Geostrophic flows control future changes of oceanic eastern boundary upwelling

Equatorward alongshore winds over major eastern boundary upwelling systems (EBUSs) drive intense upwelling via Ekman dynamics, surfacing nutrient-rich deep waters and promoting marine primary production and fisheries. It is generally thought, dating back to Bakun’s hypothesis, that greenhouse warming should enhance upwelling in EBUSs by intensifying upwelling-favourable winds; yet this has not been tested. Here, using an ensemble of high-resolution climate simulations with improved EBUS representation, we show that long-term upwelling changes in EBUSs differ substantially, under a high-emission scenario, from those inferred by the wind-based upwelling index. Specifically, weakened or unchanged upwelling can coincide with intensified upwelling-favourable winds. These differences are linked to long-term changes of geostrophic flows that dominate upwelling changes in the Canary and Benguela currents and strongly offset wind-driven changes in the California and Humboldt currents. Our results highlight the controlling role of geostrophic flows in upwelling trends in EBUSs under greenhouse warming, which Bakun’s hypothesis overlooked. Oceanic eastern boundary currents are regions with strong upwelling, which is expected to intensify with global warming through enhanced winds. Here the authors show that geostrophic flow dominates over wind effects on long-term upwelling changes for the major eastern boundary upwelling systems.

the base of the surface Ekman layer but provide no information on the vertical structure of upwelling. The latter affects the source depth of upwelled waters, which is closely related to the efficacy of upwelling in fuelling biological productivity 21 . Extension of a two-dimensional Ekman model 22 by incorporating the effects of geostrophic flows demonstrates that the geostrophic flows play an important role not only in regulating the intensity of upwelling but also its vertical structure 17 .
Climate simulations make it possible to directly evaluate the response of upwelling in the EBUSs to greenhouse warming on the basis Chlorophyll-a concentration (mg m -3 )

Result
Consistent with the existing theoretical arguments and high-resolution regional ocean simulations [24][25][26][27][28][29][30] , the simulated upwelling in the four EBUSs by CESM-H consists of a rapid coastal component driven by the alongshore wind stress and confined to a narrow band (<50 km) next to the coast and a slower component driven by the wind stress curl and extending further offshore ( Fig. 1c-f). By contrast, the simulated upwelling by an ensemble of coarser-resolution CGCMs (Extended Data Table 1) participating in the Coupled Model Intercomparison Project phase 6 (CMIP6) 23 is weaker and more diffusive (Fig. 1g-j), with the prominent coastal upwelling zone being absent. The outperformance of CESM-H over CMIP6 CGCMs in representing the upwelling in the EBUSs can be further inferred from the alleviated warm sea surface temperature (SST) bias in these regions (Extended Data Fig. 1), in view of the strong imprint of upwelling on SST 31,32 . Improved upwelling simulation in CESM-H is attributed primarily to a better resolution of coastal upwelling 17,22 and may also benefit from a more realistic representation of the cross-shore wind stress structure, seafloor topography and oceanic mesoscale eddies 26,29,[33][34][35][36] , which all connect to the high resolution in oceanic or atmospheric model configurations.
Note that even CESM-H is not fine enough to well resolve the coastal upwelling, resulting in an overly wide coastal upwelling zone relative to the reality 17,22,30,34 . On the one hand, a further increase of the oceanic model resolution would probably make the coastal upwelling stronger and narrower until it is fully resolved. On the other hand, the integrated vertical velocity over a sufficiently wide region should be less sensitive to the model resolution and more faithfully simulated by CESM-H. For this reason, we integrate the vertical velocity within ~200 km from the coast in the individual EBUSs, referred to as the upwelling transport henceforth (Upwelling transport), and compare their long-term changes under greenhouse warming with those inferred from the WUIs. Such integration covers the coastal upwelling and a large fraction of offshore wind stress curl-driven upwelling, both of which are suggested to influence the ecosystem 6 . For the climatological mean upwelling transport in the EBUSs, it peaks around 30-40 m, comparable to the surface Ekman layer depth, and attenuates rapidly further downwards (Fig. 2). This vertical structure of upwelling transport is consistent with the dominant role of winds in driving the upwelling via the Ekman dynamics 24 . Indeed, a particular WUI used in this study (WUI) is comparable to the peaking value of upwelling transport in the vertical (upwelling transport intensity (UTI)) for the individual EBUSs. Despite such qualitative agreement, there are noticeable quantitative differences between the WUI and UTI, especially in the CanCS and BCS, where the WUI overestimates the UTI by about 40% and 60%, respectively. This overestimation is ascribed primarily to the downwelling caused by the convergent geostrophic flows in the CanCS and BCS (Extended Data Fig. 2).
The closeness between the WUI and UTI for the climatological mean state does not extend to their long-term changes under greenhouse warming (Fig. 3a-d). In the CalCS and HCS, the fitted linear trends of WUI during 2006-2100 are −1.6 × 10 5 m 3 s −1 and 4.5 × 10 5 m 3 s −1 per century, respectively. They severely overestimate the trends of UTI Upwelling transport (10 6 m 3 s -1 ) Vertical velocity (10 -6 m s -1 ) Vertical velocity (10 -6 m s -1 ) Vertical velocity (10 -6 m s -1 ) Vertical velocity (10 -6 m s -1 ) We remark that the evident decoupling between the trends of WUI and UTI in the EBUSs is not specific to CESM-H but qualitatively reproduced by CMIP6 CGCMs (Fig. 3e-h), providing strong evidence on its robustness. There are, however, quantitative differences between the projected trends in CESM-H and CMIP6 CGCMs, which is due partially to the insufficient resolution of CMIP6 CGCMs in representing the upwelling dynamics.
As suggested by Bakun's hypothesis, the long-term change of upwelling-favourable winds in a warming climate should be more evident in the warm season 10,11 . To avoid degrading the validity of WUI in representing the response of UTI to greenhouse warming, we repeat the preceding analysis for the warm season only. Despite some quantitative differences from the annual-mean case, the basic conclusion that the long-term change of UTI under greenhouse warming is decoupled from that of WUI still holds in the HCS, CanCS and BCS (Extended Data Fig. 3). In the CalCS, the trends of WUI and UTI in the warm season are qualitatively consistent, but the former is about 40% larger in magnitude than the latter. In addition, given the latitude-dependent long-term change of upwelling-favourable winds 12 , we examine the relationship between the trends of WUI and UTI at different latitudes. Their values differ substantially from each other over a large fraction of latitude bands in all the four EBUSs, lending further support to our argument (Extended Data Fig. 4).
Considering the distinctive underlying dynamics and ecological impacts of the rapid coastal upwelling, we recompute the WUI and UTI for the approximately 50-km-wide coastal zone (Fig. 3i-l). The trends of coastal WUI and UTI diverge greatly, with their differences in the individual EBUSs resembling those calculated for the approximately 200-km-wide upwelling band from the coast. Such resemblance suggests that the decoupling between the long-term changes of WUI and UTI under greenhouse warming is a robust feature that is not sensitive to the width of the upwelling band selected for analysis.
The WUI does not and is not intended to provide any measurement of upwelling transport below the surface Ekman layer. Yet it is found that the long-term change of upwelling transport is more evident in the thermocline than at the surface Ekman layer base in all the EBUSs except the BCS (Fig. 2). This feature is a strong implication that other processes aside from the wind-driven Ekman transport play a crucial role in the response of upwelling to greenhouse warming. Moreover, as the upwelling transport in the thermocline affects the source depth of upwelled waters, its change in a warming climate is likely to have an influence on the efficacy of upwelling in nourishing the ecosystem 21 , which cannot be captured by the WUI.
To shed light on the underlying processes accounting for the decoupled responses of WUI and UTI to greenhouse warming, we decompose the upwelling transport into components associated with the horizontal mass-flux divergence caused by geostrophic and ageostrophic flows (referred to as the geostrophic and ageostrophic upwelling transports), respectively (Upwelling transport). This decomposition is made for only one member of the CESM-H ensemble due to the unavailability of sea surface height in the model output of the other two members. Nevertheless, similarity in the trends of upwelling transport among the three members (Extended Data Fig. 5) provides us confidence that the decomposition results derived from any member should be qualitatively representative of the ensemble mean. In all four EBUSs, the climatological mean ageostrophic upwelling transport and its long-term change under greenhouse warming are comparable to those of WUI below the surface Ekman layer (Fig. 4 and Extended Data Fig. 2), suggesting that the ageostrophic upwelling transport is attributed largely to the horizontal mass-flux divergence caused by wind-driven Ekman transport. Although the geostrophic   Article https://doi.org/10.1038/s41558-022-01588-y upwelling transport contributes negligibly (CalCS and HCS) or secondarily (CanCS and BCS) to the climatological mean UTI, its contribution to the long-term change of UTI becomes much more important and is primarily responsible for the difference between the trends of WUI and UTI ( Fig. 4 and Extended Data Fig. 2). In particular, the trend of geostrophic upwelling transport peaks in the thermocline in the CalCS, HCS and CanCS but not the BCS, explaining the more pronounced long-term changes of upwelling transport in the thermocline than at the surface Ekman layer base in the former three EBUSs.

Discussion
This study reveals the crucial role of geostrophic flows in controlling the response of upwelling to greenhouse warming in the EBUSs, providing new insights overlooked by the existing literature 7,10-14 . It is generally thought that the intensified stratification in a warming climate should cause shoaling of the source of upwelled waters 7,8,14,37 . However, the enhanced geostrophic upwelling transport in the thermocline of CanCS is likely to deepen the source of upwelled waters despite the stronger stratification under greenhouse warming ( Fig. 2c and Extended Data Fig. 6). Moreover, the role of geostrophic flows is not uniform among the four EBUSs. It is more prominent in the EBUSs in the Atlantic basin (CanCS and BCS) than in the Pacific basin (CalCS and HCS), in terms of both the climatological mean state and long-term change of upwelling. Previous limited assessment on the effects of geostrophic flows on the long-term change of upwelling happens to be in the Pacific EBUSs 18,20 , which underestimates the fundamental contribution of geostrophic flows to the response of upwelling in the global EBUSs to greenhouse warming. So far, effects of anthropogenic climate changes on the ecosystems in the EBUSs remain poorly understood. There is an ongoing debate about to what extent the long-term change of biological productivity of EBUS ecosystems is related to that of upwelling in a warming climate 7,8,30 . In addition to the upwelling, the responses of SST, stratification and mesoscale eddy field to greenhouse warming and their interactions with the upwelling are all suggested to play an important role 7,8,21,38 . In particular, the mesoscale eddies, generated primarily through the baroclinic instability of upwelling jet 36,39 , transport the nutrient offshore 26 and heat onshore 36 , counteracting the effects of upwelling on the coastal SST and nutrient supply. It is thus important to understand the changes of mesoscale eddies and their interactions with the upwelling changes under greenhouse warming. There is some evidence that the mesoscale eddies in CalCS would become stronger under a high carbon-emission scenario due to the enhanced baroclinic instability of upwelling jet caused by intensified upper-ocean stratification 40,41 . However, it remains unclear whether a stronger mesoscale eddy activity in response to greenhouse warming is universal among all the EBUSs and what its implication on the ecosystem is. Simulation of mesoscale eddies is beyond the resolution capacity of most CMIP6 CGCMs but is possible for CESM-H. Coupled with a reliable biogeochemical model, CESM-H can provide us with a better knowledge of the response of EBUS ecosystems to greenhouse warming and its underlying dynamics.

Upwelling transport
The upwelling transport (UT) is computed as the horizontal integration of model-simulated vertical velocity zonally within 20 model grids (∼200 km) from the coast: UT (z, t) = ∫∫w (x, y, z, t) dxdy (1) where w is the vertical velocity and x, y, z, and t are the zonal, meridional, vertical, and temporal coordinates, respectively. The northern and southern boundaries for integration are 48° N and 23° N for CalCS, 15° S and 45° S for HCS, 36° N and 15° N for CanCS, and 10° S and 30° S for BCS, respectively. Similarly, the coastal upwelling transport is defined as the horizontal integration zonally within five model grids (∼50 km) from the coast. The (coastal) UTI is defined as the value of (coastal) upwelling transport at its peaking depth, that is, 30 (20)  The upwelling transport can be further decomposed into components associated with horizontal mass-flux divergence caused by geostrophic and ageostrophic flows, respectively. Under the rigid lid approximation for the sea surface, the geostrophic upwelling transport (UT g ) is computed as 17 : UT g (z, t) = ∫∫∫ 0 z ( ∂u g (x, y, s, t) ∂x + ∂v g (x, y, s, t) ∂y ) dsdxdy (2) where s is the dummy variable in integral and u g = (u g , v g ) is defined as the reference seawater density and p the seawater pressure, except along the coastal boundary where u g is set as zero. The value of p is calculated on the basis of the hydrostatic approximation; that is, p = ρ 0 gη + ∫ 0 z ρ (x, y, s, t) gds, with η the sea surface height, g the gravity acceleration and ρ the in situ seawater density. The horizontal divergence of u g is computed following the discretization scheme in POP2. Once UT g is obtained, the ageostrophic upwelling transport UT a is computed by subtracting UT g from UT.

WUI
The WUI is defined as the total Ekman transport into/out of the integration region as 19,20 : where U E = (U E , V E ) is defined as τ ρ 0 f × k with τ = (τ x , τ y ) the surface wind stress and k the unit vector pointing upwards, except along the coastal boundary where U E is set as zero. The horizontal divergence of U E is computed using the same discretization scheme as that of u g . Note that equation (3) accounts for the vertical velocity at the surface Ekman layer base via the coastal divergence/convergence due to the cross-shore Ekman transport driven by the alongshore wind stress and via the Ekman pumping driven by the wind stress curl ∂τ y /∂x − ∂τ x /∂y (refs. 19,20 ). As to the WUI in CMIP6 CGCMs, we first bilinearly interpolate τ in the individual CMIP6 CGCMs onto the grids of POP2. Then WUI is computed according to equation (3) on the basis of the ensemble mean τ.