Dynamical Downscaling of Climate Simulations in the Tropics

The long‐existing double‐Intertropical Convergence Zone (ITCZ) problem in global climate models (GCMs) hampers accurate climate simulations in the tropics. Using a regional climate model (RCM) over the tropical and sub‐tropical Atlantic with a horizontal resolution of 12 km and explicit convection, we develop a bias‐corrected downscaling methodology to produce limited‐area simulations with a realistic ITCZ, despite the double ITCZ in the driving GCM. The methodology effectively removes GCM biases in the RCM boundary conditions, such as to produce more realistic large‐scale driving conditions. We show that the double‐ITCZ problem persists with conventional dynamical downscaling, but with bias‐corrected downscaling the RCM simulations yield credible ITCZ with a realistic seasonal cycle. Detailed analysis attributes the main cause of the double‐ITCZ problem of the selected GCM to the sea surface temperature bias. Compared to the GCM's AMIP simulations, RCMs with higher resolution allow explicit deep convection and enable a better simulation of tropical convection and clouds.


Introduction
Dynamical downscaling-that is, the spatial refinement of low-resolution global climate models (GCMs) using limited-area regional climate models (RCMs)-is mainstay in climate-change impact assessment and in the planning of local adaptation measures (Senior et al., 2021).It has successfully been used in the extratropics for many decades.For instance, over Europe a large set of simulations is currently available at resolutions from 12 km (Jacob et al., 2014;Sørland et al., 2021) to 3 km (Ban et al., 2021;Ferraro et al., 2017;Iguchi et al., 2017;Lee et al., 2017;Pichelli et al., 2021;Tian et al., 2017).Downscaling relies on the consistency between the synoptic-scale fields of the driving GCM and the driven RCM (Jones et al., 1995).Large differences in circulations are undesirable since they inevitably lead to inconsistencies near the lateral boundaries.It then follows that significant large-scale biases of the driving GCM are problematic, since in general one would expect the same biases in the RCM.In the tropics, significant biases are common, indeed the representation of the Intertropical Convergence Zone (ITCZ) is fraught with difficulties.These largescale biases lead to challenges with downscaling methodologies (de Medeiros et al., 2020;Nobre et al., 2001;Sun et al., 2005;Tang et al., 2019).
The ITCZ, which exists due to the convergence of the trade winds, plays an important role in the tropical climate (Waliser & Jiang, 2015).The ITCZ locates mainly in the Northern hemisphere throughout the year except for boreal spring.During this period, the ITCZ reaches its southernmost location due to solar heating, when the observations show a strong precipitation band north of the equator and a secondary precipitation band south of the equator in the Western Pacific, and a single band straddling the equator over the tropical Atlantic.However, GCMs have difficulty simulating asymmetric precipitation distribution.In boreal spring, they produce too strong precipitation within the secondary band over the Pacific and a miss-placed band over Tropical Atlantic, which is too far in the south (G.J. Zhang et al., 2019).The annual mean precipitation projected by GCMs thus shows two distinctive bands on both sides of the equator instead of producing a single northern band indicated by the observation, which is called the double ITCZ problem (Adam et al., 2018;Lin, 2007;Mechoso et al., 1995;Tian & Dong, 2020;Si et al., 2021;G. J. Zhang et al., 2019).
The double ITCZ bias is more distinctive among coupled ocean-atmosphere models compared with those models forced with observed sea surface temperature (SST) (F.Song & Zhang, 2016;F. Song & Zhang, 2017).The coupled models typically produce warmer SST in the east of the tropical Pacific and Atlantic near the coast and colder SST in the west of the tropical Atlantic and middle of the Pacific.On the one hand, SST is closely related to the convective activity over tropical oceans by affecting the surface flux of heat and moisture (Hirota et al., 2011).On the other hand, the SST gradients also impacts lower-level wind convergence (Lindzen & Nigam, 1987), thereby affecting the simulation of the ITCZ.
While the double-ITCZ problem is less severe among GCMs with prescribed sea surface temperature, it still exists (Richter & Xie, 2008;Xiang et al., 2017).Convection and boundary layer parameterizations of the GCMs are believed to play one of the most important roles in the misrepresentation of the ITCZ (Bellucci et al., 2010;Hirota et al., 2011;Landu et al., 2014;Zhou et al., 2022).Many studies have been working on improving the convection schemes to alleviate the double ITCZ problem (X.Song & Zhang, 2009;Möbis & Stevens, 2012;X. Song & Zhang, 2018).Nolan et al. (2016) found that aquaplanet simulations with explicit instead of parameterized convection would smooth out the double ITCZ structures due to a better representation of squall lines.Therefore, using km-scale models with explicit convection can reduce the double ITCZ bias and enable a better representation of the tropical climate and quantification of climate sensitivity (Tian, 2015).
The long-existing double-ITCZ biases in GCMs pose a major challenge to dynamical downscaling since the lateral boundary bias from the driving GCMs might make it hard to accurately produce limited-area simulations with RCMs.In this context, it is important to investigate how the double-ITCZ in the driving GCMs affects the limited-area simulations and whether the problem can be circumvented.Heim et al. (2023) explored the pseudoglobal warming (PGW, see Brogli et al. (2023)) approach which uses a reanalysis-driven control simulation and therefore is unaffected by GCM control biases.They showed that the approach enables a credible representation of the tropical climate change without double-ITCZ bias in the limited-area simulation (Heim & Schär, 2023).However, a potential disadvantage of the PGW approach is the neglect of changes in short-term synoptic climatology.Here we apply another methodology to adjust the bias of the driving fields before conducting the dynamical downscaling (Misra & Kanamitsu, 2004).Previous studies using the approach mainly focus on extratropics (Colette et al., 2012;Hernández-Díaz et al., 2019).Here we thus try to assess the potential of the biascorrected downscaling approaches over the tropics.
In this study, we use the Consortium for Small-Scale Modeling (COSMO) in climate mode with explicit deep convection combined with a bias-correction method to downscale the GCM MPI-ESM1-2-HR model results over tropical Atlantic to investigate whether the double-ITCZ problem could be removed through such kind of downscaling and thus provide a possibility for constraining the cloud feedbacks.

Model and Set-Up
We use the fully compressible non-hydrostatic limited-area COSMO model (Baldauf et al., 2011;Rockel et al., 2008) version 6 to conduct the dynamical downscaling.This version of COSMO exploits graphics processing units which speeds up the simulation and enables experiments with high computational demand (Leutwyler et al., 2016).Rayleigh damping is applied for the upper boundary following Durran and Klemp (1983).The computation of radiative fluxes follows the δ-two-stream approach after (Ritter & Geleyn, 1992).For the computation of subgrid-scale vertical turbulent flux, we employ a 1D TKE-based model (Raschendorfer, 2001).
The Tiedtke scheme (Tiedtke, 1989) is applied as convection parameterization, but in some simulations we switch off this parameterization, or only switch on the shallow convection scheme (Vergara-Temprado et al., 2020;Zeman et al., 2021).Over the ocean, the sea-surface temperature is prescribed.
All simulations are run with 60 vertical levels and a horizontal grid spacing of 12 km.To determine the parameter settings and the convection parameterization scheme, we applied the systematic calibration developed by S. Liu et al. (2022) based on the work of Bellprat et al. (2012Bellprat et al. ( , 2016)).The calibration and downscaling simulations are performed over the tropical and sub-tropical Atlantic with a size of 867 × 658 grid columns (green domain in Figure 1).Details about the model calibration can be found in the Supporting Information S1.

Conventional Downscaling
Dynamical downscaling is applied to the result of the CMIP6 historical simulation of the MPI-ESM1-2-HR model (Max Planck Institute for Meteorology, 2020;von Storch et al., 2017), following a recent study (Heim et al., 2022).The MPI-ESM1-2-HR input for the COSMO model has a horizontal resolution of around 100 km and 95 vertical levels.The boundary condition is updated 6-hourly.2D surface pressure, skin temperature, 3D temperature, wind and specific humidity are included as the lateral-boundary conditions.SST is prescribed based on the MPI-ESM1-2-HR result.The GCM results are downscaled to 12 km using the calibrated parameters as described in the Supporting Information S1.

Bias-Corrected Downscaling
We use a bias-corrected downscaling methodology, where the GCM data is corrected using the European Center for Medium-Range Weather Forecast (ECMWF) Re-Analysis (ERA5) data (Hersbach et al., 2020) to make the climatology essentially bias free.
The bias-corrected downscaling methodology has been pioneered by Misra and Kanamitsu (2004) and it has been further applied in some recent studies (Colette et al., 2012;Hernández-Díaz et al., 2019).The basic idea is to use where OBS denotes observations (in our case the ERA5 reanalysis), HIST represent historical climate conditions taken from a GCM, both OBS and HIST periods must be chosen long enough to reduce the effects of internal variability (e.g., averages of 30 years).The climate deltas Δ = Δ(x, y, p, t m ) represent the set of 2D and 3D fields used to drive an RCM, but here merely the mean-seasonal cycle is provided with monthly resolution (i.e., m = 1-12).The bias-corrected control simulation is then driven by By design, the procedure using Equations 1-2 yields monthly-mean fields CTRL BC which are essentially identical to OBS.This means that the large-scale monthly-mean biases of the driving GCM CTRL are removed.However, there will still be some remaining biases.In particular, the short-term variations are taken from the GCM, and the statistics of synoptic systems may still deviate from reality.
The procedure is closely related to the PGW approach (Brogli et al., 2023;Misra & Kanamitsu, 2004;Schär et al., 1996), which is normally used to study regional climate change in response to global warming (Adachi et al., 2012;Prein et al., 2017;C. Liu et al., 2017;Musselman et al., 2018).As with the PGW approach, the biascorrected boundary fields must undergo a pressure adjustment to restore hydrostatic and thermal wind balance (Brogli et al., 2023).

SST-Corrected Downscaling
To see how much the bias originates from the GCM's SST bias, we will also conduct additional simulations with only the SST bias corrected.The MPI-ESM1-2-HR simulation significantly overestimates SST in an area stretching from the African to the Brazilian coast (Figure 2), especially to the south of the equator and in boreal spring.When using SST-corrected fields from the MPI-ESM1-2-HR results for downscaling, this will be referred to as "SST-corrected downscaling".All downscalings are conducted for 10 years ranging from 1995 to 2004 with a 6-month spin-up.

Results
In the following we compare the representation of the ITCZ in reanalysis data (ERA5), satellite observations (GPCP, CERES), GCM simulations (MPI-ESM1-2-HR using AOGCM and AGCM simulations), and limitedarea simulations with the COSMO model using different downscaling procedures.Figure 3 shows the meridional cross section of the 10-year-mean precipitation and vertical mass flux over domain analysis_D1 (see Figure 1, the corresponding horizontal spatial plot of precipitation is provided in Figure S2 of the Supporting Information S1).The ERA5 reanalysis produces quite good results compared to the GPCP observation (see red and black curves with the scale to the right of the panels).However, the coupled MPI-ESM1-2-HR shows a distinct double-ITCZ, which is mainly due to a misplaced ITCZ in boreal spring.In comparison, the AMIP simulation of the MPI-ESM1-2-HR model, which uses prescribed SST, produces stronger subsidence between 20°S and 10°S and much weaker updrafts as seen from the vertical mass flux (Figure 3c).The double-ITCZ bias is less severe, indicating that the atmosphere-ocean coupling enhances the ITCZ biases, as discussed in the introduction.
With conventional downscaling, one would like to find out whether the ITCZ bias is due to the large-scale forcing, or due to fine-scale processes that are better resolved in the higher-resolution RCM simulation.Results (Figure 3d) show that with conventional downscaling there are qualitatively similar results as with the driving GCM (MPI-ESM-2-HR).In comparison to the latter, the double-ITCZ bias is somewhat reduced in amplitude, but it remains a dominant feature of the response.Minor differences in comparison to the GCM simulation include the  somewhat stronger subsidence south of the equator, and enhanced updrafts between 10°S to the 0°.However, the results clearly show that the higher resolution of the RCM alone is not enough to remove the ITCZ bias induced by the driving GCM.
With the bias-corrected downscaling (Figure 3e), the large-scale climatological biases of the driving GCM are subtracted before the downscaling (see Section 2.3 for details of the bias correction).In response, the double-ITCZ bias disappears in the downscaled results.The differences between the bias-corrected and the conventional downscaling simulations mainly happen during boreal spring.There is stronger subsidence south of the equator in the bias-corrected case.In boreal summer, the vertical mass flux and precipitation in the conventional and bias-corrected downscaling simulations are similar.
To identify the responsible element of the bias, we also present results of SST-corrected downscaling.The bias correction is done similarly as in the fully bias-corrected case, but only applied to the SST field.Results are similar as in the bias-corrected version, indicating that the double-ITCZ problem of the conventional downscaling results primarily originates from the SST bias.
The time series of precipitation (Figure 4) further confirms this point.The overestimation of precipitation is highly related to the warm SST bias, as seen in the conventional downscaling case.As the SST warm bias is removed, the precipitation overestimation south of the equator mostly disappears.However, a slightly misplaced ITCZ is still present in both the bias-corrected and SST-corrected cases.For example, the bias pattern in June-September during the years 1995, 1996 and 2002 indicates an ITCZ position too far north, while in the years 1997 and 2004, the ITCZ is too far south.The ITCZ bias pattern is highly correlated with the SST bias as shown by the green lines in Figure 4.When the SST is colder, the ITCZ moves further north and vice versa.
An important element of the double-ITCZ bias are the differences in outgoing longwave radiation in particular during the February-April period (OLR, see Figure 5, second row).In comparison to CERES and ERA5, the MPI model has substantially lower OLR over the southern trades (south of the ITCZ), and higher OLR over the northern trades.We believe this is closely related to the double-ITCZ bias, but it is not clear whether this is a reason for or consequence of the double-ITCZ bias.For instance, the MPI bias in OLR will weaken subsidence over the southern trades (and strengthen it over the northern trades), potentially affecting the position of the ITCZ.
On the other hand, a too southward position of the ITCZ will lead to changes in high clouds, which can explain the OLR biases.The characteristic OLR bias has also been noted in a previous study (Heim et al., 2023).
Regarding the downscaled COSMO simulations: it is evident that the main OLR bias of the MPI model is also present under conventional downscaling (Figure 5e) with comparable amplitude.However, both the biascorrected and the SST-corrected downscaling largely reduce the OLR bias.Results show that the biascorrected downscaling has a smaller bias than the SST-corrected downscaling, suggesting that factors beyond the SST bias contribute to the biases seen in the MPI model.

Conclusions
Motivated by the uncertainties in sub-tropical and tropical clouds and precipitation, there is a large interest to apply high-resolution limited-area convection-resolving models to the tropics.One critical challenge is the occurrence of the double-ITCZ bias in GCMs.Such large-scale biases cannot be corrected by high-resolution alone, that is, downscaling current GCMs at high resolution will in general replicate the double-ITCZ bias.
In the current study we have explored to debias the GCM output before downscaling.The methodology uses the raw high-frequency output of a GCM, but corrects the data for large-scale deficiencies occurring in the control climate.The approach has successfully been applied in the extratropics (Misra & Kanamitsu, 2004), and was here explored for the first time in the tropics.This is an alternative approach to the PGW approach which has recently successfully been explored in the tropics (Heim & Schär, 2023;Heim et al., 2023).
We use a large computational domain over the tropical and sub-tropical Atlantic with a spatial resolution (grid spacing) of 12 km.We used one particular GCM for the experiments (MPI-ESM1-2-HR).The main conclusions of the study are: • When directly driving the RCM with the raw GCM control output (conventional downscaling), the RCM reproduces a double-ITCZ similar as in the driving model.The use of high resolution alone is unable to correct for the double-ITCZ bias.
• When driving the RCM with the bias-corrected GCM fields (bias-corrected downscaling), the RCM credibly reproduces the observed ITCZ, although there are some small differences in the position of the ITCZ in the boreal summer period.• In order to pinpoint the reasons for the double-ITCZ bias, we have conducted an additional simulation where the bias correction is only applied to the SST field (SST-corrected downscaling).This simulation yields a qualitative realistic simulation of the ITCZ, but analysis of the OLR biases shows that it is not as successful as the fully bias-corrected downscaling.Also, this result pertains only to the GCM used, and the role of the SST biases might be smaller in other models.There are several limitations of the current study.First of all, we merely tested one particular GCM in the downscaling approach.Although the GCM considered has a substantial double-ITCZ bias, it is not clear whether the current results will carry over to other GCMs.Second, we did not address simulations using future scenario climates, but merely worked with control climates.It is not clear whether the beneficial impacts of bias-corrected downscaling also apply to the full climate-change approach using control and scenario simulations.Applying bias correction for future scenarios would presume that the biases of the GCMs remain fairly constant into the future.While this can not be guaranteed, we still think it would be worthwhile to explore this further, and might lead to additional insights regarding climate-change impact in regions that are heavily affected by biases in the representation of the ITCZ, such as the Amazon, West Africa or Indonesia.

(
GCM) results with RCMs in the tropics is problematic, as conventional downscaling replicates the driving model's Intertropical Convergence Zone (ITCZ) bias • The bias-corrected downscaling approach enables a credible simulation of the ITCZ in the limited-area downscaling domain • For the tested GCM, the double-ITCZ bias is mainly attributed to the SST bias Supporting Information: Supporting Information may be found in the online version of this article.

Figure 1 .
Figure 1.Simulation and analysis domains.The green domain (simulation) is used for the COSMO calibration and simulations.The red domain (Analysis1) is used for the cross section analysis.The black domain (Analysis2) is used to indicate the SST bias.

Figure 2 .
Figure 2. SST bias of the MPI-ESM1-2-HR historical simulation (defined as MPI-ESM1-2-HR ERA5) over a 30 year period (1985-2014) and for the two seasons with the most southern-and northernmost position of the ITCZ.The black domain (Analysis2) represents the domain with significant SST overestimation; it will be used in some of the analyses.

Figure 3 .
Figure 3. Meridional cross section of 10-year-mean precipitation and vertical mass flux over domain Analysis1.The panels show the result of different simulations (from top to bottom: ERA5, MPI-ESM1-2-HR historical simulation, MPI-ESM1-2-HR AMIP results, COSMO conventional downscaling, COSMO bias-corrected downscaling and SST-corrected downscaling).The first column shows the annual mean result, the second column boreal spring average in February-April and the last column shows boreal summer average in July-September.The red and black lines display the zonal mean precipitation from the data sets and the GPCP satellite observations, respectively (see scale to the right).The coupled MPI simulation shows a distinct double-ITCZ.The double-ITCZ is also visible in the MPI simulations with prescribed SST, and the conventional downscaling with COSMO based on the native MPI simulations.The bias-corrected downscaling as well as the SST corrected downscaling simulations show no double-ITCZ.

Figure 4 .
Figure 4. Time series of the precipitation bias (simulation minus GPCP) in the meridional cross section over the domain Analysis1 (contours), and the SST bias averaged over domain Analysis2 (green line).From top to bottom, the panels show the results of conventional downscaling, bias-corrected downscaling, and SST-corrected downscaling.The misplaced ITCZ is correlated with the SST bias.The bias-corrected downscaling as well as the SST-corrected downscaling remove the reoccurring positive precipitation bias south of the equator in boreal spring.

Figure 5 .
Figure 5. Outgoing longwave radiation for observations and model results.The panels show (from left to right): CERES observation, ERA5, MPI-ESM1-2-HR historical simulation results, MPI-ESM1-2-HR AMIP results, COSMO conventional downscaling, COSMO bias-corrected downscaling, and COSMO SST-corrected downscaling.The first row shows the annual mean result, the second row shows the boreal spring average (February-April) and the last row the boreal summer average (July-September).As CERES data is only available since March 2000, the plot is calculated based on data from March 2000 to December 2004.