FORTE2 was developed as an intermediate-complexity coupled atmosphere-ocean general circulation model (Blaker et al., 2021). Its atmospheric module, the Intermediate General Circulation Model 4, operates at a T42 spectral resolution corresponding to roughly 2.8° horizontally, with 35σ vertical levels extending up to 0.1 hPa (Joshi et al., 2015). This atmospheric component integrates full physical parameterizations for radiation, land-surface properties, convection, precipitation, and clouds schemes (Zhong and Haigh, 1995; Betts and Miller, 1993). For the oceanic component, the Modular Ocean Model-Array is adopted (Webb, 1996), featuring a 2°× 2° horizontal grid with 15 vertical z-levels whose thickness increases with depth, ranging from 30 m at the sea surface to 800 m at the model bottom, with a total ocean depth of 5000 m (Stjern et al., 2024). Within the model system, sea ice functions as a thermal barrier restricting heat exchange between the ocean and atmosphere, and the coupled system runs without any flux adjustment terms.

Building on the FORTE2 platform, Stjern et al. (2024) designed and implemented a suite of Systematic Regional Aerosol Perturbations experiments. For brevity, hereafter we refer to these simulations collectively as FORTE2. This experimental framework supports systematic investigation of climate impacts driven by aerosols from distinct geographic regions and of different chemical compositions, across various background climate scenarios. It also enables quantitative comparison between ARI and ACI effects, facilitating assessment of their respective contributions and potential interactive mechanisms. Instead of using aerosol emission or concentration fields as forcing inputs, a standard practice in most CMIP6 models including those participating in the Precipitation Driver and Response Model Intercomparison Project (PDRMIP) (Myhre et al., 2017), the FORTE2 simulations are forced by global gridded monthly aerosol optical depth (AOD) products with explicit vertical profiles, derived from the Copernicus Atmosphere Monitoring Service Reanalysis (CAMSRA) dataset (Inness et al., 2019).

Within the CAMSRA dataset, anthropogenic emissions for BC, organic carbon, and sulfur dioxide are sourced from the MACCity emission inventory for the 2003–2010 period, and switch to the Representative Concentration Pathway 8.5 emission scenarios from 2010 onward (Granier et al., 2011; Riahi et al., 2011). In the model setup, aerosols are assigned a vertically uniform distribution spanning from the second-lowest model layer, where σ (the ratio of grid pressure to surface pressure) equals approximately 0.88, corresponding to an altitude of around 950 m above the surface, upward to a defined upper pressure boundary referred to as pmin. For each individual grid cell, the value of pmin is calculated from CAMSRA data as the lower of two thresholds: 850 hPa, or the lowest pressure level at which the 2003–2021 average mixing ratio of the combined BC, OC, and SO₄ mixture drops below 5 × 10⁻⁹ kg kg⁻¹. In areas with complex terrain, additional constraints are enforced to avoid unrealistic aerosol vertical distributions, with σmin constrained to below 0.75 and pmin to above 300 hPa (Stjern et al., 2024). To generate the regional AOD perturbation fields, monthly speciated AOD and three-dimensional mass mixing ratio data from CAMSRA (2003–2021) are first interpolated to match the T42 model resolution. Monthly climatologies are then computed for three AOD categories at each grid point: total anthropogenic aerosols (BC, OC, and SO₄), absorbing aerosols (BC and OC), and scattering aerosols (SO₄). These constructed idealized aerosol vertical profiles are subsequently input into FORTE2's radiation calculation scheme. Notably, FORTE2 does not include aerosol transport processes in its simulation configuration. A more detailed description of the aerosol implementation methodology in FORTE2 simulations is available in Stjern et al. (2024).

The FORTE2 simulations used in this study are summarized in Table 1. They include two baseline simulations without aerosol forcing: one with CO₂ concentrations at pre-industrial levels (piC, 280 ppmv), and one with elevated CO₂ (p1K, 500 ppmv). In this model, the p1K simulation yields a global-mean warming of approximately 1K relative to piC. In addition, six perturbation simulations were performed with SO₄ AOD forcing added over Asia (Fig. 1a). These comprise combined ARI and ACI effects (ARI + ACI), ARI-only and ACI-only effects, each run under both the piC and p1K background climate states. All simulations were carried out over a total 200-year period, with the first 50 years discarded as spin-up, and the remaining 150 years (model years 51–200) used for the analysis. For the climate response, subtracting each baseline from its corresponding perturbation (e.g., SO₄_p1K-p1K or SO₄_piC-piC) isolates the climate effects of sulfate aerosol relative to a no-aerosol state, including the total (ARI + ACI) effect as well as the separate contributions from ARI and ACI. The impact of the background climate is then estimated by comparing these effects between the p1K and piC backgrounds, i.e., (SO₄_p1K-p1K) - (SO₄_piC-piC), which reveals how a warmer, higher-CO₂ climate modulates the sulfate-aerosol-induced responses examined here.

For ARI, the prescribed SO₄ AOD and vertical profiles are input into the FORTE2 radiation scheme. The ACI parameterization for sulfate perturbations is applied exclusively within the Asian study domain, which spans 60–140° E and 0–53° N (marked by the white box in Fig. 1a). The ACI effect is triggered once the local AOD value surpasses a threshold of 0.07. This threshold was selected based on observed relationships between AOD variations and cloud top effective radius changes reported in Dong et al. (2019). To represent the magnitude of ACI effects, the effective radius of cloud droplets is reduced from 15 to 10 µm across low-level clouds, mid-level clouds, and shallow convective clouds. The 5 µm reduction in droplet radius falls within the range of values simulated by the majority of CMIP5 models for this cloud property (Wilcox et al., 2015).

In this experimental design, both the sulfate AOD magnitude and its vertical profile are prescribed as fixed monthly climatologies, meaning they do not evolve or adjust in response to simulated climate variations. This idealized approach means that no feedbacks exist between the climate response and aerosol distribution (e.g., enhanced precipitation does not lead to increased aerosol removal), and also excludes any interactive atmospheric chemistry changes. As a result, any observed differences in sulfate-induced climate response between the p1K and piC backgrounds can be attributed entirely to differences in the background climate state (such as warmer temperatures, higher atmospheric water vapor content, and altered large-scale circulation patterns), rather than to variations in the strength or distribution of the aerosol forcing itself.

We also qualitatively compare the FORTE2 results with simulations from the PDRMIP (Myhre et al., 2017). The PDRMIP models are fully coupled earth system models and are substantially more comprehensive than the FORTE2 framework. Specifically, we use experiments from five global climate models (CESM1-CAM5, GISS-E2-R, HadGEM3, MIROC-SPRINTARS, and NorESM1; Table 2). In the perturbation simulations, Asian SO₄ emissions/concentrations are set to ten times their year-2000 levels, while greenhouse gases are fixed at year-2000 levels. Each is compared against the corresponding model's baseline simulation with year-2000 aerosols and greenhouse gases. The climate response to sulfate aerosols is quantified as the difference between the perturbation and baseline simulations. It should be noted that the PDRMIP simulations prescribe a much stronger Asian SO₄ perturbation than FORTE2, with a regional summer multi-model mean (MMM) AOD of ∼ 2.5 over East Asia and South Asia, compared to ∼ 0.23 in FORTE2 (Fig. 1). Despite this difference in magnitude, the spatial pattern of the prescribed perturbation is similar between the two experiments (Fig. 1). Therefore, the comparison between PDRMIP and FORTE2 focuses on the sign and spatial pattern of the responses, rather than their magnitudes, in the subsequent analysis. In addition, the PDRMIP experiments are conducted under a single background climate state and therefore cannot assess the influence of a warmer background climate, which is the central focus of the present study.

To support observational comparison, daily precipitation records, monthly sea level pressure (SLP) fields, as well as monthly horizontal and vertical wind components were obtained from the fifth-generation ECMWF atmospheric reanalysis (ERA5). The dataset has a uniform horizontal grid spacing of 0.25° × 0.25° and covers the period from 1981 through 2010 (Hersbach et al., 2023a, b).

Following the standardized indicator framework put forward by the Expert Team on Climate Change Detection and Indices (ETCCDI), we derived four precipitation metrics for subsequent analysis. PRCPTOT (unit: mm) represents the cumulative precipitation sum across all wet days within the target season. R95p (unit: mm) denotes the total precipitation amount recorded exclusively on extremely wet days. R95d (unit: days) counts the total number of extremely wet days, and R95int (unit: mm d⁻¹) characterizes the average precipitation intensity of extreme events, calculated as the quotient of R95p divided by R95d. A wet day was defined as its daily precipitation reaches or exceeds 1 mm (Zhang et al., 2011). The 95th percentile of wet-day daily precipitation is adopted as the threshold for extremely wet days, with separate baseline references for different data sources: for FORTE2 and PDRMIP simulations, the percentile threshold is computed from their corresponding baseline simulations; for the ERA5 reanalysis, the 1981–2010 period is used as the reference baseline to derive the threshold. All analyses in this study focus on boreal summer (June–August, JJA).

To uncover the physical mechanisms driving precipitation changes, we employ an atmospheric column energy budget framework, which partitions precipitation-related energy variations into a thermodynamic component (denoted Q) and a dynamic component (denoted H) (Muller and O'Gorman, 2011; Richardson et al., 2016; Liu et al., 2018). In this framework, the latent heat release associated with precipitation changes (LcδP) is balanced by changes in net atmospheric diabatic cooling (δQ) and dry static energy (DSE) flux divergence (δH), as expressed in Eq. (1): 1LcδP=δQ+δH where Lc is the latent heat of condensation, P stands for precipitation, and δ denotes the change relative to the reference baseline simulation. The term δQ is calculated by summing variations in three factors: atmospheric longwave cooling, atmospheric shortwave absorption, and surface sensible heat flux. Correspondingly, δH is derived as the residual value obtained by subtracting δQ from LcδP.

The total DSE flux divergence anomaly δH is further divided into a time-mean component (δHm) and a transient eddy component (δHtrans), as shown in Eq. (2): 2δH=δHm+δHtrans δHm can be broken down into four distinct terms, which correspond to the dynamic and thermodynamic effects on vertical and horizontal DSE advection respectively. The full decomposition is presented in Eq. (3): 3δHm=δHDy_v+δHTh_v+δHDy_h+δHTh_h=∫δω‾∂s‾∂pdpg+∫ω‾δ(∂s‾∂p)dpg+∫δu‾⋅∇s‾dpg+∫u‾⋅δ(∇s‾)dpg where ω is vertical velocity (Pa s⁻¹), s is DSE (J kg⁻¹), p is pressure (Pa), g is the gravitational acceleration (m s⁻²), u is horizontal wind vector (m s⁻¹), ∇ is the horizontal gradient, and an overbar indicates climatological monthly means. Physically, δHDy_v reflects the dynamic effect arising from changes in vertical velocity; δHTh_v corresponds to the thermodynamic effect induced by changes in vertical DSE gradients; δHDy_hrepresents the dynamic effect caused by changes in horizontal wind fields; δHTh_h captures the thermodynamic effect related to changes in horizontal DSE gradients. Finally, δHtrans is calculated as a residual between δH and δHm.

To understand whether the models produce reasonable precipitation patterns and physically plausible large-scale circulation, we compare the FORTE2 p1K baseline and the PDRMIP baseline simulations with ERA5 (1981–2010). It is important to note that the background forcing differs among these datasets: the FORTE2 p1K simulation has no aerosol forcing and the CO₂ concentration that is slightly higher than present-day levels, whereas the aerosol and greenhouse gas forcing in PDRMIP is representative of year-2000 conditions. Given these idealized and differing forcing configurations, the comparison is intended as a sanity check of whether the models produce reasonable background climate states, rather than as a validation of the models' ability to reproduce the absolute observed climate. We therefore emphasize the spatial structures of precipitation and circulation over the exact magnitudes of the climatological fields.

In ERA5, R95p shows a spatial pattern similar to PRCPTOT, with maxima over northern India, Southeast Asia and South China (Fig. 2a and b). R95d is generally higher in the tropics than at mid- to high-latitudes, with a local maximum over Northwest China (Fig. 2c). R95int shows its highest values over the Asian summer monsoon region (Fig. 2d). The PDRMIP MMM reasonably reproduces the observed spatial patterns of PRCPTOT and extreme precipitation, with pattern correlation coefficients exceeding 0.85 (Fig. 2e–h). All individual PDRMIP models show pattern correlations above 0.6 for these indices, indicating reasonable agreement with the observed spatial patterns. FORTE2 also reasonably simulates these precipitation indices, although its pattern correlations are generally lower than those of the PDRMIP MMM, with values of 0.56 for PRCPTOT and 0.63 for R95p (Fig. 2i–j). Notable dry biases are also evident over India for PRCPTOT and R95p, a feature common among many CMIP5/6 models (Wilcox et al., 2020). The correlation is lower for R95d (0.39), largely associated with its relatively low values in the tropics, while R95int shows a comparatively higher correlation of 0.68 (Fig. 2k–l). These discrepancies may reflect both the differing prescribed external forcing and limitations in the model's convective parameterization scheme.

The simulated precipitation structures are further supported by the representation of the associated large-scale summer circulation. Both the PDRMIP MMM and FORTE2 reasonably simulate the basic circulation features relevant to the Asian summer monsoon compared to ERA5, including the land-sea pressure gradient, the continental low, the western North Pacific Subtropical High, and the associated horizontal and vertical wind fields (Fig. 3). However, FORTE2 differs from both the PDRMIP MMM and ERA5 in the intensity and spatial extent of some circulation features, most notably a stronger continental low and a weaker western North Pacific Subtropical High (Fig. 3a–c). The horizontal and vertical wind fields also show regional differences, particularly over the tropical Pacific, the Tibetan Plateau, and the tropical Indian Ocean (Fig. 3d–f).

Overall, the comparison suggests that, while the models differ from ERA5 in the magnitude and regional details of their climatological fields, they capture the key spatial structures of precipitation and large-scale circulation. Moreover, these precipitation and circulation characteristics in the FORTE2 p1K simulation mirror those found in its piC simulation (Fig. S1 in the Supplement), suggesting that their basic spatial structures remain robust across the two forcing conditions.

The spatial patterns of precipitation indices in response to increased Asian sulfate aerosols are illustrated in Fig. 4 for the PDRMIP MMM and the SO₄_p1K and SO₄_piC simulations in FORTE2. To intuitively reflect the magnitude of regional precipitation responses, relative changes in PRCPTOT, R95p and R95int with respect to the respective baseline simulations are shown in Figs. 4, 7–8, 11 and 13. It should be kept in mind that the sulfate perturbation in PDRMIP is roughly an order of magnitude stronger than the FORTE2 perturbation. Hence, the response magnitudes are expected to differ considerably between the two datasets. The PDRMIP MMM and the two FORTE2 simulations show significant reductions in PRCPTOT and R95p over East China and India, and enhancements over northwestern India (Fig. 4a–b, e–f, i–j), in response to increased sulphate, consistent with previous work (Liu et al., 2018). R95p exhibits a stronger response than PRCPTOT, suggesting that extreme precipitation is more sensitive to sulfate forcing than mean precipitation, consistent with Samset et al. (2018). The responses of R95d and R95int are similar to those of R95p, indicating that the reduction in R95p is characterized by a lower frequency and weaker intensity (Fig. 4c–d, g–h, k–l). While FORTE2 is a model of lower complexity, it broadly reproduces the key regional sign patterns of the five PDRMIP models, particularly drying over East Asia and South Asia and wetting over northwestern India.

In general, the changes in extreme precipitation are consistent with those in total precipitation, despite differences in magnitude, suggesting that the decreases in mean and extreme precipitation share some common drivers, such as large-scale circulation changes. To the extent that this holds, understanding the mechanisms behind mean precipitation changes can shed light on those driving extreme precipitation changes. Figure 5 shows the area-averaged atmospheric column energy budget terms (see Eqs. 1–3) for East Asia and South Asia (red and purple boxes in Fig. 4a, respectively). In both regions, the responses of LcδP are nearly equal to the responses of δH in the PDRMIP MMM and FORTE2 simulations, a result that is consistent across the five PDRMIP models. δQ is relatively small compared to δH and remains close to zero in the PDRMIP MMM. Hence, the dynamic effects induced by Asian sulfate forcing play a dominant role in decreasing summer precipitation over East Asia and South Asia.

Further, δH can be decomposed into δHm and δHtrans. δHm comprises four terms:δHDy_v, δHDy_h, δHTh_v, and δHTh_h, which represent dynamic and thermodynamic contributions to vertical and horizontal DSE advection, respectively. For the PDRMIP MMM (gray bars in Fig. 5), δHDy_v shows relatively larger negative changes than the other terms over both regions, and thus serves as the primary contributor to δH. Over East Asia, δHTh_h and δHtrans exhibit negative changes and contribute to δH, whereas δHDy_h provides a partial offset (Fig. 5a). Over South Asia, δHTh_v and δHDy_h act as negative contributors to δH, while δHtrans partially counteracts this reduction (Fig. 4b). However, some differences exist among the PDRMIP models. For instance, the contribution of δHtrans in NorESM1 (green asterisk) exceeds that of δHm over East China, which is opposite to the results in the other two models (purple triangle and blue cross) (Fig. 5a).

3D atmospheric outputs from FORTE2 were archived at three pressure levels (250, 500, and 850 hPa), allowing identification of the leading term within δHm. In the FORTE2 simulations (blue and green bars in Fig. 5), the remaining three terms are consistently smaller in magnitude than δHDy_v in both simulations, a finding that aligns with the PDRMIP MMM results. Hence, the dynamic effect of vertical circulation (δHDy_v) is the dominant driver of the precipitation reduction over both East China and India.

Figure 6 shows the spatial patterns of summer responses for the relevant variables in the PDRMIP MMM and in the SO₄_p1K and SO₄_piC simulations of FORTE2. The decrease in δHDy_v is associated with anomalous descent (Fig. 6a–c), accompanied by high-pressure SLP anomalies (Fig. 6d–f). These SLP anomalies result from surface cooling induced by enhanced AOD forcing (Fig. 6g–i), which reduces incoming shortwave radiation (SW) (Fig. 6j–l). The reduced SW partly results from direct scattering of SW through ARI, and partly from low cloud changes through ACI (Fig. 6m–n). The above analysis indicates that the responses to Asian sulfate forcing, along with the related physical processes simulated by FORTE2, agree with those of the PDRMIP models. The robustness of these responses confirms that FORTE2 provides a suitable tool for investigating precipitation responses under contrasting climate backgrounds.