# High-Resolution Precipitation Modeling in Complex Terrains Using Hybrid Interpolation Techniques: Incorporating Physiographic and MODIS Cloud Cover Influences

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## Abstract

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^{2}range of 0.75–0.96. The findings of this study showed that the incorporation of MODIS–CCF with physiographic variables as covariates significantly improved the interpolation accuracy by 5–20%, with the largest improvement in modeling precipitation in March.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area and Data Collection

^{2}(Figure 1). The study area is characterized by a continental climate with a wet-cold climate in the winter and a dry-hot climate in the summer. The average summer temperature varies between 18 and 32 °C in July, while the winter average varies between 3 and 10 °C in January. The regional mean annual precipitation is 283 mm (the 25th and 75th percentiles are 200 and 350 mm, respectively), with a maximum rainfall of roughly 470 mm (1982–2015) [78]. The mean annual CCF is 20–55%, with the highest value of 40–95% in February (2000–2015). According to the Köppen–Geiger classification, the region is located in the temperate-wet climatic zone in the central and western hilly regions. In contrast, the climate is desert (arid climate) and continental or steppe (semi-arid climate) toward the east [78]. The region is classified into three physiographic units: (i) mountain region in the western and central area (Mount Hermon and Jabal Al Arab), (ii) plateau in the northwestern part (Golan Heights extent), and (iii) a plain area that occupies most of the study area (Horan plain) with an altitude varying between -18 in the southwest (lower part of the Yarmouk river) and 2814 m above mean sea level (m asl) in the northwest (Mount Hermon or Jabal El Sheikh).

#### 2.1.1. Monthly Observed Precipitation Data

#### 2.1.2. Auxiliary Remote Sensing Data

#### 2.2. Data Analysis

#### 2.2.1. Preliminary Analysis of Monthly Precipitation Series

#### 2.2.2. Preprocessing of Explanatory Variables

#### 2.2.3. Fine-Scale Modeling Using Regression-Kriging (RK)

#### 2.2.4. Steps Involved in Fitting, Calculating, and Assessing the CMRM and RK Models

^{2}), and Pearson’s correlation coefficient (r) [57,85,96].

Model | Description | Included Variables | Benefits |
---|---|---|---|

Regression model: CMRM-SW (GT) | Fitting the CMRM function using the stepwise regression (SW) method. | Both geographical and topographical factors (elevation, longitude, latitude, and distance to the coast) by including only significant independent variables. | Calculating geographical and topographical contribution (GT) in precipitation modeling. |

Regression model: CMRM-PCs (GT+ CCF) | Using the extracted PC scores from the PCA to fit the CMRM function. | Geographical and topographical factors (elevation, longitude, latitude, and distance to the coast) were included, besides the CCF data. The extracted PC scores from the PCA. | Calculating remotely sensed CCF contribution in precipitation modeling besides GT effects. |

Hybrid model: RK (GT + CCF) | Using the extracted PC scores from the PCA to fit the CMRM function and then adding the CMRM’s residuals using OK with exponential variogram model. | As presented in the CMRM-PC (GT + CCF) scheme. | CMRM’s residual correction to improve the outputs. |

**Figure 3.**Flowchart of the methodology of fitting, calculating, and assessing the CMRM and RK models.

## 3. Results

#### 3.1. Effect of Topographical–Geographical Factors on the Spatial Variability of Precipitation

#### 3.2. Spatial Distribution of CCF and Its Effect on the Average Monthly Precipitation

#### 3.3. Interrelationships between Explanatory Variables and PC Analysis

#### 3.4. Modeling of Monthly Precipitation Using the CMRM

^{2}) and standard error. This indicates that the geographical–topographical factors influence the spatial variation of monthly precipitation. The interpretation of the statistical significance of the factors demonstrates high adequacy in explicating the monthly precipitation patterns in the complex topography, specifically in the winter months (Dec, Jan, and Feb), with an Adj. R

^{2}of 0.71, 0.70, and 0.66, respectively, whereas the precipitation patterns are well interpreted for the remaining months, with an Adj. R

^{2}ranging from 0.42 to 0.61.

^{2}and that the CCF has an obvious influence on the spatial variation of monthly precipitation besides the geographical–topographical factors. The CCF demonstrates high performance in improving the CMRMs’ outputs, specifically during spring (March, April, and May), with an Adj. R

^{2}of 0.83, 0.72, and 0.73, respectively. Additionally, the spatial precipitation patterns are exceedingly interpreted in December, January, and February, with an Adj. R

^{2}of 0.78, 0.781, and 0.77, respectively. Once the CMRMs-PCA (GT + CCF) method was used instead of the CMRMs-SW (GT), the standard error of the estimation became lower.

#### 3.5. Interpolation of the CMRM’s Residuals

#### 3.6. Performance of CMRMs and RK Models in the Prediction of Precipitation

^{2}range of 0.75–0.96. The present study showed that the GT variables explained 42–70% of the total spatial variance in precipitation. Incorporating CCF as a covariate significantly improved the interpolation accuracy by 5–20%, with the biggest improvement in the March, May, and April models, respectively. On the other hand, the kriging of the CMRMs’ residuals significantly improved the interpolation accuracy by 12–28%, with the biggest improvements in the November, October, and April models, respectively (Figure 10).

^{2}of 0.9 and 0.993 for monthly and annual precipitation, respectively. This confirms that the hybrid method outperforms the single methods and that the CCF significantly improves the interpolation accuracy for all months and at the annual scale. Figure 12 shows the final monthly precipitation distribution using the RK method.

## 4. Discussion

^{2}in the range of 0.75 to 0.96 in different months (pooled R

^{2}= 0.90). The models’ residuals were normally distributed, indicating the model’s interpolation capability.

^{2}when it was applied at a regional scale in this study.

## 5. Conclusions

- The optimal MODIS-CCF surface effects on monthly precipitation patterns are most significant at a horizontal scale of 7 km, and the maximum correlations are in April and March (r > 0.8, p < 0.05).
- The RK method outperforms the single methods, i.e., the multivariate regression models.
- The geographical and topographical factors can explain 42–70% of the total spatial variance in precipitation. Incorporating CCF as a covariate significantly improves the interpolation accuracy by 5–20%. The kriging of the CMRMs’ residuals significantly improves the interpolation accuracy by 12–28%.
- Both the single and the hybrid models are better than the global models (WorldCim, CHELSA, and TerraClimate) in estimating regional precipitation in terms of all statistical indicators.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**The location of the study area, the regional seasonal cycle of precipitation (mm.), the average temperature (°C) for the 1982–2015 period, and the average cloud cover frequencies (CCF, %) for the 2000–2015 period.

**Figure 2.**Rectangular neighborhood method using height and width (3 by 3) to determine the new value of each elevation/CCF cell.

**Figure 4.**The spatial correlation between elevation using smoothed DEMs at multiple horizontal scales (e.g., 1, 2, 3, and 5 km) and average monthly precipitation.

**Figure 5.**The spatial distribution of smoothed monthly CCF (%) at a 7 km horizontal scale and its correlation with observed average monthly precipitation at 57 rain gauges.

**Figure 6.**Correlation matrices between the explanatory variables: (

**a**) the topographical–geographical factors with the monthly CCF, and (

**b**) correlation matrix of monthly CCFs.

**Figure 7.**A scree plot presenting the cumulative variance (%) for the extracted PCs (

**a**) and the loading matrix of the explanatory variables on the PCs (

**b**).

**Figure 8.**Histograms of CMRMs-PCA (GT + CCF) standardized residual distribution and normal P–P plots of CMRMs-PCA (GT + CCF) standardized residual.

**Figure 9.**Spatial distribution of CMRMs-PCA (GT + CCF) residuals using the OK method (right maps), and the empirical semi-variogram of the CMRM’s residuals and its fitting using the exponential variogram (Exp.) model (left panels).

**Figure 10.**Assessment of the CMRMs versus the RK model in the prediction of monthly precipitation (r correlation, R

^{2}, MAPE, and RMSE), and the covariables’ contribution to improving the RK model’s accuracy (right panel).

**Figure 11.**Scatter plots of observed monthly precipitation versus predicted precipitation for all months using the CMRM and RK models.

**Figure 13.**Taylor diagram showing the performance of the models against WorldCim, CHELSA, and TerraClimate monthly precipitation surfaces.

Variable | Data Type | Number of Stations/Points | Spatial Resolution | Reference Period | Source |
---|---|---|---|---|---|

Observed precipitation (mm) | Rain gauge and climatic stations (Historical) | 57 | – | 1984–2015 | SMA SMOAAR JMD |

CRU Ts4.3 precipitation (mm) | Gridded data (Historical) | 9 gridded points | 0.5 degree | 1984–2015 | https://crudata.uea.ac.uk/cru/data/hrg/, (accessed on 7 September 2022) |

TerraClimate precipitation (mm) | Gridded data (Monthly average) | – | ~4 km (2.5 arc. min) | 1970–2000 | https://www.climatologylab.org/, (accessed on 7 September 2022) |

WorldClim V. 2.1 precipitation (mm) | Gridded data (Monthly average) | – | ~1 km (30 arc-second) | 1981–2010 | https://www.worldclim.org/, (accessed on 7 September 2022) |

CHELSA V1.0 precipitation (mm) | Gridded data (Monthly average) | – | ~1 km (30 arc-second) | 1979–2016 | https://chelsa-climate.org/, (accessed on 7 September 2022) |

**Table 4.**Eigenvectors of the correlation matrix between the observed monthly precipitation (n = 57) and extracted PCs after varimax rotation method with Kaiser normalization.

PCs/Prc. | January | February | March | April | May | June | July | August | September | October | November | December | Annual |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

PC1 | −0.415 | −0.39 | −0.38 | −0.45 | −0.35 | – | – | – | −0.34 | −0.30 | −0.36 | −0.42 | −0.36 |

PC2 | 0.47 | 0.51 | 0.005 | 0.49 | 0.64 | – | – | – | 0.12 | 0.55 | 0.46 | 0.46 | 0.55 |

PC3 | 0.14 | 0.13 | 0.56 | 0.13 | 0.30 | – | – | – | 0.27 | 0.34 | 0.33 | 0.17 | 0.17 |

**Table 5.**Unstandardized coefficients of the CMRMs-SW (GT) used ($\mathsf{\beta}$ ) to estimate average monthly precipitation and some statistical indicators to assess the models’ performance (the GT effect-based potential precipitation surfaces using the SW method).

Variables | $\mathsf{\beta}$ | January | February | March | April | May | June | July | August | September | October | November | December |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Constant | ${\mathsf{\beta}}_{0}$ | 3303 | 3013 | 1706 | 600 | 4.8 | – | – | – | 51.1 | 13.5 | 44.9 | 2610 |

Elv. | ${\mathsf{\beta}}_{1}$ | 0.083 | 0.088 | 0.053 | 0.017 | 0.005 | – | – | – | 0.001 | 0.010 | 0.025 | 0.064 |

Lon. | ${\mathsf{\beta}}_{2}$ | −85.4 | −83 | −46.9 | −16.5 | – | – | – | – | −1.42 | – | – | −71.8 |

Lat. | ${\mathsf{\beta}}_{3}$ | – | – | – | – | – | – | – | – | – | – | – | – |

CDist. | ${\mathsf{\beta}}_{4}$ | – | – | – | – | –0.04 | – | – | – | – | −0.10 | −0.28 | – |

r correlation | 0.84 | 0.81 | 0.79 | 0.77 | 0.73 | – | – | – | 0.69 | 0.75 | 0.65 | 0.843 | |

Adj. R^{2} | 0.70 | 0.66 | 0.61 | 0.6 | 0.53 | – | – | – | 0.46 | 0.56 | 0.42 | 0.71 | |

RMSE (mm.) | 16.25 | 18.4 | 11.8 | 4.1 | 1.25 | – | – | – | 0.42 | 2.6 | 10.2 | 13.3 | |

Sig. value (p) | <0.01 | <0.01 | <0.01 | <0.01 | <0.01 | – | – | – | <0.01 | <0.01 | <0.01 | <0.01 |

**Table 6.**Unstandardized coefficients of the CMRMs-PCA (GT + CCF) used to estimate average monthly precipitation and the statistical indicators to assess the models’ performance (i.e., the GT and CCF effect-based potential precipitation surfaces using the PCA).

Variables | $\beta $ | January | February | March | April | May | June | July | August | September | October | November | December |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Constant | ${\mathsf{\beta}}_{0}$ | 33.4 | 36.6 | 26.2 | 8.05 | 2.8 | – | – | – | 0.18 | 6.8 | 23.7 | 28 |

1CP | ${\mathsf{\beta}}_{1}$ | −37.7 | −37.4 | −21.5 | −9.6 | −1.62 | – | – | – | −0.47 | −3.6 | −11 | −29.1 |

2CP | ${\mathsf{\beta}}_{2}$ | 18.8 | 18.9 | 2.02 | 3.54 | 1.03 | – | – | – | 0.31 | 2.35 | 6.74 | 15.3 |

3CP | ${\mathsf{\beta}}_{3}$ | −0.09 | 1.1 | 12.3 | 0.13 | 0.14 | – | – | – | −0.01 | 0.42 | 1.9 | −1.6 |

r correlation | 0.885 | 0.88 | 0.91 | 0.85 | 0.856 | – | – | – | 0.72 | 0.82 | 0.76 | 0.88 | |

Adj. R^{2} | 0.781 | 0.77 | 0.83 | 0.72 | 0.73 | – | – | – | 0.51 | 0.67 | 0.53 | 0.78 | |

RMSE (mm.) | 14.37 | 15.7 | 8.3 | 3.5 | 0.98 | – | – | – | 0.42 | 2.4 | 9.0 | 11.8 | |

Sig. value (p) | <0.01 | <0.01 | <0.01 | <0.01 | <0.01 | – | – | – | <0.01 | <0.01 | <0.01 | <0.01 |

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**MDPI and ACS Style**

Alsafadi, K.; Bi, S.; Bashir, B.; Sharifi, E.; Alsalman, A.; Kumar, A.; Shahid, S.
High-Resolution Precipitation Modeling in Complex Terrains Using Hybrid Interpolation Techniques: Incorporating Physiographic and MODIS Cloud Cover Influences. *Remote Sens.* **2023**, *15*, 2435.
https://doi.org/10.3390/rs15092435

**AMA Style**

Alsafadi K, Bi S, Bashir B, Sharifi E, Alsalman A, Kumar A, Shahid S.
High-Resolution Precipitation Modeling in Complex Terrains Using Hybrid Interpolation Techniques: Incorporating Physiographic and MODIS Cloud Cover Influences. *Remote Sensing*. 2023; 15(9):2435.
https://doi.org/10.3390/rs15092435

**Chicago/Turabian Style**

Alsafadi, Karam, Shuoben Bi, Bashar Bashir, Ehsan Sharifi, Abdullah Alsalman, Amit Kumar, and Shamsuddin Shahid.
2023. "High-Resolution Precipitation Modeling in Complex Terrains Using Hybrid Interpolation Techniques: Incorporating Physiographic and MODIS Cloud Cover Influences" *Remote Sensing* 15, no. 9: 2435.
https://doi.org/10.3390/rs15092435