nonstationarities and at-site probabilistic forecasts of

ARTICLE

Nonstationarities and At-site Probabilistic Forecasts of SeasonalPrecipitation in the East River Basin, China

Peng Sun1,2,3 • Qiang Zhang2,3,4 • Xihui Gu5 • Peijun Shi2,3,4 • Vijay P. Singh6 •

Changqing Song2,3,4 • Xiuyu Zhang7

Published online: 8 March 2018

� The Author(s) 2018. This article is an open access publication

Abstract Seasonal precipitation changes under the influ-

ence of large-scale climate oscillations in the East River

basin were studied using daily precipitation data at 29 rain

stations during 1959–2010. Seasonal and global models

were developed and evaluated for probabilistic precipita-

tion forecasting. Generalized additive model for location,

scale, and shape was used for at-site precipitation fore-

casting. The results indicate that: (1) winter and spring

precipitation processes at most stations are nonstationary,

while summer and autumn precipitation processes at few of

the stations are stationary. In this sense, nonstationary

precipitation processes are dominant across the study

region; (2) the magnitude of precipitation is influenced

mainly by the Arctic Oscillation, the North Pacific Oscil-

lation, and the Pacific Decadal Oscillation (PDO). The El

Nino / Southern Oscillation (ENSO) also has a consider-

able effect on the variability of precipitation regimes across

the East River basin; (3) taking the seasonal precipitation

changes of the entire study period as a whole, the climate

oscillations influence precipitation magnitude, and this is

particularly clear for the PDO and the ENSO. The latter

also impacts the dispersion of precipitation changes; and

(4) the seasonal model is appropriate for modeling spring

precipitation, but the global model performs better for

summer, autumn, and winter precipitation.

Keywords China � ENSO regimes � GAMLSS

model � Nonstationarity � Probabilistic precipitation

forecasting

1 Introduction

An investigation of precipitation changes is one of the key

steps in understanding hydrological response to climate

change at the local, regional, and global scales, and is of

critical importance for the management of water resources

and agricultural development. This is especially important

in China (Xia et al. 1997; Zhang et al. 2012b)—the largest

agricultural country with the largest population in the

world. Precipitation forecasts play a crucial role in the

planning of water resource use, agricultural management

(Wei et al. 2005; Kisi and Cimen 2012; Ortiz-Garcıa et al.

2014), and flood forecasting (Francesco and Rebora 2015).

Multitudes of studies have addressed precipitation

forecasting using a variety of techniques. Ortiz-Garcıa

et al. (2014) predicted daily precipitation using the support

& Qiang Zhang

[email protected]

& Xiuyu Zhang

[email protected]

1 College of Territorial Resources and Tourism, Anhui Normal

University, Wuhu 241000, Anhui, China

2 Key Laboratory of Environmental Change and Natural

Disaster, Ministry of Education, Beijing Normal University,

Beijing 100875, China

3 State Key Laboratory of Earth Surface Processes and

Resource Ecology, Beijing Normal University,

Beijing 100875, China

4 Academy of Disaster Reduction and Emergency

Management, Beijing Normal University, Beijing 100875,

China

5 School of Environmental Studies, China University of

Geosciences, Wuhan 430074, Hubei, China

6 Department of Biological and Agricultural Engineering and

Zachry Department of Civil Engineering, Texas A&M

University, College Station, TX 77843, USA

7 South China Institute of Environmental Sciences,

Guangzhou 510655, Guangdong, China

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vector machine (SVM) and pointed out its excellent per-

formance in comparison with other neural computation-

based approaches, such as multilayer perceptron, extreme

learning machine, and classical algorithms such as decision

trees and K-nearest neighbor classifier. Manzato (2007)

applied a neural computation approach to the short-term

forecasting of thunderstorm rainfall. Shukla et al. (2011)

indicated the importance of El Nino / Southern Oscillation

(ENSO) indices in precipitation forecasting. With the help

of a neural network, Shukla et al. (2011) forecasted pre-

cipitation in India due to the summer monsoon by con-

sidering ENSO indices. Nastos et al. (2013) applied an

artificial neural network to forecast precipitation in Athens,

Greece. Ingsrisawang et al. (2008) compared several

machine learning algorithms, such as decision trees (DT),

neural networks (ANN), and SVMs for short-term precip-

itation prediction in Thailand. Lu and Wang (2011) pre-

dicted monthly rainfall in China, using an SVM approach

with different kernel functions. These forecasts are deter-

ministic (point forecast representing our best guess) or

probabilistic (providing the forecast in terms of probability

of exceedance that reflects a range of possible values for

the variable of interest), and are statistical in nature or

based on numerical models.

In the above studies, deterministic forecast has been

widely used. However, statistical models have also been

widely used in precipitation forecasting (Villarini and

Serinaldi 2012; Wang et al. 2013). Advantages of statistical

models include the ability to identify changing patterns, the

estimation of parameters, uncertainty analysis, and diag-

nostic checking (Mishra and Desai 2005; Wang et al.

2013). Some statistical models, such as the autoregressive

moving average (ARMA) models, can predict the output

from the values of the output at previous time points. These

models are only suitable for a stationary system (Wang

et al. 2013), although it has been stated that seasonal

autoregressive integrated moving average (SARIMA)

models can model time series that exhibit nonstationary

behavior (Box et al. 2015).

The generalized additive model for location, scale, and

shape (GAMLSS) developed by Rigby and Stasinopoulos

(2005) has been used in this study. It can be devised to

cope with nonexponential distribution families and is able

to incorporate covariates not only in the position parameter

but also in the scale and shape parameters. Thus, GAMLSS

allows for a better control and representation of dispersion,

skewness, and kurtosis (Rigby and Stasinopoulos 2005;

Jones et al. 2013) and provides a suitable framework to

model the discrete–continuous distribution of daily pre-

cipitation accounting for seasonality and exogenous forc-

ing variables, such as alternative climate states (Francesco

and Kilsby 2014; Francesco and Rebora 2015). In this

study, the GMALSS model was used with exogenous

forcing variables such as the ENSO to simulate and fore-

cast precipitation in the East River basin, China.

The East River basin is a major tributary of the Pearl

River basin in South China with a drainage area of

35,340 km2, which accounts for about 5.96% of the Pearl

River basin area (Fig. 1). Water resources in the East River

basin have been highly developed for a variety of uses,

such as municipal and rural water supply, hydropower

generation, navigation, irrigation, and suppression of sea-

water invasion (Chen et al. 2010). In recent years the East

River has been supplying water to meet about 80% of Hong

Kong’s annual hydrological demand (Chen et al. 2010;

Wong et al. 2010). Therefore, the vulnerability of the East

River water resource system is of great importance for the

sustainable social and economic development of the Pearl

River Delta, one of the economically most developed

regions in China, and also for the sustainable water supply

of Hong Kong (Chen et al. 2013). In this context, precip-

itation changes play a critical role. Investigations of pre-

cipitation structure indicate higher frequencies of heavy

precipitation (defined as events with C 50 mm/day pre-

cipitation) in the eastern parts of the Pearl River basin and

the East River basin in recent decades (Zhang et al. 2012a).

Therefore, forecasting of precipitation variations in the

East River basin is important for the planning and man-

agement of water resources. The influence of large-scale

climate oscillations, for example ENSO, on precipitation

changes in the East River basin has been established and

corroborated (Zhang et al. 2013; Huang et al. 2017). Thus,

large-scale climate oscillations are used as exogenous

factors in precipitation forecasts.

The objectives of this study are to: (1) screen the models

that can forecast the precipitation behavior at a seasonal

temporal scale; and (2) forecast precipitation changes while

taking account of nonstationarity and uncertainty, includ-

ing those stemming from climate oscillations. Results of

this study will provide a framework for precipitation

forecasting in humid regions and guidance for planning and

management of water resources and agricultural activities

at the regional scale.

2 Data

Monthly precipitation data, covering the period of

1959–2010 and derived from 29 meteorological stations in

the East River basin, were analyzed in this study. The

locations of these stations are shown in Fig. 1. The dataset

was compiled by the Climatic Data Center of the National

Meteorological Information Center at the China Meteoro-

logical Administration.1 The quality of the data was

1 http://www.nmic.cn/web/channel-8.htm.

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Int J Disaster Risk Sci 101

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controlled before its release (Zhang et al. 2013). Seasonal

average precipitation changes were also analyzed, based on

four seasons: winter (December to February of the subse-

quent year), spring (March to May), summer (June to

August), and autumn (September to November).

The climatic indices used in this study for seasonal

average precipitation forecasts were the Arctic Oscillation

(AO) index, the North Pacific Oscillation (NPO) index, the

Pacific Decadal Oscillation (PDO) index, and the Southern

Oscillation Index (SOI). Many researchers have found that

precipitation changes in the East River basin are signifi-

cantly influenced by these four climate oscillations (Feng

and Li 2011; Zhang et al. 2013, 2014; Ding et al. 2014).

Data on the climatic indices were obtained from an Internet

source of the NOAA Earth System Research Laboratory.2

3 Methodology

Due to the influence of human activities and climate

change itself, precipitation changes are considered non-

stationary (Li et al. 2016; Chang et al. 2017). Therefore, a

nonstationary model should be used with parameters

changing along with the explanatory variables. In this

study, the GAMLSS model was selected for at-site pre-

cipitation forecasting.

3.1 The Generalized Additive Model for Location,

Scale, and Shape (GAMLSS)

The GAMLSS model (Rigby and Stasinopoulos 2005)

assumes a parametric distribution for the response variable

Y, the seasonal precipitation amount in this study, and

models the distribution parameters as functions of an

explanatory variable, time ti and the climatic indices—AOi,

NPOi, PDOi, and SOIi. It is assumed that in GAMLSS,

random variables yi, for i = 1,…, n, are mutually inde-

pendent and are from the same distribution function,

FY(yi|hi) with a vector of p distribution parameters,

hi = (h1, h2,…, hp), accounting for location, scale, and

shape parameters. Generally, p B 4 in that a 4-parameter

distribution family can describe distribution characteristics

of different hydrometeorological variables. Assume that

gk(�) shows monotonic relations between hk, the explana-

tory variable Xk, and the random term, that is:

gkðhkÞ ¼ gk ¼ Xkbk þXJk

j¼1

Zjkcjk ð1Þ

Fig. 1 Location of the study

region—the East River basin—

and the 29 precipitation stations

used in the study

2 http://www.esrl.noaa.gov/psd/data/climateindices/list/.

123

102 Sun et al. Probabilistic Forecasts of Seasonal Precipitation in the East River Basin

http://www.esrl.noaa.gov/psd/data/climateindices/list/

where gk and hk are the vectors with the length of n,

bkT = {b1k, b2k, …, bJk} is the parameter vector with the

length of Jk, Xk is the explanatory variable matrix with the

length of n 9 Jk, Zjk is the fixed design matrix with the

length of n 9 qjk, and cjk is the random variable following

the normal distribution. In this study, a cubic spline func-

tion was used as the link function between parameters and

covariate variables. Five two-parameter functions were

selected and are displayed in Table 1: Gumbel (GU),

Weibull (WEI), Gamma (GA), Lognormal (LOGNO), and

Logistic (LO).

The Akaike information criterion (AIC) technique was

used to select the distribution function with the highest

goodness-of-fit. To ensure the quality of the fit, a worm

plot was applied to estimate the fitting performance of the

distribution functions. More details can be found in Rigby

and Stasinopoulos (2005).

3.2 At-site Probabilistic Forecast

At-site (rain station) probabilistic forecasting was done

using the GAMLSS model, taking time, t, and the climatic

indices AO, NPO, PDO, and SOI as covariates. Two

forecasting modes were developed: (1) Taking the seasonal

precipitation series of each individual season—spring,

summer, autumn, and winter—as a sole series, this kind of

forecasting was denoted as the seasonal model; and (2)

Filtering out each seasonal precipitation component such as

spring, summer, autumn, and winter with a seasonal factor,

for example, 1, 2, 3, and 4 standing for spring, summer,

autumn, and winter, respectively, from each year and forms

the annual series of spring, summer, autumn, and winter

precipitation series. The forecasts were done on the reor-

ganized annual variations of seasonal precipitation com-

ponents. This kind of forecasting was denoted as the global

model. The seasonal and global models were then com-

pared to determine which model produces better forecasts.

Two precipitation forecasting practices were used: the

track precipitation forecast and the cross-validation pre-

cipitation forecast. In track precipitation forecasting,

parameter estimation is done using the seasonal precipita-

tion data covering the period of 1959–2000 and the esti-

mated parameter(s) is(are) used to forecast the precipitation

in 2001. The forecasted seasonal precipitation in 2001 is

added to the seasonal precipitation series of the period of

1959–2000 and parameters are estimated again, based on

the newly produced seasonal precipitation series. Then, the

seasonal precipitation is forecasted for 2002, using the

newly estimated parameters based on the newly produced

seasonal precipitation series of the period of 1959–2001.

This procedure is repeated until the forecasted seasonal

precipitation for 2010 is attained. In cross-validation pre-

cipitation forecasting, parameter estimation is done using

the seasonal precipitation data covering the calibration

Table 1 The five distribution functions considered in this study

Distribution

function

Probability density function Distribution moment Link functions

h1 h2

GumbelfY y h1; h2jð Þ ¼ 1

h2exp � y � h1

h2

� �� exp � y � h1ð Þ

h2

� ��

�1\y\1;�1\h1\1; h2 [ 0

E Y½ � ¼ h1 þ ch2 ffi h1 þ 0:57722h2

Var½Y � ¼ p2h22=6 ffi 1:64493h22

Identity Log

WeibullfY y h1; h2jð Þ ¼ h2yh2�1

hh21exp � y

h1

� �h2( )

y[ 0; h1 [ 0; h2 [ 0

E Y½ � ¼ h1C1

h1þ 1

� �

Var½Y � ¼ h21 C2

h2þ 1

� �� C

1

h2þ 1

� �� 2( )

Log Log

Gamma

fY y h1; h2jð Þ ¼ 1

h22h1� 1=h22

y1

h22

�1

exp �y= h22h1� �

Cð1=h22Þ

y[ 0; h1 [ 0; h2 [ 0

E½Y � ¼ h1

Var½Y � ¼ h21h22

Log Log

LognormalfY y h1; h2jð Þ ¼ 1ffiffiffiffiffiffiffiffiffiffi

2ph22

q 1

yexp � logðyÞ � h1j j2

2h22

( )

y[ 0; h1 [ 0; h2 [ 0

E½Y � ¼ x1=2eh1

Var½Y � ¼ xðx� 1Þe2h1 ; where x ¼ exp h22�

Identity Identity

LogisticfY y l;rjð Þ ¼

exp � y�lr

�

r 1þ exp � y�lr

� �2

�1\y\1;�1\l\1;r[ 0

E½Y � ¼ r

Var½Y � ¼ r2p2

3

Identity Log

123


period, such as 1959–2000, and then the estimated

parameter(s) is(are) used to forecast the seasonal precipi-

tation for the verification period, such as 2001–2010.

In track precipitation forecasting, the naıve model

(simple linear regression) is introduced and a comparison

of the forecast performances of the seasonal and global

models and the naıve model (Mason and Baddour 2008;

Gabriele and Francesco 2012) is done. In cross-validation

precipitation forecasting, time, t, is taken as the covariate

variable for seasonal precipitation forecasting, called the

time model. Comparison is done for evaluating the fore-

casting performances of seasonal and global models as well

as the time model.

3.3 Evaluation of the At-site Probabilistic Forecast

Eight evaluation criteria were applied to evaluate the

forecasting accuracy of seasonal precipitation. Since each

method has its own advantages and limitations, it is

assumed that these methods can combine to evaluate the

forecasting accuracy of the models considered, thus

avoiding the uncertainty and unreliability due to limitations

of the individual method. These methods (Table 2) are:

absolute mean error (AME), mean absolute error (MAE),

median absolute error (MdAE), root mean squared error

(RMSE), mean absolute percentage error (MAPE), median

absolute percentage error (MdAPE), and root mean squared

percentage error (RMSPE). It should be noted that AME,

MAE, MdAE, and RMSE are absolute error indices and

MAPE, MdAPE, and RMSPE are comparative error indi-

ces. The geometric reliability index (GRI) was also used to

evaluate the performance of models from a geometric

perspective.

4 Results

Based on the aforementioned analysis procedure, we

obtained the following interesting and important results

and findings.

4.1 Nonstationarity of Seasonal Average

Precipitation Changes and Teleconnections

with ENSO, AO, PDO, and NPO Events

The AIC method was used to screen the models that sat-

isfactorily simulate seasonal and integrated seasonal pre-

cipitation and the related distribution functions (Fig. 2). It

can be seen from Fig. 2a that the distribution functions

with the highest goodness-of-fit for spring precipitation

series (seasonal model) are Gamma and Logistic models

for 19 out of the 29 stations. The location parameter, l, wasinfluenced mainly by PDO and AO (Fig. 3a) and had a

linear relation with AO but a nonlinear relation with PDO

(Fig. 3a). The scale parameter, d, had a close relation with

AO, PDO, and SOI (Fig. 4a). A significant influence of AO

on scale parameter, d, was observed for 16 out of the 29

stations (Fig. 4a). AO had a linear relation with the scale

parameter and a nonlinear relation was detected between d,and PDO and SOI. In general, spring precipitation in the

East River basin was influenced mainly by AO and PDO.

Meanwhile, PDO mainly impacted the location parameter,

l, implying that PDO altered the changing magnitude of

spring precipitation in the East River basin. However, AO

and ENSO mainly influenced the scale parameter, d, that isthe statistical dispersion properties of spring precipitation

changes (Figs. 3a and 4a). Besides, Figs. 3a and 4a show

that l and d for 4 and 3 out of the 29 stations were constant,

Table 2 Eight estimation methods for evaluation of modeling accuracy

Estimation INDICES Equations LB UB No errors

AME 1n

Py � yð Þ

0 Inf 0

MAE 1n

Py � yj j 0 Inf 0

MdAE Median ( y � yj j) 0 Inf 0

RMSEffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1n

Py � yð Þ2

q0 Inf 0

MAPE 1n

P y�yy

� 100 0 Inf 0

MdAPE Median y�yy

� 100

� �0 Inf 0

RMSPEffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1n

P y�yy

� �2r

� 1000 Inf 0

GRI1þQ1�Q

, where Q ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1n

P y�yyþy

� �2r

1 Inf 1

Low boundary (LB) and Upper boundary (UB) stand for the maximum and minimum values in theory, respectively; y stands for the measured

values, and y stands for the modeled values

123


indicating that spring precipitation changes at these stations

were stationary. In this sense, spring precipitation changes

at most of the stations were nonstationary.

Figure 2b indicates that Gamma distribution is the best

model for summer precipitation changes (seasonal model)

for 18 out of the 29 stations. In comparison, different

Fig. 2 Spatial distribution of

the best models in the East

River basin study area in

southeastern China based on

seasonal and global models with

the highest goodness-of-fit

123


changing properties of summer precipitation were detected

when compared to spring precipitation changes. The

influence of AO on scale parameter, d, was linear for 18 outof 22 stations (Fig. 4b). However, the location parameter,

l, was largely free from the influence of climate oscilla-

tions (Fig. 3b), implying that the mean value of summer

precipitation had stationary changes to a certain degree.

Figure 2c indicates that the Gamma distribution func-

tion was also the best model for autumn precipitation

changes (seasonal model) for 21 out of the 29 stations. A

closer look at Figs. 2c, b, 3c, and 4c indicates similar

changes in the properties of autumn precipitation changes

when compared to summer precipitation. However, com-

plicated changing characteristics were detected for winter

precipitation changes.

Figure 2d shows that the Weibull distribution function

was the best choice for modeling winter precipitation

changes (seasonal model) for 10 out of the 29 stations in

the East River basin. When compared to climatic indices

that are related to seasonal precipitation changes in summer

and autumn, more climate oscillations had considerable

impacts on winter precipitation changes, especially

Fig. 3 The climatic indices that

are closely related to the

location parameter in the

seasonal models in the East

River basin study area in

southeastern China. The

numbers in the parentheses

denote the number of stations

with nonlinear relations

between seasonal precipitation

and climatic indices; ct means

that the location parameter (l) isconstant

123


location and scale parameters. Specifically, AO, NPO,

PDO, and ENSO influenced the location parameter, l, ofwinter precipitation changes with different degrees and

magnitudes in both space and time (Fig. 3d). Statistically,

the impact of ENSO on the location parameter, l, wasnonlinear for 8 out of the 29 stations but the influence of

AO and NPO on l was respectively mostly linear and

linear. The impact of AO and PDO on the scale parameter

was linear for 13 and 17 out of the 29 stations, respectively.

ENSO had little impact on the scale parameter (Fig. 4d).

Based on the spatiotemporal properties of l and d, winter

precipitation changes were nonstationary. Therefore, a

nonstationary model is necessary to describe the properties

of seasonal precipitation changes in the East River basin.

In general, stationarity properties of seasonal precipita-

tion changes were different from one season to another and

climatic indices that were evidently related to seasonal

precipitation changes also differ. Specifically, summer and

autumn precipitation changes shared similar changing

properties, being influenced mainly by AO. Summer and

autumn precipitation changes were roughly stationary;

spring and winter precipitation changes were

Fig. 4 The climatic indices that

are closely related to the scale

parameter in the seasonal

models in the East River basin

study area in southeastern

China. The numbers in the

parentheses denote the number

of stations with nonlinear

relations between seasonal

precipitation and climatic

indices; ct means that the scale

parameter (d) is constant

123


nonstationary. Spring precipitation changes were influ-

enced mainly by PDO. Winter precipitation changes were

influenced by more climate oscillations. The impacts of

ENSO and PDO on winter precipitation changes were

pronounced. ENSO began to influence precipitation chan-

ges during autumn, and the influence of ENSO became

significant during the winter season.

In addition to the seasonal analysis, the spring, summer,

autumn, and winter season precipitation series were inte-

grated into one series and seasonal precipitation changes

were analyzed, based on the identification of seasonal

components, that is, the global model method (Fig. 5). It

can be seen from Fig. 2e that the Weibull distribution

function satisfactorily described the integrated seasonal

precipitation changes for 20 out of the 29 stations. PDO

and ENSO influenced the location parameter, implying that

these two climate oscillations impacted the changes in the

precipitation amount. The scale parameter, however, was

impacted mainly by ENSO.

4.2 Seasonal Precipitation Modeling for Spring,

Summer, Autumn, and Winter

For concise presentation, Xunwu, Dongyuan, Lingxia, and

Shenzhen stations were selected to illustrate the results of

the seasonal and global models because these four stations

are located along the main stream of the East River. Fig-

ure 6 shows the results of seasonal and global models for

spring precipitation changes. Due to the length limit of the

article, the results of the remaining 25 stations that were

also considered in this study are not presented here. The

seasonal model better captured the spring precipitation

changes than the global model, mirrored by the narrower

confidence interval circled by the 25 and 75% percentile

curves. The seasonal model captured higher and lower

amounts in the precipitation variations. This is particularly

important in the analysis of precipitation extremes. This

analysis was also corroborated by the worm plots in Fig. 7.

The results of the seasonal and global models for sum-

mer precipitation are shown in Fig. 8. The fluctuations of

summer precipitation were smaller than the spring precip-

itation changes. Generally, the global model had better

modeling efficacy than the seasonal model (Fig. 8). Sta-

tionary changes are shown by the seasonal model at the

Fig. 5 The climatic indices that are closely related to the location (l)and scale (d) parameters in the global model. The numbers in the

brackets denote the number of stations with nonlinear relations

between integrated seasonal precipitation and climatic indices; ct

means that the parameter is constant

123


Dongyuan and Shenzhen stations (Fig. 8b-1, d-1). How-

ever, the global model, as shown by the 50% percentile

curves, mirrored the average changes of summer precipi-

tation amounts. The confidence interval of the global

model defined by the 25 and 75% percentiles was narrower

than for the seasonal model. The 5 and 95% percentiles of

the global model better captured the changing features of

summer precipitation than did the seasonal model, partic-

ularly the peak and trough values of summer precipitation

variations (for example, Fig. 8d-2). The worm plots also

verified these results.

Figure 9 illustrates the results of the seasonal and global

models for autumn precipitation. Stationary changes of

autumn precipitation were revealed by the seasonal model

with no evident temporal changes of percentiles. The glo-

bal model satisfactorily depicted the changes in the mean

autumn precipitation, as reflected by the 50% percentile

curves (Fig. 9). The confidence intervals, defined by the 25

and 75% percentiles and also by the 5 and 95% percentiles,

well represented the changes in autumn precipitation,

especially precipitation magnitudes. The global model

better depicted the peak and trough values of the autumn

precipitation than did the seasonal model, as mirrored by

the 5 and 95% percentiles. The seasonal model showed

stationary changes in autumn precipitation, similar to

summer precipitation for some of the stations, and as a

result, the seasonal model did capture details of the

changing properties of autumn precipitation.

The results of the seasonal and global models for winter

precipitation changes are shown in Fig. 10. Winter pre-

cipitation had larger fluctuations than had spring, summer,

and autumn precipitation. A closer look at Fig. 10 indicates

the global model had higher modeling efficacy than the

seasonal model. The temporal variations of winter precip-

itation were simulated well as shown by the 50% per-

centile. The global model had narrower confidence

intervals than the seasonal model as defined by the 25 and

75% percentiles for simulation of the winter precipitation

changes. The global model also mirrored the nonstationary

changes in winter precipitation.

Figures 6, 7, 8, 9 and 10 show that both the seasonal and

global models can model temporal changes in seasonal

precipitation at 4 out of the 29 stations. Similar results can

be obtained for other stations considered in this study. A

similar efficacy in the simulation of the spring precipitation

changes was observed for the seasonal and global models.

However, the results of these two models are subject to

large discrepancies in the modeling of seasonal precipita-

tion changes in summer, autumn, and winter. Stationary

changes of summer, autumn, and winter precipitation were

detected by the seasonal model, though the precipitation

changes were nonstationary in the global model output. In

Fig. 6 Modeled spring

precipitation by the seasonal

model (left) and the global

model (right) at four selected

stations (Xunwu, Dongyuan,

Lingxia, and Shenzhen) in the

East River basin in southeastern

China. The black dashed line

denotes the 50% percentile, the

pink region denotes the interval

defined by 25 and 75%

percentiles, and the greenish-

blue region denotes the interval

defined by the 5 and 95%

percentiles. The grey points

denote the observed

precipitation data

123


summary, the seasonal model was the best choice for the

modeling of spring precipitation, and the global model was

the best choice for the modeling of seasonal precipitation

changes in summer, autumn, and winter. Thus, the global

model should be used for the modeling, simulation, and

forecasting of seasonal precipitation changes in the East

River basin, China. These results do not indicate, however,

which model is the best choice for forecasting regional

precipitation changes.

4.3 Integrated Precipitation Forecasting

by Seasonal and Global Models

The seasonal precipitation series in spring, summer,

autumn, and winter, respectively, were integrated into an

entire seasonal precipitation series, and then the seasonal

and global models were developed, based on the integrated

seasonal precipitation series, to model and forecast pre-

cipitation changes using the track precipitation forecasting

and cross-validation precipitation forecasting techniques.

In this study, the forecasting accuracy was evaluated by

eight methods (Table 2). In the track precipitation fore-

casting practice, the naıve model was used to evaluate the

forecasting performance of the seasonal and global models;

in the cross-validation precipitation forecasting practice,

the time model was used to compare and evaluate the

forecasting performance of the seasonal and global models.

To evaluate the overall performances of these models in

a region, Fig. 11 displays the performances of the seasonal,

global, and naıve models in the track precipitation fore-

casting practice for the forecasting of precipitation changes

during the period of 2006–2010. The seasonal model better

forecasted precipitation changes in spring, autumn, and

winter than did the global model, but did worse than the

global model in forecasting precipitation changes in sum-

mer. Based on AME and MAE, the seasonal and global

models had the smallest error in their modeling perfor-

mance. However, MAPE indicated differently, that is, the

seasonal and global models better forecasted precipitation

changes in spring and summer than in autumn and winter.

However, in general, the seasonal and global models

forecasted better than the naıve model (Fig. 11). Figure 12

shows the performance of the seasonal, global, and naıve

models in the track precipitation forecasting practice for

the forecasting of precipitation changes during the period

of 2001–2010. These results indicate that the longer the

forecasting time interval, the lower the forecasting

accuracy.

Figure 13 shows the performance of the seasonal, glo-

bal, and time models in the cross-validation precipitation

Fig. 7 The worm plot for the

simulation of spring




stations (Xunwu (a-1, a-2),Dongyuan (b-1, b-2), Lingxia(c-1, c-2), and Shenzhen (d-1,d-2)) in the East River basin in

southeastern China. The two

black dashed lines denote the

95% confidence intervals

123


Fig. 8 Modeled summer









pink region stands for the

interval defined by the 25 and

75% percentiles, and the

greenish-blue region displays

the interval defined by the 5 and

95% percentiles. The grey

points denote the observed

precipitation data

Fig. 9 Modeled autumn









pink region shows the interval


percentiles, and the greenish-

blue region indicates the


95% percentiles. The grey

points denote the observed

precipitation data

123


forecasting practice for the forecasting of precipitation

changes during the period of 2006–2010. In general, the

seasonal model better forecasted precipitation in spring,

autumn, and winter than the global model; but the global

model did better in forecasting precipitation in summer.

Based on AME, MAE, MdAE, and RMSE, the forecasting

accuracy of the global and seasonal models for winter

precipitation was the lowest. MAPE seemed to show the

highest efficacy of the global and seasonal models for the

forecasting of precipitation in spring and summer. Higher

forecasting efficacy was detected for the seasonal model

than the time model, but no distinct differences in the

forecasting performance were observed between the global

and time models. Other evaluation indices, except MAPE

and RMSPE, indicated the larger forecasting accuracy of

the seasonal model than the time model. Figure 14 shows

the forecasting performance of the seasonal, global, and

time models in the cross-validation precipitation forecast-

ing practice for the forecasting of precipitation changes

during the period of 2001–2010. Similar conclusions were

Fig. 10 Modeled winter








denotes 50% percentile, the

pink region represents the


75% percentiles, and the cyanic

region occupies the interval


percentiles. The grey points

denote the observed

precipitation data

SGNSGNSGNSGN0

100

200

300

AME

SGNSGNSGNSGN0

200

400

MAE

SGNSGNSGNSGN0

200

400

MdA

E

SGNSGNSGNSGN0

200

400

600

RMSE

SGNSGNSGNSGN0

50

100

150

200

MAPE

SGNSGNSGNSGN0

50

100

150

MdA

PE

SGNSGNSGNSGN0

50

100

150

200

250

RMSP

E

SGNSGNSGNSGN1

2

3

GRI

S:Seasonal model G:Global model N:Naive model

(a) (b) (c) (d)

(e) (f) (g) (h)

Fig. 11 The eight modeling

accuracy indices for the track

predictions of seasonal

precipitation (from left to right:

spring, summer, autumn, and

winter) during 2006–2010,

using the seasonal, global, and

naıve models in the track

precipitation forecasting

practice for all 29 stations in the

East River basin of southeastern

China

123


obtained from Fig. 14. However, when compared to

Figs. 13, and 14 indicates that the longer the forecasting

time, the smaller the advantage of the time model over the

seasonal and global models in precipitation forecasting

practice—for example, MAPE and RMSPE—indicate that

the seasonal model was better than the time model in terms

of forecasting accuracy.

SGNSGNSGNSGN0

100

200

AME

SGNSGNSGNSGN0

200

400

MAE

SGNSGNSGNSGN0

200

400

600

MdA

E

SGNSGNSGNSGN0

200

400

600

RMSE

SGNSGNSGNSGN0

100

200

MAPE

SGNSGNSGNSGN0

100

200

MdA

PE

SGNSGNSGNSGN0

100

200

300

RMSP

E

SGNSGNSGNSGN

1.52

2.53

GRI

S:Seasonal model G:Global model N:Naive model

(a)

(e) (f) (g) (h)

(b) (c) (d)Fig. 12 The eight modeling

accuracy indices for the track

predictions of seasonal

precipitation (from left to right:

spring, summer, autumn and

winter) during 2001–2010,

using the seasonal, global, and

naıve models in the track


practice using for all 29 stations

in the East River basin of

southeastern China

TSGTSGTSGTSG0

100

200

300

AME

TSGTSGTSGTSG0

100

200

300

400

MAE

TSGTSGTSGTSG0

200

400

MdA

E

TSGTSGTSGTSG0

200

400

600

RMSE

TSGTSGTSGTSG0

50

100

150

MAPE

TSGTSGTSGTSG0

50

100

MdA

PE

TSGTSGTSGTSG0

50

100

150

200RMSP

E

T SGTSGTSGTSG

1.5

2

2.5

GRI

T:Time model S:Seasonal model G:Global model

(a) (b) (c) (d)

(e) (f) (g) (h)


accuracy indices for the

seasonal precipitation (from left

to right: spring, summer,

autumn, and winter) during

2006–2010, using the time,

seasonal, and global models in

the cross-validation


practice for all 29 stations in the

East River basin of southeastern

China

TSGTSGTSGTSG0

50100150200250

AME

TSGTSGTSGTSG

100

200

300

400

MAE

TSGTSGTSGTSG0

100

200

300

400

MdA

E

TSGTSGTSGTSG

100200300400500

RMSE

TSGTSGTSGTSG0

100

200

300

400

MAPE

TSGTSGTSGTSG0

50

100

150

200

250

MdA

PE

TSGTSGTSGTSG0

200

400

RMSP

E

T SGTSGTSGTSG

1.52

2.53

3.54

GRI

T:Time model S:Seasonal model G:Global model

(a) (b) (c) (d)

(e) (f) (g) (h)


accuracy indices for the

seasonal precipitation (from left

to right: spring, summer,

autumn, and winter) during

2001–2010, using the time,

seasonal, and global models in

the cross-validation


practice using all 29 stations in

the East River basin of

southeastern China

123


5 Conclusions

Precipitation forecasting plays a critical role in the man-

agement of water resources and agricultural activities, and

that is particularly true for the East River basin in China

where water resources have been highly developed and

exploited. Hong Kong, for example, meets approximately

four-fifths of its current annual water demand by with-

drawals from the East River basin. In this study, modeling

of precipitation changes is done using GAMLSS-based

nonstationary techniques with consideration of the influ-

ence of large-scale climate oscillations on precipitation

changes in the East River basin. Important conclusions of

the study are as follows:

(1) Spring precipitation follows the gamma and logistic

distributions and exhibits nonstationary changes. The

changing magnitude of spring precipitation is influ-

enced mainly by AO and PDO; and the changing

dispersion is impacted by AO. The summer and

autumn precipitation changes follow the gamma

distribution. Summer and autumn precipitation at

most of the stations exhibits stationary changes. The

changing magnitude of summer and autumn precip-

itation is effected by NPO and ENSO, respectively. In

contrast, the precipitation variability in summer and

autumn is influenced mainly by AO. Winter precip-

itation follows the Weibull distribution and shows

nonstationary changes. The causes behind winter

precipitation changes are complicated when com-

pared to those in spring, summer, and autumn. More

or less, NPO, ENSO, AO, and PDO have evident

influences on the changing magnitude of winter

precipitation. But the influence of ENSO on the

changing magnitude of winter precipitation is signif-

icant when compared to NPO, AO, and PDO.

Integrating seasonal precipitation series into one

whole series may tell a different story. The whole

seasonal precipitation series, that is, the precipitation

series after integration of the precipitation series of

spring, summer, autumn, and winter, follows the

Weibull distribution. The location parameter, that is,

the changing magnitude, is influenced mainly by PDO

and ENSO. However, the precipitation variability is

influenced mainly by ENSO alone.

(2) Both seasonal and global models depict temporal

changes in seasonal precipitation in the East River

basin. The seasonal model is the best choice for

modeling spring precipitation, and the global model is

the best choice for modeling seasonal precipitation

changes in summer, autumn, and winter.

(3) In both the track precipitation forecasting and cross-

validation precipitation forecasting practices, the

seasonal model better forecasts precipitation changes

in spring, autumn, and winter; however, the global

model better forecasts summer precipitation changes.

In this sense, the global model performs better than

the seasonal model in the simulation of seasonal

precipitation changes, however, that is not the case in

precipitation forecasting. It is not a good idea to use

only one model, either the global model or the

seasonal model, in precipitation forecasting. In the

track precipitation forecasting and cross-validation

precipitation forecasting practices, the seasonal model

should be the choice in the forecasting of seasonal

precipitation changes. Results of this study help

clarify the selection of models in modeling, simula-

tion, and forecasting of seasonal precipitation varia-

tions, particularly considering the influence of ENSO

regimes. Because spatial dependence cannot be

neglected, a regional method that considers the

influence of spatial dependence may be of help in

improving the performance of the seasonal precipita-

tion forecast, and this will be addressed with consid-

erable consideration in our subsequent research.

Acknowledgements This work is financially supported by the Fund

for Creative Research Groups of the National Natural Science

Foundation of China (Grant No. 41621061), the National Science

Foundation for Distinguished Young Scholars of China (Grant No.

51425903), and the National Science Foundation of China (Grant

Nos. 41601023; 41401052). Our cordial gratitude should be extended

to the editor, Dr. Ying Li, and anonymous reviewers for their pro-

fessional and pertinent comments and suggestions, which were

greatly helpful for further quality improvement of this manuscript.

Open Access This article is distributed under the terms of the

Creative Commons Attribution 4.0 International License (http://crea

tivecommons.org/licenses/by/4.0/), which permits unrestricted use,

distribution, and reproduction in any medium, provided you give

appropriate credit to the original author(s) and the source, provide a

link to the Creative Commons license, and indicate if changes were

made.

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