar has a533
narrower distribution of 𝐵𝐿than other regions. This suggests that 𝐵𝐿values in that region may534
be higher than in other places with comparable rain rates, e.g., upstream of the Western Ghats or535
PNG. Nonetheless, one might still expect a monotonic relationship between 𝐵𝐿and 𝑃, perhaps536
with variations across regions.537
We compute 𝐵𝐿from ERA5 temperature and moisture data at 0.25◦and daily resolution, then538
average temporally over each region’s rainiest season (see Table 1) for 20 years. The resulting539
maps are shown in Fig. 11. We note that the boundary layer top is taken as the 900 hPa level,540
which ignores spatial variations in boundary layer depth. Including these variations (using ERA5541
estimates of boundary layer depth; not shown) does not affect the results presented here. Spatial542
features on these maps are broadly consistent with the maps of mean precipitation in Fig. 3. A543
distinct peak is visible upwind of each orographic barrier, with decreased 𝐵𝐿values in the lee: this544
confirms that mechanical forcing spatially distributes precipitation in a manner consistent with its545
effect on the temperature and moisture fields. This effect was already noted in Section 4 in the546
26
maps of time-averaged 𝑇𝐿and 𝑞𝐿(Figs. 8 and 9, where upstream cold anomalies were present in all547
regions, and moist anomalies in several regions). 𝐵𝐿peaks are collocated with rainfall peaks (see548
Fig. 3) in all regions. One small exception is the easternmost 𝐵𝐿peak in Myanmar, which extends549
farther inland than the observed precipitation maximum. We note that the ERA5 precipitation550
distribution (not shown) follows the 𝐵𝐿pattern, with higher values than TRMM PR/GPM DPR551
inland. This may indicate that the reanalysis does not accurately represent the underlying 𝐵𝐿
552
distribution there.553
Except for the special case of Myanmar, rain shadows are consistent with the time-mean buoy-554
ancy distribution. Reduced values of 𝐵𝐿, mostly associated with a warmer and/or drier lower-555
troposphere, are visible downstream of the mountain ranges, consistent with the expected effect of556
gravity wave subsidence there. In the Western Ghats and in PNG, 𝐵𝐿does not drop as sharply as557
precipitation downstream of the rainfall maximum. Once again, ERA5 precipitation (not shown)558
partly reflects this fact, with overestimated rainfall values especially downstream of PNG. This559
could mean that ERA5 underestimates the warm and dry anomalies resulting from mechanically560
forced subsidence there (perhaps because the topography is under-resolved). Alternatively, the561
𝐵𝐿framework may only partially account for the suppression of precipitation in rain shadows.562
Convection may be affected by higher-order variations in the vertical structures of temperature and563
moisture, or by neglected dynamical effects (e.g., mountain lees are regions of strong wind shear).564
6. A linear model for seasonal-mean tropical orographic precipitation565
Section 5 suggests that the spatial organization of tropical orographic rainfall is adequately566
captured by the time-mean plume buoyancy distribution. However, we have yet to quantify the567
effect of orography on this distribution. Here, we delve further into the physical drivers through568
which orography influences 𝐵𝐿and sets the strength and location of rainfall peaks and rain shadows.569
We use a simple theory that solves, for any topographic shape, the time-mean temperature and570
moisture anomalies carried by a stationary mountain wave (including convective feedback on the571
moisture anomalies) to estimate the time-mean precipitation distribution. The model describes572
mechanically forced rainfall in tropical regions, and neglects thermal forcing and Earth’s rotation.573
We compare its predictions with observations and with two existing theories for mechanically574
forced orographic rainfall.575
27
a. Derivation576
The theory we present closely follows the one developed in NB22, but extends it to two horizontal577
dimensions. We give an outline of the derivation, and refer readers to that work for more details.578
A low-latitude domain with topography ℎ(𝑥, 𝑦)has a constant background wind u0=(𝑢0, 𝜐0)and579
Brunt-V¨
ais¨
al¨
a frequency 𝑁. The flow is decomposed as the sum of a basic state, a “dry” mode (that580
carries temperature and moisture perturbations from a stationary mountain wave), and a “moist”581
mode (that consists of a convective response to these perturbations). The dry mode influences582
the moist mode by altering convective heating and moistening, that are parameterized as functions583
of lower-tropospheric temperature and moisture following the 𝐵𝐿framework, but the moist mode584
does not affect the dry mode. This simplifying assumption allows for analytical tractability, and585
was tested in NB22; idealized simulations showed that the moist mode does reduce the temperature586
perturbations carried by the dry mode, but that this effect is of second-order importance. In this587
section only, temperature and moisture are in energy units (compared to the previous sections, they588
are multiplied by 𝑐𝑝), for consistency with NB22.589
Steady-state thermodynamic and moisture equations for the moist mode read:590
u0· ∇𝑇𝑚+𝜔𝑚
𝑑𝑠0
𝑑𝑝 =𝑄𝑐−𝑅, (7a)
u0· ∇𝑞𝑚+𝜔𝑚
𝑑𝑞0
𝑑𝑝 =𝑄𝑞+𝐸, (7b)
where 𝑠0(𝑝)and 𝑞0(𝑝)are the background dry static energy profile and moisture profile (in energy591
units). 𝑄𝑐and 𝑄𝑞denote convective heating and moistening, while 𝑅and 𝐸are radiative cooling592
and surface evaporation rates. 𝜔is the pressure velocity, and the subscript 𝑚is used for moist593
mode quantities (we will similarly use a subscript 𝑑for dry mode properties), so 𝑇𝑚and 𝑞𝑚are,594
respectively, the moist mode temperature and moisture perturbations.595
We use the weak temperature gradient approximation for the moist mode, which implies that596
𝑇𝑚is horizontally uniform. This allows us to set 𝑇𝑚=0: one can add any horizontally uniform597
nonzero 𝑇𝑚(𝑝)to the reference profile 𝑇0(𝑝), hence resulting in 𝑇𝑚=0. Truncating the vertical598
velocity profile as 𝜔𝑚(𝑥, 𝑦, 𝑝)=𝜔1(𝑥 , 𝑦)Ω(𝑝), where Ωis a fixed vertical profile, and vertically599
28
averaging over the depth of the troposphere yields600
−𝜔1𝑀𝑠=⟨𝑄𝑐⟩−⟨𝑅⟩,(8a)
u0· ∇⟨𝑞𝑚⟩ + 𝜔1𝑀𝑞=⟨𝑄𝑞⟩+⟨𝐸⟩,(8b)
where 𝑀𝑠=−⟨Ω𝜕 𝑠0/𝜕 𝑝⟩,𝑀𝑞=⟨Ω𝜕𝑞0/𝜕 𝑝⟩, and ⟨·⟩ denotes a vertical average in pressure coor-601
dinates. 𝑀=𝑀𝑠−𝑀𝑞is known as the gross moist stability, and 𝑀/𝑀𝑠as the normalized gross602
moist stability (NGMS, Raymond et al. 2009).603
Following Ahmed et al. (2020), the precipitation-𝐵𝐿relationship is linearized (and boundary-604
layer 𝜃𝑒is assumed constant), yielding605
⟨𝑄𝑐⟩=𝑞′
𝐿
𝜏𝑞
−𝑇′
𝐿
𝜏𝑇
=𝑞𝑑𝐿 +𝑞𝑚𝐿
𝜏𝑞
−𝑇𝑑𝐿
𝜏𝑇
,(9)
where 𝑞𝑑𝐿 and 𝑞𝑚𝐿 are lower-free-tropospheric moisture perturbations carried by the dry and606
moist modes, 𝑇𝑑𝐿 is the dry mode temperature perturbation (recall 𝑇𝑚=0), and the convective607
time scales 𝜏𝑇and 𝜏𝑞are constants appearing from the linearization. For seasonal-mean rainfall,608
these are taken as 𝜏𝑇=7.5 hr and 𝜏𝑞=27.5 hr, a factor 2.5 higher than their values when used to609
represent precipitation at the hourly scale. Because the vertical structure of moisture perturbations610
is horizontally uniform, 𝑞𝑚 𝐿 and ⟨𝑞𝑚⟩are proportional to each other; we therefore define an611
adjustment time scale for vertically averaged moisture, ˜𝜏𝑞=0.6𝜏𝑞such that 𝑞𝑚 𝐿 /𝜏𝑞=⟨𝑞𝑚⟩/ ˜𝜏𝑞.612
We now use conservation of energy to relate convective heating, moistening, and precipitation613
by614
⟨𝑄𝑐⟩=−⟨𝑄𝑞⟩=𝜌𝑤𝐿𝑣𝑔
𝑝𝑇
𝑃, (10)
where 𝑝𝑇=800 hPa is the depth of the troposphere and 𝜌𝑤=1000 kg m−3is the density of water.615
The first factor on the right-hand-side converts a precipitation rate (in m s−1or mm day−1) into a616
convective heating rate (in J kg−1s−1). We henceforth define 𝛽=𝑝𝑇/(𝜌𝑤𝐿𝑣𝑔). Using this definition617
and combining (8a), (8b), (9), and (10), we derive an equation for 𝑃:618
u0· ∇𝑃+NGMS
˜𝜏𝑞(𝑃−𝑃0)=𝛽u0· ∇ 𝑞𝑑𝐿
𝜏𝑞
−𝑇𝑑𝐿
𝜏𝑇,(11)
29
65°E 70°E 75°E 80°E
10°N
15°N
20°N
(a)
TRMM PR/GPM DPR JJA 2001-2020
65°E 70°E 75°E 80°E
(b)
Nicolas & Boos
(2022) mod l
65°E 70°E 75°E 80°E
(c)
Smi)h & Bar()ad (2004) mod l
10 m (
−1
65°E 70°E 75°E 80°E
(d)
U&(lo& mod l
0
5
10
15
20
mm day
−1
Fig. 12. Maps of mean precipitation in the Western Ghats. (a) Observations (TRMM PR and GPM DPR), (b)
Nicolas and Boos (2022) theory, (c) Smith and Barstad (2004) theory, (d) upslope model (IVT · ∇ ℎ/𝐻sat).
619
620
where 𝑃0=𝛽𝑀𝑠⟨𝐸⟩ − 𝑀𝑞⟨𝑅⟩
𝑀is a background rain rate. The right-hand-side of equation (11)621
represents a forcing of convection by the dry mode. The second term on the left-hand-side622
represents convective relaxation: precipitation forced by the cool and moist perturbations of623
the dry mode dries the lower-free-troposphere, which in turn relaxes rainfall back towards the624
background rate 𝑃0. The reverse process happens when precipitation is suppressed by warm625
and dry perturbations. This process happens on a length scale 𝐿𝑞=˜𝜏𝑞|u0|/NGMS. We note626
that this framework is suitable for various vertical structures of convection, and that changes in627
the vertical structure Ω(𝑝)only affect the solutions through the NGMS. Remarkably, solutions628
can be obtained with negative NGMS (which typically results from bottom-heavy vertical motion629
profiles, e.g., Back and Bretherton 2006). In these cases, convection amplifies (rather than damps)630
the precipitation perturbation forced by the dry mode.631
Solving for 𝑇𝑑𝐿 and 𝑞𝑑𝐿 using mountain wave theory allows us to map a given topographic shape632
to the associated precipitation distribution using a Fourier transform. In the dry mode, moisture is633
conserved and there are no diabatic processes. Hence, horizontal advection terms are balanced by634
vertical advection:635
u0· ∇ 𝑞𝑑𝐿
𝜏𝑞
−𝑇𝑑𝐿
𝜏𝑇=𝑤𝑑𝐿 1
𝜏𝑇
𝑑𝑠0
𝑑𝑧 −1
𝜏𝑞
𝑑𝑞0
𝑑𝑧 ,(12)
30
where 𝑤𝑑𝐿 is the vertical velocity of the dry mode (we use height coordinates in the spirit of linear636
mountain wave theory). We define637
𝜒=𝛽1
𝜏𝑇
𝑑𝑠0
𝑑𝑧 −1
𝜏𝑞
𝑑𝑞0
𝑑𝑧 (13)
and substitute (12) into (11), which becomes (defining 𝑃′=𝑃−𝑃0)638
u0· ∇𝑃′+𝑁 𝐺 𝑀 𝑆
˜𝜏𝑞𝑃′=𝜒𝑤𝑑𝐿 .(14)
Here, 𝑤𝑑𝐿 is given by linear mountain wave theory, in two horizontal dimensions under the639
Boussinesq approximation, by (Smith 1979):640
ˆ𝑤𝑑(𝑘𝑥, 𝑘𝑦, 𝑧)=𝑖 𝜎 ˆ
ℎ(𝑘𝑥, 𝑘𝑦)𝑒𝑖𝑚 (𝑘𝑥, 𝑘 𝑦)𝑧(15)
where 𝑘𝑥and 𝑘𝑦are the horizontal wavenumbers, hats denote Fourier transforms, 𝜎=𝑘𝑥𝑢0+𝑘𝑦𝜐0,641
and 𝑧is the vertical coordinate. Defining 𝐾2=𝑘2
𝑥+𝑘2
𝑦, the vertical wavenumber 𝑚(𝑘𝑥, 𝑘𝑦)is642
𝑚=
sgn(𝜎)𝐾2𝑁2
𝜎2−1if 𝜎2< 𝑁2
𝑖𝐾21−𝑁2
𝜎2if 𝜎2> 𝑁2
.(16)
Fourier-transforming (14) and using (15) gives a closed expression for the Fourier-transformed643
precipitation anomaly ˆ
𝑃′:644
ˆ
𝑃′(𝑘𝑥, 𝑘𝑦)=𝑖 𝜎 𝜒
𝑖𝜎 +𝑁 𝐺 𝑀 𝑆
˜𝜏𝑞
ˆ
ℎ(𝑘𝑥, 𝑘𝑦)h𝑒𝑖𝑚 (𝑘𝑥, 𝑘 𝑦)𝑧i𝐿.(17)
The main controlling parameters are topography ℎ(𝑥), background wind 𝑢0, stratification 𝑁and645
a background moisture lapse rate. We note that in this model, the lower troposphere is defined646
between 1 km and 3 km above sea level. With this choice, mountain waves that have small647
vertical wavelengths may have positive temperature anomalies and negative moisture anomalies in648
the lower troposphere upstream of topography, and the model predicts small or negative rainfall649
enhancement in these cases. For 𝑁≃0.01 s−1, this happens when 𝑈 < 8 m s−1; the model is not650
31
recommended for use below this wind speed without some attention to redefining the vertical span651
of the lower troposphere, as well as taking thermal forcing into account. We now apply this model652
to the real-world tropics.653
b. Comparing observed and modeled rainfall distributions654
The ingredients comprising the above theory (weak temperature gradient approximation,661
quasiequilibrium precipitation closure) make it especially suited to tropical regions. SB04 de-662
veloped a model of mechanically forced orographic rainfall for convectively stable flows that has663
been used to represent midlatitude orographic precipitation. While SB04 did not intend their model664
for use in tropical regions, it is arguably the most widely used theoretical model of orographic665
precipitation, and as such provides a point of comparison with the present theory. Their model666
assumes that condensation results from ascent in a saturated atmosphere (see (1)). Unlike the667
upslope model, however, vertical motion is computed using linear mountain wave theory, and668
the effects of finite hydrometeor growth times and downwind advection are parameterized. The669
fundamental difference between the models of SB04 and NB22 is the mechanism linking mountain670
waves to precipitation: in the former, rain is associated with the ascent rate 𝑤, while in the latter,671
it is associated with vertical displacement of the lower-free-troposphere from a background state.672
This results in shorter length scales for the upstream enhancement of rainfall and rain shadows673
in SB04’s model. This can be understood qualitatively with the idealized topographic profile674
used in the Appendix, which decays as ℎ(𝑥) ∝ 𝑥−2upstream of the mountain; while the vertical675
displacement should scale approximately like ℎ(𝑥), the vertical motion will scale as 𝑑ℎ/𝑑𝑥 and676
thus have a faster decay rate of 𝑥−3.677
We compare observed and modeled seasonal-mean rainfall maps4in the Western Ghats in Fig.678
12. Both the SB04 and NB22 models use a uniform static stability; we choose 𝑁=0.01 s−1, which679
corresponds to a lapse rate of 6.5 K km−1, close to the free-tropospheric lapse rate in the Ghats.680
Because tropical lapse rates are steeper than moist adiabats, we do not use SB04’s “moist static681
stability” (which is negative in all regions) to calculate stationary mountain waves in the SB04682
model. SB04 further require a moist adiabatic lapse rate, taken as Γ𝑚=4.3 K km−1(corresponding683
to a lower-tropospheric average for a surface temperature of 300 K), and hydrometeor growth and684
4For both models, the domain shown in Fig. 12 is padded to a square domain of side length 7500 km, with topography smoothed down to zero
elevation 100 km outside of the main domain.
32
Fig. 13. Cross-sections of observed and modeled precipitation in all regions, along the direction of the
seasonal-mean wind. The insets show the orientation and width of the areas used to define cross sections (the
background shows mean observed precipitation from TRMM PR and GPM DPR, as in Fig. 3). The gray shadings
represent topography. The dark blue lines are observed mean precipitation during each region’s rainiest season.
Other lines show precipitation from the Nicolas and Boos (2022) theory (black), the Smith and Barstad (2004)
theory (solid green), and the upslope model (dashed green).
655
656
657
658
659
660
fallout times, both taken as 1000 s (as suggested in SB04). To account for non-precipitating times,685
the SB04 perturbation precipitation rates are divided by the factor 2.5, chosen in NB22 to fit peak686
rain rates from SB04 to convection-permitting simulations. For the NB22 model, we choose a687
lower-tropospheric moisture lapse rate of −8 K km−1and NGMS=0.2, representative of all the688
regions studied herein. Finally, the background wind and precipitation rate are given in Table 4,689
chosen to match upstream values from ERA5 and TRMM PR/GPM DPR. Both theories (Fig. 12,690
panels b and c) produce an upstream precipitation peak that is commensurate with observations691
(around 20 mm day−1). As explained above, precipitation enhancement happens much closer to692
the ridge in the SB04 model, which fails to account for high precipitation rates over the Arabian693
sea upstream of the Western Ghats. It also predicts a second rainfall peak downstream, by the694
33
eastern coast of India, associated with vertical motion predicted by linear mountain wave theory695
there. This is unlike the NB22 model which features an extensive rain shadow. Although central696
and northeastern India do receive precipitation during summer (panel a), this is commonly thought697
to arise from the dynamics of synoptic-scale disturbances such as monsoon depressions (Sikka698
1977) rather than mountain wave ascent downstream of the Indian topography.699
For reference, Fig. 12d shows precipitation from the upslope model (eq. 2). We convert the700
condensation rate into a precipitation rate using an efficiency factor 𝜖=0.25, chosen to match peak701
precipitation rates in the Ghats. We use 0.25◦×0.25◦topography, as higher resolutions lead to702
unrealistic small-scale features in this model. Because it only predicts precipitation above mountain703
slopes, it does not account for any upstream rainfall enhancement. By design, this model predicts704
peak rainfall to occur on the steepest upstream slopes, and does capture a large part of the observed705
peak directly above the windward Ghats.706
We extend this analysis to all regions, and show cross-sectional averages of the observed and707
modeled mean precipitation rates in Fig. 13. The insets show the direction and width of the cross708
sections, which were chosen normal to topography and following the prevailing wind direction.709
Background wind speeds and precipitation rates are listed in Table 4. With the fixed precipitation710
efficiency 𝜖=0.25 that produced a match to the peak precipitation magnitude in the Western711
Ghats, the upslope model underestimates peak precipitation rates in nearly all other regions. Thus,712
in addition to missing the upstream enhancement of precipitation, this model requires region-713
specific tuning to yield accurate peak rainfall rates. The SB04 and NB22 models produce similar714
peak rain rates in all regions, differing primarily in the upstream extent of the orographic rainfall715
enhancement and in the leeside precipitation rates. The NB22 model accurately predicts the rainfall716
enhancement upstream of certain regions (especially the Western Ghats and Vietnam), while the717
SB04 model predicts rainfall to pick up much closer to the topography, at odds with observations.718
The description of orographic rainfall as the result of forced temperature and moisture perturbations719
in a lower-tropospheric quasiequilibrium state is thus consistent with observations there. In other720
regions (most notably the Philippines and PNG), both models greatly underestimate precipitation721
rates compared to observations. In the NB22 model, this failure results from an underestimation722
of the moisture anomaly 𝑞′
𝐿(not shown). We speculate that positive 𝑞𝐿perturbations are not only723
the result of orographic lifting in these regions, and that climatological mean large-scale ascent,724
34
Table 4. Parameters used in the precipitation models of Smith and Barstad (2004) and Nicolas and Boos (2022)
Region name 𝑢0(m s−1)- 𝜐0(m s−1)𝑃0(mm day−1)
Western Ghats 10 1 3
Myanmar 8 8 6
Vietnam -7 -5 4
Malaysia -7 -5 10
Philippines -8.5 -3 4
PNG -7.5 5.5 3
forced by non-orographic factors, plays a key role in producing the observed rainfall patterns. The725
fact that PNG is located within the SPCZ is consistent with this hypothesis.726
Differences between observed and modeled precipitation rates are also apparent downstream727
of the mountain ranges. The NB22 model seems to strongly overestimate the drying effect of728
orography there. The main reason for this flaw is that the model assumes a time-independent729
background wind, which leads the lee of mountains to be persistently warm and dry. In reality,730
some days exhibit reversed flow or have a stronger along-slope component, creating more favorable731
conditions for convection in the lee. Additionally, synoptic disturbances (such as monsoon de-732
pressions downstream of the Indian subcontinent) may occasionally propagate into these regions,733
contributing to small positive seasonal-average precipitation there. As explained above in the case734
of the Western Ghats, the SB04 model predicts higher leeside precipitation rates, because linear735
mountain wave solutions produce ascent there. This leads to localized downstream precipitation736
peaks that are not seen in observations.737
7. Discussion and conclusions738
Here we investigated the spatial and temporal distribution of mechanically forced orographic739
rainfall in six tropical regions. We showed that a buoyancy proxy, evaluated from reanalysis data,740
captures many aspects of both daily variations and the seasonal-mean spatial distribution of rainfall741
in all regions. In this framework, the interaction of orography with the background wind creates742
temperature and moisture anomalies in the lower troposphere, affecting the buoyancy of convective743
plumes and thereby controlling precipitation.744
This work confirms the important role of lower-free-tropospheric moisture (𝑞𝐿) in controlling745
temporal variations in orographic convection. In the absence of background horizontal moisture746
35
gradients, 𝑞𝐿variations would be fully controlled by orographic uplift, hence primarily by the747
cross-slope wind speed. The presence of large-scale 𝑞𝐿gradients leads alternate directions of748
wind anomalies to favor rainfall in some regions, namely down-moisture-gradient winds. These749
results indicate that mechanical forcing only exerts a partial control on rainfall variations in the750
regions studied. Together, these findings establish a new view of tropical orographic precipitation751
being enhanced by moistening of the lower troposphere due to both upslope flow and large-scale752
horizontal advection.753
Despite the nonlinear relationship between plume buoyancy 𝐵𝐿and precipitation, time-averaged754
𝐵𝐿captures many spatial features of observed seasonal-mean precipitation maps. Discrepancies755
appear in the rain shadows, where 𝐵𝐿(as estimated from a reanalysis) overestimates precipitation.756
This points to a possible limitation of the present framework, in which convective dynamics are757
assumed identical over oceans and in mountains, with mountains only affecting plume buoyancy.758
Nevertheless, our goal here is to provide a first-order understanding of the mechanisms govern-759
ing tropical orographic precipitation. We recognize that this approach neglects the influence of760
some aspects of orographic dynamics, such as strong wind shears and gravity wave breaking, on761
convection.762
We present a linear theory that predicts the time-mean rainfall distribution for arbitrary 2D763
topography and uniform wind. It quantifies the lower-tropospheric temperature and moisture per-764
turbations caused by stationary mountain waves, and takes into account the feedback of convection765
on the moisture distribution. The theory accurately predicts upstream rainfall in some regions,766
especially the Western Ghats and Vietnam. In other regions (mainly the Philippines and PNG),767
it yields weaker peak rainfall than observations. It is likely that mechanical forcing alone cannot768
explain the strong rain bands observed there. The presence of climatological-mean ascent, due to769
non-orographic factors (such as the SPCZ in PNG), plays a key role in setting the lower-tropospheric770
moisture gradients, hence the rainfall patterns, in these regions.771
The theoretical model presented herein only describes mechanically forced rainfall in tropical772
regions. As such, it is expected to work with small nondimensional mountain heights and suf-773
ficiently strong winds (we recommend its use for wind speeds of at least 8 m s−1). The model774
does not describe thermal forcing (expected to dominate in weak horizontal winds and/or large775
nondimensional mountain heights), nor is it suitable for moist convectively stable ascent cases,776
36
more common in midlatitude winter. Our use of the weak temperature gradient approximation777
for the moist mode, and neglect of the Coriolis parameter, may make it most appropriate for the778
tropics.779
One other limitation of this study is that it does not investigate the vertical structure of convection,780
which past work has shown varies in tropical orographic regions (Kumar and Bhat 2017; Shige781
and Kummerow 2016). However, we have demonstrated that the buoyancy framework accurately782
characterizes precipitation in the six regions studied, irrespective of the mean depth of convection.783
Furthermore, the theoretical model assumes a fixed but arbitrary vertical structure of upward784
motion, and is thus applicable to a wide range of tropical regions (perhaps with modification of785
the coefficients that depend on the vertical structure of ascent). However, the buoyancy framework786
might not apply in trade wind regions, which are characterized by very shallow convection beneath787
an inversion layer (for a study of orographic precipitation in the trades, see Kirshbaum and Smith788
2009).789
This work suggests that two ingredients are needed to accurately represent tropical orographic790
convection: free-tropospheric temperature and moisture anomalies generated by flow over terrain,791
and the dependence of convection on those thermodynamic perturbations. This implies that792
a coarse-resolution model with a good convective parameterization may perform well around793
orography, as long as the magnitude of lower-tropospheric vertical displacement over the terrain794
is captured. We hope that future work will investigate the representation of tropical orographic795
rainfall in climate models under this lens.796
37
Acknowledgments. This material is based on work supported by the U.S. Department of Energy,797
Office of Science, Office of Biological and Environmental Research, Climate and Environmental798
Sciences Division, Regional and Global Model Analysis Program, under Award DE-SC0019367.799
It used resources of the National Energy Research Scientific Computing Center (NERSC), which800
is a DOE Office of Science User Facility.801
Data availability statement. The code containing linear precipitation models, the code used in802
producing the figures, and the processed ERA5 and precipitation data are archived at Zenodo803
(Nicolas 2023).804
APPENDIX805
Lower-tropospheric temperature and moisture perturbations forced by an idealized ridge806
We consider an infinite two-dimensional (𝑥-𝑧) domain whose surface height is807
ℎ(𝑥)=ℎ𝑚
𝑙2
0
𝑥2+𝑙2
0
,(A1)
where 𝑙0is the mountain half-width and ℎ𝑚is the maximum height. This topographic profile,808
commonly known as a Witch-of-Agnesi, has a convenient Fourier transform, which renders the809
treatment of mountain wave solutions analytically tractable. The background horizontal wind speed810
𝑈and static stability 𝑁are supposed uniform. We now estimate mechanically forced temperature811
perturbations using linear mountain wave theory, which is approximately valid under the assumption812
of small nondimensional mountain height 𝑁 ℎ𝑚/𝑈. Queney (1948) gives an analytical solution for813
𝜁(𝑥, 𝑧), the vertical displacement at 𝑥of a streamline originating upstream at 𝑧:814
𝜁(𝑥, 𝑧)=ℎ𝑚
cos(𝑁 𝑧/𝑈)𝑙2
0−sin(𝑁 𝑧/𝑈)𝑙0𝑥
𝑥2+𝑙2
0
.(A2)
This expression is valid when 𝑙0𝑁/𝑈≫1, which is largely satisfied with a half-width 𝑙0≃100815
km, 𝑈≃10 m s−1, and 𝑁≃0.01 s−1. With uniform static stability, and in the absence of diabatic816
processes, a parcel lifted by 𝜁experiences a cooling of magnitude 𝜁 𝑑𝑠0/𝑑𝑧. Thus, the lower-free-817
38
tropospheric temperature perturbation is818
𝑇′
𝐿(𝑥)=−ℎ𝑚
𝑑𝑠0
𝑑𝑧
𝛼𝑐𝑙2
0−𝛼𝑠𝑙0𝑥
𝑥2+𝑙2
0
,(A3)
where 𝛼𝑐=[cos(𝑁 𝑧/𝑈)]𝐿,𝛼𝑠=[sin(𝑁𝑧/𝑈)]𝐿, and [·]𝐿denotes a lower-tropospheric average.819
𝑠0(𝑧)is the background dry static energy profile profile (divided by 𝑐𝑝). Minimizing (A3) gives820
the peak lower-tropospheric temperature perturbation:821
𝑇′
𝐿,max =−ℎ𝑚
𝑑𝑠0
𝑑𝑧 𝛼2
𝑐+𝛼2
𝑠+𝛼𝑐,(A4)
Evaluating 𝜕𝑇′
𝐿,max /𝜕𝑈 with a 1-km high mountain and 𝑁=0.01 s−1gives (5).822
The peak moisture perturbation is given by the same expression as (A4), replacing 𝑑𝑠0/𝑑𝑧 with823
𝑑𝑞0/𝑑𝑧 (where 𝑞0(𝑧)is a background moisture profile). Using a lower-free-tropospheric moisture824
lapse rate representative of our regions (8 K km−1), we obtain (6).825
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