Transient, spatially varied groundwater recharge modeling

Authors

  • Kibreab Amare Assefa,

    Corresponding author
    1. Department of Civil Engineering, University of Manitoba, Winnipeg, Manitoba, Canada
    • Corresponding author: K. A. Assefa, Department of Civil Engineering, University of Manitoba, E1-368A Engineering Bldg., 15 Gillson St., Winnipeg, MB R3T 5V6, Canada. (umassefk@cc.umanitoba.ca)

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  • Allan D. Woodbury

    1. Department of Civil Engineering, University of Manitoba, Winnipeg, Manitoba, Canada
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Abstract

[1] The objective of this work is to integrate field data and modeling tools in producing temporally and spatially varying groundwater recharge in a pilot watershed in North Okanagan, Canada. The recharge modeling is undertaken by using the Richards equation based finite element code (HYDRUS-1D), ArcGIS™, ROSETTA, in situ observations of soil temperature and soil moisture, and a long-term gridded climate data. The public version of HYDUS-1D and another version with detailed freezing and thawing module are first used to simulate soil temperature, snow pack, and soil moisture over a one year experimental period. Statistical analysis of the results show both versions of HYDRUS-1D reproduce observed variables to the same degree. After evaluating model performance using field data and ROSETTA derived soil hydraulic parameters, the HYDRUS-1D code is coupled with ArcGIS™ to produce spatially and temporally varying recharge maps throughout the Deep Creek watershed. Temporal and spatial analysis of 25 years daily recharge results at various representative points across the study watershed reveal significant temporal and spatial variations; average recharge estimated at 77.8 ± 50.8 mm/year. Previous studies in the Okanagan Basin used Hydrologic Evaluation of Landfill Performance without any attempt of model performance evaluation, notwithstanding its inherent limitations. Thus, climate change impact results from this previous study and similar others, such as Jyrkama and Sykes (2007), need to be interpreted with caution.

1. Introduction

[2] Groundwater is a main source of direct water supply for about 40% of the world's population and major source of irrigation water for about 50% of the global food production [Seiler and Gat, 2007]. Sustainable use and management of this crucial resource highly depends on the amount of water that actually replenishes groundwater aquifers; this is often simply referred to as recharge.

[3] Accurate representation of groundwater recharge in groundwater models is necessary for effective water resources management. For example, the current water resource regulation policy in British Columbia, Canada, is designed for surface water sources without considering groundwater storage. However, groundwater and surface water are in continuous dynamic interaction. This interaction predominantly occurs as discharge of groundwater to surface water and recharge of groundwater by surface water [Winter, 1999]. Therefore, the spatially and temporally varied groundwater recharge produced here will have a fundamental role in developing a sustainable groundwater resources management policy in the study area. Note that recharge has generally been defined as soil water in excess of the soil moisture deficit and evapotranspiration [Lerner et al., 1990]. However, all the excess soil water does not necessarily reach the saturated zone due to the storage property of the vadose zone or because the groundwater system may not be able to accommodate additional recharge. For example, the infiltrated water might be obstructed by semipervious materials and drain as lateral subsurface flow [De Vries and Simmers, 2002]. In cases of shallow aquifers on the other hand, recharge may lead to local seepage discharge by initiating a rise of the water table; and/or the recharge that joins the groundwater storage might subsequently be extracted by evapotranspiration [De Vries and Simmers, 2002].

[4] Recharge may be estimated by making use of various methods. Frequently used techniques include direct measurement by lysimeters, tracer techniques, and stream gauging [Lerner et al., 1990]. However, these methods are susceptible to measurement errors and spatial variability and are often limited by their cost [Jyrkama et al., 2002]. Groundwater models may also be used to estimate recharge if other components in the hydrologic cycle are known to sufficient accuracy. However, as groundwater hydraulic parameters are also highly uncertain, recharge is often crudely estimated as a lumped fitting parameter together with other uncertain parameters during calibration [Varni and Usunoff, 1999; Ping et al., 2010]. Subsequently, it can be argued that an improved calibration can be achieved only if known values of recharge can be supplied as input to a groundwater model. In recognition of this fact, recent studies in the Okanagan Basin, and other parts of North America, have used the Hydrologic Evaluation of Landfill Performance (HELP) code for recharge estimation [Jyrkama et al., 2002; Liggett and Allen, 2010; Toews and Allen, 2009; Jyrkama and Sykes, 2007]. However, water budget models such as HELP [Schroeder and Ammon, 1994] are known to be less accurate particularly in semiarid and arid regions, because recharge in these regions is smaller than the other water balance components and thus the recharge term in the water balance equation accumulates the errors in all the other terms [Scanlon et al., 2002]. HELP has further been cited by various comparative studies [Khire et al., 1997; Gogolev, 2002] mainly for its overestimation of the “true” recharge.

[5] This current study presents an integrated process-based procedure that can help address some of these often neglected modeling challenges by taking advantage of long-term gridded climate data [Neilsen et al., 2010], ArcGIS [Environmental Systems Research Institute (ESRI), 2011], ROSETTA [Schaap et al., 2001], in situ observations of soil water content and soil temperature, and soil physics as represented by the finite element code (HYDRUS-1D) [Simunek et al., 2005]. The latter code is a physically based model that can fully describe the natural system using mathematical formulations of the fundamental physical processes. Spatially variable discretization and system-dependent, time-variable boundary conditions (BCs) are also implemented to better simulate sources and sinks and hence actual recharge joining the groundwater system. To our knowledge, such an approach combining all these facets has not been attempted before. The detailed calculations of groundwater recharge here show that previous estimates using the HELP code are suboptimal. While this is generally known, it is not clearly documented in the literature or recognized by regulatory agencies (e.g., EPA).

2. Study Area and Data

[6] The Okanagan Valley is situated in the semiarid southern interior of British Columbia (B.C.), Canada. Deep Creek is one of the many watersheds located in the northern part of the Okanagan Valley approximately between 334,550 and 348,750 m (latitude) and 5,577,750 and 5,611,650 m (longitude). It covers about 245 km2 and consists of a relatively narrow flat valley bottom bounded by undulating mountains. The elevation of the bottom part of the basin ranges between 340 and 520 m, while upper part ranges from 370 to 1620 m above sea level (Figure 1).

Figure 1.

Location and topography of study area in South Central British Columbia, Canada.

[7] The Okanagan valley is selected as a pilot watershed because of its diverse topography and complex groundwater aquifers as well as the significant variations in climate, land covers, and soil type. Climate data and the aforementioned characteristic of a watershed are indispensable parts of recharge modeling.

2.1. Climate Data

[8] A climate data set was prepared in gridded format for the entire Okanagan Valley through collaboration between Environment Canada, Agriculture and Agri-foods Canada, the British Columbia Ministry of Agriculture, and the University of Lethbridge as part of a basin-wide assessment of agricultural irrigation requirements [Neilsen et al., 2010]. The gridded data were prepared by making use of meteorological data from various sources such as the Canadian Daily Climate Data [Environment Canada, 2002] and data from other weather data networks including the BC Environment Snow Pillow stations; BC Ministry of Transportation Highways Network; and the BC Ministry of Forests Fire Weather Network. The data acquired from the above sources were used to generate basin-wide 500 m × 500 m gridded surfaces using Geographic Information System interpolation methodology [Neilsen et al., 2010]. These climate data are stored in a standard ESRI ASCII grid file format using single precision values. The database consists of 46 years (1960–2006) of daily minimum, maximum temperatures, precipitation, and potential evapotranspiration. The latter was calculated using the Penman-Monteith method [Monteith, 1965]. Hence, the climate data for study area are contained in a total of 68,631 files (the product of the number of variables and number of days in 47 years). Time series data were extracted from this database using a MATLAB code and the values were assigned to each and every grid (500 m × 500 m) of the watershed in ArcGIS. These data are used to represent the spatial distribution of precipitation and evapotranspiration in the study watershed. Spatial and temporal analysis of the extracted climate data was conducted. Based on this analysis, long-term average annual precipitation and potential evaporation over the Deep Creek watershed is estimated at 496.5 ± 77.9 mm and 749.6 ± 23.8 mm, respectively. The large standard deviations indicate the fact that the climate data exhibit large spatial variability throughout the watershed.

[9] Next, the spatially variable climate data were prepared to be input to the HYDRUS-1D code at different areas of interest in the watershed. Daily weather data (precipitation and evapotranspiration) were used in HYDRUS-1D. More coarse time averaging of weather data (weekly or monthly) generally leads to lower recharge estimates. The climate data were further analyzed by aggregating the spatially averaged daily data into annual values. Average annual precipitation and evapotranspiration plots are shown on the same graph (Figure 2). In addition to that shown in the temporal analysis (Figure 2), evapotranspiration was also calculated here by using the Hargreaves formula [Samani, 2000]. This method is integrated to HYDRUS-1D to calculate potential evapotranspiration (ET0) with minimal user input: Minimum temperature and maximum temperature. The long-term average annual evapotranspiration results were found to be 733.4 ± 35 mm/annum (Hargreaves) and 741.6 ± 31 mm/annum (Penman-Monteith). Further comparative analysis between the two data sets showed a good agreement with high degree of correlation estimated at r ≈ 0.99 (Figure 3). This comparison shows that the Hargreaves method is worthwhile provided adequate data is available. Although the two ET0 estimates are statistically close to each other, we decided to use the gridded ET0 data based on Penman-Monteith as it has a stronger physical foundation [Simunek et al., 2005].

Figure 2.

Annual precipitation and Penman-Monteith potential evapotranspiration.

Figure 3.

Evapotranspiration estimates, Hargreaves and Penman-Monteith.

2.2. Land Use Data

[10] The majority of the Deep Creek watershed is covered by agricultural lands that cover about 45% of the total watershed, followed by forests which make up 43%. The remaining 12% of the study area is covered by rangelands, bare lands, water bodies, urban areas, and so on. The land use map shown in Figure 4 was prepared by the Province of British Columbia (2008) and is available from GeoBC (http://geobc.gov.bc.ca/). The information from this land use map was used to retrieve additional data required to partition potential evapotranspiration into potential evaporation and potential transpiration. Time-variable leaf area index (LAI) values, representative of the land uses in the watershed are shown in Table 1. The monthly average LAI values were organized by M. Rodell (2010) available from the NASA land data assimilation systems (http://ldas.gsfc.nasa.gov/).

Figure 4.

Combined inputs to HYDRUS-1D across the watershed: EC (Environment Canada), pixel size 500 m × 500 m, HOBOTM stations on Silver Star Mountain and valley bottom.

Table 1. Monthly LAI
Land UseLAI
JanuaryFebruaryMarchAprilMayJuneJulyAugustSeptemberOctoberNovemberDecember
Forest5.86.06.46.97.68.48.38.07.66.76.15.8
Rangeland1.81.92.02.22.63.64.03.82.92.32.01.8
Cropland0.80.91.01.11.83.74.84.22.01.21.00.9
Barren surfaces0.00.00.00.00.00.00.00.00.00.00.00.0

2.3. Groundwater Levels

[11] Ground water levels are also important for recharge modeling. Well locations in the Deep Creek watershed are shown in Figure 4. Detailed investigation of the wells in the watershed was conducted by the University of British Colombia [Ping et al., 2010]. According to that groundwater study, water levels were found to be at much deeper depths than the bottom of the soil column in most cases. For instance, soil data at the majority of the agricultural areas in the valley bottom is available only up to a depth of 90 cm, whereas the groundwater level as approximated from nearby wells is at a depth greater than 15 m. This fact was an important consideration in deciding the type of lower BCs necessary for recharge modeling.

2.4. Soil Data

[12] A vector data map of spatially distributed soil types (Figure 5) was found from the Okanagan Plus Project of Agriculture and Agri-Food Canada [Kenny and Frank, 2010]. The soil map contains soil texture data that, of course, vary vertically at each grid location as well as horizontally from grid to grid. Soil codes indicated in Figure 5 were used to retrieve spatially varied soil texture data for soil columns of variable depth (0.6–1.5 m) across the study area. For example, Tables 2 and 3 contain soil texture data corresponding to the soil codes “EBY” and “CNN” at the locations of the HOBO weather stations in the northern half of the valley bottom and the Silver Star Mountain. These and similar data retrieved from each of the 11 soil codes were used to produce unsaturated soil hydraulic parameters, described later (section 'Hydraulic Retentivity and Conductivity Functions').

Figure 5.

Soil map, soil codes to retrieve spatially varied soil texture data for soil columns of variable depth (0.6–1.5 m) across the Deep Creek watershed.

Table 2. Soil Texture Data (%) and VGM Parameters at Valley Bottom (EBY)a
Soil Code/Soil LayerUnits of VGM Parameters: Qr,s (cm3 cm−3), Alpha (cm−1), n[–], Ks (cm day−1)
Depth (cm)SandSiltClayQrQsAlphanKsl
  1. a

    Parameters (in parentheses) are obtained from calibration.

10–151268200.0730.450.0051.6150.5
215–241270180.0710.450.0051.6160.5
324–391070200.0740.46 (0.5)0.005 (0.002)1.5 (1.65)140.5
439–64770230.0790.46 (0.55)0.006 (0.004)1.5 (1.7)120.5
Table 3. Soil Texture Data (%) and VGM Parameters at Silver Star Mountain (CNN)
Soil Code/Soil LayerUnits of VGM Parameters: Qr,s (cm3 cm−3), Alpha (cm−1), n[–], Ks (cm day−1)
Depth (cm)SandSiltClayQrQsAlphanKsl
10–10643150.03190.39440.03121.415159.010.5
210–24593380.03740.39030.02331.415141.920.5
324–38593380.03740.39030.02331.415141.920.5
438–68652870.03570.38960.03161.412650.040.5

3. Methods

3.1. Field Work

[13] While the above data set was fundamental to derive recharge values, an additional effort had to be expended to evaluate the performance of the groundwater recharge model in the study area. To this end, two portable state-of-the art HOBO™ weather stations, which can automatically record various data at a user defined time step, were installed in the summer of 2010 and 2011. The weather stations are located in the valley bottom and in the mountainous areas of the Deep Creek Watershed which are characterized by different soil type and vegetative cover (Figure 4). The devices contain sensors for soil temperature, soil moisture, and climate data including temperature, radiation, wind speed, relative humidity, and pressure. Trenches were excavated to install soil temperature and frequency domain reflectometry soil moisture probes. The sensors were installed horizontally into a vertical trench face to record soil moisture and soil temperature data at different depths. While the sensors at the valley bottom were installed at a depth of 10 and 50 cm, the ones at high elevation were installed at 20 cm depth.

3.2. Model Description

[14] A wide range of computer programs are available to simulate water and/or heat movement processes in the vadose zone. Based on current understanding, the Richards equation for vadose zone water movement, and the Fickian-based advection-dispersion type equation for heat transport are believed to appropriately describe the underlying physical processes. HYDRUS is one of such software packages that uses the above concepts for simulating water and heat movement in the vadose zone [Simunek et al., 2005]. Details on the historical development and various application of HYDRUS can be found in Simunek et al. [2008, 2012]. Recent applications of HYDRUS for recharge calculations can be seen in Jimenez-Martinez et al. [2009], Mastrociccoa et al. [2010], Kurtzman and Scanlon [2011], Lu et al. [2011], and Holländer et al. [2009].

[15] The basic form of Richards equation may be described in three forms: The “ψ-based” form, the “θ-based” form, and the “mixed form” [Celia et al., 1990]. The same study by Celia et al. [1990] showed that “ψ-based” formulations are subject to large mass balance errors. And the “θ-based” have known limitations associated with the discontinuous nature of moisture content; they cannot be used in wet regions near saturation. The “mixed form” on the other hand can minimize the mass balance error without affecting modeling capability near saturation [Celia et al., 1990]. We used HYDRUS in one dimension and used the version 4.xx noted as HYDRUS-1D. HYDRUS-1D solves the “mixed form” equation (equation (1)) by using Galerkin-type linear finite element schemes [Simunek et al., 2005].

display math(1)

where ψ is the pressure head [L], θ is the volumetric water content [L3L−3], t is the time [T], z is the spatial coordinate positive upward [L], and S is the sink term [L3L−3T−1]. k, the unsaturated hydraulic conductivity function, is a function of the pressure head, ψ is the soil water retention parameters and the saturated hydraulic conductivity, Ks [LT−1].

[16] The above equation describes water flow without accounting for the effect of vapor movement on the total water flux. However, studies have shown that vapor can have significant effect on total water fluxes in unsaturated zone of arid and semiarid regions [Scanlon et al., 2003]. Thus, vapor movement is simulated here along with the water movement and heat transport routines of HYDRUS-1D [Simunek et al., 2005]. Heat flux due to vapor flow is formulated in HYDRUS-1D as convection of sensible heat by water vapor and convection of latent heat by vapor flow [Scanlon et al., 2003; Simunek et al., 2005].

[17] Freezing and thawing is another phenomenon that is particularly important in cold regions. In equation (1), soil freezing can be accounted by using a simple snow module at the surface boundary. This module is implemented in the public domain version of HYDRUS-1D to stop seepage (lowering conductivity) in the subsurface when the soil is frozen. However, a detailed representation of the actual process requires a freezing and thawing module that can account for frozen water and ice blocking effect of pores in frozen soils. A freezing and thawing module was developed and coupled with equation (1) by Hansson et al. [2004]. An additional term that accounts for the energy stored in the frozen water was also developed and coupled with the heat transport equation of HYDRUS-1D [Simunek et al., 2005] by the same authors [Hansson et al., 2004]. The modified HYDRUS-1D code with the capability to simulate freezing and thawing processes was used here. We hypothesize that the detailed freezing and thawing routine of HYDRUS will not change water and heat movement simulation results in our semiarid study area, and this is verified by comparing estimates from the two versions of HYDRUS-1D with observed soil moisture and soil temperature data.

[18] Using HYDRUS to numerically solve the governing equations requires not only the input data set discussed above, but also a good understanding of the following: Spatial and temporal discretization, soil water retentivity and hydraulic conductivity functions, BCs, and sink term estimation procedures. Given below is a brief description of each item as used in this modeling exercise.

3.3. Hydraulic Retentivity and Conductivity Functions

[19] Actual measurements of soil hydraulic properties are often costly and time consuming to obtain. As a result, several indirect methods ranging from simple look up tables to methods with more physical foundations have been developed [Valiantzas and Londra, 2008; Kosugi, 1994; Durner, 1994]. Retentivity and conductivity functions are one category of indirect methods which can be formulated from empirical nonlinear regression equations and/or methods with more physical foundations [Van Genuchten, 1980; Mualem, 1976]. The Van Genuchten-Mualem (VGM) model consists of five parameters: Residual soil water content (θr), saturated soil water content (θs), shape parameters (α and n), and saturated hydraulic conductivity (KS). These parameters are determined by making use of a computer program called ROSETTA [Schaap et al., 2001]. Tables 2 and 3 show the mean VGM parameters estimated at our experimental sites. The reliability of ROSETTA has been accessed in various studies [Scott et al., 2000; Abbasi et al., 2004], which compared soil parameters derived from pedotransfer functions with those determined from model calibration. The aforementioned studies concluded that ROSETTA is a reliable and efficient method for estimating soil hydraulic properties.

[20] On the other hand, the heat transport parameters were derived from the HYDRUS-1D data base based on soil textural classes. These parameters were used to estimate thermal conductivity according to the Chung and Horton [1987] equation, which is integrated to the HYDRUS-1D code. Other required inputs such as the volumetric heat capacity of the porous media were determined from the default values of HYDRUS-1D based on soil textural classes [Simunek et al., 2005].

3.4. Boundary Conditions (BCs)

[21] BCs can be either system independent, such as constant flux, or system dependent. The latter refers to those conditions that depend on the external situation and the prevailing soil moisture conditions. Upper BCs in HYDRUS-1D can be defined by applying either prescribed flux or prescribed pressure head BCs [Simunek et al., 2005]:

display math(2)

and,

display math(3)

where E is the maximum potential rate of evaporation or infiltration [LT−1], and ψA and ψs are minimum and maximum pressure head at the soil surface, respectively (L). However, it is possible that either of the conditions can be violated in the process of computation. For instance, when one of the end points of equation (3) [Simunek et al., 2005] is reached; the actual surface flux will be calculated using a prescribed head boundary. If, at any point in time the calculated flux exceeds the specified potential flux indicated in equation (2), the potential value will be used as a prescribed flux boundary which results in saturation excess surface runoff on top of the soil surface. Runoff can also be simulated in HYDRUS-1D when the precipitation rate exceeds the infiltration capacity of the soil. This time variable atmospheric BC, coupled with a snow module, is implemented in the current study. The snow routine in the public domain version of HYDRUS-1D assumes that precipitation is in the form of liquid only when the air temperature is above +2°C. When it is below −2°C, precipitation is not applied as a flux BC until temperatures rise above zero and snow melts [Simunek et al., 2005]. The proportion of snow water equivalent which joins the groundwater table largely depends on the antecedent soil moisture. Note also that the snow water equivalent in excess of maximum pressure head at the soil surface is simulated as runoff (section 'Temporal Variation of Recharge').

[22] The lower BC for most of the cases in this study was taken to be “free draining” which is appropriate for the situation, where the water table is far below the bottom node of the soil column. In such cases, the specific discharge rate, q(n) assigned to bottom node n, is considered to be “potential” recharge. This can be used as a flux BC in groundwater models, especially for semiarid areas like the Okanagan Basin where the saturated zone transmits away more recharge than provided by the climate and soil [Sanford, 2002]. In areas where groundwater tables are expected to be near surface, however, recharge can cause local seepage discharge due to a possible rise of the water table. Therefore, a different system dependent lower boundary which has the capability to handle “saturation excess” conditions is specified. This type of BC assumes no flux when the pressure head is negative. When the pressure head is zero at saturation of the lower boundary, however, the corresponding outflow is calculated. Hence, part of the potential recharge that disappears from the soil zone through local seepage is simulated giving a more reliable estimate of actual recharge. Details on the influence of water table depth on groundwater recharge can be found in Smerdon et al. [2008]. On the other hand, the BCs for temperature at the upper and bottom of the soil columns of all the representative points in the Deep Creek Watershed are defined as Dirichlet and Cauchy type (heat flux), respectively [Simunek et al., 2005].

3.5. Sink Term

[23] A good estimate of this term is particularly important in shallow water level aquifers, where water may initially contribute to groundwater storage but might later be extracted by transpiration. To better estimate this flux, a fine discretization of soil profile is implemented specifically in the root zone and lower boundaries, where highly variable fluxes are expected. The advantage with variable discretization in terms of accuracy and simulation time was justified in a previous study by Carrera-Hernández et al. [2012]. The sink term was calculated as a function of potential transpiration and the pressure head with the Feddes-type uptake functions [Feddes et al., 1978]. Potential transpiration flux is estimated in HYDRUS-1D from potential evapotranspiration and LAI [Simunek et al., 2005]. Root water uptake parameters for various vegetation cover are integrated to HYDRUS-1D. The land use information discussed in section 'Land Use Data' was used to derive these parameter as well as the root depths at each of the various representative areas in the Deep Creek Watershed.

4. Model Results

4.1. Model Evaluation Using Field Data

[24] The public version of HYDUS-1D with an empirical snow routine [Simunek et al., 2005] as well as another version of HYDRUS-1D with a detailed freezing and thawing module [Hansson et al., 2004] were first used to simulate soil temperature, snow pack, and soil moisture over a one year (December 2010 to December 2011) experimental period. The recorded climate data as well as soil moisture and soil temperature data were of paramount importance in evaluating the performance of HYDRUS code, with and without the freezing and thawing module. Model initial conditions are estimated by setting the initial pressure head in Fall (of 1960) and running the model for 21 years. An atmospheric BC and free drainage condition were imposed at the soil surface and bottom boundary of the flow domain, respectively. Model results in both cases (HYDRUS-1D with and without freezing and thawing module) were evaluated by making use of the following statistical measures: average error (AE), root mean square error (RMSE), and correlation coefficient (r).

display math(4)

where Si is the simulated value, Oi is the observed value, math formula and math formula are the mean of simulated and observed values, respectively, and n is the number of data point.

4.2. Hydrus-1D Simulations: Snow Depth, Soil Moisture, and Soil Temperature

[25] Figures 6 and 7 show comparative plot between the observed and simulated soil temperatures at two depths. A strong correlation (r = 0.97) was found between the simulated and observed soil temperature records (Table 4). While the observed soil temperature records over a year study (December 2010 to December 2011) were all above zero degrees centigrade, it can be seen from Figure 6 that the simulated values at near surface were slightly under estimated between mid-November and the end of February. Snow depth simulations showed that the site was likely covered with snow during this period when the air temperature drop below zero (Figure 8). This insulation phenomenon is known to cause bias toward underestimation of soil temperature as indicated by the negative AE values (Table 4). However, the error values obtained here are relatively closer to zero than values reported in similar studies [Hejazi and Woodbury, 2011], showing a promising performance of the model in our study area. Details on the impacts of a snow pack on soil temperature can be found in Hejazi and Woodbury [2011].

Figure 6.

Simulated versus observed daily soil temperature at 10 cm depth, valley bottom.

Figure 7.

Simulated versus observed daily soil temperature at 50 cm depth, valley bottom.

Table 4. Measured Versus Simulated Variables at Valley Bottoma
Depth (cm)Average ErrorRMSECorrelation
Soil TemperatureSoil MoistureSoil TemperatureSoil MoistureSoil TemperatureSoil Moisture
  1. a

    Values (in parentheses) are based on the calibrated soil hydraulic parameters.

10−1.080.0092.50.0360.970.84
50−0.25−0.04 (0.03)2.30.11 (0.08)0.960.57 (0.79)
Figure 8.

Air temperature and simulated snow depth at the valley bottom.

[26] Not surprisingly, the HYDUS-1D model with the freezing and thawing module reproduced the same results as that without the freezing and thawing module. As a matter of fact, no freezing of soil profile can be expected when all the soil temperature records are above zero. Note that the snow routine of the public version of HYDRUS-1D has the capability to halt seepage (lowering conductivity) in the subsurface when the soil is frozen (Figure 6). As can be seen in Figure 7, however, no freezing was simulated at the 50 cm depth. Additional analysis conducted at a different location in the Deep Creek Watershed also showed no freezing of soil at 20 cm depth—all the simulated and observed soil temperature values were above zero.

[27] Figures 10 and 9 compare the distribution of the simulated and measured water content at two depths in the soil profile at the valley bottom. Soil moisture correlations were generally found to be good especially in the top layer (0.84). As indicated by relatively small AE values (Table 4), model biases in predicting soil moisture from mean VGM parameters at depths of 10 cm and 50 cm were also generally small (0.009 and −0.04, respectively). However, a significant mismatch was noted at the 50 cm depth between measured and observed moisture content. This can possibly be attributed to the significant spatial variability of soil moisture and/or the degree to which the sensors are in contact with the soil material. Note that the correlation coefficient estimated at the 50 cm depth (r = 0.57) is higher than values reported in previous soil moisture modeling studies such as Hejazi and Woodbury [2011]. However, additional effort was expended here to see if results can be improved by inverse estimation of soil hydraulic parameters from measured transient soil moisture data. To this end, the relatively simple local optimization approach, which is implemented into the HYDRUS 1D code was used. The required upper and lower bounds of the VGM parameters were defined from ROSETTA outputs as μ ± 4 × σ, where μ and σ are average and standard deviation, respectively. The upper and lower bounds were defined based on previous Bayesian inverse modeling study by Scharnagl et al. [2011]. The calibrated VGM parameters, for the lower two layers, as well as the improvement on soil moisture simulation results (r = 0.79) are shown within Tables 2 and 4, respectively. It is, however, important to note that the gradient-based optimization method of HYDRUS-1D is highly sensitive to the initial values of the VGM parameters, and thus the calibrated parameters indicated in Table 2 may not be the global minimums—this algorithm is used here only to help us improving soil moisture simulation results at the 50 cm depth. Details on this and other more robust global optimization techniques can be found in Simunek et al. [2012].

Figure 9.

Simulated versus observed soil moisture at 50 cm depth, valley bottom.

Figure 10.

Simulated versus observed soil moisture at 10 cm depth, valley bottom.

[28] Further to the comparative analyses made at the valley bottom, a HYDRUS 1D run was completed at the location of the second weather station on Silver Star Mountain in order to assess the degree to which the field site results can be extrapolated to the other areas of the basin. The contrasts in land cover and soil type at the location of the two weather stations can be seen in Figure 4 and Tables 2 and 3. Figures 11 and 12 compare the distribution of the simulated versus measured water content and soil temperature, respectively, at 20 cm depth over a one year experimental period (July 2011 to July 2012). Statistical analyses show very good performance of the model in this area of the basin as well (Table 5) highlighting the robustness of the methodology developed in this study. Note that the VGM parameters used in the model are estimated using pedotransfer functions; indicating that ROSETTA can be taken as a reliable method for estimating soil hydraulic properties.

Figure 11.

Simulated versus observed soil moisture at the Silver Star Mountain at 20 cm depth.

Figure 12.

Simulated versus observed soil temperature at the Silver Star Mountain at 20 cm depth.

Table 5. Measured Versus Simulated Variables at Silver Star Mountain
Depth (cm)Average ErrorRMSECorrelation
Soil TemperatureSoil MoistureSoil TemperatureSoil MoistureSoil TemperatureSoil Moisture
200.18−0.021.20.0020.980.6

4.3. Transient, Spatially Varied Groundwater Recharge

[29] After evaluating the performance of HYDRUS-1D using field data and ROSETTA derived VGM parameters, groundwater recharge was simulated at various locations in the Deep Creek watershed by making use of the long-term gridded climate data and ROSETTA derived VGM parameters. The various locations termed here as representative points were determined after discretizing and combining the HYDRUS-1D input variables into 500 m × 500 m cells in ArcGIS™. For each of the 14 HYDRUS columns shown in Table 6, a total of 46 years and four months simulation was accomplished. Twenty one years and four months of which are used to estimate model initial condition. There are two options in HYDRUS for supplying initial conditions: Pressure head or moisture content. In this study, pressure head is used as initial condition for all soil materials in the flow system as it is known to exhibit lesser spatial variability than that of moisture content. The initial condition was estimated by setting the initial pressure head in Fall (of 1960) and running the model for 21 years. Soil moisture content in Fall is generally believed to be at the wilting point and soil moisture conditions and groundwater recharge are considered to stabilize after a 21 years model spin-up.

Table 6. Representative Locations and IDs for Model Inputs
Representative Area (#)UTM_EAST (m)UTM_NORTH (m)Climate IDSoil CodeLand UseArea Coverage % of Total Area
1343,586.8915,592,329.645440142EBYAgriculture45.4
2343,096.175,593,010.22430141BDVAgriculture
3342,021.55,595,030.61520137BDVAgriculture
4342,274.135,595,603.6380139AMGAgriculture
5341,877.135,585,964.09570140BDVAgriculture
6340,848.045,605,693.08180133CYVForest42.6
7341,146.325,608,663.41120133HOSForest
8338,150.895,589,981.43500132TUNForest
9345,158.835,584,603.06590147CLPForest
10338,717.95,588,885.09520.133HSTForest
11346,739.005,584,908.00580150CNNForest
12346,311.835,581,980.19640150SNWBarren surface0.1
13338,304.935,580,400.64690134AMGRangeland3.5
14335,198.565,584,724.03610127GGIRangeland

4.3.1. Temporal Variation of Recharge

[30] The daily recharge results were aggregated into monthly and annual time series. Long-term average monthly recharge results are analyzed to study seasonal variation at various parts of the watershed (Table 7).

Table 7. Average Monthly and Annual Recharge (mm) at Various Parts of the Watershed
 Recharge (mm)
Valley BottomWestern DCSouth DCEastern DCNorth DC
Annual35.290.019152.066.3
% Precipitation7.414.0521.010.5
January3.34.00.76.54.2
February12.07.118.611.6
March11.537.8472.632.9
April3.426.84.941.212.5
May1.46.82.88.92.2
June0.72.41.64.40.6
July0.41.01.11.90.2
August0.30.40.70.90.1
September0.20.20.50.50.1
October0.10.10.40.40.0
November0.10.50.31.70.2
December1.72.80.44.31.5

[31] The monthly data were further analyzed by plotting the three major water balance components as shown in Figure 13. High recharge values were generally estimated in February, March, and April, because of the lagged response to higher precipitation combined with spring snow thaw. This pattern was further explained by simulating snow depth and runoff in the different representative areas within the study area.

Figure 13.

Average monthly variations in recharge, precipitation, and evapotranspiration.

[32] Figures 14 and 15 show monthly averaged snow depth and runoff variation throughout a year in the valley bottom. The snow pack plays a significant role on the groundwater recharge pattern. The peak months for snow depth were simulated in December, January, and February. The snow started to melt in March, as evapotranspiration started rising, causing runoff to be initiated (Figure 15). The snow pack then progressively decreases to zero in spring and summer until another snow starts to accumulate in November. The recharge simulated in spring and summer is thus attributed to snow melt.

Figure 14.

Average monthly variations in snow depth, recharge, and evapotranspiration.

Figure 15.

Average monthly variations in runoff and snow depth.

[33] Temporal recharge analysis was further conducted by using annual recharge results. Any informative recharge estimate should give an indication of how recharge varies over time. Figure 16 shows annual variation of recharge, along with precipitation and evapotranspiration, at the valley bottom. Analysis of the result shows a wide variation, ranging from 0.2 to 17% of annual precipitation over the 25 years simulation period. This is a significant variation over the years, caused by antecedent soil moisture condition and climatic conditions. It illustrates the common flaw of assigning a constant percentage of precipitation throughout the simulation period. For instance, the recent work in the Deep Creek watershed by Ping et al. [2010] used a groundwater model to estimate recharge as a fitting parameter. They assumed initial value of recharge (5%) from similar works in North America which has the same climate as the Okanagan basin, and calibrated this value to 5.5%. However, similarity in climate is not a sufficient condition for similarity in recharge estimates. To this end, a relatively simple sensitivity analysis was conducted at the location of the HOBO weather station in the valley bottom by varying land use, soil type, and water table depth, while keeping the climate data the same. The actual land use, dominant soil type and lower BCs at this particular location are pasture land, silty clay loam, and free draining, respectively (sections 'Land Use Data'–2.5), whereas synthetic situations of clay soil, alfalfa crop, and seepage lower BCs were assumed to study the magnitude of change in the recharge results. The simulation results show that average annual recharge, in the latter case, would be about 75% less than that estimated using the actual condition (53.3 mm/year). This significant difference in recharge clearly shows the fact that the two study areas need to have similar soil profiles and land uses as well as other model input data in order to transpose parameters/model results from one area to the other, if possible at all. Besides, recharge also exhibits significant spatial variation across the Deep Creek Watershed.

Figure 16.

Temporal variation of annual recharge at the valley bottom.

4.3.2. Spatial Distribution of Recharge

[34] The combined model inputs were used to produce 25 years of daily recharge estimates at each of the 14 representative points in the Deep Creek watershed (Table 6). The recharge results from each of the 14 unique HYDRUS columns were then assigned to all areas in the watershed that have similar input data. This approach, which is similar to that of Liggett and Allen [2010] and Jyrkama et al. [2002], is used here to produce raster maps of recharge. Figure 17 shows a map of long-term average annual recharge throughout the Deep Creek watershed.

Figure 17.

Spatial map of average annual recharge.

[35] Long-term average annual recharge values estimated at different parts of the watershed are shown in Table 7. The results indicate significant spatial variation across the watershed. For instance, the mean recharge at the valley bottom was estimated to be 35.2 ± 30.5 mm/year, whereas a higher recharge amount estimated at 152.1 mm/year ± 61.5 mm/year was simulated in the mountains. The large differences in recharge can be accounted for temporal and spatial variations in antecedent soil moisture and climatic conditions, as well as for the contrasts in soil hydraulic parameters.

5. Discussion and Conclusions

[36] This study has produced detailed temporally and spatially varied groundwater recharge values throughout the Deep Creek watershed in British Columbia, Canada. The recharge modeling was undertaken by making use of a Richards equation based finite element code (HYDRUS-1D), ArcGIS™, ROSETTA, in situ observations of soil temperature and soil moisture, and a long-term gridded climate data.

[37] The HYDUS-1D model, both with and without a freezing and thawing module, was first used to simulate soil temperature, snow pack, and soil moisture over a one year experimental period. Comparison between simulated results from both versions of HYDRUS-1D and in situ observations of soil temperature and soil moisture at a field station were made by using various statistical measures. An analysis of the results shows both versions of HYDRUS-1D reproduce the observed data to the same degree, proving our hypothesis that rigorously accounting for freezing and thawing will not change subsurface water and heat movement in our semiarid study area. The statistical comparisons were performed at two different locations in the Deep Creek watershed (Valley bottom and Silver Star Mountain) in order to assess the degree to which the field site results can be extrapolated to the other areas of the basin with different soil type and land cover. Results of the statistical analyses show good performance of the model at both locations suggesting a robustness of the methodology developed in this study. The results also support conclusions made by previous studies about the code deployed to determine unsaturated hydraulic properties; ROSETTA is a reliable method for estimating soil hydraulic properties.

[38] After evaluating the performance of HYDRUS-1D and ROSETTA at our experimental sites, the HYDRUS-1D code was coupled with ArcGIS™ to produce spatially and temporally variable recharge maps throughout the Deep Creek watershed. Fourteen unique HYDRUS columns were identified across the watershed after discretizing model inputs into 500 m × 500 m cells in ArcGIS™. A total of 46 years and four months simulation was completed at each of the 14 columns; and the recharge results from each column were used to produce a raster map of recharge. Averaged spatially and temporally, the mean annual recharge throughout the Deep Creek watershed was estimated at 77.8 ± 50.8 mm/year. As evident from the large standard deviation, recharge in the Deep Creek watershed was found to exhibit significant spatial and temporal variation.

[39] It has been discussed earlier that groundwater recharge estimation has been attempted in the Okanagan Basin and other parts of Canada by making use of the HELP code. However, HELP consists of several empirical relationships which may not be appropriate in some applications [Schroeder and Ammon, 1994]. The limitations are even more pronounced in semiarid areas like the Okanagan Basin where upward fluxes can be high, because HELP assumes that water below evaporative zone simply drains to the base of a soil column without accounting for upward fluxes. HELP is also limited by BCs as well as spatial and temporal discretization options, and thus cannot simulate highly variable fluxes near boundaries. In addition to these limitations, previous studies that used HELP for recharge estimation [Toews and Allen, 2009; Jyrkama and Sykes, 2007], did not attempt to verify model performance in their study area. On the other hand, HYDRUS-1D, being a Richards equation based finite element code, provides flexibility in defining physically realistic BCs, has the option for variable temporal and spatial discretization and allows water to move up or down depending on the pressure head gradient. Although as stated by Jyrkama and Sykes [2007], direct comparison of model estimated recharge to field observations are challenging and expensive, this current study has conducted one year field study at our experimental sites and verified that HYDRUS-1D can, in fact, simulate heat and water movement in the vadose zone, and thus groundwater recharge. Unfortunately, HELP has not been used in the Deep Creek Watershed to quantitatively compare results although it has been used in Vernon area (south of the Deep Creek Watershed) where average annual recharge was estimated at 109 mm/year [Liggett and Allen, 2010]. To their credit, Liggett and Allen [2010] acknowledged the fact the HELP over predicts recharge. Note that Liggett and Allen [2010] used the most recent version of HELP (Version 3.80D). While their result is significantly higher than the mean annual recharge estimated at the southern part of the Deep Creek watershed (19 mm/year) as well as the watershed average (77.8 mm/year), it closely compares to the values estimated at the mountainous eastern part of the study watershed (Figure 17).

[40] The methodology developed here is expected to be implemented in various watersheds across the Okanagan Basin. The results so produced may eventually play a role in improving water resource management and policy in the province (British Columbia, Canada). Furthermore, it could also be taken as a base model to study climate change impacts on groundwater recharge. Note that previous climate change studies in the Okanagan Basin [Toews and Allen, 2009] used HELP without any attempt of model performance evaluation, notwithstanding its inherent limitations. Thus, climate change impact results from this previous study and similar other studies, such as Jyrkama and Sykes [2007], need to be interpreted with caution.

Acknowledgments

[41] This study was financially supported by Natural Sciences and Engineering Research Council of Canada (NSERC) and Canadian Water Network (CWN). We are grateful to Adam Wei and Craig Nichol, professors at UBCO, for their valuable discussion regarding the complex aquifer of the study watershed and other information that were necessary in deciding the location of the HOBO™ weather stations. We would also like to thank Mike Oberding, Mesfine Fentabil, and Getnet Dubale for their assistance during the field works.

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