Introduction

Accurately simulating the Indian Summer Monsoon (ISM) remains a persistent challenge for global climate models, despite advances in model physics and parameterizations. Reliable ISM simulation is crucial due to the high socioeconomic dependence of South Asia on monsoon precipitation. In India, where most agriculture is rain-fed, 70–80% of the annual precipitation occurs during the ISM (June-September) (e.g., Webster et al.1; Goswami et al.2; Sahany et al.3. However, Coupled Model Intercomparison Project (CMIP) models continue to exhibit precipitation biases4,5,6,7particularly over South and East Asia, the Indian Ocean, and the Intertropical Convergence Zone (ITCZ), adversely affecting regional climate predictions (e.g., Saha et al.8; Sukumaran et al.9; Tian and Dong10. These biases persist across multiple CMIP generations4,5,6,11indicating that increased resolution and updated physics alone have not resolved key ISM simulation deficiencies.

A major contributor to these precipitation biases is the inadequate simulation of large-scale circulation features, such as the upper-level tropical easterly jet (TEJ) and subtropical westerly jet (STJ), low-level Somali jet, and meridional shifts of the ITCZ (e.g., Wang et al.12; Kumar et al.7; Li et al.13. Inaccurate representation of the meridional tropospheric temperature gradient (MTTG) and vertical wind shear influence ISM precipitation variability7,11,14,15. Additionally, biases in simulating teleconnections between large-scale climate modes (e.g., El Niño–Southern Oscillation) and ISM affects precipitation variability on interannual to multidecadal timescales61,62.

Pathak et al.5,6 identified convective parameterization deficiencies, particularly assumptions in closure and trigger mechanisms as the primary cause of precipitation biases in CMIP models over South Asia. One key factor is the convective adjustment time-scale (\(\:\tau\:\)), which controls how quickly deep convection stabilizes the atmosphere. \(\:\tau\:\) strongly influences precipitation intensity and distribution, intraseasonal variability, and the simulation of equatorial waves and tropical cyclones17,18,20,21,22,23. Traditionally, \(\:\tau\:\) is prescribed as a fixed value (typically 1–3 h) based on expert opinion and observed cloud lifetimes24,25,26,27. However, a fixed \(\:\tau\:\) fails to represent the spatiotemporal variability of convection, contributing to biases in both precipitation and circulation (e.g., Liu et al.16; Jain et al.18. High-resolution regional climate model studies indicate that increasing \(\:\tau\:\) (e.g., to 24 h) reduces subgrid precipitation, while decreasing \(\:\tau\:\) (e.g., to 600 s) increases it28. These findings highlight the need for a dynamically varying \(\:\tau\:\) to improve model fidelity.

Besides convection, recent advances underscore the importance of microphysical parameterizations in precipitation simulation. Processes such as auto-conversion and the representation of stratiform low clouds significantly affect precipitation partitioning and intraseasonal variability63,64,65,66. Pathak et al.15 showed that improved representations of ice-to-snow auto-conversion and stratiform low clouds improve Somali Jet and TEJ simulation. Similarly, Dutta et al.64,65 and Bhowmik et al.66 demonstrated that improved microphysical processes, including convective auto-conversion, enhance ISM precipitation and tropical variability. These findings argue for coordinated improvements in convective and microphysical schemes to address ISM biases.

However, the present study focuses specifically on convective process improvements, particularly in representing \(\:\tau\:\). Prior efforts linked \(\:\tau\:\) to environmental factors such as vertical velocity, cloud depth, and model resolution. For example, Bechtold et al.16 implemented a resolution-dependent \(\:\tau\:\) in the ECMWF Integrated Forecasting System, improving tropical wave simulation. Bullock et al.19 introduced a cloud-depth-dependent \(\:\tau\:\) in the Kain-Fritsch scheme, resulting in a 15% improvement in tropical storm precipitation over North America. Despite these attempts, to the best of our knowledge, no study has systematically assessed the effects of a space-time-varying \(\:\tau\:\) on ISM simulation in a global model framework.

In this study, we implement a dynamic space-time-varying \(\:\tau\:\) in the deep convection parameterization of the Community Atmosphere Model version 5 (CAM5)29 within the Community Earth System Model (CESM1.2), replacing its default fixed value. CAM5 uses the Zhang-McFarlane25 deep convection scheme, which currently employs a constant \(\:\tau\:\) of 3600 s at ~ 1° resolution. Our approach modifies \(\:\tau\:\) formulation of Bechtold et al.17 (initially designed for the KF scheme) by incorporating the updraft vertical velocity dependence proposed by Sahany et al.30. This allows \(\:\tau\:\) to vary dynamically based on atmospheric conditions, aiming to improve the representation of convection and reduce associated biases. This paper is organized as follows: Sect. 1 provides an introduction; Sect. 2 presents the results; Sect. 3 offers conclusions, and Sect. 4 details the model, formulation, and data.

Results

As noted earlier, varies significantly across monsoon regions due to differences in convective cloud depth and vertical velocity (Fig. 1). Regions with strong large-scale ascent tend to exhibit longer , as deep convection sustains itself over extended timescales and causes enhanced precipitation. In contrast, regions with weaker ascent and shallower convection exhibit shorter τ, and reduced precipitation. This relationship is broadly supported by Fig. 1, where high values coincide with high CAPE over the ITCZ and core monsoon zone (CMZ; 18-28°N, 65-88°E). However, alone does not uniquely define convective regimes. Since is calculated as the ratio of cloud depth (H) to mean updraft velocity (\(\:{\stackrel{-}{w}}_{u}^{H}\) ), similar values can result from different dynamical conditions, for example, a deep convective column with strong updrafts versus a shallow cloud with weak updrafts. Thus, τ's physical interpretation requires additional diagnostics. To bridge this gap, we analyze vertically integrated moist static energy (MSE) and vertically integrated moisture convergence flux (VIMC) as complementary measures of column energy content and the large-scale forcing of convection30[,31[,67.

Notably, the \(\:\tau\:\)-precipitation relationship is not uniform across the Indian monsoon domain. For instance, over the Western Ghats, extreme rainfall is often produced by shallow, warm cloud systems linked to orographic uplift and persistent low-level moisture convergence. These systems are associated with short \(\:\tau\:\) but still produce intense rainfall, as shown by Romatschke and Houze67. Thus, while the \(\:\tau\:\) correlates with precipitation in large-scale convective regions, orographic zones require separate consideration. In the following subsections, we assess how dynamic \(\:\tau\:\) affects precipitation and monsoon characteristics across South Asia.

Taylor diagram analysis of precipitation and associated fields

Implementing a dynamic τ in CAM5 (DtauCAM5) leads to substantial improvements in precipitation simulation over South Asia (8.5°S-40°N, 40°E-120°E) and globally (40°S-40°N and 0°−360°E). The Taylor diagram (Fig. 1) highlights these improvements in terms of increased spatial correlation, reduced centered root mean square (RMS) error, and more realistic spatial variability compared to the fixed \(\:\tau\:\) in CAM5 (DefCAM5). Over South Asia during ISM, DtauCAM5 achieves higher correlation and lower RMS error, though it slightly underestimates spatial variability. Alongside precipitation, similar improvements are observed in associated variables such as low-level winds, humidity, and cloud characteristics (Fig. 1). DtauCAM5 shows higher correlations and reduced RMS error for most variables. However, low-level clouds remain poorly simulated in both models, with weak correlation (> 0.2) and large RMS error. These challenges persist globally, as seen in the annual-scale comparison (Supp. Figure 1), though DtauCAM5 consistently outperforms DefCAM5.

Fig. 1
figure 1

Taylor diagram evaluating the performance of DefCAM5 (red) and DtauCAM5 (blue) over the South Asia monsoon domain (8.5°S-40°N, 40°E-120°E) during June-September. The diagram compares model outputs against observations based on three metrics: normalized spatial standard deviation (radial distance from the origin), pattern correlation (angle from the x-axis), and centered root mean square error (RMS; distance from the reference point, REF). The REF point on the x-axis denotes the observed reference field. Solid black contours indicate RMS error levels, and dashed arcs represent standard deviation isolines.

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Biases in Spatial precipitation distribution

Despite overall improvements, regional precipitation biases persist. In DefCAM5, excessive precipitation is simulated over the Arabian Sea (AS), Western Ghats, Himalayan foothills, and peninsular and western India. At the same time, dry biases dominate over eastern India, the Bay of Bengal (BoB), and the eastern Equatorial Indian Ocean (EIO) (Fig. 2a–c). DtauCAM5 significantly reduces wet biases, with normalized RMS bias decreasing across key regions (Fig. 2b, d,e), e.g., in the Himalaya (from 2.1 to 0.77) and AS (from 2.07 to 1.04). However, dry biases over the BoB and eastern India worsen slightly.

Fig. 2
figure 2

Evaluation of precipitation characteristics from observations and model simulations. (a) JJAS mean precipitation from IMERG. (b) Precipitation performance metrics: pattern correlation coefficient (PCC) and normalized root mean square error (NRMSE). (c–e) Spatial precipitation biases for JJAS: (c) DefCAM5-IMERG, (d) DtauCAM5-IMERG, and (e) DtauCAM5-DefCAM5. In (e) blue (red) hatching indicates statistically significant bias reduction (increase) at the 95% confidence level based on a two-tailed Student’s t-test. (f) Annual cycle of precipitation (mm/day) from IMERG, DefCAM5 and DtauCAM5. (g) Annual cycle of evaporation (E; solid lines) from ERA5, DefCAM5, and DtauCAM5, and large-scale moisture convergence (P–E, i.e., Precipitation-Evaporation; dashed lines) from IMERG/ERA5, DefCAM5, and DtauCAM5. (h) Probability distribution of daily rainfall during JJAS, computed using a bin size of 4 mm. The annual cycle and probability distribution are computed for the core monsoon zone (CMZ; 18-28°N, 65-88°E). SAD: South Asia monsoon domain; WG: Western Ghats; EHIM/CHIM/WHIM: East/Central/West Himalaya; EIO: Equatorial Indian Ocean; AS: Arabian Sea; BoB: Bay of Bengal.

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These precipitation patterns stem from corresponding changes in the precipitation partitioning between convective and large-scale precipitation components (Supp. Figure 2). In CAM5, convective precipitation arises from parameterized deep and shallow convection, whereas large-scale precipitation results from microphysical processes25,27,29. The difference plots between DtauCAM5 and DefCAM5 (Supp. Figure 2a, b) indicate that precipitation improvement over the Western Ghats and Himalayas are due to reductions in both convective and large-scale precipitation components. In other regions, the changes are mainly driven by a reduction in large-scale precipitation. This suggests a coupled response between convection and microphysics in the updated parameterization63,64,65.

A further decomposition of convective precipitation into deep and shallow convective components shows that deep convection increases over most South Asia in DtauCAM5, except over the northern AS, Western Ghats, and BoB (Supp. Figure 3). Shallow convection decreases widely. Thus, the reduction in convective precipitation over the Western Ghats and adjoining AS, and over the BoB are attributed to reduced deep convection. However, the increased deep convection over EIO is causing enhanced convective precipitation, supported by positive SST anomaly (Supp. Figure 4) and higher MSE over the region (Supp. Figure 5). The higher SST and MSE can explain persistent convection4,5 and for longer τ values (Fig. 3).

Fig. 3
figure 3

Spatial distribution of convective adjustment time-scale (τ) and convective available potential energy (CAPE) during July. (a) Mean τ and (b) maximum τ simulated by DtauCAM5. Panels (c–e) show mean CAPE from (c) ERA5 reanalysis, (d) DefCAM5 simulation with fixed τ, and (e) DtauCAM5 simulation with dynamic τ.

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Biases in precipitation annual cycle and probability distribution

Beyond spatial patterns, we assess how models capture the annual precipitation cycle and the intensity distribution. In DefCAM5, the monsoon onset is too early and withdrawal too late, with excessively high peak precipitation (Fig. 2f). DtauCAM5 improves withdrawal timing and reduces peak overestimation, but now underestimates peak precipitation, resulting in a dry bias over the CMZ. Both models, however, show early onset compared to observations, indicating this aspect remains unresolved. Following Fasullo and Webster31, precipitation cycle depends on both local evaporation and large-scale moisture convergence, with the latter contributing 60–70% over India (e.g., Anand et al.23; Mishra et al.32. Figure 2g shows that both local evaporation and convergence are overestimated in DefCAM5, mirroring precipitation excess. In contrast, DtauCAM5 underestimates large-scale moisture convergence, consistent with its dry bias during the peak monsoon.

Moreover, in case of precipitation intensity distribution, DtauCAM5 continues to underestimate high-intensity and overestimate low-intensity events over CMZ (Fig. 2h). Compared to DefCAM5, the high-end tail of precipitation is slightly lower in DtauCAM5, likely due to the suppression of excessively deep convection caused by faster atmospheric stabilization and limited vertical moisture buildup. This behaviour reflects a well-documented bias in GCMs, where model simulations tend to overestimate light rainfall and underestimate extreme events7,41. We expect that combining dynamic τ formulation with stochastic deep convection triggering and horizontal entrainment could address the limitation. Previous work by Pathak et al.11 has shown that incorporating stochasticity improves extreme precipitation simulation and may offer a valuable extension to the current τ formulation.

Cloud characteristics

Alongside precipitation, cloud-related processes also improve with dynamic \(\:\tau\:\), particularly cloud cover and radiative forcing. Compared to DefCAM5, DtauCAM5 better captures cloud cover distribution (Fig. 4). Observations show high-level clouds cover ~ 38%, mid-level ~ 18%, and low-level ~ 16% over South Asia (Fig. 4a–c), except over the northern AS, where low clouds could reach ~ 40%. DefCAM5 overestimates cloud cover at all levels across most regions, except low-level clouds over western India, which are underestimated (Fig. 4d). These biases persist in CAM33,34,57. They are significantly reduced in DtauCAM5, particularly low clouds (~ 14% improvement) (Fig. 4g–l). Quantitatively, the PCC and normalized RMS error for DefcAM5 are (0.12, 1.19), (0.63, 0.84), and (0.61, 0.67) for low-, mid-, and high-level cloud cover, respectively, over South Asia. In DtauCAM5, these scores are enhanced to (0.18, 1.03), (0.61, 0.81), and (0.67, 0.62). Additionally, cloud water path and its partitioning liquid and ice water path for DtauCAM5 also show a substantial reduction in DefCAM5 overestimated cloud water path over the Indian land (Supp. Figure 6). However, a significant deterioration in cloud water path over the BoB is found with dynamic τ. It coincides with the region where deep convection has also reduced substantially.

Fig. 4
figure 4

JJAS mean cloud cover fraction (%) at different atmospheric levels. (a–c) Low-level, mid-level, and high-level cloud cover, respectively, from ISCCP. (d–f) Biases in DefCAM5 relative to ISCCP for each cloud level. (g–i) Biases in DtauCAM5 relative to ISCCP. (j–l) Differences between DtauCAM5 and DefCAM5. In panels (j-l), blue (red) hatching indicates statistically significant bias reduction (increase) at 95% confidence level, based on a two-tailed Student’s t-test.

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The associated cloud radiative forcings also show relative enhancement (Supp. Figure 7). Observations indicate that shortwave cloud forcing (SWCF) is highest over the high orographic region of Himalaya, Western Ghats, and BoB (Supp. Figure 7a). In contrast, the long-wave cloud forcing (LWCF) dominates over peninsular India, the BoB, and the broader Indo-Pacific region (Supp. Figure 7b). DefCAM5 overestimates SWCF across most of South Asia, except in the eastern EIO and BoB, where it underestimates (Supp. Figure 7d, j). In comparison, LWCF is overestimated over AS and Peninsular India and underestimated over central India, the BoB, and the broader Indo-Pacific regions (Supp. Figure 7e, k). DtauCAM5 alleviates these biases significantly by ~ 17% to SWCF and ~ 6% to LWCF (Supp. Figure 4j–l). The improved SWCF is due to reduced low-level cloud cover, indicating improved convective detrainment and stratiform cloud radiative properties after implementing dynamic τ, consistent with Zhang and McFarlane25.

Large-scale circulation characteristics

In DefCAM5, Somali Jet over the AS, a moisture carrier to the CMZ region44is weaker simulated in both strength and spatial extent (Fig. 5a, b, d). Similarly, low-level winds over the Peninsular India and BoB are too weak, limiting inland moisture transport and convergence (Supp. Figure 8). With the dynamic τ implementation, DtauCAM5 shows an improved spatial structure and intensification of Somali Jet (Fig. 5c, e, f). The weaker simulated STJ and Tibetan Anticyclone in DefCAM5, are also substantially improved in DtauCAM5 (Fig. 5g–l). Quantitatively, Somali Jet strengthens by ~ 20% in DtuCAM5 to DefCAM5. However, no substantial improvement is seen in TEJ, which remains underestimated in intensity and zonal extent (Fig. 5j–l). This bias in TEJ, we expect, arises from underestimated diabatic heating over the BoB and South China Sea (Supp. Figure 9).

Fig. 5
figure 5

JJAS mean winds (vector) and speed (contour) at low-level (850 hPa) and upper-level (200 hPa) levels. (a–c) Low-level wind fields from ERA5, DefCAM5, and DtauCAM5, respectively. (d–f) Low-level wind differences between: (d) DefCAM5 and ERA5, (e) DtauCAM5 and ERA5, and (f) DtauCAM5 and DefCAM5. (g–i) upper-level winds from ERA5, DefCAM5, and DtauCAM5, respectively. (j–l) upper-level wind differences between: (j) DefCAM5 and ERA5, (k) DtauCAM5 and ERA5, and (l) DtauCAM5 and DefCAM5.

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The low-level and upper-level wind circulation changes in DtauCAM5 are physically consistent with the improved thermodynamic gradients. Specifically, DtauCAM5 shows a relative improvement in MTTG (Fig. 6a) and ESZW (Fig. 6b), known to modulate monsoon strength and northward propagation35,36. DefCAM5 considerably overestimates MTTG and underestimates ESZW during the active monsoon phase, whereas DtauCAM5 simulates values closer to ERA5. However, a slight overestimation in MTTZ during onset and underestimation in ESZW during active monsoon remain (Fig. 6a, b). These adjustments enhance the vertical coupling between lower and upper tropospheric flows. The previously exaggerated Hadley circulation in DefCAM5, characterized by overly intense mid-to-upper tropospheric ascent between 10–20°N, is improved mainly in DtauCAM5 (Supp. Figure 10). However, unlike DefCAM5, DtauCAM5 underestimates ascent in the lower troposphere compared to ERA5. This reduction weakens the structure of the ITCZ (Fig. 6c–h), whose strength and extent depend critically on low-level convergence and ascent37,38. While DtauCAM5 captures a more realistic ITCZ position and retreat, the suppressed low-level ascent underestimates ITCZ-related rainfall, particularly during the withdrawal phase (Fig. 6h), reinforcing the seasonal dry bias (Fig. 3e).

Fig. 6
figure 6

Evaluation of large-scale thermal and dynamical characteristics and their influence on the ITCZ annual cycle. (a–b) mean annual cycle of the meridional tropospheric temperature gradient (MTTZ) and easterly shear in zonal wind (ESZW) from ERA5, DefCAM5, and DtauCAM5. MTTG is calculated as the difference in vertically averaged temperature (600−200 hPa) between land (5°N-35°N, 40°E-100°E) and ocean (5°N-15°S, 40°E-100°E). ESZW is calculated as the difference between 850 hPa and 200 hPa zonal wind over the Indian region (0°−15°N, 50°E-90°E). (c–e) Zonal-mean annual cycle of meridional total precipitation (averaged over 65°E-95°E), representing the intensity and seasonal migration of the ITCZ, from IMERG, DefCAM5, and DtauCAM5, respectively. (f–h) Differences in ITCZ annual cycle: (f) DefCAM5 and IMERG, (g) DtauCAM5 and IMERG, and (h) DtauCAM5 and DefCAM5. In panel (h) blue (red) hatching indicates statistically significant ITCZ bias reduction (increase) at the 95% confidence level based on a two-tailed Student’s t-test.

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In parallel, in DefCAM5, VIMC is overestimated over the Arabian Sea, Peninsular India, and northwest India, contributing to excessive rainfall in these regions (Supp. Figure 8). DtauCAM5 reduces these biases, consistent with improved low-level wind convergence and a better-resolved Hadley circulation. However, over BoB, VIMC is further reduced in DtauCAM5, likely worsening dry biases in eastern and northeastern India. This limitation may stem from unresolved deficiencies in simulating air-sea coupling68 and local convective processes (Supp. Figures 2, 3). Additionally, although the overall structure of the Hadley cell is improved, the underestimated lower-tropospheric ascent in DtauCAM5 may weaken moisture transport into BoB and adjacent land regions, further contributing to suppressed rainfall.

Intraseasonal oscillations

Furthermore, the monsoon system is strongly influenced by intraseasonal oscillations and tropical wave activity7,11,39,40. Figure 7a–c shows the north-south space-time spectra of daily precipitation from IMERG observation and model simulations. The two pronounced spectral peaks are observed between 10 and 20 days and 30–90 days at wavenumber 1. In particular, 10–20 days is the quasi-biweekly north-westward propagating mode (Fig. 7d–i) and 30–90 days is the north-eastward propagating intraseasonal mode over the CMZ11,39,40 (Fig. 7j–o). While both models capture the westward movement of 10–20 days of the quasi-biweekly mode, DefCAM5 shows a weaker movement at 100–110°E and a lagged propagation, which DtauCAM5 improves (Fig. 7g–i). However, both models struggle with the northward propagation component, showing no improvement in DtauCAM5 (Fig. 7d–f). This limitation may stem from inadequate microphysics-convection coupling, orographic influences, and biases in land-ocean thermal contrast4,40,42,64, which the dynamic τ formulation does not address explicitly. Similarly, for the monsoon intraseasonal mode (Fig. 7j–o), both model simulations exhibit a north-westward bias (Fig. 7g–l). While DtauCAM5 facilitates minimal improvement in the eastward component between 60°E to 80°E, it struggles beyond 80°E (Fig. 7o). These propagation biases warrant further investigation to identify root causes and improvement strategies.

Fig. 7
figure 7

Evaluation of intraseasonal variability during JJAS using spectral and Hovmöller analyses. (a–c) North-south wavenumber-frequency spectra of precipitation (averaged over 70°E–90°E) from (a) IMERG, (b) DefCAM5, and (c) DtauCAM5. (d–f) Longitude-time Hovmöller plots of 10-20-day filtered rainfall anomalies (mm/day), averaged over 10°N-20°N, for (d) IMERG, (e) DefCAM5, and (f) DtauCAM5. (g–i) Latitude-time Hovmöller plots of the same 10-20-day filtered anomalies, averaged over 70°E–90°E, for (g) IMERG, (h) DefCAM5, and (i) DtauCAM5. (j–l) Same as (d–f), but for 30-60-day filtered rainfall anomalies. (m–o) Same as (g–i), but for the 30-60-day filtered anomalies. Filtered anomalies are computed using a Lanczos bandpass filter and regressed onto area-weighted, filtered rainfall anomalies over central India during JJAS.

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Additionally, we have analysed both the unfiltered and filtered precipitation variance for 2–10-day and 10–90-day timescales over South Asia (see Supp. Figure 11). While DtauCAM5 shows a modest improvement in filtered variance across both bands, the overall filtered and unfiltered variances remain underestimated. This suggests that, although the dynamic \(\:\tau\:\) enhances variance generation slightly, further improvement is necessary to simulate the full range of monsoon variability.

The spectral power of the Madden-Julian Oscillation (MJO) and equatorial Kelvin and Rossby waves improves substantially in DtauCAM5 (Fig. 8). Importantly, the MJO, which was not adequately captured in DefCAM5, is now substantially closer to observations. This improvement aids value over the prior persistent biases in simulating the intraseasonal variability of the ISM43. This indicates that dynamic adjustment enhances the coupling between convection and large-scale dynamics, resulting in better eastward propagation of the MJO and more accurate tropical wave activity depiction. However, substantial biases still exist, and further improvement is needed.

Fig. 8
figure 8

Symmetric component of the Wheeler-Kiladis space-time power spectra of precipitation over the equatorial region (15°N-15°S) from IMERG observations, DefCAM5, and DtauCAM5. Spectra are computed using daily total precipitation time-series over a 10-year period.

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Discussion and conclusion

The dynamic \(\:\tau\:\) formulation represents a significant advancement in simulating the ISM. This study demonstrates substantial improvements in precipitation simulation by replacing the fixed τ with a dynamic approach based on cloud depth and updraft velocity. These enhancements include reduced precipitation biases in regions such as the Western Ghats, peninsular India, and the Himalayan foothills, aligning model results more closely with observations4,5. This stems from improved precipitation partitioning components between convective and large-scale precipitation processes facilitated by a better representation of CAPE consumption. The dynamic \(\:\tau\:\) formulation also exhibits improved temporal evolution of the precipitation annual cycle. Unlike DefCAM5, which simulates an earlier onset and peak7,11, DtauCAM5 although persist earlier onset and peak rainfall underestimation, maintains a well-defined peak in July-August, and captures the gradual withdrawal by late September as in observations and reported in Goswami et al.2 and Fasullo and Webester31. This improved seasonal pattern reflects a deeper consistency between convective processes and moisture convergence patterns8,31.

Beyond precipitation, the dynamic \(\:\tau\:\) formulation enhances cloud characteristics. For instance, the overestimation of total cloud cover over South Asia and the underestimation over the equatorial Indo-Pacific Oceanic region, as observed in this study and previously reported for CAM6 in Kumar et al.7 and CAM5 in Pathak et al.11, are significantly reduced. Dutta et al.62 have shown that teleconnections with global SST patterns strongly influence total cloud cover over the ISM region. Moreover, the biases in cloud radiative forcing seen in DefCAM5 are also improved in DtauCAM5. These improvements reflect better coupling of convective activity and radiative processes, aligning with findings by Neale et al.47.

Furthermore, with the dynamic \(\:\tau\:\), relatively better represented key circulation features such as the STJ, and Somali Jet lead to improved low-level wind field, essential for moisture transport and convective triggering44. Previous studies have consistently highlighted the inadequate representation of these jets as a key source of model bias over the South Asian monsoon domain4,5,12. Improved depiction of the ITCZ’s northward migration with accompanying rain bands further enhances spatial and temporal precipitation patterns37,38. Additionally, enhanced simulation of tropical waves indicates that the dynamic approach benefits not only the atmospheric mean state but also its variability on seasonal to decadal time-scales43,64. This improvement has significant implications for short-term monsoon variability and extreme weather event prediction40,45. Such improvements also align with model evaluations indicating the crucial role of convective timescale in organizing mesoscale systems and tropical disturbances17,18,19,20.

Despite these advancements, challenges remain, particularly in regions like the northern Bay of Bengal, where precipitation biases persist. Additionally, while the dynamic τ improves tropical wave simulation, biases in the monsoon intraseasonal oscillations require further improvement. Future studies should focus on optimizing convective parameterizations and exploring coupled ocean-atmosphere frameworks for deeper insights into convection-SST feedback and monsoon variability. These findings highlight the potential of dynamic parameterizations to bridge the gap between model simulations and observed atmospheric behaviour, offering a promising direction for future climate model development29.

Model description, formulation approach, and data details

Model description

The CAM5, under the CESM-1.2 framework, with finite volume dynamical core29,46, is used for model simulations. In CAM5, deep convection scheme is parameterized using the Zhang-McFarlane deterministic scheme25, with updates from Neale et al.47 to account for the dilute entrainment of the rising parcel in computing the convective available potential energy and from Richter and Rasch48 to incorporate convective momentum transport. Besides deep convection, CAM5 employs several other parameterization schemes: the moist turbulence scheme from Bretherton and Park49, the shallow convection scheme from Park and Bretherton50, the cloud macrophysics scheme from Park et al.51, the cloud microphysics scheme from Morrison and Gettelman52 and Gettelman et al.53, and the radiative transfer scheme from Iacono et al.54.

It is important to note that a newer version of CAM5, i.e., CAM6, is also available29. However, CAM5 is preferred for this study due to its well-established validation in past research (e.g., Pathak et al.11; Yang et al.22; Wang et al.41, making it a reliable reference for testing convective parameterization schemes. Also, the structural changes introduced in CAM655, such as the Cloud Layers Unified By Binormals (CLUBB) scheme for turbulence, shallow convection, cloud macrophysics, and new dynamical core configurations, require careful evaluation before implementing modifications. Testing parameterizations in CAM5 first is considered prudent, as the impacts may differ in CAM6 due to these added complexities7,29,63.

Formulation approach

The closure for the ZMNR scheme is based on the budget equation for the convective available potential energy (CAPE):

$$\:\left(\frac{\partial\:CAPE}{\partial\:t}\right)=\:-{M}_{b}F+G$$
(1)

where: \(\:G\) represents the large-scale CAPE production from grid-scale dynamics; \(\:-{M}_{b}F\) represents the subgrid-scale CAPE consumption by deep convection; \(\:{M}_{b}\) is the cloud base mass flux, and \(\:F\) is the rate at which cumulus clouds consume CAPE per unit cloud base mass flux.

The CAM5 model uses a diagnostic closure for the cloud-base mass flux \(\:{M}_{b}\), given by:

$$\:{M}_{b}=\:\frac{A}{\tau\:F}$$
(2)

where \(\:\tau\:\) is the convective adjustment time-scale (3600 s for ~ 1° resolution), and \(\:A\) is the excess CAPE \(\:(CAPE-70J/kg)\).

This closure assumes that cumulus convection consumes CAPE at an exponential rate (\(\:1/\:\tau\:\)), substituting Eq. (2) into Eq. (1), we obtain:

$$\:\left(\frac{\partial\:CAPE}{\partial\:t}\right)=\:-\text{A}/\tau\:+G$$
(3)

In the absence of large-scale CAPE generation (\(\:G=0\)), Eq. (3) reduces to:

$$\:\left(\frac{\partial\:CAPE}{\partial\:t}\right)=\:-\text{A}/\tau\:$$
(4)

and if the \(\:CAPE\) at \(\:t=0,\:\text{i}\text{s}\:A0\), then the solution of Eq. (4) becomes:

$$\:A={A}_{0}\:exp(-t/\tau\:),\:\:\:\:\:\:\:\:for\:t>0$$
(5)

This formulation indicates that increasing \(\:\tau\:\) reduces \(\:{M}_{b}\), which affects updraft mass flux and influences convective precipitation. The deep convective precipitation (DCP) at a level \(\:i\) is computed as:

$$\:{\left[DCP\right]}_{i}\:=C0\:\times{\left[Mu\right]}_{i}\:{\left[L\right]}_{i}$$
(6)

where: \(\:C0\) is the DCP production efficiency parameter, \(\:Mu\) is the updraft mass flux and \(\:L\) is the cloud liquid water at a level \(\:i\).

The total surface-reaching DCP is computed by integrating Eq. (6) over all levels.

A physically-based formulation for \(\:\tau\:\) at each grid point is derived using the convective cloud depth and average updraft vertical velocity:

$$\:\tau\:=\text{m}\text{a}\text{x}\left(\frac{H}{{\stackrel{-}{w}}_{u}^{H}},\:timestep\right)$$
(7)

where: \(\:H\) is the depth of convective cloud, and \(\:{\stackrel{-}{w}}_{u}^{H}\) is the average updraft vertical velocity. Moreover, Eq. (7) is analogous to the formulation implemented in ECMWF IFS by Bechtold et al.17. In ZMNR, we compute \(\:H\) as a difference between the height of the equilibrium level \(\:\left({z}_{LEL}\right)\) and lifting condensation level \(\:\left({z}_{LCL}\right)\), and \(\:{\stackrel{-}{w}}_{u}^{H}\) following Sahany et al.30as given below:

$$\:{\stackrel{-}{w}}_{u}={\left({z}^{-c}{\int\:}_{{z}_{LCL}}^{{z}_{LEL}}a{\stackrel{\backprime }{z}}^{c}Bd\stackrel{\backprime }{z}\right)}^{1/2}$$
(8)

where: \(\:a\) and \(\:c\:\)are constants, \(\:B\) is the buoyancy term, and \(\:z\) is the height from the surface.

The values of \(\:a\) and \(\:c\) have kept one similar to Sahany et al.30. The buoyancy (\(\:B\)) at a particular height is calculated as:

$$\:B=g\left(\frac{{T}_{v,parcel}\left(z\right)-{T}_{v,env}\left(z\right)}{{T}_{v,env}\left(z\right)}\right)$$
(9)

where \(\:g\) is the gravitational acceleration and \(\:{T}_{v,parcel}\left({T}_{v,env}\right)\) is the virtual temperature of the parcel (environment).

The model-computed spatially varying \(\:\tau\:\) is shown in Supp. Figure 1, which presents the mean and maximum \(\:\tau\:\) for July, alongside corresponding fields of CAPE from both the model and ERA5 reanalysis. This figure illustrates substantial variability, indicating that \(\:\tau\:\) varies markedly globally, with values ranging from 100 s to ~ 7 h. While \(\:\tau\:\) is dynamically computed at each model timestep, the minimum value is fixed to the model timestep. This \(\:\tau\:\) variation is driven by changes in \(\:H\) and \(\:{\stackrel{-}{w}}_{u}^{H}\), modulated by large-scale atmospheric conditions. In particular, Bullock et al.19 and Done et al.28 showed that in regions with strong large-scale ascent and enhanced moisture convergence, deeper convection develops, leading to larger \(\:\tau\:\). In contrast, in regions with weaker ascent, shallow convection dominates, resulting in shorter \(\:\tau\:\). This relationship is evident in Supp. Figure 1a–e, where high \(\:\tau\:\) values coincide with higher CAPE over the ITCZ and ISM region, while lower \(\:\tau\:\) values occur over subsiding and high-latitude regions with low CAPE. The updraft vertical velocity is also crucial: stronger buoyancy-driven updrafts accelerate CAPE consumption30, which can reduce \(\:\tau\:\), while weaker updrafts allow for a longer \(\:\tau\:\). These factors collectively explain the substantial spatial variation observed in Supp. Figure 1.

Data details

The model simulations span 11 years, using both the default \(\:\tau\:\) (~ 3600 s; DefCAM5) and the dynamic \(\:\tau\:\) (DtauCAM5) formulations, with prescribed climatological sea surface temperature (SST) data from 1981 to 2010. The first year is discarded for spin-up, and the last 10 years are analysed. All simulations are performed at a horizontal resolution of ~ 1° with 30 vertical levels.

Observational datasets include monthly and daily total precipitation from the NASA global precipitation measurement (GPM) integrated multi-satellite retrievals for GPM (IMERG; Huffman et al.56. Monthly vertical-level cloud data is taken from the International Satellite Cloud Climatology Project (ISCCP) High-resolution Global Merged (HGM) (Rossow and Schiffer58. The horizontal and vertical winds, cloud cover, precipitable water, humidity, latent heat flux, and air temperature are used from the ERA5 (Hersbach et al.59. Outgoing longwave radiation and cloud radiative forcings are sourced from NASA Clouds and Earth’s Radiation Energy Systems (CERES) Energy Balanced and Filled (EBAF) (Loeb et al.60. All observational and reanalysis data are regridded to model resolution.