# The Role of Hydrological Signatures in Calibration of Conceptual Hydrological Model

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## Abstract

**:**

## 1. Introduction

## 2. Study Area and Data

## 3. Methods

#### 3.1. Bilan Hydrological Model

#### 3.2. Calibration Strategies

#### 3.2.1. Expert Calibration

#### 3.2.2. Standard Automatic Calibration

#### 3.2.3. Calibration with Hydrological Signatures

- Single-component OFs with runoff (R);
- Single-component OFs with soil moisture (SW);
- Two-component OFs with runoff (R2);
- Two-component OFs with soil moisture (SW2);
- Two-component OFs with runoff and soil moisture (RSW);
- Three-component OFs (RSW2).

#### 3.3. Model Evaluation

- (a)
- Goodness-of-fit expressed (GOF) as the root mean square error (RMSE; [40]) and Kling–Gupta efficiency (KGE; [41]) of the simulated runoff with respect to runoff simulated by the parameter set resulting from the expert calibration (further denoted as the expert simulation).The RMSE is given by$$RMSE=\sqrt{(\frac{1}{n})\sum _{i=1}^{n}{({y}_{i}-{x}_{i})}^{2}}$$The KGE is calculated according to$$KGE=1-\sqrt{{\left(s\left[1\right]\times (r-1)\right)}^{2}+{\left(s\left[2\right]\times (\alpha -1)\right)}^{2}+{\left(s\left[3\right]\times (\beta -1)\right)}^{2}},$$
- (b)
- difference in the distribution of Bilan model parameters (BP) Spa (controlling soil depth) and Grd (controlling baseflow) between expert-calibrated parameters (see Section 3.2) and calibration with particular OF.
- (c)
- relative difference in mean and the 20th (Q20) and 80th (Q80) percentile of runoff and soil moisture from the expert simulation with respect to the same signatures from the simulation calibrated with particular OF.

## 4. Results and Discussion

#### 4.1. Runoff Difference Probability Curve

#### 4.2. Goodness-Of-Fit

#### 4.3. Uncertainty of Bilan Model Parameters

#### 4.4. Runoff Signatures

#### 4.5. Summary of OFs’ Performance

## 5. Concluding Remarks

- The standard automatic calibration performs best for most of the evaluation criteria, except for low flows;
- The objective functions (OFs) utilizing time series are always performing better than those based on signatures only;
- It is however clear that the good performance of automatically calibrated models can be counterbalanced by poor representation of hydrological processes, important hydrological signatures and overall increasing uncertainty of model parameters. Therefore, evaluation metrics accounting for biases in hydrological processes representation and objective functions combining the bias in runoff time series with that of other runoff characteristics should be considered;
- In the cases where the runoff time series are not available, it is possible to get sufficient fit even using signatures representing runoff mean and variability;
- The role of the runoff and soil moisture signatures is significant, in particular for low flows and parameters of the hydrological model.

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

GOF | Goodness-of-fit between observed and simulated runoff |

RMSE | Root mean square error |

KGE | Kling–Gupta efficiency |

BP | Uncertainty of the estimated Bilan model parameters |

RS | Selected runoff and soil moisture signatures |

Q20 | Percentile of runoff and soil moisture |

Q80 | Percentile of runoff and soil moisture |

P | Precipitation (mm) |

R | Runoff (mm) |

RH | Relative air humidity (%) |

PET | Potential evapotranspiration (mm) |

RM | Simulated runoff (mm) |

DR | Direct runoff (mm) |

DS | Runoff storage (mm) |

BS | Baseflow (mm) |

GS | Groundwater storage (mm) |

I | Interflow (mm) |

Spa | Capacity of soil moisture storage |

Dgm | Temperature and snow melting factor |

Dgw | Water available on the land surface under winter conditions |

Alf | Direct runoff parameters |

Soc, Mec, Wic | Divide percolation into interflow and groundwater recharge under summer, Snow melt and winter conditions |

Grd | Parameter controlling the outflow from groundwater storage |

SCE-UA | Shuffled complex evolution |

DE | Differential evolution method |

OF | Objective function |

R | Single-component OFs with runoff |

SW | Single-component OFs with soil moisture |

R2 | Two-component OFs with runoff |

SW2 | Two-component OFs with soil moisture |

RSW | Two-component OFs with runoff and soil moisture |

RSW2 | Three-component OFs with runoff and soil moisture |

## Appendix A

**Table A1.**Optimal OFs are denoted in bold. The time series column contains time series as runoff (R) and soil moisture (SW). The column’s hydrological signature of (R) and (SW) is combined with statistical indicators as mean, IQR, sd and selected settings (*).

ID | Time Series | R-Signatures | SW-Signatures | |||||
---|---|---|---|---|---|---|---|---|

R | SW | mean | IQR | sd | mean | IQR | sd | |

Automatic | * | |||||||

R-mean | * | |||||||

R-iqr | * | |||||||

R-sd | * | |||||||

SW-mean | * | |||||||

SW-iqr | * | |||||||

SW-sd | * | |||||||

SW-optim | * | |||||||

R2-mean-sd | * | * | ||||||

R2-mean-iqr | * | * | ||||||

R2-mean-optim | * | * | ||||||

R2-sd-iqr | * | * | ||||||

R2-sd-optim | * | * | ||||||

R2-iqr-optim | * | * | ||||||

SW2-mean-iqr | * | * | ||||||

SW2-mean-sd | * | * | ||||||

SW2-mean-optim | * | * | ||||||

SW2-sd-iqr | * | * | ||||||

SW2-sd-optim | * | * | ||||||

SW2-iqr-optim | * | * | ||||||

RSW-mean-mean | * | * | ||||||

RSW-mean-sd | * | * | ||||||

RSW-mean-optim | * | * | ||||||

RSW-mean-iqr | * | * | ||||||

RSW-sd-sd | * | * | ||||||

RSW-sd-optim | * | * | ||||||

RSW-sd-iqr | * | * | ||||||

RSW-optim-optim | * | * | ||||||

RSW-optim-iqr | * | * | ||||||

RSW-iqr-iqr | * | * | ||||||

RSW2-mean-mean-sd | * | * | * | |||||

RSW2- mean-mean-optim | * | * | * | |||||

RSW2-mean-mean-iqr | * | * | * | |||||

RSW2-sd-sd-mean | * | * | * | |||||

RSW2-sd-sd-optim | * | * | * | |||||

RSW2-sd-sd-iqr | * | * | * | |||||

RSW2-optim-optim-sd | * | * | * | |||||

RSW2-optim-optim-mean | * | * | * | |||||

RSW2-optim-optim-iqr | * | * | * | |||||

RSW2-iqr-iqr-mean | * | * | * | |||||

RSW2-iqr-iqr-sd | * | * | * | |||||

RSW2-iqr-iqr-optim | * | * | * | |||||

RSW2-mean-sd-optim | * | * | * | |||||

RSW2-sd-mean-optim | * | * | * | |||||

RSW2-optim-mean-sd | * | * | * | |||||

RSW2-iqr-sd-optim | * | * | * | |||||

RSW2-sd-iqr-optim | * | * | * | |||||

RSW2-optim-iqr-sd | * | * | * | |||||

RSW2-iqr-mean-optim | * | * | * | |||||

RSW2-mean-iqr-optim | * | * | * | |||||

FDC-all | * | |||||||

FDC-180 | * | |||||||

FDC-300-330-355-364 | * |

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**Figure 3.**Runoff ((

**a**)-calibration, (

**b**)-validation) relative difference probability curve (red line—manual calibration settings, green line—selected calibrations strategies, orange line—non-selected calibrations strategies).

**Figure 4.**The density of differences in RMSE (

**a**) and KGE (

**b**) between expert calibration and the rest of the objective functions (OFs). The dotted line corresponds to mean of the selected best-performing OFs, the dashed line to the mean for the OFs, including time series, and the solid line to the mean of the OFs that were not selected.

**Figure 5.**The density of relative errors in Spa (

**a**) and Grd (

**b**) based on selected best-performing OFs (green area) and the rest (red area). The dotted line correspond to the mean of the selected best-performing objective functions, the dashed line to the mean OFs, including time series, and the solid line to the mean of the OFs that were not selected.

**Figure 6.**Density of error in runoff signatures in Q20 (

**a**) and Q80 (

**b**) based on selected best-performing OFs (green area) and the rest (red area). Dotted line correspond to mean of selected best-performing objective functions, dashed line to mean OFs including time series and the solid line the mean of the OFs that were not selected.

Input Variables | Units | |
---|---|---|

Variables | Description | |

P | precipitation | (mm) |

R | runoff | (mm) |

T | air temperature | (°C) |

H | relative air humidity | (%) |

PET | potential evapotranspiration | (mm) |

TS | optional time series | (mm) |

Calculated variables | ||

Fluxes | Description | |

PET | potential evapotranspiration | (mm) |

ET | basin evapotranspiration | (mm) |

INF | infiltration into the soil | (mm) |

PERC | percolation throught the soil layer | (mm) |

I | interflow | (mm) |

DR | direct runoff | (mm) |

BF | base flow (simulated) | (mm) |

RM | total runoff (simulated) | (mm) |

State variables | Description | |

SS | snow water storage | (mm) |

SW | soil moisture | (mm) |

GS | groundwater storage | (mm) |

DS | direct runoff storage | (mm) |

DEFV | deficet volumes | (mm) |

Model parameters | ||

Parameters | Description | |

SPA | capacity of soil moisture storage | |

DGM | temperature and snow melting factor | |

DGW | water available on the land surface under winter conditions | |

ALF | controls the proportion of precipitation transformed into the direct runoff | |

SOC | distribution of percolation into interflow and groundwater recharge under summer cond. | |

MEC | distribution of percolation into interflow and groundwater recharge under conditions of snow melting | |

WIC | distribution of percolation into interflow and groundwater recharge under winter cond. | |

GRD | parameter controlling outflow from groundwater storage (base flow) |

**Table 2.**Difference in RMSE (a) and KGE (b) for all groups of objective functions with respect to expert calibration. Automatic, time series + signatures and signatures only mean calibration strategies which combine runoff (R), soil moisture (SW) or runoff + soil moisture (R + SW).

GOF | Automatic | Time Series + Signatures | Signatures Only | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

R | SW | R + SW | R | SW | R + SW | |||||||||

Mean | Median | Mean | Median | Mean | Median | Mean | Median | Mean | Median | Mean | Median | Mean | Median | |

RMSE | 0.134 | 0.142 | 0.125 | 0.138 | −0.560 | −0.478 | −0.257 | −0.183 | −0.303 | −0.222 | −0.537 | −0.454 | −0.383 | −0.295 |

KGE | −0.097 | −0.077 | −0.099 | −0.080 | 0.270 | 0.265 | 0.151 | 0.129 | 0.098 | 0.107 | 0.236 | 0.232 | 0.170 | 0.156 |

**Table 3.**Relative difference of Bilan model parameters Spa and Grd between expert calibration and other calibration strategies. Automatic, time series + signatures and signatures only mean calibration strategies which combinate runoff (R), soil moisture (SW) or runoff + soil moisture (R + SW).

BP | Automatic | Time Series + Signatures | Signatures Only | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

R | SW | R + SW | R | SW | R + SW | |||||||||

Mean | Median | Mean | Median | Mean | Median | Mean | Median | Mean | Median | Mean | Median | Mean | Median | |

Spa | 0.202 | 0.121 | 0.204 | 0.122 | 0.282 | 0.285 | 0.275 | 0.267 | 0.243 | 0.163 | 0.297 | 0.269 | 0.305 | 0.272 |

Grd | 0.163 | 0.158 | 0.164 | 0.161 | 0.388 | 0.363 | 0.233 | 0.169 | 0.232 | 0.148 | 0.391 | 0.358 | 0.252 | 0.164 |

**Table 4.**Relative difference in Q20 and Q80 for runoff. Automatic, time series + signatures and signatures only mean calibration strategies which combinate runoff (R), soil moisture (SW) or runoff + soil moisture (R + SW).

RS | Automatic | Time Series + Signatures | Signatures Only | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

R | SW | R + SW | R | SW | R + SW | |||||||||

Mean | Median | Mean | Median | Mean | Median | Mean | Median | Mean | Median | Mean | Median | Mean | Median | |

Q20 | 0.224 | 0.172 | 0.225 | 0.181 | 0.568 | 0.570 | 0.391 | 0.323 | 0.354 | 0.299 | 0.545 | 0.565 | 0.482 | 0.439 |

Q80 | 0.075 | 0.056 | 0.073 | 0.057 | 0.182 | 0.159 | 0.114 | 0.087 | 0.141 | 0.106 | 0.221 | 0.173 | 0.155 | 0.127 |

**Table 5.**The best OFs according to goodness-of-fit (GOF), parameters of the hydrological model (BP) and high and low flow indices (RS). Time series, R-signatures and SW-signatures mean characteristic which combined times series or signatures of runoff (R) and of soil moisture (SW), their statistic indicators are mean, interquartile range (IQR), sd and selected settings (*).

ID | Time Series | R-Signatures | SW-Signatures | Evaluation Metrics | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|

R | SW | mean | IQR | sd | mean | IQR | sd | GOF | BP | RS | |

automatic | * | * | * | * | |||||||

R2-mean-sd | * | * | * | ||||||||

R2-mean-iqr | * | * | * | * | |||||||

R2-mean-optim | * | * | * | * | * | ||||||

R2-sd-iqr | * | * | * | * | |||||||

R2-sd-optim | * | * | * | * | |||||||

R2-iqr-optim | * | * | * | * | * | ||||||

RSW-mean-mean | * | * | * | * | |||||||

RSW-mean-iqr | * | * | * | ||||||||

RSW-sd-sd | * | * | * | * | |||||||

RSW-optim-optim | * | * | * | * | |||||||

RSW-optim-iqr | * | * | * | * | |||||||

RSW-iqr-iqr | * | * | * | ||||||||

RSW2-sd-sd-optim | * | * | * | * | |||||||

RSW2-optim-optim-sd | * | * | * | * | * | ||||||

RSW2-optim-optim-mean | * | * | * | * | * | ||||||

RSW2-optim-optim-iqr | * | * | * | * | * | ||||||

RSW2-optim-mean-sd | * | * | * | * | * | ||||||

RSW2-optim-iqr-sd | * | * | * | * | * | ||||||

FDC-all | * | * | * | * | |||||||

FDC-300-330-355-364 | * | * | * | * |

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## Share and Cite

**MDPI and ACS Style**

Melišová, E.; Vizina, A.; Staponites, L.R.; Hanel, M.
The Role of Hydrological Signatures in Calibration of Conceptual Hydrological Model. *Water* **2020**, *12*, 3401.
https://doi.org/10.3390/w12123401

**AMA Style**

Melišová E, Vizina A, Staponites LR, Hanel M.
The Role of Hydrological Signatures in Calibration of Conceptual Hydrological Model. *Water*. 2020; 12(12):3401.
https://doi.org/10.3390/w12123401

**Chicago/Turabian Style**

Melišová, Eva, Adam Vizina, Linda R. Staponites, and Martin Hanel.
2020. "The Role of Hydrological Signatures in Calibration of Conceptual Hydrological Model" *Water* 12, no. 12: 3401.
https://doi.org/10.3390/w12123401