Understanding the Biases in Daily Extreme Precipitation Climatology in CMIP6 Models

Abstract

Future projections in extreme precipitation depend heavily on climate models. Therefore, assessing their fidelity in reproducing the extreme rainfall characteristics in historical simulation is critical. We evaluated CMIP6 models' performance in reproducing the climatology of daily extremes, focusing on the global land monsoon (GLM) domain that feeds two‐thirds of the world's population. Compared with ERA5, models demonstrate a significant wet bias in GLM domain for the annual maximum daily precipitation (14.14%) and the extreme tail of daily precipitation distributions (32.53%), more than twice the global average. Decomposition of biases reveals that dynamic processes, particularly vertical velocity, primarily drive these biases. Using the quasi‐geostrophic $$\omega $$ equation, we determined that the component associated with large‐scale adiabatic disturbances ($${\omega }_{D}$$) mainly drives vertical velocity biases, with diabatic heating term amplifying them. Furthermore, a significant correlation between $${\omega }_{D}$$ biases and baroclinicity biases in midlatitude suggests that baroclinicity biases are a key contributor to the vertical velocity biases.

Introduction

In recent decades, global warming has increased atmospheric water vapor, leading to more frequent and intense extreme precipitation events globally (Alexander et al., 2006; O’Gorman, 2015; Prein et al., 2017; Shiu et al., 2012; Sun et al., 2021; Tabari, 2020). As temperatures rise, theoretically, the response rate of extreme precipitation is expected to be approximately 6%–7% per degree of warming (Allan & Soden, 2008; Norris et al., 2019; Trenberth, 1999), posing significant challenges for disaster mitigation and risk management. However, climate models, as the primary tool for simulating past and projecting future climate changes, still struggle with biases in capturing the mean state, interannual variations, and long-term trends of precipitation extremes (Chen et al., 2014; Dong & Dong, 2021; Kharin et al., 2013; Martinez-Villalobos & Neelin, 2021; Seneviratne et al., 2021; Srivastava et al., 2020; S. Kim et al., 2020). Even the latest models from the Coupled Model Intercomparison Project Phase 6 (CMIP6), despite improvements, continue to face significant biases, showing limited progress compared to CMIP5 in addressing them, with both phases exhibiting persistent systematic errors (Y.-H. Kim et al., 2020; Martinez-Villalobos et al., 2022; Norris et al., 2021; Seneviratne et al., 2021; Wang et al., 2021; Wehner et al., 2020). For instance, the CMIP6 models demonstrate substantial climatological biases in simulating extreme precipitation in various regions like tropical, arid, and semi-arid areas (Abdelmoaty et al., 2021; Y.-H. Kim et al., 2020). Overall, compared with ERA5, these daily extreme precipitation biases manifest as a wet bias across the globe, with particularly pronounced effects in many regions, such as North Africa and the South Atlantic, where the wet bias exceeds 45% (Seneviratne et al., 2021). Additionally, the uncertainty among models remains considerable (S. Kim et al., 2020). Therefore, understanding these biases remains one of the primary scientific challenges in the CMIP6 phase (Eyring et al., 2016).

The global land monsoon (GLM) regions, which support approximately two-thirds of the global population, experience intense precipitation predominantly during the local summer season, making them highly susceptible to extreme precipitation events (W. Zhang & Zhou, 2019). However, in the GLM regions compared with ERA5, the CMIP6 models still exhibit significant positive biases in extreme precipitation ranging from 17% to 38%, nearly twice or more than the global average biases ranging from 8% to 15% (Figure S1 and Table S3 in Supporting Information S1), an issue that has been recognized by many studies (e.g., Gusain et al., 2020). For example, in the South Asian monsoon region, most CMIP6 models struggle to reproduce the spatial distribution of extreme precipitation indices, generally exhibiting significant positive bias, with different model biases for the precipitation of very wet days (R95p) in Indochina ranging from −42.59% to +203.37% and in South China ranging from −38.29% to +97.79% (Tang et al., 2021). Some CMIP6 models still consistently exhibit a severe overestimation of the climatological extreme precipitation in parts of West Africa, with area-averaged biases exceeding 60% (Faye & Akinsanola, 2022). Several CMIP6 models do not accurately capture the spatial distribution and observed amplitude of the simple precipitation intensity index over the East Asian region (Ayodele et al., 2022). These significant biases highlight the urgent need to study the underlying mechanisms in extreme precipitation to improve climate models in the GLM regions. Consequently, our research focuses on investigating the causes of model biases across global and regional monsoon domain to enhance our understanding of extreme precipitation mechanisms in both model simulations and observations.

Various extreme precipitation indices have been used to investigate the biases in climate models, such as the annual maximum daily precipitation (Rx1day), mean intensity of top 5% and 1% daily precipitation over wet days (R95, R99). Besides, the cutoff scale of daily precipitation probability distributions (P_M) has also been applied to evaluate the model biases. Compared to other well-known conventional indices, the P_M is an index with a clear physical meaning, as briefly explained in Section 2.3, which has already been extensively discussed in other studies (Chang et al., 2022; Martinez-Villalobos & Neelin, 2018; Neelin et al., 2017).

In past studies, the evaluation of extreme precipitation simulations has primarily relied on model performance metrics based on mean values and variance (Sillmann et al., 2013; Tang et al., 2021). Additionally, shape properties (e.g., skewness coefficient) have also been considered (Abdelmoaty et al., 2021). For mechanism research of model biases in extreme precipitation, numerous previous studies have investigated the sources of these biases, generally focusing on a single model (K. Zhang et al., 2017; Terai et al., 2018). These studies have laid a solid foundation for conducting multi-model research on the underlying mechanism driving extreme precipitation. The physical scaling diagnostic approach has been widely used in previous studies (Chang et al., 2022; Dai & Nie, 2020; Nie & Fan, 2019; O’Gorman & Schneider, 2009; Pfahl et al., 2017). This method quantitatively decomposes the impacts of dynamics and thermodynamics, thereby significantly improving our understanding of extreme precipitation model biases. To further dissect the dynamic components, we utilized the Quasi-Geostrophic (QG) $$\omega $$ equation to analyze the vertical velocity. The dynamic contributions related to vertical velocity were further decomposed into those arising from large-scale disturbances and diabatic heating processes, facilitating a deeper understanding.

The remainder of this study is organized as follows. The data sets and methodologies used in this research are described in Section 2. In Section 3, we investigate the climatological characteristics of CMIP6 model biases in extreme precipitation, and review the mechanisms by decomposing the contributions from dynamic and thermodynamic processes to these biases, and further explore the sources of the dynamic contributions. Finally, conclusions are drawn in Section 4.

Data and Methods

Reanalysis Data Set and Model Output

In this study, we used the ERA5 reanalysis data set (Hersbach et al., 2023a, Hersbach et al., 2023b) and CMIP6 historical simulations (Eyring et al., 2016; Table S1 in Supporting Information S1) to investigate model biases in extreme precipitation. Both data sets provide daily data from 1979 to 2014, including precipitation, air temperature, zonal wind, vertical pressure velocity and geopotential height, with surface pressure on a monthly timescale. Due to the variable availability, 11 models were used, with average Rx1day bias consistent with results from 37 models (Figures S1 and S2 in Supporting Information S1). To reduce errors arising from the resolution difference between ERA5 (0.25°) and the 11 CMIP6 models (range from ∼0.7° in EC-Earth3 to ∼2.8° in MIROC-ES2L), we employed a two-step interpolation strategy. First, high-resolution ERA5 data were interpolated to the native grid of each model to calculate the individual model bias. Second, these biases were re-interpolated to a uniform 1-degree grid to derive multi-model ensemble bias. Besides, to evaluate the robustness of using ERA5 as a reference, five additional observational data sets were employed (Text S2 in Supporting Information S1).

Definition of the Monsoon Regions

We calculated the GLM domain following Kitoh et al. (2013), identifying land areas where differences in precipitation intensity between summer (May–September) and winter (November–March) exceeds 2.5 mm/day, using Global Precipitation Climatology Project data for the period 1979–2014. Note that the definition of the regional monsoons is distinct from that of the GLM domain. We adopt the IPCC AR6 boundaries for regional monsoon domains to facilitate separate analyses of each monsoon region (IPCC et al., 2021). As shown in Figure 1g, these regional monsoons include the South and South East Asian, East Asian, West African, North American, South American and Australian-Maritime Continent monsoons.

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Indicators of Extreme Precipitation

We primarily used the cutoff scale of daily precipitation distributions as the indicator of extreme precipitation. Physically, the cutoff scale, where precipitation likelihood sharply declines with event size, reflects the balance between moisture loss and convergence (Chang et al., 2022; Neelin et al., 2017). Conventional indicators such as Rx1day and high percentiles (99th and 95th) of precipitation on wet days (≥1 mm/day) were also utilized to facilitate comparisons with other studies.

To simplify calculations, we used the moment ratio $${P}_{M}$$ to indicate the cutoff scale $${P}_{L}$$ as they are proportional (Chang et al., 2022; Martinez-Villalobos & Neelin, 2018). The moment ratio $${P}_{M}$$ is expressed as: 1 $$\begin{array}{c}{P}_{M}=\frac{\left\langle {P}^{2}\right\rangle }{\langle P\rangle },\end{array}$$ where $$\left\langle {P}^{2}\right\rangle $$ and $$\langle P\rangle $$ denote the variance and mean precipitation across all wet days (≥1 mm), respectively.

Decomposition of Biases in Extreme Precipitation

To decompose biases in extreme precipitation into dynamic and thermodynamic contributions, we used a physical scaling diagnostic. Following previous studies (O’Gorman & Schneider, 2009; Pfahl et al., 2017), daily extreme precipitation ($${P}_{e}$$) can be estimated using vertical velocity ($${\omega }_{e}$$) and the vertical derivative of saturation specific humidity $${q}_{s}$$ when the saturation equivalent potential temperature $${\theta }^{\ast }$$ is constant, 2 $$\begin{array}{c}{P}_{e}\mathit{\sim }-\left\{{\omega }_{e}{\frac{d{q}_{s}}{dp}\vert }_{{\theta }^{\ast }}\right\}.\end{array}$$ Here {·} denotes a mass-weighted integral over the troposphere.

The biases in extreme precipitation ($$\mathit{{\increment}}{P}_{e}$$) between CMIP6 models and ERA5 were decomposed into dynamic ($${{\Delta }P}_{\mathrm{e}\_\text{dyn}}$$) and thermodynamic ($$\mathit{{\increment}}{P}_{\mathrm{e}\_\text{thermo}}$$) components using the following equations, 3 $$\begin{array}{c}{{\Delta }P}_{\mathrm{e}\_\text{thermo}}=-\left\{\overline{{\omega }_{e}}{\mathit{\vert }}_{\text{ERA}5}{\frac{d{q}_{s}}{dp}\vert }_{\text{CMIP}6}\right\}+\left\{\overline{{\omega }_{e}}{\mathit{\vert }}_{\text{ERA}5}{\frac{d{q}_{s}}{dp}\vert }_{\text{ERA}5}\right\},\end{array}$$ 4 $$\begin{array}{c}\mathit{{\increment}}{P}_{\mathrm{e}\_\mathrm{d}\mathrm{y}\mathrm{n}}=\mathit{{\increment}}{P}_{e}-\mathit{{\increment}}{P}_{\mathrm{e}\_\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{m}\mathrm{o}}\end{array}$$

Note that all fractional biases in this study are expressed relative to ERA5 extreme precipitation values.

Decomposition of the Vertical Velocity by the QG $$\boldsymbol{\omega }$$ Equation

The QG $$\omega $$ equation is applied to decompose vertical velocity into different contributions to understand factors controlling biases in extreme precipitation. It represents a method for diagnosing midlatitude synoptic-scale vertical motion at a specified time: 5 $$\begin{array}{c}\left({\mathit{\partial }}_{\mathit{pp}}+\frac{\sigma }{{f}^{2}}{\mathit{\nabla }}^{2}\right){\omega }_{\mathit{qg}}=-\frac{1}{f}{\mathit{\partial }}_{p}Ad{v}_{\xi }-\frac{R}{p{f}^{2}}{\mathit{\nabla }}^{2}Ad{v}_{T}-\frac{R}{p{f}^{2}}{\mathit{\nabla }}^{2}Q,\end{array}$$ where $$\sigma $$ represents the dry stability, $${\omega }_{\mathit{qg}}$$ is the vertical velocity calculated by QG $$\omega $$ equation, $$f$$ is the Coriolis parameter, and Q is diabatic heating. $$Ad{v}_{\xi }=-\overrightarrow{{\boldsymbol{v}}_{\boldsymbol{g}}}\mathit{\cdot }\mathit{\nabla }\xi $$ and $$Ad{v}_{T}=-\overrightarrow{{\boldsymbol{v}}_{\boldsymbol{g}}}\mathit{\cdot }\mathit{\nabla }T$$ denote the horizontal advections of absolute vorticity ($$\mathit{\nabla }\xi $$) and temperature ($$\mathit{\nabla }T$$), respectively. This allowed us to decompose $$\omega $$ into a dry adiabatic dynamic term induced by large-scale motions ($${\omega }_{D}$$) and diabatic heating term ($${\omega }_{Q}$$). Specifically, $${\omega }_{D}$$ consists of contributions from the vorticity advection ($${\omega }_{\xi }$$), temperature advection ($${\omega }_{T}$$), and lower boundary forcing ($${\omega }_{\mathit{BF}}$$). Thus, the total vertical velocity can be expressed as, 6 $$\begin{array}{c}\omega ={\omega }_{\mathit{qg}}+{\omega }_{\mathit{aqg}}={\omega }_{D}+{\omega }_{Q}+{\omega }_{\mathit{aqg}}={\omega }_{\xi }+{\omega }_{T}+{\omega }_{\mathit{BF}}+{\omega }_{Q}+{\omega }_{\mathit{aqg}},\end{array}$$ where $${\omega }_{\mathit{aqg}}$$ represents error due to the QG approximation. Notably, the QG $$\omega $$ equation is unsuitable for tropics, so we excluded latitudes between 10°S and 10°N. This inevitably excludes a portion of the monsoon regions from our analysis. To optimize the decomposition, each grid point was calculated within a 7.5° × 7.5° regional box, see details in the Supporting Information S1, as previous studies show the validity of QG approximation for wavelengths above 500 km (Nie & Sobel, 2016). Considering the horizontal scale of extreme precipitation events in climate models is approximately 700 km (Dwyer & O’Gorman, 2017), a resolution of 7.5° is appropriate for our analysis.

Baroclinic Instability Criterion

To evaluate model performance in simulating baroclinicity, we employ the Baroclinic Instability Criterion (BIC), which offers a reliable estimate of baroclinicity as previous studies showed (Phillips, 1954; Seo et al., 2023), expressed as, 7 $$\begin{array}{c}\text{BIC}=\frac{{f}^{2}\left({u}_{250}-{u}_{850}\right)}{\beta gH\left({\theta }_{250}-{\theta }_{850}\right)/{\Theta }_{0}},\end{array}$$ where $$f$$ is the Coriolis parameter, $$g$$ is gravity, $$H$$ is the thickness between 250 hPa and 850 hPa, $$\beta $$ is $$\frac{df}{dy}$$, and $${\Theta }_{0}$$ (set at 290 K) is the standard potential temperature.

Results

Climatological Characteristics of Model Biases in Extreme Precipitation

As observed, a general global wet bias in extreme precipitation is prominent across several indices, including Rx1day, P_M (Figures 1a and 1b), and the mean intensity of top 5% and 1% daily precipitation over wet days (R95 and R99, Figure S2 in Supporting Information S1). For Rx1day, approximately 81% of the global regions show a wet bias compared with ERA5. Globally, the CMIP6 multi-model ensemble overestimates extreme precipitation by 6.21% ± 20.64% for Rx1day and 14.14% ± 27.16% for P_M. The spatial distribution of these biases is consistent across the different indices, with significant wet biases observed in regions such as Africa, the Tibetan Plateau, central South America, the Maritime Continent, the northeastern Pacific, the southeastern tropical Pacific and the southern tropical Atlantic (Figure S2 in Supporting Information S1). Meanwhile, regions such as the northern Arabian Sea, the southeastern Indian Ocean, the equatorial Pacific, and the northern Atlantic exhibit notable dry biases.

In terms of zonal mean, the CMIP6 models generally capture the observed latitudinal distribution of extreme precipitation but significantly overestimate it across most latitudes (Figures 1c and 1d). The overestimation is particularly pronounced in the southern tropics, with biases being significantly higher in the Southern Hemisphere compared to the Northern Hemisphere. Specifically, the Rx1day biases are 4.31 mm/day in the Southern Hemisphere versus 0.38 mm/day in the Northern Hemisphere, while the P_M biases are 2.64 mm/day versus 1.49 mm/day, respectively. It is also crucial to highlight that individual model biases can vary considerably from the multi-model mean, leading to substantial intermodel uncertainty (Figure 1d).

In the GLM area, both the zonal mean results (Figure 1e) and regional averages (Figure 1g) reveal more significant biases and greater intermodel uncertainty (Figure 1f) when compared to global averages. For instance, biases averaged over the GLM area for Rx1day (14.14% ± 30.91%) and P_M (32.53% ± 43.46%) are more than twice the global averages. Regionally, the averaged biases in the South American Monsoon, North American Monsoon, West African Monsoon and AusMCN Monsoon regions are comparable to or greater than the GLM area average. Though the South Asian Monsoon and East Asian Monsoon regions exhibit the smaller wet biases, it partly results from the cancellation of dry biases over the central Indian and the Sichuan Basin, respectively.

These substantial biases in densely populated regions prone to extreme precipitation make it challenging to accurately understand and predict precipitation patterns. Besides, in the GLM regions, the spatial pattern of P_M biases closely resembles those of traditional indices (Figure S1 and Figure S2 in Supporting Information S1), but with greater amplitude (Figure 1g), which facilitates further research and investigation. Consequently, our subsequent analysis will primarily focus on GLM area, using P_M as the main index.

Decomposition of Extreme Precipitation Biases

The scaling approach (Equation 2) effectively captures the biases in extreme precipitation as characterized by P_M, achieving a pattern correlation coefficient of 0.97, and exceeding 0.89 for other indices such as Rx1day, R99, and R95 (Figure S3 in Supporting Information S1) in the GLM regions. Furthermore, when P_M is used as the precipitation indicator in GLM regions, the scaling approach can explain approximately 80% of the model bias. To investigate the underlying causes of these systematic biases, we performed a thermodynamic and dynamic decomposition of extreme precipitation model biases based on Equations 3 and 4, using P_M as the index. As shown in Figure 2, the spatial pattern of the dynamic contribution closely matches the overall bias pattern, with the pattern correlation coefficients reaching up to 0.99 in GLM regions. Moreover, in the GLM regions, the dynamic contribution accounted for 28.58% ± 48.85% of the total wet bias of 32.53% ± 43.46%, confirming biases in dynamic processes as the dominant driver of the overall bias. This characteristic is consistent across various extreme precipitation indices (Figure S3 in Supporting Information S1) and models (Figures S4 and S5 in Supporting Information S1). In contrast, the thermodynamic contribution is minimal and largely negative (−1.23% ± 2.23%).

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For the regional monsoon domains, model biases in extreme precipitation are similarly driven predominantly by dynamic processes, with these wet biases almost resulting from the contribution of dynamic processes (Figure 2d). By comparison, the thermodynamic contributions are mostly negative and nearly negligible. A significant correlation is found between biases in dynamic processes and biases in column averaged vertical velocity (correlation coefficient of 0.97, Figure S6 in Supporting Information S1), underscoring that vertical velocity biases are the primary drivers of the wet biases in extreme precipitation.

Causes of Model Bias in Vertical Velocity

Given that dynamic processes, particularly vertical velocity, dominate the biases in extreme precipitation, in this section, we investigate the sources of vertical velocity biases, mainly focusing on the GLM regions and using P_M as the indicator. Here we applied the QG $$\omega $$ equation, widely used in research on extreme precipitation (e.g., Li & O'Gorman, 2020; O’Gorman, 2015; Tandon et al., 2018), to investigate biases in vertical velocity associated with large-scale disturbances. In the GLM regions, the spatial distribution of vertical velocity biases for extreme precipitation days can be largely captured by the QG $$\omega $$ equation, with the pattern correlation coefficients exceeding 0.90 (Figure S7 in Supporting Information S1 and Figure 3a). These biases, which are predominantly negative, correspond to the extreme precipitation biases. The decomposition shows that the large-scale adiabatic forcing term ($${\omega }_{D}$$), that is, the sum of $${\omega }_{\xi }$$, $${\omega }_{T}$$ and $${\omega }_{\mathit{BF}}$$, and the diabatic heating term ($${\omega }_{Q}$$) bear high pattern similarity (Figures 3b and 3c). Though $${\omega }_{Q}$$ biases are larger than $${\omega }_{D}$$ biases, as noted in previous studies (Dai & Nie, 2021; Nie et al., 2020), $${\omega }_{Q}$$ biases can be regarded as the feedback term and are largely driven by $${\omega }_{D}$$ biases in extratropics. As shown in Figure 3d, significant correlation is found between the column averaged $${\omega }_{D}$$ bias and $${\omega }_{Q}$$ bias in GLM regions. Moreover, this relationship is more pronounced in the midlatitudes (Figure S8 in Supporting Information S1). These results indicate that biases in $${\omega }_{D}$$ are crucial in forming the overall vertical velocity bias.

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As mentioned above, $${\omega }_{D}$$ can be divided into the vorticity advection term ($${\omega }_{\xi }$$), the temperature advection term ($${\omega }_{T}$$) and the lower boundary forcing ($${\omega }_{\mathit{BF}}$$) (Equation 6). Since both $${\omega }_{\xi }$$ and $${\omega }_{T}$$ are closely related to atmospheric baroclinicity (Dai & Nie, 2020; Eady, 1949; Trenberth, 1991; Yin, 2005; Figure S9 in Supporting Information S1), we refer to their sum as the baroclinic term $${\omega }_{\mathit{BC}}$$ (Figure 4a). Consequently, $${\omega }_{D}$$ can be expressed as the sum of $${\omega }_{\mathit{BC}}$$ and $${\omega }_{\mathit{BF}}$$. Among these components, $${\omega }_{\mathit{BF}}$$ emerges as a major source of biases in regions with significant topography, such as the Tibetan Plateau, Rocky Mountains, and Andes (Figure 4b), which is possibly linked to model resolution. Higher-resolution models from the same institution show notable reduction in biases over topographical regions: MPI-ESM1-2-HR reduces biases by approximately 17% compared to MPI-ESM1-2-LR, and NorESM2-MM achieves nearly 29% reduction over NorESM2-LM (Figures S10 and S11 in Supporting Information S1).

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Due to the coarse vertical resolution of CMIP6 daily output, for example, in regions where surface pressure ranges between 1,000 and 850 hPa, $${\omega }_{\mathit{BF}}$$ is calculated using 850 hPa as the boundary level, introducing influences from other factors, which are likely dominated by $${\omega }_{\mathit{BC}}$$. In the GLM regions without significant topography, $${\omega }_{\mathit{BF}}$$ is predominantly modulated by $${\omega }_{\mathit{BC}}$$, with a spatial correlation coefficient exceeding 0.6. Therefore, in regions outside of significant topographical areas, $${\omega }_{D}$$ bias is largely associated with $${\omega }_{\mathit{BC}}$$ bias.

To reveal the relationship between $${\omega }_{\mathit{BC}}$$ biases and biases in atmospheric baroclinicity, we calculated the BIC for both 36-year mean and extreme precipitation days (Figure S12 in Supporting Information S1). The models demonstrate an overall overestimation of baroclinicity, with this overestimation being even more pronounced on extreme precipitation days. Model biases in BIC show a pattern similar to the $${\omega }_{\mathit{BC}}$$ biases (Figures 4a and 4c), particularly in midlatitudes where atmospheric baroclinicity is significant. In midlatitude monsoon regions poleward of 30°N/S, BIC and total $${\omega }_{\mathit{BC}}$$ biases are highly correlated, with pattern correlations of −0.65 and −0.74 for the North American and East Asian Monsoon regions, respectively. Across midlatitudes (30°–60°) in both hemispheres, BIC and total $${\omega }_{\mathit{BC}}$$ biases also show a significant spatial correlation (−0.57). Meanwhile, a strong correlation exists between regionally averaged BIC bias and total $${\omega }_{\mathit{BC}}$$ bias, suggesting the intermodel spread of total $${\omega }_{\mathit{BC}}$$ biases are closely linked to BIC bias (Figure S13 in Supporting Information S1).

Conclusions and Discussion

In this study, we evaluate the performance of 11 CMIP6 models in reproducing the climatology of daily extreme precipitation, and further investigate the main source of biases in extreme precipitation, focusing on the GLM regions. We primarily use the ERA5 data set as the reference, since ERA5 data set provides global coverage over an extended period of time at high resolution, which is other data sets not available, and has been widely used in the study of extreme precipitation (e.g., Y.-H. Kim et al., 2020; Seneviratne et al., 2021; Wehner et al., 2020). An overall wet bias in extreme precipitation is found in GLM regions for Rx1day (14.14% ± 30.91%) and P_M (32.53% ± 43.46%), representing the extreme right-tail, more than twice the global average bias. Similar wet biases are also present in other data sets, such as Rainfall Estimates on a Gridded Network (REGEN; Contractor et al., 2020; Seneviratne et al., 2021). To enhance the robustness of our main conclusion, we also used five observational precipitation data sets to calculate model biases in extreme precipitation (details in Text S2 of Supporting Information S1). In the GLM domain, ERA5 is comparable in magnitude to at least two of these data sets, reinforcing confidence in the reliability of ERA5-based conclusions. Caution is warranted when focusing on regions with larger observational spread, particularly in tropical and high-latitude oceans (see Text S2 of Supporting Information S1).

By decomposing P_M biases using the physical scaling diagnostic, we find that dynamic processes (28.58% ± 48.85%) predominantly cause extreme precipitation biases across the GLM regions, accounting for most of the total wet bias. In contrast, thermodynamic contributions (−1.23% ± 2.23%) are minimal and tend to offset the total wet bias. To explore the causes of wet biases in dynamic processes, we employ the QG $$\omega $$ equation to decompose vertical velocity biases. Our results indicate that biases in the large-scale adiabatic forcing term ($${\omega }_{D}$$), which comprises the vorticity advection term ($${\omega }_{\xi }$$), temperature advection term ($${\omega }_{T}$$) and lower boundary forcing ($${\omega }_{\mathit{BF}}$$), are pivotal in shaping vertical velocity biases, with the diabatic heating term ($${\omega }_{Q}$$) further amplifying these biases. In regions with significant topography, the boundary-forcing term ($${\omega }_{\mathit{BF}}$$) exhibits substantial bias, which can be effectively reduced by increasing model resolution. In land areas without significant topography, $${\omega }_{\mathit{BF}}$$ biases largely include influences from the baroclinic term ($${\omega }_{\mathit{BC}}$$) due to the coarse vertical resolution in CMIP6 daily output. We also found a solid link between biases in the baroclinic term $${\omega }_{BC}$$ ($${\omega }_{\xi }+{\omega }_{T}$$) and the models' overestimation of atmospheric baroclinicity. In midlatitudes, BIC biases and $${\omega }_{\mathit{BC}}$$ biases exhibit significant spatial correlations, with regionally averaged BIC biases and $${\omega }_{\mathit{BC}}$$ biases also showing significant intermodel correlations. These findings suggest that biases in atmospheric baroclinicity may play a critical role in shaping vertical velocity biases, thereby providing insight into extreme precipitation biases. Note that the vertical velocity we used in analyzing the sources of bias was based on the ERA5 data set, and more data sets should be used to account for the uncertainty. Besides, while the scaling diagnostic performs well in the GLM domain, caution is advised in interpreting absolute bias magnitudes, especially in tropical ocean regions outside the GLM domain where discrepancies may be larger.

Acknowledgments

This study was supported by the National Natural Science Foundation of China (Number 42125502, 42375037, 42005118, 42205008), the Data Observatory Foundation ANID Technology Center (Number DO21000), the Proyecto ANID Fondecyt Iniciación 11250471, and the National Key Scientific and Technological Infrastructure Project Earth System Numerical Simulation Facility (EarthLab, No. 2023-EL-PT-000465).

Data Availability Statement

The data used in this study are publicly available. The CMIP6 model outputs can be accessed through the Earth System Grid Federation portal (). The ERA5 reanalysis data (Hersbach et al., 2023a, Hersbach et al., 2023b) are available at the Copernicus Climate Change Service (C3S) Climate Data Store at .