Analysis of Spatiotemporal Distribution and Non-stationary of

Extreme Precipitation Events during 1960-2018 in the Yellow River

Basin

Xianglin Lv

, Hongjing Yu

, Hao Dong

, Shibao Ji

, Yaqin Qiu

1,*

, Xvdong Duan

, Hao Zheng

National Key Laboratory of Basin Water Cycle Simulation and Control, China Institute of Water Resources &

Hydropower Research, Beijing 100078, P. R. China

Laboratory of Coastal Groundwater Utilization & Protection, Tianjin University of Science and Technology, Tianjin

300450, P. R. China

Keywords: Extreme precipitation, The Yellow River, Non-stationary

Abstract: Climate change has changed the extreme precipitation pattern in the Yellow River Basin (YRB). In this

article, total of six extreme indices of rainfall were employed to assess the spatial and temporal distribution

characteristics of extreme precipitation in YRB, and the GAMLSS model is applied in two typical stations

(Xinghai, Yuncheng) to investigate the non-conformity in terms of persistence-CDD, intensity-R95p, and

frequency-R20, respectively. The results showed that: a) In YRB, CDD had a significant upward trend,

while there was a clear downward trend in R20 and SDII (Simple daily intensity index), and the spatial

distribution of temporal trends varies greatly among regions, with an increasing tendency in the northwest

of YRB and decreasing tendency in the southeast of YRB, which was the opposite of the spatial distribution.

Indicating that rainfall decreased in the downstream of relatively wet basins, while rainfall increased in the

upstream of relatively dry basins. b) Both representative stations expressed non-stationarity, but with

different characteristics. In the stationary model (Model 0), the WEI (Weibull) was selected at most indices,

In the non-stationary model (Model 1), the GA (Gamma) was selected at most Climate indices. In Station

Xinghai in upper of YRB, drought days decreased, the mean and variance of the R20 and R95p distribution

functions were increasing which indicates that the inter-annual variation became larger and more prone to

extreme flooding or extreme drought. Station Yuncheng in lower of YRB also has fewer drought days,

however the mean and variance of the R20 and R95p are decreasing which indicates more stable

precipitation and a lower chance of extreme events than before.

1 INTRODUCTION

For hydrological cycle, precipitation is vital and

directly affects the flood and drought events in an

area. Warming leads to greater evaporation, 7%

increase in air holding capacity for every 1 degree

rise in temperature, more intense precipitation events

would be widespread, even in places where total

precipitation is reduced (Trenberth, 2011).

Furthermore, precipitation change may differ in

different aspects, such as totals and extremes (Donat

et al., 2016). In addition, non-stationarity has been

widely reported in hydrological time series analysis,

and related studies have shown that rainfall series

also exhibit non-stationary characteristics (Zhang et

al., 2016; Gu et al., 2019; Wu et al., 2021; Medeiros

et al., 2019). Consequently, research about the

spatiotemporal dynamics of extreme precipitation

and its distribution pattern under the changing

environment is significant for the monitoring and

prevention of climate disasters like floods and

droughts (Zou et al., 2021).

For the latest years, the dynamic changes of

spatial and temporal variability and non-stationarity

of extreme precipitation has attracted the attention of

many scholars. Gao et al. (2018) used six climate

variables based on GAMLSS showing the existence

of non-stationarity in the Coastal areas of Southeast

China. Lei et al. (2021) pointed out the intensity

indices (PRCPTOT, SDII, R99P) and frequency

indices (R20, R10) of extreme precipitation showed

stationary characteristics, however the duration

indices (CWD, CDD) showed non-stationary

494

Lv, X., Yu, H., Dong, H., Ji, S., Qiu, Y., Duan, X. and Zheng, H.

Analysis of Spatiotemporal Distribution and Non-stationary of Extreme Precipitation Events during 1960-2018 in the Yellow River Basin.

In Proceedings of the 7th International Conference on Water Resource and Environment (WRE 2021), pages 494-503

ISBN: 978-989-758-560-9; ISSN: 1755-1315

characteristics in the Poyang Lake Basin of China.

Hao et al. (2019) used two precipitation indices

(RX5day, R20) which choose two covariates, time

and climate, to determine the non-stationarity of

extreme precipitation in the Han River basin of

China. Liu et al. (2008) shows that precipitation is

significantly correlated with longitude and not with

latitude, and exhibits a downward trend at most

stations in the YRB. S Swain et al., showed that

annual rainfall has increased by 10.65% from 1901-

2002 by Sen’s slope and Mann-Kendall (M-K) test

(Swain et al., 2019). He et al., used M-K method to

analyze the temporal trends of extreme rainfall index

in YRB from 1960 to 2012, and its spatial

distribution (He & He, 2014). Yang et al. (2017)

pointed out that the frequency of extreme

precipitation exists significant increasing trends by

POT sampling method.

Existing studies have been concentrating on the

Spatiotemporal patterns of extreme rainfall indices

and their effects. This research adopts the Modified

Mann-Kendall (MM-K) method to compensate for

the shortcomings of autocorrelation in the MK test,

and establishes the GAMLSS model with time as the

independent variable to investigate the change of the

distribution function of extreme rainfall index in

YRB.

2 STUDY AREA AND DATA

COLLECTION

YRB is located in the arid and semi-arid regions

(between 96°-116°E and 32°-42°N), arid in the west,

wet in the east, dry in winter and dry in spring, rainy

in summer and autumn. YRB has an important

influence in northern China (Fig 1.). YRB has a huge

difference in elevation from east to west, and the

geomorphology varies greatly between different

regions. In addition, it is in the mid-latitude zone,

which is affected by atmospheric circulation and

monsoon circulation in a complex way, and the

climate varies significantly in different areas of YRB.

The data used were obtained from the daily

precipitation data of 874 stations from 1960 to 2018

provided by the China Meteorological Science Data

Sharing Service, including 91 precipitation stations

in the Yellow River basin, and the location of

precipitation stations is shown in Figure 1. To ensure

the continuity and uniformity of the precipitation

data, only the years with continuous measured data

were included. Secondly, all data were checked for

outliers to ensure data integrity and accuracy.

Figure 1: Location of meteorological stations and study area.

Analysis of Spatiotemporal Distribution and Non-stationary of Extreme Precipitation Events during 1960-2018 in the Yellow River Basin

495

3 METHODS

3.1 Extreme Precipitation Index

Six extreme precipitation indices were selected from

the 27 extreme climate indices recommended by the

Expert Group on Climate Change Monitoring and

Indicators jointly established by WMO, Commission

for Climatology (CCI) and other meteorological

organizations (Costa & Soares, 2009), as shown in

Table 1. All extreme precipitation indices were

calculated using RClimate software.

Table 1: Definition of extreme precipitation indices.

Index Name Definition Unit

SDII

Simple daily intensity

index

Annual total precipitation divided by the number of wet days

(

defined as PRCP>=1.0mm

)

in the

mm/d

PRCPTOT

Annual total wet-day

recipitation

Annual total PRCP in wet days (Rain Rate (RR)>=1mm) mm

R95P Ver

wet da

s Annual total PRCP when RR>95

ercentile m

CDD Consecutive dr

s Maximum number of consecutive da

s with RR<1m

R10

Number of heavy

reci

itation da

Annual count of days when PRCP>=10mm d

R20

Number of very heavy

recipitation days

Annual count of days when PRCP>=20mm d

3.2 MM-K Trend Analysis Method

The M-K test is an important nonparametric trend

test for time series, which is widely used in the field

of hydrological statistics because it does not require

the series to be examined to obey a certain

probability distribution, overcoming the problems of

bias, non-identical distribution, and having outliers

in hydrological data. Although the MK method has

the advantages of nonparametric tests, it does not

solve the problem of data independence required in

statistical tests of hydrological series (Zhang et al.,

2013). Hamed and Rao (1998) proposed a Modified

Mann-Kendall test which corrected V (S) by using

the effective sample size (ESS), which reflects the

effect of serial autocorrelation on the test results

(Tian et al., 2017). Swain et al. (2021) showed a

significantly increasing trend of drought in Narmada

River Basin. The corrected V (S) equation is as

follows:

𝑉

∗

(

𝑆

)

=𝑉

(

𝑆

)



∗

(1)



∗

=1+



 () ()

∑

(𝑛 − 𝑘) (𝑛 − 𝑘 − 1) (𝑛 − 𝑘 − 2)𝑟









(2)

𝑟







∑[







(





)]

[



 (



)]









∑

[



 (



)]







(3)

𝐸

(

𝑋



)





∑

𝑋







(4)

3.3 GAMLSS Model

The GAMLSS model is a generalizable additive

model based on the location parameter, scale

parameter and shape parameter (Rigby &

Stasinopoulos, 2005). It extends the form of the

assumption of the distribution from exponential

distribution to a more generalized form, which can

be parametric or nonparametric model for the

location parameter, scale parameter and shape

parameter of a distribution simultaneously under

various distribution assumptions, describing the

linear or nonlinear relationship between any

statistical parameter of the sequence of random

variables and the explanatory variables (Zhang et al.,

2015; Zhang et al., 2014). Then the regression

relationship between the distribution factors,

explanatory variables, and random effects are as

follows:

𝑔



(

𝜃



)

=𝑋



𝛽



∑

ℎ



(𝑥



)





(5)

Where 𝑔



is the monotonic connection function;

𝜃



is the vector of k distribution parameter with

length n; 𝑋



is the explanatory variable in the n ×m

matrix; 𝛽



is the parameter vector of length m;

and ℎ



(.) represents the joint function (the cubic

WRE 2021 - The International Conference on Water Resource and Environment

496

spline function is applied here) between the

distribution parameters and explanatory variables 𝑥



The linear function and cubic spline function are

chosen as the parameter to explain the function of

association between variables. Five distributions,

lognormal (LOGNO), gamma (GA), normal (NO),

Weibull (WEI) and logistic (LO), were applied to

model the extreme precipitation data. The Akaike

Information Criterion (AIC) was used to penalize

overfitting of the models and to select the best model

(Arnold, 2010). The best model fit is evaluated by

snail plot and the independence and normality of the

residuals are checked.

4 RESULTS

4.1 Temporal Variation of Extreme

Precipitation Characteristics in the

Yellow River Basin

According to the daily data from 91 precipitation

stations in YRB, a total of six extreme precipitation

indices, CDD, PRCPTOT, R10, R20, R95P and SDII,

were calculated for each precipitation station year by

year, and the Thiessen polygon method was used to

calculate the extreme precipitation indices. The

MMK test results for these indices are presented in

Table 2.

Table 2: MMK trend results.

trend h z-value slope intercept mean

CDD decreasing TRUE -4.49 -1.08 101.34 85.55

PTOT no trend FALSE -0.66 -0.34 579.37 568.45

R10 no trend FALSE 0.16 0.005 15.78 15.92

R20 increasing TRUE 2.03 0.02 5.20 5.58

R95P no trend FALSE -0.90 -0.36 142.21 134.80

SDII increasing TRUE 2.83 0.02 7.30 7.34

As shown in Figure 2, CDD, PRCPTOT, and

R95P showed a decreasing trend, and R10, R20, and

SDII showed an increasing trend and slope of -1.08/a

(CDD), -0.34mm/a (PRCPTOT), 0.005mm/a (R10),

0.02mm/a (R20), - 0.36mm/a (R95P), and 0.02mm/a

(SDII). The decreasing trend of CDD was significant

(Z=-4.49), and the increasing trend of R20 (Z=2.03)

and SDII (Z=2.83) was significant. Hence the trend

of drought is decreasing, and precipitation

distribution is more homogeneous in annual basis.

Daily precipitation intensity showed a significant

increasing trend, while annual precipitation showed

a non-significant decreasing trend. In contrast, R20

shows a significant increasing trend and R10 shows

a non-significant increasing trend, indicating that the

frequency of extreme precipitation in YRB in recent

years is dominated by moderate and heavy rainfall,

and the precipitation process is more concentrated.

From Figure 3, the number of CDD in YRB basin

showed a decreasing trend, with the most drastic

decrease in the northwestern and northeastern parts

of YRB, the trend of PRCPTOT is increasing in the

northwestern part of the basin. In the southern parts

of the basin, the number of consecutive dry days

decreased the least, the number of wet days

increased the least, and the PRCPTOT was also in a

decreasing trend and more significant.

The number of light rain days, R10, was on a

decreasing trend in the central, southern, and eastern

parts of the study area. The trend in the northwest is

consistent with that of PRCPTOT, but differs in the

Yellow River source area, where the annual

precipitation increases, and the number of light rain

days R10 shows a decreasing trend and the number

of medium rain days R20 shows an increasing trend.

Compared with PRCPTOT and R10, R20 and

R95P also showed an increasing trend in the middle

part of YRB, indicating that the decrease in annual

precipitation in the middle part of YRB was mainly

caused by the decrease in the number of light rain

days, and the number of medium rain days showed

an increasing trend in contrast to the decrease in

annual precipitation. The increase in the frequency

of moderate and heavy rainfall somewhat suppressed

the decrease in annual precipitation caused by the

decrease in light rainfall.

4.2 Spatial Distribution of Extreme

Precipitation in the Yellow River

Basin

From Figure 4, significant differences could be

found in different regions of YRB, the CDD values

range from 40.2-147.6, PRCPTOT ranges from

Analysis of Spatiotemporal Distribution and Non-stationary of Extreme Precipitation Events during 1960-2018 in the Yellow River Basin

497

155.4-1144, light rain days between 4.716-29.59,

medium rain days between 0.679-17.38, R95P

between 39.96-73.38, and SDII between 3.27-15.95.

In the study area, except for SDII, the multi-year

average of extreme precipitation indices basically

shows a distribution characteristic of gradually

increasing from northwest to southeast, and SDII

shows a distribution characteristic of gradually

increasing from west to east. The results are

consistent when comparing the spatial distribution of

Yang Peiyu using POT sampling with 95% quantile

as the threshold.

Figure 2: Time series of extreme precipitation index in YRB.

4.3 Non-stationary Analysis of Extreme

Precipitation in YRB

From the upper and lower reaches of YRB, two

stations (Xinghai, Yuncheng) were selected as the

representative stations for non-stationarity analysis.

Three indices were selected from six extreme

climate indices as mentioned in preceding part of the

paper. These are Consecutive dry days (CDD) that

can describe the persistence of extreme precipitation

events, the number of very heavy rainfall days (R20)

which can describe the frequency of extreme

precipitation events, the Very wet days (R95p) which

can indicate the intensity of extreme precipitation

events.

WRE 2021 - The International Conference on Water Resource and Environment

498

Figure 3: Spatial distribution of MMK test results in the Yellow River Basin.

Based on the AIC values, one distribution with

the best fit was selected for each site. (from Table 3).

In the Model 0, the WEI was selected at most indices

(4 indices), GA and LOGNO performed best at one

Indexes. In the Model 1, the GA was selected at most

Climate indices (4 indices), NO and WEI performed

best at one index.

Table 3: Summary for the fitted models with time as the covariate: cs () indicates the dependence is via the cubic splines;

and ct refers to a parameter that is constant.

Model 0 Model 1

Extreme Index Distribution AIC Distribution θ

AIC

Xinghai

CDD WEI 630.3423 NO cs (t,3) ct 596.2364

R95p WEI 628.8753 WEI cs (t,0) cs (t,2) 622.2544

R20 GA 192.6919 GA cs (t,3) ct 189.9838

Yuncheng

CDD LOGNO 571.527 GA

cs (t,0) 565.378

R95p WEI 697.5988 GA cs (t,0) cs (t,2) 697.0961

R20 WEI 309.0856 GA ct cs (t,2) 308.5433

Analysis of Spatiotemporal Distribution and Non-stationary of Extreme Precipitation Events during 1960-2018 in the Yellow River Basin

499

Figure 4: Spatial distribution of extreme precipitation in the YRB.

Model 0 is a steady-state model with constant

mean and variance, and Model 1 is a non-stationary

model with varying mean and variance which time is

covariate). The smaller AIC values for the non-

stationary model 1 compared to the stationary model

0 suggest that the non-stationary model 1 indicates

that the model with time as a covariate performs

better than the model with constant parameters. From

table 3, the parameter θ

is the cubic spline function

with degree of freedom 3 and the parameter θ

constant in Xinghai-CDD and Xinghai-R20. The

parameter θ

is constant and the parameter θ

the

cubic spline function with degree of freedom 3

Yuncheng-CDD and Yuncheng-R20. The parameter

is linear trend function and the parameter θ

is the

cubic spline function with degree of freedom 2 in

Xinghai-R95p and Yuncheng-R95p.

Figure 5, whose vertical coordinate is the normal

normalized residual series, and the horizontal

coordinate is the theoretical residual value, shows

the worm plot of the residuals of the optimal model

for each index, and the red line in the middle is a

cubic polynomial curve fitted by the series of scatter

points in the plot. All the scatter points in the worm

plot lie within the confidence interval between the

upper and lower curves. The above fitting results

show that the residual series of the optimal model for

each site can be considered to obey the standard

normal distribution, and thus the distribution type

and parameter selection of each preferred model

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500

constructed earlier can be judged to be reasonable.

Based on the distribution and parameters of each

preferred model, the quantile values corresponding

to each indicator series at the specified time and at

the specified percentile can be calculated. Figure 6

shows the quantile plot for each indicator series,

where the dots represent the measured values for

each year at the site, and the solid lines of different

colors represent the quantile values corresponding to

the five percentiles of 5%, 25%, 50%, 75%, and 95%,

respectively. Most of the data points are between 5%

and 95% of the quantile curve. It indicates that the

simulation results of the theoretical distribution of

each station match well with the distribution of the

actual measured points.

Figure 5: The residual worm diagram of the optimal model.

In terms of persistence of dry day (CDD), the

parameter θ

related to the mean value of the

extreme precipitation events has a nonlinear

decreasing trend in station Xinghai, the parameter θ

related to the fluctuation of the extreme precipitation

events has no significant trend in station Xinghai.

The parameter θ

is on a linear decreasing trend in

station Yuncheng, The parameter θ

also has a linear

decreasing trend in station Yuncheng.

In terms of intensity (R95p), the parameter θ

on a nonlinear decreasing trend in station Xinghai,

the parameter θ

has a nonlinear increasing trend in

station Xinghai. The parameter θ

is on a nonlinear

decreasing trend in station Yuncheng, the parameter

also has a nonlinear decreasing trend in station

Yuncheng.

In terms of frequency (R20), the parameter θ

on a nonlinear increasing trend in station Xinghai,

the parameter θ

also has a nonlinear increasing trend

in station Xinghai. The downward trend of parameter

is non-significant in station Yuncheng, the upward

of parameter θ

is non-significant in station

Yuncheng.

5 CONCLUSION

In this paper, we analyzed the spatiotemporal

variation of six extreme precipitation indices in the

YRB from 1960 to 2018 by MMK trend test and

selected three indices in terms of persistence (CDD),

frequency (R20) and intensity (R95p) for non-

stationary analysis through GAMLSS model.

In YRB, CDD has a significant upward trend,

R20 and SDII have a significant downward trend,

and other indicators have no significant changes. In

addition, the spatial distribution of temporal trends

varies considerably between regions, with an upward

trend in the northwest and a downward trend in the

southeast. However, the spatial distribution of the

multi-year average values of the basin precipitation

indices shows an opposite trend which gradually

Analysis of Spatiotemporal Distribution and Non-stationary of Extreme Precipitation Events during 1960-2018 in the Yellow River Basin

501

increases from northwest to southeast. Rainfall

decreases in the relatively wet downstream portion

of basin and increases in the relatively dry upstream

portion of basin, the gap between upstream and

downstream will gradually decrease.

In the Model 0, the WEI performed best at most

indices (4 indices), GA and LOGNO performed best

at one index. In the Model 1, the GA performed best

at most Climate indices (4 indices), NO and WEI

performed best at one index. In Station Xinghai in

upper parts of YRB, decreasing drought days, along

with the increasing mean and variance of the R20

and R95p distribution functions with time indicates

that the inter-annual variation became larger and

more prone to extreme flooding or extreme drought.

Station Yuncheng in lower of YRB also has fewer

drought days, however the mean and variance of the

R20 and R95p are decreasing which indicates more

stable precipitation and a lower chance of extreme

events than before.

Figure 6: 5%, 25%, 50%, 75% ,95%for two representative stations CDD, R95p, R20. 95% quantile.

ACKNOWLEDGMENTS

The researchers would like to extend their thanks to

the National Natural Science Foundation of China

(No. 52009140). The Independent Research Project

of State Key Laboratory of Simulations and

Regulation of Water Cycle in River Basin

(SKL2020ZY04).

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