# The Response of the HydroGeoSphere Model to Alternative Spatial Precipitation Simulation Methods

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

^{2}watershed and the runoff response of the physically based hydrological models for three methods used to generate the spatial precipitation distribution: Thiessen polygons (TP), Co-Kriging (CK) interpolation and simulated annealing (SA). The HydroGeoSphere model is employed to simulate the rainfall-runoff process in two watersheds. For a large precipitation event, the simulated patterns using SA appear to be more realistic than those using the TP and CK method. In a large-scale watershed, the results demonstrate that when HydroGeoSphere is forced by TP precipitation data, it fails to reproduce the timing, intensity, or peak streamflow values. On the other hand, when HydroGeoSphere is forced by CK and SA data, the results are consistent with the measured streamflows. In a medium-scale watershed, the HydroGeoSphere results show a similar response compared to the measured streamflow values when driven by all three methods used to estimate the precipitation, although the SA case is slightly better than the other cases. The analytical results could provide a valuable counterpart to existing climate-based drought indices by comparing multiple interpolation methods in simulating land surface runoff.

## 1. Introduction

^{2}), there are still many issues that need to be addressed.

^{2}) when driven by uncertain precipitation patterns over large areas.

^{2}), Li, Unger [15] (area: 285.6 km

^{2}), Goderniaux, Brouyre [17] (area: 480 km

^{2}). When the basin is relatively large (over thousands of square kilometers) many issues need to be considered when physically based hydrological models are used to simulate the rainfall-runoff process, including (1) uncertainty in the model output arising from uncertainty in the input data (measurement and interpolation errors) and in the models themselves (conceptual, logical, mathematical, and computational errors) and (2) the limited computational capacity available to many users. The growing trend of model complexity, data availability, and physical representation has always pushed the limits of computational efficiency, which in turn has limited the application of physically based hydrological models to small domains and for shorter durations [18]. To our knowledge, the use of a fully integrated physically based hydrological model to simulate the rainfall-runoff process over thousands of square kilometers is rare.

## 2. The Study Area

^{2}and Jiangji is the basin outlet. The basin slopes from south to north with the elevation changing from 1536 to 18.7 m over a horizontal extent of about 128 km. It is an important tributary of the Huai River and originates from the northern slope of the Dabie Mountain in the south Huai River Basin. The river system has two major tributaries: the Shi River to the east and the Guan River to the west, and they merge near the Jiangji outlet (Figure 1). The two tributaries are regulated by the Meishan and Nianyushan reservoirs that have watershed areas of 1970 and 924 km

^{2}respectively, with corresponding travel distances of 88 and 89 km from the reservoir outflow point to the Jiangji outlet.

^{2}resolution.

^{2}resolution (CK method); (3) the simulated spatial precipitation distribution for a 5 $\times $ 5 km

^{2}resolution using the simulated annealing algorithm (SA method).

^{2}) was also selected to study the impact of the rainfall distribution methods on a medium-scale.

## 3. Methodology

#### 3.1. The Physically Based Hydrological Model

#### 3.2. Discretisation, Boundary Conditions, and Computational Process

#### 3.3. Spatially-Distributed Precipitation Patterns

- The initial weight coefficient.
- The energy is given by the objective function (Equation (6)), ${O}_{old}={\sigma}_{0}^{2}$.
- The initial temperature is determined as: ${T}_{0}=1000{\sigma}_{0}^{2}$, where ${T}_{0}$ are the initial temperature and some parameters are selected (Figure 4).
- The initial configuration is perturbed by randomly selecting one from the rain gauges and the DEM locations, and the objective function is calculated.
- Let $\mathsf{\Delta}\mathrm{OF}={O}_{new}-{O}_{old}$. If $\mathsf{\Delta}O\le 0$, the new configuration is accepted because the objective function has been minimized. However, if $\mathsf{\Delta}O>0$, the new configuration is accepted with probability acceptation criterion, ${e}^{\frac{-\mathsf{\Delta}O}{{T}_{k}}}$ and $n=n+1$. If $n<N$, step 4 is applied again.
- The temperature is decreased at a certain amount, ${T}_{k+1}=R\cdot {T}_{k}$, 0 < R < 1 and step 4 is applied again.
- The running of the simulation process is defined by steps 4–6 continues until:
- A number of prefixed numbers of iterations are reached;
- At a given constant T none of the numbers of new configurations have been accepted;
- Changes in the objective function for various consecutive $T$ steps are slight.

#### 3.4. Calibration Procedure

#### 3.5. Statistical Analysis

## 4. Results

#### 4.1. Calibrated Parameters and Initial Condition

#### 4.2. Spatial Distribution of a Typical Precipitation

^{−1}and the variance is 11,630.69 mm

^{2}d

^{−1}between 48 gauging stations. The minimum is 8.5 mm d

^{−1}and the maximum is 167.9 mm d

^{−1}. This indicates that the difference in the daily precipitation between the observation points is very high. The daily spatial precipitation data at every grid for this single event was calculated using the TP, CK, and SA methods.

^{−1}. The different precipitation patterns can be obtained using the CK and SA methods. Figure 6 illustrates these differences. In Figure 6, the spatial resolution is 5 km × 5 km. Figure 6A indicates a region of high precipitation at the southern end of the Shiguan river basin and confirms that the CK method tends to smooth extreme values of the precipitation data set. Although they exhibit the general spatial patterns of the precipitation distribution, the CK method may overestimate the size of areas of high and low precipitation.

#### 4.3. Transient Simulations

#### 4.3.1. Large-Scale Simulated Streamflow Results

^{3}/s. The TP case underestimated the peak streamflow, where the CK cases slightly overestimated the peak flow. The reason for the overestimation was because of the spatial differences in the rainfall patterns. The flood peak arrived too early and the flood waters recede too late. However the SA case caught the peak value of the flood. For the other days, the precipitation was small, the runoff was small and most of the discharge was less than 100 m

^{3}/s. The simulated streamflow was most accurate for three cases.

#### 4.3.2. Medium-Scale Simulated Streamflow Results

^{3}/s), the observed streamflow was overestimated for the TP case. The reason for overestimating was because the forcing precipitation data are the surface average and therefore could not capture accurately the information of the distribution of the precipitation. For the CK case, the streamflow was underestimated. This was because the gridded CK precipitation data underestimated the actual maximum precipitation location and overestimated the minimum precipitation zone. The SA method was the best among the three cases and the RMSE of the SA case was the lowest among the three cases.

^{3}/s. For the TP case, the streamflow was overestimated. The reasons were that (1) the spatial differences for the precipitation were relatively large; and (2) for physically based surface-subsurface hydrological models, the spatially gridded precipitation data had a large impact on the simulated results. If the observed streamflow was less than 50 m

^{3}/s, there was no clear difference between the simulation results and the observed data between all three of the cases. The CK data and SA data generally reflect the spatial variations of the rainfall, and the use of more than one method to estimate the gridded precipitation data may be more suitable to force distributed hydrological models.

## 5. Summary and Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**Land use characteristics, soil types, and hydrogeology types within the Shiguan river basin.

**Figure 5.**(

**A**) Computed steady-state surface water depth. (

**B**) Computed steady-state subsurface saturation, with nearly full saturation shown in red.

**Figure 6.**The spatial distribution of precipitation for a large rainfall in the simulation period using CK (

**A**) and SA (

**B**).

Subsurface Domain | Meaning | Unit |
---|---|---|

$K$ | Saturated hydraulic conductivity | ${\mathrm{LT}}^{-1}$ |

$\varphi $ | Porosity | - |

${S}_{s}$ | Specific storage | ${\mathrm{L}}^{-1}$ |

$\alpha $ | van Genuchten parameter | - |

$\beta $ | van Genuchten parameter | ${\mathrm{L}}^{-1}$ |

${S}_{wr}$ | Residual water saturation | - |

Surface domain | ||

${l}_{e}$ | Coupling length | L |

${n}_{x}$ | Manning roughness coefficient | ${\mathrm{L}}^{-1/3}\mathrm{T}$ |

${n}_{y}$ | Manning roughness coefficient | ${\mathrm{L}}^{-1/3}\mathrm{T}$ |

Evapotranspiration | ||

${L}_{e}$ | Evaporation depth | L |

${\theta}_{e1},{\theta}_{e2}$ | Evaporation limiting saturations | - |

$LAI$ | Leaf area index | - |

${L}_{r}$ | Root depth | L |

${C}_{1},{C}_{2},{C}_{3}$ | Transpiration fitting parameters | - |

${\theta}_{wp},{\theta}_{fc},{\theta}_{0},{\theta}_{an}$ | Transpiration limiting saturations | - |

${C}_{int}$ | Canopy storage parameter | L |

Land Use | ${\mathit{n}}_{\mathit{x}},{\mathit{n}}_{\mathit{y}}$ | ${\mathit{l}}_{\mathit{e}}$ |
---|---|---|

m^{−1/3} d | m | |

Forest | $6.9\times {10}^{-6}$ | 0.1 |

Agricultural | $2.3\times {10}^{-6}$ | 0.1 |

Bare rock | $3.5\times {10}^{-7}$ | 0.1 |

Urban and rural | $2.3\times {10}^{-6}$ | 0.1 |

Alluvium | $8.9\times {10}^{-7}$ | 0.1 |

**Table 3.**Van Genuchten parameters, total porosity, specific storage and full saturated hydraulic conductivities.

Layer | Type | $\mathit{\alpha}$ | $\mathit{\beta}$ | ${\mathit{S}}_{\mathit{w}\mathit{r}}$ | $\mathbf{\varnothing}$ | ${\mathit{S}}_{\mathit{s}}$ | K |
---|---|---|---|---|---|---|---|

[-] | [d^{−1}] | [-] | [-] | [d^{−1}] | [m d^{−1}] | ||

Soil | Anthrosols | 0.059 | 1.480 | 0.256 | 0.5 | $2.6\times {10}^{-4}$ | 0.008 |

Luvisols | 0.006 | 1.590 | 0.166 | 0.45 | $9.2\times {10}^{-4}$ | 0.019 | |

Semi-hydromorphic soil | 0.009 | 1.510 | 0.188 | 0.35 | $4.9\times {10}^{-4}$ | 0.022 | |

Entisols | 0.020 | 1.410 | 0.149 | 0.45 | $5.0\times {10}^{-4}$ | 0.016 | |

Rock | Clastic rock | 30.00 | 3.000 | 0.050 | 0.25 | $4.0\times {10}^{-5}$ | 0.2 |

Magatic rock | 30.00 | 3.000 | 0.050 | 0.01 | $3.4\times {10}^{-6}$ | 8.64 × 10^{−8} | |

Gravel sand | 0.145 | 2.68 | 0.105 | 0.25 | $4.0\times {10}^{-4}$ | 864 | |

Metamorphic rock | 44.6 | 0.21 | 0.030 | 0.01 | $3.3\times {10}^{-7}$ | 6.0 |

Forest | Grass | Dryland | Urban and Rural | Beach | |
---|---|---|---|---|---|

Evaporation depth [m] | 2.0 | 2.0 | 2.0 | 2.0 | 2.0 |

Root depth (${L}_{r}$) [m] | 5.2 | 2.6 | 0.0 | 0.0 | 0.0 |

$LAI[-]$ | 5.12 | 2.5 | 0.0 | 0.40 | 0.0 |

${C}_{1}[-]$ | 0.3 | 0.3 | 0.3 | 0.3 | 0.3 |

${C}_{2}[-]$ | 0.2 | 0.2 | 0.2 | 0.2 | 0.2 |

${C}_{3}\left[\mathrm{m}{\mathrm{d}}^{-1}\right]$ | 1 | 1 | 1 | 1 | 1 |

${C}_{int}\left[\mathrm{m}\right]$ | ${10}^{-5}$ | ${10}^{-5}$ | ${10}^{-5}$ | ${10}^{-5}$ | ${10}^{-5}$ |

**Table 5.**Statistical analysis of 10 spatial precipitation simulations in the Shiguan Basin and the Huangnizhuang basin using the SA method.

Shiguan | Huangnizhuang | |||||
---|---|---|---|---|---|---|

SA Cases | Max | Min | Var | Max | Min | Var |

1 | 190.78 | 9.66 | 25.51 | 91.40 | 38.13 | 18.55 |

2 | 151.40 | 7.66 | 20.25 | 93.79 | 39.12 | 19.04 |

3 | 189.01 | 9.57 | 25.28 | 120.86 | 50.42 | 24.53 |

4 | 150.68 | 7.63 | 20.15 | 84.94 | 35.43 | 17.24 |

5 | 196.73 | 9.96 | 26.31 | 104.25 | 43.49 | 21.16 |

6 | 157.82 | 7.99 | 21.11 | 90.77 | 37.87 | 18.42 |

7 | 147.52 | 7.47 | 19.73 | 124.72 | 52.03 | 25.32 |

8 | 151.18 | 7.65 | 20.22 | 113.58 | 47.38 | 23.05 |

9 | 175.69 | 8.89 | 23.50 | 104.70 | 43.68 | 21.25 |

10 | 166.11 | 8.41 | 22.21 | 103.47 | 43.16 | 21.00 |

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**MDPI and ACS Style**

Lü, H.; Wang, Q.; Horton, R.; Zhu, Y.
The Response of the HydroGeoSphere Model to Alternative Spatial Precipitation Simulation Methods. *Water* **2021**, *13*, 1891.
https://doi.org/10.3390/w13141891

**AMA Style**

Lü H, Wang Q, Horton R, Zhu Y.
The Response of the HydroGeoSphere Model to Alternative Spatial Precipitation Simulation Methods. *Water*. 2021; 13(14):1891.
https://doi.org/10.3390/w13141891

**Chicago/Turabian Style**

Lü, Haishen, Qimeng Wang, Robert Horton, and Yonghua Zhu.
2021. "The Response of the HydroGeoSphere Model to Alternative Spatial Precipitation Simulation Methods" *Water* 13, no. 14: 1891.
https://doi.org/10.3390/w13141891