1. Introduction
Coupling between soil moisture and evapotranspiration modulates the moisture and energy balances at the land surface (Bonan 2008; Seneviratne et al. 2010; Santanello et al. 2018). As water escapes from land to atmosphere, it can induce a chain of consequences (Findell and Eltahir 1997; Eltahir 1998). A decline in soil moisture content can cause moisture stress that increases the resistance to evaporation, and secondarily can result in a higher surface albedo that reduces absorbed incoming solar radiation. Surface latent heat flux decreases while surface sensible heat flux increases under conditions with lower moisture availability. This change in the partitioning of surface heat fluxes results in a warmer and drier atmosphere that is further conditioned against the formation of clouds and limits precipitation. Without a source of water going into land surface, it dries further. Such a soil moisture–evapotranspiration–precipitation feedback has a significant impact on the subseasonal time scale as it links to extremes such as heat waves and droughts, which can cause significant economic and societal damage (Fischer et al. 2007; Hirschi et al. 2011; Herold et al. 2016; Miralles et al. 2019). Therefore, the role of soil moisture in current and future climate is a topic of growing importance.
The existence of these feedbacks at any location mainly depends on whether variations in latent heat flux are limited by soil moisture content or energy availability (Dirmeyer et al. 2009). As has long been recognized, the relationship between soil moisture and latent heat flux (hereafter abbreviated SM–LE) is not linear. It exhibits threshold behavior; LE behaves dramatically differently when SM crosses critical values (Budyko 1974; Eagleson 1978; Vargas Zeppetello et al. 2019). The values typically defined are the permanent wilting point, field capacity, and a critical SM threshold above which the SM–LE relationship weakens or reverses (Seneviratne et al. 2010). The permanent wilting point is the minimum required SM above which vegetation transpires; a criterion of hydraulic pressure such that osmosis, the process that allows roots absorb water, can transmit water up the vascular system of the plants. Field capacity is the amount of water in the soil that can be maintained as a balance between gravity and capillary forces.
There is a critical SM threshold that lies below field capacity and depends on available energy. If SM exceeds the critical vthreshold, further increases in SM do not increase evapotranspiration; rather, available energy determines LE. The critical SM threshold depends on multiple climate variables (Haghighi et al. 2018). LE increases with increasing SM content when water is between the wilting point and the critical threshold. This range is often called the transitional regime for SM (part of the water-limited regime). In other words, the conditions when SM lies within, or shifts into, the transitional regime is the soil moisture–induced land–atmosphere feedback regime. Within this regime, SM–LE coupling is dominant. The variations in LE become uncoupled from SM when it is below the wilting point (dry regime) or exceeds the critical SM threshold (wet regime or energy-limited regime), thus the transitional regime is where nearly all of the sensitivity of LE to SM occurs.
Several studies have examined when and where the SM variability-induced feedback exists by using climate models, reanalyses, and observations. Metrics for such identification have been built upon testing the null hypothesis that there is no statistically significant dependency between SM and other meteorological variables, such as surface heat fluxes (Dirmeyer 2011; Hsu and Dirmeyer 2021), air temperature (Seneviratne et al. 2006; Miralles et al. 2012; Gevaert et al. 2018), and precipitation (Koster et al. 2004; Santanello et al. 2011; Guillod et al. 2015; Hsu et al. 2017; Lei et al. 2018; Tao et al. 2019). The feedback was first found in climate model studies to be strongest over semiarid to semihumid regions, the so-called land–atmosphere coupling “hotspots” (Koster et al. 2004), where SM frequently lies in the transitional regime and varies strongly. Multiple studies using a variety of datasets and coupling metrics have agreed with the locations of strong SM–LE coupling (e.g., Koster et al. 2006; Zhang et al. 2008; Dirmeyer 2011; Diro et al. 2014; Hirschi et al. 2014; Liu et al. 2014; Lorenz et al. 2015; Hsu and Dirmeyer 2021).
Although the existence of a specific sensitive range for SM–LE coupling has been long recognized (e.g., Koster and Milly 1997), the coupling metrics in most studies customarily consider the full range of SM without attempting to quantify how the distribution of the three SM regimes relates to the coupling. This may dilute the aim of detecting locations where SM dominates the LE in two ways. First, during extremely wet and energy-deficient conditions, variations in available energy govern the release of LE. Consequently, LE may decrease while SM increases as a result of reduced net radiation in very wet, cloudy conditions. Such a situation may be identified as SM–LE coupled by having a significant, albeit negative, correlation even though energy availability is the cause and SM changes are a response to changing evaporation rates.
Second, LE is positively correlated with SM only when LE is moisture limited, but if all data are included, one location may be found to be more strongly coupled than another simply because it spends more days within the transitional regime even though they have the same sensitivities within the transitional regime. To illustrate this, the schematic plots in Fig. 1 show how the range of soil moisture, on the abscissa, is a factor in determining SM–LE coupling. Figure 1a shows the conventional approach including all data in the estimation of a single regression. Considering the dry, wet, and sensitive regimes of Seneviratne et al. (2010) separately (Fig. 1b), shows a piecewise linear fit to the same set of points. Figures 1c and 1d show the methods when only data within the transitional regime are considered—the result is then identical. Within the transitional regime, the true sensitivity (slope of the fitted line) is arguably underestimated when the fit is applied to the full range of SM (Fig. 1a). This raises further questions: could some overlooked regions be strongly, but infrequently, coupled due to high SM–LE sensitivities in a transitional SM regime that is not routinely experienced? In other words, will locations of strong land–atmosphere coupling corresponding to the canonical hotspots remain if the analysis only considers those days when SM values lie within transitional regime? Also, whereas the full distribution of points (Figs. 1a,b) clearly shows a nonlinear relationship between SM and LE, if the wilting point and critical soil moisture can be established, is the best fit in the transitional regime truly linear?
Schematic plot showing how assessment of SM–LE sensitivity can be biased if SM regime is not determined in the analysis. (a),(c) The linear fitting without considering SM regime. (b),(d) The linear fitting separately within each SM regime. Vertical dashed lines denote wilting point and critical soil moisture.
Citation: Journal of Hydrometeorology 23, 7; 10.1175/JHM-D-21-0224.1
Characterizing SM regimes has been shown to improve understanding of the features of surface energy partitioning (Feldman et al. 2019; Denissen et al. 2020), the controls of soil moisture and/or surface heat fluxes on air temperature (Koster et al. 2009; Schwingshackl et al. 2017; Dong and Crow 2018), and soil moisture dry-down (Akbar et al. 2018; Sehgal et al. 2021). Such investigations require a classification of SM regimes and estimate the relationship between variables for targeted SM regimes. For example, Schwingshackl et al. (2017) statistically estimated the critical SM values that separate SM into dry, transitional, and wet regimes with a piecewise-linear regression analysis. The sensitivity of near-surface air temperature to SM variations has also been estimated for the transitional regime to obtain a clearer picture of how SM affects the lower troposphere and episodes of extreme heat. Extending the focus to the dry regime, Dirmeyer et al. (2021) and Benson and Dirmeyer (2021) have found that the sensitivity of extremes in near surface air temperature to declining SM is amplified when SM declines below a quantifiable threshold corresponding roughly to the local wilting point. Such a hypersensitive regime arises because strengthened positive feedbacks are triggered by a chain of processes linking drier SM, depleted LE, increased sensible heat flux, and increased atmospheric temperature.
This study targets the transitional SM regime, corresponding to conditions when SM is assumed to control LE, to quantify linear and nonlinear SM–LE coupling within that regime. Using observationally based datasets, reanalyses, and climate models, we first determine the spatial distribution of the various SM regimes including the determination of areas that routinely cross thresholds and inhabit multiple regimes. We then quantify the total, linear, and nonlinear dependencies of LE to SM within the transitional regime using daily fields of SM and LE. This two-step method focuses on the dependency within the transitional regime where the bulk of sensitivity resides, instead of including all available days in the analysis. This helps to determine whether SM conditions lingering in the transitional regime are all that is necessary to ensure a strong coupling. In addition, this filters out nonlinearity in the SM–LE relationship contributed by merely crossing the threshold. Details of the datasets, the method for critical value detection, and mutual information are described in section 2. Section 3 presents the results, and conclusions are presented in section 4.
2. Methods
a. Data
This study uses datasets that provide daily global fields of both surface SM and LE. Multiyear daily fields are used from climate models, reanalyses, and observationally based datasets to maximize statistical robustness. Table 1 summaries the datasets used in this study. Multiple climate models participating in phase 6 of the Coupled Model Intercomparison Project (CMIP6) are included in this study. We select models that have a historical run in which both daily SM and LE fields were available online (https://esgf-node.llnl.gov/search/cmip6/) at the time of our analysis. Thirty years of output spanning 1986–2015 from a total of 11 models have been used.
Sources of gridded global SM and LE data used in this study.
Two sources of reanalysis data are used. First, the NASA Modern-Era Retrospective Analysis for Research and Applications version 2 (MERRA-2) provides hourly fields of variables at a resolution of 0.5° latitude × 0.625° longitude (GMAO 2015). In MERRA-2, a major feature is that the land is forced by gridded observed precipitation, instead of model-generated precipitation. This strategy makes observed precipitation the main driver of SM, of which time series have been shown to have better agreement with independent observational datasets (Reichle et al. 2017a). Second, the ECMWF Reanalysis version 5 (ERA5) provides hourly grids of a variety of variables at a resolution of ∼31 km (Hersbach et al. 2020). Daily fields covering the period 1986–2015 are calculated from both reanalyses by averaging in time relative to UTC. It is noted that ERA5 assimilates satellite SM data while MERRA-2 does not, although this difference is not a focus of this study.
To provide a perspective from a more observationally constrained soil moisture analysis, the NASA Soil Moisture Active Passive (SMAP) mission (Entekhabi et al. 2010) Level‐4 Soil Moisture (L.4_SM) is used. SMAP L4 (Reichle et al. 2017b) assimilates the SMAP observations into the same land surface model used in MERRA-2, but completely uncoupled from the atmospheric model; it is also forced by observed precipitation. Although only a relatively short period is available beginning in early 2015, SMAP L4 provides complete global coverage of SM and LE in space and time, and thus is ideal for this analysis. In contrast, the Level-3 product of SMAP, available at the same spatial resolution and composed only of quality-controlled observations of SM from the SMAP platform, provides coverage over only about one-third of the global land surface per day and lacks LE estimates. SMAP L4 is assumed here to be the closest to representing real conditions among these datasets. However, considering the short period of data as well as the involvement of a land model in the data assimilation process, SMAP L4 is rather like another reanalysis product and serves here as an additional “ensemble member” when we present composite results.
We note that the variable called “surface soil moisture” used in this study represents different thicknesses of soil layer wetness in different datasets. In CMIP6, surface soil moisture represents wetness in the top 10 cm of the model soil column whereas it represents the top 5 cm for MERRA-2, 7 cm for ERA5, and 5 cm in SMAP L4. Theoretically, this induces a deviation in the SM as well as its variability in time, and thus may slightly affect the magnitude of the critical SM values between products. Nevertheless, the resulting translation of SM–LE patterns does not greatly affect the detection of SM regimes. All analysis is done at the native resolution of each dataset except for SMAP. To compensate for the smaller sample size attributed to the shorter period in SMAP, analysis is done on a scaled up grid (18 km × 18 km) consisting of 2 × 2 grid cells (9 km × 9 km), assuming that the heterogeneity of land cover type and topography at this larger domain is not sufficient to induce a stark change in how LE behaves with SM variations. Trading space for time, this simulates a quadrupling of the time series length to ∼26 years (a 9 km × 9 km grid cell contains 77 months of data. Thus, a scaled-up grid cell contains 4 × 77 = 308 months of data, but admittedly does not quadruple the degrees of freedom in the scaled-up grid cell).
b. Critical value detection
We employ the segmented regressions approach proposed by Schwingshackl et al. (2017) to define the wilting point and critical SM thresholds, and the slope of the SM–LE relationship between them. Theoretically, as wilting point (WP) and critical soil moisture (CSM) separate the SM into dry, transitional, and wet regimes, a total of five candidate segmented regressions can result depending on which regimes are detected in the data (Fig. 2a) and each are tested to find the best fit at each location. We name these five candidates using three-digit binary numbers consisting of 0 or 1 to indicate the absence or presence of, in order: the dry, the transitional, and the wet regime. These possible segmented regression candidates are illustrated in Fig. 2a and are listed below:
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No dependency on SM: indicating SM either never reaches values above the WP or never falls below the CSM (candidates 100 or 001). Practically, locations identified with no SM–LE dependency are found over energy-limited regions such as rain forests, high latitudes, and alpine locations where soils are almost always wet. Cases of no SM–LE dependency can also be found at coastal regions dominated by maritime air where SM nevertheless spans a wide range of values. Thus, we treat all cases without SM–LE dependency as candidate 001.
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One-segment regression consisting solely of a segment with positive slope: indicating SM always lies in the transitional regime (candidate 010).
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Two-segment regression consisting of a constant (dry) segment and a segment with positive slope: indicating SM spans the WP (candidate 110).
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Two-segment regression consisting of a segment with positive slope and a constant (wet) segment: indicating SM spans the CSM (candidate 011).
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Three-segment regression consisting of a segment with positive slope between two constant segments: indicating SM spans all regimes (candidate 111).
(a) Five potential segmented regression candidates used to fit the data. (b) An example that depicts MERRA-2 data at (10°N, 20°E) is best fitted by the candidate 111. Gray and red shading shows the density of data in each interval of 0.01 SM (unitless) and 1 W m−2 LE.
Citation: Journal of Hydrometeorology 23, 7; 10.1175/JHM-D-21-0224.1
Figure 2b displays an example in which the candidate 111 has been selected as the best fit for a MERRA-2 grid cell in the tropics (10°N, 20°E). In this case, both the WP and CSM are detected, indicating SM crosses all three regimes, although kernel density indicates that many more days lie near the wilting point. The color scheme in Fig. 2a is used hereafter to indicate the five candidates for SM–LE relationships.
We note that this method assumes both WP and CSM are well defined. However, unlike WP, CSM is not a single value of SM but a range of SM whose exact value can depend on other meteorological factors, as has been implied in the analysis of Dirmeyer et al. (2000), Haghighi et al. (2018), and Feldman et al. (2019). Nevertheless, the key element for this analysis is the detection of a CSM point optimally separating transitional and wet SM segments; the uncertainty in its precise value results from sample size limitations that affect all aspects of this analysis and are comparable to other sources of uncertainty.
c. Normalized mutual information
Mutual information I(X; Y) can be decomposed as linear information I(X; Y) and nonlinear information I(X; Y)′ (Smith 2015). In Eq. (3a), I(X; Y) is quantified as the difference between I(X; Y) and I(X; Y)′; their linkage with NMI is shown in Eq. (3e). Nonlinear information I(X; Y)′ is obtained by calculating mutual information between X and Y′ [Eq. (3b)]. Y′ is a nonlinear residual term calculated by the following procedure: a linear regression model [Eq. (3d)] is fitted to the time series to calculate the residual of the Y by Eq. (3c). Then, quantile normalization is applied to Y′ based on the quantile of the Y. This ensures the equivalence of total entropy of Y and Y′ so that I(X; Y) and I(X; Y)′ are comparable. Since there is no linear dependency between X and Y′, it can be recognized that a positive value of I(X; Y′) must come from a nonlinear dependency. More details of the procedure can be found in Smith (2015).
We note that the fitted line with positive slope used in the linear segmented regression to determine WP and CSM may be different from the fitted line used to decompose the mutual information into linear and nonlinear components for the transitional regime. The nonlinearity of SM–LE dependency resulting from such a two-step method crucially ensures that the nonlinear SM–LE relationship can be contributed by properties other than the threshold behavior. This helps to classify whether the nonlinear SM–LE relationship found in our previous work (Hsu and Dirmeyer 2021) is mostly attributable to the transitions of sensitivity of LE to SM induced by WP and CSM.
d. Workflow
All analysis is done for each grid cell in each dataset except for SMAP L4, which has an effective grid cell domain consisting of 2 × 2 actual grid cells described earlier. Total values of all daily time steps of SM and LE are used to detect soil moisture regimes by breakpoint analysis. WP and CSM thresholds, if detected, are recorded simultaneously for further dependency analysis.
After CSM detection, we remove variability in the original time series having frequencies lower than 1/365 days using a high-pass filter. Then, concatenated time series grouped by calendar month spanning the whole period are constructed. For instance, daily data for each June are connected from each 30 June of one year to 1 June of the next year to produce the multiyear June time series. Discontinuities do not negatively affect the NMI calculations. Such a month-by-month analyses enables us to avoid artificial dependencies which would be introduced if the data distribution were modified by other approaches for removing seasonality.
Daily time steps of SM and LE when SM is below WP or above CSM are removed from the time series. Thus, only data in the SM transitional regime are used for dependency calculations. Since the retained data size is different between different locations and products within any calendar month, subsampling is used to provide a bootstrap estimation of uncertainty. When the sample size of a grid cell for the specific month is larger than 500 days (around half of the original time series), we randomly subsample 300 days from the constructed time series. Fixed binning with 10 × 10 bins is used to compute the two-dimensional probability distribution functions constructed from SM and LE and to obtain NMI and its decomposition. This is repeated 100 times and averages of NMI, NMI, and NMI′, named as mNMI, mNMI, and mNMI′, respectively, are obtained. We note that though the choice for the number of bins affects the magnitude of mutual information and the ratio of information partitioned into nonlinearity, it does so systematically such that it does not affect the relative spatial patterns of mNMI, mNMI, and mNMI′ so long as the same number of bins are used everywhere. In this study, we focus on the comparison among the products instead of comparison between the information components within a single product. Thus, sensitivity of information content to the number of bins does not affect the interpretation of our results.
e. Significance testing
Statistical significance is tested in different ways for total, linear, and nonlinear mutual information on each grid cell and each calendar month. For total mutual information, a shuffled surrogates method is applied on mNMI with the null hypothesis that no total dependency exists. Once a value of mNMI is obtained by the workflow described in section 2d, daily values of SM and LE selected only from days when SM in dry and wet regimes are removed are randomly permuted by breaking original SM–LE pairs and then randomly matching them. Each permutation of the time series yields a new estimate of mNMI. By repeating the process 30 times, a probability distribution of randomized values of mNMI as well as its mean μ and standard deviation σ are obtained. Observed mNMI is 99% statistically significant if it is larger than μ + 3σ.
For nonlinearity, the identical procedure and null hypothesis are used to obtain the significance of mNMI′. The actual mNMI′ is compared to the distribution of mNMI computed from the shuffled surrogates method with Y′ time series (which is LE here; the linear fit is subtracted after each permutation). An observed mNMI′ larger than μ + 3σ indicates a statistically significant dependence at the 99% confidence level and such a dependence is only contributed by the nonlinear relationships.
The workflow and significant testing are nearly identical to that described in Hsu and Dirmeyer (2021) where more discussion on the seasonality issue, bin size sensitivity, and validation of the significant testing can be found.
3. Results
a. Global soil moisture regimes
The most likely SM–LE candidate at each grid cell for each product. Grid cells with climatological annual mean 2-m air temperature below 5°C are masked out. Color coding is as in Fig. 2a.
Citation: Journal of Hydrometeorology 23, 7; 10.1175/JHM-D-21-0224.1
(a) Mode of the candidate among 14 analyzed products. (b) Agreement on the elected candidate calculated as the fraction of the products that vote for the same candidate as the mode. (c) Consensus of soil regime quantified by summation of the degree of disagreement δ calculated by Eq. (5). (d)–(f) As in (c), but for each regime δdry, δtran, and δwet, respectively. Grid cells with climatological annual mean 2-m air temperature below 5°C are masked out.
Citation: Journal of Hydrometeorology 23, 7; 10.1175/JHM-D-21-0224.1
Besides measuring the uniformity of the selected candidate as that in Fig. 4b, δ considers the inherent differences between the regimes included in each candidate. For example, the δ between candidates 111 and 001 is 2, which is larger than that between candidates 111 and 011; meanwhile, a selected candidate 111, which represents SM spanning full regimes, is closer to candidate 011 than candidate 001, since candidate 001 means only wet regime is detected. The summation of δ across all products measures the degree of consensus, and is shown in Fig. 4c. Figures 4d–f are the degree of consensus among the products in detection of dry, transitional, and wet regime, respectively. Compared to the rest of the world, the summation of δ is moderate over the tropical regions. As shown in Figs. 4d–f, consensus is greatest for very dry and wet regimes, but whether SM lies in the transitional regime is often in dispute among the analyzed products.
Semiarid regions are dominated by candidates 011 and 111 (Figs. 3 and 4a). Among the CMIP6 models, there is a prominently different width of territory occupied by candidate 111 in the Sahel, whereas in the reanalyses, candidate 111 dominates over North Africa. This indicates that, in some CMIP6 models, there is a lack of dry days (the dry season is not dry enough or the model has a lower SM limit at the WP value) to reflect the dry regime, implying a different degree of distinction between dry and wet seasons. This might be attributed to the varying character of the simulated West African monsoon among the climate models. In the SMAP product, candidate 111 has a distinctly narrow band in the Sahel. In other monsoon regions, although candidate 111 is often detected in the reanalyses (e.g., over Mexico, India, and Australia), most CMIP6 models show a lack of a dry regime leading frequently to candidate 011 (Fig. 4a). Semiarid regions located in temperate zones have larger discrepancies of the elected candidate. In addition to the North American Great Plains and regions with a humid continental climate, agreement barely reaches 50% over South Africa, Europe, sections of South America, and southern Australia. In these regions, even though the presence of the transitional regime is typically detected without disagreement (Figs. 4a,e), whether SM routinely crosses into either the dry or wet regime is disputed even among the reanalyses.
Counterintuitively, arid regions are dominated by candidates 110 and 111 (Figs. 3 and 4a). This seems to indicate that the land surface in deserts can occasionally be moistened by occasional precipitation events beyond the WP or even the CSM. Actually, it is not striking that LE can occur in arid regions given that 30 years of daily data are analyzed, and the stark response of LE to even infrequent rainfall is easily detected by the Schwingshackl et al. (2017) methodology. In addition, early in situ studies [e.g., Agam (Ninari) et al. 2004] had already shown the importance of LE even in the dry season of the arid zones. Nevertheless, whether climate models reproduce the observed behavior of LE in dry conditions needs deeper investigation. Whether SM normally lies in the wet regime is also disputed (Fig. 4f) not only among the climate models but between the reanalyses. All three SM regimes (candidate 111) are generally found in ERA5 over the Sahara, Arabian Peninsula, Australian outback, and Chile, but only fragmentarily in MERRA-2 (Fig. 3). For SMAP, candidate 111 is found sporadically over those regions. CanESM5 and MIROC6 stand out among CMIP6 models as many arid regions are occupied by candidate 011, indicating an unrealistically wet climate in the desert in these models.
Overall, the hydroclimate reflected by SM–LE behavior is shown to have fairly low consensus among the products. Large differences among detected SM regimes between products are seen over arid regions. Over deserts, whether SM can frequently cross the CSM seems uncertain. A deeper investigation of the precipitation frequency, the physics of surface soil water retention and drydown in the dry climate regions is needed to resolve the discrepancy. Meanwhile, good agreement is reached within semiarid regions implying that, as observed in the real world, climate models simulate strong seasonal variations of wetness.
The regional spatial patterns are much more heterogeneous in SMAP and the reanalyses than in the climate models. In addition to resolution differences, this may be attributed by more complex surface conditions in the real world affecting the assimilated observational data streams that are not fully represented in the parameterizations within climate models, or by the effects of the data assimilation process itself, which introduce extra variability when adding observational increments of SM and/or near surface atmospheric conditions that can impact the SM–LE relationship.
Figure 5 shows the probability density functions (PDF) of SM over regions dominated by each candidate (colored curves) and the combined climatological SM (stepped black area) over the world for each data product (the grid cells with climatological 2-m temperature < 5°C have been masked out). Different patterns of climatological SM PDF are seen among products and even the two reanalyses do not agree on whether SM is bimodally distributed. Such discrepancies reveal that an essential difference of model-simulated moisture fields among different land surface models, as reported by Koster et al. (2009), still exists in current climate models. A relatively moisture-limited world is portrayed by SMAP as well as AWI-ESM and IPSL, while several climate models and ERA5 suggest bimodal global distributions.
Probability distribution functions of SM (volumetric water content; m3 m−3) over the locations governed by each candidate (colored lines) and the total global SM distribution (black histogram). Regions where climatological 2-m temperature < 5°C are excluded from the analysis. All PDFs are estimated by kernel density estimation with fixed-width bins (0.01 m3 m−3 intervals).
Citation: Journal of Hydrometeorology 23, 7; 10.1175/JHM-D-21-0224.1
As to the SM regimes, in general candidate 001 is found mostly in wet soil conditions and candidate 110 is more common over drier regions. Candidate 111 is found across a wide range of climatological wetness conditions. Strong discrepancies are seen between the climate models and the reanalyses in the area under the curve of each candidate (Fig. 5). In most climate models, candidate 011 accounts for the highest proportion of land area. Even though locations with SM spanning the full set of regimes are detected more in the reanalysis, the relative proportions of each candidate are similar among products. The dominance of candidate 011 seen in the climate models could be related to an unrealistic homogeneity of land surface properties. The relative rareness of dry regimes in climate models might be attributable to biases in radiation, precipitation, precipitation frequency, or soil water retention in their land surface models.
b. Global SM–LE coupling
We examine the coupling strength between SM and LE only when daily SM values are in the SM transitional regime. This ensures a positive SM–LE dependency that implies that a change in LE is principally due to a change in SM. Focusing just on June–August (JJA), Figs. 6–8 display the total, linear, and nonlinear contributions to the mean normalized mutual information (mNMI) between SM and LE, respectively. Accordingly, the summation of patterns in Figs. 7 and 8 is equal to that in Fig. 6.
Average of JJA mean normalized mutual information (mNMI; units: bits) between SM and LE within the transitional regime. Locations where values of all three analyzed months are statistically significant (p value < 0.01) are dotted. Gray shaded areas are statistically insignificant for all months and white land areas are not included in the analysis due to insufficient days (<500) with SM in the transitional regime within the analyzed period or climatological annual mean 2-m air temperature below 5°C. For SMAP, each cell in an analyzed set of 2 × 2 grid cells is treated as a separate day: spanning 7 years, this yields ∼810 days for boreal summer months.
Citation: Journal of Hydrometeorology 23, 7; 10.1175/JHM-D-21-0224.1
As in Fig. 6, but for linear mNMI only.
Citation: Journal of Hydrometeorology 23, 7; 10.1175/JHM-D-21-0224.1
As in Fig. 6, but for nonlinear mNMI only.
Citation: Journal of Hydrometeorology 23, 7; 10.1175/JHM-D-21-0224.1
In Fig. 6, locations having at least 500 days when SM is within the transitional regime are found over most of the world, indicating that a positive SM–LE relationship exists nearly everywhere, as can be seen among all analyzed products. Nevertheless, the total dependency of SM–LE measured by normalized mutual information exhibits strong spatial variability and the largest values are found mostly over semiarid regions. Several studies that have investigated coupling strength using the full range of SM showed regions with strong coupling are also mostly over semiarid regions. Logically, this has been attributed to the fact that SM usually lies within transitional regime in those locations. Other regions may spend fewer days in the transitional regime, but they also appear to have a weaker SM–LE relationship even while in the transitional regime. Thus, our results still find these transition zones are strongly coupled compared to the rest of the world.
Spatial patterns of mNMI (Fig. 6) are similar among all the products as quantified by spatial Spearman correlation coefficient shown in the similarity matrix (Fig. 9a). The correlation coefficient between any pair of panels in Fig. 9a is usually larger than 0.4 without any single product standing out. Regions with strong coupling are in better agreement, in terms of latitudinal distribution, among ERA5, MERRA-2, and SMAP than that among the CMIP6 models. This can be seen prominently by comparing the position and meridional span of the strongly coupled band in the Sahel region of West Africa. In the tropics, though SM can still affect LE when SM falls into transitional regime, the dependency is relatively weak or statistically insignificant, as is particularly clear in MERRA-2 and several of the CMIP6 models. On the other hand, dry areas such as the Sahara, Arabian Peninsula, Western Australia, and Chile, when significant, have strong SM–LE coupling.
Similarity matrix showing (a) spatial Spearman correlation coefficient calculated by all pairs of total mNMI location between any two different data product. (b) As in (a), but for (top) linear and (bottom) nonlinear mNMI. When resolutions differ between compared products, the product with the higher spatial resolution is upscaled to the lower resolution product’s grid by nearest-neighbor interpolation before correlation calculations.
Citation: Journal of Hydrometeorology 23, 7; 10.1175/JHM-D-21-0224.1
Similar patterns are found for linear mNMI among the analyzed products (Figs. 7 and 9b). Strong linear SM–LE dependency is mostly found over semiarid regions, e.g., the Sahel, Southern Africa, and the Great Plains. A few climate models (CanESM5, CESM2, MIROC6) show a strong linear SM–LE coupling over arid regions (Fig. 7). The pattern of strong linear coupling corresponds well to the hotspots identified by previous studies using metrics involving a linear statistical framework (e.g., Koster et al. 2004; Dirmeyer 2011; Hsu and Dirmeyer 2021) applied on the full range of SM. Much of the world contains a sufficient number of days with SM values in the transitional regime, yet the linear dependency in most regions is statistically insignificant. Again, this reveals that the frequency of transitional SM values is a necessary condition but not the deciding factor to determine if the land–atmosphere coupling strength is strong.
The nonlinear component (Figs. 8 and 9b) shows a broadly similar but lower magnitude pattern compared to total mNMI (Fig. 6) in most data products. Nonetheless, the nonlinear SM–LE dependency in most locations tends to be statistically significant in the CMIP6 models while only hotspot regions bear strong nonlinearity in the observationally constrained datasets. The cause for this discrepancy is unclear and needs further examination. Arid regions such as North Africa emerge in the analysis for a few climate models (INM, CanESM5, CESM2, MIROC6) and all of them suggest that nonlinearity in dry regions is strong. This could be attributed to the abundant energy and weak water retention capacity over these regions—once a precipitation event occurs, it induces a spike in SM and thus strong LE. Combined with a short drydown period, this typically leads to sporadic high values of LE and thus total mutual information is less dominated by linear dependencies.
Patterns of nonlinear mNMI among products bear a stronger similarity than that of linear mNMI. Linear mNMI patterns show strong, consensus values mostly over semiarid regions with insignificant values spreading around the rest of the world, resulting in lower spatial correlations for the linear comparisons in Fig. 9b than the nonlinear or total. Aside from SMAP L4 having a markedly lower nonlinear mNMI spatial correlation coefficient with other products, the high similarity among mNMI patterns can be appreciated by the fact that it would not otherwise be obvious which products were the analyses if they were not labeled in Figs. 6–9.
4. Discussion and conclusions
Daily fields of surface SM and LE from climate models, reanalyses, and satellite-based products are used to assess the coupling strength constrained within the SM transitional regime where most sensitivity exists. The transitional regime is constrained by the SM wilting point (WP) and a critical value (CSM) above which LE ceases to increase with increasing SM. Five candidate segmented regressions based on a conventional SM–heat flux conceptual framework (Schwingshackl et al. 2017) are statistically derived to determine the prominent SM regimes at each location in each dataset. The method detects where changes in feedback regimes exist, indicated by the detection of WP and/or CSM, and where the positive slope of the SM–LE segment indicates a transitional regime that is critical to physical processes linking land and atmosphere via the SM–LE relationship. Thus, we provide the first global maps of SM regimes relevant to the SM–LE relationship and patterns of SM–LE coupling within the active-feedback regime for many datasets.
An index δ is proposed to quantify the degree of discrepancy among products in detecting SM regimes. The spatial distribution of detected SM regimes is found to vary strongly among the datasets, although for certain regions of the globe there is good agreement, such as in the subtropics and semiarid regions. Though the causes of most of these disagreements can be inferred, further study examining the relationship between LE and SM in different datasets would help to determine the reasons for low consensus. Two factors determine our regime detection and candidate selection for any product: the values of WP and CSM, and the distribution of daily soil moisture values between and beyond WP and CSM. Except where candidate 111 is detected, it is not possible to separate the two without model codes in hand to explore the full range of SM at every grid cell.
The degree of consensus in SM regimes among climate models can act as a confidence score when using multiple climate models to explore extremes in current and/or projected climate. Shifts in SM regimes reflect a “change of gears” in land–atmosphere coupling, and thus the impacts of extremes. For example, when conditions switch from the transitional regime into the dry regime, disconnection of SM from LE and a stronger sensitivity of sensible heat flux to SM are implied (Dirmeyer et al. 2021; Benson and Dirmeyer 2021). Accordingly, if the existence of such a shift in a SM regime lacks consensus among climate models, it could degrade the robustness of assessments related to processes or extremes that involve land–atmosphere interactions.
Days with SM in the transitional regime are used to evaluate the dependency of LE on SM across climate models and observationally constrained products using the nonparametric bootstrap-mean normalized mutual information statistic mNMI calculated month by month across the annual cycle. A limitation is that any given calendar month must contain at least 500 days in the datasets with SM in the transitional regime during the analysis period for stable statistics; much of the world passes this test during boreal summer. Generally, spatial patterns of mNMI and its decomposition are similar among the data products, although a smaller percentage of grid cells are found to be statistically significant in observationally based datasets (ERA5, MERRA-2, and SMAP). The SM–LE dependency, especially the linear component, within the transitional regime is found to be relatively strong over semiarid regions. Due to the universally positive dependency of LE to SM within the transitional regime, one might expect that much of the analyzed area would show strong SM–LE coupling. However, the strongly coupled areas found here remain limited in extent, like the land–atmosphere interaction hotspots in the previous studies that used data spanning the full range of SM values. This implies that the reason SM and LE are strongly coupled in semiarid regions is not merely due to the preponderance of time SM values spend in the transitional regime.
The nonlinear dependency in SM–LE coupling has been quantified in Hsu and Dirmeyer (2021) using the full range of SM from MERRA-2. Although the nonlinearity was found to be statistically significant over several locations, it has been determined that the use of the full range of SM obscures the multiple factors that contribute to nonlinear SM–LE dependency. In this study, only within the threshold regime between WP and CSM is linearity versus nonlinearity of SM–LE behavior estimated, removing the source of nonlinearity that is due to mixing insensitive and sensitive SM–LE ranges in the same analysis. The result is a more focused analysis of just the sensitive moisture-limited range of SM, showing that the nonlinear SM–LE dependency remains statistically significant across most of the world and is actually more widespread than for the linear component. This implies that linear quantification of SM–LE coupling might bias the true coupling strength even in the transition regime.
Though strong differences exist in the distribution of SM regimes among the data products, the regions with strong SM–LE coupling are fairly consistent and similar to the previously identified hotspots. Combining the findings of this study, the low consensus of SM regimes yet similar patterns of SM–LE dependency among the datasets yields the inference that despite a strong dispersion of local hydroclimates among the datasets, attributable to diverse potential factors such as monsoon extent or the physics of soil water retention, the inherent physics of how LE reacts to SM variability is well represented by land models. Nevertheless, considering that land models are part of the modeling infrastructure that produce the reanalyses and the SMAP L4 analysis, direct observations with independent sources of LE and SM at a global scale are needed to obtain a true estimate of land–atmosphere coupling. Recent studies have examined the relative role of net radiation to SM in determining surface heat fluxes (Haghighi et al. 2018; Hsu and Dirmeyer 2021). A further investigation of how daily variability of quantities such as wind speed, atmospheric moisture deficit, and air temperature compares to the relative importance of SM variations in determining LE can help to clarify the source or absence of locally strong coupling.
The framework presented here to determine any location’s span of SM regimes and critical SM values, as well as associated coupling strength, has several potential applications. For forecasting, diagnosing the position and transition of SM among wet, transitional, and dry regimes enables inference of when and where land–atmosphere feedbacks, which play a crucial role in extremes such as heat waves and drought, may become important. Getting these transitions right, as well as the slope and degree of nonlinearity within the sensitive regime, would be an indication of correct process representation and should improve model skill. Meanwhile, the disagreement index δ can be used with climate projections to quantify the credibility of shifts in terrestrial hydrology in different climate change scenarios.
Finally, this study is confined to the SM–LE relationship and not the other links in the process chains linking land and atmosphere because of the lack of availability of daily fields of sensible heat flux and boundary layer properties from many of the CMIP6 models. Given that it has been increasingly common for studies to apply their own frameworks on long-term daily datasets of land surface variables and several new features of SM–surface heat flux relationships have been discovered, we encourage CMIP modeling groups to provide complete daily fields of surface heat fluxes relevant to surface water and energy balances for both historical and projected simulations.
Acknowledgments.
This research was supported by the National Aeronautics and Space Administration (80NSSC20K1803). We are grateful to the developers of the data products used in this study.
Data availability statement.
ERA5 (Hersbach et al. 2020, doi:10.1002/qj.3803) was downloaded from the Copernicus Climate Change Service (C3S) Climate Data Store. MERRA-2 was downloaded from Global Modeling and Assimilation Office (GMAO 2015, doi:10.5067/RKPHT8KC1Y1T). SMAP L4 (Reichle et al. 2017b, doi:10.5067/B59DT1D5UMB4) data were downloaded from NASA National Snow and Ice Data Center. CMIP6 data were downloaded from https://esgf-node.llnl.gov/search/cmip6/.
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