Soil Science Society of America Journal 66:1571-1583 (2002)
© 2002 Soil Science Society of America
DIVISION S-5—PEDOLOGY
Spatially Explicit Treatment of Soil-Water Dynamics along a Semiarid Catena
F. Chamrana,
P. E. Gessler*,b and
O. A. Chadwickc
a The RETEC Group Inc., Long Beach, CA 90815
b Dep. of Forest Resources, Univ. of Idaho, Moscow, ID 83844-1133
c Dep. of Geography, Univ. of California Santa Barbara, Santa Barbara, CA 93106
* Corresponding author (paulg{at}uidaho.edu)
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ABSTRACT
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Volumetric soil-water depth profiles at nine sample locations on a 2-ha hillslope were monitored throughout the 1997-1998 El Niño and the 1998-1999 La Niña cycles. A hydrological model integrating the soil-water measurements with digital terrain analysis and a one-dimensional water balance model was developed to map dominant hydrological patterns of soil-water storage and lateral flow redistribution. Statistical correlations between hydrologic behavior and the compound topographic index (CTI) generated from a digital elevation model (DEM) were used to generate spatially distributed input parameters of initial water storage and soil-controlled evapotranspiration utilized in the model. The results suggest that differences in water storage and availability are highly modified by climatic conditions and local topography. Nearly three times higher than normal rainfall in the El Niño year caused deeper infiltration of water and led to significant subsurface water redistribution into the concave hillslope positions which remained moist throughout the 1998 summer. Water infiltration and distribution was diminished considerably in the drier than normal La Niña, and led to a complete dry-down in 1999. Actual evapotranspiration was 87% of total precipitation during the El Niño, compared with 100% in the subsequent La Niña. The good correlation between modeled and measured water storage shows that even a simple one-dimensional model combined with the appropriate input parameters is a suitable tool for estimating changes in soil-water content on hillslopes where lateral flow is a significant functional component of the soil hydrology.
Abbreviations: DEM, digital elevation model • GIS, geographic information system • CTI, compound topographic index • TDR, time domain reflectometer • Et, actual evapotranspiration • Et,w, potential evapotranspiration • Et,s, soil controlled evapotranspiration
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INTRODUCTION
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AVAILABILITY OF WATER to terrestrial ecosystems is a major determinant of ecosystem production and health because it supports plant growth directly and redistributes nutrients within landscapes (Aber and Mellilo, 1991; Schuur et al., 2001). It follows that the role of topography in determining water movement in local landscapes must be well characterized to provide an accurate picture of ecosystem function. On hillslopes, knowledge of the topographical influence on water flow is essential in understanding soil differentiation (Milne, 1935; 1936), and hence the patterns of ecosystem process such as evapotranspiration, C storage, and net primary productivity (Band et al., 1993; Gessler et al., 2000). For this reason, some hydroecological models have incorporated topographical analysis in their model structures either by deriving a set of flow planes (TOPMODELTOPMODEL: Beven and Kirkby, 1979; TOPOGTOPOG: Vertessey and Elsenbeer, 1999), or dividing watersheds into smaller landscape units (FOREST-BGCFOREST-BGC: Running and Coughlan, 1988). In either case, limited point-data obtained from ground observation stations and gauges are typically used to define the input parameters and are often used for model calibration. Thus, less effort has been expended in developing comprehensive statistical methods to characterize the spatial variability of hydrological and ecological processes, especially at scales appropriate for hillslope analysis.
Statistical correlations among soil properties and terrain attributes generated from a DEM have greatly enhanced the quantitative investigation of hydrological processes in soils (Beven and Kirkby, 1979; O'Loughlin, 1986; Moore et al., 1991). Similarly, soil-landscape models developed by integrating digital terrain analysis and statistical modeling have enhanced prediction and mapping of soil properties (Moore et al., 1993; Gessler et al., 1995, 2000; McKenzie et al., 2000). Integration of GIS-based digital terrain analysis with monitoring studies can provide simultaneous feedback to predictive models and facilitate quantitative and dynamic modeling of distributed ecological processes. For example, the effect of water distribution and the resulting patterns of available soil water on net primary productivity, soil organic C, and soil respiration deduced from monitoring sites, can be evaluated in the context of predicted soil-landscape relationships. Using this approach, we can explore, capture, map, and interpret spatial variability of hydrological patterns and related ecological responses based on their appropriate spatial and temporal resolution.
In a previous study, we utilized terrain analysis, statistical modeling, and field sampling to model the distribution of soil properties on a 2-ha hillslope catena in California (Gessler et al., 2000). Here, we extend this analysis to visualize the spatial variability of hydrological processes on the same catena. Using data from soil-water profile monitoring stations (point location), we test the hypothesis that water in excess of evapotranspiration follows clearly defined patterns as it moves downslope through the soil and along the soil–rock interface. We place point-location soil-water profile measurements in a topographic context by developing statistical relationships with terrain attributes calculated from a DEM. Finally by linking water-balance model parameters with terrain attributes, we portray the water dynamics over two distinctly different hydrological years. The first was the wettest on record driven by an unusually strong El Niño weather pattern, whereas the second was drier than normal, driven by a La Niña pattern.
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MATERIALS AND METHODS
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Study Site and Topographic Characterization
The catena study was established on a 2-ha zero-order watershed within the San Ynez Basin in Santa Barbara County, CA (Fig. 1a) . The hillslope is approximately 100 m wide by 200 m long, extends from ridge-top to valley-bottom and encompasses both convex (hydrologically divergent) and concave (hydrologically convergent) landform components (Fig. 1b). The soil is extensively burrowed by gophers (Thomomys bottae) resulting in very high infiltration rates as observed in the field during the most intense (El Niño) rainstorms during the monitoring period. There is no incised drainage and no indication of overland fluvial transport on the site. Hillslope elevations range from 332 to 365 m and slopes range from 0 to 66% and average 22%. The study area contains blue (Quercus douglasii) and coast live (Quercus agrifolia) oaks and grassland vegetation is dominated by annual Mediterranean grasses (see Gessler et al., 2000).
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Fig. 1. Study site at the University of California Sedgwick Natural Reserve in Santa Barbara County, CA. The study site is shown both as (a) a drape of a digital orthophoto over a 30-m digital elevation model; and (b) with the individual soil profile locations displayed on a 1-m contour shade map of the hillslope.
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Histograms and summary statistics that characterize the distribution of the quantitative topographic attributes (Gallant and Wilson, 1996) along with spatial displays were used to guide the distribution of 20 sample locations over the range of elevation, slope, and landform curvatures (Gessler et al., 2000). These preliminary soil pits indicated that the surface soil patterns strongly reflect landform curvatures, therefore a subset of nine sample locations (Fig. 1b; Profiles 1, 2, 4, 8, 10, 12, 14, 18, and 19) encompassing this variation was chosen for soil excavation. Three soil orders (Entisols, Alfisols, Mollisols) were identified on the catena hillslope all with thermic temperature and xeric moisture regimes. The soil types and landscape positions are summarized in Table 1 (see Gessler et al., 2000 for a more detailed description).
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Table 1. Soil classification and compound topographic index (CTI) values for the nine soil profiles used in this study.
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Soil-Water Monitoring
To measure volumetric soil-water content in the nine profiles, buriable three-pronge TDR probes (Soilmoisture Equipment Corp., 2000) were placed in all major horizons down to rock (or 3 m, whichever occurred first). The probes were inserted parallel to the soil surface in the upslope direction and the pit was then back-filled around a vertically oriented PVC conduit protecting the lead wires. The number of probes per soil profile varied from two probes in Profile 12 to a maximum of eight probes in Profile 19. Data collection was initiated in April 1997, but to remove any effects of initial conditions a 6-mo settling period was allowed. Here we report on measurements starting November 1997 (beginning of the 1997-1998 hydrologic year), and continuing through October 1999. The TDR probes were read weekly except for high-intensity rainfall periods and the critical wet-up period when readings were acquired twice per week. Because the soil horizons have differing amounts of clay and thus differing amounts of water held at low potential, an estimate of -1500 kPa water from the driest period in September 1997 was selected to normalize all probes to a common zero point.
Water Balance Model
A soil-water balance model described by Scotter et al. (1979), expressed as
 | [1] |
was used to predict daily, depth-integrated soil-water content (S) for each of the nine soil profiles. Each term is an equivalent volume of liquid water with So representing the initial soil-water content referenced to field capacity (at which it is assigned the value zero), P is the daily precipitation, Et is evapotranspiration, and D is surface runoff or drainage from the profile. Surface runoff and drainage are assumed to be zero until the profile has been rewetted to field capacity. Then any excess of rainfall over evapotranspiration is assumed to leave the profile as D within the same day. Initial soil-water is measured as a percentage using the buried TDR probes. Each depth interval is equal to TDR installation depth plus half the distance (mm) to the probes below and above. The upper surface interval is equal to the top-most TDR installation depth plus half the depth increment to the probe below. Volumetric water content for each depth interval around the TDR probe is then obtained by multiplying the soil-water percentage by the depth for that interval. The initial depth-integrated volume of water (So) for a given soil profile is calculated by summing each interval for the entire profile.
The water balance model is controlled by two stages of evapotranspiration (Et). In the first stage known as the climate-controlled or potential state (Et,w), the moist soil profile can fully supply all the water demanded by the atmosphere. The modified Penman equation (Penman, 1948) is used for generating daily values of Et,w, where daily meteorological observations of solar radiation (Rn), temperature, wind speed, and relative humidity are obtained from a nearby (800 ft) climate station.
 | [2] |
where, Et,w is potential evapotranspiration (mm d-1), s is vapor pressure gradient (mb deg C), Rn is net radiation (W m-2), 
is density of air (kg m-3), Cp is specific heat of air at constant temperature (J kg-1), 
e is vapor pressure deficit (mb), ra is aerodynamic resistance (s m-1), 
is the psychometric constant equal to 0.66 (mb C-1), and L is the conversion to millimeters per day (681.67 W mm-1).
In the second stage, evapotranspiration depends on the ability of the soil to supply moisture. Therefore, as the soil moisture drops below field capacity the moisture delivery rate is limited by the amount of stored soil water (S). This stage is known as the soil-controlled evapotranspiration (Et,s) and is estimated using a linear function (Scotter et al., 1979):
 | [3] |
where, a and b are experimentally determined constants defined by the actual rate of water loss (Et,s) during the dry-down period. Twenty TDR measurements from the dry-down period of May through September 1998 were used to plot the relationship between loss (Et,s) and soil-water content (S). A linear regression through the points was used to find the constants a and b for Eq. [3]. The Et,s parameters (a and b) were determined independently for each of the nine soil profiles. Because soil property parameters vary spatially, this method defines Et,s as a direct function of the soil moisture content, and an indirect function of the soil properties (e.g., clay and gravel content).
Based on the above inputs (Et,w and Et,s), on any given day the model calculates Et as the lesser of Et,w and Et,s. However, to account for the effect of rain when the soil profile is relatively dry, the first 25 mm of rain goes into soil-water storage and is evaporated at Et,w regardless of S. The 25-mm value is an empirical value that approximates field capacity in the top 20 cm of most loamy soil profiles (Scotter et al., 1979). Unlike the Et,s parameters (a and b), Et,w is assumed to be spatially constant for the hillslope catena.
Model Error and Confidence Intervals
As described above, a maximum of 20 points was used to determine the rate of Et,s during the spring dry-down for each soil profile. The empirical measure of Et,s carries an error that must be considered in the comparison of modeled versus measured soil-water values. A 95% confidence interval for the predicted (Et,s) was constructed, using the mean square error of the regression (MSE) and standard error (S
k) (Clark and Hosking, 1986):
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 | [5] |
where n is the number of observations, x is the independent variable (S), and 
is the mean of x. Given Sk, a 95% band will be given by:
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where, 
i is the predicted value (Et,s). These interval bands were then used with the water balance model (Eq. [1]) to develop 95% confidence bands for extrapolation to the entire data set. Figure 4 illustrates the 95% confidence intervals contributed by the (Et,s) term for the water balance model.
Estimating Lateral Flow
The difference between the modeled and measured soil-water values is important because it represents periods where the actual soil-water profile is out of sync with the one-dimensional water-balance model. On this hillslope, we assume that the primary phenomenon that would create either a positive or negative difference from modeled values is net addition or loss of water by lateral, subsurface flow. The 95% confidence interval bands were used as a guide for discriminating between the differences contributed by model error and ones caused by lateral gain or loss. Only values outside the 95% confidence intervals are considered true variations.
Spatial Implementation
A principal application of soil-landscape modeling is to predict ecosystem properties at nonsampled locations using terrain attributes derived from a DEM or other spatially continuous environmental variables (Gessler et al., 2000; McKenzie et al., 2000). We used this technique to systematically evaluate and predict the a and b coefficients which define Et,s, and the So values over the hillslope.
Statistical summaries, exploratory data analysis, and statistical modeling for derivation of quantitative soil-landscape models were accomplished using the Splus statistical analysis package (Mathsoft, 1999). Scatterplot matrices (Cleveland, 1993; Moore et al., 1993) were used for exploring the data to find useful combinations of explanatory terrain attributes for predicting the a, b and So variables. The regression searches employed the Akaike Information Criterion (Akaike, 1974), which develops a statistic using the residual deviance penalized by the number of parameters requiring estimation in a model fit. Model fits were then developed and intercept terms, regression model coefficients, and goodness-of-fit parameters were output. Due to the small sample number, only linear relationships were evaluated in the regression search.
Using this process, CTI was identified as a single statistically significant explanatory variable for predicting the parameters a, b, and So for each 2-m grid cell. These were combined with daily input parameters of precipitation and potential evapotranspiration (Et,w) to develop a daily depth integrated soil-water balance at each grid point. This method provides an extension of the one-dimensional model to all the 3974 cells composing the hillslope. Arc/Info and ArcView (Environmental Systems Research Institute, 1996) tools were used to display resulting daily maps of water storage (S) in a GIS context. By using two spatial techniques described below, we expand this approach to create maps of spatial soil-water distribution and residuals outside the 95% confidence interval. The steps required were to: (i) create predicted surfaces of soil-water storage using measured values at the nine soil profiles; and (ii) subtract values of soil water determined from the one-dimensional model, from the values of soil water predicted from the actual measurements.
Correlations between the response variable (in this case measured soil water using the TDR probes) and the explanatory variable (CTI) were used to predict values of soil-water storage at nonsampled locations. These maps are limited in that they are only available on a weekly or biweekly time frame, when the field measurements were taken. Grid algebra tools (Arc/Info) were used to subtract values of soil water determined from the one-dimensional model, from the values of soil water predicted from the actual measurements for every 2-m grid cell. The difference between the two for a given cell, indicates whether water is being added to the cell (measured > modeled), or lost from the cell (measured < modeled).
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RESULTS
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Precipitation Data
Driven by a strong El Niño, the 1997-1998 hydrologic year was the wettest on record in Santa Barbara County with 961 mm recorded on the hillslope study site at the Sedgwick Natural Reserve. Rainfall began in November and, with the exception of a few lulls, was well distributed through out the hydrologic year including some late events in May (Fig. 2)
. In the 1998-1999 hydrologic year, a contrasting La Niña lowered rainfall totals to 358 mm, somewhat below the long-term average of 380 mm. Little rain fell in the early part of the hydrologic year; most fell between March and April, unusually late in the season. The timing of plant growth responded to the differences in the two hydrologic years. In the El Niño year, plants became active in November; they reached peak growth in March and April, before senescing in June. In the following year, they became active late in December, reached peak growth in the middle of April, and senesced by early May.
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Fig. 2. Daily and cumulative values of precipitation for the hillslope study area measured using a nearby weather station.
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Variations of Soil Water with Time and Depth
Spatial and temporal variations of soil water as measured for the nine profiles within the hillslope study site are depicted in Fig. 3
. Profiles 1, 8, and 12 on the convex slopes had low available water content (18–23%), exhibited rapid drying between rainfall events, and dried out early. In contrast to the profiles on the convex slopes, Profiles 10, 14, and 19 in the concave hollow, and Profile 18 on a convex cross-slope profile near the lower end of the hillslope, have water contents in the range of 25 to 30%. Beginning in February 1998, these profiles exhibited a sudden 15 to 20% increase in moisture levels in the layers below 120-cm depth suggesting a considerably higher accumulation of moisture at these locations. Drying between rainfall events was gradual, and dry-down was not complete until June. Moisture fluctuations in Profiles 2 and 4 were larger than on the convex slopes, but smaller than the concave profiles suggesting a more complex nature of water flow in these soils with argillic horizons. Both profiles exhibited gradual drying patterns between rainfall events and a seasonal dry-down in mid May. Without exception, the soil water fluctuations were more pronounced in the El Niño than in the La Niña water year. Soil water content values did not exceed 22% in any of the profiles during the dry year and the seasonal dry-down occurred earlier in the season for all profiles.
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Fig. 3. Measured available soil water content (%) using time domain reflectometer probes (TDR). Weekly and biweekly values of soil water for each profile were interpolated onto an evenly spaced grid where the x and y axes are time and depth respectively. The shades of color were created to help visualize wetting and drying patterns.
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Water Balance
The soil-controlled evapotranspiration parameter (Et,s) was calculated for each profile using the relationship between soil-water content (S) and change in soil water content S during the May to September (1998) dry-down period. The regression coefficients a and b relating Et,s to S for the nine profiles are shown in Table 2. The slope coefficient (b) varies between .02 and .07, while the intercept terms (a) have a wide range between 1.7 and 17.4. Variation in the Et,s parameters indicate that different locations on the hillslope are hydrologically and pedologically distinct and lose water by evapotranspiration at different rates. Any inaccuracy in data extrapolation at high values of S is of minimal importance, because over this part of the range potential evapotranspiration (Et,w) is far less than soil-controlled evapotranspiration (Et,s) (Scotter et al., 1979).
Also shown in Table 2 are the values for initial soil-water content (So) as measured using TDR probes for 1 Nov. 1997. Profiles 12, 1, and 8 have the lowest field capacity, followed by increasing values in profiles 4, 2, and 18 respectively. Profiles 10, 14, and 19 situated in the concave slope positions have the highest available soil water contents.
Figure 4
shows results of the soil-water balance model compared with the depth-integrated water storage (measured by TDR) for the nine soil profiles between 1 Nov. 1997 and 31 Oct. 1999. Measured values falling outside the upper and lower 95% confidence intervals represent a significant variance from the modeled moisture patterns and indicated the influence of hydrological processes that are not accounted for by the one-dimensional balance model. The modeled and measured values for Profiles 1 and 12 on the convex hillslope position are closely coupled, with the majority of the measured values plotted within the 95% confidence interval band (Fig. 4a,d). The maximum soil-water storage was 120 mm, a level reached during the heavy rainfall events in February 1998. The significant amount of vertical drainage (100 mm) predicted by the model for this time period indicates that the convex profiles reached their maximum soil-water holding capacity and excess water flowed out. Model results for Profile 8, also a convex profile, are more complex (Fig. 4f). The model significantly underestimated soil-water storage during the slow wet-up period in December 1997 and January 1998. However, the intense rains in February 1998 resulted in close agreement between the measured and modeled values and indicated up to 50 mm of drainage from the bottom of the profile. There was a very good agreement between measured and modeled soil water for Profiles 1 and 12 in the contrasting La Niña, whereas for Profile 8 the modeled values significantly underestimated measured values.
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Fig. 4. Daily values of soil-water storage and drainage as predicted by the one-dimensional water balance model in comparison with storage values measured using time domain reflectometry (TDR) probes. Upper and lower 95% confidence intervals are constructed around the model predictions based on the error involved in estimating the a and b parameters during soil dry-down. Differences between measured and modeled values that lie within the error band are considered insignificant because of uncertainty in model parameterization. Modeled drainage is shown as negative values for when occurred.
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Model results for Profiles 2 and 4 on the more stable shoulder positions are similar to each other when compared with profiles on other landscape positions, however there are important differences between the two (Fig. 4b,c). Early in the El Niño year there is a significant disagreement between the measured and modeled values in Profile 2, which probably is due to net addition of water from upslope (see below). In contrast, the more dramatic soil moisture change in February was portrayed well by the model where measured and modeled water content values reached a maximum of 300 mm. Modeled and measured values for Profile 4 were closely coupled early in the El Niño hydrologic year, where the modeled values fluctuated around the measured with no significant differences (Fig. 4c). The intense rains in February increased soil moisture to 300 mm, but the model called for 350 mm with small losses by vertical drainage. The subsequent rainfall events in March and April 1998 and final dry-down in June led to model estimates that were not significantly different from the measured values partly because of broad error bands around the model estimates. The model results for the 1998-1999 La Niña were in very good agreement with the measured values, with a few exceptions where the model underestimated water content during the relatively light March and April showers. Stored water only reached a maximum of 150 mm during the peak rainfall events in May, half of what was recorded in the previous year.
Profiles 10, 14, 18, and 19 in the concave hollow have very similar patterns of daily water storage fluctuations (Fig. 4e,g–i). There was a close agreement between the measured and modeled soil-water storage up to 150 mm early in the 1997 season. However, following the rains in February 1998 and throughout the spring, the model significantly underestimated soil-water storage for Profiles 10 and 19, and to a lesser extent for Profiles 14 and 18. For this period, the model predicted soil-water storage up to 400 mm for Profiles 10, 14, 18, and 450 mm for profile 19. The measured soil-water values were much higher than the modeled estimates (up to 150 mm difference), suggesting net addition of water that was not accounted for by the model. Despite the high soil-moisture levels, the model did not predict any vertical drainage from these profiles, because of their large soil-water holding capacity. After the dry-down in the of summer 1998, both the measured and modeled moisture values gained between 90 and 200 mm water that was in excess of the previous year's moisture, suggesting that the El Niño water year led to soil-water recharge that carried over into the subsequent year.
Cumulative values of P, S, Et, and D derived from model calculations are summarized in Table 3. A total of 961 mm of rainfall was recorded between September 1997 and October 1998. Predicted allocations of soil-water storage, evapotranspiration, and drainage during this period vary considerably within the nine soil profiles. On the convex slopes, the model predicted a sizable vertical drainage for Profiles 12 and 1 (up to 32% of P), and to a lesser extent Profile 8 (6% of P). For the same profiles, storage was minimal or close to zero, suggesting that drainage and evapotranspiration were efficient in removing all the water input. The model predicted zero vertical drainage for Profiles 10, 14, and 19 in the concave positions highlighting the large soil-water storage capacity of the deeper profiles. In addition, the significant soil-water storage predicted for Profiles 10, 14, and 19, suggests that evapotranspiration was not efficient in removing the above-normal water input from the concave profiles. Model results were quite similar in Profiles 2, 4 and 18. A minimal amount of storage (up to 3% of P) was predicted for all three profiles, again suggesting that evapotranspiration was not fully efficient in removing all the rainfall. However, vertical drainage was only allocated to Profiles 4 and 18, indicating that Profile 2 has a slightly higher storage capacity than Profiles 4 and 18.
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Table 3. Yearly total precipitation (P), evapotranspiration (Et), and vertical drainage (D), for the El Niño (1997–1998) and La Niña (1998–1999) hydrologic years calculated using the one-dimensional water balance model.
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Of the 358 mm of rainfall recorded between September 1998 and October 1999, almost all was removed by evapotranspiration. In fact, model results for the concave profiles indicate that evapotranspiration consumed all the rainfall input during the 1998-1999 season and the stored water from the 1997-1998 season. Profile 12 was the only profile with a sizable predicted drainage during this period, however it amounted to only 8% of the drainage predicted in 1997-1998.
The one-dimensional water-balance model quantifies the fate of added rainfall and demonstrates significantly different soil-hydrology behavior during the different hydrologic years. For example, there are significant differences in actual evapotranspiration rates between the El Niño and La Niña water years. During the La Niña year, Et is close to 100% of precipitation. In contrast, the El Niño rainy season caused deeper infiltration of water and led to significant drainage and water storage, and therefore evapotranspiration averaged around 87% of precipitation. The isolated one-dimensional models cannot fully represent the prevailing hydrological conditions where lateral fluxes contribute significantly to the total water budget. Below we link the nine one-dimensional models into explicit spatial and temporal models depicting soil water content and movement through the catena.
Model Parameters
The correlation between CTI and So for the El Niño and La Niña water years results in r2 values of 0.89 and 0.73 respectively, suggesting a strong relationship that is useful for modeling initial water conditions over the hillslope catena. The predictive relationship between CTI and a is also quite strong (r2 of 0.63), highlighting the influence of available soil water on the rate of evapotranspiration (Table 4). Thus the moisture delivery rate is limited by soil profile properties and landscape position as quantified by CTI. Inspection of Table 2 shows that variation in parameter b for the individual soil profiles is minimal, so an average value of (0.04) was chosen as a constant value for the hillslope.
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DISCUSSION
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Conceptual Model of Lateral Flow
Given the higher-than-normal rainfall in 1997-1998, the significant increase of soil water in the deeper profiles of 10, 14, and 19, and lack of surface runoff suggest that subsurface lateral flow is an important mechanism in redistributing water on the hillslope. The soil-water monitoring probes located in a variety of topographic positions and depths collect soil-water data at representative points across the spatially variable hillslope. Each probe detects soil water at a given point in time and space without distinguishing the direction or source of input and output flow. The water-balance modeling provides a one-dimensional mass balance limited to vertical exchanges between precipitation and losses to evapotranspiration and drainage. Hence, the difference between soil water detected by the buried probes and soil water predicted using the one-dimensional model at any given point in time may provide information on the net lateral redistribution of water from upslope to downslope positions. A positive difference suggests that water was added to the profile in excess of that determined by the one-dimensional model, resulting in a net gain. A negative difference indicates that water was lost from the profile in excess of that predicted by the model resulting in a net loss. Equal net lateral gain and loss simply show as zero. Net lateral gain and loss of soil water for the nine profiles are depicted in Fig. 5
. Because the profiles do not lie in connected flow paths, a thorough interpretation requires spatial modeling. However, significant patterns emerge based on a visual inspection of the residuals in the context of the hillslope positions.
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Fig. 5. Net lateral flux (gain/loss) of soil water is calculated by subtracting the measured soil-water content from the predicted values for periods when the measured values fall outside the 95% confidence interval bands. Measured values outside the band are considered significant and indicate influence of other hydrological processes that are not accounted for by the one-dimensional balance model.
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Profile 2 (Fig. 5b), which is located immediately above Profiles 10, 14, and 19 (Fig. 5e,h,i), shows a significant gain in soil water early in the 1997-1998 water year. In contrast, lateral additions of water to Profiles 10, 14, 18, and 19 (Fig. 5e,h,i) lag by nearly 2 mo probably because early in the season there is not enough water in the hillslope profiles to drive a significant redistribution downslope into concave positions. During February 1998 and throughout the spring, Profile 2 has an equal amount of gain and loss, while the concave position profiles continue to accumulate a considerable excess of water over that predicted by the water balance model.
The frequent alternation between net gain and loss illustrated in Profiles 1 and 12 (Fig. 5a,f) suggests a dynamic distribution pattern on the convex slopes. The steep topographic gradients and low upslope contributing areas contribute to rapid throughflow drainage, while the shallow soil provides a low water holding capacity. Consequently, these profiles experience rapid wetting and exhibit frequent loss to downslope drainage. Profile 8 (Fig. 5f) is also located on a convex hillslope position but is characterized by frequent positive deviations. There was a significant amount of gain early in the 1997-1998 season, followed by alternating gain and loss between February and March, and another gain in response to the showers in late March. Despite their similar slope gradients, Profile 8 has a slightly deeper soil profile than Profiles 1 and 12 (Fig. 5a,f). The deeper soil profile stored more water before the excess was lost to drainage.
Profile 4 (Fig. 5c), located above Profile 8 (Fig. 5f), on the more stable shoulder showed an opposing pattern to that in Profile 2. Except for a slight net gain in January 1998, the profile was characterized by a significant net loss in February and March. This suggests that early in the wetting season, there was more upslope water added into Profile 2 than to Profile 4. The slightly concave landscape position of Profile 2 probably explains why a net addition of water was more pronounced in this profile than in Profile 4.
The overall excursions for the 1998-1999 hydrologic year were less pronounced than the 1997-1998 year. Profiles 1 and 8 showed an alternating pattern between gain and loss throughout the rainy season. Profile 2 shows a significant amount of net gain in response to the rainfall in March. Profiles 4, 10, and 14 follow a similar pattern but showed a minimal net gain during the peak rainfall event in March. Only Profiles 18 and 19 had significant additions throughout the rainy season in 1999. It is probable that the net lateral losses indicated for November were an artifact of evaporation off the plant surfaces. As described earlier, the model did not account for soil-water loss because of interception, therefore it usually overestimated the measured values early in the season. Such overestimation by the model was apparent with the onset of rainfall in both the El Niño and La Niña water years.
Spatial and Temporal Changes in Soil-Water Storage
Spatial maps of soil-water storage on the hillslope, as calculated by the one-dimensional water balance model, display key hydrologic variations between the concave and convex slopes. Changes in soil-water stored following the major rainfall events in the El Niño and La Niña water years are illustrated in Fig. 6
. By January 5 1998, a cumulative amount of 200 mm of rainfall was recorded at the study location (Fig. 2). The model for 5 January predicted a uniform increase in soil water (84–125 mm) for most of the soil profiles. The profiles with less water were limited to the convex slopes and display a range of 42 to 83 mm in soil-water storage (Fig. 6a). Additional rainfall in mid January resulted in an increase in moisture into the 126- to 167-mm range in the higher and lower hillslope elevations and the concave hollow (Fig. 6b). The convex slopes remained slightly drier (84–125 mm) and actually expanded during this time. With a dramatic increase in rainfall on 3 February, a contrast developed; the upper slopes, concave hollow and toe slope positions stored as much as 420 mm while the convex slopes retained a maximum of 167 mm (Fig. 6c). Lower rainfall totals in mid March resulted in a drop in moisture on the convex and upper elevation slopes (Fig. 6d). Rainfall on 24 March slightly raised soil-water storage in all the profiles, however the hydrological variation on the upper hillslope was retained (Fig. 6e). The subsequent drying into the summer months is portrayed in Fig. 6f through 6h. By the end of June, soil moisture in the concave slope remained in the 100- to 200-mm range, while the convex slopes had dried to summer conditions.
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Fig. 6. Predicted maps of soil-water storage for the hillslope study site during the El Niño (1997-1998) and La Niña (1998-1999) water years. The shades represent volumetric soil-water content integrated over soil depth on a 2-m grid scale. Overlaid are positive (+) and negative (-) symbols indicating net gain or loss as a result of the significant differences between measured and modeled soil-water content calculated for the nine sample locations.
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The overall spatial pattern of soil moisture in the La Niña water year (Fig. 6i–o) is qualitatively similar to that of the El Niño year; higher levels of moisture occurred within the concave hollow and at the base of the slope, less moisture was stored on the convex slopes, and the convex slopes dried much more rapidly. By 4 Jan. 1999, only 50 mm of rainfall had been recorded at the site. Consequently, soil-water content predicted for 4 January ranged from 42 to 83 mm, approximately half of what was predicted in the El Niño year (Fig. 6a). By February moisture levels increased slightly into the 84- to 125-mm range, and a minor patchiness showing different moisture contents was observed on the convex slope to the left (Fig. 6j). By mid March soil-water content showed distinctly higher values in the concave hollow and upper shoulder areas (Fig. 6k). With additional rainfall in April, the wettest pattern for the La Niña year emerged as depicted in Fig. 6l. Figure 6m through 6o illustrates a dramatic dry-down sequence for the remainder of April through May. The convex slopes as well as the upper hillslope section dried rapidly and by 31 May the hillslope was completely dry (not shown).
The spatial maps of soil-water storage do not represent quantitative lateral exchange processes between the 2-m grid cells. The positive and negative symbols shown in Fig. 6 (a–o) assist in visualizing the qualitative net gain or loss for each sample location and in conceptualizing water redistribution. After the initial wetting, the visualization suggests increasing lateral flow redistribution over time. As seen in Fig. 6a–h and indicated by (+), the concave and lower elevation profiles continued to gain moisture throughout the El Niño water year. The concave hollow accumulated water by lateral convergence of flow lines. The convex slope to the left of the concave hollow was characterized by net soil-water loss (-) suggesting divergent flow losses. The convex slope to the right was characterized by alternating gain and loss because it had greater upslope contributing area compared with the left side. Patterns of net gain and loss during the La Niña water year were less pronounced than in the El Niño (Fig. 6i–o). Between January and March 1999, net lateral gains occurred sporadically and were limited to the lower elevation profiles (Fig. 6i–k). The effects of water redistribution became especially apparent on April 12 (Fig. 6l), but dry-down was more rapid (Fig. 6m–o).
Spatial and Temporal Changes in Soil-Water Movement
To visualize the results of the modeling, measurement, and residual analysis process, we implement a spatial model by using model coefficients and intercept terms derived from the empirical regressions between measured soil-water content and CTI at the nine sample points (see Chamran, 2000). Prior to the intense rainfall in February 1998, the CTI provided low correlation coefficients of 0.3 through 0.4. However, beginning in February the correlation coefficient increased to 0.9. This suggests that during initial stages of soil wetting topographic position plays a relatively minor role in determining moisture status on the hillslope. However, once field capacity has been reached, soil-water storage becomes a direct function of topography (i.e., upslope drainage area and slope). A similar observation was made with the correlation coefficients during the La Niña water year, where prior to the wetting events in March 1999, CTI accounted for only 30 to 40% of the soil-water variation. However, after the major wetting event in mid March, correlation coefficients increased to 0.7 to 0.8.
Figure 7
shows selected maps of lateral flow redistribution created by subtracting the spatial maps of soil water determined from the one-dimensional model from spatial maps of predicted soil water. On 4 Feb. 1998 (Fig. 7a), the soil profiles had either reached or exceeded field capacity. The upper shoulder and side slopes immediately surrounding the concave hollow lost 10 to 49 mm to downslope flow. The concave toeslopes gained between 51 and 200 mm through recharge from upslope. Areas of equal gain and loss were mostly seen within the convex slopes. Throughout February and March, with the exception of the concave slopes that continued to accumulate moisture, a distinct pattern of net loss dominated the shoulder and upper convex hillslope positions (Fig. 7b). In April, the upper elevation and shoulder slopes gained in the range of 11 to 50 mm of water from upslope contribution, while the convex slopes continued to lose water to downslope positions (Fig. 7c). This shift in the distribution patterns was driven by additional rainfall in April, which caused considerable rewetting of the soil profiles. In May, net loss dominated most of the upper elevation, shoulder, and convex slopes, however net gain continued to dominate the concave zone (Fig. 7d).
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Fig. 7. Selected maps of lateral flow distribution for the El Niño (1997-1998) and La Niña (1998-1999) water years. Blue shades depict areas of net loss. Green, yellow, and red depict a widespread range of net gain, and white shades are areas where net loss equals net gain. The delineated catchment (black polygon) defines hydrologic boundaries at the top and sides of the hillslope with a spatially distributed outlet at the downslope end.
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In January 1999, a major portion of the hillslope gained water (Fig. 7e). Net gain in the upper elevation and shoulder positions was mostly within the 11- to 50-mm range. Most of the convex slopes lost between 10 and 49 mm to the lower profiles. In February (Fig. 7f), more profiles within the upper and shoulder positions showed equal gain and loss. The concave slope was dominated by net gain (101–150 mm) and the convex slopes by net loss (10–99 mm). Early in March (Fig. 7g), areas of net loss dominated the hillslope, while net gain only occurred within a narrow path within the concave slope. Areas of equal gain and loss were seen on the upper hillslope surface. The map for April (Fig. 7h) showed a similar pattern of distribution to that in February (Fig. 7f).
SUMMARY
This study documents the role of topography in modifying soil-water distribution under differing rainfall conditions. Nearly three times the normal rainfall in the 1997-1998 El Niño year caused deeper penetration of water in the soil profiles, and evidence of much greater subsurface lateral redistribution of water especially in the concave profiles. In the subsequent 1998-1999 La Niña year, flow in both the vertical and lateral directions was dampened considerably because of lower than normal rainfall. These provide baseline estimates of hydrological patterns in the grassland soils of southern California where lack of water limits growth for much of the year.
The good correlation between modeled and measured water contents during the low rainfall year shows that even a simple one-dimensional model is a suitable tool for estimating changes in soil-water storage on hillslopes. Much care is needed when using such a model during unusually wet water-years when lateral flow becomes a strong functional component of the soil hydrology. With the simple one-dimensional model used here, lateral flow would have a feedback influence on the climate versus soil-controlled evapotranspiration and drainage components of the one-dimensional water balance model. In these instances, TDR monitoring may be used to estimate the lateral redistribution of soil water by comparing modeled results and measured values. Work here also demonstrates the potential use of digital terrain attributes integrated with monitoring instrumentation for characterizing the spatial and temporal dynamics of lateral redistribution.
It is important to note that there have been few previous field investigations that document the occurrence of lateral redistribution on hillslopes in this region. Previous work (Gessler et al., 2000) hypothesized that lateral surface redistribution of water and sediments is important in these landscapes based on analysis of soil samples collected prior to hillslope instrumentation. However, the analysis here suggests that variations in A horizon depth, soil depth, C mass, and net primary productivity may be influenced more by subsurface lateral redistribution. The specific processes driving lateral redistribution are yet to be examined in detail and were beyond the scope of this study. The results shown here are likely specific to water-limited ecosystems and to the range of moisture conditions considered. We were fortunate that the 1997-1998 water year provided indications of how these hillslopes behave under occasional very wet conditions. Under conditions drier than those considered here, it seems likely that all water would be lost by evapotranspiration and there would be none left for downslope movement. Thus our results are quite inclusive of the broad weather conditions and hillslope behavior found in southern and central California grasslands.
The hillslope study site, though small in size, shows a tremendous amount of variation in soil hydrological behavior. As shown by comparative evaluation of measured and modeled soil water, these variations strongly relate to hillslope topography and landform structure. Although the sample size was limited, correlation of the hydrological properties with digital terrain attributes can be quantified statistically and applied with GIS to predict values at nonsampled locations. This provides explicit and quantitative models that can be tested, updated, and used for visualizing spatially distributed ecosystem processes. They may also be used to parameterize spatially distributed hydrological and ecosystem simulation models to help understand landscape control on biogeochemical cycling.
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ACKNOWLEDGMENTS
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The authors acknowledge support for this project from the NASA Mission to Planet Earth, and by the University of California, Campus-Lab Cooperation Grant. We also thank Hamish Cresswell, Lynne Dee Althouse, Josh Schimel, Karen Holmes, Thomas Gotthold, Aaron Miller, Sue Trumbore, and Ted Schuur for assistance in implementation of this study.
Received for publication December 20, 2000.
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TOP
ABSTRACT
INTRODUCTION
parameters used in the one-dimensional water balance model.