(AgES) Response-Function Model Simulates Layered ...

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Vadose Zone Journal Accepted paper, posted 04/29/2015. doi:10.2136/vzj2014.09.0119

The AgroEcoSystem (AgES) Response-Function Model Simulates Layered Soil-Water Dynamics in Semi-Arid Colorado: Sensitivity and Calibration Timothy R. Green 1*, Robert H. Erskine 1, Michael L. Coleman 2, Olaf David2, James C. Ascough II1, Holm Kipka2 Abstract Simulation of vertical soil hydrology is a critical component of predicting more complex multidimensional soil water dynamics in space and time. The AgroEcoSystem (AgES) model is identified here as a single land-unit application of the three-dimensional AgES-W (Watershed) model. AgES simulates vertical soil water dynamics using global and layered soil response functions with conceptual storages as state variables. A detailed description of the response functions that control infiltration, evaporation and soil-water processes facilitates sensitivity analysis, model calibration and evaluation against volumetric soil-water content (SWC) at measured layers. The Object Modeling System links AgES to a Shuffled Complex Evolution calibration tool called Luca. We used Luca and fractional factorial experimental designs to analyze parameter sensitivities, then applied different strategies of implementing Luca to layered SWC data. The profile dynamics of simulated SWC resulted in depth-averaged Nash-Sutcliffe Efficiency (NSE) values of 0.60 to 0.95 for calibration in years 2003 and 2005, and up to 0.80 over four years used for (cross-)evaluation. Using the 2005 calibration parameters, NSE became negative in years 2009 and 2011 due to large negative values at some depths with low variance in SWC. Optimal parameter sets for each calibration year were not unique, and model results did not fully capture the measured dynamics. Even so, AgES simulations compared favorably with previous simulations of SWC at this site using a Richards’ equation model. These results provide new understanding of the model responses and interactions between functions controlling the vertical flow and storage of water to aid watershed modeling.

USDA, Agricultural Research Service (ARS), Agricultural Systems Research Unit, Fort Collins, CO 80526 *Corresponding author email: [email protected] 1

2

Colorado State University, Department of Civil and Environmental Engineering, Fort Collins, CO 80524

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Vadose Zone Journal Accepted paper, posted 04/29/2015. doi:10.2136/vzj2014.09.0119

Introduction Accurate representation of water storage and movement in soil profiles is essential for simulation of complex soil-water processes. Thus, simulation of vertical soil hydrology is a critical component of simulating even more complex soil water dynamics in space and time, including land-atmosphere, vegetation and subsurface interactions. Although integrated responses over a whole watershed can be simulated with relatively simple, parsimonious conceptual models (e.g., IHACRES (Jakeman and Hornberger, 1993; Jakeman et al., 1999; Ye et al., 1997)) or lumped hydrology (e.g., SWAT (Arnold et al., 1998; Arnold et al., 1999)), process interactions in space and time need to be represented explicitly in order to estimate emerging landscape patterns related to soil water. Precision management and conservation planning require such spatially variable process modeling. Detailed soil-water processes have been simulated using numerical solvers of the Richards’ equation (Richards, 1931) in one dimension (Fang et al., 2010; Ma et al., 1998) or multiple dimensions (e.g., Mirus et al., 2011; Simunek et al., 1999). The computational demands of such numerical methods are often too great for applications across even “small” watersheds (tens of hectares). Thus, we have adopted and developed an intermediate level of process complexity using depth-variable response functions for simulating soil hydrology in the AgES-W (AgroEcoSystem-Watershed) model (Ascough et al., 2012). Other hydrologic models have used conceptual compartments in the soil and vadose zone to store and release water at rates designed to simulate rainfall runoff. Notable examples include the Hydrologic Simulation Program in FORTRAN (HSPF; Bricknell et al., 1997), the Sacramento Soil Moisture Accounting Model (Sac-SMA; Burnash et al., 1973; Burnash, 1995; Koren et al., 2002), and the Precipitation Runoff Model (PRMS; Leavesley et al., 1983; Leavesley and Stannard, 1995). Vertical hydrology within these models was simplified to contain an upper zone and lower zone with response functions in each horizon. Koren et al. (2000) related parameters in Sac-SMA to soil properties, assuming that fast and slow storages are related to gravitational and capillary soil water, where the threshold may be defined using a field capacity value estimated from STATSGO soil data. These concepts are similar in AgES-W, which was derived from the J2000 (Krause et al., 2006) and J2000-SN models (Fink et al., 2007) and allows finer subsurface layers and interactions between layers. Here, we describe and test the AgroEcoSystem (AgES) model as a single land-unit application of the full AgES-W (Watershed) model. The primary objectives of this study were to provide detailed understanding of the vertical soil hydrology and the simulated process interactions by calibrating and evaluating AgES using daily soil water content (SWC) data over multiple depths on a dryland field (Green and Erskine, 2011). In the process of testing AgES, we explain details of the vertically layered soil hydrology, illustrate key response functions in the model, and evaluate different calibration approaches using a Shuffled Complex Evolution (SCE; Duan et al., 1993) tool called Luca (Hay and Umemoto, 2006). Finally, the AgES simulation results are compared with previous simulations of SWC using a Richards’ equation-based model (Fang et al., 2010), which is considered more physically realistic. Page |2

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Vadose Zone Journal Accepted paper, posted 04/29/2015. doi:10.2136/vzj2014.09.0119

Methods and Materials This study focuses on the first detailed description and sensitivity analyses of the soil hydrologic response functions in AgES, followed by testing of alternative calibration approaches using Luca. Test data for calibration and evaluation of AgES were collected on a dryland farm field in eastern Colorado under fallow conditions without live vegetation (disregarding any weeds). Daily soil water contents are simulated at multiple measurement depths (0.3 to 1.7 m). First, sensitivities of the simulated SWC to AgES model parameters are analyzed using two approaches: 1) Fractional Factorial Experimental Design (FFED) and 2) marginal sensitivity analysis using Luca. These sensitivities are based on probe E2 (site in the northwest of the field map in Fig. 1) using 10 sensor depths. Next, AgES is calibrated for probe E2 with cross-evaluations for periods in 2003 and 2005 using two approaches (Table 2) and the calibrated model is further evaluated using data from 2009 and 2011 using eight sensor depths. Finally, other probes under the same management phase (Fig. 1) are calibrated and evaluated using four sensor depths. Descriptions of the field site and the soil hydrologic processes in AgES follow. Field data and site description The present study builds upon previous work at the field site. Green and Erskine (2011) analyzed the soil water data used here. Fang et al. (2010) simulated soil-water dynamics at five summit locations using the Root Zone Water Quality Model (RZWQM; note that RZWQM2 was the version used in that study). We processed hourly data from SentekTM capacitance sensors (Schwank et al., 2006; Starr and Rowland, 2007; Wendroth et al., 2013) to estimate daily values of soil water content (SWC) following the methods of Green and Erskine (2011). Standard errors in the absolute values of SWC are estimated to be approximately 0.02 m3 m-3 or 2% volumetric SWC, even though errors in the relative changes of SWC at each sensor may be less (Green and Erskine, 2011). Detailed descriptions of the field site have been reported previously (Green and Erskine, 2011; Green et al., 2009; McMaster et al., 2012). Here, we highlight only the data used for simulations (meteorological data and SWC). Figure 1 is a map of the field site showing spatial locations of all Sentek probes, rain gauges, and meteorological stations. Daily averaged values of atmospheric inputs to AgES were assumed to be uniform over the field. When temporal data were missing from the base station (i.e., weighing rain gauge in the northwest corner for precipitation), other sensors were used to fill in the missing data without any spatial interpolation. Simulating profile soil water dynamics using the AgES Model Application of AgES to simulate vertical soil water dynamics requires specification of the initial volumetric SWC by depth (soil horizon or layer). AgES computes daily SWC as a state variable, which is used here for model parameter calibration. Model parameters in AgES describing storage capacities are entered by volume fraction, instead of depth of water as implemented in J2000.

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Vadose Zone Journal Accepted paper, posted 04/29/2015. doi:10.2136/vzj2014.09.0119

In this study, SWC was measured at discrete depth intervals of 0.1 m based on the capacitance sensors used (Green and Erskine, 2011), centered at profile depths ranging from 0.3 to 1.7 m. Initial values of SWC were set to the measured values at these depths at the beginning of each simulated period, where values were interpolated between sensors and set to the uppermost sensor SWC above 0.3 m. Due to this approximation, a “burn-in” period of approximately one month was used before the calibration period to remove the main effects of memory in the system. Actual simulation periods spanned Dec. 14 of the previous year through Oct. 1, 2003 or 2005. This approach is appropriate for the long system memory of a soil profile under semiarid conditions. AgES was calibrated separately for two years (2003 and 2005) under fallow conditions. The weather patterns in these years differed primarily due to a large snow event (37 mm water equivalent in approximately 48 hours) in March 17-19, 2003 followed by 51 mm of rain on April 23, 2003 versus primarily rainfall (66 mm in 2 days, and 137 mm in 14 days) in May 30 – June 12, 2005. Cumulative precipitation amounts (water equivalents) for January 1 – June 30 were 214 and 230 mm in 2003 and 2005, respectively. The values of the measured SWC averaged over all sensor depths at the beginning of each calibration period were 0.144 m3 m-3 and 0.166 m3 m-3 on January 14th of 2003 and 2005, respectively. In both years, the wetting front propagated deep into the soil profile, as shown previously for the measured data (Green and Erskine, 2011, Fig. 4). However, the dampened wetting front reached soil layers below 0.9 m in 2005, but not in 2003. Simulated responses will be discussed along with other results below. After calibrating AgES separately for the two years, the model performance was evaluated on the alternate years (“cross-evaluation” on 2003 and 2005 data) at all probe locations where data were available in both years. Some probes were missing sufficient data for calibration and evaluation in 2005 (Table 5). Calibrated parameters from 2003 and 2005 were also used to evaluate AgES using data from two independent years (2009 and 2011) at probe E2 (Fig. 1). Overview of AgES AgES-W is a spatially distributed watershed model (Ascough et al., 2012) with hydrologic components taken primarily from the J2000 (Krause et al., 2006) and J2000SN (Fink et al., 2007) models. Overland flow routing between delineated land areas or hydrological response units (HRUs), interflow, and groundwater discharge to channel flow can be simulated in the full AgES-W. For a single HRU, AgES simulates values of infiltration, runoff and vertical redistribution of soil water at a daily time step. Description of layered soil hydrology in AgES The AgES component that simulates surface water infiltration and layered soilwater movement is called ProcessLayeredSoilWater. Figure 2 is a flow diagram of the fluxes and storages over the top two soil layers, down to a bottom layer (n). The interactions between Layer 1 and Layer 2 are available for any two adjacent layers throughout the soil profile. Conceptual storages (rectangles) include surface Depression Storage (DPS), along with Medium Pore Storage (MPS) and Large Pore Storage (LPS) for Page |4

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Vadose Zone Journal Accepted paper, posted 04/29/2015. doi:10.2136/vzj2014.09.0119

each layer. Total soil porosity (Porosity) or saturated SWC is comprised of three storages, LPS + MPS + DeadCapacity (immobile water), where water in LPS exceeds FieldCapacity (FC), and MPS is less than FC and above DeadCapacity. This is a practical and conceptual definition of FC in AgES, rather than a more physically based definition, such as the SWC at 33 kPa matric potential (e.g., Ahuja et al., 2010). In this diagram, inactive lateral fluxes (i.e., fluxes between HRUs in cases of multiple-HRU applications of AgES-W) are shown in gray-filled shapes (including Overland Flow as surface run-on, and subsurface Interflow) with opaque connecting lines. If interflow is active, it first fills the MPS and the excess goes to the LPS for each layer. All other fluxes are active in our vertical application of AgES, but transpiration is not simulated from the layers during fallow conditions (assuming no live vegetation). Surface fluxes include vertical water inputs (rain and snowmelt) and losses (surface evaporation from DPS and from MPS in Layer 1) and lateral Direct Runoff (Fig. 2). Infiltration of precipitation and surface ponded water or snowmelt is computed using the following equation (Eagleson, 1970),

Infiltrationmax  SoilMaxInfS ,W 1  soil   Kf

[1]

where the subscript max denotes an upper bound of water intake, S and W designate Summer (SoilMaxInfSummer) and Winter (SoilMaxInfWinter), soil is the combined saturation of LPS and MPS in the layer, and Kf is the field saturated hydraulic conductivity in the first layer transformed to consistent units of mm d-1. Equation [1] differs from the previous version of AgES-W (Ascough et al., 2012), which used a multiplicative form (Krause et al., 2006), such that the new parameter values and sensitivities differ between model versions. The infiltrability parameters SoilMaxInfSummer and SoilMaxInfWinter are applied to the fixed months of May-Oct and Nov-Apr, respectively. If snow is present, SoilMaxInfSnow replaces SoilMaxInfS ,W 1  soil  in Eq. [1], such that Infiltrationmax is independent of SWC under the snow. Infiltration passes through DPS into LPS and/or MPS of Layer 1, where the flux partitioning is controlled by the parameter soilDistMPSLPS (Table 1) in the exponential function:



 - soilDistMPSLPS    MPSsat   

MPSin  Infiltration  1- exp  

[2]

LPSin  Infiltration  MPSin where the subscript in denotes inflow (mm d-1) to MPS or LPS, Infiltration (mm d-1) is computed from Infiltrationmax [1] and the available storage in Layer 1, and MPSsat is the saturation of MPS relative to its maximum capacity, MPSmax. The family of scaled response functions for partitioning Infiltration into MPS is shown in Figure 3a. If soilDistMPSLPS is small (e.g., 0.05), the fraction of infiltrated water going into MPS reduces rapidly with its MPSsat. Conversely, large values force MPS to fill before water is partitioned into LPS. Conceptually, we expect capillarity to cause water to be absorbed first into smaller pores before filling larger pores. Page |5

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Vadose Zone Journal Accepted paper, posted 04/29/2015. doi:10.2136/vzj2014.09.0119

Soil water is allowed to move between soil layers from one MPS to another. The potential capillary flux between layers can be up or down depending on the difference between the average MPSsat of both layers and MPSsat in layer h. This potential flux is also limited to half of MPSmax in layer h. Finally, the potential flux is scaled by a set of logarithmic functions of MPSsat in both layers (equations not shown here), and divided by a calibration constant kdiff_layer in the resistance term. Thus the maximum capillary flux of soil water between adjacent layers will be inversely proportional to kdiff_layer, with kdiff_layer > 0. Large pores drain based on the soil water content, soil, raised to an exponent, soilOutLPS as shown in Figure 3b. The governing equation is,

LPSout   soil soilOutLPS LPSact

[3]

where soil is the combined saturation of LPS and MPS in the layer (excluding DeadCapacity). Since  soil  1, values of soilOutLPS > 1 dramatically reduce the drainage from LPS as soil decreases, while values of soilOutLPS < 1 increase the fraction of outflow from available water in LPS (LPSact) and allow the layer to dewater more rapidly toward field capacity. Daily actual evapotranspiration (ET) is computed as a function of potential ET (PET) and MPSsat using:

ET  PET 10 or

 -10 1- MPS sat      soilPolRed 

 ET log10   PET

1  MPSsat   =  10  soilPolRed 

[4a]

[4b]

where soilPolRed is a polynomial reduction factor (Table 1), and the response functions are shown in Figure 3c. As soilPolRed increases, ET increases for a given value of MPSsat, and the response functions take on S-shapes. The ratio of ET/PET is very sensitive to soilPolRed in the range of values plotted. For example, if MPSsat = 0.3, ET = 0 for soilPolRed = 4, but ET = 0.5 PET for soilPolRed = 10. Thus soilPolRed is a key calibration parameter, as shown in the results below. In this study, we simulate infiltration, local runoff, soil evaporation, and vertical soil-water redistribution only during fallow periods, such that plant transpiration from soil layers was set to zero. However, AgES will compute depth-distributed transpiration if needed. Plant transpiration T is controlled by the parameter  in an exponential function:

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Vadose Zone Journal Accepted paper, posted 04/29/2015. doi:10.2136/vzj2014.09.0119

  layer depth   1  exp       root depth    T  PET  1  exp    

[5]

where layer depth is the depth to the soil layer of interest, and root depth is maximum rooting depth, which can vary with time. As  goes toward zero, the relationship becomes linear. Model parameter sensitivity, calibration and evaluation of responses As the first detailed investigation of soil-water dynamics using AgES, we performed sensitivity analyses to help us understand parameter and process interactions, and to focus on a feasible set of parameters to calibrate. Table 1 is a list of model parameters (global and layered) used in the present application of AgES. The Object Modeling System (OMS) (David et al., 2013) links AgES to a parameter calibration tool (Luca, based on Hay and Umemoto (2006)), which we used to test parameter sensitivities and different approaches of implementing Luca for model calibration using SWC data. Sensitivity analyses for AgES global and layered (soil horizon) parameters The parameters in AgES explored here are given in Table 1, where “global” parameters are scalar values specified in the main input file, and “layered” parameters are vectors of values that can vary with depth by soil horizon. Global parameters apply either to surface processes only or across all depths (e.g., kdiff_layer). Soil horizons (depth intervals) were kept the same for all simulations with intervals of 0 – 5 cm, 5 – 15 cm, 15 – 25 cm, continuing in 10 cm layers to the deepest sensor at 165 – 175 cm, followed by two more fine layers to 200 cm and a thick bottom layer to 500 cm. Fractional Factorial Experimental Design Fractional factorial experimental design (FFED) (Box et al., 2005) is used widely in the electronics, agriculture, defense, chemical processing, general manufacturing, automotive and aircraft industries to provide process information through a relatively limited number of experiments. Full factorial experimental designs explore all possible parameter combinations at a defined number of values (levels) for each parameter (factor). Therefore, a full factorial design for 2 values of n parameters requires 2n experiments. Alternatively, FFED explores a subset of parameter combinations by exploiting the expected redundancy of excess interactions estimated by full factorial designs (Box and Bisgaard, 1988; Montgomery, 2000). This is done through orthogonal combinations of parameter values such that all parameters occur the same number of times at high and low values, and requires 2n-p experiments, where n is the total number of parameters and p is the number of parameters in our sensitivity analysis. Careful FFED limits unexplored effects to higher-order interactions between parameters, providing information about main and lower-order interaction effects. The resolution, R, of a fractional factorial design indicates the order of the effects left unexplored. In this work, we used designs with R = “IV” to evaluate the main effects, where the main Page |7

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effects are not confounded by 2-factor interactions but may have 3-factor or higher interactions. The main effect of each parameter was estimated by selecting high and low values, then computing the difference of the average model response (e.g., mean absolute difference of SWC over all sensors and days) when the parameter of interest is high and low. For only the global parameters, the specific experiment is 2(9-4) or the “2 to 9m4”design‡, and for all parameters (global and layered), we used 2(11-6) or the “2 to 11m6” design§ (NIST, 2003). The two global parameters with least sensitivity in the global analysis were dropped from the mixed analysis. In addition to FFED methods, we analyzed sensitivities using the Luca model calibration tool, which includes a trace file that outputs the objective function (OF) and parameter values for every model run. Marginal responses can be plotted for each model parameter with other parameter interactions causing a Pareto-optimal front (Zitzler and Thiele, 1999) for the parameter of interest (e.g., Ginter, 2013; Kunz, 2013). A simpler approach, implemented here for the global parameters, is to calibrate each parameter step-wise. Luca uses the concept of calibration “steps” and “rounds” where each step calibrates a specified set of related parameters using SCE, and each round is comprised of all steps. Repeated rounds allow for recalibration over all steps with updated parameter values. For the sensitivity analyses, Luca ran for three rounds, with the assumption that two rounds were sufficient for parameter stability near a global optimum. We then analyzed the 95th percent confidence interval (95%CI = four standard deviations) of the OF values (mean absolute difference, MAD, in these runs) and of the parameter values explored within each step. The main sensitivity rank was based on the variation of model response (95% CI of the OF) divided by the normalized 95% CI of the parameter values. Alternative rankings were based on only the OF using the range, coefficient of variation (CV) and 95%CI. Shuffled Complex Evolution using Luca Various approaches and methods are feasible for calibration of model parameters to best match some OF. In this case, we matched daily time series of soil water content at multiple depths in each soil profile. Various parameters identified in the sensitivity analysis above controlled the model responses. The SCE engine also has default settings that control the number of points (sets of AgES input parameters) that occur in each complex, the number of shuffles, etc. These were not modified from the original setup (Hay and Umemoto, 2006). The Luca code was ported into the Object Modeling System (OMS) Version 3 for automated execution. In OMS, simulation runs are deployed using a main simulation (.sim) file to specify global controls, such as the period of simulation. Likewise, a Luca (.luca) file specifies the Luca controls, which include the observed data set, period of calibration (which may differ from the full simulation period), weighted objective function, steps and rounds, and convergence criteria.

‡

http://www.itl.nist.gov/div898/handbook/pri/section3/eqns/2to9m4.txt

§

http://www.itl.nist.gov/div898/handbook/pri/section3/eqns/2to11m6.txt

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Vadose Zone Journal Accepted paper, posted 04/29/2015. doi:10.2136/vzj2014.09.0119

In this study, the Nash-Sutcliffe Efficiency (NSE) statistic (Nash and Sutcliffe, 1970) was computed for each measured layer over the calibration period as follows: ∑(

)

∑(

̅̅̅̅̅̅̅ )

[6]

where denotes summation over all dates with measured SWC, subscripts s and m denote simulated and measured SWC, respectively, and the overbar denotes the mean value over calibration or evaluation period. A perfect match yields NSE = 1, a value of NSE = 0 is equivalent to replacing all simulated values with the measured mean, and negative values indicate that the mean squared error (difference between simulated and measured values) is greater than the variance of the measurements. As the latter value (denominator) becomes small, values of NSE often become negative and may take on large negative values. The OF for model calibration was the average value of NSE weighted equally over all sensor depths. Thus the OF may be affected strongly by a large negative value at one depth, which will be discussed in the results. For this reason, the mean bias, root mean squared difference (RMSD), and mean absolute difference (MAD) were computed along with NSE for evaluation statistics. Here, RMSD is specifically defined as follows:

√ ∑

(

)

[7]

where n is the number of measurements in time. Likewise, MAD is computed as,

∑

|

|

[8]

All of these statistical measures of model fit to SWC data were computed over time at each sensor depth, then the average values are computed over all calibrated sensor depths for each location. For consistency with the FFED sensitivity analysis, Luca simulations for parameter sensitivity used MAD averaged over all sensor layers for the OF. Otherwise the average NSE was the OF used for calibration. Limited testing on probe E2 showed that RMSD values were very similar using either NSE or RMSD as the OF (RMSD = 0.0188 and 0.0182, respectively). Various methods of model testing or “evaluation” are available, but a full treatment of techniques is beyond the current scope. Recent publications (Malone et al., 2015; Moriasi et al., 2012) offer reviews of model calibration and “validation” methods and guidelines for their implementation in hydrologic modeling. Leavesley and Stannard (1995) applied Luca to the Precipitation Runoff Modeling System. They grouped parameters by type (soil, plant, etc.), and parameters in one group were calibrated while other groups were held constant. Each group of parameters defined a “step” in Luca. After stepping through all of the parameter groups, defined as a “round”, the process iterates for a specified number of rounds (five rounds were used here for calibration). As part of the present effort, Luca was implemented Page |9

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with AgES under OMS to allow for calibration of parameters in multiple files. Thus we enabled calibration of layered soil parameters (e.g., soil-water storage parameters) together with the global parameters. Alternative calibration approaches and assessment methods Luca offers alternatives for how each vector (layered values) of a variable may be adjusted. In this study, we used either (1) independent shuffling of vertically distributed values (see “Layered Parameters” in Table 1) in each layer h, or (2) adjustment of a specified depth distribution of each parameter using a common multiplier applied to all layer values. Table 2 gives a comparison of the two main approaches or strategies for calibration with Luca. For both strategies, global parameters were either grouped into one step or added step-wise. We also tried grouping similar global parameters into three steps based on simulated processes, but there was no apparent advantage, so those results are not reported below. The Independent Layer Shuffling (ILS) approach allows Luca to vary each parameter independently or progressively by layer. Here, we grouped soil layer parameters of all layers above and including the sensor layer of interest in each step. In each subsequent step, the calibration parameters progressed with depth to include all model layers down to and including the sensor layer of interest. In this way, soil parameters are free to vary with depth, and each step allows further adjustment of parameters calibrated in the previous step. The OF includes all sensor layers so that it was consistent from one step to the next. The Distributional Layer Shuffling (DLS) approach (Table 2) describes a more parsimonious strategy for calibrating layered soil parameters by assuming that soil storage parameters (DeadCapacity, FieldCapacity, and Porosity) are uniform with depth. Any initial distribution could be specified. The values of storage parameters were constrained based on physical bounds, which do not overlap (e.g., maximum FieldCapacity < minimum Porosity). As defined here, FieldCapacity in AgES delineates MPS and LPS, but FieldCapacity is not necessarily equal to the one-third-bar SWC, such as in other studies (Ahuja et al., 2010). The value of Kf in the surface layer was calibrated to control the minimum value of daily infiltration (Eq. 1). For other layers, Kf controls the maximum percolation rate, and lower percolation rates are determined using LPSout in Eq. [3]. Results Model sensitivity to global and soil horizon parameters Model parameter sensitivities calculated using the FFED approach are shown in Table 3. The top section of the table shows sensitivities when only the global parameters were included, with layered parameters held constant (uniform with depth). Model sensitivities to the global parameters were ranked: soilPolRed (evaporation), kdiff_layer (vertical capillary flux from/to MPS), and soilDistMPSLPS (distribution of infiltration into MPS and LPS) had the greatest effects on SWC. AgES was least sensitive to soilOutLPS and soilMaxInfWinter, which were dropped from the subsequent FFED analysis. P a g e | 10

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In mixed global and layered sensitivity analysis using FFED (lower section of Table 3), layer parameters were varied, but specified to be constant with depth for simplicity. Even so, the second most sensitive parameter was FieldCapacity, and DeadCapacity was third. Rankings of the global parameters changed somewhat in the mixed analysis, but soilPolRed remained #1, while kdiff_layer moved down to #4 (remaining second among the globals), and soilMaxDPS (depression storage) moved up to #5 (third among the globals). By including the layered soil hydraulic parameters, AgES became relatively insensitive to the global infiltration parameters (soilMaxInfSummer, soilMaxInfSnow, and soilDistMPSLPS) along with soilDiffMPSLPS (flux between storages within each layer). These results highlight some of the parameter interactions in AgES under the present semi-arid site conditions, where surface runoff is infrequent and SWC dynamics are controlled largely by evaporation and vertical redistribution of soil water. For comparison, marginal sensitivities were evaluated using the 3rd round of parameter iterations from Luca. Each global parameter was calibrated in a separate step, so analysis of the spread of objective function (OF = MAD here) values relative to individual parameters gave the marginal sensitivities with all other parameters near optimal values. Unlike the FFED approach, layered parameters varied with depth. Table 4 shows the results ordered by rank based on the ratio of 95% confidence intervals of the OF over the parameter value. Alternative ranks varied slightly for the top three, but generally agreed across rank metrics. Rankings differed from the FFED results, but also confirmed the relative unimportance of parameters not included in FFED. Again, soilPolRed ranked high (#1 using OF only ranks), which is consistent with our understanding that surface evaporation controls the overall soil water balance under fallow conditions. Unlike FFED, the global parameter soilOutLPS ranked #2 as a key control of the layer dynamics, and soilMaxInfSummer ranked #1 (2 or 3 using only OF) versus 7th or 8th in the FFED results. These apparent inconsistencies suggest a high likelihood for non-uniqueness of optimal parameter sets during calibration. Contrary to more physically based models, such as RZWQM (Fang et al., 2010), field saturated hydraulic conductivity Kf did not rank highest among the soil hydraulic properties (Table 3). The response functions (e.g., Fig. 3a-b) are controlled strongly by the relative saturations of MPS or MPS+LPS and the parameters in the exponents of those functions. Also, runoff producing events are very infrequent and account for a small fraction of the total precipitation and infiltration, making AgES potentially less sensitive to the surface Kf in this study. Calibration of parameters using different Luca approaches The methods outlined in Table 2 were used to calibrate AgES, and the calibration results are illustrated in Figure 4 for SWC in 2005. Simulated values (lines) match the observed data (black circles) to differing degrees quantified by the corresponding OF (NSE values) and RMSD in Table 5. Because the mean bias is small in all cases, it is not reported in Tables 5 and 6. In addition to the variations in responses (i.e., different temporal features in Fig. 4), Table 5 shows broad ranges of some parameter values for different calibration methods. Values of Kf were allowed to vary from 0 to 200 cm d-1, based on surface soil Kf values measured during steady infiltration experiments (Green et al., 2009). The DLS method resulted in poorer model fits to data, as reflected in lower P a g e | 11

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NSE values. In Figure 4, we see early arrival of the wetting front at 90 cm using calibration DLS, which resulted in a poor NSE value for that layer and a lower depthaveraged NSE. At 30 cm, simulated responses for ILS are too peaked (higher temporal variance than others), but the peaks dampen by 50 cm. The ILS calibration had the best overall fit (NSE = 0.84 averaged over 10 layers, and NSE = 0.95 over 4 layers in 2005), which resulted from better timing and amplitude of the wetting front at most depths. Model evaluation using cross-evaluation with calibrated parameters After calibrating AgES with SWC data in 2003 and 2005, parameter sets from each period were used to simulate the alternate period. Such “cross-evaluation” at a site over time provides the best measure of a model’s ability to predict the observed responses under different weather patterns. Table 6 shows the cross-evaluation results at probe E2 for AgES using Luca calibration methods (cf. Tables 2 and 5), plus the results from Fang et al. (2010) for comparison. Figure 5 illustrates the associated scatter plots of simulated versus measured SWC. Not only is there deviation from the 1:1 line of perfect fit, but the graphs show temporally correlated deviations caused by model error in the timing of the wetting front reaching different depths. For example, Fig. 5 parts (a) and (c) show the simulated SWC at 60 cm in 2003 increasing rapidly to approximately 0.33 m3 m-3 for calibration (a) and 0.35 m3 m-3 for evaluation (c) before the measured SWC rises. Thus, measured SWC continues to rise after the simulated SWC has levelled off, but the two eventually converge near the 1:1 line. In 2005, the opposite phenomenon occurs, where simulated SWC lags measured SWC at 60 cm for calibration (b), and all four layers illustrated (30, 60, 90 and 120 cm) show lags for the cross-evaluation results (d). Thus, Fig. 5 demonstrates that model errors are not random, which should be considered when reviewing the statistical measures of goodness-of-fit in Table 6. The results of calibration and cross-evaluation using 10 sensors (Table 6) were consistent for the ILS approach, with good calibrations (NSE = 0.80 and 0.84 in 2003 and 2005, respectively) and reasonably good cross-evaluation results (NSE = 0.55 and 0.58 in 2003 and 2005, respectively). Comparing DLS with ILS approaches, the greater flexibility and increased degrees of freedom for ILS improved the calibrated fits considerably. Cross-evaluation results were also better using ILS. Table 6 also shows the corresponding values of RMSD, which range from 1.7% to 4.4%. The reported NSE values for DLS were averaged over all 10 sensor depths, and negative values reflect negative NSE values typically in lower depths where the observed variance in SWC is low. For ILS, Figure 6 shows both NSE and RMSD values versus sensor depth (vertical axis) for probe E2 for calibrations and cross-evaluations in 2003 and 2005. For the calibration periods, values of NSE are positive at all depths. However, evaluation results show negative NSE values at 120 and 150 cm, which were lowest (most negative) for the parameter set calibrated using 2005 SWC data and evaluated on the 2003 data. At these same depths, the corresponding RMSD values were relatively low, confirming that those negative NSE values were due to the small temporal variance in measured SWC at these depths. The largest RMSD values at E2 are also at 120 and 150 cm, but for the model evaluation on 2005 SWC data. The timeseries plots of SWC at different depths (Fig. 4) show that the seasonal wetting front in 2005 penetrated to 150 cm (black symbols are measured SWC), but the calibration data for 2003 did not; thus, the evaluation results for 2005 are poor (high RMSD) at these depths, but the NSE values P a g e | 12

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remain positive due to the relatively large temporal variance of the measured data relative to 2003. Calibration ILS4 was performed in the same manner as ILS, but using only four observed depths (30, 60, 90 and 120 cm). These four depths were selected to match the measurement depths on the A1-A4 and C1-C4 probes (Fig. 1). Calibrated fits at E2 were excellent over the four depths for both calibration periods (NSE = 0.88 and 0.95 for 2003 and 2005, respectively), but the cross-evaluation for 2005 produced a lower NSE (0.39). Also, when ISL4 calibrations were evaluated over all ten sensor depths for the same periods, the fits were much worse (NSE = -0.78 and 0.29 for 2003 and 2005, respectively). Unlike Fang et al. (2010), we cannot conclude that four measurement depths are sufficient for characterizing responses over all ten depths. Overall, the current simulations using AgES compared favorably with simulations by Fang et al. (2010) using the Richards’ equation-based RZWQM calibrated with the Parameter ESTimation (PEST) method (Doherty and Johnston, 2003). Both the AgES and RZWQM models and associated calibration methods tended to do reasonably well when cross-evaluated, but with typical reductions in model performance (Table 6). When AgES was evaluated on two other years (2009 and 2011), the NSE values averaged over the eight depths in common across all years were 0.80 and 0.76 using the 2003 calibration parameters, but the NSE values dropped below zero to -0.35 and -0.24 using the 2005 calibration parameters. These negative values were caused by relatively poor fits to the small absolute temporal changes below 90 cm. The average NSE values including only six sensors at 90 cm and above are 0.92 and 0.91 for years 2009 and 2011, respectively, using the 2005 calibration. The absolute errors based on RMSD values are also large in the deep layers (6.4% at 150 and 170 cm in 2009, and 4.8% at 150 cm and 8.3% at 170 cm in 2011). Thus, this study demonstrated the capabilities of AgES to simulate SWC well across different years to depths down to 90 cm, but deeper layers encountered greater model errors. These differences between simulated and measured SWC at depth include both timing and absolute changes in SWC. The timing of flow is controlled by response functions illustrated in Figures 2 and 3 that affect vertical redistribution of soil water, while the magnitude of change in SWC at depth is also related the net water balance, which is controlled by the balance of infiltration and evaporation. That is, the balance must provide enough water to percolate to the deeper layers. Differences in weather patterns and associated seasonal wetting of the soil profile appear to be primarily responsible for variations in (cross-)evaluations. As noted in the site description data, a large snow event in 2003 dominated the precipitation pattern, while greater cumulative precipitation in 2005 occurred primarily as rainfall over a longer period. Years 2009 and 2011 were more typically dry initially and experienced primarily rainfall infiltration. Unlike 2005, however, the full profile did not wet up, which made these evaluation years more similar to 2003 despite the lack of such a large snowfall event. Thus, differences in model performance across years appear linked to unique seasonal weather patterns and interannual variability. Finally, AgES was applied at all probe locations (Fig.1) assuming vertical flow, even though some locations are subject to lateral flow from upslope. The terrain-based Specific Contributing Area (SCA) is a measure of the potential for lateral overland and P a g e | 13

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subsurface flow from upslope, which was not simulated in the present vertical testing, but can be in the full watershed implementation of AgES-W. Table 7 shows the natural logarithm of SCA for each probe along with calibrated NSE and MAD values for the calibrated model in 2003 and in 2005 where data were available. Cross-evaluation (“Eval”) results are also shown where available. Figure 7 illustrates the relationships between the goodness-of-fit measures and ln(SCA), showing a linear decrease in NSE and associated increase in MAD with increasing ln(SCA). From these results, we infer that lateral hydrologic processes must be included at downslope positions to improve model performances based on SWC. The results also verify that vertical processes are dominant at upslope landscape positions, as previously assumed (Fang et al., 2010). Discussion and Conclusions In this study, we described the response functions within the subsurface layered hydrology (ProcessLayeredSoilWater) component of AgES for simulating dynamic SWC at different depths in a monitored soil profile. Sensitivity analyses identified model parameters with primary controls on SWC, but some inconsistencies between sensitivities (e.g., soilOutLPS) indicated potential process interactions and nonuniqueness of optimal parameter sets in AgES. Non-uniqueness of calibrated parameter sets (Table 5) were revealed by the largest variations of parameters soilPolRed (controlling evaporation), soilDistMPSLPS (controlling the distribution of infiltrated water between pore-size classes) and soilDiffMPSLPS (controlling redistribution of water within a soil layer between pore sizes). Assessment of AgES for simulation of daily profile water dynamics Calibrated parameters were evaluated using a cross-evaluation method between two simulations periods (2003 and 2005). The layered response-function model (AgES) produced similar results to those obtained with a more physically based model (RZWQM) at this site (Fang et al., 2010). The calibrated model was also evaluated on two other years (2009 and 2011) with similar goodness of fit against the 2003 calibration. Model performance was problematic (NSE