1. Introduction
Evapotranspiration E from the land surface can be considered in terms of two critical elements: (i) the ability of the soil and plants to provide water to the atmosphere and (ii) the ability of the atmosphere to take up that water. When the soil is sufficiently dry, the first element is the limiting factor in the chain, leading to a sensitivity of E to soil moisture—all else being equal, a wetter soil should allow higher E. However, once the soil becomes sufficiently wet, the second element becomes the limiting factor, at which point E becomes relatively insensitive to soil moisture variations.
This idea is not new; it was effectively explored by Budyko (1974) and explicitly developed over the years by, for example, Manabe (1969) and Eagleson (1978). The overall idea is illustrated by the thick black curve in Fig. 1. The x axis represents soil moisture W (in volumetric units, i.e., m3 m−3), and the y axis represents E normalized by the net radiation energy at the surface (shortwave plus longwave). A transition soil moisture value WT separates the two regimes of interest: (i) the water-limited regime (i.e., the drier regime, wherein the normalized E is sensitive to W) and (ii) what we will call the energy-limited regime (wherein the normalized E is insensitive to W). While for simplicity the functional relationship in the water-limited regime is shown here as linear, a somewhat nonlinear curve could be more realistic. Also, the distinct transition point shown here is a simplification, as the operating relationship in nature may be more continuous in slope, with a high slope toward the dry end and a clearly shallower slope toward the wet end (e.g., Sud and Fennessy 1982). These issues aside, which presumably are amplified when considering E and soil moisture averaged over large spatial scales, the solid black curve in Fig. 1 is a convenient and useful framework for analysis.
Idealized relationship between evaporation efficiency (here, E normalized by net radiation using the latent heat of vaporization λ) and soil moisture (in volumetric units). Included are some representative ranges for the functionally unique evaporative regimes identified in the analysis.
Citation: Journal of Hydrometeorology 25, 3; 10.1175/JHM-D-23-0140.1
The land surface schemes used with Earth system models typically have some version of this canonical relationship built into them, sometimes explicitly (e.g., Manabe 1969) but often implicitly—in most schemes, the effective relationship is not hardwired, being instead the net result of complex interactions between various model parameterizations and between land and atmospheric processes (e.g., Vargas Zeppetello et al. 2019). Note that while it is generally easy to find code in a land surface model that assigns soil moisture stress to specific fluxes, the effective relationship operating for the land surface as a whole generally turns out to be more complex, affected by these coded equations but not fully defined by them. The individual stress equations specified in different schemes, by the way, vary considerably (e.g., Trugman et al. 2018).
The effective relationship operating within a given model can be inferred from output model diagnostics (Koster and Milly 1997; Dirmeyer et al. 2006). Such model diagnostics can be used to determine if a given region, over a given time period, is operating in a purely water-limited regime (with a range such as that indicated in Fig. 1), a purely energy-limited regime (again see Fig. 1 for a potential range), or in both—sometimes in one regime, and sometimes in the other. Koster et al. (2009) used diagnostics from an atmospheric general circulation model (AGCM) simulation to produce maps of these different regimes for the AGCM’s climate. Dirmeyer (2011) processed diagnostics from long-term land model simulations driven with realistic meteorological forcing to quantify E sensitivity to soil moisture as a function of season, effectively isolating water-limited areas from energy-limited areas. Schwingshackl et al. (2017) analyzed several model-produced datasets to examine evaporative regime as a function of location and season, producing maps of the transition soil moisture value WT.
Such model-based studies, of course, have an important limitation—their findings regarding E sensitivity to soil moisture depend strongly on the specific assumptions built into the model parameterizations regarding the impacts of soil moisture stress on E. For this reason, a purely observation-based analysis would have advantages. The relationship in Fig. 1 has indeed been measured directly, although at only a handful of local sites (e.g., Ford et al. 2014a). In another locally focused study, this one utilizing precipitation and soil moisture data in Illinois, Salvucci (2001) used a “conditionally averaged precipitation” approach to infer rather than directly measure the shape of the function in Fig. 1. Such local analyses largely confirm the conventional wisdom regarding soil moisture control over E; however, while useful, they do little in the way of continental-scale characterization of the sensitivity.
More recently, a wealth of satellite-based data has led to larger-scale characterizations of evaporative regimes. Akbar et al. (2018a) processed Soil Moisture Active Passive (SMAP) surface soil moisture retrievals into estimates of loss functions, from which they inferred evaporative regime distributions. Sehgal et al. (2020) and Dong et al. (2023) also examined SMAP data in the context of loss functions, deriving their own estimates of energy-limited versus water-limited regimes. Feldman et al. (2019) assessed evaporative regimes using SMAP data in conjunction with geostationary EUMETSAT land surface temperature (LST) diurnal cycles. Denissen et al. (2020) examined energy versus water controls on E using a correlation-difference metric in conjunction with several observational datasets. Jonard et al. (2022), utilizing multiple remote sensing datasets, analyzed the connections between evaporative regime and photosynthesis.
The characterization of evaporative regime—how it varies in time and space—is more than an academic exercise. The E variations, with their concomitant impacts on boundary layer behavior, can have a substantial impact on the evolution of the overlying atmosphere. This, coupled with the known memory of soil moisture anomalies (Seneviratne et al. 2006), suggests that soil moisture initialization in a prediction model could provide skill to meteorological forecasts provided that E is sensitive to soil moisture variations (Koster et al. 2011; van den Hurk et al. 2012). By characterizing the geographical distributions of evaporative regime, we effectively determine where such soil moisture impacts might be felt—where, for example, the accurate initialization of soil moisture in prediction models would provide the greatest benefit. We also establish a useful validation target for the land surface models used in such forecasts (see, e.g., Lei et al. 2018)—do they accurately capture the spatial and temporal variations in regime seen in nature?
Such considerations motivate us to expand on the existing analyses of evaporative regime through the use of two untapped (for this purpose) observational datasets, each used here in conjunction with SMAP-based estimates of deep soil moisture (section 2d). We aim, for example, to determine if the regime estimates obtained with these independent data are consistent with those determined in earlier studies. Because the large-scale patterns of regimes in nature cannot be directly measured, such independent confirmation would be valuable in itself. Our use of multiple datasets to address the problem (rather than, say, SMAP data in isolation) offers, however, an additional potential advantage: by including more independent data to address the problem, we can potentially generate regime estimates that are particularly robust. We will show in any case that the joint consideration of multiple datasets allows a description of evaporative regimes with relatively high time specificity: their evolution on a month-to-month basis.
The first dataset we examine consists of daily continental-scale E distributions derived from satellite-based thermal remote sensing measurements [Atmosphere–Land Exchange Inverse (ALEXI); Anderson et al. 2007]. Note that while the ALEXI E data are themselves a product of a model calculation, their use is not burdened with the aforementioned limitation regarding model-based evaporative regime analyses. This is because the model underlying the ALEXI data makes no use whatsoever of soil moisture information—the ALEXI framework makes no assumptions about how soil moisture affects E. The ALEXI calculations are instead tied to estimates of boundary layer development as captured by satellite-based observations of surface temperature increases over the course of the morning (section 2b).
The second dataset examined here is a daily time series of 2-m air temperature (T2M) diurnal amplitudes (maximum daily temperature minus minimum daily temperature, hereinafter referred to as Tdif; see section 2c) constructed from meteorological station data (Climate Prediction Centre, or CPC; https://www.esrl.noaa.gov/psd/data/gridded/data.cpc.globaltemp.html). The idea behind using Tdif to study E’s response to soil moisture is simple—in the soil moisture–limited evaporative regime, a wetter soil can induce increased E and thus an increased evaporative cooling of the surface, so that the surface temperature (and, by extension, potentially the overlying T2M) cannot increase as much over the course of the day from its nighttime value. That is, a wetter soil may induce a lower Tdif. Arguably, the diurnal amplitude of LST, rather than T2M, would be the more appropriate variable to examine in the context of this mechanism, as it is tied more logically to surface energy partitioning (Bateni and Entekhabi 2012); relevant sensitivities have been demonstrated empirically using diurnal LST retrievals from a geostationary satellite and SMAP soil moisture over Africa (Feldman et al. 2019). The translation from LST diurnal amplitudes to T2M diurnal amplitudes is far from perfect (e.g., Gallego-Elvira et al. 2016), and some strongly question the ability of the latter to capture the signature of E variations (Panwar et al. 2019) given the potentially dominating impact of, for example, advection effects on T2M. Even so, some studies do show a very strong connection between LST and T2M (e.g., Good et al. 2017). We focus in this paper on Tdif as derived from T2M rather than from LST for two reasons: (i) the ALEXI E data are already, in effect, a direct reflection of satellite-based measurements of the LST diurnal cycle, making the T2M station data (which are only peripherally used in ALEXI algorithms) a more independent dataset to consider, and (ii) the station-based global T2M dataset comes with a few advantages over satellite-based LST datasets, not being affected, for example, by substantial data dropouts due to cloud masking or by difficulties in interpreting the measurements in terms of separate contributions from bare soil and vegetation.
Our examination of T2M-based Tdif data is, in fact, partly motivated by the following question: given the disconnect suggested in the literature between the LST and T2M diurnal cycles, can the air temperature data nevertheless be shown to contain information relevant to the determination of evaporative regime? In a sense, we use the ALEXI E-based evaporative regimes over the conterminous United States (CONUS) as a means of evaluating those generated with the Tdif data. We will show that the latter provide, to first order, a reasonable picture of evaporative regime. It is this success that encourages us to extend the Tdif-based results to the globe.
Section 2 below describes in more depth the data we analyze in this study, along with the approaches we use to (i) infer deeper soil moisture from the near-surface SMAP soil moisture retrievals and (ii) identify evaporative regime. Our resulting maps of evaporative regime as derived from both the ALEXI E and Tdif data are provided in section 3. Additional discussion and conclusions are provided in sections 4 and 5.
2. Data and methods
a. SMAP data
Since 31 March 2015, the National Aeronautics and Space Administration (NASA) SMAP mission (Entekhabi et al. 2010) has been providing retrievals of soil moisture in (nominally) the top 5 cm of soil (O’Neill et al. 2021). The retrievals, based on L-band brightness temperature measurements, have been evaluated extensively against in situ soil moisture data and successfully match their variations (e.g., Chan et al. 2016). Here, we utilize the current baseline SMAP level-2 (L2) dataset: the L2 Radiometer Half-Orbit Soil Moisture, version 8 (R18), which was constructed using the dual channel algorithm of Chaubell et al. (2021). In particular, we use only the data collected on the descending branch of the SMAP orbit (0600 local overpass time) that are flagged as having either “recommended” or “uncertain” quality. The data are examined here on version 2 of the 36-km Equal Area Scalable Earth (EASE) grid (Brodzik et al. 2012), a grid that approximates the data’s true underlying resolution. An exponential filter is used to process the surface soil moisture retrievals into estimates of moisture deeper into the soil (section 2d). Data covering the period 2015–22 are used in this analysis.
b. ALEXI evapotranspiration efficiency estimates
The ALEXI surface energy balance model is designed to estimate E for continental to global scale applications (Anderson et al. 2007, 2011). It maintains a physically realistic representation of land–atmosphere exchange over a wide range of landscapes, while being relatively independent of ancillary meteorological or plant functional information. Importantly for the present analysis, it does not require any knowledge of soil moisture conditions. The main diagnostic inputs to the ALEXI model are land surface temperature, net radiation (and its components), leaf area index (to inform partitioning of radiation between soil and canopy), wind speed, and the early morning lapse rate profile. The internal model structure solves the energy balance for the soil and canopy separately. ALEXI uses an atmospheric boundary layer model to translate the change in temperature over the morning hours into a self-consistent boundary layer temperature and to constrain the sensible heat flux. Table S1 in the online supplemental material provides information on ALEXI data sources.
For this analysis, we regridded the 4-km CONUS ALEXI E daily product (v10E) for the 2015–22 period and the corresponding downwelling shortwave radiation Rsw, obtained from the Climate Forecast System Reanalysis (Saha et al. 2014) to the coarser 36-km grid of the SMAP data. The Rsw values are used to normalize the E values (see section 2e) to produce the E efficiency Eeff, corresponding to the y axis in Fig. 1; such normalization allows E variations with soil moisture to be isolated from those associated with cloudiness. We use Rsw here for the normalization rather than net radiation (as in Fig. 1) to avoid potential additional errors associated with inaccurate specifications of longwave radiation and surface albedo.
c. CPC-based daily air temperature amplitudes
The CPC near-surface air temperature (T2M) dataset comprises station-based T2M measurements at 0.5° × 0.5° resolution, with the gridded values interpolated from the point measurements using the Shepard algorithm (Shepard 1968). The particular data used here are the daily minimum and maximum temperatures (Tmin and Tmax, respectively) over the period 2015–22; more specifically, we use the daily temperature amplitudes, Tdif = Tmax − Tmin, over this period. Prior to use, the Tdif values are regridded conservatively to the 36-km EASE grid.
d. Inferring deeper soil moisture from SMAP level-2 soil moisture retrievals
A number of recent studies have demonstrated clear connections between near-surface soil moisture measurements and deeper soil moisture, into the root zone. Dong et al. (2022), for example, demonstrate that near-surface soil moisture (as measured with in situ sensors) by itself provides information on overall evaporative regime. Akbar et al. (2018b) quantify vertical length scales of relevance for SMAP retrievals that, due to spatial correlations between surface and deeper soil moisture, exceed the nominal 5-cm sensing depth of the L-band instrument. Feldman et al. (2023), in a review of such studies, argue that satellite-based soil moisture estimates are indeed relevant to the rootzone and thus strongly tied to overall vegetation water uptake across much of the globe. Overall, the studies indicate a distinct relevance of L-band soil moisture to total evapotranspiration (not just bare soil evaporation) and its water limitation.
It is appropriate to note the limitations of the exponential filtering approach. The filtering used in (1) oversimplifies the time history of infiltration, exfiltration, and evapotranspiration that determines a given soil moisture profile. Also, in areas where the water table is close to the surface, the water table’s influence on the deeper soil moisture may overwhelm any signal contained in the surface SMAP measurements. We do not explicitly account for such complexity in our analysis, noting only that if these issues do degrade the deeper soil moisture estimates, the relationships we obtain between the estimates and the ALEXI E evapotranspiration rates would suffer—the relationships we derive would be noisy. Our determination instead of strong relationships across CONUS (see section 3a for representative examples) gives us confidence that the exponential filtering approach does indeed provide useful approximations of the deeper moisture.
e. Evaporative regime: Strategy for fitting relationships
We now describe the means by which ALEXI E data (section 2b) and SMAP-based deeper soil moisture data (section 2d) are examined together to determine evaporative regime—that is, which category in Fig. 1 applies to a given location at a given time of year. The approach is essentially the same as that described by Feldman et al. (2019). The approach is also used here (with any differences noted) to examine the Tdif data in conjunction with the SMAP-based deeper soil moisture data.
We use 6-day averages for our analysis. For a given 6-day period, we average the daily values of W, E, and Rsw; the ratio of the 6-day E and RSW averages (with E first converted to a latent heat flux via the latent heat of vaporization) is then computed to produce the evapotranspiration efficiency, Eeff, for the period. Because our data cover 8 years (2015–22), a given month offers 40 separate data pairs of [W, Eeff] from which to determine evaporative regime. (To be precise, only 35 data pairs are available for January through April, since the SMAP data we use begin in May of 2015.)
Three possible functional forms are fit independently through the 40 data pairs, as illustrated in Fig. 2: (i) a line with zero slope, representing the energy-limited regime; (ii) a line with nonzero slope, representing the water-limited regime; and (iii) two lines, one with nonzero slope toward the drier end and the other with zero slope toward the wetter end, representing the transitional regime. (See Fig. 1; as discussed below, we do not attempt to detect separately the very dry regime in that figure). The Akaike information criterion is used to select the best-fitting functional form—a criterion that balances the need for both a low total error (as represented by the residual sum of squares, or RSS) and a low number of model parameters. In other words, the fit in Fig. 2c may appear to fit the data best, but to conclude that the points do indeed indicate a transitional regime, the reduction in RSS must be large enough to make up for the fact that this fit uses a higher number of parameters. See Feldman et al. (2019) for details; in essence, the fit that produces the lowest value of 2k + N ln(RSS), where k is the number of parameters and N is the number of points considered, is the chosen optimal fit. (The number of parameters underlying the forms in Figs. 2a, 2b, and 2c are 2, 3, and 4, respectively; the variance of residuals is one of the parameters in each.)
The three functional forms fit to a single (idealized) set of 40 data pairs.
Citation: Journal of Hydrometeorology 25, 3; 10.1175/JHM-D-23-0140.1
If the 40 data points span a very small soil moisture range, the fitting algorithm cannot be sensibly applied. We accordingly do not apply it if the standard deviation of the volumetric soil moisture—that is, σW—falls below 0.005 m3 m−3. This happens almost exclusively in very dry areas, and these, we can logically infer, would lie wholly within the water-limited regime. Of course, we cannot dismiss the possibility that very wet areas, which would presumably lie wholly in the energy-limited regime, might also show a low σW value.
Another threshold we apply involves very low slopes—if the derived slope at a location is positive yet very small, we arbitrarily assign energy-limited conditions to that location. The idea is to distinguish between slopes that are clearly tied to water limitations from those that are potentially artifactual, perhaps related to sampling or to some second-order mechanism unrelated to water limitations (e.g., some statistical connection between Eeff and soil moisture borne of both being influenced by cloudiness). In this study, we assume slopes below a value of 0.4 [in units of (m3 m−3) −1] to be negligible. Given that the soil moistures we consider tend to have a range of less than 0.2 m3 m−3 (see section 3a for examples), this slope threshold corresponds to a Eeff change of less than 10% over the whole range, as will be made visually clear in section 3a. The smallness of the imposed slope threshold relative to slopes more clearly reflecting a soil moisture control over Eeff will be made particularly clear in section 3c. Note that we do not apply a similar threshold in the Tdif analysis. Given the noise associated with Tdif—noise that significantly exceeds that associated with the E data—the algorithm is already overly conducive to producing zero slopes when the underlying relationship is weak.
f. An alternative metric: Overall slope
The determinations of evaporative regime (section 2e) will be supplemented by the examination of a much simpler metric: the slope, S, of the regression line through the 40 points analyzed at each grid cell for each month, without any explicit consideration of the transition point between regimes. In the context of Fig. 2, S is simply the slope of the regression line through the points in Fig. 2b, with an imposed minimum (for the W–Eeff relationship) of zero. While not as nuanced as the evaporation regime calculation, separate consideration of the gross S metric has its advantages, as discussed in section 3c.
3. Results
a. Illustration of relationships at representative locations
Representative examples of the diagnosed relationships are presented in Figs. 3–5. Figure 3a shows the locations of two western grid cells, and Figs. 3b and 3c show, for these grid cells, scatterplots of soil moisture W against both Eeff and Tdif. Each of the 40 plotted points represents a 6-day average for June. The points are color-coded by year.
(a) Locations of two western U.S. grid cells considered in the scatterplots. (b) Relationship between SMAP-based deep soil moisture estimates and both evaporation efficiency (E divided by incoming solar radiation; top half of panel) and Tdif (lower half of panel) at location 1, a very dry location. (c) As in (b), but at location 2, a moderately dry location.
Citation: Journal of Hydrometeorology 25, 3; 10.1175/JHM-D-23-0140.1
As in Fig. 3, but for a single location in the south-central United States. The vertical dashed line at W = 0.21 is the transition soil moisture identified by the regime-fitting algorithm.
Citation: Journal of Hydrometeorology 25, 3; 10.1175/JHM-D-23-0140.1
As in Fig. 3, but for two locations in the eastern United States. The red line in (c) represents the threshold slope used in this analysis (positioned with an arbitrary y intercept); any slope (such as that for location 5) found to be shallower than this slope is assumed to be causally unrelated to soil moisture variations and thus indicative of an energy-limited regime.
Citation: Journal of Hydrometeorology 25, 3; 10.1175/JHM-D-23-0140.1
Figure 3b shows the results for a very dry region (along the lines of that indicated on the far left of Fig. 1). Soil moisture does not vary much at this location, and indeed σW here is below the aforementioned critical value of 0.005 m3 m−3 we use to identify very dry points. Again, sensibly fitting a relationship to any such set of points is untenable, and we do not attempt it here.
Figure 3c focuses on a somewhat wetter grid cell. The western United States is generally dry, and thus at western locations for which σW lies above the critical value, we expect the algorithm to identify a water-limited E regime. This indeed generally turns out to be the case. Plotted in Fig. 3c over the data points are the corresponding regression lines; these lines represent our derived W–Eeff and W–Tdif relationships for this location and month. As appropriate for this regime, Eeff increases and Tdif decreases with increasing soil moisture. Note, however, that the W–Tdif relationship is quite a bit noisier. As discussed above, this extra noise—both here and at the other locations—is not unexpected. Tdif, in addition to varying with soil moisture, also varies with incident radiation, and this radiation varies on a daily basis; more radiation (regardless of soil moisture content) implies an enhanced ability to heat up the surface. Of course, E also varies with incident radiation, but this is largely dealt with by the normalization with SW in the calculation of the Eeff variable, a normalization that cannot be done as sensibly for Tdif. Also, there is the potential disconnect between surface temperatures (on which evaporative cooling should have a direct effect) and the air temperatures measured at the meteorological stations (Panwar et al. 2019) given, for example, advection effects—there is no guarantee that surface and air temperatures should vary in tandem.
Such noise, it turns out, has an apparent impact on the identification of a transition regime at a south-central U.S. grid cell (Fig. 4). The W–Eeff relationship shows a clear transition at W = 0.21 m3 m−3 between water-limited and energy-limited regimes—for conditions drier than this transition point, Eeff increases linearly with soil moisture, and for wetter conditions, Eeff is effectively insensitive to it. On the other hand, for the noisier Tdif data, the regime-identifying algorithm (section 2e) fits a single line through the [W, Tdif] points, suggesting purely water-limited conditions. One can see how the noise in the W–Tdif plot might obscure the true underlying relationship—how a sloping line to the left of 0.21 m3 m−3 and a horizontal line to the right might just as easily characterize the points. These noise-related difficulties, seen here and elsewhere, give us an overall higher confidence in the results obtained with the ALEXI Eeff data.
Noise issues aside, it is worth remembering that neither the Eeff data nor the Tdif data were generated using any explicit knowledge of soil moisture. The fact that reasonable sensitivities do fall out when these data are plotted against the fully independent SMAP data (and again, these are representative results) is encouraging; it suggests that despite all the assumptions made on the way to getting the datasets in place, we are capturing some of nature’s real behavior.
Figure 5 shows results for two locations in the eastern United States, where conditions are significantly wetter and thus likely associated with a wholly energy-limited regime. The representative location 4 (Fig. 5b) indeed shows the expected general insensitivity of both Eeff and Tdif to soil moisture. The fitted horizontal lines are set to the mean of the 40 Eeff or Tdif values. The relationship, once again, is noisier for Tdif.
Figure 5c shows results illustrating one of the arbitrary rules in our fitting algorithm. A careful look at the fitted line through the Eeff points will reveal a nonzero regression slope; accordingly, from the regression, one could infer a dependency of Eeff on soil moisture at this location and thus could conclude that the location falls within the water-limited regime. The dependency, however, is slight. In our algorithm, because the slope lies below 0.4 [in units of (m3 m−3) −1], we assume it to be unrelated to water stress (see section 2e)—because the slope is so shallow, we assign energy-limited conditions to this location. The threshold slope of 0.4 used in this study is illustrated in Fig. 5c by the red line. We will show in section 3c that this threshold slope lies well below those typically characterizing soil moisture control over Eeff.
b Maps of evaporative regime
Curve fitting as illustrated in Figs. 3–5 is performed at every point in CONUS for which adequate data are available. This allows us to produce, as a function of month, evaporative regime distributions across CONUS based on both Eeff data (Fig. 6) and Tdif data (Fig. 7). Locations for which the data volume is inadequate (mostly during winter due to snowpack) are whited out in the maps. Locations in the “very dry” regime, for which the different soil moisture values are too closely packed to allow a sensible curve fitting, are shown in red. As expected, this dry regime is most spatially extensive during the hot summer months in the far west. Still, even during these months, most of snow-free CONUS is amenable to our analysis.
Evaporative regime as a function of month, as determined by the joint analysis of SMAP-based deep soil moisture estimates and ALEXI Eeff values.
Citation: Journal of Hydrometeorology 25, 3; 10.1175/JHM-D-23-0140.1
Evaporative regime as a function of month, as determined by the joint analysis of SMAP-based deep soil moisture estimates and station measurement–based Tdif values.
Citation: Journal of Hydrometeorology 25, 3; 10.1175/JHM-D-23-0140.1
Considering the ALEXI Eeff-based maps first (Fig. 6), we see the expected structures: energy-limited conditions in the east and water-limited conditions in the west, particularly in the southwest. The energy-limited regime is particularly extensive during the first part of the year (January–March), a time when soil moisture is relatively high and incoming radiation and air temperatures—and thus evaporative demand—are low. As the months progress into summer, the regime gradually shrinks so that by July it covers only the eastern third of the area. The shrinkage, of course, is largely due to warm season evapotranspiration, which in western and central CONUS draws the average soil moisture levels down to the point where soil moisture stress becomes important to E. As solar radiation levels recede into autumn and winter, evaporative demand also recedes, reducing the potential for water limitation; also, the associated reduced E allows precipitation to more easily bring the soil moisture levels back up, which further favors the energy-limited regime. The northwest of CONUS appears to recover its energy-limited status more quickly than the southeast during autumn.
During summer, one might expect the transition regime (shown in yellow) to lie mostly between the energy-limited regime (in blue) in the humid east and the water-limited regime (in orange) in the west. Hints of this expectation are seen in June and July; however, the two drier regimes are largely mixed in the west across the months, with transitional regime identification often speckled randomly within that for water limitation. Such speckling is common among observation-based analyses (Akbar et al. 2018a; Sehgal et al. 2020) due to sampling error and other sources of noise; model-based analyses tend to have smoother maps (Schwingshackl et al. 2017). As will be discussed in section 3c, our analysis of the slope metric will significantly mitigate such speckling. In any case, we see that while the areas covered by the water-limited and transition regimes in the western half of CONUS are of the same order in June, the area covered by the water-limited regime clearly dominates by July. The growing dominance of the purely water-limited regime must reflect the drying of the soil through the warm summer months, with soil moisture conditions drying away from the relevant transition soil moisture.
Consider now the Tdif-based maps in Fig. 7. The maps show a first-order agreement with those in Fig. 6, with an energy-limited regime in eastern CONUS that shrinks as the months progress to July and then expands again going into winter. This first-order agreement is further illustrated in Fig. 8, which shows, as a function of month for both sets of calculations, the fraction of the continental area determined to lie in the energy-limited regime.
Monthly variation of the fraction of CONUS determined to lie within the energy-limited regime. The solid line reflects the Eeff-based results (effectively, for each month, the fraction of the non-red area in Fig. 6 that is colored blue), and the dashed line reflects the Tdif-based results.
Citation: Journal of Hydrometeorology 25, 3; 10.1175/JHM-D-23-0140.1
Of course, as might be expected, many differences between the Eeff-based and Tdif-based plots in Figs. 6 and 7 do appear. For example, in the Tdif-based plots, the water-limited regime is more extensive in July, whereas the energy-limited regime is more extensive in April (as also seen clearly in Fig. 8). Using a spatial correlation metric to compare Figs. 6 and 7 quantitatively is inappropriate given that each plotted datum is one of a few discrete regime designations rather than a numerical value drawn from a continuous field. We do, however, provide a quantitative comparison of the maps in Fig. S3 in the online supplemental material. That figure shows that, on a pixel-by-pixel basis, the Eeff-based and Tdif-based analyses agree only two-thirds of the time about whether an individual 36-km pixel is energy limited, indicating that the qualitative agreement seen in Figs. 6 and 7 between the two analyses is much stronger at the larger spatial scale. In any case, as discussed in connection with Fig. 4b, the Tdif-based analysis has more difficulty identifying transition regimes, as indicated by the relative lack of yellow coloring in the corresponding plots (though in November, both the Eeff-based and Tdif-based results show a transition regime in the Mississippi–Alabama region).
Despite the multiple local differences, we are encouraged by the overall similarity in the large-scale characters of the two sets of maps—particularly given the independence of the ALEXI E and Tdif datasets and the critical fact that neither dataset has built into it any assumptions about how the data therein should be affected by soil moisture variations. The two independent datasets provide similar broad-brush pictures of both the spatial and temporal variations in evaporative regime (Figs. 6–8), strongly suggesting these patterns successfully represent nature. This first-order agreement at the larger scale has the additional effect of indicating that the Tdif data, despite being unavoidably noisy given advection effects, variations in incoming radiation, and representativeness issues associated with the placement of the measurement stations, nonetheless contain within them useful information relevant to the determination of evaporative regime.
c. Overall slope
We now supplement our analysis with calculations of the much simpler S metric (section 2f). While this gross measure of E sensitivity cannot capture the nuances in regime behavior represented in Fig. 1, it does offer unique advantages and is thus worthy of consideration in its own right. For example, unlike the quantal identification of evaporative regime in Figs. 6 and 7, S is a relatively continuous variable and is less subject to the speckling noticed in those figures. Indeed, the evaporative regimes plotted in Figs. 6 and 7 reflect, to some extent, the number of years examined. For example, if we had data for 2014 (i.e., outside the 2015–22 range considered, as limited by the length of the SMAP mission) at Location 4 in Fig. 5b, and if the soil had been much drier in 2014 than in other years, we may have identified this location as being in the transition regime rather than the energy-limited regime. The simple S metric has the advantage of relative insensitivity to such considerations—with the addition of dry 2014 data, the slope S might become nonzero, but it would still be small. That is, S would still indicate a low broad-brush sensitivity at the location to soil moisture variation. Of course, slopes computed in dry areas with very low water variability (as in Fig. 3b) could themselves be spurious; areas with σW < 0.005 m3 m−3 still need to be masked out.
The left column of Fig. 9 shows the distribution of S over CONUS for four different months, as derived from the ALEXI E and SMAP soil moisture data. To emphasize the larger-scale features, the derived slope plotted at a given grid cell is the average of the 5 × 5 set of grid cells centered on it, for an effective spatial scale of ∼180 km. Slopes are generally low in eastern CONUS, though the southeast picks up some significant slopes in summer and autumn, and slopes are generally large across the west in all months, where we expect water-limited conditions to dominate. Curiously, S is particularly high along a swath down the center of CONUS during July.
(left) Slope [(m3 m−3) −1] of the regression line between SMAP-based deep soil moisture estimates and ALEXI E/SW values. (right) Negative of the slope [°K (m3 m−3) −1] of the regression line between SMAP-based deep soil moisture estimates and station measurement-based Tdif values. In both cases, the slope at each grid cell is smoothed by taking the average of the 25 grid cells (i.e., the 5 × 5 box) surrounding it. Also indicated in the right panels is the spatial correlation between the slope maps derived from ALEXI and Tdif.
Citation: Journal of Hydrometeorology 25, 3; 10.1175/JHM-D-23-0140.1
Note that the 5 × 5 averaging used for Fig. 9 reflects another advantage of the slope metric: relative to the quantal regime metric plotted in Figs. 6 and 7, the averaging of slopes makes intuitive sense. (Maps of the unsmoothed slopes are provided in Fig. S4 in the online supplemental material). Another advantage of using the simple slope metric is the ability to dispense with a slope threshold, as was used in Fig. 5c to place location 5 in an energy-limited regime. A low slope such as that in Fig. 5c (and indeed the earlier imposed slope threshold of 0.4) simply shows up as a near-zero value in the maps.
The right column of Fig. 9 shows the corresponding regression-based slopes determined from the 40 [W, Tdif] data pairs for each month at each cell, again after smoothing the computed slopes to an ∼200-km spatial scale. (We in fact plot the negative of the Tdif–W slopes for comparison with the Eeff–W slopes, given that water limitations have an opposite impact on the two variables—a drier soil moisture is expected to lead to a reduced Eeff but to an increased Tdif. Also, because the units of these slopes are different, the color bar has been adjusted to allow a reasonable comparison. The idea here is to focus on how the spatial patterns of the slopes compare between the two columns—to see whether the locations for which Eeff varies strongly with W agree with those for which Tdif varies strongly, although in the opposite direction, with W). To first order, we see the expected similarity, both spatially and temporally, between the Eeff–W slopes and Tdif–W slopes. The east–west distinction is seen in both sets of plots, as are, for example, higher values across the southern tier of CONUS in October and a smattering of nonzero slopes along the east coast in July. The Tdif–W slope plot for July even shows a hint of the aforementioned high-slope swath down the center of CONUS. This agreement is far from perfect; the spatial correlations, R, between the two sets of maps (provided in the right panels) can be considered modest. Such modest agreement is nonetheless encouraging given the independent sources of the data—and, again, the fact that the Tdif data are potentially affected by a number of processes not involving soil moisture.
d. Global maps of inferred E sensitivity to soil moisture
In the above analyses, the ALEXI Eeff data are from the well-tested GOES-based implementation of ALEXI (Anderson et al. 2007, 2011), which provides data only over CONUS; accordingly, this particular version (v10E) cannot be used to examine E behavior outside this area. In contrast, the CPC-based Tdif data are global. Having demonstrated a first-order agreement between the ALEXI E-based and Tdif-based evaporative regimes over CONUS, we now use the Tdif data to generate global maps of evaporative regime. First, though, to provide context, we present in Fig. 10 a map of the measurement locations underlying the Tdif data, the idea being that results in areas of high station density should be more reliable. Density is reasonably high, for example, across CONUS, Europe, and China. We process the Tdif data into evaporative regimes wherever the interpolated data allow; however, Fig. 10 should be used to call into question any results in areas of relatively low station density. Note that while reanalysis-based air temperature data are available globally at high resolution, we have refrained from using them because they partially reflect the assumptions built into the background atmosphere and land models. The CPC-based Tdif data have the advantage of being purely observational, though largely reflecting interpolation in the data-poor regions indicated.
Average number of Tdif station measurements per day during the period 2015–22 for each 0.5° × 0.5° grid cell in the raw CPC temperature dataset (https://ftp.cpc.ncep.noaa.gov/precip/PEOPLE/wd52ws/global_temp). Note that some grid cells feature more than one measurement station and thus average more than one measurement per day; here, the colors saturate at 1. Values less than 1 but greater than 0 indicate incomplete temporal coverage.
Citation: Journal of Hydrometeorology 25, 3; 10.1175/JHM-D-23-0140.1
Figure 11 shows the global distribution of evaporative regime as determined by the Tdif data for a representative month of each season. As noted earlier in conjunction with Fig. 7, the algorithm has difficulty identifying transition regions from the Tdif data; as a result, only a small amount of yellow appears on the maps in Fig. 11. Mostly these maps serve to categorize Earth’s regions, to first order, as either energy limited or water limited. For example, most of the northern tier of North America and Asia is energy limited (when not covered by snow). The Sahel is mostly water limited in July and October, and while it is too dry in January and April to make a determination using the fitting algorithm, water limited conditions presumably apply then as well. Europe is energy limited during the winter and spring but, for the most part, is water limited in summer and autumn. China shows water-limited conditions only in July.
As in Fig. 7, but extended to the globe for four specific months.
Citation: Journal of Hydrometeorology 25, 3; 10.1175/JHM-D-23-0140.1
Figure 12 in turn shows the global distribution of overall slope, S, as determined from the Tdif data. Because the slopes can be sensibly averaged in space and time (again, this is not possible with the regime identifiers in Fig. 11), we average the slopes spatially as in Fig. 9 and also across each season. As a result, the value plotted at each grid cell is the average of up to 75 values (25 slopes in the 5 × 5 set of cells centered on the grid cell for each of the three months). If a value for a given grid cell and month is undefined (e.g., due to snowcover), the value is excluded from the averaging. Areas with σW < 0.005 m3 m−3 or with undefined SMAP-based soil moistures for all of the values considered in the averaging are whited out in Fig. 12.
As in the right panels of Fig. 9, but extended to the globe. The slope plotted at a given grid cell is averaged over a season as well as over the 5 × 5 box encompassing it.
Citation: Journal of Hydrometeorology 25, 3; 10.1175/JHM-D-23-0140.1
The low slopes in Fig. 12 correspond reasonably well to the energy-limited areas in Fig. 11. (Note that perfect agreement is not expected given the larger spatial and temporal averaging applied to the slopes.) In agreement with Fig. 11, for example, the slopes in Europe are minimal during winter and maximal during summer. Particularly large slopes are seen in desert areas such as southwestern CONUS, Australia, and, for SON, southwestern Asia (although note the low station densities in Australia in Fig. 10).
Taken together, Figs. 11 and 12 provide a global-scale description of how Tdif varies with soil moisture. To the extent that day–night air temperature differences do reflect E rates (Figs. 6–9), the maps provide a fully observation-based description of how E varies with soil moisture across the globe.
4. Discussion
a. Comparison with existing studies
In this study, we use both a satellite-based evapotranspiration product (ALEXI Eeff estimates) and station-based diurnal temperature amplitude measurements (Tdif) separately in conjunction with an independent satellite-based soil moisture product (SMAP level-2 soil moisture retrievals) for the identification of evaporative regime. We also analyze the slope of the fitted line through the [W, Eeff] (or [W, Tdif]) data pairs. The two metrics each have their advantages and disadvantages. The evaporative regime metric is more nuanced, allowing the identification of areas that straddle the water-limited and energy-limited regimes; however, the information is more discretized (essentially trinary), with maps subject to speckling due to the limited data period (here, 8 years). The slope metric is much simpler but has the advantage of being continuous and thus not as subject to the speckling; also, it is amenable to averaging in time and space. Looked at together, the two metrics provide a comprehensive picture of E sensitivity to soil moisture variations. Though not further described here (but addressed in Fig. S5 in the online supplemental material), the 40 data pairs (e.g., Figs. 3–5) examined in each calculation can be further processed to determine, as a function of season, the fraction of time a location spends in energy-limited versus water-limited conditions.
Our analysis complements past studies of evaporative regime by applying the otherwise untapped E and Tdif data to the problem. Over CONUS, the patterns we derive with either dataset are generally consistent with those of Akbar et al. (2018a) for the warm season (May–September) period they examined. Across the globe, they are generally consistent with the patterns produced by Sehgal et al. (2020) for the different seasons. Naturally, though, differences do abound. For example, Sehgal et al. (2020) show less of a water limitation over CONUS during June–August, and they show water limitations maximizing over India during boreal winter and spring rather than in boreal autumn (Fig. 11). The regime breakdowns provided by Dong et al. (2023) differ even more significantly from ours, showing, for example, less seasonality over CONUS and less in the way of energy-limited regimes on the global scale (their Fig. 4).
Note that our analyses differ from those of Akbar et al. (2018a), Sehgal et al. (2020), and Dong et al. (2023) in two important ways. First, these earlier analyses determined more than just evaporative regime from their SMAP-based soil moisture loss functions; they also identified regimes characterized by strong gravitational drainage. We do not attempt this in our study. Second, and arguably more important in the context of evaporative regime, the earlier studies essentially derived their regimes from SMAP data alone. We emphasize that we do not claim our distribution maps to be more accurate; still, we speculate that if our approach does have an advantage, it is the utilization of a greater amount of independent data to derive the evaporative regime distributions. In effect, by addressing the problem with a greater amount of data (data that, importantly, do not have built into them any assumptions regarding soil moisture impacts), it is possible that we have produced results that are especially robust. To some degree, such robustness is demonstrated by the similarities found upon the separate applications of the ALEXI E data and CPC T2M data. At the very least, a greater amount of data allows for a greater level of time specificity; we generate here maps of evaporative regime that vary with month, something not provided in the earlier studies.
Another evaporative regime study that supplemented SMAP data with independent data is that of Feldman et al. (2019), who, over Africa, related SMAP soil moisture retrievals to satellite-derived diurnal amplitudes of LST (rather than of T2M, as in the present study). Their map of the fraction of time a region spends in the water-limited regime is largely consistent with our breakdown of evaporative regime (Fig. 11), though our analysis indicates more of an energy-limited condition in southeastern Africa.
A metric akin to our overall slope metric was examined by Lei et al. (2018), who regressed global ALEXI E data against remotely sensed soil moisture data to compute correlations, with higher correlations considered a measure of greater land–atmosphere coupling. Interpreting a higher correlation as a greater impact of water stress on E, their estimates of warm season coupling strength (their Fig. 5c) do appear roughly consistent with our slope-based maps (Fig. 12 above).
b. Inferences regarding T2M data
In regard to our use here of T2M rather than LST diurnal amplitudes, a somewhat unexpected finding [given, for example, the analysis of Panwar et al. (2019)] is the fact that the distributions of evaporative regime generated with T2M-based Tdif data are largely consistent with those obtained using the ALEXI data and, at least over CONUS, with those obtained with the purely SMAP-based methods. Advection issues and daily (e.g., cloud-induced) variations in incoming radiation add noise to the examined soil moisture–Tdif relationships but apparently do not preclude the usefulness of T2M data for analysis of evaporative regime. The key point is that any process, such as advection, that acts to obscure the connection between T2M and E would only tend to reduce the slopes in Figs. 9 and 12 toward zero. The fact that these slopes are nonzero and are indeed consistent over CONUS with those determined with the ALEXI data serves as evidence that soil moisture conditions, by controlling evapotranspiration, do significantly imprint themselves on T2M.
Stated another way, knowing the soil moisture implies some knowledge of the 6-day average diurnal temperature amplitude. This has important implications. An accurate medium-range or subseasonal prediction of soil moisture [made possible by soil moisture’s inherent memory (Seneviratne et al. 2006)] should provide a corresponding prediction of Tdif with some skill—skill that should feed significantly into the skill of predicting average T2M itself. This connection, demonstrated here with the purely observational SMAP and Tdif data, must certainly underlie documented soil moisture–related accuracy in subseasonal T2M predictions (Koster et al. 2011).
c. Spatial variation of transitional soil moisture
The calculations underlying Fig. 6 provide, as a by-product, estimates of the transitional soil moisture (WT in Fig. 1) that separates energy-limited conditions from water-limited conditions—at least for those grid cells identified as being in the transitional regime (those colored yellow in Fig. 6). The distributions over CONUS of these transitional soil moistures are provided in Fig. S6 in the online supplemental material. At a given location, the transitional moistures appear reasonably constant with month. Note that such temporal stability is not theoretically guaranteed based on past analyses (Feldman et al. 2019; Haghighi et al. 2018).
Geographically, the transitional soil moistures vary significantly, with values well below 0.2 m3 m−3 in western CONUS and exceeding 0.2 m3 m−3 in the east, and with particularly high values (exceeding 0.3 m3 m−3) in the deep South and the far Northeast. These geographical variations are presumably tied to soil texture. While a careful analysis of the connections between soil texture and transition moisture is beyond the scope of this study—indeed, such connections have been examined in past analyses (Akbar et al. 2018a; Fu et al. 2022)—we provide in Fig. S7 in the online supplemental material maps showing the percentages of sand and clay in the soils covering CONUS, as utilized in the development of the SMAP level-2 product (O’Neill et al. 2021). The sand percentage is distinctly higher in the west, which should encourage, through higher hydraulic conductivity and associated easier drainage, lower soil moistures there and, accordingly, lower transition moistures. The high transitional soil moistures in the Mississippi Delta region are quite possibly tied to the high clay contents there.
5. Summary
We provide, on a monthly basis over CONUS, estimates of evaporative regime (water limited, transitional, and energy limited) based on two separate analyses: (i) the joint analysis of SMAP soil moisture retrievals (processed to reflect variations in deeper soil moisture) and satellite-based estimates of E efficiency, and (ii) the joint analysis of these SMAP data and meteorological station-based estimates of air temperature diurnal amplitudes (Tdif). The basic patterns produced in the two analyses are similar to each other, supporting the idea that the patterns are, to first order, accurate and also supporting our extension of the Tdif analysis to the globe. Our study complements existing studies in the literature, our evaporative regime patterns (particularly those based on the satellite-based E data) perhaps benefitting from additional robustness through the utilization of a greater amount of independent information and, in any case, provided here with higher time specificity. The fact that soil moisture–evaporation sensitivities also show up in the near-surface air temperature data has relevance to the usefulness of soil moisture in medium-range and subseasonal weather forecasting, especially in water-limited locations.
Acknowledgments.
Funding for this work was provided by the NASA SMAP mission and the SMAP Science Team. We thank Wei Shi for help with the data underlying Fig. 10.
Data availability statement.
The version-8 SMAP L2 retrievals are available online (https://doi.org/10.5067/LPJ8F0TAK6E0). The CPC T2M data underlying Tdif were obtained online (https://www.esrl.noaa.gov/psd/data/gridded/data.cpc.globaltemp.html). The ALEXI E and CFSR-based downwelling solar radiation data used in this study are archived online (https://zenodo.org/doi/10.5281/zenodo.10557863).
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