# Assessing the Performance of SHETRAN Simulating a Geologically Complex Catchment

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

^{2}) was modelled using the free-license PBD code SHETRAN. The SHETRAN evaluation took place by comparing its predictions with (i) discharge and piezometric time series observed at different locations within the catchment, some of which were not taken into account during model calibration (i.e., multi-site test); and (ii) predictions from a comparable commercial-license code, MIKE SHE. In general, the discharge and piezometric predictions of both codes were comparable, which encourages the use of the free-license SHETRAN code for the distributed modelling of geologically complex systems.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. The Study Site

^{2}) which is in the central part of Belgium (Figure 1a). The ground elevation (Figure 1b) ranges from approximately 27 m in the north to 174 m in the south. Land use in the area is mainly agricultural, including pasture and cultivated fields, with some local forested patches. Soils have a loamy texture and are deep; nine soil units can be distinguished according to the Belgian soil map. The groundwater table is generally at a depth of 3 to 10 m below surface. The complex lithostratigraphy of the study site comprises nine units, some of which occur only in isolated parts of the catchment. The main units are shown in Figure 1c and this includes a narrow Quaternarian loamy deposit on top of deeper sandy and clayey units resting on top of a low-permeable Palaeozoic rocky basement. The local weather is characterised by moderate humid conditions.

#### 2.2. Hydrological Codes

#### 2.2.1. SHETRAN Hydrological Code

#### 2.2.2. MIKE SHE Hydrological Code

#### 2.2.3. Comparison between SHETRAN and MIKE SHE

#### 2.3. Data Availability and Code Parameterisation

^{2}, which is a coarse discretisation for describing accurately hillslope processes happening in the study catchment. Nevertheless, aiming at attaining reasonable simulation times, other studies have been carried out in the past using even coarser discretisations for study sites of comparable size and which are far less complex in geological terms [5,6,20,23,25]. Thus, given that the number of catchment grid elements in the computational domain (Figure 1b) is 1629 (out of 3025 cells that form the computational domain), it is believed that the current modelling resolution represents a fair compromise between representativeness of catchment variability, the complex vertical description of the catchment (six geological layers) and computational time.

_{p}, estimated through the FAO-24 method [12,39,40] obtained from the meteorological data at two stations. Thiessen polygons were used to account for the spatial distribution of rainfall and ET

_{p}. In SHETRAN ET

_{act}is calculated from the ET

_{p}depending on the crop coefficient for each land cover and a soil water coefficient which reduces ET

_{act}as the soil dries [41]; the associated parameter values were obtained from the literature [39,42,43]. Additional information required for the evapotranspiration (ET) module [44] of SHETRAN included canopy storage and drainage parameters, the Leaf Area Index (LAI) and the root density function. These values were also generated from the literature on the basis of the land cover of the catchment [39,43,45,46]. Parameters of the MIKE SHE ET module [47] were assessed on the basis of prior analyses, i.e., Vázquez [9], Vázquez and Hampel [12].

_{riv}) and overland flow (n

_{ov}), and the horizontal (K

_{x}) and vertical (K

_{z}) saturated hydraulic conductivity of the geological units, were selected for calibration (Table 1). The range for n

_{ov}was derived from Engman [48] for the different LUC classes. The range for n

_{riv}was derived from Chow, et al. [49]. The ranges of variation for K

_{x}and K

_{z}were defined based on Anderson, et al. [50] and Vázquez, Feyen, Feyen and Refsgaard [3].

#### 2.4. Model Performance

#### 2.4.1. Multi-Objective Model Performance Statistics

_{i}is the i-th simulated value, O

_{i}is the i-th observed value and n is the number of observations [7]. The Coefficient of Efficiency [55], also known as the Nash and Sutcliffe [56] Efficiency and shown in Equation (2) where ${\mathsf{\sigma}}_{\mathrm{obs}}^{2}$ is the observed variance and MSE is the Mean Squared Error, is commonly used for an estimation of the overall (combined systematic and random) average error [9]. A third statistic, R

^{2}, the square of the Pearson’s type (linear) correlation coefficient was also used, particularly for potential comparison with the results of similar modelling studies, despite the fact that it is not that appropriate for measuring model performance [3,55]. Objective functions that consider low flows were not used as they are considered in the analysis of the time series in the next section:

#### 2.4.2. Analysis of Simulated Time Series

_{th}(i.e., x − x

_{th}). The GPD is shown in Equation (3) [57,59], where κ

_{sh}and κ

_{sc}are respectively the shape and scale parameters of the distribution:

_{sh}= 0, G(x) is the exponential distribution. Weibull [9,37,57,60] plotting position of a quantile (observed extremes) was used for calculating the empirical probabilities of exceedance (and the respective empirical return periods). The daily peaks were selected from the total discharge series through a partial duration time series (PDS) approach [11,61,62]. Further information on the above methods can be found in Vázquez, Willems and Feyen [28].

_{bs}) component of the total hydrograph was used. This considers whether both the shape and magnitude of low flows were acceptably reproduced by the SHETRAN model. Q

_{bs}was estimated from the hydrograph for both the observed as well as the simulated hydrographs. This was achieved using a recursive digital filtering approach [63,64,65]. The approach assumes that Q

_{bs}, at every time step, evolves proportionally to Q, as given by the general expression used in signal analysis and processing [28]:

^{3}T

^{−1}]; F

_{h}(t) = high frequency filtering signal (quicker than the flow-component to be filtered) at time t [L

^{3}T

^{−1}]; b

_{F}= proportionality factor [-]; a

_{F}and c

_{F}= filter coefficients [-]. a

_{F}may adopt a value between 0 and 1 (and may be thought of as the recession coefficient); the closer its value is to 1, the flatter the flow-component becomes. On the other hand, b

_{F}= (1 + a

_{F})/2, whilst, c

_{F}= 1.0. The diverse variations of the high frequency filter used in this study (for instance, Vázquez [9],Nathan and McMahon [63], Arnold, Allen, Muttiah and Bernhardt [64], Chapman [66], Willems [67]) differ mainly on the values adopted by these three coefficients a

_{F}, b

_{F}and c

_{F}in response to the physical reasoning behind the formulation.

_{l}(t), is obtained at time t after subtracting the filtering signal, F

_{h}(t), from the total flow, that is F

_{l}(t) = Q

_{bs}= Q(t) − F

_{h}(t). Further details can be found in Vázquez [9]. The filter is passed over the data several times in the forward and backward senses; commonly, three passes (forward, backward and forward again) are implemented with the intention of providing to the user some flexibility to adjust the baseflow estimation product more accurately to site-specific conditions.

## 3. Results

#### 3.1. Values of the Effective Model Parameters

_{ov}. With the same purpose in mind, only one value for n

_{riv}, the average for the whole river network, is listed. Further, the table includes the values of the hydrogeological parameters, calibrated for the geological formations that are in direct contact with the river network, considering two main subcatchments (i.e., zones “A” and “B”) defined by the water divide between the two main river branches of the study site (Figure 3a). For the other geological formations, the average parameter value for the whole catchment area is provided. The table shows that for some of the parameters the calibrated values obtained for both models are very similar in terms of magnitude; for the majority of the parameters, however, the respective calibrated values are importantly different in the two hydrological models.

#### 3.2. Multi-Objective Model Performance Statistics

_{2}. Indeed, this index shows that the predictions were worse for the Kleine Gete station, for which a negative EF

_{2}value was obtained (Figure 5a). In general, streamflow predictions were better at the Grote Gete station (Figure 3d), although many lower, medium and peak flows were over predicted by the model (Figure 5b).

#### 3.3. Comparison of the SHETRAN and MIKE SHE Predictions

_{SHET}) and MIKE SHE (Q

_{MSHE}). This is emphasised by Figure 7, which shows that both SHETRAN (Figure 7a) and MIKE SHE (Figure 7b) had problems simulating streamflow at the outlet of the catchment in terms of peaks and low flows, which can also be seen in the performance statistics. Overall, peak flows were slightly better simulated by MIKE SHE (EF

_{2}= 0.74; Figure 7b) than by SHETRAN (EF

_{2}= 0.70; Figure 7a).

#### 3.4. Analysis of Simulated Time Series

_{th}) of 10.9 m

^{3}s

^{−1}(Gete station), 3.9 m

^{3}s

^{−1}(Grote Gete station) and 4.4 m

^{3}s

^{−1}(Kleine Gete station), with which the empirical peak flow distributions of the simulated hydrographs were defined. With respect to the outlet of the study catchment at Gete station, peak flows were better simulated by MIKE SHE (Figure 9b); SHETRAN tended to over-predict them with a higher tendency than MIKE SHE. Moreover, both models had problems producing good predictions for the river discharge in the two internal stations, Grote Gete and Kleine Gete (Figure 9c,d) that were not part of the model calibration (i.e., MS test). However, the SHETRAN results were better than those from MIKE SHE, particularly at Grote Gete.

_{bs}time series for the Gete station. Four series corresponding to four (forward and backward) passes of the filter are plotted in the figure. Flatter series were obtained for the higher passes. Additionally, the higher the value adopted by the a

_{F}coefficient, the flatter the Q

_{bs}series became. A value of 0.94 for a

_{F}and the third pass of the filter applied on the observed streamflow were used after comparison with the estimates produced by a previous work that used a more sophisticated recursive filter [9]. This a

_{F}value and the third pass were also used for filtering the simulated streamflow from SHETRAN and MIKE SHE.

_{bs}series obtained for the simulated hydrographs are, in general, higher than the respective magnitudes of the series derived from the observed streamflow in the Gete station, particularly in the periods May-December in 1987 and 1988 (Figure 10b). This accentuates what was already observed in Figure 4: an over-prediction of low flows for both the calibration and validation periods for the SHETRAN model. Q

_{bs}estimates were higher for the model predictions than for the observations in the case of the Grote Gete station (Figure 10c). Whereas for the Kleine Gete station (Figure 10d), an under-prediction of the baseflow was observed.

_{bs}) fraction was 69.2%. This shows the dominant contribution of Q

_{bs}to the overall discharge, and is in agreement with the importance of aquifers not only in Flanders, the northern region of Belgium, but also throughout Belgium [68].

## 4. Discussion

^{2}modelling scale and the point scale at which observations were collected; and (ii) the significant load of uncertainty attached to some of the geological data used to build the geological model of the study catchment.

_{act}approaches in SHETRAN and MIKE SHE. There are other related issues that are different between the codes which are more related to data format, etc. Hence, in the MIKE SHE code there is a clear differentiation between “soils” (UZ) and the underlying geological units (SZ), not only in terms of the different physical and hydraulic parameters, but also, geometrically and functionally (i.e., water table fluctuates only in the SZ, implying a readjustment of the uppermost limit of the SZ). In SHETRAN, this differentiation is less clear, at least in terms of the definition of the physical parameters. For instance, in MIKE SHE, the specific storage is exclusively a hydrogeological parameter, whilst in SHETRAN it is also stored in the soils database. Further, in MIKE SHE both, the specific yield (S

_{y}) and the specific storage (S

_{s}) need to be specified for, respectively, unconfined and confined aquifers, which is not the case for SHETRAN where only a single storage value needs to be specified (and the code decides how to use it under, either, unconfined or confined conditions).

^{®}(Linux

^{®}) based graphical user interface (GUI) versions that were commercially “adapted” to work in Windows

^{®}. Before focusing entirely on a 100% Windows

^{®}based GUI, the producer of the code (Danish Hydraulic Institute, DHI) incorporated in this version 2001 a second option for (1D) river modelling, which was DHI code MIKE 11 [69]. Starting from the fully Windows

^{®}based version in 2002 this became its only river modelling module until very recently, when they added as a newer option their code MIKE HYDRO River [70]. Although it was never the aim of this study to assess the effects of these MIKE SHE code structural changes, because we were always focused on the performance of SHETRAN, we are in a position to state that, despite these structural changes, the respective MIKE SHE based model predictions of the discharge at the outlet of the study site (using MIKE 11) are similar to the ones reported herein. Further, the newest versions of MIKE SHE still use a simplified 1D UZ modelling approach, implying that this part of its structure has not (yet) been modified.

## 5. Conclusions

^{2}catchment. The complex geometry of the study catchment that included six geological units, as well as the spatial variability of the different physical parameters, was successfully incorporated into the distributed model of the site. The model was calibrated by tuning the values of the Manning’s roughness parameters for the simulation of overland flow and river discharge, as well as, the hydraulic conductivities of the geological units. In general, the discharge simulation at the catchment outlet was acceptable, although some peak and low flows were not well simulated. Discharge predictions were of inferior quality for the two internal stations that were not considered in model calibration. The quality of the piezometric predictions varied, mainly as a function of the location of a given piezometric well in the catchment and of the geological unit where its screen was located. Overall, the discharge and piezometric predictions of SHETRAN and the similar but commercial-license MIKE SHE code were comparable. Further, all the modelling approaches and tests that could be implemented with the MIKE SHE code could be also implemented with SHETRAN, although SHETRAN needed the programming of a larger number of specific-task subroutines for data handling. All this encourages the use of the free-license SHETRAN code for carrying out the distributed modelling of geologically complex systems.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**(

**a**) Location of the study site, the Gete catchment (after Vázquez, Willems and Feyen [28]); (

**b**) digital terrain model (DTM) of the study site and horizontal distribution of (

**c**) the vertical profiles of the simplified geological model of the study site (600 × 600 m

^{2}) showing the thin loamy Quarternarian deposits (Kw) overlaying the dipping formations, sandy Brusseliaan (Br), clayey sand Landeniaan (Ln), sandy very fine marls Heers (Hr), white chalk Cretaceous (Cr). Below these layers is the Palaeozoic strongly folded rocky basement.

**Figure 3.**600 × 600 m

^{2}model river networks for (

**a**) SHETRAN and (

**b**) MIKE SHE; (

**c**) distribution of rainfall stations used in the modelling and associated Thiessen polygons (after Vázquez [9]); and (

**d**) location of the calibration and evaluation stream gauging stations and observation wells (after Vázquez [9]). Topographical colour scales are different in (

**a**,

**b**) owing to the use of different software tools (accompanying the SHETRAN and MIKE SHE codes) to create the plots. Plot (

**a**) shows the water divide (white dashed line) that determines subcatchments (zones) A and B that were considered for the spatial calibration of some hydrogeological parameters. MS = multi-site model performance validation test; SS = split-sample model performance validation test. Coordinates system: Lambert conformal conic for Belgium.

**Figure 4.**Scatter plots of total streamflow observed (Q

_{obs}) and predicted (Q

_{sim}) by SHETRAN, at the outlet of the catchment, for (

**a**) the calibration period [1 of January 1985–31 of December 1986]; and (

**b**) the validation period [1 of January 1987–31 of December 1988]. EF

_{2}= Coefficient of Efficiency (Nash and Sutcliffe Efficiency); R

^{2}= square of the Pearson’s type (linear) correlation coefficient; MAE = Mean Absolute Error.

**Figure 5.**Multi-site (MS) scatter plots for the validation period [1 January 1987–31 December 1988] of observed (Q

_{obs}) and SHETRAN predicted (Q

_{sim}) total streamflow at the non-calibrated stations (

**a**) Grote Gete; and (

**b**) Kleine Gete (Figure 3d). EF

_{2}= Coefficient of Efficiency (Nash and Sutcliffe Efficiency); R

^{2}= square of the Pearson’s type (linear) correlation coefficient; MAE = Mean Absolute Error.

**Figure 6.**Scatter plots and hydrographs of MIKE SHE (Q

_{MSHE}) and SHETRAN (Q

_{SHET}) total streamflow simulations at the outlet of the catchment for (

**a**) the calibration period [1 January 1985–31 December 1986]; and (

**b**) the validation period [1 January 1987–31 December 1988]. EF

_{2}= Coefficient of Efficiency (Nash and Sutcliffe Efficiency); R

^{2}= square of the Pearson’s type (linear) correlation coefficient.

**Figure 7.**Scatter plots and hydrographs of total streamflow observed (Q

_{obs}) and predicted (Q

_{sim}) at the outlet of the catchment, for the validation period. Predictions were produced by (

**a**) SHETRAN; and (

**b**) MIKE SHE. EF

_{2}= Coefficient of Efficiency (Nash and Sutcliffe Efficiency); R

^{2}= square of the Pearson’s type (linear) correlation coefficient; MAE = Mean Absolute Error.

**Figure 8.**Observed and simulated piezometric levels for some selected wells included in the analysis throughout calibration (

**left column**) and validation (

**right column**) periods. Screens of wells are located in the geological layers: (

**a**) Quaternarian; (

**b**) Landeniaan; (

**c**) Cretaceous; and (

**d**) Landeniaan.

**Figure 9.**(

**a**) Illustration of the process followed to determine the threshold value (x

_{th}) in the peaks over threshold (POT) method using a partial duration time series (PDS) of daily peak values; and (observed and simulated) peak flow empirical distributions for stations (

**b**) Gete, (

**c**) Grote Gete, and (

**d**) Kleine Gete.

**Figure 10.**Flow component hydrographs showing the filtered baseflow (Q

_{bs}) estimates for (

**a**) the observed hydrograph at the outlet of the study catchment for some months of the year 1985 (plotted Q

_{bs}hydrographs correspond to passes 1 to 4, namely, Q

_{bs_1}, Q

_{bs_2}, Q

_{bs_3}and Q

_{bs_4}); and for (

**b**–

**d**) the hydrographs simulated by both SHETRAN (Q

_{bs_SHET}) and MIKE SHE (Q

_{bs_MSHE}) for the three study river stations in the validation period [1 January 1987–31 December 1988] (Q

_{bs}was estimated using 3 passes). The observed total hydrograph (Q_

_{obs}) as well as the respective estimated baseflow (Q

_{bs}_

_{obs}, after 3 passes) are plotted in (

**b**–

**d**) for comparison purposes.

Model Parameter | Geological Unit | Bound of Interval | |
---|---|---|---|

Lower | Upper | ||

n_{ov} (s m^{−1/3}) | Not applicable | 0.025 | 0.070 |

n_{riv} (s m^{−1/3}) | Not applicable | 0.10 | 6.25 |

K_{x} (m s^{−1}) | Quaternarian Brusselian Landeniaan Heers Cretaceous | 1.0 × 10^{−7}7.0 × 10 ^{−5}5.0 × 10 ^{−6}5.0 × 10 ^{−7}1.0 × 10 ^{−6} | 4.0 × 10^{−5}2.0 × 10 ^{−3}5.0 × 10 ^{−4}5.0 × 10 ^{−5}1.0 × 10 ^{−5} |

K_{z} (m s^{−1}) | Quaternarian Brusselian Landeniaan Heers Cretaceous | 1.0 × 10^{−8}7.0 × 10 ^{−6}5.0 × 10 ^{−7}1.0 × 10 ^{−8}1.0 × 10 ^{−8} | 1.0 × 10^{−6}7.0 × 10 ^{−5}5.0 × 10 ^{−5}5.0 × 10 ^{−6}1.0 × 10 ^{−7} |

_{ov}= overland Manning’s “coefficient”; n

_{riv}= river Manning’s “coefficient”; K

_{x}= horizontal saturated hydraulic conductivity; K

_{z}= vertical saturated hydraulic conductivity.

**Table 2.**Values of the effective (calibrated) model parameters as a function of the hydrological code used in the study. The values are listed for different spatial zones depending on the type of parameter.

Parameter | (Spatial) Zone | Geological Unit | SHETRAN | MIKE SHE |
---|---|---|---|---|

n_{ov} (s m^{−1/3}) | Maize crop fields | Not applicable | 0.44 | 0.29 |

n_{riv} (s m^{−1/3}) | Average (river network) | Not applicable | 0.065 | 0.065 |

K_{x} (m s^{−1}) | A (Figure 3a) | Quaternarian | 1.00 × 10^{−7} | 1.0 × 10^{−7} |

Landeniaan | 8.80 × 10^{−5} | 7.87 × 10^{−5} | ||

K_{z} (m s^{−1}) | Quaternarian | 1.00 × 10^{−8} | 9.10 × 10^{−7} | |

Landeniaan | 5.00 × 10^{−5} | 2.75 × 10^{−6} | ||

K_{x} (m s^{−1}) | B (Figure 3a) | Quaternarian | 1.00 × 10^{−7} | 1.00 × 10^{−7} |

Landeniaan | 8.28 × 10^{−5} | 7.87 × 10^{−5} | ||

K_{z} (m s^{−1}) | Quaternarian | 1.00 × 10^{−8} | 1.90 × 10^{−7} | |

Landeniaan | 5.00 × 10^{−5} | 2.98 × 10^{−5} | ||

K_{x} (m s^{−1}) | Average (whole catchment) | Brusselian | 6.43 × 10^{−4} | 1.65 × 10^{−3} |

Heers | 2.84 × 10^{−5} | 4.55 × 10^{−5} | ||

Cretaceous | 4.27 × 10^{−6} | 1.00 × 10^{−6} | ||

K_{z} (m s^{−1}) | Brusselian | 7.00 × 10^{−5} | 7.00 × 10^{−6} | |

Heers | 5.00 × 10^{−6} | 2.28 × 10^{−6} | ||

Cretaceous | 1.00 × 10^{−7} | 7.54 × 10^{−8} |

_{ov}= overland Manning’s “coefficient”; n

_{riv}= river Manning’s “coefficient”; K

_{x}= horizontal saturated hydraulic conductivity; K

_{z}= vertical saturated hydraulic conductivity.

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## Share and Cite

**MDPI and ACS Style**

Vázquez, R.F.; Brito, J.E.; Hampel, H.; Birkinshaw, S.
Assessing the Performance of SHETRAN Simulating a Geologically Complex Catchment. *Water* **2022**, *14*, 3334.
https://doi.org/10.3390/w14203334

**AMA Style**

Vázquez RF, Brito JE, Hampel H, Birkinshaw S.
Assessing the Performance of SHETRAN Simulating a Geologically Complex Catchment. *Water*. 2022; 14(20):3334.
https://doi.org/10.3390/w14203334

**Chicago/Turabian Style**

Vázquez, Raúl F., Josué E. Brito, Henrietta Hampel, and Stephen Birkinshaw.
2022. "Assessing the Performance of SHETRAN Simulating a Geologically Complex Catchment" *Water* 14, no. 20: 3334.
https://doi.org/10.3390/w14203334