# Revisiting SWAT as a Saturation-Excess Runoff Model

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Background for Changing SWAT-2012 to a Saturation-Excess Model

_{s}, as [23]:

_{c}is the contributing area, R is a steady-state recharge rate term, K

_{s}is the saturated conductivity, D is the depth to the impermeable layer, and sin α is the topographic slope of the cell. In practice and employed in this manuscript, the steady rainfall rate was assumed unity. In addition, the contributing area was specified per unit length (hence W equaled 1). The topographic index became:

#### 2.1. SWAT-2012

^{*}(mm) at each time step $\Delta t$ by:

^{*}(mm d

^{−1}) is the effective rainfall and equal to the precipitation minus both the evapotranspiration and infiltration excess runoff. ${Q}_{lat}^{*SWAT2012}$ is the lateral flow per unit area in (mm d

^{−1}), ${Q}_{perc}^{*SWQAT2012}$ is the percolation of soil water from the bottom of the soil profile. The * superscript indicates that the units in SWAT were used and the SWAT2012 superscript indicates that the derivation of the flux was particular to SWAT-2012.

_{s}, and the soil depth D (mm), the soil profile saturates to the surface and excess soil water becomes saturated overland flow per unit area, ${Q}_{sof}^{*}$ (mm d

^{−1}):

^{−1}) in SWAT-2012 is expressed as [29]:

^{*SWAT2012}(SLSOIL in SWAT) is the slope length (m) and K*

_{sat}is given on an hourly basis in mm h

^{−1}; SW

^{*}

_{excess}is the storage of water above field capacity per unit area in mm and φ

_{d}is the drainable porosity and is taken as the difference between the soil water contents at saturation and field capacity. Lateral flow, thus, only occurs when the soil is above field capacity. Equation (12) can be rewritten in consistent metric units of length (L) and time (T) without the 0.024 unit conversion factor as:

^{SWAT2012}is the fraction lost in the lateral flow of water stored in the HRU above field capacity. Note that the variables without a star superscript have metric units that are internally consistent and do not have a constant for converting units, but otherwise, Equations (13) and (14) are the same as Equation (12).

#### 2.2. SWAT-wil

^{2}T

^{−1}) for a hillslope can be calculated with Darcy’s law for slopes over 1–2% where gravity dominates:

_{excess}(L

^{3}L

^{−2}), can be written when the capillary fringe is neglected as:

_{excess}(L

^{3}L

^{−2}), is the amount of water in the profile above field capacity per unit area and φ

_{d}(L

^{3}L

^{−3}) is drainable porosity and is equal to (θ

_{s}− θ

_{fc}), where θ

_{s}is the saturated water content and θ

_{fc}is soil water content in the unsaturated zone above the water table. Combining Equations (15) and (16) gives:

_{excess}in SWAT-2012) is determined. These soil water content and corresponding water table height (as will see below) are found using the SCS curve number interpretation expressed in Equation (3) with the considerations below.

^{will}:

_{0}is the saturated soil water content of the rootzone for an HRU. Using the first two terms of the exponential series, Equation (21) can be written as:

_{0}C

^{will}Δt) and is, thus, equal in absolute value to σ in Equation (3), that is defined as the amount of water to saturate the soil for the HRU in the wetness class. Hence:

^{will}expressed in Equation (24) instead of C

^{SWAT2012}(Equation (14)) for each HRU that is located on an impermeable layer in SWAT-2012, we have created SWAT-wil which has a water table that varies along the hillslope as a function of A

_{s}, where A

_{s}is the likelihood of the area remaining unsaturated; A

_{s}is zero for the area always being saturated and 1 for most unlikely to become saturated. For A

_{s}= 0, C

^{will}= 0 (Equation (24)) and the area remains near saturation even when it does not rain the next day (Equation (22). Only evapotranspiration will lower the moisture content. The fractions of water lost, C

^{SWAT2012}, and thus C

^{will}cannot be directly input into SWAT. The slope length L

_{will}is the input variable (Equation (19)) that can be used to determine the fraction lost for each wetness class.

_{s}= 0 will be overland flow.

## 3. Materials and Methods

#### 3.1. Town Brook Watershed

^{2}Town Brook watershed in the Catskills, NY (Figure 2), the observed extent of saturated areas in 2006 and 2007 were available from previous studies [23,29,30]. The average annual temperature is 8 °C and average annual precipitation is 1123 mm a

^{−1}. The landscape is characterized by steep to moderate hillslopes of glacial origin with shallow permeable soils. Elevation ranges from 493 to 989 m. Most soils are silt loam and silty clay loam overlaying a glacial till. The upper terrain on the north facing slope of the watershed is characterized by shallow soil (average thickness 80 cm) overlaying fractured bedrock, steep slopes (average slope 29%), and deciduous and mixed forests (60% of the watershed). The south facing slopes and lowland areas of the watershed have deeper soils (average thickness 180 cm) underlain by a dense fragipan restricting layer, more gentle slopes (average slope 14%), and are predominantly occupied by pasture and row crops (20%) and shrub land (18%). Water and wetland comprise only 2% of the watershed while impervious surface is insignificant. The dominant land cover is forest with 32% agricultural land (Figure 2).

#### 3.2. Description of SWAT-Hillslope

#### 3.3. Model Setup for SWAT-wil

^{will}cannot be directly inputted into SWAT currently. We can set the value of Cwill by choosing the appropriate hillslope length, L

^{wil}, which is an input parameter. To calculate L

^{wil}, for each HRU, we substitute Equation (24) into Equation (18).

_{0}/φ

_{d}is equal to the depth of the root zone, reordering Equation (25), L

^{wil}can be found as:

^{wil}is in m, ${K}_{sat}^{*}$ in mm h

^{−1}, and S and D in mm. The hill slope length, L

^{wil}, for the various classes was determined with Equation (23) by calibrating the S value with the daily time step Δt = 1.

#### 3.4. Model Calibration

^{wil}lengths were an unrealistically low and overestimated lateral flow, underestimated of overland flow, and poorly simulated the hydrograph. We, therefore, calibrated the S parameter. An S value of 5.8 mm was selected based on the separated surface and subsurface flow components from the SWAT-HS simulations of the hydrograph.

#### 3.5. Code Changes

## 4. Results

^{−1}comes from just 13% of the watershed (HRUs 1,2,3). In SWAT-wil, without a transfer mechanism, 90% of the annual lateral flow comes from 80% of the watershed (HRUs 4–10). The wettest HRUs are, therefore, located downslope and the driest upslope (Figure 6).

## 5. Discussion

^{wil}values. Other distributions have been employed such as the Pareto distribution in SWAT-HS. Despite this uncertainty, the spatial pattern of VSAs predicted by SWAT-wil and inferred by the Equation (24) with the calibrated S parameter matched the VSA pattern predicted by SWAT-HS (Figure 4).

^{wil}. This is counter intuitive because the HRUs are ranked according the topographic index. We can show, however, that L

^{wil}is independent of the HRU physical properties by substituting Equation (4) in Equation (26), the slope length can be directly related to the topographic index, for example:

_{c}, a measure that the HRU becomes saturated, A

_{s}, the average water storage in the watershed, S, and the time period of the simulation, Δt. This is not to say that the that ${L}^{wil}$ is independent of the HRU characteristics, because the topographic index λ calculation (Equations (4) and (5)) includes the physical properties of the HRU (i.e., slope, saturated conductivity, and soil depth).

^{wil}values. The same calibration routines (such as SWAT-CUP) can be used for SWAT-wil with HRUs located on soils with a hardpan.

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 3.**Comparison of monthly time series of streamflow simulated by SWAT-2012, SWAT-wil, and SWAT-HS with measured streamflow in Town Brook for the calibration and validation period 2001–2012.

**Figure 4.**Simulated surface runoff contributing areas (VSAs) as indicated by average surface flows over 250 mm a

^{−1}component by SWAT-2012, SWAT-wil, and SWAT-HS for the Town Brook watershed.

**Figure 5.**Simulated lateral flow by SWAT-wil and SWAT-HS for the Town Brook watershed. The lateral flows by SWAT-2012 are small and not shown.

**Table 1.**Hydrologic response unit (HRU) level parameters for the SWAT-wil model application in Town Brook. DEPIMP is the depth of the impermeable layer, D; KSAT is the saturated conductivity, K

_{s}; HRUSLP is the slope; SLSOIL is the calculated slope length L

^{wil}. R2ADJ a parameter that adjust the SCS curve number runoff. A value of 100 turns the curve number runoff to zero.

HRU | Topographic Index λ | AreaHRU % | DEPIMP mm | KSAT mm h ^{−1} | HRUSLP mm mm ^{−1} | SLSOIL m | CN2 | R2ADJ |
---|---|---|---|---|---|---|---|---|

1 | >17.7 | 0.59 | 457 | 33 | 0.040 | 1662 | - | 100 |

2 | 16.7–17.7 | 6.06 | 457 | 33 | 0.093 | 307 | - | 100 |

3 | 15.8–16.7 | 6.24 | 457 | 33 | 0.116 | 135 | - | 100 |

4 | 14.8–15.8 | 6.18 | 457 | 33 | 0.128 | 87 | - | 100 |

5 | 13.8–14.8 | 6.37 | 457 | 33 | 0.141 | 65 | - | 100 |

6 | 12.9–13.8 | 6.20 | 457 | 33 | 0.152 | 51 | - | 100 |

7 | 11.9–12.9 | 6.90 | 457 | 33 | 0.167 | 43 | - | 100 |

8 | 10.9–11.9 | 6.67 | 457 | 33 | 0.183 | 36 | - | 100 |

9 | 10.0–10.9 | 6.04 | 457 | 33 | 0.198 | 31 | - | 100 |

10a | 10–7.6 | 33.7 | 457 | 33 | 0.263 | 21 | 35 | 1 |

10b | <7.6 | 15 | 6000 | 33 | 0.116 | 1600 | - | 100 |

**Table 2.**Basin level parameters for SWAT-wil and SWAT-HS model applications for Town Brook; n.a. is not applicable because the lateral flow was calculated in the SWAT-HS model.

Hydrologic Component | Parameter | SWAT-wil Value | SWAT-HS Value |
---|---|---|---|

Snow | SFTMP | −0.58 | −0.58 |

SMTMP | 1.10 | 1.10 | |

SMFMX | 7.62 | 7.62 | |

SMFMN | 2.68 | 2.68 | |

TIMP | 0.022 | 0.022 | |

ET | ESCO | 1.00 | 0.691 |

EPCO | 0.10 | 0.989 | |

Overland Flow | SURLAG | 2.20 | 4.00 |

Groundwater Flow | ALPHA_BF | 0.37 | 0.05 |

GW_DELAY | 3.45 | 31.00 | |

Lateral flow | LAT_TTIME | 0.22 | n.a. |

**Table 3.**Statistical evaluation of different SWAT models of Town Brook using the Nash Sutcliff Efficiency (NSE) and the linear regression coefficient (R

^{2}).

SWAT-2012 | SWAT-wil | SWAT-HS | |||||
---|---|---|---|---|---|---|---|

Time Step | NSE | R^{2} | NSE | R^{2} | NSE | R^{2} | |

2001–2008 | Daily | 0.53 | 0.54 | 0.61 | 0.61 | 0.65 | 0.64 |

2001–2008 | Monthly | 0.67 | 0.73 | 0.81 | 0.82 | 0.80 | 0.86 |

2009–2012 | Daily | 0.50 | 0.50 | 0.51 | 0.52 | 0.53 | 0.54 |

2009–2012 | Monthly | 0.68 | 0.68 | 0.73 | 0.74 | 0.73 | 0.74 |

Flow Component | SWAT-2012 (mm/day) | SWAT-wil (mm/day) | SWAT-HS (mm/day) |
---|---|---|---|

Surface runoff | 1.20 | 0.36 | 0.22 |

Lateral flow | 0.26 | 1.34 | 1.25 |

Groundwater flow | 0.29 | 0.30 | 0.29 |

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## Share and Cite

**MDPI and ACS Style**

Steenhuis, T.S.; Schneiderman, E.M.; Mukundan, R.; Hoang, L.; Moges, M.; Owens, E.M.
Revisiting SWAT as a Saturation-Excess Runoff Model. *Water* **2019**, *11*, 1427.
https://doi.org/10.3390/w11071427

**AMA Style**

Steenhuis TS, Schneiderman EM, Mukundan R, Hoang L, Moges M, Owens EM.
Revisiting SWAT as a Saturation-Excess Runoff Model. *Water*. 2019; 11(7):1427.
https://doi.org/10.3390/w11071427

**Chicago/Turabian Style**

Steenhuis, Tammo S., Elliot M. Schneiderman, Rajith Mukundan, Linh Hoang, Mamaru Moges, and Emmet M. Owens.
2019. "Revisiting SWAT as a Saturation-Excess Runoff Model" *Water* 11, no. 7: 1427.
https://doi.org/10.3390/w11071427