# Extraction of Spatiotemporal Distribution Characteristics and Spatiotemporal Reconstruction of Rainfall Data by PCA Algorithm

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Technical Processes

#### 2.2. Methods

#### 2.2.1. Constructing a Dynamic Characteristics Matrix of the Spatial and Temporal Distribution of Heavy Rainfall

#### 2.2.2. Dimensionality Reduction and Feature Extraction

_{t}can be expressed as:

_{t}were extracted after Gt was formed. The eigenvectors corresponding to the cumulative contribution rate $\alpha =0.9\sim 0.99$ were selected to form a projection matrix $U=\left[{u}_{1},{u}_{2}\cdots {u}_{k}\right]\in {R}^{n\times k}$. Then, ${F}_{i}={Q}_{i}\xb7U\in {R}^{m\times k}$, which is the projection of the sample ${Q}_{i}$ in direction U, was obtained. That is, after feature extraction, only the number of bits in the matrix column vector was reduced, with the row vector dimension remaining unchanged.

#### 2.2.3. Dynamic Clustering Analysis

#### 2.2.4. Reconstruction of High-Resolution Spatial Data

#### 2.3. Regional Overview

#### 2.4. Data

## 3. Results and Discussion

## 4. Conclusions

- The PCA algorithm was successfully applied for data reconstruction with spatio-temporal attributes. Reconstruction from low-dimensional to high-dimensional data was consistent with spatiotemporal variation characteristics. The reconstructed data better reflected the concentrated rainfall process and spatiotemporal distribution characteristics of the rainfall.
- Machine learning algorithms can extract clear features of the three types of rainfall that match the climatic characteristics of the region. The extracted features quantitatively described the dynamic spatiotemporal distribution characteristics of the various types of rainfall.
- Compared with average interpolated data, the reconstructed data had a 45–85% reduction in error in high-value areas and a 10–40% reduction in low-value areas. The refined rainfall process of the reconstruction effectively reduced the error in high and low-value areas.
- Although the types of rainfall identified in this study are specific to Luzhou, the proposed method can be universally applied. This study used hourly rainfall spatial data. In the future, feature matrices could be extracted at the minute level to achieve a more precise reconstruction of historical rainfall data. Precise rainfall data can assist in managing urban flash flood risks, including dispatching flood prevention, emergency personnel, and material resources.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 5.**Actual Rainfall Process on 22 June 2003 (6 h rainfall): (

**a**) 6 h, (

**b**) 12 h, (

**c**) 18 h, (

**d**) 24 h.

**Figure 7.**Actual Rainfall Process on 11 September 2012 (6 h rainfall): (

**a**) 6 h, (

**b**) 12 h, (

**c**) 18 h, (

**d**) 24 h.

**Figure 9.**Actual Rainfall Process on 12 May 2012 (6 h rainfall): (

**a**) 6 h, (

**b**) 12 h, (

**c**) 18 h, (

**d**) 24 h.

**Figure 10.**Actual Rainfall Processes at Each Station on 22 June 2003: (

**a**) measured rainfall data (6 h interval) and (

**b**) reconstructed rainfall data (1 h interval).

**Figure 11.**Actual Rainfall Processes at Each Station on 11 September 2012: (

**a**) measured rainfall data (6 h interval) and (

**b**) reconstructed rainfall data (1 h interval).

**Figure 12.**Actual Rainfall Processes at Each Station on 12 May 2012: (

**a**) measured rainfall data (6 h interval) and (

**b**) reconstructed rainfall data (1 h interval).

**Figure 13.**Comparison of reconstructed data, traditional interpolation results and measured data: (

**a**) Lizuhang, (

**b**) Luzhou, and (

**c**) Hejiang.

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**MDPI and ACS Style**

Liu, Y.; Liu, Y.; Liu, S.; Ren, H.; Tian, P.; Yang, N.
Extraction of Spatiotemporal Distribution Characteristics and Spatiotemporal Reconstruction of Rainfall Data by PCA Algorithm. *Water* **2023**, *15*, 3596.
https://doi.org/10.3390/w15203596

**AMA Style**

Liu Y, Liu Y, Liu S, Ren H, Tian P, Yang N.
Extraction of Spatiotemporal Distribution Characteristics and Spatiotemporal Reconstruction of Rainfall Data by PCA Algorithm. *Water*. 2023; 15(20):3596.
https://doi.org/10.3390/w15203596

**Chicago/Turabian Style**

Liu, Yuanyuan, Yesen Liu, Shu Liu, Hancheng Ren, Peinan Tian, and Nana Yang.
2023. "Extraction of Spatiotemporal Distribution Characteristics and Spatiotemporal Reconstruction of Rainfall Data by PCA Algorithm" *Water* 15, no. 20: 3596.
https://doi.org/10.3390/w15203596