# Spatiotemporal Variability of Extreme Summer Precipitation over the Yangtze River Basin and the Associations with Climate Patterns

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## Abstract

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## 1. Introduction

- (1)
- Analyze the spatiotemporal variability of extreme season-scale precipitation through the AA, and perform the trend analysis of the archetype occurrence;
- (2)
- Identify the most variable seasonal precipitation that more archetypes dominate; and
- (3)
- Discuss the underlying physical mechanisms of how the climate patterns influence the variability of the extreme precipitation.

## 2. Data Sources

## 3. Methodology

#### 3.1. Spatiotemporal Modes of Seasonal Extreme Precipitation

**X**onto the k-th archetype ${z}_{k}$, in the same way to PC scores in PCA. It is also referred to as the mixture coefficients. The archetypes $\mathit{Z}=\left\{{z}_{1},\dots ,{z}_{p}\right\}$ are convex combinations of the data

**X**when p > 1 and, thus, the archetypes are either actual observations or convex mixtures of the observations [27]. Here, to perform the trend analysis and clearly present the result in Section 3.2, we firstly define the archetype that represents the event with minimum precipitation as null archetype and assign it with ${z}_{p}$ [15].

**X**in AA should be optimized to minimize the $RSS=//\mathit{X}-\mathit{XBA}//$, with $\mathit{B}=\left\{{\beta}_{1}{,\dots \beta}_{p}\right\}$, $\mathit{A}=\left\{{\alpha}_{1,1}{,\dots \alpha}_{p,n}\right\}$, where RSS is the residual sum of square errors and $\Vert \xb7\Vert $ is the spectral norm.

#### 3.2. Trend Analysis of the Archetype Occurrence

**A**of mixture coefficients rather than

**B**as the temporal variability of archetypal patterns of the seasonal precipitation [15]. Although the matrix

**B**also contains the time series of length n, it describes which day is characterized best by one particular pure archetypal pattern. Thus, the time series of the k-th column of

**B**may miss the day when an archetype is active if another archetype is also active, and does not represent how dominant each archetype is in any given days.

#### 3.3. Climate Teleconnections to the Extreme Precipitation

^{2}from univariate regression, and the full model’s R

^{2}is the sum of all univariate R

^{2}. Thus, each explanatory variable’s contribution is the ratio of univariate R

^{2}to the full model’s R

^{2}[32]. However, for the climate patterns, there is likely a high correlation among them, and this method should not work. Here, we applied an “LMG” method proposed by Lindeman et al. [33] (implemented with the R package “relaimpo” by Grömping [32]). This considers one individual explanatory variable’s effect while combining with the other variables. It allows the correlated explanatory variables to benefit from each other’s shares, and can be seen as a way to take care of the uncertainty of information regarding the true underlying structure. The approach is based on a sequential R

^{2}, but take cares of the dependence on orderings by averaging over orderings using simple unweighted averages. We would like to direct readers to [32] and therein for a detailed mathematical formulation.

## 4. Results and Discussion

#### 4.1. Archetypal Analysis of the Seasonal Precipitation

#### 4.2. Trend Analysis of the Archetype Occurrence

#### 4.3. Climate Teleconnections to the Archetypes of Summer Precipitation

^{2}into shares from the individual climate pattern. However, in the field of climate science, the indices are typically correlated. Therefore, we performed the further analysis considering these correlations to assess the relative importance, and presented the result in Figure 7.

#### 4.4. Discussion of the Physical Mechanisms for Climate Teleconnections to the Extreme Precipitation during Summer

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 1.**The spatial distribution of precipitation stations in the Yangtze River Basin used in this study.

**Figure 2.**Scree plot of the result from AA. The maximum number of archetypes is initially set as 16 and eight chains were set to run to obtain a global optimum. We used the non-interference-based “elbow criterion” on the RSS curve to select the appropriate number of archetypes.

**Figure 3.**Simplex plot of seasonal precipitation with respect to the decomposed 6 archetypes. The data points are colored by the average observed precipitation over the whole Yangtze River Basin. The archetypes at the corners represent the extremal patterns, and are notated as Ak for the k-th archetypal pattern.

**Figure 4.**Loading patterns of archetypes for seasonal extreme precipitation across stations over the Yangtze River Basin.

**Figure 5.**Dominant archetypes for seasonal precipitation across years and seasons. The blank area in the figure represents the seasonal precipitation is dominated by the null archetype A6, relating to the events with little total or no precipitation for that season.

**Table 1.**Correlations of the identified climate patterns and the summer archetypes at 95% confidence level. The time period of the archetypes is from 1960 to 2014 and the time period of the climate patterns is from 1959 to 2013. The season in the parentheses indicates the season for climate patterns with the strong correlation.

Climate Patterns | A1 | A2 | A4 | A6 |
---|---|---|---|---|

AMO | 0.27 (July–September) | 0.37 (May–July) | ||

Niño12 | −0.28 (November–January) | 0.34 (September–November) | ||

Niño3.4 | −0.23 (May–July) | |||

Niño4 | −0.32 (February–April) | 0.27 (February–April) | −0.30 (March–May) | |

PDO | 0.33 (August–October) |

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**MDPI and ACS Style**

Su, Z.; Hao, Z.; Yuan, F.; Chen, X.; Cao, Q.
Spatiotemporal Variability of Extreme Summer Precipitation over the Yangtze River Basin and the Associations with Climate Patterns. *Water* **2017**, *9*, 873.
https://doi.org/10.3390/w9110873

**AMA Style**

Su Z, Hao Z, Yuan F, Chen X, Cao Q.
Spatiotemporal Variability of Extreme Summer Precipitation over the Yangtze River Basin and the Associations with Climate Patterns. *Water*. 2017; 9(11):873.
https://doi.org/10.3390/w9110873

**Chicago/Turabian Style**

Su, Zhenkuan, Zhenchun Hao, Feifei Yuan, Xi Chen, and Qing Cao.
2017. "Spatiotemporal Variability of Extreme Summer Precipitation over the Yangtze River Basin and the Associations with Climate Patterns" *Water* 9, no. 11: 873.
https://doi.org/10.3390/w9110873