# Mutation Characteristics of Precipitation Concentration Spatiotemporal Variation and Its Potential Correlation with Low-Frequency Climate Factors in the LRB Area from 1960 to 2020

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Research Area, Data and Methods

#### 2.1. Research Area

^{2}. It is one of the seven major rivers in China. The LRB has a semi-humid monsoon climate in most parts. Floods in the basin are frequent, and a large flood occurs every 7–8 years on average. The LRB is becoming a key research objective in the field of climate and hydrology. The range of 116° E–129° E, 38° N–46° N was selected as the research area.

#### 2.2. Data

#### 2.3. Methodology

#### 2.3.1. The PCD and PCP

- where, n is the total number of days in year i;
- j is the daily ordinal number in year i;
- r
_{ij}is the precipitation of a station in year i on day j; - R
_{i}is the total precipitation of the station in year i, Divide $\left[-\mathsf{\pi},\mathsf{\pi}\right]$ equally according to the number of days in year i, and θ_{j}is the azimuth of the jth day.

#### 2.3.2. Sliding t-Test

_{i}is the i

_{th}element in the time series, and the sample length n before and after the mutation point can be set artificially to make the test more reliable.

_{i}with n

_{i}sample sizes, a certain time was artificially set as the reference point, and two sub-sequences x

_{i}

_{1}and x

_{i}

_{2}before and after the reference point, with ${\overline{{x}_{i}}}_{1}$ and ${\overline{{x}_{i}}}_{2}$ are the mean values, variances of s

_{i}

_{1}

^{2}and s

_{i}

_{2}

^{2}and H: ${\overline{{x}_{i}}}_{2}-{\overline{{x}_{i}}}_{1}=0$, t meets the distribution of (n

_{1}+ n

_{2}− 2) t; and $\alpha $ is the given significance level (this study takes n

_{1}= n

_{2}= 10, α = 0.05). If $\left|t\right|>{t}_{\alpha}$, then H is false, that means if the mean difference between two sequences exceeds a certain level of significance ${t}_{\alpha}$, a mutation can be considered to have occurred.

#### 2.3.3. Student t-Test

_{1}and x

_{2}have different sample numbers n

_{1}and n

_{2}and their respective variances s

_{1}

^{2}and s

_{2}

^{2}are not equal, then the following statistic t-test can be used:

_{0}: μ

_{1}− μ

_{2}= μ

_{0}is true, where μ

_{0}is some specified difference that you wish to test. The critical values of t, t

_{α/}

_{2}(α/2 = 0.05) are based on (n

_{1}+ n

_{2}− 2) df [34].

#### 2.3.4. Cross Wavelet Transform (CWT) Analysis

_{X}and σ

_{Y}are the standard deviations of time series X and Y, respectively. The freedom degree (v) of the Morlet wavelet transform is set as 2. When the left term exceeds the upper bound of 95% confidence limit of the power spectrum of red noise, it is considered to pass the test of the standard spectrum of red noise with a significance level of 0.05.

## 3. Results and Discussions

#### 3.1. Mutation Points Identification of the PCD and PCP

#### 3.2. Spatial Pattern of PCD and PCP

#### 3.3. Relationship between Precipitation Indexes and Low-Frequency Climate Factors

#### 3.3.1. PCD

#### 3.3.2. PCP

## 4. Conclusions

- (1)
- Mutations occurred in the PCD sequence in 1980 and the PCP sequence in 2005 in the LRB area from 1960 to 2020.
- (2)
- Over the past 60 years, the annual PCD variation range was between 0.53 and 0.80 and it tended to decrease. The decrease in PCD was −0.03/10 a before the mutation (1960–1979), and −0.01/10 a after the mutation (1980–2020). The PCP decreased by −0.09/a before the mutation (1960–2004) and increased by 1.01/a after the mutation (2005–2020). The daily sequence of PCP in this basin was quite concentrated and ranged from 184th to 218th d, that is, from early July to early August.
- (3)
- In the LRB, PCD increased from southeast to northwest. Two high PCD (>0.72) areas were concentrated separately in the northwest of the upstream and downstream in Changchun. The spatial distribution of the PCD generally tended to flatten over the entire study period.
- (4)
- PDO, SS, and AO were the important climate factors driving the abrupt change of PCD, and the resonance between climate factors and the PCD was characterized by complexity and diversity. Before the mutation year 2005, the PCP was mainly affected by AO and SS, both of them showed anti-phase resonance with the PCP, and evolution lagged. ENSO had an important effect on both PCD and PCP but had no significant correlation with the occurrence of the mutations.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Moving t-test schematics of (

**a**) PCD and (

**b**) PCP; (The dashed line is the annual PCD/PCP series, the black solid line is the 10-year moving average, and the blue (red) solid line shows the linear regression before (after) the mutation point) and the t values of (

**c**) PCD and (

**d**) PCP (The black solid lines represent the t-values, and the red (blue) dashed lines represent the 0.05 significance upper (lower) bound).

**Figure 3.**Spatial distribution maps of PCD&PCP: Spatial distribution of (

**a**) PCD and (

**b**) PCP before mutation year; spatial distribution of (

**c**) PCD and (

**d**) PCP after mutation year; differences before and after the mutation of (

**e**) PCD and (

**f**) PCP.

**Figure 4.**CWT spectrum between PCD and PDO/AO/ENSO/SS. (

**a**,

**c**,

**e**,

**g**) show the results of XWT; (

**b**,

**d**,

**f**,

**h**) show the results of WTC.

**Figure 5.**CWT spectrum between PCP and PDO/AO/ENSO/SS. (

**a**,

**c**,

**e**,

**g**) show the results of XWT; (

**b**,

**d**,

**f**,

**h**) show the results of WTC.

PCD | XWT | WTC | |||

Period | Years | Period | Years | ||

PDO | 1–4 a 1–4 a 8–11 a | 1981–2001 2003–2007 1988–2004 | 3.5–5 a 1–3 a 8–10 a | 1968–1974 1988–2001 1980–2019 | |

AO | / | / | 3.5–5.5 a 8–10 a | 1968–1971 1980–1994 | |

ENSO | 0–5 a | 1964–2013 | 1–6 a | 2006–2014 | |

SS | 8–12 a | 1973–2003 | 2–3.5 a 0–3.5 a 1–3 a 8–15 a | 1974–1981 1988–1992 2010–2012 1975–2005 | |

PCP | XWT | WTC | |||

Period | Years | Period | Years | ||

PDO | 2–6 a 5–7 a 8–9 a | 1986–2009 2008–2011 1986–2008 | 0–1.5 a 7 a 2 a 5.5 a | 1964–1968 1981–1988 2008–2009 2009–2011 | |

AO | / | / | 3.5–5.5 a 3–10 a | 1968–1974 1971–1999 | |

ENSO | 0–4.5 a 1–6 a | 1964–1972 1980–2013 | 0.5–4 a 11–14 a 2–6 a | 1964–1973 1978–1984 2009–2013 | |

SS | 7.5–14 a | 1974–2001 | 1.5 a | 2009 |

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**MDPI and ACS Style**

Zhang, L.; Cao, Q.; Liu, K.
Mutation Characteristics of Precipitation Concentration Spatiotemporal Variation and Its Potential Correlation with Low-Frequency Climate Factors in the LRB Area from 1960 to 2020. *Water* **2023**, *15*, 955.
https://doi.org/10.3390/w15050955

**AMA Style**

Zhang L, Cao Q, Liu K.
Mutation Characteristics of Precipitation Concentration Spatiotemporal Variation and Its Potential Correlation with Low-Frequency Climate Factors in the LRB Area from 1960 to 2020. *Water*. 2023; 15(5):955.
https://doi.org/10.3390/w15050955

**Chicago/Turabian Style**

Zhang, Lu, Qing Cao, and Kanglong Liu.
2023. "Mutation Characteristics of Precipitation Concentration Spatiotemporal Variation and Its Potential Correlation with Low-Frequency Climate Factors in the LRB Area from 1960 to 2020" *Water* 15, no. 5: 955.
https://doi.org/10.3390/w15050955