Mechanical forcing of the North American monsoon by orography

A band of intense rainfall extends more than 1,000 km along Mexico’s west coast during Northern Hemisphere summer, constituting the core of the North American monsoon1,2. As in other tropical monsoons, this rainfall maximum is commonly thought to be thermally forced by emission of heat from land and elevated terrain into the overlying atmosphere3–5, but a clear understanding of the fundamental mechanism governing this monsoon is lacking. Here we show that the core North American monsoon is generated when Mexico’s Sierra Madre mountains deflect the extratropical jet stream towards the Equator, mechanically forcing eastward, upslope flow that lifts warm and moist air to produce convective rainfall. These findings are based on analyses of dynamic and thermodynamic structures in observations, global climate model integrations and adiabatic stationary wave solutions. Land surface heat fluxes do precondition the atmosphere for convection, particularly in summer afternoons, but these heat fluxes alone are insufficient for producing the observed rainfall maximum. Our results indicate that the core North American monsoon should be understood as convectively enhanced orographic rainfall in a mechanically forced stationary wave, not as a classic, thermally forced tropical monsoon. This has implications for the response of the North American monsoon to past and future global climate change, making trends in jet stream interactions with orography of central importance. The core North American monsoon arises through topographic steering of the jet stream, and should be considered as convection-enhanced orographic rainfall produced by a mechanically forced stationary wave.

A band of intense rainfall extends more than 1,000 km along Mexico's west coast during Northern Hemisphere summer, constituting the core of the North American monsoon 1,2 . As in other tropical monsoons, this rainfall maximum is commonly thought to be thermally forced by emission of heat from land and elevated terrain into the overlying atmosphere [3][4][5] , but a clear understanding of the fundamental mechanism governing this monsoon is lacking. Here we show that the core North American monsoon is generated when Mexico's Sierra Madre mountains deflect the extratropical jet stream towards the Equator, mechanically forcing eastward, upslope flow that lifts warm and moist air to produce convective rainfall. These findings are based on analyses of dynamic and thermodynamic structures in observations, global climate model integrations and adiabatic stationary wave solutions. Land surface heat fluxes do precondition the atmosphere for convection, particularly in summer afternoons, but these heat fluxes alone are insufficient for producing the observed rainfall maximum.
Our results indicate that the core North American monsoon should be understood as convectively enhanced orographic rainfall in a mechanically forced stationary wave, not as a classic, thermally forced tropical monsoon. This has implications for the response of the North American monsoon to past and future global climate change, making trends in jet stream interactions with orography of central importance.
Tropical monsoons occur when a surface of low heat capacity transfers the energy of intense summer solar radiation to the overlying atmosphere, creating thermally direct, precipitating flow. Such circulations supply water to billions of people and set the climate of large swaths of Earth's surface. The North American monsoon (NAM) is commonly viewed in this paradigm, being a low-latitude summer circulation crucial for the hydrology of western Mexico and the southwestern USA 1,2,6,7 .
Orography strongly alters this simple description of monsoons, with the core NAM consisting of a narrow tongue of high precipitation stretching over 1,000 km north-south just west of the Sierra Madre Occidental (SMO) mountains ( Fig. 1a; summer means are taken July-September). The mechanisms that organize NAM precipitation around orography remain unclear, but most hypotheses invoke thermal forcing from terrain. Early global climate model (GCM) simulations showed that NAM rainfall decreases greatly when mountains are flattened globally 8 , perhaps because sensible heat fluxes from orography into elevated levels of the atmosphere draw water vapour from the Gulf of California up SMO slopes to condense and precipitate 2,3,9,10 .
The high-amplitude diurnal cycle of precipitation in the NAM has also been taken to suggest the importance of orographic thermal forcing, with near-surface air flowing upslope during daytime and downslope at night [11][12][13] , as expected for a sea breeze or mountain-valley breeze driven by solar heating. Despite the prominence of this diurnal cycle, horizontal moisture fluxes produced by transients (for example, diurnally reversing sea breeze circulations) are an order of magnitude smaller in the core NAM than those produced by seasonal mean winds 12 , suggesting that core NAM precipitation is controlled by the forcings that produce seasonal mean flow.
Mechanical, rather than thermal, effects of orography are known to drive summer winds east and northeast of the NAM, in the central USA. A GCM and stationary wave model were used to show that the eastern Sierra Madre deflect trade winds northward to become the Great Plains low-level jet 14,15 , which transports water into the central USA from the Gulf of Mexico but is not traditionally seen as a main NAM component. Both orographic elevated heating and orographic blocking of zonal winds have been mentioned as plausible NAM causes 16 , but models integrated at resolutions fine enough to resolve the SMO [17][18][19] have not been used to distinguish between these possibilities.
Our goal is to determine the mechanisms that cause the intense rainfall maximum in the core NAM. We are interested in whether it is generated primarily by a thermodynamic forcing (for example, elevated heating) or a mechanical one (mechanical blocking). Given the prior finding that time-mean vertically integrated moisture flux convergence in the core NAM is produced by time-mean winds 12 , this task amounts to determining the cause of seasonal-mean eastward, upslope flow over the SMO.
Article zero over most of Mexico (FlatMex). The Control integration produces a realistic seasonal cycle and spatial pattern of NAM precipitation and wind (Fig. 1a, b and Extended Data Figs. 1-3; the model has a positive precipitation bias but falls in the range of observed interannual variability). As in observations 12 , model NAM precipitation is balanced by moisture converged by time-mean flow, with transients producing some compensating drying (Extended Data Fig. 4).
The model resolves the SMO as a ~3-km-high ridge along Mexico's west coast, and reproduces observed eastward low-level winds extending roughly 1,000 km west of that (Fig. 1a, b). This wind distribution is suggestive of the midlatitude eastward jet being deflected towards the Equator by the SMO; the broader North American Cordillera is known to deflect the jet in such a stationary wave 14 , but the equatorial part of that wave has not been argued to play a role in the NAM, or adequately resolved in stationary wave models of the region.
We obtain the net response to all dynamic and thermodynamic effects of Mexico's orography by subtracting the FlatMex state from the Control. Nearly all core NAM precipitation is caused by local orography, with the rainfall maximum on Mexico's west coast disappearing in the FlatMex state despite continued land surface thermal forcing (Fig. 1c). Without the SMO, westward trade winds span Mexico, separating two zones of eastward flow: one in the extratropics and another in the oceanic intertropical convergence zone south of Mexico (near 15° N). The region of high near-surface moist static energy (MSE), which in observations and the Control is confined to the Gulf of California and the Gulf of Mexico, expands inland to cover central Mexico when the orography is flattened ( Fig. 1d; surface air MSE is hereafter written h s and expressed in temperature units through normalization by the specific heat of air).
The h s response to the SMO suggests that core NAM precipitation is not forced primarily by orographic elevated heating, which would drive the overlying atmosphere towards higher h s values than would be achieved over the same surface at sea level 20 . Additionally, the dynamical response to tropical heating typically includes poleward flow through the heated region in a state of Sverdrup balance, with a low-level cycloneto the west 21,22 . Instead, we see anomalous eastward flow over the orographic forcing, with a low-level cyclone to the north and anticyclonicflow to the southwest (Fig. 1d). However, as much of this reasoning employs comparisons with previous idealized solutions that might be complicated by strong background flows, we now systematically assess the response to separate mechanical and thermal forcings.

Mechanically forced response
We estimate the response to the mechanical influence of orography with a stationary wave model that has been used to study a range of orographically influenced circulations 14,23,24 , but integrated here at finer resolution. We impose as a basic state the three-dimensional summer-mean flow from the FlatMex GCM, and then use this model to find the adiabatic response to Mexico's orography (the forcing is the Control -FlatMex surface height anomaly).
This mechanically forced response consists of a meridional dipole in low-level vorticity, with a cyclone over much of the western USA and an anticyclone southwest of Mexico (Fig. 2c). This structure strongly resembles the GCM response (Control -FlatMex; Fig. 2a), even though the GCM also includes diabatic feedbacks and any orographic thermal forcing. The stationary wave includes anomalous eastward flow   upstream of and over the SMO, opposing the basic-state trade winds, with a vertical structure and amplitude similar to that of the net GCM response (Fig. 2b, d). Between the surface and ~850 hPa, the total flow (basic state plus stationary wave anomaly) is eastward upstream of and over the SMO western slopes (orange contours in Fig. 2b, d).
The stationary wave thus produces the time-mean upslope wind associated with core NAM moisture convergence and precipitation in this model (Extended Data Fig. 4) and observations 12 .
The stationary wave is nonlinear, with isentropes (constant potential temperature surfaces) intersecting orography instead of bowing upward around it 25 (Fig. 2b, d; Extended Data Fig. 5 shows the linear response), but is straightforward to understand. When orography is high enough to block zonal winds, adiabatic flow, which in the time mean follows isentropes, must deviate northward or southward depending on where isentropes intersect the ground. In contrast with the regions and seasons used in prior studies of flow perturbed by narrow orography 25 , peak temperatures in the NAM lie near 38° N, so isentropes over Mexico tilt downward to the north, intersecting the ground over the southwestern USA (Fig. 2a, c and Extended Data Fig. 6). Adiabatic zonal flow must thus ascend and turn southward as it encounters the SMO, because northward flow is blocked as it follows isentropes into the ground. Lower-resolution stationary wave solutions have a weaker anticyclone south of Mexico and give greater prominence to the northward Great Plains low-level jet (Extended Data Fig. 7a), perhaps explaining why orographic mechanical forcing has previously been more closely associated with that circulation 14 .

Seasonal and diurnal thermodynamic maxima
We now discuss how observations of strong diurnal and seasonal cycles of the thermodynamic state of the core NAM [11][12][13] are consistent with the hypothesis that upslope flow and precipitation there are produced by a mechanically forced stationary wave. Moist convection requires both a reservoir of convective available potential energy (CAPE) and, typically, some lifting to overcome convective inhibition or release conditional instability. CAPE generally increases with h s (refs. 26,27 ), and a large pool of air with high time-mean h s lies over the Gulf of California and Gulf of Mexico (Fig. 1d). However, a strong diurnal cycle of h s over land, caused by solar heating, produces a strong diurnal cycle of CAPE with a mid-afternoon peak over the western SMO ( Fig. 3b; despite observational uncertainty, all estimates show high h s over the western SMO with a large diurnal cycle over land). Thus, a warm and moist air layer from the Gulf of California flows eastward at low levels in the mechanically forced stationary wave, and its MSE is increased further by daytime surface heat fluxes while its temperature drops adiabatically owing to upslope flow, producing moist convection. Prior work 16 showed that the observed CAPE distribution does not explain why NAM precipitation favours the west coast of Mexico versus the east coast; release of CAPE through upslope flow in the stationary wave resolves this issue.
These effects can be synthesized by examining the seasonal cycle of h s and near-surface zonal wind averaged in and upstream of the core NAM region, respectively. Upslope flow peaks in spring, before the observed rainy season, but h s is low then so ample convective precipitation is not produced (Fig. 3c). Peak precipitation occurs a few months later when   upslope flow is still strong and h s has increased to its summer peak. Flattening Mexico's orography produces a slight increase in summer h s , presumably because orography blocks the inland penetration of warm and moist oceanic air, yet NAM precipitation decreases greatly as upslope flow is reduced (Fig. 1c). The seasonality of NAM precipitation thus seems to arise from the seasonal cycle in h s (and CAPE) but, consistent with CAPE being a necessary but insufficient condition for convection, mechanically forced ascent in the stationary wave is needed to turn that thermodynamic seasonal cycle into rainfall.
The h s distribution (Fig. 3a) also illustrates the deviation of NAM structure from that of classic tropical monsoons. In the latter we expect peak rainfall and peak low-level eastward wind on the equatorial side of the h s maximum 28,29 . Instead, peak NAM rainfall occurs slightly east of (or even directly over) the peak h s , and low-level eastward winds lie west of the peak h s . This suggests that the classic, thermally forced tropical monsoon in North America consists of the oceanic precipitation maximum just south of Mexico, which would exist without Mexico's orography (Fig. 1c); southward deflection of prevailing extratropical winds by the SMO superimposes on that tropical monsoon the intense band of rainfall along Mexico's west coast (the core NAM).

Response to a pure thermal forcing
We test the alternative hypothesis that the core NAM is primarily driven by thermal, rather than mechanical, orographic forcing using a third GCM integration in which the albedo of the surface that was flattened (most of Mexico) is reduced to 0.05 (FlatMexLowAlb). This provides a strong thermal forcing, with land albedo in much of the NAM region reduced below that of open ocean, yielding a local increase of about 20 W m −2 in the net energy input to the atmosphere (the sum of radiative and surface turbulent fluxes into each atmospheric column; Fig. 4a). In response, the high-h s region expands poleward and the oceanic precipitation maximum follows, expanding inland (compare Figs. 4b and 1c, d; Extended Data Fig. 9 shows anomalies). Anomalous low-level poleward flow over the region in which the albedo forcing was applied (Fig. 4a) is consistent with the Sverdrup balance achieved in the linear response to tropical thermal forcings 21 . As expected for a thermally forced tropical monsoon 28,29 , peak rainfall lies on the equatorial side of the high-h s region, and precipitation increases by about 2 mm day −1 over the broad region of the albedo forcing (Fig. 4b).
The spatial structure of the response to the albedo forcing is highly distinct from the observed monsoon, with the former lacking both a precipitation maximum along Mexico's west coast and eastward flow extending 1,000 km west of the SMO.

Synthesis and implications
The NAM is commonly categorized as a thermally forced tropical monsoon, with most previous work describing it as either: similar to though smaller in scale than the South Asian monsoon 11 , with a central role played by elevated plateau heating 3 ; or caused by land-ocean thermal contrast 4,25,30 . Our results suggest that core NAM precipitation instead requires mechanical forcing by the SMO, producing eastward, upslope flow that organizes convection to occur in a small part of a horizontally extensive pool of high-h s air. The seasonal cycle of insolation generates that pool of high-h s air in summer, with the diurnal cycle of insolation further enhancing h s over coastal Mexico in afternoons. We expect mechanically forced stationary waves to be modified by moist convective heating, but the resemblance between horizontal winds in the adiabatic stationary wave solutions and in the moist GCM suggests that this has only a modest effect on horizontal flow (Fig. 2).
These findings have implications for NAM variability in past and future climates, placing new emphasis on the jet stream and trade winds, and their interaction with orography. Accurate dynamical forecasts of NAM rainfall will require models with an unbiased jet stream and resolutions fine enough to represent the SMO. Thermodynamic controls on convection, long thought to dominate NAM rainfall, are important, but their representation in models should be evaluated  in terms of how they affect convection in upslope flow. In contrast, surface conditions and convective stability over central Mexico may primarily affect the low amounts (1-2 mm day −1 ) of summer rainfall received there. Finally, global climate change may alter the NAM through changes in both the extratropical jet stream and convective stability in regions of upslope flow, rather than through its influence on more general land-ocean thermodynamic contrasts.

Online content
Any methods, additional references, Nature Research reporting summaries, source data, extended data, supplementary information, acknowledgements, peer review information; details of author contributions and competing interests; and statements of data and code availability are available at https://doi.org/10.1038/s41586-021-03978-2.

Observations
We obtain estimates of Earth's atmospheric state from ERA5, the fifthgeneration atmospheric reanalysis from the European Centre for Medium-Range Weather Forecasts [31][32][33] . For years 1979-2019, we use ERA5 surface air temperature, surface air dewpoint (which we convert to specific humidity to calculate h s ), surface height and 100-m zonal wind.
We also obtain surface air temperature, surface air dewpoint and surface height from the Modern-Era Retrospective analysis for Research and Applications, version 2 (MERRA-2) 34,35 . Precipitation estimates are drawn from the Global Precipitation Measurement (GPM) mission Integrated Multi-Satellite Retrievals for GPM (IMERG), Final Precipitation L3 Daily 0.1 degree × 0.1 degree V06 product (GPM_3IMERGDF) 36 . We averaged years 2001-2020 to obtain the precipitation climatology shown in Fig. 1a. In addition to IMERG, we also use two land precipitation datasets to evalaute model performance over land: the Global Precipitation Climatology Centre dataset, version 7, at 0.5° horizontal resolution 37,38 , and the Climate Research Unit gridded monthly rainfall from the University of East Anglia, version 3.24, at 0.5° horizontal resolution 39,40 . Plots of surface height use estimates from the ETOPO1 global relief model 41 We compute h s for all minutes within the 1 utc and 13 utc hours, corresponding to late afternoon and early morning in local time, respectively. We average for all days from July to September for both datasets, and retain only those stations for which there are fewer than ten days of missing data. Data for stations within 0.5° latitude of 28° were used for the transect. Changing the latitude of the MSE transect to 26° N, which was used for the wind sections in Fig. 2, does not change the qualitative results obtained from the reanalyses, although sufficient station data are not available at that latitude to conduct a comparison with direct observations.

GCM.
Simulations were performed using the Community Atmosphere Model, version 5.1 (CAM5) 46 coupled to the Community Land Model, version 4 (ref. 47 ), within the software infrastructure of the Community Earth System Model, version 2.1.3. We use the finite-volume dynamical core, which is typically configured with a horizontal resolution of 0.9° (latitude) by 1.3° (longitude); to better resolve the topography of the NAM region, we use a global horizontal resolution of 0.23° × 0.31° (that is, approximately 25 km at the Equator) with 30 vertical levels. We use the Sea ICE model, version 5, with prescribed ice cover and prescribed cyclic sea surface temperature (SST) from the year 2000. This model configuration is largely the same as that used in projections of the future behaviour of tropical cyclones 48,49 , and prior work has shown that the finer horizontal resolution used here improves the representation of the NAM in CAM5 (ref. 19 ).
As discussed in previous work 17,18,50 , climate models with relatively coarse horizontal resolution fail to resolve features such as the Gulf of California and the Sierra Madres, thereby misrepresenting key NAM processes such as Gulf of California moisture surges 2,51,52 , land-sea contrast 53 and mechanical flow-blocking by orography 54 . Furthermore, SST biases in coupled GCMs can have a detrimental impact on simulation of the NAM, biasing its seasonal evolution to produce a late withdrawal and thus an overly wet late summer and autumn [55][56][57] . Therefore, using a high-resolution configuration with climatological SST reduces the model's bias and brings the regional circulation closer to observations (Extended Data Figs. 1-3).
To assess the influence of elevated terrain on the core NAM, we integrate the model with standard orography (Control) and again with flattened orography over most of Mexico (FlatMex). When flattening orography, we set both the surface height and the subgrid-scale standard deviation of orography to zero, with the latter used as input to both the vertically nonlocal subgrid-scale orographic gravity wave drag parameterization and the near-surface turbulent mountain stress scheme. In the integration with flattened orography over Mexico, we set surface height to zero within a quadrilateral having these vertices: (33° N, 245° E), (29° N, 265° E), (15° N, 257° E) and (15° N, 265° E). Orography on the Baja Peninsula is unaltered (it lies outside this quadrilateral). To avoid creating a high vertical wall of orography at the northern edge of this quadrilateral, where Mexico's orography joins the greater North American Cordillera, the surface height is set to decrease linearly to zero over 2° of latitude immediately south of the northern edge of the quadrilateral; the same procedure is used for the subgrid-scale standard deviation of orography. To help distinguish between the thermal and mechanical influence of orography, we conduct a third integration in which the surface albedo of the flattened land is set to 0.05 (FlatMexLowAlb); this is performed for both the direct and diffuse albedo by altering the land model (Community Land Model, version 4). This third integration has both flattened orography over Mexico and reduced surface albedo, in an attempt to impose an enhanced thermal forcing without the mechanical effects of orography. The spatial pattern of the albedo forcing does not exactly match the spatial pattern of orography because the albedo is uniformly set to 0.05 over the entire region where land was flattened; the effective forcing furthermore depends on the Control albedo rather than the Control terrain height. Nevertheless, the relatively weak magnitude and distinct spatial structure of the response to this albedo forcing (Fig. 4) suggest that further tuning would not greatly change the result. All three of the GCM configurations (Control, FlatMex and FlatMexLowAlb) are run for 11 years of simulated time, with the last 10 years analysed.
To understand how orography deflects the midlatitude westerlies towards the Equator and then forces convection through upslope flow (Fig. 1), we analyse the time-mean zonal wind on a terrain-following level located within a typical subcloud layer (the atmospheric layer that lies below cloud base). For ERA5 we choose the level 100 m above Earth's surface, while for the GCM we use the horizontal wind on the third model level above the surface (level 957.5).
Stationary wave model. To isolate the mechanical influence of Mexico's orography on the atmospheric circulation, we use a fully nonlinear stationary wave model. The model was introduced by Ting and Yu (1998) 58 , and solves the primitive equations in terms of vorticity, divergence, temperature and the logarithm of surface pressure, using spherical harmonics 24,59,60 . Important distinctions with the GCM are that the stationary wave model: solves these equations for anomalies relative to a specific three-dimensional basic state; and is adiabatic aside from a 15-day Newtonian relaxation of temperature towards the basic state, as used in prior work 58,61 . Transients, such as midlatitude baroclinic instabilities, are suppressed using drag and scale-selective diffusion. Specifically, interior Rayleigh drag on the anomalies is imposed with a 15-day timescale, with surface drag represented by gradually reducing this timescale to 0.3 days over the lowest 4 levels. Biharmonic diffusion with a coefficient of 10 17 m 4 s −1 acts on vorticity, divergence and temperature. The original version of this stationary wave model 58 was created with a rhomboidal truncation at wavenumber 15 (R15 spectral resolution) and 12 vertical levels. Later work integrated the model at R30 resolution with 14 vertical levels 23 and R30 resolution with 24 vertical levels 24 . We enhanced the resolution to R63 with 24 levels, on the basis of code supplied by Isla Simpson. At R63, the model closely approximates the full-width at half-maximum height of the SMO when compared to ETOPO1 data and our CAM5 model, while this width was overestimated by more than 60% at R30.
The model was forced by imposing Mexico's orography on a basic state obtained by time-averaging the summer atmospheric state from the GCM without that orography. Specifically, we obtain the basic state by taking the 10-year July-September average atmospheric state from the FlatMex GCM run, and use the surface height difference between the Control and FlatMex GCM runs as the forcing. The stationary wave model nears a steady state after about 20 days, with the exception of the lowest model level, which drifts towards a steady state over about 60 days. Therefore, the model was run for 90 days of simulated time with the last 20 used for analysis. Linear stationary wave solutions were approximated, following previous work 62 , by scaling the Control -Flat-Mex surface height forcing by 10 −6 and then multiplying the response by 10 6 , thus rendering quadratic terms in the conservation equations a factor of 10 −6 smaller than linear terms. The same integration and averaging periods were used for the linear solutions and for an integration of the model at the lower R30 resolution (Extended Data Figs. 5 and 7).

Data availability
The ERA5 monthly averaged data by hour of day were downloaded from the Copernicus Climate Change Service Climate Data Store (identifiers cited in Methods). MERRA-2 and GPM data were downloaded from the NASA Goddard Earth Sciences Data and Information Services Center (identifiers cited in Methods). ETOPO1 data were downloaded from the National Centers for Environmental Information at the National Oceanic and Atmospheric Administration (identifiers cited in Methods). David K. Adams provided access to GPS Hydromet 2017 data; Trans-boundary, Land and Atmosphere Long-term Observational and Collaborative Network data; and GPS Transect Experiment 2013 data. The time-mean summer climatology from the GCM and time-mean output from the stationary wave model are archived at https://doi. org/10.5281/zenodo.5076509.

Code availability
The Community Earth System Model, which is supported primarily by the National Science Foundation, was obtained from https://www.cesm. ucar.edu. Isla Simpson provided code for the stationary wave model, the original version of which was written by Mingfang Ting and Linhai Yu.