# Soil-moisture-atmosphere coupling hotspots and their representation in seasonal forecasts of boreal summer

Jonathan J Day, Frederic Vitart, Tim Stockdale, Patrica de Rosnay, Constantin Ardilouze, Daniele Peano, Antonella Sanna, Kristina Fröhlich, Martin Andrews

► To cite this version:

Jonathan J Day, Frederic Vitart, Tim Stockdale, Patrica de Rosnay, Constantin Ardilouze, et al. Soil-moisture-atmosphere coupling hotspots and their representation in seasonal forecasts of boreal summer. Climate Dynamics, 2025, 63 (6), pp.275. 10.1007/s00382-025-07753-1. hal-05136376

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# Soil-moisture-atmosphere coupling hotspots and their representation in seasonal forecasts of boreal summer

Jonathan J. Day<fnref n="1" />☐, Frederic Vitart<fnref n="1" />, Tim Stockdale<fnref n="1" />, Patrica de Rosnay<fnref n="1" />, Constantin Ardilouze<fnref n="2" />, Daniele Peano<fnref n="3" />, Antonella Sanna<fnref n="3" />, Kristina Fröhlich<fnref n="4" />, Martin Andrews<fnref n="5" />

Received: 21 November 2024 / Accepted: 31 May 2025

© The Author(s) 2025

## Abstract

This study examines soil-moisture-atmosphere coupling “hotspots” across the Northern Hemisphere during the summer months and evaluates their representation in seasonal forecasting systems. Using hindcasts from the Copernicus Climate Change Service (C3S) multi-model seasonal forecast ensemble, the analysis explores the predictability of land-atmosphere interactions related to soil moisture anomalies. The results indicate that regions with strong soil-moisture-atmosphere coupling, such as parts of western North America, southern Europe, and Central Asia, exhibit potential for predicting seasonal temperature and precipitation patterns a season or more in advance. However, significant uncertainty exists in estimates of the soil-moisture initial conditions and soil-moisture persistence timescales. Moreover, while some regions exhibit realistic coupled behaviour, others, including a large swathe of North America, Eastern Europe, and Northern India display exaggerated coupling, resulting in systematic errors in temperature forecasts. This study underscores the potential for predicting the atmosphere in summer based on memory of soil-moisture initial conditions whilst highlighting the need to improve the representation of soil-moisture atmosphere feedbacks in order to enhance the skill of seasonal climate predictions over land.

**Keywords** Land–atmosphere coupling · Seasonal forecasting · Soil-moisture initialisation · C3S seasonal · Multi-model ensemble · Summer climate anomalies

## 1 Motivation

Due to its inherent long-memory (e.g. Delworth and Manabe 1988) and profound role in modulating surface exchanges of heat and moisture (Shukla and Mintz 1982), soil moisture is a major source of potential forecast skill over land at sub-seasonal and seasonal timescales (Rind 1982; Koster et al. 2000). By modulating sensible and latent heat fluxes, soil moisture can directly influence near-surface temperature

and precipitation locally (Seneviratne et al. 2010; Miralles et al. 2019; Materia et al. 2022; Ardilouze et al. 2022), but can also influence remote areas by exciting quasi-stationary Rossby waves in the atmosphere (Koster et al. 2016; Teng et al. 2019).

However, the importance of soil-moisture for seasonal prediction over land is not ubiquitous in space or time but instead occurs in certain “hotspots” of forecast opportunity, where both intense land-atmosphere coupling and strong soil moisture persistence are features of the local climate (Koster et al. 2004; Seneviratne et al. 2006a, 2010; Dirmeyer 2011).

The strength and the location of coupling hotspots varies considerably between different climate models submitted to the Global Land-Atmosphere Coupling Experiment (GLACE Koster et al. 2006), a coordinated set of idealized experiments designed to assess the importance of land-atmosphere coupling to atmospheric predictability. Similarly, diagnostic measures of land-atmosphere coupling applied to climate models submitted to the Fifth Coupled Model Intercomparison Project (CMIP5), show a wide

<footnote>Jonathan J. Day
jonathan.day@ecmwf.int</footnote>

<footnote n="1">¹ European Centre for Medium-Range Weather Forecasts,
Reading, UK</footnote>

<footnote n="2">² CNRM, Université de Toulouse, Météo-France, CNRS,
Toulouse, France</footnote>

<footnote n="3">³ Fondazione Centro Euro-Mediterraneo sui Cambiamenti
Climatici, CMCC, Bologna, Italy</footnote>

<footnote n="4">⁴ Deutscher Wetterdienst, Offenbach, Germany</footnote>

<footnote n="5">⁵ Met Office Hadley Centre, Exeter, UK</footnote>
range of soil-moisture-evaporation coupling strength, which through local feedbacks creates large inter-model range in the projected temperature response to anthropogenic forcing (Berg and Sheffield 2018; Maloney et al. 2019).

The inter-model differences in land–atmosphere coupling described above suggests that the strength and location of land–atmosphere coupling hotspots in some models may diverge significantly from the real world. This is likely to degrade forecast skill. For example, over the Central USA, realistic soil moisture initialization (compared to climatology) does not improve forecast quality for near-surface temperature at sub-seasonal (Koster et al. 2011) and seasonal (Ardilouze et al. 2017) timescales. At seasonal timescales this unexpected lack of improvement has been linked to errors in the strength of the coupling related to a dry bias in the region (Ardilouze et al. 2017 and 2019).

In this study we take a diagnostic approach to evaluate and understand errors in land–atmosphere coupling strength and their importance in seasonal hindcasts of summer months from the systems that contribute to the Copernicus Climate Change Service (C3S; Buontempo et al. 2022). The results are structured as follows. In Sect. 3.1 we identify regions of high potential predictability, or “hotspots”, by selecting regions where both land–atmosphere coupling is strong and soil-moisture predictability is high. Then in Sect. 3.2 we investigate the skill of seasonal hindcasts of soil-moisture and temperature to see whether we actually see enhanced skill in the regions highlighted as having high potential predictability in Sect. 3.1. Section 3.2 also considers the importance of both errors in the soil-moisture initial conditions and errors in model land–atmosphere coupling strength for forecast skill. The potential causes of biases in land–atmosphere coupling are discussed in Sect. 3.3.

# 2 Data and methods

## 2.1 Overview of C3S multi-model system

The C3S Seasonal forecasting system, which is an evolution of the European Multimodel Ensemble System for Seasonal to Interannual Prediction project (DEMETER; Palmer et al. 2004), is comprised of nine different forecasting systems from multiple producing centres: the European Centre for Medium-Range Weather Forecasts (ECMWF), Météo-France, Deutscher Wetterdienst (DWD), the UK Met Office (UKMO), Centro Euro-Mediterraneo sui Cambiamenti Climatici (CMCC), National Centers for Environmental Prediction (NCEP), Japan Meteorological Agency (JMA) and Environment and Climate Change Canada (ECCC, two systems). The NCEP and JMA systems were excluded from this analysis because soil-moisture fields for those models were not submitted to the C3S archive.

In this study we focus on hindcasts of boreal summer: June–July–August (JJA), initialised on (or in the month leading up to) the 1st May, between 1993 and 2016. Except for Meteo-France-System8, which generates initial conditions by nudging the atmospheric circulation of a coupled General Circulation Model (GCM) to the ECMWF’s fifth reanalysis (ERA5), the land-surface initial conditions for the hindcasts all come from standalone free-running (i.e. no assimilation) simulation with each coupled model’s land-surface model (LSM). These are forced with reanalysis as boundary conditions: ERA5 (Hersbach et al. 2020; in the case of CMCC, DWD, ECCC-GEM5-NEMO), ERA-Interim (Dee et al. 2011; in the case of ECCC-CanCM4 and SEAS5), Japanese global atmospheric reanalysis (JRA55; Kobayashi et al. 2015; in the case of the Met Office) or NCEP reanalysis (Kalnay et al. 1996; in the case of CMCC). Most of the centres initialised all hindcast ensemble members with the same land-surface initial conditions. The exceptions being CMCC, who generate a 3-member ensemble of land-surface states by forcing an LSM with different reanalyses which are selected at random to initialise each member, and ECMWF who employ perturbations based on the operational ensemble of data assimilation. The systems from Meteo-France and the UK Met Office, who employ a lagged ensemble approach, also have different initial conditions in some hindcasts since the lagged initialisation approach means that hindcasts are started on different dates. All the other systems considered use a so-called “burst ensemble” approach, where all ensemble members are initialised from the same date.

The specifics for each system are summarised in Table 1 and detailed documentation can be found in the Copernicus Knowledge Space (ECMWF 2025). Soil-moisture fields for these models are archived on model levels, with the number of levels and their depths varying between each model. In order to compare models to each other and to observational products like GLEAM, a weighted average of the layers contained in the top 1 m was calculated for each model as a proxy of the root-zone soil moisture. This depth was chosen partly for practical considerations, but also based on the fact that the top 1 m of the soil encompasses the majority

<table><caption>Table 1 C3S seasonal system hindcast information</caption><thead><tr><th>Centre</th><th>System</th><th>Key references</th><th>1st May Ens size</th></tr></thead><tbody><tr><td>CMCC</td><td>SPS3.5</td><td>(Gualdi et al. 2020)</td><td>40</td></tr><tr><td>DWD</td><td>GCFS2.1</td><td>(Fröhlich et al. 2021)</td><td>30</td></tr><tr><td rowspan="2">ECCC</td><td>CanCM4i</td><td>(Lin et al. 2020)</td><td>10</td></tr><tr><td>GEM5-NEMO</td><td></td><td>10</td></tr><tr><td>ECMWF</td><td>SEAS5</td><td>(Johnson et al. 2019)</td><td>25</td></tr><tr><td>Meteo-France</td><td>System8</td><td>(Batté et al. 2021)</td><td>25</td></tr><tr><td>UKMO</td><td>GloSea6</td><td>(MacLachlan et al. 2015)</td><td>28</td></tr></tbody></table>
of the root fraction for most vegetation types (Zeng 2001). For example, 81–100% of the root fraction for SEAS5 is included in the top 1 m, with the fraction depending on the plant type (ECMWF 2017).

## 2.2 Coupling metrics

Since Dirmeyer et al. (2011) it is common to consider land–atmosphere coupling in terms of two pathways: a terrestrial segment linking the state of the land to the surface fluxes and an atmospheric segment linking the surface fluxes to the state of the atmosphere. The first leg indicates the potential of the land surface to influence the atmosphere, so it is a necessary but not sufficient condition (Dirmeyer 2011). The second leg refers to the influence of the surface fluxes on the atmospheric state. Both legs need to be active in a given region for a full land–atmosphere feedback to occur.

In this study we apply the scaled correlation metrics defined in Dirmeyer (2011) and Dirmeyer et al. (2014) to both seasonal and monthly mean fields to evaluate the representation of these coupling legs in the seasonal hindcasts. The first of these measures the strength of the terrestrial leg of the coupling (i.e. the link between the root-zone soil-moisture (SM) and the evaporation (E):

$$I_{SM-E} = \sigma(E)\rho(SM, E) \qquad (1)$$

where $\rho(SM, E)$ denotes the correlation between SM and E, and $\sigma(E)$ is the standard deviation of E. The second:

$$I_{SM-X} = \sigma(X)\rho(SM, E)\rho(E, X) \qquad (2)$$

where X is any atmospheric variable measures the strength of the terrestrial leg and the atmospheric leg (i.e. the link between evaporation and variable X) together. This approach was initially proposed by Dirmeyer (2011) and builds on the simple correlation metrics: $\rho(SM, E)$ and $\rho(E, X)$ used in previous studies to measure the strength of the terrestrial and atmospheric legs respectively (see review by Seneviratne et al. 2010). Equation 2 will only have a large magnitude in regions where both correlation terms are large (i.e. both terrestrial and atmospheric legs are active) and the atmospheric variable, X, has a large variance. This makes $I_{SM-X}$ a practical measure of coupling for predictability studies.

To identify summer hotspots these are applied to JJA seasonal means from the observations and each seasonal hindcast set. Since the focus in this study is the role of soil-moisture-atmosphere coupling in the prediction of seasonal climate anomalies, the coupling metrics were calculated from seasonal means, as has been done in e.g. Seneviratne et al. (2006b) or Berg and Sheffield (2018). The motivation being that what is important for this application is measuring the propensity of a seasonal soil-moisture anomaly to

influence a seasonal anomaly in an atmospheric field. However, we note that the identification of hotspots depends on the timescale of interest (Yin et al. 2023) and definition of coupling strength (e.g. Lorenz et al. 2015).

Since much of the large-scale multidecadal variability of surface temperature anomalies can be explained by changes in radiative forcing due to increasing greenhouse gases, and other anthropogenic and non-anthropogenic forcings, which don't follow a linear trend we removed a 3rd order polynomial from each grid point in order to focus on inter-annual variability (following Collins 2002). For the hindcasts, these coupling metrics are calculated for each ensemble member, i.e. if there are 25 ensemble members, we calculate 25 indices using all member 1 s, all member 2 s, etc. from each hindcast set and then calculate the mean of the 25 resulting values.

## 2.3 Observation types

We perform evaluation of the seasonal hindcasts against ERA5 (Hersbach et al. 2020), which is a commonly used reference for evaluating seasonal forecast skill (e.g. Molteni and Brookshaw 2023). However, because ERA5 was produced in a number of parallel streams (initialised from ERA-Interim every ~5 years) discontinuities have been identified in ERA5 root-zone soil moisture (Muñoz-Sabater et al. 2021), reducing fit to in-situ observations compared to other products (Beck et al. 2021). So for root zone soil-moisture and evapotranspiration we also use version 3.7 of the Global Land Evaporation Amsterdam Model (GLEAM, Miralles et al. 2011; Martens et al. 2017) which utilises a range of satellite inputs to estimate terrestrial evaporation, based on Penman's equation, and root-zone soil moisture. Using both ERA5 and GLEAM to calculate the land–atmosphere coupling metrics partly, but not fully, addresses the fact that there is inherent uncertainty in assessing the true coupling strength of the real world. This uncertainty stems from both random and systematic errors in each of the datasets. Such uncertainty is challenging to quantify, particularly for soil-moisture and evaporation, given the lack of direct observations globally.

To provide further context to the evaluation of root-zone soil moisture initial conditions (Sect. 3.2) in the C3S models we also use soil-moisture from Version 2.0 (prior to 2015) and 2.2 (post 2015) of NASA's Global Land Data Assimilation System-Catchment LSM (GLDAS-CLSM Rodell et al. 2004) and the ERA5-land (Muñoz-Sabater et al. 2021). The use of multiple datasets is an attempt to account for the fact that root-zone soil moisture is not measured globally and the values in these different products reflects model assumptions, so we must be careful in interpreting them (see Koster et al. 2009 for further discussion).
For 2 m-air temperature we use the Berkeley Earth Surface Temperatures (BEST; Rohde et al. 2013), which provides spatially complete monthly station-based air-temperature estimates over land. For monthly precipitation estimates, we use Version 2.3 of the Global Precipitation Climatology Project (GPCP; Adler et al. 2018), based on satellite and gauge analysis (over land) data. For monthly downwelling shortwave radiation at the surface we use the EUMETSAT Satellite Application Facility on Climate Monitoring (CM SAF) CLoud, Albedo and surface RAdiation dataset (CLARA-A3; Karlsson et al. 2023a, 2023b).

# 3 Results

## 3.1 Identifying important coupling hotspots for seasonal prediction

### 3.1.1 Coupling strength

By applying the coupling metrics described in Sect. 2.2 to summer (JJA) means of root-zone soil moisture and evaporation from GLEAM, 2 m-air temperature (T2m) from BEST, total precipitation from GPCP and z500 from ERA5 (described in Sect. 2.3) we can identify regions of high soil-moisture-atmosphere coupling for the boreal summer months (Fig. 1a, c, e, f). For example, the southwestern part of North America (W-USA; blue box in Fig. 1a), Southeastern Europe (SEEuro; yellow box in Fig. 1a), the South-Eastern European Plain (EuPl; cyan box in Fig. 1a)

<figure><img src="image_2.png" /><figcaption>**Fig. 1** Estimate of $I_{\text{SM-E}}$ (a), $I_{\text{SM-T2m}}$ (c) and $I_{\text{SM-E}}$ (e) and $I_{\text{SM-z500}}$ (g) coupling metrics for JJA from GLEAM, BEST, GPCP and ERA5. **b, d, f,** **h** as **a, c, e, g** but for the average of the C3S models</figcaption></figure>
and the area around Afghanistan-Pakistan (AfPak; green box in Fig. 1a) are all regions where the various coupling metrics are high. Regions where $I_{SM-E}$ is positive indicate that the evaporation rate is limited by the available soil-moisture. Conversely, negative values indicate that the evaporation is limited by the available energy (see Seneviratne et al. 2010 for further discussion about soil-moisture limited and energy limited regimes).

We also calculate these indices from each system's hindcast set, and then present the mean index across the seven models in Fig. 1b, d, f, h. From this, one can see that each index has similar spatial variations to the estimate using GLEAM, BEST, GPCP and ERA5, however the model values are overall larger, indicating generally stronger coupling than in reality with the area that is soil-moisture limited being more extensive.

Although, the identified regions have strong coupling on the relevant timescale, in order to have high predictability on seasonal timescales it is also important that the soil-moisture persistence is high.

### 3.1.2 Soil moisture predictability

The potential forecast skill that can be gained from soil-moisture and soil-moisture atmosphere coupling is dependent on the timescale of soil-moisture memory or persistence. Areas with longer memory have the potential to be more predictable. However, it is also important for the seasonal forecasting systems to capture the correct timescales and spatial variation in persistence, otherwise anomalies will persist for the wrong length of time in a given region, leading to a degradation in forecast skill.

To assess this, we calculate the lagged-correlation of monthly detrended root-zone soil-moisture for the land-surface analysis products and C3S seasonal hindcasts over the hindcast period (1993–2016). This has been used to quantify the timescale of soil-moisture memory in numerous studies (e.g. Koster and Suarez 2001; Seneviratne et al. 2006a; Orth and Seneviratne 2012).

Spatial maps of the May–August (4-month) lagged-correlation (Fig. 2) show large spatial variations in soil moisture predictability but suggest deterministic predictability from persistence in coupling-hotspot regions, identified in Fig. 1a, in both land-surface analysis products and seasonal hindcasts. However, there is a lack of agreement between these estimates over how the strength of lagged-correlation varies with region. For example, GLDAS exhibits much higher persistence than ERA5-land over high latitudes.

A lack of global observations of root-zone soil-moisture makes it hard to know the true character of soil-moisture memory in the real world and consequently makes it hard to evaluate how well forecast models capture persistence. What we can say, is that there are large inter-model differences in persistence timescales for any given region (Fig. 3), with in the most extreme case the 4-month autocorrelation for the W-USA region having a range from 0 to 0.9. This wide range of autocorrelation values is in line with what has been seen in free-running climate models by Seneviratne et al., (2006a) who showed that this largely relates to differences in soil water-holding capacity and biases in radiation forcing in the models. The persistence timescale is strongly determined by the modelling assumptions underlying those analyses. We also note that different models will have different root-zone definitions, further complicating such comparisons.

<figure><img src="image_3.png" /><figcaption>**Fig. 2** 4-month lagged-correlation (May correlated with August) of root-zone soil moisture for GLEAM (a) and 100 cm soil moisture for ERA5-land (b) and GLDAS (c) and the multi-model mean of autocorrelation from C3S forecasts initialised on (or around) 1st May</figcaption></figure>
<figure><img src="image_4.png" /><figcaption>**Fig. 3** Lagged-correlation of root-zone soil moisture for GLEAM, ERA5, ERA5-land, GLDAS and C3S hindcasts (initialised 1st May), as a function of leadtime [i.e., from left to right, May correlated with</figcaption></figure>

May (lag 0), May correlated July (lag 1), etc.], in each of the “coupling hotspots” identified in Fig. 1a

### 3.1.3 Composites conditioned on wet/dry initial conditions

To infer predictable links between soil-moisture conditions at the start of May, when most systems are initialised, and the state of the atmosphere during the following summer one can compare composites of summers preceded by dry soil-moisture conditions with those preceded by wet (see e.g. Koster et al. 2014). Here we look at the difference between dry and wet years in both observations and seasonal forecast models, focussing on some of the land-atmosphere coupling hotspots that can be seen in Fig. 1a.

Specifically, we select years based on whether the area mean 1st May root-zone soil moisture within each “hotspot” (shown in yellow in Fig. 4) is within the driest or wettest

terciles in the GLEAM dataset (see Table 2 for the list of years selected). In Fig. 4 we plot the difference between the JJA average of the dry and wet years for soil-moisture and evaporation (Fig. 4a, c, e, g) as well as for 2 m temperature and z500 (Fig. 4b, d, f, h). For all these regions, years with drier(wetter) soil-moisture on 1st May tend to be followed by summers with drier(wetter) soil-moisture, lower(higher) evaporation, warmer(colder) temperatures and, with the exception of AfPak, elevated(reduced) geopotential height at 500 hPa (z500), compared to years with wetter(drier) soil-moisture. This reflects both the persistence of soil-moisture anomalies from 1st of May into the summer months and the influence of soil-moisture on evapotranspiration, temperature and z500. Note that composites produced with

<figure><img src="image_5.png" /></figure>
<figure><img src="image_6.png" /><figcaption>**Fig. 4** Difference between dry and wet composites of JJA soil moisture and evaporation (left column), T2m and z500 (middle column) and precipitation (right column) for various regions, based on whether the 1.st May soil moisture inside each the yellow box was in the dryest or wettest terciles (see Table 2 for a list of years). Each yellow box corresponds to one of the hotspots identified in Fig. 1a. Soil</figcaption></figure>

moisture and evapotranspiration were taken from GLEAM, T2m from BEST and z500 from ERA5. Blue and red lines indicate ±0.2 mm/day contours for evaporation (in **a**, **c**, **e** & **g**) and black lines (in **b**, **d**, **f** & **h**) indicate ±10 m z500 contours (with dashed lines for negative anomalies)
<table><caption>**Table 2** List of years with 1st of May soil moisture in the driest tercile and the wettest tercile of the GLEAM dataset in each hotspot (locations in Fig. 1a)</caption><thead><tr><th>Region</th><th>Dry years</th><th>Wet years</th></tr></thead><tbody><tr><td>SE Europe</td><td>1993, 2002, 2003, 2004, 2007, 2009, 2012, 2013</td><td>1995, 1996, 1997, 1998, 1999, 2000, 2006, 2011</td></tr><tr><td>Western USA</td><td>2000, 2002, 2007, 2008, 2012, 2013, 2014, 2015</td><td>1993, 1995, 1997, 1998, 1999, 2005, 2011, 2016</td></tr><tr><td>AfPak</td><td>1999, 2000, 2001, 2002, 2004, 2006, 2008, 2010</td><td>1995, 1997, 1998, 2005, 2009, 2013, 2014, 2016</td></tr><tr><td>South-Eastern European Plain</td><td>2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015</td><td>1993, 1994, 1997, 1998, 2000, 2004, 2005, 2016</td></tr></tbody></table>

ERA5 are very similar to those produced with GLEAM and BEST (see Figs S1-S4). Producing composites for the same years with the C3S systems show some similarities, but also important differences to the observed patterns (Figs S1-S4).

The link between soil-moisture and z500 anomalies (see Fig. 4b, d, f, h) is consistent with previous studies which have identified a link between low soil moisture, heat lows and upper-level anti-cyclonic flow over the USA (Koster et al. 2014, 2016; Teng et al. 2019) and Europe (Fischer et al. 2007). This is thought to result from anomalous heating of the lower troposphere in dry soil conditions, through enhanced vertical diffusion and longwave heating (Teng et al. 2019).

In this section we have identified several regions, where high soil-moisture persistence and high levels of land-atmosphere coupling suggest high potential for skillful seasonal forecasts. In the next section we will look at whether these regions show enhanced skill compared to other regions and look to identify areas of where the C3S models can improve.

## 3.2 Hindcast skill and the impact of SM-atmosphere coupling biases

### 3.2.1 Soil moisture

To assess the skill of soil-moisture forecasts we calculate the anomaly correlation (AC) of the hindcast ensemble mean top 1m soil-moisture for each model with the root-zone soil-moisture from GLEAM (shown in Fig. 5), where the ensemble mean anomaly is calculated using the model climate (for the whole period 1993–2016). The AC of the JJA soil moisture anomalies is generally highest in the regions of high persistence indicated in Figs. 2b & d and 3. However, with significant variations between the different models. These are easiest to see in Fig. 6, with for example the CMCC model having anomaly correlation values close to zero in the EuPl region (see Fig. 6c).

These differences in anomaly correlation between the different models will have a number of causes, related to processes in the forecast model, as well as the quality of the initial conditions. The land-surface initial conditions for

each hindcast set were produced with a free running land-surface model, as described in Sect. 2.1. As a result errors in soil-moisture will reflect those in the atmospheric forcing and assumptions in the representation of land-surface processes in the underlying model.

However, the timeseries consistency, as measured by the Pearson cross correlation, between the different land-surface initial conditions and analysis products is generally high, particularly in W-USA (with values generally above 0.8, see Fig. 7a) and SE-Euro (with values typically above 0.7, see Fig. 7b) but lower agreement for the EuPl and AfPak regions (Fig. 7c and d). In particular, the CMCC and DWD models have much lower cross correlations than the other models in EuPl, which is reflected in the low anomaly correlations in these regions in the subsequent hindcasts (see Figs. 6c and d).

The initial conditions for the CMCC model are derived from three LSM simulations with different forcings: ERA5, NCEP and a third with a linear combination of the two as forcing. We found that for EuPl the initial conditions from ensemble members generated from the ERA5 forced LSM were much more consistent with the other centres ($r=0.65$, when compared to ERA5-land for example) than those derived from the NCEP forced LSM ($r=0.0$, compared to ERA5-land), indicating low agreement between the NCEP and ERA5 forcing in this region (not shown). Note that NCEP also has low correlation with GPCP precipitation in the EuPl (see Fig. 12 of Janowiak et al. 1998), suggesting the reason for difference is an issue in the NCEP forcing.

Most of the C3S models use initial conditions created using the same or similar forcing, namely ECMWF reanalyses (see Sect. 2.1), which doubtless contributes the high cross correlation. On the other hand, the different observationally derived estimates of soil moisture, including ERA5, have high correlation with each other, suggesting that in terms of correlation using an offline land-surface model forced with reanalysis works reasonably well in these regions. This result is consistent with Koster et al., (2009), who found that after a simple scaling of land-surface model output based on the mean and variance, different land models tend to produce very similar information on temporal soil moisture variability in most parts of the world.
<figure><img src="image_7.png" /><figcaption>**Fig. 5** Anomaly correlation of ensemble mean top 1m JJA soil moisture hindcasts of each model and the average AC, with respect to GLEAM root-zone soil-moisture for all hindcasts (1993–2016)</figcaption></figure>
<figure><img src="image_8.png" /><figcaption>**Fig. 6** Area mean of the anomaly correlation of the top 1 m soil moisture of each model against GLEAM root-zone soil moisture as a function of leadtime</figcaption></figure>

### 3.2.2 Temperature skill

To assess hindcast skill for temperature we use the Continuous Ranked Probability Skill Score (CRPSS; Wilks 2011), calculated for JJA at each grid point for each year of the reforecast period. In the CRPSS the Continuous Ranked Probability Score (CRPS) from each dynamical seasonal forecasting system is compared to the CRPS of an ensemble forecast generated from observed climatology for 24 year hindcast period is used as the reference forecast. Therefore, the CRPSS represents the added value of a forecasting system over climatology: a value of 1 indicating perfect forecasts, 0 showing no improvement over

climatology and negative values indicating a system that is worse than climatology.

The results from the previous section suggest several regions where soil-moisture persistence and land-atmosphere coupling combine as a source of potential predictability on seasonal timescales. This suggests that if these processes are well captured these regions may have higher skill than other land areas. Spatial maps of T2m CRPSS (Fig. 8) show this, to some extent, with regions, such as Western USA, South-Eastern European Plain having relatively high (skillfull) values compared to the surrounding land areas.

Concerningly, there are also some land areas which show negative values of CRPSS, i.e. the skill of the ensemble

<figure><img src="image_9.png" /></figure>
<figure><img src="image_10.png" /><figcaption>**Fig. 7** Correlation heatmaps of area averaged 1st May soil moisture between soil moisture analyses (GLEAM, GLDAS, ERA5 and ERA5-land) and C3S initial conditions in the four regions identified in Fig. 1a</figcaption></figure>

forecasts is lower than the skill of a climatological forecast. Overplotting contours of the bias in the *I*<sub>SM-T2m</sub> suggests that many of these areas of low skill correspond to regions where the land–atmosphere coupling is overestimated. This is the case in regions of the central USA, central south America. Indeed, depending on the model, between 18 and 50% of the 1° by 1° gridpoints with CRPSS values less than -0.1 also have *I*<sub>SM-T2m</sub> values more than 0.3 °C lower (i.e. more coupled) than the estimate based on GLEAM and BEST.

CRPS for a bias-corrected gaussian random variables, such as seasonal T2m, can be shown to depend on the

reliability of the forecast, indicated by the spread-error
ratio (SER), and the mean absolute error (e.g. Leutbecher
and Haiden 2021). Comparing these three metrics with
*I*<sub>SM-T2m</sub> for the regions of enhanced coupling shown in
Fig. 8, namely, the South-Eastern USA (SE-USA), East-
ern Europe (EEURO) and North India (NIND), shows
that models with higher coupling tend to perform worse
in terms of all three metrics than models with lower cou-
pling strength, with lower CRPSS values, larger values of
MAE and SER, the latter indicating that the model is too
dispersive (see Fig. 9).
<figure><img src="image_11.png" /><figcaption>**Fig. 8** T2m CRPSS for JJA for each system (filled contours) and the bias in $I_{SM-T2m}$. Line contours at ±0.4 °C enclose areas which are too coupled in green and not coupled enough in red. The average CRPSS and coupling bias across the models is shown in the bottom right panel</figcaption></figure>

This makes sense intuitively since errors in coupling strength will mean that even well predicted anomalies in soil moisture may not result in the appropriate T2m anomalies,

with anomalies being too large in regions where the coupling is too strong and too small, where coupling is too weak. This can be seen, for example, in the bias of anomaly forecasts

<figure><img src="image_12.png" /></figure>
<figure><img src="image_13.png" /><figcaption>**Fig. 9** Scatter plots of coupling strength, *I*<sub>SM-T2m</sub>, against T2m scores: CRPSS (top), MAE (middle) and SER-1 (bottom). Vertical and horizontal solid lines indicate the estimate of *I*<sub>SM-T2m</sub> derived from GLEAM, and the dashed line indicates that derived from ERA5</figcaption></figure>

during wet (Fig. 10) and dry (Fig. 11) years in the Western USA (shown in Table 2). Soil-moisture anomaly forecasts are generally good over Western and Central parts of the USA (see Figs. 5 and 6a) so it is a good place to see the impact of coupling errors.

The wet year composites show a wet soil anomaly extending over much of North America, well into the Eastern half of the continent (Fig. 10a). However, the direct atmospheric response, i.e. positive anomalies in evaporation and negative

anomalies in T2m and z500 (Fig. 10b), is concentrated in the west. The positive z500 and warm temperature anomalies in the East are not associated with local anomalies in soil moisture, rather they are likely to be a dynamical response to the cyclonic circulation to the west (see Koster et al. 2014 and 2016). This picture is mirrored in the dry year composite (Fig. 11a & b).

The C3S models broadly capture the sign and shape of the soil-moisture anomalies (Figs. 10c & 11c), and
<figure><img src="image_14.png" /><figcaption>**Fig. 10** Mean JJA anomaly in soil-moisture, evaporation (both from GLEAM), T2m (from BEST) and z500 (from ERA5) for wet years (see Table 2) (**a**, **b**). The mean anomaly from C3S systems (**c**, **d**) and mean bias in the anomaly forecast from the C3S systems (**e**, **f**) are shown for the same years. Soil-moisture (**a**, **c** & **e**) is shown in filled</figcaption></figure>

contours with ±0.15 mm/day evaporation contours shown in blue and red. T2m is shown in filled contours (**b**, **d** & **f**). The solid black and dashed lines correspond to z500 anomaly or bias of 4 m and -4 m respectively

the associated atmospheric response (Figs. 10d & 11d). However, the evaporation, T2m and z500 anomalies are too small in the west, where the models underestimate the coupling strength, and the evaporation and T2m anomalies

extend too far to the east, where the coupling strength is too high (see Fig. 8), resulting in a warm/cold bias for the wet/dry composites respectively (Figs. 10f and 11f).

<figure><img src="image_15.png" /></figure>
<figure><img src="image_16.png" /><figcaption>Fig. 11 Same as Fig. 10, but for dry years</figcaption></figure>

We can also hypothesise that the large, over dispersive, SER values can also be explained by the influence of the coupling strength on the ensemble distribution of T2m. If the coupling is too strong, deviations of T2m and soil moisture from the ensemble mean may be too large (assuming reasonable spread in soil-moisture) and too correlated with soil-moisture. Dry members will tend to be too warm and

wet members will tend to be cold. This could potentially affect any region with sufficient spread in soil-moisture, affecting the reliability of forecasts. Indeed, one can see that in the regions of too-strong coupling, identified in Fig. 8, the hindcasts are under confident, as indicated by values of SER-1 of greater than zero. One would also expect the opposite in regions where coupling strength is underestimated.
## 3.3 Causes of bias in land–atmosphere coupling

### 3.3.1 Summer mean biases

In Sect. 3.1 it was shown that although overall the C3S hindcasts showed similar spatial variations in soil-moisture atmosphere coupling strength, this coupling extended to areas where observations suggest that evaporation is energy-limited (see Fig. 1). In this section we investigate these biases in coupling strength further to determine the causes.

The multi-model mean bias of the various coupling metrics highlights specific areas (Fig. 12a–c), including a broad swathe of North America, extending from the Canadian Prairies to the South-Eastern USA, Eastern Europe and Northern India and all seven C3S systems analysed agree in the sign of this error, as indicated by the stippling in that figure. The errors in coupling-strength in these regions go hand in hand with large biases in temperature and precipitation (Fig. 12d and e).

Berg and Sheffield (2018) found that mean precipitation was an important driver of model spread in soil-moisture-evaporation coupling strength in the CMIP5 ensemble. The patterns for SE-USA and EEURO regions seen in Fig. 12 are broadly consistent with their analysis, i.e. the models

with the largest biases in precipitation, also have the largest overestimates in coupling strength, $I_{SM-E}$ (Fig. 13). However, we cannot infer a significant correlation based on only seven models. Note that we do not find a similar link in the NIND region.

### 3.3.2 Lead time dependence of coupling and mean state biases.

#### 3.3.2.1 South-Eastern USA and Eastern Europe
The warm/dry bias over the mid-latitude continents during the summer is a well-known feature of GCMs in both free-running climate simulations (Lin et al. 2017; Zhang et al. 2018) and weather forecasts (Weverberg et al. 2018). The reason, as identified in these previous studies is tied to a feedback loop: Too much insolation results in high near-surface temperature and high evaporation leading to too much drying of the soil and boundary layer which results in too little cloud which in turn leads to too much insolation.

Looking at these biases in both SE-USA and EEURO regions (shown in Fig. 12e), as a function of leadtime, one can see a picture consistent with the feedback described above. Apart from the CMCC model, the coupling strength is too high from the first month in the hindcasts initialised 1st of

<figure><img src="image_17.png" /><figcaption>**Fig. 12** Multi-model mean bias in JJA coupling metrics (a, c and e) and 2 m-temperature (d), total precipitation (e) and downwelling shortwave radiation (f). Note that the stippling is added where all seven C3S systems agree in the sign of the error</figcaption></figure>

<figure><img src="image_18.png" /></figure>
<figure><img src="image_19.png" /><figcaption>Fig. 13 Scatter plots of JJA mean T2m bias for each model against precipitation bias (top row) and coupling metric I<sub>SM-E</sub> against precipitation bias (bottom row). The regions correspond to the boxes in Fig. 12e. Vertical and horizontal solid lines indicate the estimate</figcaption></figure>

derived from GLEAM, and the dashed line indicates that derived
from ERA5 (not visible for NIND as it has the same value as
GLEAM)

May and this bias increases through the summer (Fig. 14a) and this result is robust to resampling the ensemble members. The land-surface receives too little precipitation, which during the summer months is underestimated by more than 1 mm/day (or 1/3 of the observed total) in some models (Fig. 14g). It also receives too much insolation through the summer months (Fig. 14j), leading to excessive drying of the soil (Fig. 10m), enhanced sensible heating and a warm bias in 2 m-temperature (Fig. 14d). One can also see that ERA5 also has the biases of the same sign in I<sub>SM-E</sub> and precipitation, telling us that the bias in rainfall and enhanced coupling are a feature of short (12 h) forecasts with the ERA5 system, consistent with the results from Weverberg et al. (2018).

At this point it is worth reviewing the mechanisms
through which the soil-moisture content can influence
evapotranspiration, and how this is parameterised. Modern
LSMs typically follow the approach of Jarvis (1976) where
the evapotranspiration is expressed as:

$$
E_{TR} = \rho_a \left[ \frac{q_{sat}(T_s) - q_{lml}}{r_a - r_c} \right] \quad (3)
$$

where, ρ_a is the air density, r_a is the aerodynamic resistance
between the surface and the lowest layer of the atmosphere,

q<sub>sat</sub>(T<sub>s</sub>) is the saturation water-vapour specific humidity at
the temperature of the surface, q<sub>lml</sub> is the water vapour spe-
cific humidity at the lowest atmospheric model level and r<sub>c</sub>
is the canopy resistance:

$$
r_c = \frac{r_{smin}}{LAI} f(\theta) \dots \quad (4)
$$

where $r_{s \ min}$ is the minimum stomatal resistance, LAI is the
leaf area index and:

$$
\frac{1}{f(\theta)} = \frac{\theta - \theta_{pwp}}{\theta_{cap} - \theta_{pwp}}, \text{ when } \theta_{pwp} < \theta < \theta_{cap} \quad (5)
$$

$$
1/f(\theta) = 1, \text{ when } \theta_{\text{cap}} \le \theta, \text{ and}
$$

$$
1/f(\theta) = 0, \text{ when } \theta \le \theta_{\text{pwp}}
$$

where θ is the soil-moisture, θ<sub>pwp</sub> is the permanent wilting
point, θ<sub>cap</sub> is the field capacity. It is through the function,
f(θ), that the dependence of evaporation on soil moisture
is expressed. As a result, the strength of coupling between
evaporation and soil moisture depends on the range of values
of θ with respect to θ<sub>pwp</sub> and θ<sub>cap</sub> in any given region.
<figure><img src="image_20.png" /><figcaption>**Fig. 14** Seasonal cycle of *I*<sub>SM-E</sub> (top row), T2m (second row), Total precipitation (third row) and incoming shortwave radiation (bottom row) in regions with large coupling bias (see Fig. 8c): Central USA (left column), Eastern Europe (middle column) and North India (right column)</figcaption></figure>

<figure><img src="image_21.png" /></figure>
<figure><img src="image_22.png" /><figcaption>**Fig. 15** Soil-moisture-evaporation scatter plots for regions of large bias (see Fig. 8c). Stars indicate the area-averaged value of $\theta_{cap}$ for the same region, which marks the transition between energy-limited</figcaption></figure>

and soil-limited evaporation regimes and crosses indicate the values of $\theta_{pwp}$. Each colour corresponds to a different model

To investigate the model behaviour within this framework we can look at evaporation as a function of soil moisture for the various C3S models (see Fig. 15), to infer the strength of coupling. By plotting this for individual months,

we can also see how the coupling changes over time. For example, in both the SE-USA and EEURO regions, but with the exception of Sys8 and ECCC-CAM_CM4, which are already coupled in May, the other systems are above
$\theta_{cap}$ in the energy limited evaporation regime. However, as the soil in the other models dries out during the subsequent summer months the strength of the correlation between E and $\theta$ increases as they enter the soil-moisture limited zone between $\theta_{cap}$ and $\theta_{pwp}$. This is a contrast with GLEAM and ERA5, which show no such correlation during the months between May and August, suggesting that the real world is typically in an energy-limited evaporation regime in this region during these months.

### 3.3.2.2 Northern India
Over NIND, many of the months have positive values of $I_{SM-E}$ from GLEAM and ERA5, i.e. the region is in a soil-moisture limited regime (Fig. 14). However, there is a seasonal minimum in the coupling, during July-Oct, which results from an increase in soil-moisture during the monsoon season, where the soil transitions into an energy-limited regime. From the regime diagrams Fig. 15, we can indeed see a strong correlation between the GLEAM soil moisture and evaporation in May, but a decoupling (reduced correlation) of these variables as the soil-moisture increases during subsequent months until there is no correlation in Aug.

The hindcasts initialised on the 1st May, again apart from CMCC, generally overestimate the coupling strength in the forecasts. In some of the models this is likely related to underestimating the rainfall associated with the monsoon between the months of June-August (e.g. the two ECCC models). In others it may be due to a positive bias in insolation, both of which will contribute to a slower wetting of the soil, than seen in GLEAM or ERA5. Partly as a result of this the soil-moisture does not move past the $\theta_{cap}$ out of the soil-moisture limited regime and some coupling is maintained, in contrast to GLEAM and ERA5.

Interestingly even some of the models that have precipitation, SW and soil-moisture climatology close to the observations (e.g. SEAS5 and MF-Sys8) have too much coupling. This may be related to the values of $\theta_{cap}$ and $\theta_{pwp}$, which varies by a factor of two between the models (see Fig. 15) and affects the strength of coupling between $\theta$ and E, which is inversely proportional to $\theta_{cap} - \theta_{pwp}$ (see Eq. 5). More generally because $\theta$ is really a model dependent index and $\theta_{cap}$ and $\theta_{pwp}$ are so uncertain, it is not really possible to say that errors in the coupling strength are caused by errors in one or the other, only that the relative position of $\theta$ with respect to $\theta_{cap}$ and $\theta_{pwp}$ is wrong.

## 4 Conclusions

In this paper we have investigated the importance of soil-moisture predictability and soil-moisture-atmosphere coupling for seasonal prediction in the northern hemisphere, during boreal summer, and investigated how these aspects

are represented in seasonal hindcasts from the C3S multi-model system. Through this analysis we reached the following conclusions:

1. We have identified Western North America (indicated in Fig. 4d) and the South-Eastern European Plain (indicated in Fig. 4g) as regions that are likely to have particularly high potential predictability (of T2m and z500) in JJA based on the strength of both land-atmosphere coupling (see Fig. 1) and soil-moisture persistence (see Figs. 2 and 3a & c). This leads to a predictable link between the sign of soil-moisture initial conditions and the atmospheric anomalies (e.g. T2m and z500) in the same region with dry (wet) soil conditions (in May) tending to be followed by warm (cold) temperature anomalies and high (low) z500 anomalies during the following summer (see Fig. 4).

2. These predictable links are captured, to some extent, by the various C3S systems which generally show relatively high soil-moisture (Fig. 5) and T2m (Fig. 8) skill in these regions compared to other parts of the northern hemisphere extra-tropics.

3. However, the C3S systems tend to overestimate the strength of the coupling, compared to estimates of the true coupling strength derived from GLEAM, BEST and ERA5, exhibiting strong land-atmosphere coupling in regions not supported by these reference datasets (particularly over a large swathe of North America, Eastern Europe and Northern India) (see Figs. 1 and 12).

4. These biases in the coupling strength go hand in hand with poor hindcast skill indicated by negative CRPSS values (indicating that performance is worse than climatology, see Fig. 8), and biases in the mean state (Fig. 13) with the systems with the smallest errors in coupling strength tending to perform better in terms of CRPSS (Fig. 9).

These results confirm that there is high potential predictability coming from the land-surface that is relevant for seasonal forecasts of both land-surface and atmospheric properties in summer months. But also suggest that there is much to improve in order to harness this high potential predictability. The high disagreement (low cross-correlation) in soil-moisture in some regions indicates that there is potential to improve soil-moisture initial conditions, potentially through use of land-surface data assimilation, but this must be done alongside improvements that address the coupling strength errors which lead to poor skill in some regions.

We show in Sect. 3.3 that errors in the soil-moisture-evaporation coupling can be explained in terms of inconsistencies, compared to the real world, in the relative position of the model soil-moisture with respect to the model wilting point and field capacity, which determine the range
over which, and the extent to which, evaporation is soil-
moisture limited. Developing methods which can improve
this consistency will be a necessary step to improve the
coupling-strength in the model.

As well as the important link to forecast skill, the
enhanced coupling in the models will strongly influence
the outcome of predictability studies using these GCMs.
One would expect that hindcasts with randomly selected
soil-moisture initial conditions would tend to perform
better than those initialised with the true state in regions
where the CRPSS is negative due to too-strong soil-mois-
ture atmosphere coupling. This may explain the limited
impact of accurate soil moisture initialisation over the cen-
tral USA seen in sensitivity studies by Koster et al. (2011)
and Ardilouze et al. (2017).

An important limitation for the evaluation of land–atmos-
phere processes in seasonal hindcasts is the high uncertainty
in observationally derived gridded estimates of soil-moisture
and evaporative fluxes. This makes it hard to quantitatively
evaluate how well climate models capture both the mean
climate and variance as well as the strength of land–atmos-
phere coupling. However, the co-location of biases in cou-
pling strength and poor hindcast skill (shown in Fig. 8), pro-
vides some confidence that the biases in coupling strength
identified in this study are genuine. However, it is hoped that
future studies comparing the various observationally derived
estimates of soil-moisture and evaporation, will provide
more clarity on the strength and limitations of these datasets.

**Supplementary Information** The online version contains supplementary material available at https://doi.org/10.1007/s00382-025-07753-1.

**Acknowledgement** The authors would like to the editor Jianping Li as well as Randal Koster and one anonymous reviewer for their insightful and constructive comments, which have helped improve the manuscript.

**Author contributions** The study was designed by JD in consultation with FV, TS, PR and CA. JD created all figures and drafted the manuscript. CA, DP, KF and AM provided soil-moisture parameters used in Fig. 11. All authors commented on the manuscript.

**Funding** This work was supported by the Copernicus Climate Change Service Evolution (CERISE) project. The CERISE project (grant agreement No101082139) is funded by the European Union. Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the Commission. Neither the European Union nor the granting authority can be held responsible for them.

**Data availability** The C3S multi-model seasonal forecasts are publicly available from the C3S Climate Data Store: https://cds.climate.copernicus.eu/datasets/seasonal-monthly-single-levels?tab=overview

**Declarations**

**Conflict of interest** The authors have no relevant financial or non-financial interests to disclose.

**Open Access** This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

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