Enhancing sub-seasonal soil moisture forecasts through land initialization

Introduction

The Subseasonal-to-Seasonal (S2S) forecast spans from two weeks to six weeks, bridging the gap between short-range weather forecasts and long-range seasonal outlooks. S2S forecasts offer a broad spectrum of potential applications, encompassing public health, disaster preparedness, water management, energy, and agriculture¹. Nonetheless, significant challenges persist, particularly as the S2S forecast accuracy declines noticeably in initial condition-based numerical weather prediction systems² and their Artificial Intelligence (AI) counterparts³. Forecast accuracy, attributed to high-fidelity process representation, is hypothesized to emerge at S2S time scales (Fig. 1). For example, coupled ocean-atmosphere variability modes, such as the El Niño Southern Oscillation, the Madden-Julian Oscillation, and tropical-extratropical teleconnections, are recognized as sources of S2S predictability^4,5,6. Additionally, persistent circulation anomalies in the stratosphere and their dynamic linkages to the troposphere during the winter season⁷ and land surface memory and its interactions with the atmosphere contribute to further S2S predictability^8,9.

Enhancing sub-seasonal soil moisture forecasts through land initialization — **Fig. 1: An Earth System Predictability (ESP) framework for enhancing soil moisture forecasts in agriculture and water resources applications.**

Water-related S2S forecasts pose unique challenges, with the precipitation forecast skill quantified by the Anomaly Correlation Coefficient (ACC) falling below 0.1 in the mid-latitude regions¹⁰. We posit that an Earth System Predictability (ESP) framework (Fig. 1), characterized by a skillful prediction (ACC > 0.5) in the land component, can benefit food and water sectors^11,12,13. The land surface integrates less predictable precipitation signals with soil moisture memory and the soil-plant-atmosphere interaction processes, resulting in a more predictable soil moisture signal critical for agricultural and water planning^12,14,15. Soil moisture variability is significantly correlated with water availability in the Southwestern US¹⁶, including the Colorado River basin¹⁷. Soil moisture observations serve as the reference data to assess the performance of various drought indices for crop yield monitoring^18,19. Henceforth, we refer to root zone soil moisture integrated from the surface to a 0.5-meter depth, focusing mainly on agricultural applications²⁰. We examined the relative contributions of the ocean, land, and atmosphere components and their interactions to S2S soil moisture forecasting through an extensive set of eight sensitivity experiments (see Method)¹⁰. We determined that land initializations and soil moisture memory processes primarily influence soil moisture predictability (demonstrated subsequently).

Soil moisture, a key component of land processes, exhibits slower variability than atmospheric conditions and is recognized as a source of predictability for S2S forecasting^9,21,22. Soil moisture is more predictable^12,23 due to its memory effects¹⁴ and feedback to the meteorological drivers, e.g., temperature and precipitation^9,22. Standalone land-only or hydrology sensitivity studies have emphasized the importance of initial conditions and climate forcing in improving hydrological forecasts^24,25. However, the limited skill improvement in the coupled forecasting system^10,22 poses a challenge in assessing the effects of land surface initializations. Given its importance for the agriculture and water sectors, we demonstrate that soil moisture forecast is a robust metric, providing a pathway to process-level investigation in improving water-related S2S forecasting.

Results

Sub-seasonal soil moisture forecast skill attributed to land initializations

We employed the Community Earth System Model version 2 sub-seasonal prediction system (CESM2-S2S) to evaluate the skill of soil moisture forecasts^26,27 (see Method). Land initialization significantly improves the skill of week 3–4 soil moisture forecasts, as shown in Fig. 2 and Table 1. In single-component initialization experiments, land consistently yields the most significant contribution to the forecast skill, followed by the atmosphere (Fig. 2b–m). Across all four seasons, the forecast skill from land-only initialization is twice as high (ACC = 0.38) as from atmosphere-only initialization (ACC = 0.20). In the most agriculturally intensive region, the Prairie Peninsula (NEON #6), the ACC for land-only initialization is three times higher (ACC = 0.39) than atmosphere-only initialization (ACC = 0.13). Ocean-only initializations contribute minimally to week 3–4 soil moisture forecast.

**Fig. 2: Sources of predictability for sub-seasonal (week 3–4) root zone soil moisture forecasts.**

Table 1 Sub-seasonal Soil Moisture Forecast Skill (ACC) in CESM2-S2S Experiments for JJA and DJF Seasons

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A low ACC for atmosphere-only (ATM) and ocean-only (OCN) initializations can be attributed to the absence of soil moisture memory effects, which are critical for soil moisture predictability^12,14. Soil moisture memory, which arises from the slow dynamics of soil water retention and decay, plays a significant role in influencing predictability when the land component is properly initialized (LND). However, when the land is not initialized, such as when land climatology (anomaly = 0) is used, the memory-driven ‘anomaly persistence’ cannot contribute to predictability, as demonstrated in the ATM and OCN initialization cases.

Land initialization synergistically enhances sub-seasonal forecast skill, particularly in the interior of the US (NEON #6, 7, 8, 9, and 10), where agricultural activity is prominent and predictability from atmospheric and oceanic sources is limited. For example, in the Northern Plains (NEON #9), land is the sole source of predictability (Fig. 2 and Table 1). Conversely, atmospheric contributions, and to a lesser extent ocean contributions to the forecast skill, are more pronounced in coastal ecoclimatic regions such as the southeast, southern plains, and southwest (NEON #2, 3, 4, 11, 14, 15, and 17; Table 1 and Supplementary Table S1). Next, we investigated forecast skill variations with lead time, averaging across all four seasons.

Throughout all forecast lead times and four seasons, the land remains the primary source of predictability (Fig. 3). However, as expected, forecast skill decreased from week 1–2 (ACC = 0.54) to week 5–6 forecasts (ACC = 0.37) in the standard forecast where all three components are initialized. Removing atmosphere initialization results in a skill drop of 5% or less, with the ACC decreasing from 0.43 in the standard forecast to 0.39 in the climoATM experiment for week 3–4 forecasts (3rd column in Fig. 3). Furthermore, eliminating ocean initialization minimally impacts forecast skill, with a 1% decrease observed in the longer lead, i.e., 5–6 weeks forecasts (2nd column in Fig. 3). However, removing land initialization dropped the forecast skill almost 50% across all forecast lead times, e.g., ACC decreased to 0.23 in the climoLND experiment for week 3–4 forecasts (Fig. 3h).

**Fig. 3: Sources of predictability in multi-component initialized CESM2-S2S forecasts.**

Predictability sources and their regional and seasonal variations

During summer (JJA), the peak growing season, land contributions to the total forecast skill are maximized. Specifically, land accounts for 93 ± 3% of the total root zone soil moisture forecast skill, as observed in the control experiment averaged across 17 NEON ecoclimatic regions covering the contiguous US (Fig. 4, and Table 1 and S1, top panels). Hereafter, X ± Y represents the mean, with two times the standard error estimates calculated across the 17 NEON ecoclimatic regions. A significant portion of atmospheric contributions (45 ± 10%) is attributed to land-atmosphere coupling (42 ± 8%), which is already accounted for within the land contribution (compare yellow dashed line with red solid line in Fig. 4). Consequently, the addition or removal of atmospheric initialization does not substantially affect soil moisture forecast skill (Fig. 4).

**Fig. 4: Components of soil moisture predictability sources – regional and seasonal variations.**

A linear combination of three predictability sources – land, atmosphere, and ocean – and their couplings mainly explains the total predictability observed in the control experiment (compare the sum line with the standard forecast line in Fig. 4, see Method). The summation of individual predictability components can elucidate 94 ± 8% of total predictability in the JJA season. A more considerable uncertainty ( ~ 25%) is observed in the central US region, such as NEON #6 and #9, where oceanic sources negatively contribute to total predictability (Table 1, top panel), likely due to significant dry biases in the CESM2’s precipitation forecast²⁸, thereby resulting in the summation line appearing greater (by 25%) than the standard forecast (see Method). Additionally, we found land-atmosphere coupling as the uncertainty source in the Pacific Southwest (NEON # 17) and northern Rockies (NEON # 12), where atmosphere-only initialization shows a smaller skill than land-atmosphere coupling effects; thus, the sum of predictability components is 20–25% smaller than the standard forecast (see Method).

Land remains the primary source of soil moisture predictability even during winter, where its contribution (88 ± 6%) is slightly less than that in summer (93 ± 3%). Additionally, the contribution of the land-atmosphere coupling (28 ± 7%) is smaller than that of the atmosphere (39 ± 10%). Furthermore, oceanic contributions become more prominent with longer lead times, particularly in the coastal ecoclimatic regions. For instance, oceanic contributions to total predictability are 58%, 51%, and 32% in the Atlantic Neotropical (NEON #4), Southern Plains (NEON #11), and the Southeast (NEON #3), respectively. Most oceanic contributions came through the land-ocean coupling process in the Southeast and Atlantic Neotropical regions (compare cyan dashed lines with blue solid lines for NEON # 3 and 4 in Fig. 4). Therefore, in the Southeast region, total predictability only marginally improved (10-15%) compared to land-only predictions.

Predictability of hydroclimatic extremes

The predictability of hydroclimatic extremes (i.e., droughts and pluvial events) is generally lower than that of all soil moisture conditions. To increase the sample size, we defined drought conditions as instances where observed standardized soil moisture anomalies are less than −0.5, which accounts for 30% of all forecasts. This definition represents drought events aggregated over a two-week timescale using a standardized soil moisture anomaly metric²⁹ (see Method). Averaged across the contiguous US during the JJA season, the correlation coefficient (ACC) between drought forecasts and observations is 0.22 (Fig. 5d), compared to an ACC of 0.42 for all soil moisture variability conditions (Supplementary Fig. S1). Notably, land initializations predominantly contribute to drought predictability (89 ± 5%), with nearly all predictable components originating from land sources during the summer (97 ± 10%) (see Fig. 5d, f). Conversely, the combined influence of atmospheric and oceanic initializations peaks in the spring season. Given that most oceanic and atmospheric effects manifest through interactions with the land (Fig. 4), the standard forecast skill improved marginally compared to the land-only initialization experiment (compare the first and third columns in Fig. 5).

**Fig. 5: Predictability of Soil Moisture Dry (SM-Dry) and Wet (SM-Wet) extremes and their sources.**

Drought forecast skills are notably higher across critical agricultural regions in the contiguous US, especially during the growing season (spring and summer). For example, the Prairie Peninsula (NEON # 6) demonstrates an ACC of 0.42 in spring (March-May) (Fig. 5; top panels). Similarly, the Appalachian and Cumberland Plateau (NEON # 7) and the Ozark Complex (NEON # 8) exhibit ACC values of 0.36 and 0.34, respectively, during summer (June-August). Enhanced drought prediction capabilities offer substantial potential benefits for agricultural applications, addressing significant challenges previously noted in forecasting drought onset, such as the 2012 drought in the Great Plains³⁰.

Wet extremes (pluvial), defined as standardized soil moisture anomalies greater than 0.5, exhibit slightly lower predictability compared to dry extremes, particularly during the growing season (see top and bottom panels in Fig. 5). Seasonally, the fall (September-November) shows the highest forecast skills for wet extremes, with an ACC of 0.25 ± 0.04, primarily due to land contributions (76 ± 8%). On average, across all seasons, atmospheric and oceanic sources collectively contribute more to the predictability of wet extremes (59 ± 15%) than dry extremes (42 ± 10%).

Role of climate processes

The soil moisture memory process significantly contributes to sub-seasonal soil moisture predictability from land sources (Supplementary Fig. S2). The memory process characterizes the decay rate of soil water within the root zone, influenced by coupled climate-vegetation-hydrological processes^14,16,31. We conducted lead-lag auto-correlation analysis of daily soil moisture anomalies using the Community Land Model version 5 (CLM5) offline, which serves as the land model within the sub-seasonal prediction system (see Method). The auto-correlation analysis revealed that the 21-day lag autocorrelation closely aligns with the 3–4 week soil moisture forecast skill in the land-only initialized experiment (climoATMclimoOCN). Given the limited precipitation forecast skill (ACC < 0.1) at sub-seasonal time scales¹⁰, this finding can be expected.

The soil moisture to precipitation feedback loop enhances sub-seasonal forecast skill (Fig. 6). We compared the CESM2-based soil moisture forecast skill with two other sub-seasonal experiments³² – RSMAS-CCSM4³³ and ESRL-FIM³⁴, both of which provide vertically integrated full depth (FD) soil moisture forecasts in their standard configurations. Additionally, we compared CESM2 full depth forecast skill, keeping the reference data the same as in the previous analysis. The ESRL-FIM model consistently outperforms CESM2 by 7%, which, in turn, shows improved performance compared to its predecessor version (CCSM4) (Fig. 6a). For instance, week 3 to 4 forecast skills are 0.49, 0.43, and 0.36 for ESRL-FIM, CESM2, and RSMAS-CCSM4 in the contiguous US. Full-depth soil moisture exhibits reduced variability and extended memory compared to the root zone¹⁴. Consequently, the full-depth forecast demonstrates lower skill than the root zone forecast for weeks 1 to 3, but higher skill for weeks 3 to 6 in the CESM2 forecast.

**Fig. 6: Impact of soil moisture-precipitation feedback on soil moisture forecast skills in three Subseasonal Experiments (S2S) – CESM2 (this study), RSMAS-CCSM4, and ESRL-FIM.**

The soil moisture to precipitation feedback loop was investigated by correlating initial soil moisture anomalies (FD) with the week 3–4 precipitation forecast in the two highest-performing models: ESRL-FIM and CESM2. The ESRL-FIM model demonstrates considerably stronger soil moisture to precipitation feedback in the central US, particularly during the summer season (Fig. 6e). For instance, the ESRL-FIM model shows that the week 3–4 precipitation forecast is significantly correlated with the initial soil moisture anomalies in most of the central US, with a contiguous US average ACC value of 0.14 and the highest ACC greater than 0.4 found in parts of the Northern Plains (NEON # 9). The soil moisture-precipitation feedback loop is largely missing in the CESM2-S2S precipitation forecast, particularly in the summer, with an average ACC value of −0.03 across the contiguous US (Fig. 6d). The CESM2-S2S forecast shows statistically significant feedback in parts of the Southeastern US during the spring season (Fig. 6b). The root zone soil moisture anomalies exhibit slightly weaker feedback on the week 3-4 precipitation forecast in the CESM2 model (Supplementary Fig. S3) compared to the full depth to precipitation feedback presented in Fig. 6.

Discussion

On a sub-seasonal time scale, atmospheric initializations contribute most to the forecast skill for near-surface air temperature predictability. Experiments with single-component initializations reveal that the forecast skill for atmosphere-only initialization (ACC = 0.26) is nearly twice that of land-only (ACC = 0.14) and ocean-only (ACC = 0.13) initializations, averaged across all four seasons and the contiguous US (Supplementary Fig. S4). The skill in precipitation forecasting is limited and primarily attributed to atmospheric initialization (ACC = 0.09) (Supplementary Fig. S5). These findings, discussed in our previous study¹⁰, provide context for the new results presented here.

This study demonstrates that accurate initialization of land conditions can significantly enhance sub-seasonal forecast skills for land-related quantities, such as root zone soil moisture, which is critically important for agriculture and water planning. We utilized an ensemble of four observationally constrained soil moisture datasets – ERA5-land, SMERGE, GLEAM3, and MERRA2 – for model verification, which reduces the sensitivity of our results to the selection of any single observational dataset^35,36 (see Method). The land initialization method used in this study, derived from offline land model simulations (see Method), is relatively simple. Advances in soil moisture observational networks^37,38, remote sensing technology³⁹, and data assimilation methods^40,41 are expected to improve forecast skills further.

A smaller subset of Data Assimilation (DA) experiments conducted from 2011 to 2019 shows a minor improvement (< 5%) in soil moisture forecasting skills for the contiguous US (Supplementary Fig. S6). The DA experiment utilized observationally constrained atmospheric initial conditions and the associated land surface states, as described by Raeder et al.⁴². It is important to note that soil moisture observations were not directly assimilated in the DA experiment; instead, the land states were indirectly influenced by the atmospheric drivers from the Community Atmospheric Model version 6 (CAM6), which assimilated a wide range of global observations, including aircraft, radiosonde, infrared, and radio occultation data⁴². Hence, a minor improvement in soil moisture forecasting skills can be expected. Future research should explore more advanced DA methodologies, such as four-dimensional ensemble variational (4D-EnVar)-based weakly coupled land data assimilation⁴³ and ocean data assimilation strategies^17,44. Moreover, advances in ocean-atmosphere coupling and its teleconnections to land surface processes could further enhance soil moisture predictability^45,46.

The regional variations in soil moisture predictability are influenced by biases in the climate model’s representation of land-atmosphere and ocean-atmosphere coupling, which vary significantly across different ecoclimatic regions. For example, in the central US (e.g., NEON #6 and #9), dry precipitation biases in the CESM2 model²⁸ led to an overestimation of contributions from oceanic sources, thereby diminishing forecast accuracy. Addressing these biases requires improvements in the representation of large-scale circulation patterns (e.g., Rossby waves)⁴⁷, thermodynamic processes including land-atmosphere coupling, atmospheric parameterizations⁴⁸, and high-resolution climate modeling²⁸. Additionally, enhancing the coupling of convection to the larger-scale environment may further reduce summertime precipitation biases over the central U.S.⁴⁹.

Some of our findings, such as the low precipitation forecasting skill (Supplementary Fig. S5) and weaker land-atmosphere feedback (Fig. 6) are CESM2 model dependent^10,27. Their implications for soil moisture forecasting warrant further investigation. The availability of new soil moisture forecasting datasets, such as those from the Canadian Seasonal to Inter-annual Prediction System version 2.1⁵⁰, and the Norwegian Climate Prediction Model (NorCPM) soil moisture data assimilation system⁵¹, provide an opportunity to conduct a comprehensive multi-model comparison study. To strengthen the robustness of these comparisons, additional sensitivity experiments, e.g., as outlined in Table 1, are recommended.

It is important to note that the standardized soil moisture index used in this study primarily identifies soil moisture drought, which is closely related but differs from meteorological and hydrological droughts. While meteorological droughts are driven by precipitation deficits and related atmospheric circulation anomalies³⁰, and hydrological droughts manifest as reductions in streamflow and groundwater levels, soil moisture drought is more directly associated with root-zone water availability and land-atmosphere interactions⁵². It serves as a critical link between meteorological and hydrological droughts by translating precipitation deficits into surface and subsurface water stress⁵³, influencing evapotranspiration and ecosystem responses⁵⁴. Overall, our results focus on soil moisture anomalies rather than a comprehensive assessment of all drought types^55,56.

Pluvial conditions, defined based on wet soil moisture anomalies, align with hydrometeorological studies^57,58 but do not inherently reflect hydrological flood events. A high soil moisture level indicates saturated conditions conducive to flooding⁵⁹. However, soil moisture alone does not fully define hydrological floods, as their occurrence involves complex hydrological and geomorphological processes, including antecedent moisture, topography, and drainage capacity^60,61. Our approach captures extreme soil wetness conditions relevant to land-atmosphere interactions⁵⁸ rather than a comprehensive hydrological flood classification.

Causality and predictability are distinct aspects of climate variability. While phenomena such as flash droughts can originate from large-scale atmospheric conditions, they are often not predictable in sub-seasonal prediction systems. For instance, Hoerling et al.²⁸ identified that the 2012 flash drought in the Great Plains was caused by reduced atmospheric moisture transport from the Gulf of Mexico, yet the seasonal prediction system did not predict this event. Our study demonstrates that land conditions provide a crucial predictability component that can enhance the skill of forecasting high-impact weather and climate events. Additionally, recent advancements in Artificial Intelligence (AI) and Machine Learning (ML) methodologies demonstrate the potential to enhance the predictive accuracy of hydroclimatic extremes⁶².

This study contributes to the growing body of literature highlighting the critical role of land surface processes in improving S2S forecasting while providing novel insights. Our work diverges from the studies of Lim et al.⁶³ and Nair et al.⁵¹ in terms of focus, methodology, and key findings. Lim et al.⁶³ focus on temperature predictability by employing land-atmosphere coupling metrics within a standard forecast framework, whereas our study investigates soil moisture predictability through a novel set of sensitivity experiments designed to isolate the impact of land surface initializations (Table 1). On the other hand, Nair et al.⁵¹ examine the influence of soil moisture data assimilation using the Norwegian Climate Prediction Model (NorCPM) and demonstrate improvements in S2S forecasts driven by observational constraints. In contrast, our study leverages CESM2-S2S and systematically disentangles the relative contributions of land, atmosphere, and ocean initializations to sub-seasonal soil moisture forecasts. Notably, we find that land initializations account for 91 ± 3% of the forecast skill for soil moisture, underscoring their importance. While these studies represent complementary approaches to advancing S2S forecasting, our findings uniquely establish the dominant role of land surface initializations in enhancing soil moisture predictability, with direct implications for agricultural and water resource applications.

Methods

Sub-seasonal Prediction System

The CESM2 sub-seasonal prediction system (CESM2-S2S) consists of a fully coupled CESM2 retrospective forecast at 1° nominal resolution, initialized every Monday from 1999 to 2020²⁷. Each weekly reforecast is integrated over a 45-day lead time with an 11-member ensemble size. Since April 2021, a real-time forecast with a 21-member ensemble size has been generated and contributes to the multi-model sub-seasonal prediction experiment dataset³². The atmospheric component is initialized using the National Center for Environmental Prediction (NCEP) Climate Forecast System version 2 (CFSv2) reanalysis⁶⁴. The land component is initialized using standalone Community Land Model version 5 (CLM5) simulations driven by CFSv2 reanalysis climate forcing⁶⁵. The initializations for ocean and sea-ice conditions are obtained from a standalone CESM2 ocean simulation forced with the adjusted Japanese 55-year reanalysis state field and fluxes⁶⁶. The CESM2-S2S system demonstrates temperature and precipitation skills at par with the NCEP CFSv2, slightly lower than the European Centre for Medium-Range Weather Forecasts (ECMWF) system²⁷. CESM2 is a community model that enabled us to conduct additional sensitivity experiments involving university researchers and students.

The Community Land Model version 5 (CLM5)⁶⁵ is the land component in CESM2. CLM5 represents a range of biophysical and biogeochemical processes, including land surface heterogeneity, radiation scheme, momentum, energy balance, hydrology, photosynthesis, stomatal conductance, carbon and nutrient cycling, land-use change, crops, irrigation, and fertilization^65,67. Each CLM5 1° × 1° grid cell consists of multiple soil columns, each with a vertically resolved soil profile discretized into up to 20 hydrologically active layers with spatially varying total thickness⁶⁸. CLM5 incorporates a prognostic seasonal cycle for vegetation evolution, encompassing leaf emergence, senescence, and vegetation height dynamics^69,70. Landscape heterogeneity is represented through a plant functional type tile structure, including rainfed and irrigated agricultural practices^65,67.

Experiment design

The unique set of eight experiments outlined in Table 2 enables us to discern the individual contributions of the atmosphere (ATM), land (LND), and ocean (OCN), as well as their interactions, to the forecast skill of soil moisture. These experiments further allow us to deconstruct the sources of predictability into those arising from anomalies (A), couplings (C), and the climatological state (climo) of each component. The first experiment is a control wherein all three components are initialized, as in the standard sub-seasonal prediction system²⁷. After this, seven additional experiments are conducted, wherein one or more components are maintained at their climatological state, ensuring that the anomaly of the selected component does not contribute to the forecast skill¹⁰.

Table 2 Process-based sub-seasonal climate forecast experiment¹⁰

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The coupling between two components is active if either both or one component is initialized to its anomalous state. For instance, land-atmosphere coupling (LNDATM_C) is considered the same as that of the control and climoATM experiments (Table 2). The underlying assumption is that when one component, such as LND in the climoATM experiment, is initialized using its anomalous state, it exerts stronger coupling to align the climatologically initialized component (ATM) with the land anomalous state at the surface. However, if both components are initialized to their climatological state, the coupling is set to zero, e.g., the land-atmosphere coupling is zero in the climoATMclimoLND experiment. We verify this assumption by comparing the control experiment’s forecast skill with the skill’s algebraic sum from individual sources (Fig. 4).

The summary of CESM2-S2S reforecast experiments is listed in Eq. 1 to Eq. 8. The CESM2-S2S eight experiments (bold term) are the direct output from the reforecast with eight Initial Conditions (ICs) settings. In the Equation, the Clim is climatology, A is anomaly ICs, and the C is the coupling term. The eight settings follow the same reforecast protocol, with specific climatological ICs as listed in the left-hand set of the equations, i.e., the name of the reforecast set. The right-hand set of the Equation consists of the components that contributed to the ACC. The assumption is that average couplings in different experiment sets do not change considerably. For example, the land-atmosphere coupling is supposed to be of the same value in Eqs. 2 and 3, but the difference contributes to part of the biases between the model control run and the sum of individual parts in Eq. 15. Another assumption is that two model components are set to climatological ICs; their coupling is close to zero—no coupling term in Eq. 8.

The total predictabilities include predictability from the background climatology (Clim_ALL), anomalies of each component (A_ATM, A_LND, A_OCN), and their coupling (C_LNDATM, C_OCNATM, C_LNDOCN) reflected in the standard forecast (Eq. 1). In Eqs. (2)-(4) are reforecast experiments where one of the modeling components (ATM, LND, OCN) is kept at its climatological state. In Eqs. 5 to 7, two of the modeling components are kept at their climatological states. All modeling components are kept at their climatological states in experiment 8 (climoALL).

$${boldsymbol{standard}}={Cmathrm{lim}}_{{ALL}}+{A}_{{LND}}+{A}_{{OCN}}+{C}_{{LNDATM}}+{C}_{{OCNATM}}+{C}_{{LNDOCN}}$$

(1)

$${bf{climoATM}}={Cmathrm{lim}}_{{ALL}}+{A}_{{LND}}+{A}_{{OCN}}+{C}_{{LNDATM}}+{C}_{{OCNATM}}+{C}_{{LNDOCN}}$$

(2)

$${bf{climoLND}}={Cmathrm{lim}}_{{ALL}}+{A}_{{ATM}}+{A}_{{OCN}}+{C}_{{LNDATM}}+{C}_{{OCNATM}}+{C}_{{LNDOCN}}$$

(3)

$${bf{climoOCN}}={Cmathrm{lim}}_{{ALL}}+{A}_{{ATM}}+{A}_{{LND}}+{C}_{{LNDATM}}+{C}_{{OCNATM}}+{C}_{{LNDOCN}}$$

(4)

$${bf{climoOCNclimoLND}}={Cmathrm{lim}}_{{ALL}}+{A}_{{ATM}}+{C}_{{LNDATM}}+{C}_{{OCNATM}}$$

(5)

$${bf{climoOCNclimoATM}}={Cmathrm{lim}}_{{ALL}}+{A}_{{LND}}+{C}_{{LNDATM}}+{C}_{{LNDOCN}}$$

(6)

$${bf{climoATMclimoLND}}={Cmathrm{lim}}_{{ALL}}+{A}_{{OCN}}+{C}_{{OCNATM}}+{C}_{{LNDOCN}}$$

(7)

$${bf{climoALL}}={Cmathrm{lim}}_{{ATM}}+{Cmathrm{lim}}_{{LND}}+{Cmathrm{lim}}_{{OCN}}$$

(8)

Experiments 5 to 7 have been used to determine predictability from one source only as follows:

$${P}_{{ATM}}={{P}_{{ATM}{{_}}A}+{P}_{{LNDATM}{{_}}C}+{P}_{{OCNATM}{{_}}C}+{P}_{{climoALL}}=P}_{{climoOCNclimoLND}}$$

(9)

$${P}_{{LND}}={{P}_{{LND}{{_}}A}+{P}_{{LNDATM}{{_}}C}+{P}_{{OCNLND}{{_}}C}+{P}_{{climoALL}}=P}_{{climoATMclimoOCN}}$$

(10)

$${P}_{{OCN}}={{P}_{{OCN}{{_}}A}+{P}_{{OCNATM}{{_}}C}+{P}_{{OCNLND}{{_}}C}+{P}_{{climoALL}}=P}_{{climoATMclimoLD}}$$

(11)

Here, P is the predictability contributed from the individual sources. In this study, we use the Anomaly Correlation Coefficient (ACC) between observation and forecasted anomalies as the metric to assess the predictability. Predictability from the coupling terms is derived from the linear combination of four experiments, as shown below.

$${P}_{{LNDATM}{{_}}C}=({P}_{{climoOCNclimoATM}}-{P}_{{climoALL}})-({P}_{{climoOCN}}-{P}_{{climoOCNclimoLND}})$$

(12)

$${P}_{{OCNATM}{{_}}C}=({P}_{{climoOCN}}-{P}_{{climoOCNclimoATM}})-({P}_{{standarad}}-{P}_{{climoATM}})$$

(13)

$${P}_{{OCNLND}{{_}}C}=({P}_{{climoOCN}}-{P}_{{climoOCNclimoLND}})-({P}_{{standarad}}-{P}_{{climoLND}})$$

(14)

All predictability sources are summarized in Eq. 15 and compared with the predictability in the standard forecast to assess the validity of the linear assumption.

$$begin{array}{l}{P}_{{sum}}={{P}_{{standarad}}=P}_{{climoATM}}+{P}_{{climoLND}}+{P}_{{climoOCN}}-{P}_{{climoOCNclmoLND}}\qquadquad,-{P}_{{climoOCNclimoATM}}-{P}_{{climoATMclimoLND}}+{P}_{{climoALL}}end{array}$$

(15)

Verification datasets

We utilized an ensemble mean of four soil moisture products based on reanalysis and remote sensing: ERA5-Land⁷¹, SoilMerge³⁶, the Global Land Evaporation Amsterdam Model (GLEAM)⁷², and the Modern Era Retrospective Analysis for Research and Applications version 2 (MERRA2)⁷³. The root zone soil moisture is vertically integrated from the surface to 0.5 m depth. ERA-5 land soil moisture is a reanalysis dataset based on numerical integrations of the European Center for Medium-Range Weather Forecasts (ECMWF) land surface model⁷¹. The core land model is the Carbon Hydrology-Tiled ECMWF Scheme for Surface Exchanges over Land (CHTESSEL). SoilMERGE (SMERGE) is a new root-zone soil moisture that covered the continental US with 0.125° resolution from 1979-2018. All model-observation correlations were truncated in 2018 due to the SMERGE. SMERGE root zone soil moisture is based on merging the North American Land Data Assimilation System (NLDAS) and satellite retrievals from the European Space Agency Climate Change Initiative (ESA-CCI)³⁶. The Global Land Evaporation Amsterdam Model (GLEAM) SM is a satellite-based root-zone SM from different passive and active C- and L-band microwave sensors, Ocean Salinity (SMOS) satellite in the v3c data set (European Space Agency Climate Change Initiative, ESA CCI) with 0.25° resolution^72,74. The Modern-Era Retrospective Analysis for Research and Applications (MERRA2) is a reanalysis dataset generated by rerunning a revised version of the land component of the MERRA2 system⁷⁵. The latitude and longitude resolutions are 0.5 and 0.625°. All four observations are re-gridded to CESM2 (1° × 1°) resolution using the Earth System Modeling Framework area weighted Method.

The skill of soil moisture forecasts varied across the verification datasets, with MERRA2 demonstrating the highest skill and ERA5-Land exhibiting the lowest (Supplementary Fig. S7). Therefore, employing the ensemble mean of these four observation-based products reduces uncertainty in observational data while accounting for regional variations in land use, climate, and topography³⁵. The ensemble mean approach outperforms any individual dataset as well as combinations of three datasets (SMERGE, GLEAM MEARR2). For example, the soil moisture forecast skill for weeks 3–4 (16–30 days) in the control experiment, using the ensemble mean as the observation, is 0.43 (Fig. 3e). In comparison, the forecast skill using individual datasets is 0.24 for ERA5-Land (Figure. S8e), 0.32 for SMERGE (Figure. S9e), 0.40 for GLEAM (Figure. S10e), and 0.42 for MERRA2 (Figure. S11e). Additionally, the combination of three datasets yields a forecast skill of 0.42 (Figure. S12e), which remains lower than the ensemble mean.

Furthermore, Quadruple Collocation Analysis (QCA), an extension of the Triple Collocation Method to four datasets⁷⁶, resulted in inconclusive results including negative error variance for ERA5-Land (Supplementary Fig. S13). This issue arises because several datasets share common input sources, such as ESA-CCI remote sensing-based soil moisture observations in SMERGE and GLEAM, and atmospheric reanalysis-based meteorological forcing used to drive the underlying land surface models. For example, SMERGE assigns 80% weightage to the underlying land surface model data in forested regions³⁶, further reducing the independence of error sources. As a result, the assumption of independent errors in QCA does not fully hold, particularly in data-rich regions like the U.S., where overlapping data assimilation can introduce dependencies, potentially biasing error variance estimates and reducing the reliability of QCA results.

Additionally, we employed the National Ecological Observatory Network’s (NEON) ecoclimatic domains to assess regional variations in forecast skill within the US. The NEON ecoclimatic domains (Fig. 2a) delineate distinct regions based on climate, topography, soil type, and vegetation dynamics⁷⁷.

Standardized anomalies

$${STD}left(frac{1}{14}mathop{sum }limits_{l=n,n{rm{varepsilon }}left(7,39right)}^{n+14}left(frac{1}{11}mathop{sum }limits_{e=1}^{11}left({(f}_{i,j,l,w,m,y,e})right)right)right)$$

(16)

We reorganized the forecast data into seven dimensions: latitude (25) × longitude (46) × lead time (46) × week (5) × month (12) × year (23) × ensemble (11). The CESM2 grid covers the contiguous US with 25 latitudes and 46 longitudes. In the Equation, i and j represent latitude and longitude, respectively. The variables l, w, m, and y denote forecast lead days (46), initial weeks (5), initial months (12), and initial years (1999 to 2021), while e represents ensemble members.

First, we computed the ensemble mean forecast by averaging the forecast across the 11 ensemble members. Next, we applied a 14-day running mean along the forecast lead dimension to reduce high-frequency daily variability, resulting in usable data for lead days 7 to 39. We then computed standardized anomalies along the year dimension. This Method removes the re-forecast climatology as a function of forecast lead time and initialization time, thereby minimizing the effects of forecast initialization shock and drifts in the sub-seasonal prediction system⁷⁸.

We rearranged the observation data in the same manner as the forecast and computed the observation standardized anomalies. For the ACC calculation, the forecast dimensions were transformed into latitude, longitude, lead time, and week. The week dimension totals 1200 (20 years [1999 to 2018] × 12 months × 5 weeks) for the all-year ACC calculation (e.g., Fig. 3). For seasonal correlation (Fig. 2), the week dimension was concatenated into four seasons, totaling 300 weeks (20 years × 3 months × 5 weeks). Since most months have only four weeks, the fifth-week data is considered missing, i.e., out of 1200 weeks, only 20 × 52 = 1040 weeks have the data, and the remaining 160 weeks are missing.

Evaluation metric

We calculated the Anomaly Correlation Coefficient (ACC) between the forecast and observation anomalies to assess the soil moisture forecast skill. The forecast anomaly is calculated relative to lead time and initialization time-dependent forecast climatology that minimizes the impact of initialization drift on the forecast^12,78. We applied a 14-day running mean to smooth the daily variations; hence, the valid lead days for verification are 7 to 39 days.