Temporal and Spatial Characteristics of Multidimensional Extreme Precipitation Indicators: A Case Study in the Loess Plateau, China
Abstract
:1. Introduction
2. Overview of the study area and data
3. Method
3.1. Gaussian Mixture Model
3.2. Joint Probability Distribution and Return Period
3.2.1. Joint Probability Distribution for Extreme Precipitation Indicators
3.2.2. Return Periods for Extreme Precipitation Indicators and Their Combinations
- Simulate a sample u1, ..., um from the d-dimensional copula C;
- For i = 1 ,..., m calculate wi = C(ui);
- Estimate Kc: .
4. Case Study and Results Analysis
4.1. Case Study
4.2. Changes of Different Schemes in Two 30-Year Stages
4.3. The Trend of Return Period of Multidimensional Moving Window Series
5. Discussions and Conclusions
Supplementary Materials
Author Contributions
Funding
Conflicts of Interest
References
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Indices | Abbreviations | Definitions | Unit |
---|---|---|---|
Number of extreme precipitation days | D95 | Number of days with P > 95th percentile (daily precipitation exceeding the 95th percentile of precipitation series during 1971–2000). | days |
The amount of extreme heavy precipitation | P95 | Annual total amount of precipitation with P > 95th percentile | mm |
The intensity of extreme precipitation | I95 | Average daily precipitation intensity of extreme precipitation | mm/day |
Ratio of extreme precipitation | R95 | Ratio of annual total precipitation due to events exceeding the 95th percentile | - |
ID | Combinations | ID | Combinations | ID | Combinations |
---|---|---|---|---|---|
1 | {D95, P95} | 4 | {P95, I95} | 7 | {D95, P95, R95} |
2 | {D95, I95} | 5 | {P95, R95} | 8 | {D95, I95, R95} |
3 | {D95, R95} | 6 | {I95, R95} | 9 | {P95, I95, R95} |
Scheme | Distribution | KS Test | RMSE | AIC | |
---|---|---|---|---|---|
p-Value | |||||
D95 | GMM | 0.143 | 0.568 | 0.055 | −170.089 |
P95 | GMM | 0.089 | 0.972 | 0.029 | −208.096 |
R95 | GMM | 0.082 | 0.987 | 0.032 | −202.164 |
{D95, P95} | Gaussian | 0.022 | 0.615 | 0.027 | −215.108 |
{D95, R95} | t | 0.024 | 0.697 | 0.032 | −203.671 |
{P95, R95} | Gaussian | 0.028 | 0.790 | 0.030 | −208.887 |
{D95, P95, R95} | t | 0.032 | 0.648 | 0.021 | −228.451 |
Return Periods | {D95, P95} | {D95, R95} | {P95, R95} | {D95, P95, R95} |
---|---|---|---|---|
Tor | 8.09 | 7.28 | 7.79 | 7.01 |
Tk | 11.66 | 13.50 | 11.77 | 12.66 |
Tand | 13.09 | 15.99 | 13.96 | 17.45 |
Region | Number of Stations | D95 | P95 | I95 | R95 | ||||
---|---|---|---|---|---|---|---|---|---|
A | N | A | N | A | N | A | N | ||
1 | 25 | −0.24 | 7 | −11.29 | 11 | 0.36 | 14 | −0.013 | 11 |
2 | 38 | −0.27 | 14 | −8.27 | 14 | 1.44 | 24 | −0.004 | 16 |
Indices | Region 1 | Region 2 | ||
---|---|---|---|---|
PI/TG | PD/TD | PI/TG | PD/TD | |
D95 | 0.31/0.54 | 0.46/−0.63 | 0.16/0.53 | 0.42/−0.95 |
P95 | 0.19/22.04 | 0.38/−35.7 | 0.24/39.40 | 0.50/−37.01 |
I95 | 0.27/6.79 | 0.38/−6.80 | 0.42/12.17 | 0.29/−11.63 |
R95 | 0.38/0.05 | 0.46/−0.06 | 0.34/0.04 | 0.34/−0.05 |
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Sun, C.; Huang, G.; Fan, Y. Temporal and Spatial Characteristics of Multidimensional Extreme Precipitation Indicators: A Case Study in the Loess Plateau, China. Water 2020, 12, 1217. https://doi.org/10.3390/w12041217
Sun C, Huang G, Fan Y. Temporal and Spatial Characteristics of Multidimensional Extreme Precipitation Indicators: A Case Study in the Loess Plateau, China. Water. 2020; 12(4):1217. https://doi.org/10.3390/w12041217
Chicago/Turabian StyleSun, Chaoxing, Guohe Huang, and Yurui Fan. 2020. "Temporal and Spatial Characteristics of Multidimensional Extreme Precipitation Indicators: A Case Study in the Loess Plateau, China" Water 12, no. 4: 1217. https://doi.org/10.3390/w12041217
APA StyleSun, C., Huang, G., & Fan, Y. (2020). Temporal and Spatial Characteristics of Multidimensional Extreme Precipitation Indicators: A Case Study in the Loess Plateau, China. Water, 12(4), 1217. https://doi.org/10.3390/w12041217