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Comparison of Two Tile-Drain Methods in SWAT via Temporal and Spatial Testing for an Iowa Watershed
Tassia Mattos Brighenti1,*, Philip W. Gassman1, Jeffrey G. Arnold2, Jan Thompson3
Published in Journal of the ASABE 66(6): 1555-1569 (doi: 10.13031/ja.15534). 2023 American Society of Agricultural and Biological Engineers.
1Center for Agricultural and Rural Development, Iowa State University, Ames, Iowa, USA.
2Grassland Soil and Water Research Laboratory, USDA ARS, Temple, Texas, USA.
3Department of Natural Resource Ecology and Management, Iowa State University, Ames, Iowa, USA.
*Correspondence: tassiab@iastate.edu
The authors have paid for open access for this article. This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License https://creative commons.org/licenses/by-nc-nd/4.0/
Submitted for review on 13 January 2023 as manuscript number NRES 15534; approved for publication as a Research Article and as part of the “Advances in Drainage: Selected Works from the 11th International Drainage Symposium” Collection by Community Editor Dr. Zhiming Qi of the Natural Resources & Environmental Systems Community of ASABE on 1 October2023.
Mention of company or trade names is for description only and does not imply endorsement by the USDA. The USDA is an equal opportunity provider and employer.
Highlights
Abstract. Tile drainage is a common practice to increase agricultural productivity in regions with high water tables. Ecohydrological models, such as the Soil and Water Assessment Tool (SWAT), are key tools used to simulate these subsurface drainage structures and their corresponding management effects on water balance. This study is an investigation of the application of two different SWAT tile-drain calculation methods (empirically and physically-based) in simulating the streamflow of the Des Moines River Basin (DMRB), central Iowa, USA. The model was calibrated for the DMRB outlet and validated across 24 monitoring stations. We found that both empirical function and physically-based methods have satisfactory model performance for monthly and daily calibration (NSE > 0.5; KGE > 0.6; Pbias < ±25%). The daily validation process showed that the physically-based method had more accurate spatial variability in representing the hydrological processes and a better representation of the annual tile-drain flow. The findings in this study reinforce the importance of spatial validation in assessing model performance and ensuring its suitability for practical applications.
The "Corn Belt" region is an important agricultural area in the central United States, characterized by extensive production of corn and soybean row crops. Large-scale land alterations in this area have generated natural landscape loss (e.g., reduction of wetland areas), water pollution (the northern Gulf of Mexico seasonal oxygen-depleted hypoxic zone), and other environmental problems including eutrophication, fish-kills and harmful impacts on drinking water supply (Christianson et al., 2013; Gassman et al., 2017; Schilling and Jones, 2019; INRS, 2023). Much of this region's agricultural productivity depends on tile drainage to remove water from the root zone to improve field access and reduce plant stress caused by water excess (Schilling et al., 2019; Jame et al., 2022). However, tile drainage networks are key conduits of nitrate and phosphorus to Corn Belt stream systems, contributing directly to the region’s pervasive water quality problems (Gassman et al., 2017; Schilling and Jones, 2019; Schilling et al., 2019). Thus, investigating ways to simulate these structures is fundamental to our understanding of the impacts of watershed management and hydrology.
A well-established and widely used tool that can simulate tile drainage implementation is the Soil and Water Assessment Tool (SWAT), a watershed-scale ecohydrological model (Arnold et al., 1998, 2012; Williams et al., 2008; Krysanova and White, 2015; Bieger et al., 2017). The SWAT model has been used worldwide to evaluate an extensive suite of water resource problems across a wide range of watershed scales and environmental conditions (Tuppad et al., 2011; Gassman et al., 2014; Tan et al., 2019, 2020; CARD, 2023). The model has also been used in dozens of applications within the Corn Belt region, including studies that accounted for the effects of tile drainage (e.g., Du et al., 2005; Moriasi et al., 2012, 2013, 2014; Kalcic et al., 2015; Gassman et al., 2017; Guo et al., 2018; Mehan et al., 2019).; Schilling et al., 2019).
| Table 1. SWAT model studies that have tested/applied the modified method using the Hooghoudt and Kirkham equations. | |||||
| Study | Basin Size (km2) | Time Step | Calibration | Variables Analyzed | Number of Stations for Variable |
| Moriasi et al. (2012) | 775 | daily/monthly | manual | streamflow | 1 |
| Moriasi et al. (2013) | plot scale [a] | monthly | automatic | nitrate | 1 |
| Moriasi et al. (2014) | plot scale [a] | monthly | automatic | tile flow, nitrate | 1 |
| Kalcic et al. (2015) | 56 and 45 | daily | not performed [b] | streamflow, nitrate, total phosphorus, and sediment | 2 |
| Boles et al. (2015) | 47 | daily/monthly | manual | streamflow, tile flow, nitrogen | 1 |
| Bauwe et al. (2016) | 1.9 | daily/monthly | automatic | streamflow | 1 |
| Ikenberry et al. (2017) | 2.3 and 3.1 | daily | automatic | streamflow, nitrogen | 1 streamflow 1 nitrogen |
| Merriman et al. (2018) | 125 | daily/ monthly | automatic | streamflow, phosphorus concentration | 3 streamflow 3 phosphorus |
| Guo et al. (2018) | 518 (69 [c]) | monthly | automatic | tile flow, nitrate load in tile flow, streamflow | 1 streamflow 2 tile flow |
| Mehan et al. (2019) | 46.1 | daily | automatic | streamflow, total nitrogen and phosphorus, mineral prosperous | 1 |
| Wang et al. (2019) | 40,000 | monthly | automatic | streamflow and nitrate concentration | 2 streamflow 2 nitrate |
| Bauwe et al. (2019a) | 3041 | daily | automatic | streamflow | 8 |
| Bauwe et al. (2019b) | 3041 | daily | automatic | streamflow, phosphorus concentration | 8 streamflow 5 phosphorus |
| Acero Triana and Ajami (2022) | 21,600 | daily | automatic | streamflow, potential evapotranspiration, lake level | 23 streamflow 1 lake level |
[a] 13.5 by 15.0 meters. [b]The model parameters were not calibrated because of the short period of record of available; however, the available measured data is used for a validation process. [c]Drainage area of the streamflow station used during the analysis. | |||||
The SWAT model offers two distinct methods to calculate flow through subsurface tiles: an empirical method defined as the default/original option (Du et al., 2005) and a modified physically-based Hooghoudt and Kirkham equations method (Moriasi et al., 2012). The original method is an empirical function composed of four main parameters: tile-drain depth, the time required to drain the soil to field capacity, tile-drain lag time, and an impervious layer depth. This method creates an impermeable layer and simulates the tile flow on days when the height of the water table above the impermeable layer is greater than the height of the tile above the impermeable layer (Du et al., 2005; Boles et al., 2015). The physically-based modified version simulates tile flow as a function of the lateral saturated hydraulic conductivity of the soil, profile depth, water table elevation, drain spacing, drain size, and depth. This method uses parallel drain systems and is sensitive to the depth and spacing of the drains (Moriasi et al., 2012). The choice of tile-drain method may influence the magnitude and timing of water discharges, sediment transport, and nutrient losses in watershed simulations.
A total of 83 studies are indexed in the SWAT model database (CARD, 2023) that report tile drain structures in some context, based on a search using the keyword “tile-drain” (excluding SWAT+ studies). Of those 83 studies, 61 were published between 2012 and 2023, which is the period that the Hooghoudt and Kirkham equations method was available to SWAT users. The majority of those studies used the empirical function for calculating tile flow. Fourteen studies have tested/applied the Hooghoudt and Kirkham equations (table 1, CARD, 2023). The underlined data in table 1 shows the studies that compare the two methods. Of those studies, Kalcic et al. (2015) report the use of both methods at a daily scale; however, no comparison of differences in efficiency is discussed other than the difficulty of capturing peak flow events by the modified method. Boles et al. (2015) report that the Hooghoudt and Kirkham equations resulted in decreased peaks for flow and longer storage time. Guo et al. (2018) compared the methods at a monthly scale for the tile flow, nitrate load in tile flow, and streamflow variables. For streamflow, they found that the results were slightly better using the original method. However, the modified method improved tile flow simulations for two reasons: (1) the original method did not simulate tile flow when the water table was lower than the tile depth, and (2) the modified method could simulate the process by the Hooghoudt equation. The modified method also simulated nitrate transport in the tile flow more accurately (Guo et al., 2018). It is important to note that all of these model applications (Kalcic et al., 2015; Boles et al., 2015; Guo et al., 2018) were performed for relatively small watersheds with drainage areas = 69 km2 (table 1). Wang et al. (2019) did not report significant differences between the two methods in monthly flow simulations for a 40,000 km2 watershed (table 1). However, they found that the modified method resulted in an improved match between simulated and measured nitrate loads.
All of the studies in table 1 reported satisfactory hydrologic results for SWAT calibration of the variables analyzed using either daily and/or aggregated monthly time steps. The manual calibration used in a small subset of the studies was justified on the basis of literature values, and automatic calibration was executed via optimization algorithms such as SUFI-2 (Abbaspour et al., 1997). Although the Hooghoudt and Kirkham equations method has produced accurate basin streamflow outlet results, there have been no reports on uncertainty analysis nor spatial variability efficiency (Moriasi et al., 2012, 2013, 2014; Boles et al., 2015; Kalcic et al., 2015; Bauwe et al., 2016; Guo et al., 2018; Mehan et al., 2019).
 |
| Figure 1. Location of the Des Moines River Basin in Iowa and Minnesota, U.S.; the Des Moines Metropolitan Statistical Area; and streamflow monitoring stations. |
This study focused on analyzing the impact of each tile-drain method on SWAT model streamflow and water balance simulations for a large central Iowa watershed. The study was performed in the context of the Iowa UrbanFEWS project (Thompson et al., 2021; Brighenti et al., 2022a,b), which was initiated to evaluate opportunities for table food (especially fruit and vegetable) production in the Des Moines (Iowa) Metropolitan Statistical Area (DMMSA; fig. 1). Most of the SWAT simulation analyses presented here were focused on this six–county area (Brighenti et al., 2022b). However, accurate replications of upstream processes, including tile drain impacts, are needed to verify the overall accuracy of the SWAT simulations. Thus, specific objectives include the implementation of accurate tile-drain locations, the execution of temporal (daily and monthly) calibration using an optimization algorithm, the execution of spatial validation via multiple monitoring stations, and uncertainty analysis evaluation.
Study Area
The study area is composed of the Des Moines River Basin (DMRB) (31,892 km2), which drains a small portion of southern Minnesota and much of north central and central Iowa (fig. 1). The land use consists primarily of crop land (table 2). The major soil types are Udolls (more or less freely drained soils within the Mollisols order), Aquolls (wet soils within the Mollisols order), and Udalfs (soils with a udic moisture regime within the Alfisols order) (USDA-NRCS, 2021). The climate is Dfa following the Köppen classification (Peel et al., 2007), corresponding to a humid continental climate with hot summers and cold winters. Subsurface tile-drains are distributed across most of the subwatersheds. According to USDA census data, the average percentage of overall landscapes that are managed with tile drainage is 54% (USDA-NASS, 2022). We used the Parameter-Elevation Relationships on Independent Slopes Model (PRISM) dataset to obtain daily observed precipitation and climate data (PRISM, 2022). Long-term streamflow data are available for the entire watershed in the USGS database (<https://waterdata.usgs.gov/nwis>). A total of 25 monitoring gauges were selected for the study area (fig. 1) with time-series data that overlapped the 2001-2010 simulation period.
| Table 2. Land use in the Des Moines River Basin. The distribution is based on land use maps composition from 2006–2012 (HAWQS, 2020). | |
| Land Use Type | Land Use Percentages |
| Rotation corn–soybean | 56% |
| Corn | 13% |
| Soybean | 1% |
| Hay/Alfalfa | 8% |
| Grasses | 6% |
| Urban | 8% |
| Forest | 5% |
| Wetlands/Water | 3% |
Materials and Methods
Study Design
We evaluated aggregated monthly and daily streamflow (2001-2010), and annual averages for surface runoff and baseflow (the baseflow consists of tile flow, lateral flow, and ground water flow from the shallow aquifer) as a function of the two tile-drain flow calculation methods (fig. 2). The SWAT models (Version 2012/Rev 685) used for comparisons in this study were developed from a previous model setup identified as “Baseline 10” by Brighenti et al. (2022a). Baseline 10 was one of ten different SWAT models that were tested for three basins in central Iowa, including the Des Moines River Basin (DMRB), which serves as the study region in this analysis (fig. 1). This model was the result of successive improvements representing key input data, including the location and parameterization of tile drains, nitrogen fertilizer application rates, and the selection of the runoff curve number (RCN) method. The latter was denoted by Brighenti et al. (2022a) as the “alternative RCN method” which is computed on the basis of evapotranspiration rather than soil moisture. The Baseline 10 setup represents calibration based on real system data (soft-calibrated), meaning important initial components of the model, such as the evaluation of known infrastructure, agreement with known hydrologic balance, and the reasonability of parameter values based on the physical characteristics of the simulated system are satisfied.
The model chain for this study follows two separate paths (fig. 2): (1) model calibration and validation performed with the SWAT default empirical equation (original); and (2) the use of the Hooghoudt and Kirkham equations within the calibration and validation process (modified). The simulation period for both calibration/validation paths ranges from 2001 to 2010. The temporal calibrations were performed using automatic calibration methods (i.e., SUFI-2) provided via the SWAT-CUP software (https://swat.tamu.edu/software/swat–cup/) (fig. 1 – calibration gauge). Spatial validation was then performed without any further parameter adjustments for both the original and modified tile drain methods in successive simulations using 24 upstream gauges (fig. 1 – validation gauges). The input parameter range for the Hooghoudt and Kirkham equations was established via literature review. We selected parameters from previous studies (Moriasi et al., 2012, 2013; Boles et al., 2015) and chose a combination with the best statistical performance. The final two calibrated and validated models were assessed via statistical performance for streamflow (NSE, KGE, Pbias) and hydrological agreement (baseflow, surface runoff) using graphical comparisons.
 |
| Figure 2. Methodological approach for the original and modified tile-drain method applications. |
SWAT Model
SWAT is a continuous and physically-based ecohydrological model developed to explore the effects of climate and land management practices on hydrology and pollutant transport (Arnold et al., 2012). The hydrologic component is based on the water balance equation in the soil profile that accounts for precipitation, surface runoff, infiltration, evapotranspiration, lateral flow, percolation, and groundwater flow processes. Hydrological Response Units (HRUs) serve as the basic model simulation units in SWAT, which are defined as homogeneous areas comprised of unique land cover, soil type, slope, and management within a given subbasin (Neitsch et al., 2011).
SWAT can also simulate the water path through tile drains in the soil profile using the two previously described options. In the default method (Du et al., 2005), tile drainage is simulated at the HRU level and is computed as a function of tile-drain depth (DDRAIN), the time required to drain the soil to field capacity (TDRAIN), lateral flow time, tile-drain lag time (GDRAIN), and an impervious layer depth (DEP_IMP). To use this equation, the user should insert ITDRN.bsn = 0. Tile drainage occurs when the water table is above the depth of the drains. The amount of water in a drain is given by equation 1:
(1)
(2)
where
tilewtr = the amount of water removed from the layer on a given day by the tile-drainage (mm H2O)
hwtbl = height of the water table above the impervious zone (mm)
SW = water content of the profile on a given day (mm H2O)
FC = field capacity water content of the profile (mm H2O)
tilettime = exponential of the tile flow travel time.
The second approach (Moriasi et al., 2012) utilizes the physically-based Hooghoudt and Kirkham equations that depend on the maximum surface depressional storage and requires additional inputs such as drain spacing and drainage coefficient. The Hooghoudt equation (eq. 3) is used for water tables below surface depressional storage or surface, and the Kirkham equation (eq. 4) is used to compute the ponded surface drainage flux when the water table rises to the soil surface. To use the Hooghoudt and Kirkham equations, the user should select ITDRN.bsn = 1, and determine the appropriate RE, SDRAIN, and DRAIN_CO variables for the .sdr files (eqs. 3, 4, and 5). The LATKSATF is a multiplication factor used to determine the lateral saturated hydraulic conductivity of the soil (K) using the SWAT saturated conductivity input value for each soil layer and soil type. Pump capacity for subsurface irrigation (PC, mm/h) is used only in the event of subirrigation.
(3)
(4)
(5)
where
q = drainage flux (mm/h)
m = midpoint water table height above the drain (mm)
Ke = effective lateral saturated hydraulic conductivity (mm/h)
SDRAIN = distance between drains (mm)
DDRAIN = depth from the soil surface to the drains (mm)
DRAIN_CO = drainage coefficient (mm/d)
C = ratio of the average flux between the drains to the flux midway between the drains
de = substituted for d (height of the drain from the impervious layer) in order to correct for convergence near the drains (mm)
RE = tile-drain radius (mm)
g = dimensionless factor, which is determined using an equation developed by Kirkham (1957); g is computed as a function of d, SDRAIN, m, the actual depth of the profile (mm), and the radius of the tile tube (mm)
t = average height of the water stored on the surface (mm).
SWAT Model Setup and Tile-Drain Configuration
The SWAT model Baseline 10 was used as the initial model setup, with the HAWQS platform serving as the primary source of land use, soil, topographic, hydrography, operation management schedule, and weather data for the modeling system as described in Brighenti et al. (2022a). HAWQS uses a combination of data from the 2006 National Land Cover Database (NLCD) and, for agricultural land uses, the 2011/2012 Cropland Data Layer (CDL) for its default land use input data (HAWQS, 2020). The distribution of fertilizer application rates and timing were based on previous data reported by Gassman et al. (2017). The Penman-Monteith equation was used to calculate potential evapotranspiration (ET), and the channel flood routing routine was the variable storage coefficient method. The alternative RCN approach was used to calculate the surface runoff (Kannan et al., 2008). This RCN method calculates the retention parameter as a function of ET using a CN coefficient (CNCOEF), which was set to 0.75 for this study based on previous research reported by Gassman et al. (2017) and Brighenti et al. (2022a).
The configuration of tile drainage within the SWAT models was based on tile drain maps provided by Valayamkunnath et al. (2020). These researchers developed a raster product with 86% confidence in tile-drain locations (fig. 3a). We used the 12-digit subbasin discretization and land use map categories to access this spatial tile-drain distribution. The tile locations were defined according to: (1) the percentage of the tile-drained area for each subbasin as determined by overlays of the 12-digit subbasin shapefile and the tile-drain raster file (fig. 3b), and (2) the tile-drained area was then distributed among agricultural land uses in a given 12-digit subbasin, giving priority to cropland planted in soybeans and corn (fig. 3c). The final percentage of cropland managed with tile drains across the DMRB is 55.6%.
 |
| Figure 3. (a) Spatial distribution of tile drainage (shown as green) in the study area, source: Valayamkunnath et al. (2020); (b) tile-drain zoom-in for the 12-digit subbasin map; and (c) representation of the tile drain and land use map overlap. |
Calibration and Validation Process
The SWAT model was employed to simulate the DMRB hydrological processes, and parameters related to streamflow and tile-drain characteristics were adjusted according to the respective methods being compared. Calibration and validation are standard procedures for adapting and verifying the accuracy of an ecohydrological model, where a suite of model parameters are adjusted based on comparisons with observed data (Rossi et al., 2008; Arnold et al., 2012). The calibration process can follow two paths: (1) hard data calibration using either manual or automatic calibration (Arnold et al., 2012) to compare simulated output with corresponding observed data, and (2) real system data or soft data calibration, which combines expert knowledge, literature information, agreement with known hydrologic balance, and reasonability of parameter values based on the physical characteristics of the simulated system (Seibert and McDonnell, 2002; Arnold et al., 2015; Brighenti et al., 2022a). Automatic calibration relies on optimization techniques (e.g., SUFI-2 (Abbaspour et al., 2004, 2007), GLUE (Beven and Binley, 1992), or DREAM (Vrugt, 2016)) to find an optimal set of parameters when comparing observed and simulated data. In this study, we used the Brighenti et al. (2022a) Baseline 10 soft-calibrated SWAT model and proceeded with the automatic calibration of the SWAT model for the original and modified tile-drain equations (fig. 2). The calibration was executed using the SUFI-2 algorithm and considering the streamflow data of the station closest to the DMRB outlet (fig. 1).
Uncertainty is structural and unavoidable during hydrological modeling (Efstratiadis and Koutsoyiannis, 2010). Thus, equifinality – that multiple combinations of model parameters and inputs can lead to similar model outputs – makes it challenging to uniquely identify true model structure or parameter values (Vrugt et al., 2009; Efstratiadis and Koutsoyiannis, 2010; Her and Seong, 2018; Khatami et al., 2019). A way to constrain equifinality is to target the epistemic errors in the modeling chain and not consider the calibration as a black-box approach (Efstratiadis and Koutsoyiannis, 2010). In order to not rely solely on the automatic algorithm for selection of parameters, we established a systematic approach to pursue model consistency with the real system by: (a) establishing realistic water balance proportions (i.e., the dominance of baseflow) and seasonal variability, (b) accurate simulation of corn and soybean yields, which represent 70% of the total DMRB area, (c) updated tile-drain locations (Brighenti et al., 2022a); (d) expert judgment and knowledge to define the parameters TDRAIN (1200 mm), DDRAIN (24 h), GDRAN (48 h), and DEP_IMP (1200 mm) based on real system behavior, target literature, and previous sensitivity test (Gassman et al., 2017); (e) long term temporal representation (= 10 years) and appropriate spatial variability of the monitoring streamflow data (25 gauges); and (f) use a range of parameters in the validation process to avoid inconsistencies with the model physical representation.
The set and range of model parameters used in the calibration process (table 3) were based on literature (Moriasi et al., 2012; Moriasi et al., 2013; Boles et al., 2015) and SWAT model expertise. The calibration was composed of one iteration of 400 runs to develop the best parameters, best ranges, and total uncertainty bands. Model validation was based on the Proxy-Catchment Test hypothesis described by Klemes (1986), with calibration in one basin and validation in another (spatial validation) for basins of similar land use. Once calibrated, the SWAT model was validated using independent
datasets from 24 nested basins to assess its predictive capability (figs. 1 and 2). We used 10% of the best parameters obtained during calibration (40 out of 400 runs based on NSE results) for validation.
| Table 3. Parameters used during daily calibration process. The methods used to adjust the parameter values in SUFI-2 are represented as the first letter before the parameter name (r, v, and a); the letter v represents replacing the existing parameter value, a is adding a given value to the existing parameter value, and r is multiplying (1 + a given value) by the existing parameter value. | ||
| Parameter | Calibration Range | |
| Min. | Max. | |
| Initial SCS runoff curve number for moisture condition II: r__CN2.mgt | –0.2 | 0.2 |
| Baseflow alpha factor: v__ALPHA_BF.gw | 0.001 | 0.5 |
| Manning's "n" value for the main channel: v__CH_N2.rte | 0.01 | 0.02 |
| Soil evaporation compensation factor: v__ESCO.hru | 0.6 | 1 |
| The delay time: v__GW_DELAY.gw | 0 | 60 |
| Groundwater "revap" coefficient: v__GW_REVAP.gw | 0.02 | 0.2 |
| Threshold depth of water in the shallow aquifer for “revap” or percolation to the deep aquifer to occur: v__REVAPMN.gw | 0 | 1000 |
| Surface runoff lag coefficient: v__SURLAG.bsn | 0.01 | 24 |
| Distance between drains: v__SDRAIN.sdr | 7700 | 27000 |
| Soil lateral saturated hydraulic conductivity factor: v__LATKSATF.sdr | 1 | 3.8 |
| The daily drainage coefficient: v__DRAIN_CO.sdr | 13 | 48 |
| Tile-drain radius: v__RE.sdr | 25 | 50 |
Statistical Analysis
To evaluate the difference between the Flow Duration Curves (FDC) we applied the two-sample Kolmogorov-Smirnov test (k-s), a nonparametric hypothesis test that evaluates the difference between distributions of two sample data vectors; smaller test values indicate more similarity between flow duration curves (Feller, 1948). The Nash-Sutcliffe efficiency statistic (NSE) (Nash and Sutcliffe, 1970) is one of the most widely used objective functions for hydrological modeling in general and for SWAT model applications specifically (Tuppad et al., 2011; Gassman et al., 2014; Tan et al., 2019; Chen et al., 2020). It is a normalized statistic that determines the relative magnitude of residual variance compared to measured data variance (eq. 6). NSE values range between - 8 to 1, where 1 is a perfect simulation and observations below zero represent unacceptable model performance. According to Moriasi et al. (2007, 2015), an NSE = 0.50 is satisfactory for monthly and daily model performance. The NSE was used as the objective function in the calibration processes used in this study.
The Percent Bias (Pbias) (Gupta et al., 1999) evaluates the trend that the average of the simulated values has in relation to the observed ones, and estimates how well the model simulates water volume (eq. 7). The ideal value of Pbias is zero (%); = ±15% can be considered satisfactory for monthly and daily streamflow. Positive values indicate model underestimation, and negative values indicate overestimation (Moriasi et al., 2015). Table 4 shows the recommended statistical ranges for NSE and Pbias.
(6)
(7)
where
= simulated values
= observed values
= mean of n observed values.
| Table 4. Monthly and daily classification of recommended statistical ranges for NSE and Pbias. Source: Moriasi et al. (2015). | ||
| Classification | NSE | Pbias |
| Very good | NSE > 0.80 | Pbias < ±5% |
| Good | 0.70 < NSE = 0.80 | ±5% = Pbias < ±10% |
| Satisfactory | 0.50 < NSE = 0.70 | ±10% = Pbias < ±15% |
| Not Satisfactory | NSE = 0.50 | > ±15% |
The King–Gupta Efficiency (KGE) (Gupta et al., 2009) is a decomposition of NSE and can be separated into three components: alpha, beta, and r (eqs. 8, 9, and 10). This formulation allows unequal weighting of the three components to accommodate an emphasis on certain areas of the aggregated function tradeoff space. The KGE ranges from - 8 to 1. The ideal value of the coefficient is one, and a value > 0.60 indicates good hydrological simulation, according to Patil and Stieglitz (2015).
(8)
(9)
(10)
where
r = correlation coefficient between observed and simulated data
a = measure of relative variability in the simulated and observed data
ß = bias normalized by the standard deviation in the observed values
sobs= standard deviation of the measured data
ssim = standard deviation of the simulated data
µobs = mean of the observed data
µsim = mean of the simulated data.
The uncertainty analysis is represented by the 95PPU (95% probability distribution). These are calculated at the 2.5% and 97.5% levels of the cumulative distribution of an output variable generated by the propagation of parameter uncertainties using Latin Hypercube sampling. This is referred to as the 95% prediction uncertainty. The p–factor (eq. 11) and r–factor (eq. 12) are two measures of uncertainty. The p–factor represents the percentage, in fraction (100% = 1), of observed data bracketed by the 95PPU; the uncertainty of the observed data was set up as ± 10%, such that the observed time series is a band of ± 10% from the measured data point. The r–factor is equal to the average thickness of the 95PPU band divided by the standard deviation of the observed data. A p–factor of one and r–factor of zero is a simulation that exactly matches the observed data. However, for streamflow outputs, a p–factor value above 0.70 and an r–factor under 1.5 are considered adequate simulations. The 95PPU accounts for all uncertainties combined (e.g., input data, model structure), which are mapped onto the parameter range (Abbaspour et al., 2015).
(11)
(12)
where
and 
= upper and lower simulated boundaries at the time ti of the 95PPU
n = number of observed data points
M = simulated values
ti= simulation time step
nXin = number of observed data in the 95PPU interval.
Results and Discussion
The model was calibrated (2001–2009) and validated (2001–2010) using observed streamflow data at monthly and daily time steps. The calibration process (closest gauge to the basin outlet) involved adjusting model parameters to achieve a good match between simulated and observed data. The spatial validation consisted of applying 10% of the best calibrated parameters to the remaining monitoring stations distributed in the study area (table 6). The calibrated/validated model was then used to evaluate the effects of both tile-drain methods on the hydrological response of the DMRB on an annual, monthly, and daily basis.
| Table 5. Monthly and daily calibration performance (NSE, KGE, Pbias) for original and modified tile-drain calculation methods. | ||||||||
| NSE | KGE | Pbias | ||||||
| Calibration | month | day | month | day | month | day | ||
| Original | 0.84 | 0.70 | 0.89 | 0.76 | 8.0 | 18.5 | ||
| Modified | 0.85 | 0.71 | 0.90 | 0.76 | 6.5 | 18.3 | ||
Monthly calibration (table A1) showed very good statistical agreement for both tile-drain calculation methods (table 5). The NSE and KGE results for the original and modified equations were statistically similar, although the Pbias indicated slightly better agreement (6.5% versus 8.0%) for the modified method. These results are similar to those found by Wang et al. (2019), where there were no differences between the two methods for comparing streamflow on a monthly basis. The NSE and Pbias values exceeded ratings of very good and good (table 4), respectively, underscoring that the accuracy of the hydrological simulations was maintained with both methods. The monthly uncertainty ranges were the same for both methods, with a p–factor of 0.44 and an r–factor of 0.39. Following the statistical pattern, both simulations resulted in similar hydrographs (fig. A1).
Both models were satisfactorily validated for the majority of monitoring stations (fig. 4). The NSE values ranged from 0.26 to 0.91 for the original tile-drain equation and from 0.27 to 0.93 for the corresponding modified method. Similarly, the KGE ranged from 0.31 to 0.92 and 0.30 to 0.94 for the simulations based on the original and modified methods, respectively. The majority of the NSE values were = 0.75, and many of the KGE values also exceeded 0.75. The Pbias varied equally for both methods, from -43% to 35%, and values were within ± 15% for 16 of the gauges. The modified method tended to have higher values for the NSE (17 stations had higher values for the modified method versus 4 stations for the original method, and three stations had the same value) and KGE (14 stations had higher values for the modified method versus five stations for the original method, and five stations with same value). The Pbias reflected similar behavior between the two models: Fifteen of the monitoring stations had the same results, five stations had higher results for the original method, and four stations had better agreement for the modified tile-drain calculation method.
 |
| Figure 4. Monthly spatial validation (NSE, KGE, and Pbias) for original and modified tile-drain calculation methods. The dotted line shows the threshold for satisfactory simulations described in table 4 and by Patil and Stieglitz (2015). |
We developed daily calibrated hydrographs and observed time series within the uncertainty envelope (95PPU) (fig. 5). The SWAT model daily calibration resulted in good NSE and KGE performance for both the original and modified methods. However, the Pbias was not satisfactory for simulations based on either tile-drainage method (table 5, fig. 6 and figs. 8a, 8c, 8e, 8g, 8i, and 8k). The parameter calibration process resulted in the same best parameter values (CN2, ALPHA_BF, CH_N2, ESCO, GW_DELAY, GW_REVAP, REVAPMN, SURLAG) for both methods (table 6). The p–factors were 0.39 and 0.41 for the original and modified methods, respectively; the r–factor was 0.49 for both methods. Considering the values suggested by Abbaspour et al. (2015), p–factor > 0.70 and r–factor < 1.5, the two models have acceptable simulation for the r–factor only. However, these suggested numbers are subjective, and modeler expertise should be accounted for before invalidating a model simulation. The theory behind these two parameters is that a small r–factor should follow a large p–factor; based on this and the hydrographs (fig. 5), we considered the calibrations satisfactory. Following the monthly pattern, the daily simulation of the modified tile-drainage equation has a tendency to result in higher values of statistical coefficients.
Flow duration curves are shown for both linear and logarithmic scales (fig. 6). The observed and simulated streamflow comparisons had good overall agreement for medium and high flows (below 50% on the FDC) and greater differences for low flow values (above 80% on the FDC) (fig. 6). Similar to results reported by Kalcic et al. (2015) and Boles et al. (2015), the modified method displayed a decrease in streamflow peaks (below 8% for the best simulation on the FDC). However, the modified method resulted in an increase of the streamflow between the 16% and 94% segments on the FDC. To calculate the two-sample Kolmogorov-Smirnov test (k-s), we used the observed data and the best parameter simulation as the two sample data vectors. The two models produced similar results, with the original method showing k-s = 0.2034 and the modified method k-s = 0.1912. However, the smaller value generated by the modified method suggests the equation resulted in a curve with a slightly better fit to the observed data; this can be justified by the increase in the overall streamflow simulation.
 |
| Figure 5. Daily streamflow calibration for the original and modified models. The graphs show the uncertainty envelope (95PPU) and best simulations for each method; observed data are represented by the dashed blue line. |
 |
| Figure 6. Flow duration curve for daily data at linear and logarithmic scales. The graphs show the uncertainty envelope (95PPU) and best simulations for original and modified tile-drain methods; observed data are represented by the dashed blue line. |
Spatial validation involved the comparison of model outputs (10% best simulation in the calibration process) with observed data across 24 locations to assess model performance in reproducing daily spatial patterns of hydrological variables. This validation was crucial to evaluating the model's ability to capture the spatial variability of hydrological processes and to ensure prediction reliability.
The p–factor and r–factor coefficients showed similar behavior for both methods (fig. 7). The modified method had higher p–factor values for nearly all gauges (except for
gauge 341 which had the same values for both methods). The r–factor was smaller for the original method at 13 gauges, smaller at 2 gauges for the modified method, and the same at 9 gauges (fig. 7). Importantly, eliminating equifinality is not completely possible for SWAT due to complexity and inherent uncertainties in hydrological systems (Vrugt et al., 2009; Efstratiadis and Koutsoyiannis, 2010; Her and Seong, 2018; Khatami et al., 2019). However, the use of a single set of parameters is still useful to analyze model behavior and hydrological variables and may be needed for complex co-simulation studies that integrate multiple models to simulate a variety of environments, issues and opportunities, such as in the Iowa UrbanFEWS project (Thompson et al., 2021). This is undergirded by initial efforts to replicate key aspects of the real system (Brighenti et al., 2022a).
The daily validation process showed improvements based on the modified tile-drain equation (table 7, fig. 7, figs. 8d, 8h, and 8l). We determined a negative NSE value for one gauge for simulations performed with the original tile drain method; this outcome indicates that the observed mean is a better predictor than the model simulation for these gauges. A negative KGE was computed for one gauge for the simulations using the modified tile drain method. We found that the original method had 4 gauges classified as good, 12 gauges as satisfactory, and 7 gauges as not satisfactory simulations, whereas the modified method had 8 gauges classified as good, 11 gauges classified as satisfactory, and 4 gauges classified as not satisfactory simulations (table 7).
The KGE was considered not satisfactory for 10 gauges during the original method setup, versus 8 out of 24 gauges for the modified method. The ability of the model to predict volume is indicated by the Pbias coefficient – both the original and modified methods underestimated overall volumes at all gauges, except for the modified method at the gauge 67 (marked with a blue triangle in fig. 8h). The Pbias classification for the 24 gauges for the simulations performed with the original tile drain method were “very good” (1), “good” (1), “satisfactory” (3), and “not satisfactory” (21). Simulations based on the modified tile drain method were “good” (1), “satisfactory” (1), and “not satisfactory” (19). However, if a Pbias value of ±25% is satisfactory (e.g., Moriasi et al., 2007), the number of acceptable simulations increases to 13 for both the original and modified methods (table 7).
A common element for both methods was difficulty simulating the streamflow in areas of the watershed with less tile drainage (fig. 3) based on NSE, KGE, and Pbias statistics (fig. 8). This fact can be associated with the calibration process, where the model is conditioned to a certain tile density, 55.6% on average, and validated in those areas where the tile density is ~26%. However, the original method showed a tendency to perform stronger results for the southern part of the watershed (subbasins 291, 295, 307, 323, 341, 351, 358). From the 7 gauges that compose this region, the original method performed better across all of them when considering the NSE and KGE; the Pbias results are similar for both methods, with the modified showing (positive) smaller Pbias values (table 7). These results also underscore the increased challenge for SWAT to replicate the magnitude of the daily streamflows (Supplementary Material summarizes the plotted streamflow time series for each of the 24 monitoring gauges).
The annual water balance was calculated using the best parameters simulation obtained during the validation process (table 8). The DMRB average annual (2001-2010) precipitation was 856.7 mm. The calculated evapotranspiration rates were 628 mm and 613 mm for the original and modified methods, respectively. The surface runoff was 28.6 mm/year for the original method and 25.3 mm/year for the modified method, representing 16% and 14% of the total DMRB water yield (original = 180 mm/year and modified = 187 mm/year). The baseflow is composed of tile flow, lateral flow, and ground water flow from the shallow aquifer, which resulted in 151 mm/year and 162 mm/year for the original and modified methods, respectively. The percentages of baseflow in relation to water yield are 84% for the original method and 87% for the modified method. These values are similar to those found by Schilling et al. (2019, 2021). For separate baseflow variables, the results for the original method were 33 mm/year, 119 mm/year, and 0 mm/year, for lateral flow, tile flow, and ground water contributions to the shallow aquifer, respectively. The modified method resulted in 35 mm/year, 127 mm/year, and 0 mm/year for the same variables. Given expected variable proportions (e.g., that highly drained basins have more flow passing through tile drains (Boles et al., 2015; Guo et al., 2018)) the modified model simulation is likely to be more realistic. This result also explains the reduction in evapotranspiration considering the modified method, where, with the tile drain capturing the majority of the flow, less water is available in the soil for the evapotranspiration process to occur.
| Table 7. Daily streamflow spatial validation values for the statistical efficiency coefficients (NSE, KGE, Pbias). | ||||||||
| Validation | Original | Modified | ||||||
| NSE | KGE | Pbias | NSE | KGE | Pbias | |||
| Subbasin 35 | 0.01 | 0.51 | 12.8 | 0.48 | 0.74 | 8.1 | ||
| Subbasin 67 | -0.04 | 0.43 | 2.1 | 0.37 | 0.61 | -3.8 | ||
| Subbasin 107 | 0.37 | 0.64 | 14.3 | 0.56 | 0.75 | 9.7 | ||
| Subbasin 130 | 0.5 | 0.68 | 20.8 | 0.68 | 0.78 | 15.8 | ||
| Subbasin 134 | 0.62 | 0.72 | 21.3 | 0.73 | 0.77 | 17.6 | ||
| Subbasin 153 | 0.68 | 0.65 | 26.7 | 0.67 | 0.64 | 23.3 | ||
| Subbasin 155 | 0.64 | 0.72 | 22.7 | 0.74 | 0.77 | 19.1 | ||
| Subbasin 156 | 0.61 | 0.76 | 14.7 | 0.67 | 0.8 | 10.9 | ||
| Subbasin 184 | 0.74 | 0.73 | 21.2 | 0.74 | 0.71 | 17.5 | ||
| Subbasin 222 | 0.65 | 0.72 | 21.6 | 0.68 | 0.75 | 16.8 | ||
| Subbasin 249 | 0.69 | 0.73 | 22.4 | 0.74 | 0.77 | 17.8 | ||
| Subbasin 257 | 0.68 | 0.43 | 43.9 | 0.67 | 0.43 | 42.2 | ||
| Subbasin 259 | 0.78 | 0.76 | 22 | 0.8 | 0.78 | 18.2 | ||
| Subbasin 260 | 0.75 | 0.69 | 26.7 | 0.77 | 0.69 | 23.2 | ||
| Subbasin 280 | 0.63 | 0.72 | 18.7 | 0.65 | 0.68 | 15.5 | ||
| Subbasin 282 | 0.64 | 0.81 | 5.7 | 0.66 | 0.78 | 2 | ||
| Subbasin 291 | 0.62 | 0.55 | 23.1 | 0.57 | 0.5 | 20.8 | ||
| Subbasin 295 | 0.66 | 0.47 | 42.7 | 0.64 | 0.46 | 40.6 | ||
| Subbasin 307 | 0.48 | 0.38 | 41.3 | 0.39 | 0.29 | 41.1 | ||
| Subbasin 323 | 0.59 | 0.35 | 43.7 | 0.51 | 0.28 | 43.6 | ||
| Subbasin 341 | 0.47 | 0.22 | 47 | 0.44 | 0.2 | 46.6 | ||
| Subbasin 351 | 0.42 | 0.16 | 57.7 | 0.39 | 0.14 | 57.5 | ||
| Subbasin 356 | 0.71 | 0.7 | 25.8 | 0.72 | 0.71 | 22.9 | ||
| Subbasin 358 | 0.25 | 0.02 | 66.6 | 0.08 | –0.13 | 65.2 | ||
 |
| Figure 8. Daily streamflow spatial validation using NSE, KGE, and Pbias across the study area subbasins: (a) NSE original calibration, (b) NSE original validation, (c) NSE modified calibration, (d) NSE modified validation, (e) Pbias original calibration, (f) Pbias original validation, (g) Pbias modified calibration, (h) Pbias modified validation, (i) KGE original calibration, (j) KGE original validation, (k) KGE modified calibration, and (l) KGE modified validation. For visualization, the Pbias was plotted with absolute values; the blue triangle indicates station with overestimation. |
| Table 8. Annual water balance obtained during the validation process using the best parameters simulation. | ||
| Processes (mm) | Original | Modified |
| Evapotranspiration | 628 | 613 |
| Surface runoff | 28.6 | 25.3 |
| Water yield | 180 | 187 |
| Lateral flow | 33 | 35 |
| Tile flow | 119 | 127 |
| Ground water contribution to the shallow aquifer | 0 | 0 |
Satisfactory SWAT simulation results using the Hooghoudt and Kirkham physically-based equations for the calculation of tile-drain flow have been reported for a limited number of previous studies (table 1). The fact that only a few studies have utilized the Hooghoudt and Kirkham method may reflect the perception that it is more easily applied to relatively small watersheds (table 1). This could indicate reluctance on the part of SWAT users to apply the method to larger stream systems, due to potential difficulties in configuring the required input parameters, or for other reasons. In general, our monthly results are similar to those found previously, with both equations behaving efficiently and the modified equation showing a tendency to simulate both more tile-drain flow and streamflow. However, considering daily NSE, KGE, and Pbias coefficients, the validation analysis revealed more consistency among models for the modified method. For annual values based on the largest simulated volumes (119 mm/year for the original method and 127 mm/year for the modified method), the model was a better representation of tile-drain flow when the modified method was used. In addition, we demonstrate the applicability of the modified equation to a larger and more complex hydrological system than previously studied. Spatial validation using the 24 monitoring stations highlighted differences between the methods based on model performance statistics.
Conclusions
This study presents a comparative analysis of two tile-drain simulation methods within the SWAT model, empirical (original) and physically-based (modified), to assess their effects on the simulation of watershed hydrology. Monthly simulation for the original and modified methods showed a good match between observed and simulated hydrographs, very good statistical performance for the NSE and KGE, and good evaluation for the Pbias (based on Moriasi et al. (2007, 2015)). The daily calibration was good for both methods considering the NSE and KGE statistics, again based on Moriasi et al. (2007, 2015). However, neither method was satisfactory based on the Pbias criteria suggested by Moriasi et al. (2015). The two models showed the greatest differences for the daily validation process, with the modified method generating consistently better results (figs. 7 and 8). We conclude that both tile-drain calculation methods available in the SWAT model are capable of reproducing monthly hydrological cycles with some confidence, but with challenges to replicate the magnitude of the peaks. When simulated for areas with less tile drainage, both methods showed reduced efficiency considering the NSE, KGE, and Pbias statistic. However, the daily analysis showed that the modified method (Hooghoudt and Kirkham equations) replicated spatial variability more accurately in simulations of the hydrological process for the DMRB. For future research, we plan to: (a) extend the analysis by also comparing nitrogen loads; (b) establish relationships between plot-scale tile-drain flow measured data and watershed–scale tile-drain flow calculation; and (c) test different objective functions during the calibration process (e.g., KGE).
Supplemental Material
The supplemental materials mentioned in this article are available for download from the ASABE Figshare repository at: https://doi.org/10.13031/24665997
Acknowledgments
This research was partly funded by the “Social and biophysical models to integrate local food systems, climate dynamics, built forms, and environmental impacts in the urban FEWS nexus” project, supported by the National Science Foundation Award # 1855902, and by the "#DiverseCornBelt (#DCB): Enhancing rural resilience through landscape diversity in the Midwest” project, supported by Agriculture and Food Research Initiative Competitive Grant no. 2021-68012-35896 from the USDA National Institute of Food and Agriculture. Any opinions, findings, conclusions, or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation or the United States Department of Agriculture.
Appendix
 |
| Figure A1. (a) Monthly hydrographs for the calibrated original and modified models, (b) flow duration curve (FDC), and (c) flow duration curve for the logarithmic scale. The graphs show the uncertainty envelope (95PPU) and best simulations for original and modified tile–drain methods; observed data is represented by the dashed blue line. |
| Table A1. Parameters used for the monthly calibration process, ranges, and best parameter simulations for original and modified methods (Hooghoudt and Kirkham equations). The methods used to adjust the parameter values in SUFI-2 are represented as the first letter before the parameter name (r, v, and a); the letter v represents replacing the existing parameter value, a is adding a given value to the existing parameter value, and r is multiplying (1 + a given value) to the existing parameter value. | ||||
| Parameter | Calibration Range | Best Parameters Value | ||
| Original | Modified | |||
| r__CN2.mgt | –0.2 | 0.2 | 0.13 | 0.14 |
| v__ALPHA_BF.gw | 0.001 | 0.5 | 0.14 | 0.14 |
| v__CANMX.hru______FRSE | 0 | 14 | 13.63 | 12.71 |
| v__CANMX.hru______FRSD | 0 | 10 | 0 | 0.69 |
| v__CANMX.hru______FRST | 0 | 10 | 6.37 | 5.91 |
| v__CH_N2.rte | 0.01 | 0.02 | 0.02 | 0.02 |
| v__ESCO.hru | 0.6 | 1 | 1.00 | 1.00 |
| v__GW_DELAY.gw | 0 | 60 | 10.71 | 5.57 |
| v__GW_REVAP.gw | 0.02 | 0.2 | 0.10 | 0.13 |
| v__REVAPMN.gw | 0 | 1000 | 420.52 | 428.44 |
| v__DEP_IMP.hru | 0 | 2500 | 1766.76 | 1766.76 |
| v__SDRAIN.sdr | 1500 | 27000 | – | 17251.71 |
| v__LATKSATF.sdr | 1 | 3.8 | – | 3.19 |
| v__DRAIN_CO.sdr | 10 | 51 | – | 18.92 |
| v__RE.sdr | 20 | 50 | – | 30.85 |
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