Land–atmosphere (L–A) coupling describes the covariability between the land and atmospheric states, and plays a key role for understanding states in the climate system such as the evolution of the atmospheric boundary layer (ABL) temperatures and humidities. It shapes, e.g., the atmospheric water and energy cycles, and through this influences the intensity and duration of extreme events such as heat waves (Ukkola et al., 2018; Jaeger and Seneviratne, 2011; van Heerwaarden and Teuling, 2014; Schumacher et al., 2019), drought periods (Miralles et al., 2019) or the occurrence of heavy rainfall events. Furthermore, the feedback processes influence the climate response to land surface modifications (Hirsch et al., 2014; Laguë et al., 2019) suggesting the importance of the processes' accurate representation in climate models to improve projections.

The local coupling (LoCo) process chain outlines the connection between soil moisture and precipitation through the turbulent surface fluxes modifying the evolution of the ABL, and finally, leading to different conditions for cloud and precipitation formation (Santanello et al., 2009, 2011). Various coupling metrics have been developed to investigate the nature and intensity of this and other relationships in the climate system (Santanello et al., 2018). Individual processes in the chain exhibit different intensities and the feedback sign can diverge in dependence of the region (e.g., Findell et al., 2011; Findell and Eltahir, 2003a, b; Knist et al., 2017; Koster et al., 2004) and the period of time investigated. Coupling hotspots mainly occur in transition regions between dry and wet climates (e.g., Gentine et al., 2013; Koster et al., 2004; Taylor et al., 2012). Temporal variability is apparent at interannual scales (Guo and Dirmeyer, 2013; Lorenz et al., 2015) and in trends of the coupling strength (Dirmeyer et al., 2012, 2013; Seneviratne et al., 2006).

Uncertainty remains in the accurate quantification of the coupling strength along the LoCo process chain, especially in the atmospheric segment. From the physical perspective, the strength is influenced by both the prevailing land surface and the atmospheric state. Jach et al. (2020) showed that extreme afforestation led to weaker coupling between surface moisture and convection triggering, and a less pronounced favor for convection triggering over wet soils in the European summer. The conversion of current vegetation to grassland had the opposite effect. However, Davin et al. (2020) showed that the same land use and land cover change scenarios as used in Jach et al. (2020) initiated different responses in near-surface temperature within the ensemble of regional climate models from the flagship pilot study “Land-Use and Climate Across Scales” (LUCAS) due to deficiencies in the computation of evapotranspiration. Understanding potential implications of these uncertainties for impacts of land use and land cover changes on L–A coupling strength and climate variability was one motivation of our study.

From the technical perspective, the coupling strength is influenced by the choice of the dataset used for the investigation (Dirmeyer et al., 2018; Ferguson and Wood, 2011) and, in the case of models, their configuration such as parameterization schemes (Chen et al., 2017; Milovac et al., 2016; Pitman et al., 2009), initialization (Santanello et al., 2019) or model resolution (Hohenegger et al., 2009; Knist et al., 2020; Sun and Pritchard, 2016, 2018; Taylor et al., 2013). Studies on the regional scale over Europe often use a single model (Baur et al., 2018; Jach et al., 2020; Lorenz et al., 2012) or target only the terrestrial segment (soil moisture–surface flux coupling) of the local coupling process chain (Knist et al., 2017). Coordinated model intercomparison studies such as the Global Land–Atmosphere Coupling Experiment (GLACE) initiative apply general circulation or earth system models (Guo et al., 2006; Koster et al., 2006, 2011; Comer and Best, 2012). On the one hand, this circumvents the need to use lateral boundary layer forcing. On the other hand, the horizontal resolution of these model runs is usually on the order of 1 to 2∘ grid spacing. This reduces the models' ability to represent detailed surface characteristics. These, in turn, play a key role for triggering convection, e.g., due to differential heating.

The “convective triggering potential – low-level humidity index” (CTP-HIlow) framework (Findell and Eltahir, 2003a, b) is a commonly used process-based coupling metric to investigate the link between surface moisture and convection triggering. It is based on the hypothesis that the structure of the early morning ABL (atmospheric pre-conditioning) gives an indication about the likelihood for locally triggered afternoon precipitation over differently wet soils. Later works added soil moisture (Roundy et al., 2013) or the evaporative fraction (Findell et al., 2011; Berg et al., 2013) as a third dimension. Efforts have been made to test the global applicability of the framework, which made use of climatologies of the metrics (Ferguson and Wood, 2011; Wakefield et al., 2019).

Analyzing the atmospheric segment on a process-based level requires information about the vertical structure of the atmosphere. The data requirements for studying the atmospheric segment of L–A coupling on the process level and in a spatially explicit way can be summarized as follows: vertical temperature and moisture profiles are needed (1) with a sufficiently long data record (period of at least 12 summers for metrics targeting convection triggering), to comply to the data length requirements for robust results (Findell et al., 2015), (2) with a high-enough temporal resolution to be able to extract the time step close to the local sunrise and (3) increasing vertical resolutions improve the estimate (Wakefield et al., 2021). These high requirements limit the datasets available for a study on the continental scale for Europe. Observations of early morning vertical temperature and moisture profiles are rare and usually point measurements. The typical radiosonde launch times (00:00 and 12:00 UTC) do not cover the early morning hours over Europe. Other observational products such as satellite-based profile data have been successfully used to apply the CTP-HIlow framework on Roundy and Santanello (2017), although they often have coarse vertical resolutions (Wulfmeyer et al., 2015). The lack of suitable observations challenges the validation of results, which provides the incentive for building up a network of coordinated measurement sites like the Land-Atmosphere Feedback Observatory (LAFO) of the University of Hohenheim (Wulfmeyer et al., 2020; Späth et al., 2019).

To study how sensitive the atmospheric segment of L–A coupling strength responds to differences in the atmospheric pre-conditioning, we developed an approach with which the temperature and moisture output fields from a regional climate model run were modified after the simulation and before applying the CTP-HIlow framework. The modifications are expected to change the pre-conditioning and thus potentially the coupling classification. First of all, frequent changes in the classification show that it lies at the boundaries of different classes. However, assuming that the classification framework is accurate enough, frequent changes also reveal that the expectable coupling signal remains uncertain. This is shown as changes in the atmospheric conditions in a presumably realistic range for the current climate could initiate different atmospheric responses such as triggering deep, shallow or no convection in different cases in the same region. Furthermore, it indicates a sensitivity of the coupling to changes in the atmosphere, e.g., arising from climate change or changes at the land surface.

The approach is based on our hypothesis that the temperature and moisture fields can diverge in their mean, as well as their vertical, temporal and horizontal distributions, and the framework only recognizes the differences regardless of their origin. Hence, besides identifying regions with a high sensitivity to differences in the atmospheric conditions, we are able to approximate a range in coupling strength of the atmospheric segment. Here, we focus on the impacts of differences in the mean states and the vertical gradients of temperature and specific humidity in the posterior modification cases compared to the CTRL. For this purpose, we have set up two sets of cases: one targeting the analysis of differences in the mean state and one the analysis of differences in the vertical gradients. Temperature modifications at the surface range between ±2 K, which is derived from an acceptable range of near-surface temperature biases occurring in climate simulations as defined by Kotlarski et al. (2014), and decrease over height. The a posteriori modifications of moisture were implemented under consideration of the close relationship between temperature and water vapor in the atmosphere, thus taking into account the respective temperature modification (e.g., Willett et al., 2010; Bastin et al., 2019).

With this approach we focus on two research questions:

How sensitive is the L–A coupling strength to modification of temperature and moisture profiles during the European summer months (JJA)?

We modified daily temperature and moisture profiles around local sunrise of 30 summers from a regional climate simulation to examine the sensitivity of land–convection coupling strength to differences in the thermodynamic structure over Europe. The CTP-HIlow framework was applied to each of 18 modification cases grouped into two sets, on the one hand, to understand implications of warmer, cooler, moister or dryer atmospheric conditions for the coupling strength, and on the other hand, to investigate the sensitivity of the strong coupling region's location and the predominant sign of feedbacks within the domain. Analyses of the latter base on the idea that regions lying at the boundaries of two or more categories are particularly sensitive to changes in the atmosphere, as small changes in the pre-conditioning could initiate a different atmospheric response to surface wetness conditions.

Comparing the model's mean near-surface temperature and moisture as well as their temporal distributions with reanalysis data showed that the model has a dry, warm bias over the southern part of the domain and rather a cold bias with small differences in moisture over the northern part. The differences between the temperature and moisture distributions of model and reanalysis data were statistically insignificant (Ferguson and Wood, 2011). Therefore, the relative frequencies of wet soil advantage, dry soil advantage, transition zone and AC days from the model in summer are assumed to be represented in a realistic range and relation to each other.

Nevertheless, uncertainty in the quantification of the coupling classes' occurrence arising from model specific biases has to be acknowledged. The cold bias over eastern Europe results from an overestimation of cooler days at the expense of warmer ones, while the tails of the distribution are represented well in the model (not shown). Assuming that cooler days have a more stable atmospheric layering, the cold bias suggests an underestimation of CTP, and, given that the moisture bias in the same region is small, also an underestimation of the humidity deficit. This could hint at an underestimation of the modeled dry soil advantage days but also an overestimation of wet and stable AC days in the corresponding region. In the southern, mostly atmospherically controlled part of the domain, the warm and dry bias suggests an underestimation of the relative humidity and thus and overestimation of HIlow. The dry atmospheric conditions were one of the major inhibiting factors for coupling events in the model, which hints at an overestimation of dry AC days in the model. However, the distributions of temperature and moisture diverge more in the southern part; the quantification of potential coupling days has to be treated with caution over the Iberian Peninsula and the Mediterranean.

Studying spatial differences in the impacts of temperature and moisture changes reveals a north–south dipole in the coupling strength's sensitivity to changes in both variables indicated by a switch in the sign between the northern and the southern parts of the domain. Furthermore, temperature and moisture changes have contrary effects on the coupling strength throughout the domain. This means that simultaneous increases or decreases, respectively, in temperature and moisture have small net effects, and given that atmospheric temperature and moisture are strongly positively correlated in the Northern Hemisphere (e.g., Willett et al., 2010; Bastin et al., 2019), simultaneous changes of the same sign are considered most realistic. A strengthening of the coupling as a result of atmospheric warming is in line with the trend of stronger coupling in consequence of climate change over Europe. Seneviratne et al. (2006) showed the formation and expansion of a transitional region between wet and dry climates over central and eastern Europe in which strong L–A interactions can be expected. Dirmeyer et al. (2013) showed the trend of increasing coupling strength from a global perspective for both the land and the atmospheric segment.

Analyzing the relative importance of temperature versus moisture changes for the coupling strength within the domain suggests that the temperature control on the coupling strength is stronger in northern Europe, in particular that of coupling days in wet soil advantage (Fig. 8a and b), while moisture variations rather control the coupling strength in southern Europe. Please note that the sign of changes in nAC days and the coupling classes is not sensitive to the choice of the temperature–moisture scaling rate within a tested range of about ±2 % K-1 around the Clausius–Clapeyron rate of 7 % K-1 (Fig. 3). However, the rate does impact the magnitude of changes. In the event of a rate below 7 % K-1, the impact of the respective modification cancels out in the more moisture-controlled south. The areas of temperature and moisture control for nAC days coincide with the energy- and moisture-limited regimes for evapotranspiration over Europe (Knist et al., 2017; Denissen et al., 2020; Seneviratne et al., 2006). Our findings suggest that the energy and moisture limitations further propagate from the land segment of the coupling (connection between soil moisture and surface fluxes) to the atmospheric segment (connection between surface fluxes and boundary layer properties) along the local coupling process chain (Santanello et al., 2018).

Differences in the impacts of modified temperature and moisture gradients showed that the consideration of changes in the gradients can be as important for understanding differences in land–convection coupling as the temperature or moisture change itself. Please note that the vertical resolution of the model (40 levels) limits the representation of details in the profiles, and a higher vertical resolution would provide a more accurate estimate of the temperature and moisture gradients (Wakefield et al., 2021). However, while they, on the one hand, showed that lower vertical resolution introduces uncertainty, they also showed that data with limited resolution still provide reasonable results. Thus, the effects of altered gradients are expected to remain substantially similar also with a higher vertical resolution model output. It shows that increasing the temperature gradient, and hence destabilizing the atmosphere, usually increases the number of nAC days, whereas shallower gradients reduce them. Thus, a warming signal propagating deeply through the atmospheric column (e.g., wet_abs, Figs. 10 and 11) leads to a smaller increase in the coupling strength than one that warms only the lower atmospheric levels, resulting in a greater temperature gradient between 100–300 hPa a.g.l. (hot). However, in the latter case, a stronger surface temperature inversion needs to be dissolved by surface lifting, heating or moistening to enable buoyant lifting and deep convection. Inversions potentially reduce ABL growth during mixed layer development and thus inhibit the triggering of deep convection during the subsequent day and hence weaken the coupling again. This effect cannot be represented in the framework, as it does not resolve inversions in about the lowest 1000 m of the ABL. Further, including the energy partitioning at the land surface in the analysis would inform about ABL moistening and heating during the day and in particular the period of mixed layer development. Brogli et al. (2019) projected lapse-rate decreases in consequence of stronger upper-tropospheric than surface warming over Europe by the end of the 21st century, and that the decreases are stronger over northern Europe than over the Mediterranean. Warming and decreasing lapse rates are assumed to have contrary effects on the coupling strength, showing that further research is necessary to understand and quantify impacts of future warming on the L–A coupling strength.

Finally, the reliability of the coupling hotspot as suggested by Jach et al. (2020) was analyzed, at first, by testing the sensitivity of the daily classification of atmospheric pre-conditioning in consequence of the modifications, and secondly, by checking whether and how frequently the dominance of a feedback advantage was changed over the 30-year period. We have shown that modifications of temperature and moisture cause considerable differences in both the occurrence of nAC days and their partitioning in the different coupling classes over the strong coupling region throughout the summer season. However, this does not necessarily imply a change in the dominance of a coupling class. There are two regions in which the dominant coupling class is insensitive to changes in the atmospheric structure, wherefore a consistent regime can be expected. On the one hand, the atmospherically controlled southwest and Atlantic coastal areas of Europe remain in atmospheric control in every modification case. Even considerable increases in low-level atmospheric relative humidity did not decrease the humidity deficit to a level in which local surface triggered deep convection can occur on a frequent basis. On the other hand, none of the modification cases reduced the coupling so that the strong positively coupled region over the East European Plain disappeared. Thus, this region is considered a reliable hotspot region for positive feedbacks. Evidence for the location of the hotspot is also found in Koster et al. (2004) or Seneviratne et al. (2006), who investigated hotspots of soil moisture–precipitation coupling in a global model ensemble.

Frequent changes in the coupling regime occur over parts of Scandinavia, Germany and from the Alps to around the Black Sea. Regime changes are related to two effects or a combination of those. Firstly, the modifications frequently increase the number of nAC days above the threshold to be considered nAC and hence expand the size of the hotspot. This happens at the border between the reliable AC and the strong coupling region. Differences among the modification cases are usually small, which suggests that the effect in reality is small. Secondly, the region from the Alps to around the Black Sea has always enough nAC days to be considered nAC, but the dominant coupling class regularly shifts between the wet soil advantage and transition zone depending on the atmospheric temperature and moisture. The number of wet soil advantage and transition zone days is fairly equal in this region. Differences in temperature and moisture control which class dominates, and hence, following their definition, whether deep convection or shallow convection is more likely. This makes the region particularly interesting for future research on L–A feedback.

It has to be noted that the analysis focused on analyzing differences in the mean and vertical gradients of temperature and moisture to approximate a potentially realistic spread in the atmospheric segment of L–A coupling strength for Europe. The horizontal and temporal distributions were maintained, as the modification factors cannot cover changes in variability which would change the shape of the distributions. However, differences in the temporal distribution are to be expected in consequence of non-linear feedback processes, when a change in the mean temperature and moisture occurs, which can also impact the L–A coupling (Hirsch et al., 2014). Yet, a prediction of changes in the temporal distribution is complex and beyond what can be done with a modification factor. This suggests that further investigation is necessary to understand differences in the temporal distribution of temperature and moisture in the atmosphere and link them to L–A coupling to improve the understanding of modification in the coupling under changing climatic conditions.

By studying the sensitivity of the atmospheric segment of L–A coupling strength to modifications in vertical temperature and moisture during 30 summers over Europe, we have shown that the atmospheric pre-conditioning and the coupling are indeed sensitive to changes in temperature and moisture. However, no combination of temperature and moisture changes relocated or reshaped the coupling hotspot strongly over northeastern and eastern Europe. Differences in the frequency of occurrence of advantageous atmospheric conditions for feedbacks of any kind suggest that uncertainty remains in the accuracy of the coupling strength itself, but stronger coupling relative to the rest of the domain is considered reliable there. Further research including the development of datasets usable for validation or the analysis of L–A coupling in the most recent reanalysis datasets is required for refined approximations of the L–A coupling strength. Furthermore, the predominance of positive feedbacks, meaning convection is preferably triggered over wet soils, was preserved in all cases over the northern part of the coupling hotspot. Therefore, it is predestined for future studies on the impacts of natural and deliberate land surface modifications on the local and regional climate as options for climate change mitigation, as an influence can be expected and the dominant response is certain. This is particularly interesting in light of rising temperatures and the related trend of strengthened L–A coupling under global warming (Dirmeyer et al., 2013; Seneviratne et al., 2006). In the southern part, the coupling classes wet soil advantage and transition zone have an equal share throughout summer, and temperature and moisture modifications cause a switch in the regime in several cases, implying uncertainty in the dominant coupling regime. This makes the region particularly interesting for further studies on L–A coupling, because small changes in the atmospheric conditions may lead to a different atmospheric response. Additionally, the understanding and improved representation of these feedback processes in regional climate models are expected to reduce uncertainties in summer precipitation predictions in climate projections. Especially, the parameterization of convective precipitation has been shown to introduce uncertainties and more advanced triggering mechanisms for convection may lead to an improvement of precipitation predictions (Chen et al., 2017).

Finally, process-based coupling studies still face a substantial lack of spatially comprehensive data covering the vertical structure of the ABL on the regional scale and hence the reliance on model data. Efforts of creating a network of coordinated continuous long-term measurements such as the GLAFO initiative (Wulfmeyer et al., 2020) are required to close the gap and provide a validation basis for modeling-based studies. The modeling-based studies, in turn, are confronted with data storage and computation limitations, which currently leads to the practice of storing 3-D fields only with a limited number of vertical levels. The trend of increasing complexity of atmospheric models, higher temporal and spatial resolutions, as well as spatial and temporal coverage of simulations strongly exacerbates storage limitations. Though single model studies are limited in their generalizability as, e.g., the choice of parameterizations or lateral boundary conditions cause uncertainty in coupling assessments, it is unlikely that comprehensive model ensemble studies will become feasible on the regional scale in the short and medium terms. Therefore, we consider this modification approach as a valuable alternative to study the sensitivity of the atmospheric segment of L–A coupling providing evidence for the location of a L–A coupling hotspot and a range for potential coupling strength under current climatic conditions.