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 We present empirical evidence for a relationship between the modal (most frequent) soil moisture level and the soil moisture level at which maximum evapotranspiration occurs for twenty-four flux tower sites in North America. We considered correlations and linear regressions between these two variables at annual, seasonal, bimonthly and monthly time scales for unimodal distributions of soil moisture, and found significant relationships between these two soil moisture variables at all time scales. Correlation was stronger during the summer than the winter, suggesting stronger coupling during the growing season. This coupling of modal soil moisture and soil moisture of maximum evapotranspiration suggests that vegetation may be optimizing productivity with respect to water use across different systems.
 Evapotranspiration (ET) is influenced directly and indirectly both by vegetation (e.g. type, density and distribution) and the physical environment (e.g. radiation, temperature, humidity and soil moisture, see Brutsaert ). Because ET is a dominant component in the terrestrial water balance, quantifying ET and its controls is critically important to understanding the direct and indirect impacts of global change on the hydrologic cycle [Brutsaert, 1982; Shuttleworth, 1992]. In addition, because carbon dioxide and water vapor share the common exchange pathway of stomata, ET is closely linked to the carbon cycle, and to vegetation characteristics and patterns of primary productivity in terrestrial ecosystems [Eagleson, 1982; Rodriguez-Iturbe and Porporato, 2004]. Thus, an understanding of the factors controlling ET contributes to our comprehension of both water and carbon cycles.
 Soil moisture is a key control on ET rates for terrestrial ecosystems [Rodriguez-Iturbe et al., 1999; Rodriguez-Iturbe et al., 2001; Eagleson, 2002; D'Odorico and Porporato, 2006]. It has been observed for many terrestrial ecosystems that the ratio between ET and potential evapotranspiration (PET, the maximum ET when soil moisture is not limiting) is positively correlated with soil moisture below a certain moisture threshold, and independent of soil moisture above that threshold [e.g., Thornthwaite and Mather, 1955; Rodriguez-Iturbe et al., 1999]. This conceptual model is based largely on physical limits to water transport through the soil-plant-atmosphere continuum for low soil moisture conditions [Sperry, 2000] and provides insight into the relationship between ET and soil moisture under relatively stationary conditions of insolation, atmospheric vapor pressure, temperature, and vegetation. A modification of this relationship could account for the dependence of the soil moisture-ET relationship on atmospheric conditions, which is to say that ET might decrease at very high levels of soil moisture because of conditions associated with wet soils and reduced atmospheric demand for ET. Depending on the time scale of interest, reduced ET may be caused by lower temperatures, reduced insolation, increased humidity or a combination of these factors. We present a relationship between ET and soil moisture that links probability distributions of soil moisture to maximum ET. Using data from the AmeriFlux network of micrometeorological stations (available at http://public.ornl.gov/AmeriFlux, hereinafter referred to as AmeriFlux, 2006), we generalize this relationship for different landscapes and across time scales ranging from one month to multiple years. Our results suggest that among ecosystems and across time scales, a simple linear (1:1) relationship exists between the most frequent (modal) soil moisture and the soil moisture values associated with maximum evapotranspiration. Furthermore, we propose that this relationship provides evidence of optimization of vegetation to its environment, particularly with respect to soil water availability.
 According to Eagleson , “biology is an expression of physical optimality,” meaning that the adaptation of vegetation to its environment, particularly with respect to soil water availability, may be expressed as a maximization of productivity within a range of soil water conditions that characterize a particular environment. Furthermore, plant productivity (specifically net primary productivity, NPP) is coupled to transpiration, allowing transpiration to serve as an indicator of vegetation activity and productivity [Nobel, 1999; Zhang et al., 2001; Law et al., 2002; Lee and Veizer, 2003]. During the growing season, transpiration may comprise a significant portion of the ET flux, particularly when soil moisture is limiting [Ferretti et al., 2003; Williams et al., 2004]. For these reasons, ET may be used as an indicator of growing season vegetation activity in many terrestrial ecosystems.
 Vegetation that is well-adapted to its physical environment should exhibit optimization in the form of maximal productivity at minimal water stress [Eagleson, 1982; Rodriguez-Iturbe et al., 1999; Caylor et al., 2005]. In terms of ET and water limitation, this optimization also may manifest as maximized ET (which includes plant water use) at a characteristic level of soil moisture [Eagleson, 1982]. For a given temporal scale, the site-specific distribution of soil moisture, particularly the value(s) of mode(s), is (are) functionally dependent upon the physical and biological environment (including climate, soil and vegetation) [Rodriguez-Iturbe et al., 1991; D'Odorico et al., 2000]. If the modal (most frequent) soil moisture at a particular time scale characterizes the synthesis of environmental controls acting upon an ecosystem, it follows that ecosystems where vegetation functions at maximum capacity for particular environmental conditions should experience maximum ET at the most frequent soil moisture, provided that water is among the most limiting resources, at least for some portion of the time under consideration. An example of the relationship between modal soil moisture and maximum ET is shown in Figure 1. In this illustration from a temperate, broad-leaf forest, maximum ET occurs near the modal soil moisture.
 In cases of bare soil or dormant vegetation ET is expected to be dominated by soil surface evaporation; thus the soil moisture of maximum ET should be independent of biological control. By comparing periods of actively growing vegetation to periods of dormancy, we present empirical evidence for adaptation of vegetation to optimal water use conditions.
 For each site and time scale where the distribution was significantly unimodal, daytime ET (Rsw_in > 500 W m−2) was plotted against soil moisture (e.g. Figure 1). An upper envelope of the resulting scatter plot was determined by selecting the upper five percent (i.e. the ninety-fifth percentile and greater) of ET data within each 0.01 m3 m−3–wide bin of soil moisture. From these data, locally-weighted scatter plot smoothing, LOESS [Cleveland et al., 1992], was used to estimate the upper envelope of ET as a function of θ. Maximum ET was calculated as the maximum value of this envelope function, and corresponding soil moisture of maximum ET, θET, was determined.
 The order statistic used previously to determine θET (i.e. f95(ET), the ninety-fifth percentile of ET) is formally related to the number of measurements within each bin of soil moisture by
where f95(ET) is the probability distribution of the ninety-fifth percentile of ET, N is the number of measurements (or bin size), F(ET) is the cumulative distribution function of ET and f(ET) is the probability distribution function of ET [Rose and Smith, 2005]. In this case, braces represent rounding to the nearest integer. Thus, the calculation of θET as the soil moisture of maximum ET may be sensitive to the size of bins, particularly near the mode. Because of the potential dependence of θET on N, we developed a nonparametric test to evaluate the likelihood of within-bin sample size influencing θET. For each estimate of θET, we evaluated the effect of within-bin sample size on the ninety-fifth percentile of ET by resampling Ni values of ET from each bin 100 times, where Ni was increased from 0.1 to 2.0 times the original bin sample size with increments of 0.1 times the original sample size. Using original values of ET from each bin as the underlying distributions F(ET) and f(ET), we estimated the mean of the order statistic distribution as a function of variable N. We used finite difference estimation to determine a critical sample size N* where the slope of became insignificant ([ − ]/[Ni+1 − Ni−1] < 0.05). For each bin, we compared the original sample size to N* and eliminated from further analysis any distribution where N < N* for any of the eleven bins centered at the mode (or fewer bins where the mode is less than 5 bins from the distribution edge).
 For distributions satisfying the binned sample size test, modal (most frequent) values of volumetric soil moisture θ+ and θET were converted to saturation percentages s+ and sET by dividing by the ninety-ninth percentile of the entire soil moisture distribution for each site. This method captured reasonably the upper limit of soil moisture for each site (assumed to be saturation) while eliminating spurious maxima. Least-squares linear regression (forced through the origin) and pairwise correlation analyses were used to evaluate relationships between s+ and sET among sites for each time scale.
4. Results and Discussion
 For all sites and among all time scales and time periods, 639 (95%) of 672 total soil moisture distributions were unimodal. Modality statistics by season are shown in Table 1. Of the unimodal soil moisture distributions, 213 satisfied the binned sample size test for independence (Table S2). Among these sites, s+ and sET were correlated at all time scales and time periods, although only 88% of these correlations were significant (Table 1, Figure 2).
Table 1. Statistics of Nonparametric Tests for Soil Moisture Distributions and Fit Between s+ and sETa
Pu is the proportion of unimodal sites, PN is the proportion of sites satisfying the binned sample size test, and N is the number of sites satisfying both unimodality and sample size independence tests. ρ and Pρ are Pearson's pairwise correlation coefficients and P values for this statistic, respectively. β is the least-squares regression slope (intercept forced through [0, 0]) and sβ is its standard error.
Group Avg. ρ
Group Avg. Pρ
Group Avg. β
Group Avg. sβ
 Seasonal trends in Pearson's pairwise correlation coefficient, ρ, and the slope of the least squares regression of s+ and sET are shown in Figures 3a and 3b. The greatest correlation between s+ and sET occurred during the early summer and also winter months. To determine if these correlations were merely the result of narrow soil moisture distributions and of inter-site variability in soils and rainfall regimes we compared, for each soil moisture distribution, the ratio between Δ = ∣s+ − sET∣ and the interquartile range of the soil moisture distribution (IQR). In effect, the ratio of Δ to IQR normalizes the offset between sET and s+ among distributions and indicates whether this offset is large or small compared to the width of the soil moisture distribution. Seventy-five percent of sets had Δ/IQR values less than 1.0, and 21% had Δ/IQR values less than 0.5. Instances of high correlation and low Δ/IQR occurred during the growing season and during winter months. Fifty-four percent of regression slopes were statistically indistinguishable from unity. If the dominant components of ET differ during these periods (evaporation during winter and transpiration during summer), separate mechanisms may be responsible for high correlations, low Δ/IQR, and 1:1 slopes during growing seasons and winters.
 We examined correlations and least-squares regressions of s+ and sET for trends that may suggest enhancement of this relationship during growing seasons, when ET may be dominated by transpiration. Of the 24 total sites, 14 were identified as environments having distinct growing and dormant seasons based on observed trends in the fraction of absorbed photosynthetically active radiation (fPAR) from the Moderate Resolution Imaging Spectroradiometer (MODIS). For sites exhibiting seasonality, we compared the relationship of s+ and sET in June to represent the growing season to their relationship during November through March to represent dormancy. For each of these two periods, we examined the pairwise correlation coefficients and 95% confidence intervals of the least squares regression between s+ and sET, and found that winter data exhibited significantly greater scatter than June data, although neither slope differs significantly from unity (Figure 4). Comparison of these two correlations (growing season versus dormancy) reveals tighter coupling between s+ and sET during the growing season for this subset of sites exhibiting seasonality (ρ = 0.93 versus ρ = 0.63). In fact, the winter correlation is not even statistically significant (P = 0.09). Because growing season ET is frequently dominated by transpiration, we note that periods of high correlation between s+ and sET are marked by increased vegetation activity, including transpiration. These results, combined with the well-established coupling between transpiration and productivity, suggest optimization of productivity with respect to soil water availability, and the presence of a 1:1 relationship between s+ and sET among sites at multiple time periods and time scales. Although these results suggest that this relationship may be generalized across a broad range of environmental conditions, further study is needed to evaluate specific effects of extreme phenomena such as severe water stress on the 1:1 relationship between s+ and sET.
 These results have additional implications for the seasonal dependence of ET on soil moisture across time scales. Among all sites used in this study, maximum ET was more tightly coupled to the annual phase of mean insolation (not shown) rather than the annual phase of s+ (Figures 3c and 3d). However, the phases of both s+ and sET appear to track the general seasonality of moisture availability in North America, with wetter winters and springs and drier summers and autumns. The phase difference between maximum ET and corresponding soil moisture of maximum ET creates additional complexity that may result in a modification of the traditional view of the dependence of ET on soil moisture (i.e. maximum ET/PET at high soil moisture). This study provides a context for better understanding the dependence of ET on soil moisture, and the role of vegetation and its optimization with respect to water use, in establishing this dependence among diverse landscapes at multiple time scales.
 This research was supported by NSF (grants EAR-0236621, EAR-0403924) and DOE-NIGEC (Great Plains Regional Center, grant DE-FC-02-03ER63613; Southeastern Regional Center, grant DE-FC-02-03ER63613), and Blandy Experimental Farm. The authors thank Andrew Guswa and two anonymous reviewers for their helpful comments.