How do the multiple large-scale climate oscillations trigger extreme precipitation?

Global and Planetary Change 157 (2017) 48–58

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Global and Planetary Change journal homepage: www.elsevier.com/locate/gloplacha

How do the multiple large-scale climate oscillations trigger extreme precipitation?

MARK

Pengfei Shia,b, Tao Yanga,⁎, Chong-Yu Xua,c, Bin Yonga,b, Quanxi Shaod, Zhenya Lia, Xiaoyan Wanga, Xudong Zhoua,e, Shu Lif a

State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Center for Global Change and Water Cycle, Hohai University, Nanjing 210098, China School of Earth Sciences and Engineering, Hohai University, Nanjing 210098, China c Department of Geosciences, University of Oslo, P.O. Box 1047, Blindern, 0316 Oslo, Norway d CSIRO Digital Productivity Flagship, Leeuwin Centre, 65 Brockway Road, Floreat, WA 6014, Australia e Laboratorie des Sciences du Climat et de l'Environnement, Commissariat a L'Energie Atomique, 91191 Gif sur Yvette, France f Yellow River Institute of Hydraulic Research, Yellow River Conservancy Commission, Zhengzhou 450003, China b

A R T I C L E I N F O

A B S T R A C T

Keywords: Large-scale climate patterns Climate phases Precipitation Connection Semi-humid and semi-arid region Hazard effect

Identifying the links between variations in large-scale climate patterns and precipitation is of tremendous assistance in characterizing surplus or deficit of precipitation, which is especially important for evaluation of local water resources and ecosystems in semi-humid and semi-arid regions. Restricted by current limited knowledge on underlying mechanisms, statistical correlation methods are often used rather than physical based model to characterize the connections. Nevertheless, available correlation methods are generally unable to reveal the interactions among a wide range of climate oscillations and associated effects on precipitation, especially on extreme precipitation. In this work, a probabilistic analysis approach by means of a state-of-the-art Copula-based joint probability distribution is developed to characterize the aggregated behaviors for large-scale climate patterns and their connections to precipitation. This method is employed to identify the complex connections between climate patterns (Atlantic Multidecadal Oscillation (AMO), El Niño-Southern Oscillation (ENSO) and Pacific Decadal Oscillation (PDO)) and seasonal precipitation over a typical semi-humid and semi-arid region, the Haihe River Basin in China. Results show that the interactions among multiple climate oscillations are nonuniform in most seasons and phases. Certain joint extreme phases can significantly trigger extreme precipitation (flood and drought) owing to the amplification effect among climate oscillations.

1. Introduction A number of studies have confirmed that there are connections between the large-scale climate patterns and regional hydrological extremes like floods and droughts and water budget worldwide (e.g. Kim et al., 2006; Cayan et al., 1999; Ropelewski and Halpert, 1989). For example, the record-breaking high global temperature and devastating floods worldwide in 1998 could be partly attributed to El Niño (Lean and Rind, 2008; Foster and Rahmstorf, 2011), and the 2010 Pakistan flood was linked to a strong La Niña (Coumou and Rahmstorf, 2012). Precipitation is a principle component of hydrological cycle and water balance besides evapotranspiration and runoff (Thomas, 2000; Xu et al., 2006; Wang et al., 2013a; X. Wang et al., 2017; Y. Wang et al., 2017). The qualitative analysis and quantitative evaluation of the connections between large-scale climate patterns and precipitation could provide insights into the hazard prevention and mitigation, and contribute to

⁎

Corresponding author. E-mail address: [email protected] (T. Yang).

http://dx.doi.org/10.1016/j.gloplacha.2017.08.014 Received 22 April 2017; Received in revised form 4 August 2017; Accepted 28 August 2017 Available online 31 August 2017 0921-8181/ © 2017 Elsevier B.V. All rights reserved.

improvements in regional water resources management strategy (Zhang et al., 2009; Wang et al., 2012). Several oceanic-atmospheric indices have been widely used to explain the variability of precipitation in different regions. The El NiñoSouthern Oscillation (ENSO) and Pacific Decadal Oscillation (PDO) indices are commonly recognized as important tools for investigating hydrological process (Kim et al., 2006; Chiew et al., 1998; Liu et al., 1998; Gutiérrez and Dracup, 2001). ENSO is a naturally occurring phenomenon centered referring to the cycle of warm and cold sea surface temperatures in the equatorial Pacific arising from complex interactions between the atmosphere and ocean (McPhaden et al., 2006; Collins et al., 2010). El Niño is the warm phase of ENSO, and it is often followed by a cold phase called La Niña. La Niña usually has an opposite effect compared to El Niño. El Niño occurs irregularly, at different year intervals (sometimes every 2–7 years). In some areas, it brings heavy rainfall hereby causes floods, while in other regions it

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Fig. 1. Map of the Haihe River Basin (HRB) and major precipitation stations.

oscillations and their associate effect on local precipitation are very limited now. Those atmospheric oscillations are non-independent and collectively affecting over some areas. Actually, the intricate interplay existing among the multiple large-scale climate oscillations and the regional hydrological process constitute a complex climate-land coupled system (Steinman et al., 2014). Multiple atmospheric oscillations collectively impose a more complex influence on local precipitation (Shi et al., 2016). Restricted by the current limited knowledge on underlying mechanisms, physical based methodologies generally fail to explain the complex interactions. Thus, statistical methods (e.g. correlation methods) are often used to discover and delineate these complex relationships. Unfortunately, the available statistical methodologies are generally unable to explain the interactions among a wide range of climate oscillations and associated effects on water cycle in some areas around the world (Xu et al., 2004). To date, identification of dimensional interactions among multiple large-scale circulations and associated hazardous impacts (flood and drought) is still a weak point in global change studies (Boers et al., 2014; Yang et al., 2011). It is urgent to clarify that how the multiple large-scale climate oscillations trigger extreme precipitation. Therefore, this study strives to: (1) characterize the interactions among multiple large-scale climate oscillations by means of probabilistic approach; (2) construct a series of climate phases and a quantitative connection based on the phases; (3) address the potential impacts of multiple extreme phases on precipitation in the Haihe River Basin, a typical semi-humid and semi-arid basin in China.

causes droughts. A number of studies have indicated that ENSO can drive substantial variability in rainfall (Ropelewski and Halpert, 1986; ABM and CSIRO, 2011; Power et al., 1999) in many regions around the world. The Pacific Decadal Oscillation (PDO) is a pattern of climate variability in the Pacific Ocean, north of 20° N, with a characteristic time scale of 20–30 years (Hare and Mantua, 2001). The PDO is detected as warm or cool surface waters in the North Pacific Ocean. The correspondence between PDO and extreme events was investigated by Hidalgo (2004) in the Colorado River Basin, showing that the PDO phase was correlated with the above-average and below-average precipitation. Other studies focused on the modulation of PDO cycle on the ENSO-precipitation signal (Brown and Comrie, 2004; Gutzler et al., 2009; Kurtzman and Scanlon, 2007). Brown and Comrie (2004) examined the relationships between the ENSO conditions and winter precipitation in the western U.S. within the context of decadal-scale variability, as presented by phasing of PDO, and identified the so-called ‘dipole’ signature. Goodrich (2007) investigated the influence of PDO on winter precipitation and droughts during years of neutral ENSO in the western United States, and found that the resulting winter precipitation patterns were spatially similar to those occur during years of La Niña-cold PDO and, to a lesser extent, years of El Niño-warm PDO. The Atlantic Multidecadal Oscillation (AMO) is a recent label for a climate oscillation in the North Atlantic with a period of 65–80 years (Kerr, 2000). It is defined as the detrended, regionally averaged, summer sea surface temperatures (SSTs) anomalies over the North Atlantic Ocean (Enfield et al., 2001). Previous studies have shown that the AMO could exert direct influences on the regional climate and drought (Sutton and Hodson, 2005; Knight et al., 2006; Mo et al., 2009). It has been reported that the warm-phase of AMO favors warmer winters in many regions of China, with enhanced precipitation in northern China, while reduced precipitation in the south, and vice versa (Lu et al., 2006; Li and Bates, 2007). Generally, many studies have investigated the linkage between atmospheric circulation patterns and precipitation and the associated hazard effect, and these studies have detected generally consistent and systematic relationships more or less (Hu and Feng, 2001; Timm et al., 2005; Goodrich, 2007; Stevens and Ruscher, 2014). To the best of our knowledge, studies on identifying the interplay of multiple atmospheric

2. Study area and datasets 2.1. Study area Haihe River Basin (HRB) is located in the eastern part of northern China (112–120° E, 35–43° N). The northern, south-western and eastern boundaries are Mongolian Plateau, Yellow River and Bohai Sea, respectively (Fig. 1). The basin is characterized by a continental monsoon climate. The annual mean temperature is 9.6 °C, and annual precipitation is about 530 mm, which decreases from south-eastern coastal zone to north-western inland area (Wang et al., 2015; Xing et al., 2014). 49

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The precipitation in flood seasons (June–September) accounts for 70%–85% of the annual precipitation, which mainly concentrates in several rain processes during July and August. The HRB covers 317,800 km2, of which 60% and 40% are mountains in western and northern part and plain in eastern and southern part, respectively. It is the largest water system in northern China, covering Beijing, Tianjin, most parts of Hebei and parts of Shandong, Henan, Shanxi and Inner Mongolia (Wang et al., 2013b). The basin plays an important role in the sustainable development of human society and economy over these regions. The basin has been suffering a tremendous conflict between water supply and demand, with the water volume per capita of 305 m3 from 1956 to 2004, merely 1/7 of the national average and 1/24 of the world average (Xia et al., 2006). The rapid economic development and the urban population explosion intensify the issue of water shortages and results in many severe environmental and ecological problems (Yuan et al., 2005). On the other hand, the intensive rainfall during July and August often trigger floods over the basin. The effect from multiple climate oscillations on precipitation may aggravate the issue of water shortage as well as floods. Thus, it is urgent to study the behaviors of large scale climate patterns and their joint effect on precipitation over the HRB.

et al., 2005). In addition, SPI is a function of the precipitation amount only, and is simple to calculate. It has been proven that in many situations and regions indices based solely on precipitation data perform better compared with the more complex hydrological indices (Olukayode Oladipo, 1985). Therefore, the Standardized Precipitation Index (SPI) is employed to represent the variability of precipitation in this study. Detailed information on algorithm of SPI calculation can be found in McKee et al. (1993). The SPI and corresponding wetness categories (McKee et al., 1993; Kim et al., 2006; National Climate Center, China) are shown in Table 1. 3.2. Conceptual influence indices To quantify the strength of teleconnections between the large scale climatic patterns and seasonal precipitation in the Haihe River Basin, a conceptual influence index (influence intensity index (InfInt)) by Kim et al. (2006) is introduced into this work.

InfInt =

1 Nc

Nc

∑ SPIc (i) i=1

(1)

where Nc is the number of years of a climate phase, and SPIc(i) is the seasonal SPI corresponding to year i. The SPI quantifies observed precipitation as a standardized departure from a selected probability distribution function that models the raw precipitation data (McKee et al., 1993). InfInt can be interpreted by the moisture classification shown in Table 1 (Kim et al., 2006; Mckee et al., 1993; National Climate Center, China).

2.2. Datasets In this work, three climate indices including AMOI (Atlantic Multidecadal Oscillation Index), SOI (Southern Oscillation Index) and PDO (Pacific Decadal Oscillation Index), are utilized to represent the AMO, ENSO and PDO, respectively. The monthly time series of AMOI, SOI and PDO for the period of 1951–2016 are from the Earth System Research Laboratory, NOAA (http://www.esrl.noaa.gov/psd/data/ climateindices/list/). The observed monthly precipitation data from 30 stations across the basin (Fig. 1) during 1951–2016 are used, which are compiled from the China Meteorological Data Sharing Service System (http://data.cma.cn/).

3.3. Copulas and probabilistic distribution To establish the climate phases Nc, a series of marginal probabilistic distributions and joint probabilistic distributions should be constructed. Different to the study using empirical distribution, a kernel density function and copula functions are used in this paper to construct the marginal distribution and joint distributions, respectively. The three climatic indices (AMOI, SOI and PDO) are non-independent climatic variables. To detect the interplay among them, the joint probabilistic densities obtained by copulas are used. Firstly, a kernel density function is used to estimate the marginal distribution for seasonal AMOI, SOI and PDO. Secondly, copula functions are used to construct joint probabilistic distributions for the three indices. The copula is a function which joint two or more univariate distributions to construct a multivariate distribution (Nelsen, 2006). The multivariate copula function can be used for capturing the dependence between two or more random variables (Sukparungsee et al., 2017). It is known that for n-dimensional distribution F with marginal distributions Fi , i = 1 , 2 , … , n, there exists a copula C as follows (Xie et al., 2017):

3. Methodology In this study, a consolidated framework (Fig. 2) is constructed to quantitatively detect the linkage between large-scale climate patterns and seasonal precipitation. The framework can be concisely shown as follows: (1) To detect the interactions among multiple climate oscillations based on multivariate joint probability distributions by means of Copulas, (2) To construct a series of conceptual influence indices according to the Copula-based joint probabilistic phases and standard precipitation index (SPI) and (3) To analyze the connections in terms of the changing behaviors of the conceptual influence indices. SPI at a scale of 3 months is used to represent the seasonal precipitation. Seasonal AMOI, SOI and PDO are used to denote the changing behaviors of AMO, ENSO and PDO, respectively. Joint probability distributions are constructed by using copula functions, which are used to reveal the interplay among the multiple climate oscillations and to formulate the combined climate phases that are used for building InfInt.

F (x1,…, x n ) = C (F1 (x1),…, Fn (x n )), x i ∈ (−∞,+∞), i = 1, …, n.

3.1. Standardized precipitation index

(2)

There are many families of copulas, in this study, we use copula functions including Gaussian, Clayton, Frank and Gumbel Copula to construct joint probability distribution for the three indices. These functions are widely used in hydrological studies (Fu and Butler, 2014). Akaike's information criterion (AIC) and Euclidean distance are employed to identify the appropriate function. Small values of the two measures suggest good fit (Akaike, 1974). Further details of these copulas can be referred to Abdi et al. (2017). The Copula-based joint probabilistic distribution (density) is used to detect the interplay among multiple climatic oscillations. The distributions for climate oscillations are briefly expressed as follows:

Precipitation is the primary factor controlling formation and persistence of drought along with other variables such as evapotranspiration (Sönmez et al., 2005). Several quantitative indices have been developed and adopted to measure drought or wet spells intensity. These indicators include Percent of Normal, Deciles, Standardized Precipitation Index (SPI), Palmer Drought Severity Index (PDSI), and so on. Among these indices, SPI has zero mean and unit standard deviation and provides a measure of the precipitation frequency distribution (McKee et al., 1993; Edwards and Mckee, 1997). SPI has an advantage to capture multi-temporal nature of rainfall deficiency and is usually computed for a certain time interval (monthly or seasonally) (Sönmez 50

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AMO

ENSO

PDO

Precipitation

Fig. 2. The approach of quantitative connection between large-scale climatic patterns and precipitation.

Data processing

Data processing

Monthly AMOI, SOI and

Monthly Precipitation

Seasonal AMOI, SOI and

Seasonal SPI (SPI-3)

Climate phase construction

Marginal distribution F(AMOI), F(SOI), F(PDO) Copula

Joint probability distribution (density)

Interactions among multiple oscillations Correlations Joint probability density The probability of occurrence

=

Definition: H: >75 percentile; L: <25 percentile Combination: HSLP, LSHP, HALS, HALSHP…

Conceptual influence indices

InfInt =

1

( )

is the number of years of a climate phase, and is the seasonal SPI corresponding to year .

Quantitative connection

Climate phases-based InfInt Spatial distribution of InfInt Probabilistic characteristics

F (X ) marginal distribution ⎫ P=⎧ ⎨ ⎬ F ( U , V , Z ) three dimensional joint distribution − ⎩ ⎭

Table 1 SPI, cumulative probability and their corresponding moisture classification. SPI

CDF

− 3.0 − 2.5 − 2.0 − 1.5 − 1.0 − 0.5 0 0.5 1.0 1.5 2.0 2.5 3

0.001 0.006 0.023 0.067 0.159 0.309 0.500 0.691 0.841 0.933 0.977 0.944 0.999

(3)

where P represents the probability distributions, U, V and Z represent climatic indices (i.e. AMOI, SOI and PDO), and X can be each of them. According to the fitted marginal probability distributions and joint probability densities, we define that the seasonal climate indices larger than 75 percentile is high phase and smaller than 25 percentile is low phase. Then these single phases are aggregated together to generate a series of dual and triple joint phases (Table 2). The corresponding occurrence probabilities of these phases (e.g. pHALSHP = p(AMOI > 75 percentile ∩ SOI < 25 percentile ∩ PDO > 75 percentile) can be obtained (Table 2) through integration for the joint probability density function.

Extreme dry (ED) Severe dry (SD) Moderate dry (MD) Incipient dry (ID) Nearly normal (NN) Incipient wet (IW) Moderate wet (MW) Severe wet (SW) Extreme wet (EW)

4. Results The probability distributions (density) are constructed to characterize the geostatistical interactions among multiple climate 51

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are employed. These interactions among the multiple climate oscillations clearly show the relationships including the mutual promotion and trade-off, promoting the understanding of the natural existence of joint phases and facilitating the establishment of combined climate phases that are used for constructing influence intensity indices. The effect on precipitation depends on different climate phases. It is known that HRB is a semi-humid and semi-arid basin with alternate floods and droughts, which is sensitive to the changing behaviors of climate oscillations. Hence, a more reasonable definition and construction of climate phases significantly influence the connections between precipitation and multiple climate oscillations.

Table 2 Climate phases and joint probability for the combined phases. Number

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Climate phases

HA LA HSOI LSOI HPDO LPDO HSLP LSHP HAHS HALS HAHP HALP LAHS LALS LAHP LALP HAHSLP HALSHP LAHSLP LALSHP

Definition

Years with high AMOI Years with low AMOI Years with high SOI Years with low SOI Years with high PDO Years with low PDO HSOI & LPDO LSOI & HPDO HA & HSOI HA & LSOI HA & HPDO HA & LPDO LA & HSOI LA & LSOI LA & HPDO LA & LPDO HA & HSOI & LPDO HA & LSOI & HPDO LA & HSOI & LPDO LA & LSOI & HPDO

Probability Summer

Winter

8.71% 8.71% 5.61% 4.29% 5.72% 4.43% 4.29% 6.19% 4.43% 5.72% 2.05% 1.85% 1.85% 2.05%

9.20% 9.20% 4.93% 5.19% 5.30% 4.72% 5.19% 4.93% 4.72% 5.56% 2.08% 2.06% 0.40% 2.08%

4.2. The influence intensity of climate phases on precipitation Fig. 5 show the influence intensity for 30 stations aggregated as box plots, characterizing the effects of different climate phases. The boxplots presented in Fig. 5(a) show the influence intensity for 20 climate phases for winter precipitation with no season lag. The median values in the separate climate phases (No. 1–6, Table 2) are both between 0.5 and −0.5, indicating the phase of any of the three climate oscillations does not strongly associate with drought and wetness in these regions. InfInt during joint climate phases seem to be more dynamic and greater than that during the separate ones. To interpret InfInt during joint phases, we compare the values during joint phases that include the same term. We find that high phases of ENSO (La Niña event) pose wet effect during the joint phases (i.e. LAHS, HAHSLP and LAHSLP). On the other hand, the low phase of AMO makes some part of the region dry during joint phases (i.e. LALSHP). It seems that the dry effect from low phase of AMO depends on the influence from low phase of ENSO and high phase of PDO. The effects are likely to be more obvious at a lag time of one or two seasons (Fig. 5(c, e)). The wet effect from high phase of AMO makes the region wet during joint phases (i.e. HAHP, HAHSLP, HALSHP in Fig. 5(c) and HALP, HAHSLP in Fig. 5(e)). Dry conditions emerge in some part of the region during LAHSLP and LALP (Fig. 5(c)) and LALP and LAHSLP (Fig. 5(e)). Generally, it can be concluded that the phases “HA” and “HS” seem to make wet effects and “LA” make dry effects, and these influences only take effect during the joint climate phases. An amplification effect by other climate indices is found. That is to say, single climate phases with wet effect often seem to be dormant when not accompanied by the phases of the other climate oscillations, but come alive when coincide with phases of other climate patterns. In addition, the effect from the AMO seems to be stronger than that from ENSO. The LSHP does not show obvious effect on precipitation, but makes wet effect when accompanied by “HA” (HALSHP in Fig. 5(c)). The HSLP does not show obvious effect on precipitation, but makes dry effect when accompanied by “LA” (LAHSLP in Fig. 5(c, e)). Both the high phase (‘HA’) and low phase (‘LA’) of AMO make effect on precipitation, while only high phase of ENSO (‘HS’) influences precipitation. With respect to summer precipitation, low phase of ENSO together with high phase of PDO (i.e. LSHP) trigger drought for most of the stations (Fig. 5(b)) with no season lag. Dry condition also emerges during HALSHP and LALSHP (Fig. 5(b)), the latter of which is slighter than the former. The wet effect from HSLP tends to emerges with one season lag (Fig. 5(d)). LAHS makes some of the stations wet with two season lag (Fig. 5(f)) whereas the LALS does not, indicating the wet effect from high phase of ENSO. Dry conditions appear during LAHP and LALSHP (Fig. 5(d)) with one season lag. The wet effect from HSLP disappears with two season lag (Fig. 5(f)). Different to the dry effect for winter, the LAHSLP slightly make wet effect for summer with 2 seasons lag. In general, the phase “HS” seem to make wet effects and “LS” and “LA” make dry effects, and these influences only take effect during the joint climate phases. Different to that for winter, the wet effect from “HA” for summer is not obvious. Different to that in winter, the effect from ENSO seems to be stronger than that from AMO. Both the high phase (‘HA’) and low phase (‘LS’) of ENSO make effect on precipitation,

Note: Not all combined phases are listed here, as some of which do not appear in the observation.

oscillations. Two seasons: summer (June, July and August) and winter (December, January and February)) are selected to show the influence from large-scale climate patterns in this study. The two seasons are chosen due to that these two seasons are two extremes (maximum and minimum) in terms of the amount of precipitation. There are less precipitation extremes in spring and autumn over the region. 4.1. The interactions of multi-source large-scale climatic patterns The marginal distributions for seasonal AMOI, SOI and PDO are shown in Fig. 3. As it can be seen in Table 3, the appropriate copula functions are picked out according to AIC and Euclidean distance. Subsequently, the fitted two-dimensional probability density and threedimensional joint probability distribution (Fig. 4) by the most appropriate copula functions are achieved. As can be seen in Fig. 4, the joint probability densities for climatic indices show different characteristics. In winter, the joint probability density of SOI and PDO (Fig. 4(g)) shows that the two climate patterns tend to appear in opposite phases. In other words, the probability density is high when one of the two climate patterns has a low phase and the other has a high phase, and is low when both climate patterns have the same phases. Similar characteristics exist in the probability density for AMOI and SOI (Fig. 4(c)), whereas this trend is not obvious. AMOI and PDO show notable correlation in the down tail (Fig. 4(e)). Generally, the multiple large-scale climatic patterns correlate with each other to some degree in winter, especially during the extreme phases (Fig. 4(c, e and g)). In summer, correlations still exist. AMOI and SOI show notable correlation in the down tail (Fig. 4(d)). AMOI and PDO appear to have consistent phases (Fig. 4(f)). On the contrary, SOI and PDO tend to appear in opposite phases. Till now, the complex interaction of the climate oscillations is identified based on the probabilistic approach. Though the interactions do not directly explain the associated effects on precipitation, they indeed influence the effects on precipitation to a great degree. It acts in an indirect way in terms of influencing the formulation of combined climate phases (Table 2). It is known that, manual combination of the phases from certain climate oscillations is not reasonable in terms of that not all combinable phases are rational. We combined the climate phases according to the joint probability distributions of multiple climate oscillations. The combined phases that can be found in history observation and has an occurrence probability 52

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1

empirical distribution kernel distribution

0.8

0.6

0.6 F(x)

F(x)

0.8

empirical distribution kernel distribution

0.4

0.4

0.2

0.2

0 -1.5

-1

-0.5

0 AMOI

0.5

1

0

1.5

-1

-0.8

-0.6

(a)Summer AMOI 1

-0.4

-0.2 AMOI

0

0.2

0.4

0.6

0.8

(b)Winter AMOI 1

empirical distribution kernel distribution

0.8

0.6

0.6 F(x)

F(x)

0.8

empirical distribution kernel distribution

0.4

0.4

0.2

0.2

0

0

-6

-4

-2

0

2

4

6

8

-15

-10

-5

SOI

(c) Summer SOI 1

0

5

10

SOI

(d)Winter SOI 1

empirical distribution kernel distribution

empirical distribution kernel distribution

0.8

0.6

0.6

F(x)

F(x)

0.8

0.4

0.4

0.2

0.2

0 -8

0 -6

-4

-2

0 PDO

2

4

6

8

-8

-6

-4

(e) Summer PDO

-2

0 PDO

2

4

6

(f)Winter PDO

Fig. 3. Marginal probability distributions for AMOI, SOI and PDO.

Table 3 AIC and Euclidean distance for different copula functions for joint distributions. Euclidean distance AIC value

Winter

AMO vs ENSO AMO vs PDO ENSO vs PDO AMO vs ENSO vs PDO

Summer

AMO vs ENSO AMO vs PDO ENSO vs PDO AMO vs ENSO vs PDO

Normal Copula

Clayton Copula

Frank Copula

Gumbel Copula

0.0136 − 519.6168 0.0197 − 496.8103 0.0195 − 498.5707 0.0219 − 491.6445 0.0174 − 505.9753 0.0215 − 491.5317 0.0262 − 480.0525 0.0303 − 469.9725

0.0141 − 517.5181 0.0161 − 508.8683 0.1380 − 379.2057 0.0623 − 425.9865 0.0166 − 509.2326 0.0214 − 491.8500 0.0627 − 426.5737 0.0284 − 476.6526

0.0140 − 518.1423 0.0187 − 499.7351 0.0231 − 486.9828 0.0247 − 482.8175 0.0171 − 507.0421 0.0162 − 508.9040 0.0311 − 469.4050 0.0244 − 484.3160

0.0138 −518.8533 0.0185 −500.3743 0.1380 −379.2054 0.0608 −427.4684 0.0241 −485.0196 0.0189 −499.4805 0.0627 −426.5734 0.0326 −467.9218

Note: Values in bold and italics means the best, thereby the corresponding function is selected to fit the joint probability distribution.

53

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1

0.8

0.8

0.6

PDO

PDO

0.8

1

1

0.6

0.4

0.5 0.6

0.2 0.4

0.2

0.2

0.5

0.5 1

1

0.6

0.8

SOI

00

0.2

0.4

1 SOI

AMOI

(a) Winter AMOI & SOI & PDO (

1

00

0.2

0.4

0.6

0.8

AMOI

) (b) Summer AMOI & SOI &PDO (

1 0.8

0.4

0 0

0 0

)

1

13

2.5

1

9

0.8

2

0.8 0.6

1.5

0.4

0.4

1

0.2

0.2

0.5

14

0 0

10 0.2

0.4

0.6

0.8

SOI

SOI

0.6

0.4 0.2

0.6

0 0

1

0.2

0.4

AMOI

(c) Winter AMOI & SOI (

)

1 0.8

0.6

0.8

1

0

AMOI

15

(d) Summer AMOI & SOI ( 1

1.6

11

)

1.4

1.2 1

0.8

1.2 1 0.8 0.4 0.2

0.4

0.4

12

16 0.2

0.4

0.6

0.8

0.6 0.4

0.6

0 0

0.8

0.6 PDO

PDO

0.6

0.2

0.2

0.2 1

0

0 0

0.2

0.4

AMOI

(e) Winter AMOI & PDO (

)

0.8

1

(f) Summer AMOI & PDO (

1 0.8

0.6

)

1

8

4

4.5 4

0.8

3.5

3.5

3

3

0.6

2.5 2

0.4

2.5

PDO

PDO

0.6

2 0.4 1.5

1.5 0.2 0 0

0

AMOI

1

7 0.2

0.4

0.6

0.8

0.5

0.5 0 0

1

SOI

(g) Winter SOI & PDO (

1

0.2

0.2

0.4

0.6

0.8

1

0

SOI

)

(h) Summer SOI & PDO (

)

Fig. 4. Three-dimensional joint probability distribution for AMOI, SOI and PDO (a)–(b). Two dimensional joint probability density (c)–(h). Note: the marginal probability density is normalized to uniform by Copula; the joint probability (density) are denoted by color; τ denotes the rank correlation coefficient; the numbers in black denote the climate phases listed in Table 2.

a wet effect from high phase of AMO in winter. During LALP with 2 season lag (Fig. 6(d)), the northeast part and southwest part are dominated by dry condition (ID and MD) and incipient wet condition (IW), respectively. In summer, incipient dry (ID) and incipient wet (IW) prevail in most part of the basin during LSHP with no season lag (Fig. 6(e)) and during HSLP with one season lag (Fig. 6(f)), respectively. The phenomenon implies a wet effect from high phase of ENSO and a dry effect from low phase of ENSO accompanied by phase of PDO. Incipient dry (ID) and moderate dry (MD) (even severe dry (SD)) dominate the western part of the basin during LALSHP with one season lag (Fig. 6(g)). Compared to that during HSLP with one season lag (Fig. 6(f)), the range of wet condition tends to shrink during LAHSLP with 2 seasons lag (Fig. 6(h)).

while only low phase of AMO (‘LA’) influences precipitation.

4.3. The spatial distribution of the influence intensity 8 typical jointed climate phases with different lag time with conspicuous effects are selected to show the spatial distributions of influence intensity (Fig. 6). In winter, incipient wet (IW) appears in some part of the basin during LAHS with no season lag (Fig. 6(a)), whereas incipient dry (ID), moderate dry (MD) and severe dry (SD) dominate the most northeast part of the basin during LAHSLP with one season lag (Fig. 6(c)), indicating a strong modulation effect from low phase of PDO. Compared to LAHSLP, the northern part of the basin is dominated by wet conditions (IW and MW) during HAHSLP (Fig. 6(b)), indicating 54

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(a)

(b)

(c)

(d)

(e)

(f)

Fig. 5. Influence intensity for winter (a, c, e) and summer (b, d, f) precipitation with different lag time (season). Note: The box plots show the minimum (lower cap), maximum (upper cap), median (line in the box), lower (bottom of the box) and upper (top of the box) quartiles of data.

In a word, the phases “HA” and “HS” seem to make wet effects and “LA” makes dry effects in winter, the phase “HS” seems to make wet effects and “LS” and “LA” make dry effects in summer, and these influences only take effect during the joint climate phases. An amplification effect by other climate indices is found. That is to say, single climate phases with wet or dry effect often seem to be dormant when not accompanied by the phases of the other climate oscillations, but come alive when coincide with phases of other climate patterns. In general, certain phases have been proved to be highly related to precipitation extremes (flood and drought). That is to say, the extreme precipitation in the basin is triggered by some joint climate phases of multiple climate oscillations. Meanwhile, the occurrence probabilities of these joint extreme phases (Table 2) are not low. Therefore, these joint extreme phases are worthy of more attention in water resources and agriculture management in the region with great water scarcity.

5. Discussions Many studies successfully provide qualitative understanding of relationships between large-scale climatic patterns and hydrological variability (Cayan et al., 1999; Ropelewski and Halpert, 1989; Piechota and Dracup, 1996), but fail to quantify the magnitude of hydrological responses. In this study, the SPI was employed to represent the standard variability of precipitation, and a quantitative composite analysis is performed to quantitatively link the regional precipitation to largescale climate oscillations, The diverse magnitude of precipitation responses were successfully denoted by a classification of moisture classification. Compared to the study concerning quantitative links between hydrological variability and large-scale climate patterns (Kim et al., 2006), the quantitative connections achieved in this study are more robust in terms of that the occurrence probabilities of the hazard climate phases are obtained based on the joint probability distributions by 55

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(a) Winter_Lag0_LAHS

(e) Summer_Lag0_LSHP

(b) Winter_Lag1_HAHSLP

(f) Summer_Lag1_HSLP

(c) Winter_Lag1_LAHSLP

(d) Winter_Lag2_LALP

(g) Summer_Lag1_LALSHP (h) Summer_Lag2_LAHSLP

Fig. 6. Spatial distribution of influence intensity for some typical climate phases for winter (a, b, c, d) and summer (e, f, g, h).

copulas. In addition, the establishment of climate phases based on fitted distributions is more reasonably than that based on empirical distributions. What's more, the complex interplay among multiple largescale climate oscillations is revealed by the copula based joint probability densities, which show the interrelations including the mutual promotion and trade-off. The interplay facilitates the formulation of joint climate phases and associated effect for triggering extremes. These collectively constitute the innovations and distinctive deliverables to provide beneficial insights in developing more robust links between large-scale climate patterns and hydrological variables. The previous studies have demonstrated that the warm-phase of AMO brings enhanced precipitation in northern China (Li and Bates, 2007; Wang et al., 2015). The wet effect of high phase of AMO in winter is consistent to these published before (Wang et al., 2015; Li and Bates, 2007; Lu et al., 2006), which proved the reasonability of the results in this work. What need to be pointed out is that the effect of AMO depends on the modulation effect from other phases. The dry (wet) effect from low (high) phase of ENSO are also consistent with those in previous studies (Wang et al., 2015; Y. Wang et al., 2017b), but different to that in terms of the peculiar joint effect found in our study. The joint effect of combined climate phases of multiple climate oscillations have not been reported in the past studies over the HRB. Extreme precipitations are mostly triggered by the combined extreme climate phases, rather than normal phases and single phases stated in previous studies. It is worth pointing out that the InfInt represents average influence intensity from a certain climate phase. Dry and wet spells still emerge in these normal combined phases, but the average dry-wet condition in the period is normal. In other words, transient wet or dry conditions may appear in certain periods of a climate phase, but the climate phase makes the region nearly normal as a whole. The physical models (e.g. a global circulation model or regional circulation model) usually generate precipitation through considering some climate oscillations and some other large-scale climate factors. Though it is a physical description on the relations between climate patterns and precipitation, it is not the best and direct way to detect teleconnections between climate oscillations and precipitation. In addition, the precipitation driven by physical model often has great

disparity with observations. There is almost no a physical model that is able to capture all complicated teleconnections, thus statistical techniques (e.g. correlation methods) are usually used instead to detect the complex, multiple relationships between climate oscillations and precipitations (Cayan et al., 1999; Lyon and Barnston, 2005). Nevertheless, the traditional correlation methods are not sophisticated enough to investigate the interplay among multiple climate oscillations, restricting the discovery of potential impacts of multiple extreme phases on precipitation (Piechota and Dracup, 1996; Xu et al., 2004). In this paper, a Copula-based joint probability distribution has constructed, disclosing the intricate interplay among the multiple and large-scale climate oscillations over HRB, which is not revealed by previous studies regarding on the similar study region and similar study topic (Wang et al., 2015; Kim et al., 2006). Additionally, the probabilistic analysis approach delineated the complex effect of multiple climate oscillations on precipitation. It is of great promotion to understand the behaviors of extreme precipitation, thus significantly impacts the water resources development and hazard prevention and mitigation over the highly developed social-economic regions with great water scarcity.

6. Conclusions In this work, a probabilistic analysis approach by means of a stateof-the-art Copula-based joint probability distribution is constructed to characterize the aggregated behaviors for large-scale climate patterns and their connections to precipitation. The approach helps to detect and identify the intricate interplay among the multiple and large-scale climate oscillations and their connections with extreme precipitation. These collectively constitute the distinctive deliverables to provide beneficial insights in understanding the intricate behaviors of largescale climatic patterns on local precipitation over the semi-humid and semi-arid zone, promoting the water resources management over the highly developed social-economic regions with great water scarcity. Results disclose that the response of precipitation to AMO, ENSO and PDO is highly connected to different seasons and phases, especially the latter. The assembled climate phases of multiple climate oscillations achieved via a multivariate Copula analysis, instead of a single separate 56

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