Spatial Distribution of Tree Species Governs the Spatio-Temporal Interaction of Leaf Area Index and Soil Moisture across a Forested Landscape

Quantifying coupled spatio-temporal dynamics of phenology and hydrology and understanding underlying processes is a fundamental challenge in ecohydrology. While variation in phenology and factors influencing it have attracted the attention of ecologists for a long time, the influence of biodiversity on coupled dynamics of phenology and hydrology across a landscape is largely untested. We measured leaf area index (L) and volumetric soil water content (θ) on a co-located spatial grid to characterize forest phenology and hydrology across a forested catchment in central Pennsylvania during 2010. We used hierarchical Bayesian modeling to quantify spatio-temporal patterns of L and θ. Our results suggest that the spatial distribution of tree species across the landscape created unique spatio-temporal patterns of L, which created patterns of water demand reflected in variable soil moisture across space and time. We found a lag of about 11 days between increase in L and decline in θ. Vegetation and soil moisture become increasingly homogenized and coupled from leaf-onset to maturity but heterogeneous and uncoupled from leaf maturity to senescence. Our results provide insight into spatio-temporal coupling between biodiversity and soil hydrology that is useful to enhance ecohydrological modeling in humid temperate forests.


Introduction
Vegetation plays an important role in movement of water across the landscape by exchanging water between the soil and the atmosphere via change in surface albedo and roughness [1], canopy water interception [2], and transpiration [3][4][5]; changing the hydro-mechanical properties of soil [6,7]; and redistributing water laterally and vertically in soil profile via hydraulic redistribution [8][9][10]. On the other hand, survival and distribution of plants on a landscape depend on spatio-temporal patterns of soil water availability [11][12][13][14]. Therefore, an increased understanding of spatio-temporal patterns of vegetation water use and underlying mechanisms is critical for effective watershed management and advancement of the field of ecohydrology [15,16]. Recent studies from arid ecosystems have reported the strong influence of spatiotemporal patterns of vegetation on horizontal and vertical gradients of soil moisture [17][18][19]. However, the underlying processes that create spatial and temporal patterns of leaf area index and soil moisture remain poorly understood, especially in humid regions. Understanding the governing factors of this interaction is critical for modeling carbon, water, and energy cycles at the landscape scale.
Leaf surface is the site of gaseous (water and CO 2 ) exchange, therefore leaf area controls terrestrial water, energy and CO 2 fluxes [4,20]. Leaf area index (L), defined as half of the total intercepting leaf area (m 2 ) per unit ground surface area (m 2 ) [21], is used as a key input to a variety of ecosystem and hydrologic models [22] to incorporate phenological changes. Similarly, volumetric soil water content (h) is a commonly used input in hydrologic models and indicates the available soil water for plants. Both L and h can be estimated by ground-based measurements, remote sensing derivations, and simulation modeling [7,23]. Ground-based (direct and indirect) methods are relatively accurate at the site level, but cumbersome, costly, and even destructive to conduct [7]. Remote sensing has become a time and cost effective tool for the detection of spatial and temporal changes in L and h over a large (.10 km 2 ) area [23,24], but at small scales (,10 km 2 ) detecting spatial and temporal variability in L and h is quite challenging due to problems associated with accuracy, time, and cost [23,25]. In this study, we used Bayesian kriging [26], a novel data-model fusion approach to quantify and understand the spatio-temporal dynamics of L and h. In practice, a model parameter is unknown and often replaced by estimated value as if the estimated value is true, thus ignoring the associated uncertainty in parameter estimation. Bayesian inference treats a parameter as a random variable and incorporates uncertainty in predictions (posterior probability) based on a prior probability and a likelihood function derived from the probability model for the observed data. Therefore, more realistic estimates of the model parameters and prediction variance are obtained.
The main objectives of this study were (1) to quantify the spatiotemporal interaction of L and h, and (2) to assess the governing processes of this interaction at the Susquehanna Shale Hills Critical Zone Observatory (SSHCZO). We asked: (1) what is driving the spatio-temporal patterns of L in this forested watershed? We hypothesized that the spatio-temporal patterns of L are driven by spatial patterns of different species generated due to topography, soil type and hydrology; and (2) are the spatio-temporal patterns of L controlling the spatio-temporal patterns of h? We hypothesized that the spatio-temporal patterns of L will strongly influence the spatio-temporal patterns of h across the watershed.

Data Collection
A spatial sampling grid consisting of 90 sites (observed sites varied from 60-90 depending on weather) across the watershed Vegetative Controls on Hydrology PLOS ONE | www.plosone.org was used to measure L and h. The sampling grid was optimized to minimize measurement variability (nugget) and capture spatial variability by carefully choosing sites representing different landforms units (hilltop, hillslope, swale, and valley floor) and soils (Ernest, Blairton, Weikert, Berks, and Rushtown) in the catchment. Please see Lin 2006 [28] for detailed information about sampling design. The LI-2200 plant canopy analyzer (LI-COR, Inc., Lincoln, Nebraska, USA) was used to measure ground based forest L. The above canopy measurements were taken in an open space next to the forest area and below canopy measurements were taken at a predefined spatial sampling grid ( Figure 1). Both above and below canopy measurements were taken as an average of four L measurements at each location with LI-2200 wand pointing in four (E, W, N, S) directions. A sunlit canopy was avoided by taking measurements in the early mornings, evenings or during overcast sky and a 45u restricted view of the sensor was used. Remotely sensed (MODIS) measurements of L every 8-day were obtained from ORNL-DAAC website (https://lpdaac.usgs. gov/get_data/) and rescaled for the site L.
A TRIME-FM Time Domain Reflectometry (TDR) device was used to collect volumetric soil water content (h) at 10, 20, 40, 60, and 80 cm soil depths at sites co-located with L measurements by inserting the soil moisture probe into a PVC access tube buried at each site [28]. Total profile soil moisture storage (h TS ) for a   site is calculated by the following equation [29]: where n is the number of depth points available at a site, h i is the volumetric soil moisture content at the i th depth and d i is the representative length of the i th depth interval. The depth interval length (d) was 0.15 m for 10 and 20 cm depths, and 0.20 m for 40, 60, 80 and 100 cm depths. Surface (10 cm) h showed the most spatial and temporal variability [30], so the subsequent analyses were performed on the surface soil layer only.
Elevation and slope data were derived from a high-resolution 0.560.5 m DEM raster dataset for the SSHCZO, which was gathered by a LiDAR flight in February 2011 and was preprocessed at the University of California-Merced. TerraScan (Terrasolid: http://terrasolid.fi) software was used to classify the raw LiDAR point data into ''bare-earth'' and ''above-ground'' points. Ordinary kriging was used to interpolate the ground points and generate the digital elevation model (DEM) at 1 m resolution [31]. The relief between the highest and the lowest point across the watershed was 51.4 m. Slope value (radian) was calculated from the Shale Hills DEM using Maximum Triangle Slope method [32].

Statistical Analyses
Lag Analysis. Remotely sensed canopy L data were used to gapfill ground based L data to match with h when data were not collected on the same date. In addition linear interpolation was conducted to gapfill L and h when concurrent data were missing. Regression analysis was performed between L and h at different lags.
Spatial modeling. We used Bayesian kriging, a fully probabilistic Gaussian spatial model [26,33], for spatial interpolation. A brief summary of modeling approach is given below and the detailed information can be found in [26]. Bayesian kriging assumes that observed data Yi: i = 1,…,n are conditionally independent given a Gaussian underlying process S with: Level2 :S(xi)~N(0,s 2 R(h;w)) The first level describes a spatial linear trend (b = trend parameter) based on spatially referenced explanatory variables. The variance t 2 (nugget) represents measurement variability and/ or spatial variation below the sampling grain. The second level describes a stationary Gaussian spatial process [S(xi)] with mean = 0, variance = s 2 and correlation function R(h;Q), where Q is correlation parameter (range of spatial autocorrelation = 3Q) and h is lag distance (vector distance between two locations), and the third level specifies the prior for the model parameters. We chose an exponential correlation function: The mean and variance of L and h were estimated at individual locations from the predictive distribution using the krige.bayes function of geoR library [34] in R version 2.15.0 [35]. This algorithm uses discrete distribution and parameter prior to compute the discrete posterior distribution and samples a parameter value from it. We assumed a constant trend mean model and used a multidimensional (10061006100) parameter [Q, s 2 , and t 2 .rel (relative nugget = t 2 /s 2 )] grid by choosing a sensible interval of values for each parameter considering the study site. Please see R script (Script S1) for exact intervals for individual parameters. Flat prior (see Figure 2 for an example of prior and posterior distributions) were chosen for Q, and t 2 .rel, and a reciprocal prior for s 2 . The sampled parameter value is then attached to [b | Y, Q, s 2 , t 2 .rel] and a realization is obtained from the predictive distribution at the desired location. This process was repeated several times so that the sample is large enough to permit stable estimation of the underlying distribution. The mean and the variance of the predictive distribution were computed at individual locations using 100,000 posterior draws. Leave-One-Out crossvalidation strategy was used for model validation.
Density curves. To explore the distribution of different species across a gradient of elevation, slope and h, smooth density curves, using density function in R, were calculated for LiDAR derived elevation and slope data, and spatially interpolated h data at individual tree locations. Additionally, to explore the gain in L and loss of h at individual tree location from budbreak to leaf maturity, density curves were calculated for spatially interpolated L and h at individual tree locations. Tree location data were used as a prediction grid in Bayesian kriging for spatial prediction of L and h.

Results
The ground based observations (LI2200) and the remotely sensed (MODIS) L showed similar trends of budbreak, maturity and senescence (Figure 3a), but the MODIS-L was greater than the LI2200-L. MODIS-L was rescaled to fit the highest observed value of LI2200-L and zeros were replaced with linearly interpolated data. The surface (10 cm) h explained the most variability in L, so all further analyses were performed on surface h.
What is driving the spatio-temporal patterns of L in this forested watershed? Figure 1a shows the spatial distribution of dominating tree species across the watershed. Deciduous trees (oaks, hickories, and maples) are generally present at higher elevation ( Figure 4) and in general avoid low slope locations (Figure 4), while evergreen trees (hemlock and pines) are concentrated on south ridge and southwest valley floor along the stream (Figure 1a), which have lowest slope across the watershed. Evergreen trees in general prefer lower elevation and lower slope locations (Figure 4a,d). At the species level, both maple species (ACSA and ACRU) occupied lower elevations while the four hickory species were found at moderate (CAOV and CACO) or higher (CAGL and CATO) elevations  (Figure 1a), while the other pine species (PIVI) was distributed along the dry south ridge (Figure 1a). Soil water content did not significantly influence the spatial distribution of different species ( Figure S2). Soil moisture content explained the occurrence of some species such as eastern hemlock (TSCA) and red maple (ACRU), which were restricted to the wettest region of the watershed along the stream, while mockernut hickory (CATO) and chestnut oak (QUPR) avoided the wetter regions of the watershed (Figure 1a, S2). Other species seemed to grow without any specific preference to a particular type of hydrologic regime, such as white, red and black oak (QUAL, QURU, QUVE), shagbark hickory (CAOV) and sugar maple (ACSA) ( Figure S2).
Eastern hemlock (TSCA) was restricted to the Ernest soil, red maple was found on Ernest and Rushtown soils, hickories and chestnut oak preferred Weikert soil and the rest of the species did not show any particular affinity to one type of soil. Despite the differences in elevation, soil type, and soil moisture, all evergreen species were present on relatively flat terrains (Figure 4f). The resulting spatial distribution and mixture of different species created unique spatio-temporal patterns of L, including timing of budbreak, maturity, and senescence. For instance, red maple (ACRU) showed earlier budburst, greater L, but similar senescence as red oak ( Figure S3). The variability in leaf expansion (increase in L) of different species ( Figure S2) also added complexity in spatial patterns of L resulting in a unique temporal pattern of L across the watershed ( Figure 5). Are the spatio-temporal patterns of L controlling the spatio-temporal patterns of h?
L showed an exponential increase from April (leaf onset/ budbreak) to July (leaf maturity) and reached the maximum in mid-July (leaf maturity) (19 July) (Figure 1b). Furthermore, an exponential decline in L was observed from July (leaf maturity) to November (senescence) (Figure 1b). An exponential decline in h was observed at all measured soil depths (10-80 cm) and in total moisture storage (h TS ), which coincided with the exponential increase in L. Moreover, there was a subsequent rise in h and h TS with declining L (Figure 1b). L and h were negatively correlated and their relationship showed hysteresis with ,11-day lag between increase in L and decrease in h (Figure 3b). The lower elevation species (both deciduous and evergreen) produced more leaf area and experienced less decline in surface soil moisture while higher elevation species produced less leaf area and experienced greater decline in soil moisture ( Figure S2). The spatial mean of L across the watershed (mean of all modeled values of L in the watershed at 161 m grid) increased from leaf onset to maturity and then decreased from maturity to senescence ( Figure 5), whereas spatial variability (standard error of spatial mean of L) and prediction variance were highest during budbreak and declined to a minimum during closed canopy and again increased from canopy closure to senescence ( Figure 6). On the other hand, spatial variability and prediction variance of h was correlated with the spatial mean of h (Figure 7,8). Overall the kriged maps of L ( Figure 5) and h (Figure 7) confirm the temporal trend of instantaneous measurements.
The measurement error (nugget, t 2 ) and the spatial variance (sill, s 2 ) of L and h increased with increasing spatial mean of L and h ( Table 1,2). This relationship was also reflected in the inverse temporal trends of spatial structure (spatial model parameters-b, Q, t 2 , s 2 ) of L and h (Figure 9a-d) similar to the inverse relationship of their mean values (Figure 1b). The nugget and sill of L increased from leaf onset (April) to maturity (July) and then decreased from leaf maturity to senescence (November), while the nugget and the sill of h decreased from leaf onset to maturity and then increased from leaf maturity to senescence (Figure 9a-d). Leave-one-out cross-validation showed good agreement between observed and predicted values for both L (R 2 = 0.92 20.99) and h (R 2 = 0.76-0.96) ( Figure S4, S5).

Discussion
What is driving the spatio-temporal patterns of L in this forested watershed?
Variation in phenology and factors influencing it have attracted the attention of ecologists for a long time and current literature shows that multiple factors, such as hydrology [36,37], variation in leaf longevity [38,39], tree height [40], CO 2 concentration and nutrients [41], temperature [42][43][44] and light availability [45] greatly influence leaf phenology. However, influence of biodiversity on coupled dynamics of phenology and hydrology across a landscape is largely untested. Our results support the first hypothesis partially and show that spatial distribution of tree species drives the spatio-temporal patterns of L in the watershed and depends on topography and soil type. However, soil hydrology was not a good predictor of species distribution across the watershed, possibly due to humid conditions. Topography, mainly elevation and slope, greatly influenced the spatial distribution of different tree species across the watershed (Figure 2), which created a unique spatial pattern of leaf area index. Surprisingly, soil moisture did not explain the distribution of the tree species across the watershed ( Figure S2). Soil type and slope explained the spatial distribution better than h, except for eastern hemlock which was only present on wet soil along the stream. But the presence of TSCA can be better explained by soil type than hydrology. Furthermore, spatial pattern of L exhibited strong temporal dynamics due to different timings of budbreak, maturity, and senescence of leaves and variability in leaf expansion of different species, thus creating a spatially explicit forest phenology ( Figure 5).
Are the spatio-temporal patterns of L controlling the spatio-temporal patterns of h?
Quantifying spatio-temporal patterns of L and h is becoming increasingly important, as spatially distributed approaches become more common in current and future landscape modeling [16,46]. Our results support our second hypothesis and show the coupled dynamics of L and h in spatial and temporal domains. The spatial structure of leaf phenology and hydrology showed tight coupling at the peak of the growing season (closed canopy) (Figure 9), presumably primarily through evapotranspiration, as leaves control loss of water from plants through transpiration [3][4][5]. In addition, L likely influences loss of water from shallow soil layers (evaporation) through changing surface albedo and roughness [1]. At budbreak and senescence the spatial structure of L and h were not coupled (Figure 9, shaded region) and water was distributed more uniformly (Figure 7) throughout the watershed (with variation mostly associated with the topographic complexity). L and h showed a clear seasonal pattern and supported the previous findings of Takagi and Lin [30], which suggests greater control of evapotranspiration on soil moisture under dry conditions and topography under wet conditions. However, we found a lag of about 11 days between the increase in L and decline in h, which could be due to the delay in full photosynthetic activity after leaf onset [47,48], water storage inside tree stem [48][49][50], and soil moisture buffer zone around trees due to lateral water flow in soil [49,51] and plant-aided hydraulic redistribution [8][9][10]. The temporal variation of vegetation and hydrology coupling was also visible in spatial structure of L and h across the watershed (Figure 9). At budbreak and senescence the forest canopy was patchy and highly variable for L across the watershed due to differences in phenology of different species and h showed high variability due to complex terrain [30] and variable demand of water from emerging and senescing leaves ( Figure 5,7). At leaf maturity, forest canopy was closed (maximum L) and the spatial variability of L was minimum ( Figure 5,6), while soil moisture (after 11 days) was very low and relatively uniformly distributed across the watershed and thus showed least variability (Figure 7,8).

Conclusions
Results from this study suggest that spatial distribution of tree species and different timing of budbreak, maturity, and senescence for different species across the forested landscape created unique spatio-temporal patterns of L, which created the patterns of water demands reflected in variable soil water content in space and time. The landscape canopy and soil water became increasingly homogenized and coupled from leaf onset to maturity (i.e., increasing and homogenous L, and decreasing and homogenous h), but became more heterogeneous and uncoupled from leaf maturity to senescence (i.e., patchy and decreasing L, and patchy and increasing h). Our results provide insight into tight coupling between biodiversity and soil hydrology across space and time. Incorporating these spatial and temporal feedbacks into hydrologic  Notes: NSR is noise to signal ratio and R 2 is linear model fit of leave-one-out cross validation between modeled and observed h. Parameter estimates represent mean of posterior distribution and values inside the parenthesis are quantile based 5% and 95% credible intervals. doi:10.1371/journal.pone.0058704.t002 models will improve current and future landscape modeling of humid temperate forests. Figure  Script S1 Example data and R script used in this paper.

Supporting Information
(ZIP)