Sensitivity of tropical orographic precipitation to wind speed with implications for future projections

Abstract

Some of the rainiest regions on Earth lie upstream of tropical mountains, where the interaction of prevailing winds with orography produces frequent precipitating convection. Yet, the response of tropical orographic precipitation to the large-scale wind and temperature variations induced by anthropogenic climate change remains largely unconstrained. Here, we quantify the sensitivity of tropical orographic precipitation to background cross-slope wind using theory, idealized simulations, and observations. We build on a recently developed theoretical framework that predicts enhanced seasonal-mean convective precipitation in response to cooling and moistening of the lower free-troposphere by stationary orographic gravity waves. Using this framework and convection-permitting simulations, we show that higher cross-slope wind speeds deepen the penetration of the cool and moist gravity wave perturbation upstream of orography, resulting in a mean rainfall increase of 20–30 % per m s−1 increase in cross-slope wind speed. Additionally, we show that orographic precipitation in five tropical regions exhibits a similar dependence on changes in cross-slope wind at both seasonal and daily timescales. Given next-century changes in large-scale winds around tropical orography projected by global climate models, this strong scaling rate implies wind-induced changes in some of Earth's rainiest regions that are comparable with any produced directly by increases in global mean temperature and humidity.

Full text

Sensitivity of tropical orographic precipitation to wind speed with
implications for future projections
Quentin Nicolas1and William R. Boos1,2
1Department of Earth and Planetary Science, University of California, Berkeley, CA 94720
2Climate and Ecosystem Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720
Correspondence: Quentin Nicolas (qnicolas@berkeley.edu)
Abstract. Some of the rainiest regions on Earth lie upstream of tropical mountains, where the interaction of prevailing winds
with orography produces frequent precipitating convection. Yet, the response of tropical orographic precipitation to the large-
scale wind and temperature variations induced by anthropogenic climate change remains largely unconstrained. Here, we
quantify the sensitivity of tropical orographic precipitation to background cross-slope wind using theory, idealized simulations,
and observations. We build on a recently developed theoretical framework that predicts enhanced seasonal-mean convective5
precipitation in response to cooling and moistening of the lower free-troposphere by stationary orographic gravity waves. Using
this framework and convection-permitting simulations, we show that higher cross-slope wind speeds deepen the penetration of
the cool and moist gravity wave perturbation upstream of orography, resulting in a mean rainfall increase of 20–30% per m s−1
increase in cross-slope wind speed. Additionally, we show that orographic precipitation in five tropical regions exhibits a similar
dependence on changes in cross-slope wind at both seasonal and daily timescales. Given next-century changes in large-scale10
winds around tropical orography projected by global climate models, this strong scaling rate implies wind-induced changes in
some of Earth’s rainiest regions that are comparable with any produced directly by increases in global mean temperature and
humidity.
1 Introduction
Mountains alter the distribution of rainfall in many tropical regions, including South and Southeast Asia (Shige et al., 2017;15
Ramesh et al., 2021), the Maritime continent (As-syakur et al., 2016), and the Central Andes (Espinoza et al., 2015). Because
orographic precipitation is an essential source of freshwater for much of the tropics’ population (Viviroli et al., 2020), it is
crucial to understand its interannual variability and its potential changes with anthropogenic global warming. Although such
changes in seasonal-mean tropical precipitation at large spatial scales have been widely studied (e.g., Byrne et al., 2018; Wang
et al., 2021), changes in low-latitude orographic rainfall have been the subject of much less investigation.20
Most tropical precipitation stems from convective weather systems (Houze et al., 2015), which are influenced by mountains
in two main ways (Kirshbaum et al., 2018): thermal forcing (via radiative heating of sloping terrain) and mechanical forcing
(forced ascent of background flow over orography). This paper is only concerned with mechanical orographic forcing, which
produces some of the most intense regions of precipitation in the tropics. Hereafter, “orographic rainfall” will be used to refer
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to convective rainfall altered by mechanical orographic forcing. This type of precipitation is controlled by both thermody-25
namic factors (e.g., static stability and humidity) and dynamical factors. Understanding these controls, in combination with
projected changes in large-scale conditions upstream of mountains, is key to anticipating future changes in rainfall hotspots
and freshwater resources.
Decades of observations have facilitated progress in understanding orographic rainfall, with some studies finding purely
thermodynamic controls, such as sea-surface temperature (SST) variations over the Arabian sea driving rainfall variations over30
India’s Western Ghats (Vecchi and Harrison, 2004; Roxy and Tanimoto, 2007). Other studies have proposed large-scale dy-
namical controls, such as shifts in background winds, as a cause of interannual variability (Varikoden et al., 2019; Shrivastava
et al., 2017). Using a global climate model with parameterized convection, Rajendran et al. (2012) suggested a future reduc-
tion in rainfall over the Western Ghats (despite an increase in total Indian monsoon rainfall) because of weakened winds over
the southern part of the region and increased static stability. However, none of these studies delineate clear mechanisms cou-35
pling orographic rainfall with large-scale temperature or wind changes. Here we aim to understand and quantify how changes
in large-scale horizontal winds alter tropical orographic rainfall, recognizing that global climate change includes such wind
changes together with changes in global mean temperatures and humidities (we leave the response to the large-scale thermo-
dynamic state for future work).
While it may seem evident that orographic rainfall increases with background wind speed, the magnitude of this dependence40
is less obvious. A null hypothesis can be obtained using the “upslope flow” theory (Roe, 2005), which posits that precipitation
is proportional to the surface vertical motion U∂h/∂x (Uis background wind in the cross-slope direction x, and his surface
height). Under this argument, considering a typical basic-state Uof 10 m s−1,a1m s−1change in cross-slope wind should
yield a 10% change in orographic rain. The upslope flow model turns out to be a poor descriptor of observed tropical rainfall
(Nicolas and Boos, 2024), and here we strive to obtain a more reliable estimate for the sensitivity of tropical orographic rainfall45
to cross-slope wind by building on a recently developed theoretical framework (Nicolas and Boos, 2022). We obtain a much
larger scaling rate than the above ∼10 % (m s−1)−1, then verify this scaling rate in convection-permitting simulations and
observations. We end by discussing the implications for future rainfall changes in some tropical orographic regions.
2 Sensitivity of tropical orographic precipitation to wind speed: theoretical basis
We present a new scaling for the sensitivity of orographic rainfall to changes in background wind, based on a recent theory50
that couples gravity wave dynamics with a convective closure (Nicolas and Boos, 2022). We focus on regions upstream of
mountain peaks, where precipitation rates are highest. Orographic precipitation in this theory stems from the response of
precipitating clouds to a stationary mountain wave (Fig. 1A). The orographic precipitation perturbation P′, relative to an
upstream background precipitation rate P0, is proportional to the mean buoyancy perturbation created by the wave’s lower-
free-tropospheric perturbations of temperature and humidity (denoted T′
Land q′
L), and a boundary layer equivalent potential55
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temperature anomaly θ′
eB (Ahmed et al., 2020):
P′=βθ′
eB
τb
+q′
L
τq
−T′
L
τT,(1)
where τb,τq, and τTare adjustment timescales (Appendix A). Here qis in temperature units (scaled by the latent heat of
vaporization divided by the specific heat of dry air Lv/cp), and βis a constant converting a convective heating rate into
a precipitation rate (β=cppT/(Lvg), where pT≃800 hPa is the tropospheric depth). Hereafter, boundary layer averages60
(subscript B) are taken between the surface and 900 hPa, and lower-free tropospheric averages (subscript L) from 900 hPa to
600 hPa; sensitivity of results to these choices are discussed below. (1) depends positively on θ′
eB because it increases undilute
plume buoyancy, and depends positively on q′
Lthrough its effect on entrainment (the entrainment of moister free-tropospheric
air is less efficient at reducing the buoyancy of ensembles of convective plumes). The negative dependence on T′
Larises through
its combined effect on undilute buoyancy (a colder lower-free-troposphere yields higher convective available potential energy)65
and on the subsaturation of the free troposphere (Ahmed et al., 2020).
Our simplest scaling further neglects variations in boundary layer equivalent potential temperature (θ′
eB = 0) because it is
more strongly affected by SST variations or land surface fluxes than by mechanical orographic forcing (Nicolas and Boos,
2024). This assumption is later relaxed.
The thermodynamic perturbations T′and q′result from the background wind, with speed U, being lifted by orography, as70
well as the convective response. For relatively low mountains with a weak convective feedback, these perturbations can be
approximated by a linear, adiabatic, stationary mountain wave (nonlinear effects become important when the nondimensional
mountain height Nh0/U ≳1, where Nis the Brunt-Väisälä frequency and h0the peak mountain height). The mountain wave
produces positive vertical displacement ηin the lower troposphere upstream of a ridge, resulting in a cool and moist perturbation
(e.g., Fig. 1A). These adiabatic perturbations–denoted TaL and qaL–produce, through (1), a precipitation perturbation75
Pa=β−TaL
τT
+qaL
τq≃β1
τT
ds0
dz−1
τq
dq0
dzηL,(2)
where dq0/dzis a lower-tropospheric moisture stratification and ds0/dzis a lower-tropospheric dry static energy stratification
(divided by cp).
Convection feeds back on these perturbations, modifying the precipitation given by (2). For example, enhanced precipitating
convection upstream of orography (Pa>0) heats and dries the troposphere, thereby weakening the cool and moist lower-80
tropospheric perturbation. The system can be closed using conservation of temperature and moisture with other constraints
from tropical dynamics (Nicolas and Boos, 2022), yielding a secondary precipitation perturbation Pm, obeying
dPm
dx+Pm+Pa
Lq
= 0,(3)
where Lqis a length scale for the relaxation of lower-free-tropospheric moisture by convection (Appendix A). For U= 10
m s−1,Lq≃3000 km, which is large compared with the horizontal length scale of the orographic forcing. Thus, we expect85
Pm≪Pa.
For an idealized mountain of peak height 500 m, the solutions (Appendix A) feature a broad orographic enhancement of
precipitation upstream of the mountain (Fig. 1A), peaking around 5 mm day−1on the upwind slope. The total precipitation
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-1000 -500 0 500 1000
x (km)
200
400
600
800
1000
p (hPa)
A
1.0 0.5 0.0 0.5 1.0
T
0
(K)
200
400
600
800
1000
p (hPa)
B
Theory, 10 m s 1
Theory, 12 m s 1
Simul., 10 m s 1
Simul., 12 m s 1
Pa
, Theory
P
0
, Theory
P
0
, Simul.
0
10
20
30
% (m s 1)1
Cln
P
0
max
ln
P
0
[
x
max ±30 km]
4
0
4
8
12
mm/day
P
0
, Theory
Pa
, Theory
P
0
, Simul.
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
T
0
(K)
500 250 0 -250 -500
(m)
Figure 1. Orographic perturbations of temperature and precipitation in linear theory and a cloud resolving model, with sensitivities to wind
speed. (A) Temperature perturbation Ta(x,p)in a stationary linear mountain wave with uniform static stability N= 0.01 s−1and cross-
slope wind U= 10 m s−1, for a 500 m mountain (color shading), precipitation perturbation P′= max(Pa+Pm,−P0)from the linear
theory (dark blue line, Eqs. 2 and 3), and the component of P′due to the adiabatic mountain wave alone Pa(cyan line). P′in a convection-
permitting simulation (see text) is shown in green. The gray line shows surface height. Tais proportional to the vertical displacement η(x,p)
in the mountain wave, with scale shown at the bottom of the colorbar. (B) Vertical structure of temperature perturbations at x=−100 km
in the theory (orange) and simulations (red), with U= 10 m s−1(solid) and 12 m s−1(dashed). Arrows indicate the vertical stretching of
the orographic gravity wave with increased wind. (C) Fractional increase in the maximum precipitation perturbation (hatched bars) and the
precipitation perturbation averaged within 30 km of the maximum (solid), in the linear theory with and without convective feedback, and in
the simulations. Simulation results display a 95% confidence interval (obtained by block bootstrapping, using 20 day blocks).
anomaly P′=Pa+Pmis only about 10 % smaller there than the anomaly Pathat neglects convective feedback on the gravity
wave, confirming the small damping effect of the feedback. A rain shadow extends downstream of the ridge, and negative90
precipitation values are prevented by enforcing P′≥ −P0, where we take P0= 4.5 mm day−1to conform with simulations
presented below.
The sensitivity of P′to the background wind speed Uarises through the vertical structure of ηupstream of the mountain,
which is wave-like, with wavelength λz= 2πU/N (Fig. 1A). In the linear theory (2), ηis proportional to −Ta. In order to later
compare results with simulations (for which temperature perturbations are more readily available than η), we thus show the95
vertical structure of Tain Fig. 1B (solid orange line). An increase in U(dashed orange line) results in deeper penetration of
the ascending region of the wave (where Ta<0), which amplifies Ta,L upstream of orography. Similarly, qa,L is amplified by
the same amount. By (2), this produces an increase in Pa, and, because the convective feedback Pmis modest, also in P′.
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The precipitation increase produced by an increase in background wind Uis quantified in Fig. 1C using two metrics: max-
imum precipitation perturbation P′
max, and precipitation perturbation averaged within 30 km of the maximum P′
[xmax ±30 km].100
When Uincreases from 10 m s−1to 12 m s−1, these quantities respectively increase by 27 % (m s−1)−1and 30 % (m s−1)−1.
Most of these increases (25 % (m s−1)−1and 27 % (m s−1)−1) are explained by changes in Pa. This is a large sensitivity
compared with the 10 % (m s−1)−1expected from simple upslope flow considerations (see Introduction). Here, the increase
stems from deeper vertical penetration of orographic ascent resulting in a stronger upstream cool and moist lower-tropospheric
anomaly, in turn yielding a stronger precipitation anomaly. These sensitivities exhibit little dependence on convective time105
scales: halving or doubling them changes the sensitivities by less than 2 percentage points. However, sensitivities vary strongly
with the levels used to define the lower free troposphere: lowering its top to 650 hPa from 600 hPa changes the sensitivity of
P′
max to 19 % (m s−1)−1, while raising its top to 550 hPa yields 34 % (m s−1)−1. Using a convective closure that depends
more continuously on thermodynamic perturbations at different levels (e.g., Kuang, 2010) may offer an avenue of improve-
ment, at the expense of conceptual simplicity. Next, we use convection-permitting simulations and observations to validate110
these theoretical sensitivities.
3 Sensitivity in idealized simulations
3.1 Model setup
Our model setup is very similar to that used in Nicolas and Boos (2022) and is described here succinctly. We use the Weather
Research and Forecasting model (WRF-ARW, version 4.1.5, Skamarock et al., 2019) to represent a doubly periodic long115
channel (9810 km wide in xby 198 km in y), with a y-invariant 500 m-high mountain identical to that used in the theory.
The 3 km horizontal grid spacing and 60 terrain-following vertical levels (spanning from the surface to 10 hPa) are used to
represent deep convective clouds without a convective parameterization. The domain is ocean-covered with a fixed SST of
300 K, except over the mountain where we employ the Noah-MP land surface scheme (Niu et al., 2011; Yang et al., 2011),
with a no-flux bottom boundary condition. We fix the Coriolis parameter at 20◦latitude, and prescribe a constant background120
meridional pressure gradient which maintains a uniform background geostrophic zonal wind with speed U. We use a state of
perpetual equinox (with a diurnal cycle), and calculate radiation interactively every hour using the RRTMG scheme (Iacono
et al., 2008). Turbulent fluxes are calculated diffusively with fixed horizontal diffusion of 300 m−2s−1and vertical diffusion of
100 m−2s−1, with the Mellor-Yamada-Janji´
c scheme (Mellor and Yamada, 1982; Janji´
c, 2002) used for boundary layer fluxes.
We use the Thompson scheme for microphysics (Thompson et al., 2008).125
3.2 Changes in precipitation and free-tropospheric thermodynamic perturbations
We run two simulations for 1000 days each (after discarding 250 days of spin-up), which only differ in background winds: one
has U= 10 m s−1, the other U= 12 m s−1. In the 10 m s−1run, P′(Fig. 1A, green line) has numerous similarities with the
theory, especially the peak precipitation rate and length scale of upstream orographic enhancement. Peak rainfall in the theory
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4
0
4
8
mm day 1
A
U
= 10 m s 1
U
= 12 m s 1
U
= 10 m s 1
U
= 12 m s 1
P
0
:
(
q
0
L
q
T
0
L
T
)
:
750 500 250 0 250 500 750
x (km)
4
0
4
8
mm day 1
B
U
= 10 m s 1
U
= 12 m s 1
U
= 10 m s 1
U
= 12 m s 1
P
0
:
(
q
0
L
q
T
0
L
T
+
0
eB
b
)
:
750 500 250 0
x (km)
1
0
1
mm day 1
C
[
q
0
L
/
q
]
[
T
0
L
/
T
]
[
0
eB
/
b
]
(
q
0
L
q
T
0
L
T
)(
q
0
L
q
T
0
L
T
+
0
eB
b
)
P
0
0
10
20
30
% (m s 1)1
Dln
P
0
[
x
max ± 30 km]
Figure 2. Drivers of the response of orographic precipitation to wind changes in convection-permitting simulations (A) Mean precipitation
perturbation P′for the two simulations (U= 10 m s−1and U= 12 ms−1, green lines), and an estimate of P′by a version of the buoyancy-
based closure (Eq. 1) that only considers TLand qLperturbations, clipped to eliminate negative total precipitation (blue lines). (B) As in
(A), except using the full buoyancy-based closure (Eq. 1), shown as magenta lines. (C) Changes with increased wind in the three thermo-
dynamic quantities in the buoyancy-based closure: lower-free-tropospheric moisture (blue), lower-free-tropospheric temperature (yellow),
and boundary-layer equivalent potential temperature (black). Each quantity is divided by its corresponding timescale from the convective
closure. (D) Sensitivity of the precipitation perturbation averaged within 30 km of its maximum (green bar), and estimates of this using the
two versions of the convective closure. We show 95% confidence intervals (obtained by block bootstrapping, using 20 day blocks) for each
sensitivity estimate. In A-C, vertical black lines mark the mountain’s upstream boundary and peak.
is shifted ∼25 km upstream compared to the simulations, a defect attributable to the convective closure: using (1) to diagnose130
P′with temperature and moisture perturbations from the simulations, instead of from a linear gravity wave solution, results in
a similar shift (Fig. 2A). One reason for this upstream bias is the neglect of the downwind drift of hydrometeors, with a time
scale of O(1000) s (Smith and Barstad, 2004) that can shift the precipitation profile ∼10 km. A second reason is the theory’s
vertically uniform dependence of rainfall on Tand qperturbations in the lower troposphere: giving higher weight to low levels
would shift the rainfall maximum downstream because maxima in Tand qperturbations shift downstream at lower levels (Fig.135
1A). Stronger differences appear between the theoretical and simulated P′downstream of the mountain, which we show below
is due to neglect of θeB variations in our simplest scaling.
Both P′
max and P′
[xmax ±30 km]increase between 20 and 30 % (m s−1)−1between the two simulations, commensurate with
the theoretical prediction (Fig. 1C). Is this increase attributable to a deeper penetration of the stationary gravity wave cooling
and moistening the lower free troposphere at higher U, as our theory suggests? To assess this we evaluate T′(x=−100 km,p)140
in both runs (Fig. 1B, red lines), where the reference profile is averaged over x∈(−4000 km, −2500 km).T′displays a gravity
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wave structure in many ways similar to that of the adiabatic, linear T′. With increased wind, the cool perturbation penetrates
deeper (shown by black arrows in Fig. 1B), decreasing T′
L. While quantitative differences with the theory’s T′arise because
static stability is not vertically uniform in the simulations, the change in T′with increased wind is well captured by linear
theory.145
To assess whether this deepening of the T′
Lstructure, with the accompanying changes in q′
L, can quantitatively explain the
increase in P′, we compute precipitation from the linear closure used in our theory: P′
qT =β(q′
L/τq−T′
L/τT)(Fig. 2A, blue
lines). This diagnostic captures the magnitude of the simulated precipitation peak for U= 12 m s−1with a similar upstream
shift as in the theory, but shows a too-weak dependence on U. Specifically, the change in upstream P′
qT (averaged within 30
km of its maximum) between both simulations is only 7 % (m s−1)−1(Fig. 2D, blue bar), indicating that the increase in peak150
precipitation with increased wind is only partly attributable to stronger lower-tropospheric Tand qperturbations.
3.3 Changes in boundary-layer moist entropy
We now show that this discrepancy can be resolved by considering variations in θeB, and that these variations are controlled by
the same mountain wave dynamics discussed earlier. Using θ′
eB in conjunction with T′
Land q′
L(all diagnosed from simulations)
in (1) generally improves comparison to the simulated P′, better fitting upstream rain rates and the rain shadow (Fig. 2B,155
magenta lines). The value of this diagnosed precipitation, β(q′
L/τq−T′
L/τT+θ′
eB /τb), still averaged within 30 km of its
maximum, increases by 17 % (m s−1)−1, a value much closer to the 24 % (m s−1)−1change in simulated P′(95% confidence
intervals on these two values overlap; Fig. 2D). The increase in θ′
eB and the decrease in T′
Lcontribute equally to the increase
in the P′maximum, while changes in q′
Lcontribute negligibly (Fig. 2C). Thus, the quantitative match between theoretical
and simulated precipitation changes in Fig. 1C appears in part fortuitous: the absence of free-tropospheric moistening with160
increased wind in simulations is compensated for by an increase in θ′
eB .
We now show that the increase in θ′
eB with increased wind can also be attributed to the vertical stretching of the orographic
ascent pattern that occurs with increasing U. The difference (denoted by a ∆) between boundary layer θ′
ein the 12 m s−1and
10 m s−1runs is shown in Fig. 3A, with its mass-weighted vertical average ∆[θ′
eB ]shown in Fig. 3B (solid black). θ′
eB is about
0.3K warmer over the upwind slope with increased wind. In order to understand this increase, we diagnose the θ′
ebudget over165
a subset of pressure levels which do not cross the topography, namely 900–950 hPa. ∆[θ′
e]averaged over these levels has a
qualitatively similar structure to ∆[θ′
eB ]upstream of the mountain peak (Fig. 3B), with modest variations for x < −100 km
and a sharp increase above the upwind slope.
The θ′
ebudget is
u∂θ′
e
∂x +w∂θe
∂z =Qθe,(4)170
where all quantities are time and meridional means, and Qθeis an apparent source of θedue to transients (in the boundary
layer, its main contributors are surface fluxes, turbulent mixing and penetrative downdrafts). We evaluate the two terms on the
left-hand side from temporally and meridionally averaged u,w and θefields, and compute Qθeas a residual. Upstream of the
ridge top, little accuracy is lost if we replace uby the background wind Uand ∂θe/∂z by a constant ∂θe0/∂z. The latter is
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900
950
1000
pressure
A
0.4
0.0
0.4
K
B
[
0
eB
][
0
e
,[900 950]]
0.02
0.00
0.02
K km 1
C
[
0
e
,[900 950]
x
]
[
(
w
[900 950]/
U
)
e
0
z
]
[
Qe
,[900 950] /
U
] residual
1000 750 500 250 0 250 500 750 1000
x (km)
0.001
0.000
0.001
nondim.
D
[
w
[900 950]/
U
], WRF
[
w
[900 950]/
U
], Long's equation
0.8
0.4
0.0
0.4
0.8
[
0
e
]
(K)
Figure 3. θ′
eB variations between the 10 m s−1and 12 m s−1simulations, and their physical drivers. Throughout the figure, ∆[·]≡
[·]12m s−1−[·]10m s−1. (A) ∆[θ′
e]in the boundary layer (shading). The thick gray line shows the topography. (B) ∆[θ′
eB ](solid) and ∆[θ′
e]
averaged between 900 hPa and 950 hPa (dashed). Note the qualitative similarity between the two profiles upstream of the mountain, with
a sharp increase over the upwind slope. (C) Differential budget of θ′
eaveraged over [900 hPa,950 hPa] between the two runs. Differences
in horizontal gradients of θ′
e(black) are balanced by differences in vertical advection (red line) and differences in diabatic sources (orange
line). The residual (due to horizontal variations in uand ∂θe/∂p) is shown as a thin blue line. Note the sharp peak in the black line above the
mountain’s upwind slope, mostly contributed to by changes in vertical advection. (D) Change in ascent slope w/U between the two runs, at
925 hPa, as diagnosed from simulations (red line) and from a nonlinear theory (dashed red line, see text). In panels C and D, all terms from
simulations are smoothed with a Gaussian filter of standard deviation 6 km to filter out small-scale noise from finite differentiation. In all
panels, vertical black lines indicate the upstream boundary and peak of the mountain, and gray shading indicates the downstream region, that
is not relevant to the main discussion.
averaged 2000–4000 km upstream of the mountain (∂θe0/∂z =−19.8 K km−1at 925 hPa). Hence, we re-write the budget as175
∂θ′
e
∂x ≃ − w
U
∂θe0
∂z +Qθe
U.(5)
Over the ocean part of the domain (x < −100 km), horizontal gradients in θ′
eare constrained to be small by the uniform SST,
so the two terms on the right-hand side approximately balance. Over the ridge, surface temperature is not imposed, so variation
in either of the right-hand side terms can accompany variations in θegradients.
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Fig. 3C shows the difference (denoted by a ∆) in each of the terms in (5) between the 12 m s−1and 10 m s−1runs,180
averaged over 900–950 hPa. Because ∂θ′
e/∂x is small in each run for x < −100 km, ∆[∂θ′
e/∂x]is also small there. Over the
mountain, the sharp increase in ∆θ′
eseen in Fig. 3B translates into a large peak in ∆[∂θ′
e/∂x]around x∈(−100 km, −50
km). Importantly, most of this peak is associated with the change in vertical advection (red line).
We now argue that this change in vertical advection is explained by mountain wave dynamics. Because the vertical θe
gradient has been fixed, this increase in vertical advection is driven by an increase in the ratio of vertical to horizontal flow185
w/U . Why does this ratio increase? At the surface, where w=U ∂h/∂x, it is equal to the surface slope and cannot change
as Uis increased. Aloft, however, the ascent spreads over a deeper layer with higher U(due to the vertical expansion of the
mountain wave discussed in the main text), which causes an increase in w/U. This is illustrated in Fig. 3D, where we compare
the change in w/U from simulations and from mountain wave theory. We use Long’s equation (Long, 1953) to solve for the
mountain wave, as the linearization of the boundary condition in classical linear mountain wave theory yields inaccuracies in190
the boundary layer. Neglecting damping, the vertical displacement ηsatisfies
∂zz η+N2
U2η= 0, η(z=h(x)) = h(x),(6)
with a radiation upper boundary condition. We solve (6) using an iterative procedure (Lilly and Klemp, 1979), and obtain w
as U∂η/∂x. Good agreement between the simulated and theoretical change in w/U indicates that mountain wave dynamics
explain the stronger boundary layer θ′
eperturbation and, ultimately, the stronger rainfall peak with increased U.195
4 Observed sensitivity at various time scales
Do observations support the above theoretical and model-derived sensitivities? The framework developed in this work quan-
tifies changes in the seasonal-mean orographic precipitation perturbation P′=P−P0, where Pand P0are the total and
background precipitation rates, respectively. We now aim to evaluate the observed dependence of P′on variations in the
background cross-slope wind U, recognizing that changes in Umay also be associated with changes in P0. Yet, all the oro-200
graphic regions we consider lie downstream of an ocean, over which rainfall observations at the fine spatial scales needed
here are only available for the past two decades. Therefore, because P0is 3–5 times smaller than P′in three of our regions,
we first neglect P0and estimate the sensitivity of Pto interannual changes in Uusing gauge-based rainfall observations. We
then estimate the sensitivity of P′to Uusing two other products: satellite-estimated daily precipitation for 2001–2020, and
reanalysis-derived seasonal-mean precipitation for 1960–2015 (Appendix B). These two approaches come with a caveat: one205
may question whether daily-mean P′scales similarly to seasonal-mean P′with changes in U1; and reanalysis precipitation
is largely produced by a model prior to 1979. However, the consistency of the estimated sensitivities across regions and time
scales suggest that the result is robust.
We evaluate orographic rainfall variations in five regions of South and Southeast Asia: the west coasts of India and Myanmar,
and the east coasts of Vietnam, Malaysia, and the Philippines (see Appendix B and Fig. S1 in the Supplement for details on210
1For a discussion of how the precipitation-buoyancy relationship (1) behaves at different time scales, see Ahmed et al. (2020) (their Fig. 7).
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10 m/s
70°E 75°E 80°E 85°E 90°E
5°N
10°N
15°N
20°N
25°N
A
70°E 75°E 80°E 85°E 90°E
B
Western Ghats
Myanmar
Vietnam
Philippines
Malaysia
0
20
40
% (m s 1)1
CAPHRODITE P ERA5 P' IMERG P' (daily)
0
6
12
18
24
30
mm day 1
30
20
10
0
10
20
30
% (m s 1)1
Figure 4. Evidence for large precipitation scaling rates from observational and reanalysis data at multiple time scales. (A) Observed summer
mean (June-August, 1960-2015) precipitation over India and 100 m winds from reanalysis. Gray contours mark 500 m surface height. (B)
Sensitivity of summer-mean precipitation to cross-slope wind speed upstream of the Western Ghats. Regions hatched in white satisfy the
false discovery rate criterion (Wilks, 2016) with α= 0.1. Winds are averaged in the blue dashed rectangle shown in A. (C) Sensitivity of
orographic precipitation P, and precipitation perturbation P′=P−P0, to upstream cross-slope wind in multiple regions and at multiple
time scales. In all cases, Pis averaged in the peak rainfall region and P0is averaged from 200 km to 400 km upstream (respectively dashed
and solid black boxes in B for the Western Ghats; see Fig. S1 in the Supplement for other regions). Light gray bars show the sensitivity of
observed seasonal-mean P, medium gray bars the sensitivity of seasonal-mean P′from a reanalysis, and dark bars the sensitivity of daily
observed P′over 2001-2020. A 95% confidence interval obtained by bootstrapping is shown for each estimate.
regions and seasons selected). In each region, the interaction of prevailing winds with a coastal mountain range creates a
precipitation maximum over and upstream of the mountains (Nicolas and Boos, 2024). In the Western Ghats, for example,
precipitation rates are two to three times higher than over the core monsoon region of Central India (Fig. 4A). Seasonal-mean
cross-slope wind (defined as the projection along the 70◦azimuthal angle, roughly east-northeast) is averaged upstream of
the Western Ghats (over the blue rectangle in Fig. 4A). This yields a 56-year time series of cross-slope wind speed, on which215
we regress seasonal-mean Pover the Indian subcontinent. The resulting regression slopes are divided by Pto obtain relative
sensitivities, which exhibit a dipolar pattern wherein regions upstream of mountain peaks are positively associated with U,
whereas regions in the orographic rain shadow exhibit negative sensitivity (Fig. 4B). A decrease in downstream precipitation
with increased Uis also visible in a 300-km-wide region in the simulations (Fig. 2A). Rainfall also positively correlates with
Uacross central India, consistent with the stronger diabatic heating of increased monsoon rainfall accompanying a stronger220
large-scale monsoon circulation (Rodwell and Hoskins, 2001). Absolute sensitivities over Central India are, however, 2–3 times
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1 0 1
m s 1
0
4
8
12
# models
U
= 0.49
(
U
) = 0.29
|
U
|= 0.50
Western Ghats
1 0 1
m s 1
U
= 0.21
(
U
) = 0.58
|
U
|= 0.52
Myanmar
1 0 1
m s 1
U
= 0.04
(
U
) = 0.32
|
U
|= 0.26
Vietnam
1 0 1
m s 1
U
= 0.07
(
U
) = 0.49
|
U
|= 0.42
Philippines
1 0 1
m s 1
U
= 0.20
(
U
) = 0.36
|
U
|= 0.33
Malaysia
Figure 5. Distribution of cross-slope wind changes in CMIP6 climate models under a high-emissions scenario. For each region and model,
we take the difference between 10 m cross-slope wind, averaged in the same upstream region as in Fig. 4, between 2080–2099 (in the SSP5-
8.5 scenario) and 1980–1999 (in the historical run). Results for 37 models are shown as histograms for each region, with the multi-model
mean change ∆U, standard deviation σ(∆U), and mean absolute change |∆U|.
weaker than in the peak rainfall region upstream of the Western Ghats (i.e., the relative sensitivities are elevated over Central
India because Pis comparatively small there).
Although it cannot be directly compared with our theoretical and model-derived sensitivities of P′, we evaluate the sensitivity
of spatially averaged P(in the orographic precipitation band marked by a black dashed line in Fig. 4B) to interannual wind225
changes. It scales at 15 % (m s−1)−1, with local values as high as 30 % (m s−1)−1. Fig. 4C (light gray bars) extends this
analysis to four other regions. In Myanmar and Vietnam, where P0is much smaller than P′, seasonal-mean Pexhibits a
similar sensitivity to cross-slope wind as in the Ghats (around 15 % (m s−1)−1). Sensitivities are much lower in the Philippines
and Malaysia, where increased cross-slope winds are associated with large-scale reductions in specific humidity that decrease
P0(Supplement, Fig. S2).230
We now estimate the observed sensitivity of P′, which can be directly compared with our theoretical and model estimates.
Seasonal-mean P′(from reanalysis) and satellite-based daily mean P′are estimated as the difference between Pin the peak
orographic rainfall region and Pin a region 400 km upstream (dashed and solid black rectangles in Fig. 4B for the Western
Ghats; see Fig. S1 in the Supplement for other regions). These P′values are regressed on upstream cross-slope wind at the
corresponding seasonal or daily time scales. P′is strongly sensitive to changes in Uat both seasonal and daily scales, with235
values ranging from 17 to 34 % (m s−1)−1across regions (Fig. 4C, medium and dark gray bars), in line with the theoretical and
numerical estimates. While this analysis controls for any variations in P0, it does not control for potential changes in moisture
stratification or static stability that may correlate with U(although Fig. S2 in the Supplement suggests such interannual changes
are modest in most regions). Differences in climatological cross-slope wind between regions may be another source of inter-
regional variability. However, all five regions exhibit strong sensitivities on both time scales that quantitatively agree with the240
20–30 % (m s−1)−1values seen in our theoretical and model estimates.
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5 Discussion and implication for regional rainfall change
We have presented multiple lines of evidence indicating that tropical orographic rainfall maxima increase with cross-slope wind
speed at a rate of 20–30 % (m s−1)−1. This rate is physically grounded, holds in a set of convection-permitting simulations,
and is observed in several regions on multiple time scales. While the fact that mechanically forced orographic rainfall increases245
with wind speed is not surprising, the magnitude of this sensitivity has important implications for tropical rainfall projections.
Regional rainfall changes accompanying global warming have traditionally been understood from a thermodynamic stand-
point, where an increase in specific humidity following the Clausius-Clapeyron (CC) rate of ∼7 % K−1implies a similar
increase in the magnitude of precipitation minus evaporation (Held and Soden, 2006). This thermodynamic increase has be-
come a null hypothesis for regional precipitation change, with deviations from the CC rate often attributed to changes in winds.250
Here, we presented a mechanism by which such changes in large-scale winds can affect regional precipitation.
To evaluate whether this mechanism may appreciably strengthen or offset any thermodynamic rainfall change, we evaluate
cross-slope wind changes in our five regions in 37 models from the Coupled Model Intercomparison Phase 6 (CMIP6, Eyring
et al., 2016, see Table S1 in the Supplement for full list). We evaluate wind changes between the end of the 20th century in
historical simulations and the end of the 21st century in the high-emissions SSP5-8.5 scenario2. Models agree on a weakening of255
∼0.5 m s−1in cross-slope wind upstream of the Western Ghats, consistent with a general weakening of monsoon circulations
with warming (Douville et al., 2021). Given our sensitivity estimate, this weakening would yield a 10–15 % decrease in
the orographic precipitation anomaly P′, or a 9–13 % in total precipitation P(assuming a fixed P0of 3 mm day−1). This
represents a sizeable reduction of the “null-hypothesis” 27 % increase that may result from a CC scaling, assuming a 3.5 K
warming in that region (Gutiérrez et al., 2023). In Myanmar, the Philippines, and Malaysia, models disagree on the sign of260
cross-slope wind changes, but the multi-model mean absolute wind changes remain substantial (0.3–0.5 m s−1). This implies
a potential for large changes in rainfall of either sign. In Vietnam, models agree on a more modest change in winds.
A purely thermodynamic change in orographic precipitation (i.e., one produced by climate warming with fixed cross-slope
winds) may be smaller than the CC rate discussed above. By (2), mechanically forced orographic precipitation is set by the
background moisture stratification, static stability, and orographic vertical displacement. The first of these likely increases with265
warming close to the CC rate. Tropical static stability also increases with warming, which strengthens TaL and thus Pa; at the
same time, however, this decreases vertical displacement by contracting the orographic gravity wave, weakening Pa. This may
imply a smaller thermodynamic increase than the CC rate, possibly even an overall stagnation or decrease in total precipitation
in some regions.
It may be difficult to project future changes in tropical orographic rainfall using climate models because those models do270
not resolve orographic gravity waves or moist convection, two central processes in orographic precipitation. The width of the
rainfall peaks in Fig. 4 is around 60 km, smaller than the grid scale of half the CMIP6 models analyzed here. We suggest that
two components are in principle necessary to capture this rainfall distribution: a stationary orographic wave, and the correct
sensitivity of convection to temperature and moisture perturbations. The first component can be represented by models if
2We use the high-emissions SSP5-8.5 scenario because of its higher signal-to-noise ratio, recognizing that it may not represent the most likely future.
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topography and the gravity wave structure (e.g., Fig. 1A) can be resolved, which likely requires grid scales at or below O(10275
km). Past work has evaluated the second component in CMIP6 models (Ahmed and Neelin, 2021), concluding that few models
have adequate sensitivities. Furthermore, gravity wave parameterizations in climate models are typically used to provide drag in
the upper-troposphere/stratosphere, and do not interact directly with model convection schemes. Theory, convection-permitting
models, and observational analyses may thus be the primary tools with which orographic precipitation can be reliably projected.
Our analyses have several limitations. The theoretical sensitivity estimate depends on the definition of the lower-tropospheric280
layer used to define T′
Land q′
L. There is uncertainty in the definition of its lower edge (the boundary layer top) and its upper
boundary has been chosen somewhat arbitrarily here and in past related work (Nicolas and Boos, 2022; Ahmed et al., 2020).
Using a vertically resolved sensitivity kernel (Kuang, 2010) may render the theory more robust. However, such kernels depend
on the cloud-resolving model and simulation design used to derive it, and none have yet been estimated from observations. Our
sensitivity estimate remains robust to changes in many other parameters of the theory.285
Our simulations also have limitations, as convection-permitting models exhibit differences in emergent properties such as
cloud entrainment rates and precipitation efficiencies (Wing and Singh, 2024). These might affect the sensitivity of convection
to temperature and moisture perturbations, and hence the scalings derived here. Another limitation is that we only consid-
ered one SST (300 K). Although it is representative of current conditions in most of the observed regions analyzed, warmer
SSTs may alter the sensitivity of convection. Finally, our idealized simulations may oversimplify the large-scale conditions of290
observed orographic precipitation, neglecting spatial and temporal variations in background wind and SST.
Two important unknowns preclude a projection of tropical orographic precipitation in a warmer world. First, warming-
induced changes in cross-slope wind are uncertain in many regions (Fig. 5). Second, away from midlatitudes (Siler and Roe,
2014), the sensitivity of orographic precipitation to warming with fixed wind remains unknown, even though it likely is the
most important factor in regions where wind changes are modest. Progress constraining either of these quantities will help in295
anticipating changes freshwater supplies for billions of people.
Code and data availability. The code used in producing the figures (including linear mountain wave and precipitation models), and processed
simulation, reanalysis and observational data are archived at Zenodo (Nicolas, 2024).
Appendix A: Linear theory for tropical orographic precipitation
Nicolas and Boos (2022) derive an equation for orographic precipitation in one horizontal dimension (their Eq. 7) which reads300
dP
dx=−P−P0
Lq
+βd
dxqaL
τq
−TaL
τT,(A1)
after dropping the nonlinear Heaviside function (which only affects the downstream precipitation rates) and adapting units and
notation to those of the present work. Lqis a length scale for convective relaxation of moisture, given by Lq= 0.6U τq/NGMS,
where NGMS is the normalized gross moist stability (Raymond et al., 2009) and is about 0.2. The factor of 0.6converts lower-
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free-tropospheric moisture perturbations into full-tropospheric moisture perturbations, assuming a fixed vertical profile of305
moisture variations (Ahmed et al., 2020). Using Pa=β(qaL/τq−TaL/τT)and P=P0+Pa+Pmin (A1) yields (3).
The adjustment timescales τT,τq, and τbare derived from observations at 3-hourly resolution by Ahmed et al. (2020). For
seasonal-mean precipitation rates, longer effective time scales are needed due to the inclusion of non-precipitating times. Based
on the amount of non-precipitating times in simulations of orographic rainfall, Nicolas and Boos (2022) take these timescales
to be 2.5times higher than their 3-hourly values, i.e. τT= 7.5hr and τq=τb= 27.5hr. These values are used throughout the310
paper.
The adiabatic orographic vertical displacement ηis calculated using linear mountain wave theory (e.g., Smith, 1979). For
a mountain of half-width 100 km, the waves are hydrostatic to a very good approximation. In a Boussinesq atmosphere with
uniform wind U, Brunt-Väisälä frequency N, and no rotation, vertical displacement in a hydrostatic, stationary linear mountain
wave obeys315
∂zz η+N2
U2η= 0,(A2)
with the linearized boundary condition η(z= 0) = hand a condition of upward energy radiation at the top boundary. The
addition of uniform Rayleigh damping (with coefficient ξ= 1 day−1) in the horizontal momentum equation slightly modifies
this expression, which reads in the Fourier domain
∂zz ˆη+1−iξ
kU −1N2
U2ˆη= 0,(A3)320
where hats denotes horizontal Fourier transforms and kis the horizontal wavenumber. The solution is given by ˆη=ˆ
heimz ,
where mis chosen as the root of (1 −iξ/kU)−1(N2/U2)that satisfies upward energy radiation; one can show the relevant
root is that whose real part has the same sign as k. The topographic profile considered throughout this paper is
h(x) = h0
21 + cos πx
l0,|x|< l0,(A4)
where h0and l0are the maximum height and half-width of the mountain.325
Appendix B: Regions selected, rainfall and wind products
The regions studied here are the same as in Nicolas and Boos (2024), with the exception of Papua New Guinea, which does
not have a long-term observational rainfall record. These regions were selected because they feature strong orographic rain
bands, and fall clearly within the mechanically forced regime. The rainy seasons considered are June-August for the Western
Ghats and Myanmar, October-December for Vietnam, and November-December for Malaysia and the Philippines. The azimuth330
angles used to defined cross-slope winds are respectively 70◦, 50◦, 240◦, 225◦, and 225◦. Maps of mean rainfall and regressions
of Pand P′on Uare shown in Fig. S1 of the Supplement.
Gauge-based precipitation observations are available in South and Southeast Asia for 1950-2015 (APHRODITE dataset,
Yatagai et al., 2012). We take winds from the ERA5 reanalysis (Hersbach et al., 2020; Bell et al., 2021). Because the number of
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assimilated observations in ERA5 is much smaller before the 1960s, we consider data from 1960 onwards. Hence, regressions335
of total precipitation Pon Uuse a 46-year record between 1960 and 2015. The same period is used for regressions of seasonal-
mean reanalyzed P′. Observed P′at daily scales is obtained from the IMERG dataset (Huffman et al., 2019) between 2001
and 2020, with daily upstream wind taken from ERA5 over that same period.
Author contributions. Q.N. and W.R.B. designed research; Q.N. performed research; Q.N. analyzed data; and Q.N. and W.R.B. wrote the
paper.340
Competing interests. The authors declare that they have no conflict of interest.
Acknowledgements. This research was partially supported by the Director, Office of Science, Office of Biological and Environmental Re-
search of the U.S. Department of Energy as part of the Regional and Global Model Analysis program area within the Earth and Environmen-
tal Systems Modeling Program under Contract No. DE-AC02-05CH11231 and used resources of the National Energy Research Scientific
Computing Center (NERSC), also supported by the Office of Science of the U.S. Department of Energy, under Contract No. DE-AC02-345
05CH11231. The authors thank Yi Zhang and John Chiang for helpful feedback on the manuscript.
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