# Comparison of Spatial Interpolation Schemes for Rainfall Data and Application in Hydrological Modeling

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area

^{2}. The elevation ranges between 92 m and 827 m and increases gradually from north to south. The catchment is dominated by a tropical monsoon climate, and mean annual temperature, precipitation, and runoff are 17.5 °C, 1866.5 mm, and 1017.3 mm, respectively. Precipitation is mainly concentrated from May through September (69.8% of annual precipitation and 66.6% of annual runoff). The soil texture in the watershed is mainly sandy clay and clay loam.

#### 2.2. Data

#### Data Preprocessing

#### 2.3. Interpolation Schemes

#### 2.3.1. Principal Component Regression with Residual Correction

#### Annual Precipitation Interpolation

_{1i}, X

_{2i}, X

_{3i}, ${X}_{4i},\text{}\mathrm{and}\text{}{X}_{5i}$ are the ith (i = 1, 2,..., n) grid cell values of the longitude, latitude, altitude, slope, and aspect grid surfaces.

_{ri}is the residual value of ith meteorological station, n is the number of stations used for the interpolation of residual values, ${d}_{i}$ is the distance from the interpolated point to the ith meteorological station, and P is the power of the distance.

#### Daily Precipitation Interpolation

#### Hourly Precipitation Interpolation

#### 2.3.2. Multiple Linear Regression

#### 2.3.3. Inverse Distance Weighting

#### 2.4. Hydrological Model

#### 2.5. Validation

## 3. Results

#### 3.1. Annual Analysis

#### 3.2. Daily Analysis

^{3}/s. The peak discharges determined using the three interpolation methods were lower than the measured values. The PCRR method yielded the closest estimate (83.2 m

^{3}/s), while the IDW and MLR values were 71 m

^{3}/s and 65.4 m

^{3}/s, respectively. A similar trend was observed for runoff processes on 22 May 2010. Figure 5 and Figure 6 reveal that, in general, large rainfall differences led to large peak flows, and the simulated streamflow volumes varied with the different inputs.

#### 3.3. Hourly Analysis

## 4. Discussion

^{2}, into six sub-basins; each sub-basin can represent the internal spatial distribution. The area precipitation of each sub-basin is the average of the internal grids, which can reflect the geographical features of the catchment, so it can represent the spatial precipitation distribution information within the sub-basin. This can effectively explore the performance of the spatial precipitation interpolation method. Haberlandt et al. [33], Ruelland et al. [21], Masih et al. [40], Tobin et al. [41], and others also used semi-distributed hydrological modeling for the validation of interpolation methods. In addition, the HEC model has the characteristics of easy operation, short running time, the combination of a variety of multiple runoff-convergence schemes, and so on. At the same time, the study catchment is located in Jiangxi Province, where flash floods happened frequently; previous studies have used the HEC-HMS model (Li [42]; Wu et al. [43]) with good applicability. This model and parameter calibration procedure have been successfully applied in our previous study, ‘Flash Flood Forecasting and Disaster Management of Jiangxi Province’ (grant No. 0628-156104104417) project. Therefore, the semi-distributed HEC-HMS model was chosen.

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 1.**Location of the study area and the geographic distribution of hydrometeorological stations.

**Figure 2.**Scatterplots of observed versus predicted values for all interpolation methods of annual precipitation.

**Figure 3.**Statistical error of rainfall between interpolation methods and meteorological station rainfall measurements in the basin.

**Figure 5.**Differences in monthly rainfall for the Xinxie catchment using different interpolations: (

**a**) PCRR-IDW and (

**b**) PCRR-MLR.

**Figure 6.**Modeled and measured runoff during May to June 2010 in Xinxie catchment for principal component regression with residual correction (PCRR), inverse distance weighting (IDW), and MLR rainfall interpolation.

**Figure 7.**Modeled and measured runoff of two flood events in Xinxie catchment for PCRR, IDW, and MLR rainfall interpolation.

Spatial Interpolation | Methods | Precipitation at 41 Gauges | Lat & Lon | Elevation | Slope | Aspect |

IDW | √ | √ | ||||

MLR | √ | √ | √ | |||

PCRR | √ | √ | √ | √ | √ | |

Model Application | All three methods | streamflow records at Xinxiel station | soil types | land cover data |

**Table 2.**Hydrologic Engineering Center Hydrologic Modeling System (HEC-HMS) simulation scheme of Xinxie catchment.

Runoff-Volume Model | Direct-Runoff Model | Baseflow Model | Routing Model |
---|---|---|---|

Soil moisture accounting | Clark’s unit hydrograph | Linear reservoir | Lag |

Dimension | Eigenvalue | Condition Index | Variance Proportions | |||||
---|---|---|---|---|---|---|---|---|

(Constant) | Longitude | Latitude | Elevation | Slope | Aspect | |||

1 | 4.984468 | 1 | 0.00 | 0.00 | 0.00 | 0.01 | 0.01 | 0.01 |

2 | 0.662792 | 2.742335847 | 0.00 | 0.00 | 0.00 | 0.07 | 0.22 | 0.02 |

3 | 0.185079 | 5.189568491 | 0.00 | 0.00 | 0.00 | 0.07 | 0.08 | 0.82 |

4 | 0.167639 | 5.452825175 | 0.00 | 0.00 | 0.00 | 0.55 | 0.68 | 0.09 |

5 | 2.03 × 10^{−5} | 495.2502822 | 0.03 | 0.02 | 0.99 | 0.30 | 0.01 | 0.01 |

6 | 1.57 × 10^{−6} | 1781.863642 | 0.97 | 0.98 | 0.01 | 0.00 | 0.01 | 0.05 |

**Table 4.**Cross-validation performance and ranking of different interpolation schemes for simulating annual precipitation.

Interpolation Scheme | Mean RMSE | Rank of Mean RMSE | Mean MAE | Rank of Mean MAE | Mean MRE (%) | Rank of Mean MRE |
---|---|---|---|---|---|---|

PCRR | 40.1 | 1 | 31.2 | 1 | 1.51 | 1 |

IDW | 53.1 | 2 | 39.4 | 2 | 1.98 | 2 |

MLR | 54.0 | 3 | 41.2 | 3 | 2.19 | 3 |

**Table 5.**Cross validation performance and ranking of different interpolation schemes for simulating daily precipitation.

Interpolation Scheme | Mean RMSE | Rank of Mean RMSE | Mean MAE | Rank of Mean MAE | Mean MRE | Rank of Mean MRE |
---|---|---|---|---|---|---|

PCRR | 3.92 | 1 | 3.06 | 1 | 0.49 | 1 |

IDW | 8.38 | 2 | 6.63 | 2 | 1.17 | 2 |

MLR | 12.39 | 3 | 10.55 | 3 | 1.81 | 3 |

Interpolation Scheme | Annual Precipitation (mm) | Measured (mm) | Simulated (mm) | Absolute Error (mm) | Relative Error (%) | NSE | |
---|---|---|---|---|---|---|---|

Simulated | Measured | ||||||

PCRR | 1875.5 | 1919.0 | 979.6 | 975.1 | −4.5 | −0.46 | 0.806 |

IDW | 1872.9 | 979.6 | 930.2 | −49.4 | −5.04 | 0.803 | |

MLR | 1740.0 | 979.6 | 880.1 | −99.5 | −10.15 | 0.707 |

Flow Characteristics | Obs. (cm) | PCRR (cm) | IDW (cm) | MLR (cm) |
---|---|---|---|---|

Max. annual mean flow | 152.1 | 156.9 | 162.2 | 147.5 |

Min. annual mean flow | 53.9 | 57.1 | 60.4 | 56.9 |

Upper 10 percentile | 212.6 | 189.7 | 209.4 | 202.8 |

Minimum daily flow | 13.1 | 13.1 | 9.8 | 6.5 |

Maximum daily flow | 3130.7 | 2489.5 | 2083.9 | 2460.1 |

Event | Period | Duration (h) | Average Rainfall Sum (mm/ev.) | Maximum (mm/h) | Average Rainfall Intensity (mm/h) |
---|---|---|---|---|---|

20100619 | 19 July–22 July 2010 | 69.5 | 160.3 | 14.8 | 2.3 |

20120430 | 30 April–3 May 2012 | 65.0 | 47.2 | 19.0 | 0.7 |

**Table 9.**Cross-validation performance and ranking of different interpolation schemes for simulating flood events precipitation.

Interpolation Scheme | 20100619 | 20120430 | ||||
---|---|---|---|---|---|---|

PCRR | MLR | IDW | PCRR | MLR | IDW | |

Mean RMSE | 0.712 | 1.74 | 0.83 | 0.42 | 0.96 | 0.44 |

Rank of mean RMSE | 1 | 3 | 2 | 1 | 3 | 2 |

Mean MAE | 0.52 | 0.71 | 0.65 | 0.32 | 0.72 | 0.23 |

Rank of mean MAE | 1 | 3 | 2 | 2 | 3 | 1 |

MRE | 1.07 | 2.1 | 1.39 | 7.06 | 9.54 | 2.25 |

Rank of mean MRE | 1 | 3 | 2 | 2 | 3 | 1 |

Flood Event | 20100619 | 20120430 | |||||
---|---|---|---|---|---|---|---|

PCRR | IDW | MLR | PCRR | IDW | MLR | ||

Runoff | Measured (mm) | 141.7 | 141.7 | 141.7 | 53.6 | 53.6 | 53.6 |

Simulated (mm) | 148.7 | 127.6 | 144.1 | 46.7 | 49.8 | 31.5 | |

Relative Error (%) | 4.95 | −9.97 | 1.72 | −12.82 | −7.02 | −41.24 | |

Peak Discharge | Measured (m^{3}/s) | 166 | 166 | 166 | 74.7 | 74.7 | 74.7 |

Simulated (m^{3}/s) | 160 | 145 | 188 | 82.2 | 76.3 | 83.6 | |

Relative Error (%) | −3.73 | −12.47 | 13.19 | 10.04 | 2.14 | 11.91 | |

Peak Time | Absolute Error (h) | 2 | 2 | 1.5 | 1.00 | 1.00 | 1.00 |

Nash–Sutcliffe efficiency | 0.925 | 0.9 | 0.705 | 0.908 | 0.918 | 0.808 |

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**MDPI and ACS Style**

Chen, T.; Ren, L.; Yuan, F.; Yang, X.; Jiang, S.; Tang, T.; Liu, Y.; Zhao, C.; Zhang, L. Comparison of Spatial Interpolation Schemes for Rainfall Data and Application in Hydrological Modeling. *Water* **2017**, *9*, 342.
https://doi.org/10.3390/w9050342

**AMA Style**

Chen T, Ren L, Yuan F, Yang X, Jiang S, Tang T, Liu Y, Zhao C, Zhang L. Comparison of Spatial Interpolation Schemes for Rainfall Data and Application in Hydrological Modeling. *Water*. 2017; 9(5):342.
https://doi.org/10.3390/w9050342

**Chicago/Turabian Style**

Chen, Tao, Liliang Ren, Fei Yuan, Xiaoli Yang, Shanhu Jiang, Tiantian Tang, Yi Liu, Chongxu Zhao, and Liming Zhang. 2017. "Comparison of Spatial Interpolation Schemes for Rainfall Data and Application in Hydrological Modeling" *Water* 9, no. 5: 342.
https://doi.org/10.3390/w9050342