##### 3.2.1. Supporting Synthetic Experiments

[23] Six initialization states falling within the attractor space of Figure 1b were selected from the 11-year continuous simulation, with the mean volumetric moisture contents _{ini} of the domain equal to 0.0742, 0.0843, 0.0936, 0.105, 0.116, and 0.125 [m^{3} m^{−3}] and the corresponding coefficients of variation equal to 0.121, 0.118, 0.105, 0.0939, 0.0796, and 0.0811. In order to avoid significant transient effects in the soil water dynamics, it was ensured that in each of the cases interstorm conditions lasted for at least four days prior to the time of selected moisture distribution. For the cases of ≤ 0.0936, the length of antecedent interstorms exceeded twelve days. The corresponding three-dimensional distributions of soil water content were used to explicitly initialize the pressure head distributions within the Biosphere 2 domain. Note that selecting initial states from those within the attractor space guarantees smallest possible *C*_{v} for a given at the simulation start. As argued previously, different rainfall magnitudes can lead to different patterns of temporal evolution of *C*_{v}() during the post-storm period. Therefore the chosen design allows the search of the perturbation magnitude required to deviate the evolution of the hydrological system away from the attractor. Stated differently, one can find rainfall for a given required to trigger the subsurface exchange, thereby significantly increasing moisture spatial heterogeneity.

[24] In terms of hydrometeorological conditions, the month of August was chosen as the representative period during which most of the vegetation-hydrology dynamics occur in the area of interest, driven by monsoonal precipitation and abundance of light. A set of rainfall scenarios were applied to each of the generated initialization states. In these scenarios, precipitation totals, *P*_{T}, were equal to 6.2, 11.8, 17.7, 23.7, 32.1, and 41.5 mm that corresponded to 75, 82.5, 90, 95, 98, and 99th percentiles, *n*_{P}, of August daily rainfall (computed for rainy days only), as estimated from observational data for the Lucky Hills site. For each rainfall scenario, precipitation was specified to occur at the beginning of simulation and was distributed in two and a half hours, which approximately corresponded to the mean event duration for the month of August. This also ensured that none of the synthetic events lead to infiltration excess runoff since the imposed saturated hydraulic conductivity was 146 [mm hr^{−1}] (see section 2 above).

[25] Most of the other hydrometeorological variables required for simulations, i.e., atmospheric pressure, air humidity, temperature, and wind speed were specified as their mean daily cycles for the month of August and used as forcing in each day of the considered simulation period. Input of shortwave radiation was assigned using a weather generator (S. Fatichi et al., Simulation of future climate scenarios with a weather generator, submitted to *Advances in Water Resources*, 2009) as a daily cycle corresponding to the 90th percentile of the total daily energy input for the month of August (326 W m^{−2}). All simulations were carried out for a 12-month period. The domain became very dry at the end of each simulation, which ensured that each scenario included the period of primary interest (see below). The same vegetation initialization as in the base case scenario was assumed in each of the scenarios. Additional analysis indicated that essential inferences of this study are completely insensitive with regards to whether uniform (long-term average over the entire domain) or spatially-varying (long-term average at each location) plant biomass pools are used. Obviously, vegetation gradually dies during each of these simulations because of growing lack of soil moisture. Nonetheless, the period of primary interest for the following analysis spans 1.5–2 months since the simulation start, during which biomass changes are insignificant.

##### 3.2.2. Analysis of Results

[26] The dark “Wetting” arrow in Figure 2 (top) indicates the principal direction of domain state evolution during a precipitation or, equivalently, a “perturbation” event. After the occurrence of an event, if the perturbation is small, spatial variability of soil moisture will not change significantly, staying within the band of the attractor space. The latter is reproduced in these experiments by aggregation of dots at the bottom of the pattern shown in Figure 2 (top). The overall, fairly linear time-evolution path of the state is indicated by the lightly colored “Drying” arrow pointing to the left. As argued previously and will be explicitly illustrated in the following, in this situation the subsurface lateral exchange is insignificant and rapidly suppressed by evapotranspiration. As event water percolates through the soil layer, it is taken up by roots; little reaches the soil bottom to produce the saturated conditions. Local processes (soil evaporation and transpiration) dominate the soil water dynamics. The temporal change in the spatial variability of depth-integrated soil moisture is then caused only by differences in the incoming shortwave energy and local vegetation state. Both of the latter depend on topography either explicitly (i.e., surface irradiance) or implicitly (i.e., plants). Therefore the slope of the attractor space band should also be a function of topographic conditions in the domain.

[27] Conversely, if the perturbation is sufficiently large, the evolution of domain state in time *t* leads to a pattern of *C*_{v}((*t*)) that deviates from the attractor band, exhibiting a negatively skewed shape (Figure 2, top). The corresponding temporal dynamics of the soil moisture standard deviation exhibit the same patterns (not shown). The overall time-evolution path after the rainfall has ceased is indicated by the dark “Drying” arrows drawn in the immediate vicinity of the data points corresponding to the simulation scenario with _{ini} = 0.125 and *n*_{P} = 99. In such cases, the hydrological response of the system can be attributed to rapid percolation of event moisture down to the impervious bottom of the soil profile, passing beyond depth where access by roots is possible, and generation of saturated (or nearly-saturated) conditions that result in efficient subsurface exchange. Return flow through the seepage face is produced. For the considered domain, lateral exchange is always possible as the bedrock topography replicates domain surface terrain and thus gravity-induced gradients of the pressure head act to redistribute moisture, provided the flow medium is sufficiently conductive. Non-local dynamics thus begin to dominate in determining soil water spatial variability. The period over which the first maximum in *C*_{v}((*t*)) is attained can be considered as the “effective period of redistribution.” While the interplay among the various processes is complex and changes with time, over this time interval, topography-induced lateral exchange of moisture is one of the dominant processes contributing to the spatial variability of soil moisture (a more detailed analysis is presented below). As can be inferred from Figure 2 (top), this period generally varies with both the initialization state and rainfall magnitude. For instance, for initialization _{ini} = 0.125, the period duration is between 15 days (*n*_{P} = 99) and 28 (*n*_{P} = 75) days. It might be generally noticed that the duration of the effective redistribution period increases with lower rainfall magnitude for the same initialization state. This is likely due to a decrease in effective conductivity of the soil media that positively correlates with the amount of moisture coming from the imposed precipitation. Evapotranspiration acts to slow down the percolation process, especially when its rate is comparable to the rate of water flux in the soil, further delaying accumulation of moisture above the bedrock face. Once domain spatial variability is maximized, expressed as the peak in *C*_{v}((*t*)), the strength of evapotranspiration sink defines the rate at which the topography-induced heterogeneity is destroyed. The hydrological system returns to the attractor space, which is illustrated by the descending limbs of the *C*_{v}((*t*)) curves in Figure 2 (top).

[29] To obtain deeper insights on the interplay of physical mechanisms leading to the observed behavior, a subset of simulation results used in Figure 2 (top) is shown in Figure 2 (bottom), corresponding to a single initialization _{ini} = 0.105 with *n*_{P} = 82.5 (*P*_{T} = 11.8 mm) and *n*_{P} = 99 (*P*_{T} = 41.5 mm). As seen in Figure 2 (bottom), the overall time-evolution paths have been already described in the previous discussion, which pointed to the possibility of distinct differences in the domain response. Both rainfall events lead to initially higher mean moisture and lower spatial variability, denoted by the first dot to the right of both of the initialization states. In the case of *n*_{P} = 82.5, the spatial variability in the hydrological system evolves within the attractor space; in the case of *n*_{P} = 99, heterogeneity of soil moisture strongly increases initially and gradually dissipates after the effective redistribution period has been reached. Note that in the latter case, during the first three days after the rainfall event, spatial variability remains fairly constant or even has a tendency to decrease. Theoretically, this period should correspond to the effective period of vertical flow of soil water during which saturation builds up at the bottom of the soil profile, creating gradients sufficient for subsequent lateral exchange. Further supporting analysis of this statement will be presented in the discussion that follows.

[30] Physical but insofar qualitative interpretations of the presented results have been attempted, however, further quantitative evidence is warranted. The main purpose of the analysis would be to attribute the various stages of the *C*_{v}((*t*)) dynamics to dominant processes that change as the hydrological response evolves in time. Figures 3 and 4 analyze the scenario illustrated in Figure 2 (bottom) for the rainfall case of *n*_{P} = 99.

[31] Since after the first day (omitted in the following analysis) the mean moisture continuously decreases in time, the temporal evolution of the system can be tracked from the right side of the plots to the left. The domain-averaged mean daily rates of water fluxes scaled to a unit area of level surface are plotted in Figure 3a. They represent (1) the net moisture flux normal to terrain surface, _{n}, quantifying percolation rate as the depth-integrated normal component of the flow [*Ivanov et al.*, 2008b]; (2) the net lateral influx, _{p}, illustrating the intensity of lateral subsurface exchange as the depth-integrated difference between influxes and outfluxes in all domain interior nodes; (3) transpiration, _{veg}, as the rate of moisture uptake by roots in the first 79 cm of soil; and (4) soil evaporation, _{soi}, which is applied as the moisture sink to the soil surface layer (first 20 mm). As time progresses, which can be envisioned by tracking the series from the right to the left side of the plot, the flux rates exhibit different dynamics. The flux _{n} peaks at the beginning during the period of moisture vertical redistribution, when the wetting front is above the soil bottom. As the percolation flux reaches the bedrock surface and spatial gradients are generated, the lateral flow starts to increase, which is illustrated by the dynamics of _{p}. After some time, the flux _{p} reaches the maximum value that is likely associated with maximum concentration of moisture near the domain trough area. When soil water reservoir is undepleted, both _{veg} and _{soi} are at maximum. The latter flux rapidly decays in time due to the depletion of surface soil moisture and weak soil capillarity. Vegetation uptake remains initially constant, as the applied meteorological forcing is replicated in each day, but starts to decrease once vegetation begins to experience moisture limitation and slowly dies. Apparently, as the domain gradually dries out, both due to flow through the seepage face and the evapotranspiration process, the mean fluxes diminish in their magnitudes. Figure 5a illustrates the same fluxes for the scenario shown in Figure 2 (bottom) but for the rainfall case of *n*_{P} = 82.5.

[32] In order to make a quantitative statement with regards to the transition of controls on the spatial variability of θ among these processes, spatial covariances of depth-integrated soil moisture θ with several flux variables are analyzed. A geostatistical regression approach [e.g., *Erickson et al.*, 2005] is used to represent the instantaneous values of local depth-averaged soil moisture θ as a linear combination of site-specific fluxes of *q*_{n}, *q*_{p}, *E*_{veg}, *E*_{soi}, and *S*_{atm} (incident shortwave radiation) at the hourly time step. The applicability of linear analysis is certainly questionable, especially for the periods with high *C*_{v}(). Nonetheless, the goal is not to fit a perfect statistical model but rather identify a temporal shift in the dominant model regressors, i.e., those that are likely to control the pattern of θ in space. More specifically, at each hour, (2^{5} − 1) linear combinations of regressors *q*_{n}, *q*_{p}, *E*_{veg}, *E*_{soi}, and *S*_{atm} are tested as predictors of θ (note that ‘5’ is the total number of regressors). Obviously, these variables exhibit temporal dynamics of cross-correlation among themselves. This makes difficult the identification of importance of individual covariates (e.g., *q*_{n}, *q*_{p}, etc.) with more traditional statistical techniques, such as the Principal Component Analysis, which is not concerned with the individual contributions of regressors. The utilized technique is thus based on the Bayesian Information Criterion (BIC) [*Schwarz*, 1978]. The method assigns Bayes factors that compares several alternative models simultaneously. It is based on the notion that candidate models should be compared in terms of prior and posterior information that provides evidence for a model over an alternative model [*Raftery*, 1995; V. Yadav et al., A geostatistical synthesis study of factors affecting net ecosystem exchange in various ecosystems of North America, submitted to *Biogeosciences*, 2009]. The associated probabilities quantify the need to include a given covariate into the geostatistical linear regression model, i.e., the higher the probability, the higher the likelihood that the covariate contributes to the spatial variability of soil moisture at a given instant. As a “rule of thumb”, probabilities higher than 0.9 indicate a robust statistical significance. The results of the BIC analysis are shown in Figures 3b and 5b. Snapshots of instantaneous θ spatial distribution at different times are illustrated in Figures 4 and 6. The output times were selected based on the temporal evolution of *C*_{v}() in Figure 2 (bottom).

[33] It is expected that the system heat regime exhibits a diurnal cycle because of the cycle of the energy input, i.e., *S*_{atm} . Because of the evapotranspiration process, the mass flow regime is coupled to the heat regime and therefore it is expected that all of the above regressors exhibit diurnal dynamics, which are reflected in the computed BIC probabilities. In order to eliminate these high-frequency effects, the probabilities were averaged over the 4-day time step.

[34] As Figure 3b shows, the increase of *C*_{v}() (following the temporal evolution from the right side of the plot to the left) appears to be predominantly related to the normal redistribution flow, evapotranspiration, and lateral flow. The latter flux appears to be one of the most important variables throughout the period of the ascending limb of *C*_{v}() because of the highest BIC probabilities for > 0.127. It is apparent, nonetheless, that the resulting temporal evolution of soil moisture spatial variability is an outcome of the interplay among all involved processes. As pointed out, all of them exhibit diurnal cycles (not illustrated), which likely implies diurnal shifts in controls of soil moisture spatial variability. Note also that the peak of _{p} (Figure 5a) occurs before *C*_{v}() reaches its highest value, although, a priori, one could hypothesize that the two maxima should be co-located in time. A possible (but hardly verifiable) argument is that when the net subsurface moisture exchange reaches the highest rate, other processes are at work to effectively decrease the corresponding effect on moisture spatial variability. Since the effect of these processes must be declining with time, the highest spatial variability of moisture occurs later, when the magnitude of net lateral exchange is lower but still non-negligible. The time point when *C*_{v}() reaches its maximum ( ≃ 0.113, Figure 4b) has been argued to imply the end of the effective redistribution period. At that time, the significance of *q*_{n} and *E*_{veg} fluxes in explaining the pattern of θ in space is at the minimum (Figure 3b) and *q*_{p} is the only variable that has non-negligible explanatory power according to the BIC analysis.

[35] After the peak of *C*_{v}() has been reached, plant moisture uptake gradually homogenizes soil moisture. A temporary increase of the significance of *q*_{n} at ≃ 0.1 (Figure 3b) is likely associated with the capillary pull of water from the wetter layers below the root zone. The effect is of short duration, presumably because of the weak soil capillarity that cannot sustain vertical flux when an appreciable distance forms between the bottom of the root zone and an underlying wet layer. Subsurface moisture exchange still occurs but its importance is decreasing in time, becoming negligible at later stages of the simulation period (Figure 4c).

[36] Note the difference in the *y* axis scales in Figures 3a and 5a. Figure 5b demonstrates the relative insignificance of *q*_{n} and *q*_{p} throughout the entire simulation period for the scenario corresponding to the case of system evolution within the attractor space (the rainfall case of *n*_{P} = 82.5). As Figures 6b and 6c illustrate, the spatial distribution of soil moisture does not substantially change from the initialization distribution (Figure 6a), in relative terms. This is not the case for the distributions shown in Figures 4b and 4c, corresponding to the same values of Overall, transpiration (correlated with energy input) dominates throughout the entire period thus confirming the predominant control of local dynamics in determining soil moisture spatial variability. Note that as discussed in the beginning of section 3.2.2, the temporal change in the spatial variability is caused only by differences in the incoming shortwave energy and local vegetation state. Both depend on topography but are fairly insignificant.