water

Article Entropy-Based Research on Precipitation Variability in the Source Region of China’s Yellow River

Henan Gu 1,2,* , Zhongbo Yu 1,2,*, Guofang Li 2, Jian Luo 2, Qin Ju 1,2, Yan Huang 3 and Xiaolei Fu 4

1 State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Hohai University, Nanjing 210098, China; [email protected] 2 College of Hydrology and water resources, Hohai University, Nanjing 210098, China; [email protected] (G.L.); [email protected] (J.L.) 3 Fujian Provincial Investigation, Design & Research Institute of Water Conservancy & Hydropower, Fuzhou 350001, China; [email protected] 4 College of Civil Engineering, Fuzhou University, Fuzhou 350116, China; [email protected] * Correspondence: [email protected] (H.G.); [email protected] (Z.Y.); Tel.: +86-135-8520-9927 (H.G.); +025-8378-6721 (Z.Y.)


Received: 15 August 2020; Accepted: 3 September 2020; Published: 5 September 2020


Abstract: The headwater regions in the Tibetan Plateau play an essential role in the hydrological cycle, however the variation characteristics in the long-term precipitation and throughout-the-year apportionment remain ambiguous. To investigate the spatio-temporal variability of precipitation in the source region of the Yellow River (SRYR), different time scale data during 1979–2015 were studied based on Shannon entropy theory. Long-term marginal disorder index (LMDI) was defined to evaluate the inter-annual hydrologic budget for annual (AP) and monthly precipitation (MP), and annual marginal disorder index (AMDI) to measure intra-annual moisture supply disorderliness for daily precipitation (DP). Results reveal that the AP over the SRYR exhibits remarkable variation, with an inclination rate of 2.7 mm/year, and a significant increasing trend. The climatic trend reversed from warm–dry to warm–wet around the turn of this century. The start of the wet season has advanced from May instead of June, supported by the proportion of MP in AP and the LMDI for May are both comparable with the values during June–September. May contributes the main changes in AP, as it is the only month in the wet season which shows a significant increasing trend during 1979–2015, and has a value in the LMDI that divides the basin in half spatially, the same as AP, with a high value in the northwest and low in the southeast. The AMDI roughly rises with latitude in spatial distribution, with wetlands and glaciers disturbing the continuity of the pattern for a relatively perennial moisture supply. AP has increased on northwest high-altitude areas first and then the southern corner since the beginning of this century. Wetting is mainly attributed to the enhanced southwest monsoon and the warming-induced freeze-thaw process. Meanwhile, AMDI variation concentrated on the Zoige Plateau Wetland, the headwater corner, the summit and part of the North Slope in the Bayan Har Mountain, as a result of a single or combined effect of global climate change and human protection.

Keywords: precipitation; Shannon entropy; variability; the source region of the Yellow River

1. Introduction The analysis of the long-term time series of hydro-meteorological variables is vital to assess potential water resources and to study environmental changes. Precipitation is one of the principal factors in terrestrial water cycles, and its spatial-temporal distribution is as important as the amount,

Water 2020, 12, 2486; doi:10.3390/w12092486 www.mdpi.com/journal/water Water 2020, 12, 2486 2 of 20 if not more, since the type of water demands vary with time and location [1]. Besides, global climate change has intensified the hydrological cycle with increasing evidence supporting the continued occurrence of temporal and spatial variations in precipitation around the world, which would affect the availability of water resources and accelerate the ongoing competitions. Therefore, further study into the mechanisms responsible for the variability in precipitation has become quite essential. The distribution of precipitation at multi spatio-temporal scales and its effects on ecosystems has been popular in hydrology and ecology, as a hot issue, for some time. Some methods have been developed, including the Shannon entropy method [2], principal component analysis [3], harmonic analysis techniques [4], etc. Entropy-based measures contain more information about the probability distribution among diversified statistics that generally delineate variability [5], and they also have advantages in flexibility, by which the dispersion of precipitation could be measured at multi-scales, such as annual, seasonal, or monthly. Disorder index serves as the standardized information entropy in this study to evaluate the spatial and temporal characteristics of rainfall. Although precipitation distribution is a continuous concern in the field of water science, very little research has been conducted in mountainous areas, much less the plateau mountainous area in cold regions. Complex terrain and sparse observation stations are major difficulties for such studies [6]. Weather stations tend to be built on flat terrain or in places that are easy to access and record, and that leaves a lingering problem in mountainous areas with measuring the orographic precipitation, which causes different rainfall on two sides. High elevation worsens the situation as the measurement conditions are much harsher for people to install equipment and record data. Therefore, except for the observation records, datasets from other sources should be employed for a better representation of the natural precipitation process. The application of the remote sensing product with fine resolution also enables the research on the spatial distribution of temporal variation in precipitation. The entropy-based marginal disorder index is applied to quantify the variability of the precipitation spatiotemporal distribution in the source region of the Yellow River (SRYR). Datasets employed for the entire study period between 1979–2015 are time series with an annual, monthly, and daily resolution from an assimilation precipitation product. Annual and monthly precipitation series are used in the investigation of long-term inter-annual variability, and daily series are applied to analyze the over-a-year precipitation apportionment within each year. The following aspects of temporal trends and their spatial distribution patterns of precipitation are addressed in the study: to investigate the spatio-temporal distribution of the variability of long-term precipitation over the SRYR and to determine the possible monthly series dominating the disorder of annual series, based on annual and monthly precipitation datasets; to probe the intra-annual distribution of precipitation series with daily resolution within each year and to find the time and location with a high value; to detect the stationarity and trend in long-term precipitation and its variability using the Pettitt and M–K tests, and divide the study period into stages according to typical characteristics; to evaluate the features and changes in the spatial distribution of precipitation and its variability on a decadal scale and to compare disorderliness within each decade. The specific flow is shown in Figure1. Water 2020, 12, 2486 3 of 20

Water 2020, 12, x 3 of 20

Figure 1. FlowFlow Chart. Chart. AP, AP, MP MP and and DP DP stand stand for for annual, annual, monthly monthly and and daily daily precipitation, precipitation, respectively. respectively.

2. M Materialsaterials

2.1. Study Study Basin The Tibetan PlateauPlateau (TP)(TP) is is the the world’s world’ highests highest and and largest largest plateau, plateau, termed termed “the “the Third Third Pole Pole of the of 6 2 earth”, with an average elevation exceeding 4500 m and an area of 2.5 10 km6 . It2 is also known as the earth”, with an average elevation exceeding 4500 m and an area of ×2.5 × 10 km . It is also known asthe the Asia’s Asia “water’s “water tower”, tower for”, for it is it covered is covered with with a remarkable a remarkable number number of glaciers, of glaciers, snow, snow, permafrost permafrost and andlakes, lakes, which which contain contain the mountainous the mountainous headwaters headwaters of the Yangtze, of the Salween, Yangtze, Mekong, Salween, Indus, Mekong, Brahmaputra Indus, Brahmaputraand Yellow rivers. and Yellow The TP rivers. is one The of the TP most is one vulnerable of the most areas vulnerable to environmental areas to environmenta changes for itsl changes typical forhydrological, its typical geographicalhydrological, andgeographical ecological and features ecological [7]. The features source [7 region]. The source of the region Yellow of River the Yellow (SRYR) Riverspreads (SRYR) most alpinespreads meadow most alpine grassland meadow and wetland grassland of theand TP wetland and thus of itsthe ecosystem TP and thus is strongly its ecosystem related isto strongly the variation related in precipitation, to the variation and in it isprecipitation, selected as a caseand toit is study selected the changing as a case features to study of the precipitation. changing Thefeatures SRYR ofin precipitation. the study refers The to SRY theR basin in the above study the refers Tangnaihai to the basin hydrological above the station Tangnaihai (100.15 hydrological◦ E, 35.5◦ N), 2 whichstation controls (100.15° a E, drainage 35.5° N) area, which of 121,972 controls km a betweendrainage 95.88 area◦ ofE–103.42 121,972◦ kmE and2 between 32.15◦ N–35.73 95.88° E◦ –N103 in.42 the° Enortheastern and 32.15° TPN– (Figure35.73° N2). in The the SRYR northeastern generates TP 34.5% (Fig ofure the 2). total The annual SRYR runoffgenerates and 34.5% accounts of the for onlytotal 16%annual of therunoff basin and area accounts of the Yellow for only River. 16% The of Yellowthe basin River area originates of the Yellow in the Mt.River Bayan. The HarYellow and River flows originateseastward in in general, the Mt. withBayan its Har altitude and decreasingflows eastward from 6253in general m to 2677, with m. its The altitude highest decreas elevationing isfrom found 6253 at mthe to summit 2677 m of. Mt.The Amnehighest Machin, elevation Machin is found Kangri at (summitthe summit M), whichof Mt. isAmne covered Machin, with permanent Machin Kangri snow 2 (summitand contributes M), which about is cover 98% ofed total with glacier permanent areas snow (164 km and) contributes over the basin about [8]. 9 The8% of SRYR total contains glacier areas 5300 2 (1lakes64 km with2) over a total the area basin of 2000[8]. The km SRY[9].R SRYR contains covers 5300 with lakes the with typical a total alpine area meadow of 2000 steppe, km2 [9 covering]. SRYR covers80% of with the area, the typical and is partalpine of themeadow Four Majorsteppe, Pastoral covering Areas 80% in of China. the area, However and is part the degradationof the Four Major in its Pastoralecosystem Areas has been in China. prevailing However [10]. Becausethe degradation of no large in damsits ecosystem and a low has population been prevailing density, [ the10]. impact Because of ofhuman no large activities dams isand relatively a low population low in the areadensity, [11]. the impact of human activities is relatively low in the area [11].

Water 2020, 12, 2486 4 of 20 Water 2020, 12, x 4 of 20

Figure 2. TheThe source source region region of of the the Yellow Yellow River River with with 12 12 meteorological meteorological stations (in red) and 51 CMFD (China Meteorological Forcing Dataset) grids (in black).

There areare roughlyroughly two two climate climate seasons seasons in in the the SRYR, SRYR, the the wet wet season season and dryand thedry season, the season, and about and about75–90% 75 precipitation–90% precipitation falls in falls June–September in June–September as a result as a ofresult the southwestof the southwest monsoon monsoon from the from Bay the of BayBengal of [ Bengal12]. The [12 regional]. The average regional AP average over the AP SRYR over is th aboute SRYR 540 is mm, about and 540 the amount mm, and decreases the amount from decreasesoutheasts from (SE) tosoutheast northeast (SE (NW).) to northeast The annual (NW mean). The air annual temperature mean air is abouttemperature2.5 C is over about the −2.5 SRYR, °C − ◦ overand isthe negatively SRYR, and related is negatively with the related altitude with in spatial the altitude distribution. in spatial distribution.

2.2. Precipitation Precipitation Datasets Datasets TraditiTraditionally,onally, the the characteristics characteristics of rainfall of rainfall are investigated are investigated based on based the meteorological on the meteorological observation observationdatasets [7]. Overdatasets the SRYR,[7]. Over there the are SRYR, twelve there national are raintwelve gauges, national among rain which gauges four, among were removed which fromfour werethe China removed Meteorological from the China Administration Meteorological (CMA) Administration station list gradually (CMA) before station 1998. list Thegradually geographical before 1998.information The geographical of the meteorological information stations of the meteorological is listed in Table stations1. Moreover, is listed the in eightTable weather1. Moreover, stations the eightwith long-termweather stations datasets with are in long the- elevationterm datasets range are from in 3440the elevation m to 4272 range m, while from the 3440 elevation m to of4272 SRYR m, whilestretches the fromelevation 2677 of m SRYR to 6253 stretches m, with from an average 2677 m elevation to 6253 m, of with 4126 an m. average That is toelevation say, only of an 4126 833 m. m Thatrange is out to say, of the only altitude an 833 di ffmerence range ofout 3576 of the m was altitude observed, difference with oneof 3576 station m was located observed, above thewith mean one stationheight. locat Besides,ed above weather the stations mean height tend to. Besides, be built onwea flatther terrain stations for easytend accessto be bybuilt recorders. on flat terrain Therefore, for easythe datasets access by of recorders. sparse meteorological Therefore, the stations datasets over of sparse the SRYR meteorological are not adequate stations replacements over the SRYR for ar thee notnatural adequate precipitation replacement processs for in the the natural basin. precipitation process in the basin.

TableTable 1. 1. MMeteorologicaleteorological stations stations in in the the source source region region of the Yellow River.

ID Name Longitude (°E)Longitude LatitudeLatitude (°N) AltitudeAltitude (m) PeriodPeriod (Year) ID Name 52957 1 Tongde 100.65 (◦E) 35.27 (◦N) 3289.4(m) (Year)1954–1998 1 52968 52957Zeku Tongde101.47 100.65 35.03 35.27 3662.83289.4 1954–19981957–1990 56033 Maduo52968 Zeku98.22 101.47 34.92 35.03 4272.33662.8 1957–19901953– 56041 Zhongxin56033 Maduo99.2 98.2234.27 34.924211.1 4272.3 1953–1959–1997 56041 Zhongxin 99.2 34.27 4211.1 1959–1997 56043 Guoluo 100.25 34.47 3719 1991– 56043 Guoluo 100.25 34.47 3719 1991– 56046 Dari 99.65 33.75 3967.5 1956– 56046 Dari 99.65 33.75 3967.5 1956– 56065 Henan 101.6 34.73 3500 1959– 56065 Henan 101.6 34.73 3500 1959– 56067 56067Jiuzhi Jiuzhi101.48 101.4833.43 33.433628.5 3628.5 1958– 1958– 56074 56074Maqu Maqu102.08 102.0834 343471.4 3471.4 1967– 1967– 56075 Langmusi56075 Langmusi102.63 102.63 34.08 34.08 3362.73362.7 1957–19881957–1988 56079 Ruoergai56079 Ruoergai102.97 102.9733.58 33.583439.6 3439.6 1957– 1957– 56173 Hongyuan56173 Hongyuan102.55 102.5532.8 32.83491.6 3491.6 1960– 1960– 1 gray1 gray shaded shaded represents represents an historical national national station. station.

To overcome the defects by only adopting observation datasets, an assimilation precipitation product CMFD (China Meteorological Forcing Dataset) [13] is applied in the research, which is

Water 2020, 12, 2486 5 of 20

To overcome the defects by only adopting observation datasets, an assimilation precipitation product CMFD (China Meteorological Forcing Dataset) [13] is applied in the research, which is derived from CMA station data and remote sensing datasets, and is available from the National Tibetan Plateau Data Center. The remote sensing data sources include TRMM (Tropical Rainfall Measuring Mission) satellite precipitation analysis data (3B42), GLDAS (Global Land Data Assimilation System) data, GEWEX (Global Energy and Water cycle Experiment)-SRB (Surface Radiation Budget) downward shortwave radiation data, and Princeton forcing data [14]. It currently covers the period from 1979 to 2015, with spatial resolution 0.1 0.1 and temporal resolution 3 h., containing seven variables such as × ◦ air temperature, surface pressure, relative humidity, wind, downward shortwave radiation, downward longwave radiation and precipitation rate. The effectiveness of CMFD was demonstrated with its high performance in the study of the spatiotemporal characteristics of climate-related factors, like surface temperature, precipitation and radiation [15–17]. Fifty one grids at 0.5 0.5 intervals were selected as feature objects out of the 1200 grids × ◦ covering the SRYR. According to the Natural Breaks (Jenks) classification system and the ASTER (Advanced Spaceborne Thermal Emission and Reflection Radiometer)-GDEM (Global Digital Elevation Model) [13], 10 grids each located in the area with the elevation ranges of 2677–3651 m, 4001–4305 m, 4305–4553 m, 4553–6253 m, and 11 fall in the 3651–4001 m elevation range. In other words, the selected grids are evenly distributed both horizontally and vertically (see Figure2). Daily, monthly and annual precipitation series are employed, abbreviated as DP, MP and AP respectively in the study. The basic statistical properties for the selected AP series during 1979–2015 are displayed in Table2, as mean annual precipitation (Mean), maximum annual precipitation (Max), minimum annual precipitation (Min) and coefficient of variation (CV). The grids with a high CV are mainly concentrated in the western mountainous area and on the northern edge, where AP is generally low. The range of mean, maximum and minimum AP is 270–839 mm, 482–1076 mm and 153–591 mm, respectively. The mean and minimum AP share a similar distribution; both have 28 girds lower than the average and only two do not overlap in Figure2. While 27 maximum AP series are higher than average, among them 20 are located at low altitude regions where the mean and minimum are also high, and the other numbers are 7, 10, 13, 23, 32, 33 and 37, concentrated in a small range of two latitudes.

Table 2. The mean, extremes and CV of the selected 51 AP series (1979–2015).

No. Mean (mm) Max (mm) Min (mm) CV No. Mean (mm) Max (mm) Min (mm) CV 1 321 505 197 0.24 27 532 679 394 0.14 2 453 635 263 0.19 28 494 657 307 0.17 3 347 527 197 0.24 29 429 613 285 0.19 4 474 725 285 0.22 30 622 767 460 0.14 5 348 505 219 0.20 31 573 745 417 0.15 6 270 482 153 0.37 32 521 788 372 0.19 7 498 810 329 0.25 33 442 810 307 0.24 8 350 569 241 0.22 34 727 920 569 0.12 9 287 548 153 0.38 35 691 876 527 0.13 10 488 767 329 0.23 36 625 832 438 0.15 11 339 504 220 0.17 37 536 767 372 0.18 12 533 725 350 0.16 38 413 613 286 0.22 13 515 835 372 0.23 39 763 1029 571 0.14 14 382 548 264 0.18 40 687 898 527 0.14 15 613 769 460 0.14 41 623 767 438 0.14 16 549 701 372 0.14 42 535 723 372 0.16 17 503 679 350 0.19 43 839 1076 526 0.13 18 455 679 286 0.23 44 810 1007 526 0.14 19 349 591 220 0.25 45 729 964 571 0.13 20 611 788 416 0.14 46 628 876 504 0.14 21 551 679 372 0.14 47 747 964 504 0.13 22 525 679 394 0.16 48 693 878 483 0.13 23 521 832 329 0.26 49 661 986 482 0.17 24 404 657 242 0.25 50 735 920 591 0.12 25 632 854 416 0.16 51 675 898 504 0.14 26 592 810 460 0.14 Avg 542 754 377 0.18 Water 2020, 12, 2486 6 of 20

2.3. Land Cover Map The land cover type is crucial to estimate water and carbon cycles, ecosystem dynamics and climate change. The Multi-source Integrated Chinese Land Cover (MICLCover) map is adopted in the study for its high accuracy in China [18]. The MICLCover map was derived from multi-local-source land cover and land use classification datasets including a 1:1,000,000 vegetation map, a 1:100,000 land use map for the year 2000, a 1:1,000,000 swamp-wetland map, a glacier map, and a Moderate-Resolution Imaging Spectroradiometer land cover map for China in 2001 (MODIS2001), which were integrated through the practical evidence generation scheme. The map uses the widely applied International Geosphere-Biosphere Programme (IGBP) land cover classification system, with 1 km resolution. The MICLCover map provides more spatial details at the local scale compared with other popular products, e.g., IGBP DISCover and MODIS2001, particularly for cropland, urban, glacier, wetland and water body.

3. Methods

3.1. Calculation of Variability

3.1.1. Entropy Shannon introduced entropy as a measure of information, dispersion, uncertainty and disorder. The simplified expression of the discrete form of informational entropy, termed as Shannon entropy [19], is:

Xn H(X) = p(x )log [p(x )] (1) − k 2 k k=1 where n is the number of possible events, k represents a discrete temporal interval, xk is its corresponding result, p(xk) denotes the probability of xk, and H(X) is the entropy expressed in bits as the base of logarithm takes 2. Shannon entropy reflects the uncertainty information about a certain distribution. For a variable X,

H reaches its maxima log2 n if all outcomes are equiprobable with p(xk) = 1/n, while quite the opposite, H equals its minima zero if every p(xk) but one is zero. The value of entropy varies within the range of zero to log2 n, according to the pattern of the distribution. There are other measures of dispersion degree of a random variable, among them variance is the most well-known one. The equation of variance is as below [20]: P (X µ) σ2 = − (2) N where σ2 represents the population variance, X represents the random variable, µ represents population expectation and N is population size. According to the equation, variation measures the deviation extent of the random variable compared with the population expectation or the mean, thus variation reflects the uncertainty related to the expectation. The same goes for the measures based on variation, like standard deviation and CV. While the entropy reflects the overall uncertainty, as it neither relies on the expectation nor on the sample of the population, but only on its probability. Thus entropy has obvious advantages in measuring the uncertainty of a certain distribution.

3.1.2. Entropy Application in Precipitation Analysis Shannon entropy can be served as a functional estimate of the uncertainties in a long-term time series of rainfall. In statistics, variability is the extent to which a distribution is stretched or squeezed, whose measure is a nonnegative real number that is zero if all the data are the same and increases as the data become more diverse [21]. From this aspect, the variability of precipitation can be quantitatively Water 2020, 12, 2486 7 of 20 measured by using an entropy concept. In its previous application, precipitation time series at different temporal scales, like annual, seasonal and monthly, were considered individually, to better understand the uncertainty or variability within each scale and to make a comparison among them. Take a daily series of an entire year at a fixed location, for example, to explain the application of entropy concept in precipitation time series. Daily precipitation could be viewed as a discrete equal-interval random variable. Let the discrete temporal interval be the number of days in a year (nd), e.g., 365, and its corresponding outcome is daily precipitation apportionment, and then the probability of each event is the daily precipitation (DP) divided by the aggregate precipitation during the year (AP). Hence the uncertainty degree can be determined by entropy in terms of the probability density of precipitation randomly apportioned over fragmented times. This entropy is also called marginal entropy (ME) with the annual expression as follows:

Xnd ME = (DP /AP)log (DP /AP) (3) − k 2 k k=1

Pnd where AP = k=1 DPk. If the scale changes, DPk refers to the data on that scale, and the total number (nd) and the sum (AP) change accordingly.

3.1.3. Disorder Index Entropy evaluates the uncertainty degree of time series at certain points. A quantitative measure of variability should be comparable among temporal and spatial results. The Disorder index (DI) serves as a standardized measure based on entropy, which is defined as the difference between the possible entropy maxima and the actual entropy calculated from a certain series. The maximum possible entropy refers to the value from the uniform distribution. For example, the maximum possible marginal entropy is log2 n, for a daily precipitation series with size n. DI measures the degree away from the hypothetic most-scattered distribution, the distribution with low DI is dispersive, on the contrary, the high DI distribution is non-uniformed. That is to say, the value of DI is in accordance with the degree of variation of a series. Mishra, et al. [2] defined the marginal disorder index (MDI) as the disorder index for marginal entropy. And the mean disorder index is formed as the arithmetic average of the values of DI within a given period. There are several kinds of MDI involved in the study, long-term MDI (LMDI), based on long-term annual or monthly precipitation series; annual MDI (AMDI), based on the daily precipitation series within each year; and the decadal averaged annual MDI (DAMDI). Among the derived MDI, AMDI is a series with the same length as the study years, which refers to the MDI of each year, based on daily precipitation, specifically used for revealing the throughout-the-year precipitation apportionment. And DAMDI is its decadal average value to uncover the intra- and inter-decadal variations of precipitation apportionment on a yearly basis. The equations related to the description above is listed below: MDI = log nd ME (4) 2 − where nd is the total number, and ME can be calculated by Equation (3);

ny X P   P  LMDI = log ny + k log k (5) 2 LSP 2 LSP k=1 where ny is number of years during the entire study period, LSP represents the long-term sum of precipitation, and Pk is a certain precipitation data with a given resolution, e.g., if analyzing the disorderliness in the long-term AP, Pk is APk, an AP data during the period, else if the aim is an Water 2020, 12, 2486 8 of 20

individual month, then Pk is MPk, a monthly data of the target month within the period. Thus, the LMDI Water 2020, 12, x 8 of 20 always appears with an explanation. 3.2. Statistical Test 3.2. Statistical Test The monotonic trend and the abrupt change of precipitation time series were detected by non- The monotonic trend and the abrupt change of precipitation time series were detected by parametric tests, the Mann–Kendall (M–K) test [22,23] and the Pettitt test [24], respectively. The M– non-parametric tests, the Mann–Kendall (M–K) test [22,23] and the Pettitt test [24], respectively. K test and the Pettitt test, with a rejection rate of 5%, were applied in the study. If > 1.96 or The M–K test and the Pettitt test, with a rejection rate of 5%, were applied in the study. If UMK > 1.96 or < −1.96, a significant increased or decreased trend of the targeted time series could be accepted. When UMK < 1.96, a significant increased or decreased trend of the targeted time series could be accepted. ≤− 0.05, the stationarity hypothesis would be rejected and the change-point would be When ppettitt 0.05, the stationarity hypothesis would be rejected and the change-point would be determined correspondingly.≤ Because the Pettitt test checks the stationarity assumption among determined correspondingly. Because the Pettitt test checks the stationarity assumption among populations and a population should contain at least ten elements, the detected abrupt change-points populations and a population should contain at least ten elements, the detected abrupt change-points are taken between the elevenths from the head and the end. are taken between the elevenths from the head and the end.

4.4. Results Results and and Discussion Discussion

4.1.4.1. Variability Variability of of Precipitation Precipitation

4.1.1.4.1.1. Inter Inter-Annual-Annual Variation Variation of of Annual Annual and and Monthly Monthly Precipitation Precipitation TheThe LMDI LMDI mainly mainly indicates indicates the the variation variation of of local local precipitation precipitation in ina fixed a fixed time time interval interval during during a perioda period,, and and it takesit takes a longera longer interval interval toto achieve achieve a adetectable detectable level level of of changes. changes. If Ifa afixed fixed day day was was selected,selected, for for example, example, the firstfirst dayday ofof eacheach year, year, and and the the changes changes of of daily daily rainfall rainfall happened happened on on that th dayat dayevery ev yearery yearwere wereexamined examined for a period, for a the period, high therandomness high randomness would make would the results make meaningless. the results meaningless.In the study, In monthly the study, and monthly annual datasetsand annual are selecteddatasets inare the selected long-term in the variability long-term of variability precipitation of precipitationanalysis. The analysis. LMDI isThe calculated LMDI is forcalculated the selected for the 51 selected annual and51 annual monthly and series monthly during series 1979–2015, during 1979and– the2015, statistics and the of statistics results are of displayed results are in Figuredisplayed3. It in is obviousFigure 3 that. It is the obvious LMDI on that an the annual LMDI timescale on an annualis lower timescale than those is lower of each than month. those of The each uncertainty month. The of precipitationuncertainty of distribution precipitation in distribution the dry season in the(October dry season to next (October April) isto muchnext April) higher, is andmuch contributes higher, and to thecontributes main variability to the main within variability a year; wewithin take aMay year as; we the take start May of the as the wet start season of the in this wet study. season The in this average study. LMDIs The average in the wet LMDI seasons in arethe allwet about season 0.1. areNovember all about to 0.1. next November February to have next the February highest LMDIs,have the the highest averages LMDI ofs which, the average are aboves of 0.3. which The are rest abovethree months,0.3. The March,rest three April months, and October, March, haveApril similarand October, mean LMDIs have similar of about mean 0.2. LMDI The drys of season about has0.2. a Themore dry nonuniform season has precipitationa more nonuniform distribution precipitation than the distribution wet season, whichthan the applies wet season, to spatial which distribution applies toas spatial well, as distribution the rangeof as the well, LMDI as the in range the dry of season the LMDI is wider. in the dry season is wider.

FigureFigure 3. 3. The mean mean and and extreme extreme of ofLMDI LMDI (long-term (long-term marginal marginal disorder disorder index) index) for annual for annualand monthly and monthlyprecipitation precipitation series at series 51 CMFD at 51 grids CMFD during grids 1979–2015. during 1979–2015.

ToTo better better delineate delineate the the spatial spatial distribution distribution of of the the LMDI LMDI for for AP, AP, the the method method is is generalized generalized to to all all 12001200 series series and and the the mean mean values values are are drawn drawn in inFigure Figure 4. 4High. High LMDI LMDI clusters clusters are areon the on theNW NW side side of the of basin,the basin, with with the highest the highest LMDI LMDI in red in redappearing appearing mainly mainly in inthe the northern northern highest highest attitude attitude area area in in the the SRYR,SRYR, which which basically basically matches matches with with the the white white color color on on north north part part in in Figure Figure 22;; to to be be exact, exact, the the NW NW edge and the summit M. Figure 4 have also exhibited the distribution of regions with significant trends in long-term AP series during 1979–2015, detected by the M–K test with a rejection rate of 5%. The regions covered by plus signs (+), most of the NW part, have significant increasing trends in the

Water 2020, 12, 2486 9 of 20 edge and the summit M. Figure4 have also exhibited the distribution of regions with significant trends in long-term AP series during 1979–2015, detected by the M–K test with a rejection rate of 5%. Water 2020, 12, x 9 of 20 The regions covered by plus signs (+), most of the NW part, have significant increasing trends in the amountWater of 20 AP,20, 12 and, x the regions with slashes ( ), covering a small area on the north edge of the9 SE of 20 corner, amount of AP, and the regions with slashes\ (\), covering a small area on the north edge of the SE havecorner, significant have decreasingsignificant decreasing trends. trends. amount of AP, and the regions with slashes (\), covering a small area on the north edge of the SE corner, have significant decreasing trends.

Figure 4. The spatial distribution of LMDI (long-term marginal disorder index) based on AP (annual Figure 4. The spatial distribution of LMDI (long-term marginal disorder index) based on AP (annual precipitation)precipitation) and theand Mann–Kendallthe Mann–Kendall (M–K) (M– testK) test statistic statistic of theof the AP AP series series during during 1979–2015 1979–2015 in in the the source Figuresource 4.region The spatial of the Yellowdistribution River of (SRYR LMDI). (long-term marginal disorder index) based on AP (annual regionprecipitation) of the Yellow and River the Man (SRYR).n–Kendall (M–K) test statistic of the AP series during 1979–2015 in the source region of the Yellow River (SRYR). The M–KThe M test–K test is also is also applied applied to to detect detect the the trendstrends of the the MP MP series series individually individually for the for 1200 the1200 grid grid during 1979–2015 in the SRYR; the regional mean statistic results as well as the multi-year average of during 1979–2015 in the SRYR; the regional mean statistic results as well as the multi-year average of eachThe month M– Kare test shown is also in applied Figure 5.to About detect 83%the trendsannual of precipitation the MP series falls individually in the wet seasonfor the, 1200the range grid eachduring monthof MP in1979 are May– shown2015–September inin the Figure SRYR is from5; .the About 62 regional mm 83% to mean111 annual mm, statistic and precipitation fromresults June as – fallswellJuly as inis theabove the multi wet 100 season,-year mm. average The the seven range of of MP ineMPach May–Septembers monthin the dryare shownseason is from inrange Figure 62 from mm 5. About3 to mm 111 83%to mm, 35 annual mm, and the from precipitation highest June–July month falls is inis above October,the wet 100 season mm.and the, The the value sevenrange of MPs in theofNovember dry MP seasonin May to– range Septembernext February from is 3 mmfrom is not to62 35mmhigher mm, to 111than the mm, highest6 mm. and Every monthfrom June month is– October,July show is aboves and an 100 theincreasing mm. value The oftrend seven November in to nextMPprecipitation, Februarys in the dry isamong season not higher which range the thanfrom trends 63 mm.mm of threeto Every 35 monthsmm, month the are highest shows statistically month an increasing significant is October,: trend January, and the in precipitation,Februaryvalue of amongNovemberand which May. The theto next disorderlines trends February of threes isand not monthstrends higher of are thanthe statisticallyMP 6 mm. series Every in these significant: month three show month January,s an are increasing detailed February intrend Figure and in May. precipitation, among which the trends of three months are statistically significant: January, February The disorderliness6. Comparing the and LMDI trends of ofthe the months MP series from different in these threeperspectives, month from are detailed the magnitude, in Figure May6. Comparinghas the and May. The disorderliness and trends of the MP series in these three month are detailed in Figure the LMDIlowest of LMDI, the months ranging from from di0.03fferent to 0.29, perspectives, and the LMDI from of January the magnitude, and February May is has much the higher, lowest the LMDI, 6.maximum Comparing is boththe LMDI over of1.0; the from months the spatial from different distribution, perspectives, May gradually from the increases magnitude, from May SE hasto NW, the ranging from 0.03 to 0.29, and the LMDI of January and February is much higher, the maximum is both lowestwhile theLMDI, other ranging two monthsfrom 0.03 have to 0.29, more and than the oneLMDI high of January value region. and February All three is much months higher, show the an over 1.0; from the spatial distribution, May gradually increases from SE to NW, while the other two maximumincreasing istrend both over over the 1.0; SRYR, from andthe spatialthe significant distribution, region Mays are gradually marked inincreases Figure 6from with SE plus to NW,signs monthswhile(+), haveand the the more other area thanwith two monthsmarks one high in have May value shows more region. thanmuch one All less threehigh than valuethe months other region. months. show All an The three increasing precipitation months trend show almost overan the SRYR,increasingincreases and the all trend significant over over the SRYRthe regions SRYR, in January, are and marked the except significant in in Figure the region Northern6 withs are plus Amne marked signs Machin in ( +Figure), Mountain. and 6 thewith area Theplus witharea signs in marks in May(+),February showsand the with much area awith lesssignificant marks than theinly May increase other shows months.d trendmuch, Thelesscovers than precipitation the the wholeother months. almost middle The increases region. precipitation There all over are almost three the SRYR in January,increasesmarked except parts all over in in May, the SRYR Northern the Summit in January, Amne M neighborhood, except Machin in Mountain.the Northernand the NW, The Amne areaSW Machin corner. in February Mountain.Compar withed Theto a Figure significantlyarea in 4, increasedFebruarythe high trend, LMDI with covers afor si gnificantAP the clusters wholely increasein middle the northd region. trend edge, covers Thereon both are the annual three whole and marked middle monthly parts region. scales, in There May, and thethe are SummitLMDI three M marked parts in May, the Summit M neighborhood, and the NW, SW corner. Compared to Figure 4, neighborhood,in May has anda similar the NW,pattern. SW corner. Compared to Figure4, the high LMDI for AP clusters in the the high LMDI for AP clusters in the north edge on both annual and monthly scales, and the LMDI northin edge May onhas botha similar annual pattern. and monthly scales, and the LMDI in May has a similar pattern.

Figure 5. The average of regional mean monthly precipitation and the M–K test statistic during 1979–

2015 in the SRYR. FigureFigure 5. The5. The average average ofof regional mean mean monthly monthly precipitation precipitation and the and M–K the test M–K statistic test during statistic 1979 during– 1979–20152015 in in the the SRYR. SRYR.

Water 2020, 12, 2486 10 of 20

Water 2020, 12, x 10 of 20

FigureFigure 6. 6. TheThe spatial spatial distribution distribution of of the the LMDI LMDI (long (long-term-term marginal marginal disorder disorder index) index) and and the the sig significantnificant increasingincreasing trend trend of of the the MP MP (monthly (monthly precipitation) precipitation) time time series series by by the the M M–K–K test test in in Jan January,uary, Feb Februaryruary andand May May during during 1979 1979–2015–2015 over over the the SRYR. SRYR.

4.1.2.4.1.2. Intra Intra-Annual-Annual Distribution Distribution of of Daily Daily Precipitation Precipitation TheThe d dailyaily precipitation precipitation time time series series is is employed employed in in the the calculation calculation of of the the annual annual marginal marginal disorder disorder indexindex (AMDI). (AMDI). A A s similarimilar approach approach in in inter inter-annual-annual analysis analysis is is applied applied to to investigate investigate the the long long-term-term AMDIAMDI series, series, while while different different from from LMDI, LMDI, AMDI AMDI is a is series a series instead instead of a single of a single value. value. The AMDI The AMDIseries rangesseries rangesfrom 1.52 from–1.93 1.52–1.93 during during 1979– 1979–2015,2015, with with the theminimum minimum and and maximum maximum in in 1989 1989 and and 2002 2002,, respectively.respectively. There There is an insignificant insignificant trend inin thethe AMDIAMDI onon thethe basinbasin scalescale duringduring studystudy period, period, with with a astatistic statistic as as 0.6 0.6 according according to to the the M–K M– test.K test. The The spatial spatial distribution distribution of theof the multi-year multi-year average average AMDI AMDI over overthe SRYRthe SRYR during during 1979–2015 1979– is2015 displayed is displayed in Figure in Figure7. The 7. multi-year The multi mean-year AMDImean AMDI ranges ranges from 1.46 from to 1.46 to 2.17, with the mean and standard deviation at 1.75 and 0.15, respectively. The value roughly increases with latitude, with wetlands and glaciers disturbing the continuity of the pattern by about

Water 2020, 12, 2486 11 of 20

Water 2020, 12, x 11 of 20 2.17, with the mean and standard deviation at 1.75 and 0.15, respectively. The value roughly increases Water 2020, 12, x 11 of 20 with latitude, with wetlands and glaciers disturbing the continuity of the pattern by about 0.1 in −0.1 in AMDI. Moreover, the southern edge and the summit M have the lowest AMDI, and− the −AMDI.north0.1 inern AMDI.Moreover, edge Moreoverhas the the southern highest, the south edgeAMDI, andern especially edge the summit and in the regions M havesummit around the M lowest have the AMDI, Tangnaihaithe lowest and the station AMDI, northern (Grid andedge the29) . northhasFigure theern highest8 edge serves has AMDI, as the a profile highest especially chart AMDI, in interpreting regions especially around the in feature theregions Tangnaihai of around the long station the-term Tangnaihai (Grid AMDI 29). series station Figure in8 (Grid serveseach grid,29) as. Figureaand profile wide 8 serves chart ranges interpretingas aexist profile in mostchart the feature selectedinterpreting of series. the the long-term The feature variance AMDIof the tendency long series-term in of each AMDI AMDI grid, series would and in wide helpeach ranges ingrid, the andexistunderstanding wide in most ranges selected of exist the series. temporalin most The selecteddistribution, variance series. tendency an Thed thus ofvariance AMDIthe trends wouldtendency at each help of grid inAMDI the were understanding would computed help andin of the thethe understandingtemporalsignificant distribution, ones of werethe temporal also and displayed thus distribution, the trends in Figure at an eachd 7. thus grid the were trends computed at each andgrid thewere significant computed ones and were the significantalso displayed onesin were Figure also7. displayed in Figure 7.

Figure 7. The spatial distribution of the multi-year average AMDI (annual marginal disorder index) FigureFigurebased 7. 7.on TheThe daily spatial spatial precipitation distribution distribution and of ofits the the significant multi multi-year-year tre average averagends by AMDI AMDIthe M –(annual (annualK test during marginal marginal 1979 disorder disorder–2015 over index) index) the basedbasedSRYR. on dailydaily precipitationprecipitation and and its its significant significant trends trends by theby the M–K M test–K duringtest during 1979–2015 1979– over2015 theover SRYR. the SRYR.

FigureFigure 8.8. TheThe meanmean andand extremeextreme ofof thethe long-termlong-term AMDIAMDI (annual(annual marginalmarginal disorderdisorder index)index) ofof dailydaily Figureprecipitationprecipitation 8. The during meanduring and 1979–2015 1979 extreme–2015 at at of selected selected the long grid. grid.-term AMDI (annual marginal disorder index) of daily precipitation during 1979–2015 at selected grid. 4.2.4.2. VariationVariation ofof PrecipitationPrecipitation DistributionDistribution 4.2. Variation of Precipitation Distribution 4.2.1. Abrupt Change Analysis and Stages Division 4.2.1. Abrupt Change Analysis and Stages Division 4.2.1. TheAbrupt Pettitt Change test withAnalysis a rejection and Stages rate Division of 5% is applied to the selected 51 AP and AMDI series The Pettitt test with a rejection rate of 5% is applied to the selected 51 AP and AMDI series from from 1979 to 2015, and valid results are listed in Table3. Thirty nine AP series show abrupt changes, 1979The to 2015,Pettitt and test valid with resultsa rejection are listedrate of in 5% Table is applied 3. Thirty to thenine selected AP series 51 showAP and abrupt AMDI changes, series from from from which 59% was detected in 2002 and 2003, 14 and 9 grids respectively, and no abrupt change 1979which to 2015,59% was and detected valid results in 2002 are and listed 2003, in Table14 and 3. 9 Thirty grids respectively, nine AP series and show no abrupt abrupt change changes, occurred from occurred from 1990 to 1996 and after 2005. While 32 AMDI series showed abrupt changes, and 53% in whichfrom 199059% wasto 1996 detected and after in 2002 2005. and While 2003, 32 14 AMDI and 9 seriesgrids respectively,showed abrupt and changes, no abrupt and change 53% in occurred 1997 and 1997 and 1998, 12 and 5 grids respectively, no abrupt change was detected in the years before 1991, from1998, 1990 12 and to 1996 5 grids and respectively, after 2005. While no abrupt 32 AMDI change series was showed detected abrupt in the changes, years before and 53% 1991, in 1993,1997 and1994 1993, 1994 and after 2003. That is to say, the breaks in the stationarity of AP and the AMDI series 1998,and 12after and 2003. 5 grids That respectively, is to say, the no breaksabrupt inchange the stationarity was detected of inAP the and years the beforeAMDI 1991, series 1993, is m 1994ainly is mainly concentrated during 1997–2004 and 1995–2002 respectively, and the AMDI series varied andconcentrate after 2003.d during That is 1997 to say–2004, the and breaks 1995 in–2002 the respectively,stationarity of and AP the and AMDI the AMDI series seriesvaried is generally mainly concentrateearlier. Moreover,d during the1997 spatial–2004 and distribution 1995–2002 of respectively, the abrupt and changes the AMDI of precipitation series varied amount generally and earlier.variability Moreover, is also asynchronous the spatial distribution. Examining the of meansthe abrupt for clustered changes grids of precipitationnumbered 1– 4, amount for example, and variabilitythe AP series is also all asynchronousdemonstrated. Examiningstrong increases the means in 2003, for whileclustered the meansgrids numbered of the AMDI 1–4, at for Grids example, 1 and the AP series all demonstrated strong increases in 2003, while the means of the AMDI at Grids 1 and

Water 2020, 12, 2486 12 of 20 generally earlier. Moreover, the spatial distribution of the abrupt changes of precipitation amount and variability is also asynchronous. Examining the means for clustered grids numbered 1–4, for example, the AP series all demonstrated strong increases in 2003, while the means of the AMDI at Grids 1 and 3 changed abruptly in 1995. For Grid 4, the AMDI mean changed abruptly in 2001, but no abrupt changes were noted in Grid 2.

Table 3. Abrupt change detection results of the AP (annual precipitation) series and AMDI (annual marginal disorder index) series during 1979–2015 at 51 selected grids.

AP AMDI AP AMDI Year Year Grid Count Grid Count Grid Count Grid Count 1989 34; 45 2 - 0 1999 9 1 11; 43 2 1990 - 0 - 0 2000 6; 22 2 23; 33 2 1991 - 0 - 0 2001 5; 13; 14 3 4; 41 2 1992 - 0 27; 28 2 1993 - 0 - 0 7; 8; 10; 12; 15; 1994 - 0 - 0 2002 16; 17; 21; 31; 14 18; 19; 24 3 1995 - 0 1; 3; 46 3 35; 36; 40; 41; 51 1996 - 0 40 1 1; 2; 3; 4; 28; 30; 19; 23; 12; 16; 21; 36; 2003 9 - 0 1997 3 12 32; 37; 38 50 37; 42; 44; 47; 48; 49; 50; 51 2004 11; 29; 33 3 - 0 2005 - 0 - 0 1998 18; 24 2 7; 10; 14; 39; 45 5 SUM 39 32

Abrupt changes of the amount and variability of precipitation occurred gradually over the SRYR, and it is necessary to divide the whole study period (37 years). According to the results in Table3, four equal stages were adopted, 1979–1988, 1988–1997, 1997–2006 and 2006–2015, by duplicating the breakpoints in the previous decade to the following. The first decade, 1979–1988, with scarce sudden changes, represents a “natural decade”; the second, 1988–1997, is a stage with little changes before the end, making it a “pre-change decade” when environmental changes were conceived; the third, 1997–2006, is a “changing decade”, when the effects of climate change emerged and abrupt change was concentrated; and the last, 2006–2015, during which most statistic characteristics transformed to a new population due to a changing environment, is taken as “impact decade”.

4.2.2. Annual Precipitation and Intra-Annual Variability Distribution in Stages There are widespread changes in the distribution of the decadal averaged annual precipitation (DAP). The regional mean and extremes of DAP and its inclination rate are listed in Table4. The range of AP during each decade is 186–890 mm, 166–844 mm, 237–896 mm and 314–920 mm successively. The value shows that the DAP decreases before 1997 and then increases, and the maximum value is the most sensitive statistic according to the inclination rate over each decade. The M–K test, with a rejection rate of 5% only detected an insignificant trend during each decade on the basin scale, with the statistic as 1.25, 0.36, 1.43 and 0 in sequence. The distribution patterns of DAP over each decade are shown in − Figure9. It is observed that the average of AP over the first and second decade roughly trend in the NW direction as bandings, with the highest value at the SE corner and decreasing forward. The pattern became more and more unorganized ever since 1997, and the precipitation over the summit M changed more dramatically than that of the rest of the central and upper basin. The regions with significant trends detected by the M–K test are also displayed in Figure9. In the first decade, the precipitation weakened at the range from 600 mm to 700 mm. The second decade scarcely has areas with significant trends. Most of the dry west region experienced an increased period over the third decade, and the wet southern corner increases afterwards over the most recent decade. AP increased on the NW high-altitude areas first and then in the southern corner, the summit M changed from 390 mm to the 680 mm level, and the southern corner was raised by about 50 mm. Water 2020, 12, x 13 of 20

Water 2020Table, 12 4., 2486 The regional mean and extreme values of averaged AP and AMDI with inclination rate13s of 20 during different periods over the SRYR.

1 Table 4. The regionalAvg mean AP and(mm) extreme/Rate (mm·a values− of1 ) averaged AP andAvg AMDI AMDI with/ inclinationRate (10·a− rates1) Periodduring different periods over the SRYR. Mean Min Max Mean Min Max Avg AP (mm)/Rate (mm a 1 1) Avg AMDI/Rate (10 a 1) 1979–1988Period 523/−5.4 186/−0.1 −890/−14.6 1.75/−0.10 1.41/−0.09− 2.27/−0.24 Mean Min· Max Mean Min· Max 1988–1997 497/−2.0 166/1.8 844/−13.4 1.69/0.08 1.32/−0.02 2.27/0.14 1979–1988 523/ 5.4 186/ 0.1 890/ 14.6 1.75/ 0.10 1.41/ 0.09 2.27/ 0.24 − − − − − − 1997–1988–19972006 529 497/9.8/ 2.0237 166/12.0/1.8 844/89613.4/15.3 1.69/0.081.77/0.08 1.32 / 1.300.02/−0.03 2.27 /0.142.41/0.09 − − − 1997–2006 529/9.8 237/12.0 896/15.3 1.77/0.08 1.30/ 0.03 2.41/0.09 − 2006–2006–20152015 596 596/2.8/2.8 314 314//4.94.9 920920/9.2/9.2 1.78/ 1.780.04/−0.04 1.34/0.021.34/0.022.37 /0.092.37/0.09 − 1979–1979–20152015 540 540/2.7/2.7 229 229//5.05.0 895895/1.4/1.4 1.75/0.011.75/0.01 1.35 / 1.350.03/−0.03 2.34 /0.042.34/0.04 − 1 1a arepresents represents yearyear in in this this article. article.

FigureFigure 9.9. AverageAverage values values and and monotonic monotonic trends trends of of annual annual precipitation precipitation over over a decade a decade for ( afor) 1979–1988, (a) 1979– (1988,b) 1988–1997, (b) 1988– (1997,c) 1997–2006 (c) 1997– and2006 (d and) 2006–2015. (d) 2006–2015.

ExtensiveExtensive changes changes exist exist among among the thedistribution distribution patterns patterns of the decadalof the decadal averaged averaged annual marginal annual disordermarginal indexdisorder (DAMDI), index (DAMDI), which are which displayed are displayed in Figure in 10Figure. The 10. DAMDI The DAMDI roughly roughly increased increased with latitudewith latitude before before 1997, and 1997, the and pattern the has pattern been has broken been by broken the summit by the M summitneighborhood M neighborhood afterwards. Itafterwards. is a remarkable It is a factremarkable that the highestfact that DAMDI the highest gathers DAMDI around gathers the basin around export the (Gridbasin 29).export The (Grid range 29) of. DAMDIThe range during of DAMDI each decade during over each the decade SRYR over is 1.41–2.27, the SRYR 1.32–2.27, is 1.41– 1.30–2.412.27, 1.32 and–2.27, 1.34–2.37 1.30–2.41 successively, and 1.34– and2.37 the successi regionalvely, mean and firstthe regional decreases mean and then first increases decreases thenand decreases then increase again,s then however decrease thes change again, ishowever slight, withthe change the inclination is slight, with rate ofthe inclination0.10 (10 a 1rate), 0.08 of − (100.10a (10·a1), 0.08−1), 0.08 (10 (10·aa 1)−1 and), 0.08 (10·a0.04− (101) anda 1−)0.04 in − · − · − · − − · − sequence,(10·a−1) in accordingsequence, toaccording the statistic to the in Tablestatistic4. The in Table maximum 4. The is maximum the most sensitive is the most value, sensitive and the value, rate ofand the the mean rate DAMDIof the mean is 0.01 DAMDI over the is 0.01 study over period. the study The M–Kperiod. test, The with M– aK rejection test, with rate a rejection of 5%, did rate not of detect5%, did any not significant detect any trendsignificant during trend each during decade each on thedecade basin on scale, the basin the statistics scale, the are statistic0.72,s 0.36,are −0.72, 0.54 − and0.36, 0.540.18 and in sequence,−0.18 in sequence, while certain while certain parts show parts significant show significant trends trend withins with a smallin a small area duringarea during one − decade.one decade. For theFor firstthe decade,first decade, the Grid the Grid 11 neighborhood 11 neighborhood shows shows decreasing decreasing trends trend withs verticalwith vertical strip shape;strip shape; the second the second decade decade has a circle has a shape circle increasing shape incr trendeasing around trend Grids around 27–28; Grids there 27– were28; there two spotswere withtwo trendsspots with in the trends third decade, in the thirdone decreasing decade, one at the decreasing WN origin at corner, the WN the origin other increasing corner, the around other theincreasing SE Grid around 45; the the most SE recent Grid decade45; the most has multiple recent decade small areashas multiple with trends, small two area decreasings with trends, ones two are noticeable,decreasing theones Summit are noticeable, Grid 18 andthe Summit Grid 46 nearGrid the18 and Zoige Grid wetland. 46 near the Zoige wetland.

Water 2020, 12, 2486 14 of 20

Water 2020, 12, x 14 of 20

Figure 10. 10. DecadalDecadal average average intra-annual intra-annual variability variability for daily for precipitationdaily precipitation series and series its trends and its measured trends measuredby decadal by averaged decadal annual averaged marginal annual disorder marginal index disorder (DAMDI) index and (DAMDI UMK respectively,) and UMK forrespectively, (a) 1979–1988, for ((ab)) 1979 1988–1997,–1988, ( (bc) 1997–20061988–1997, and(c) 1997 (d) 2006–2015.–2006 and (d) 2006–2015.

TThehe evolution of annual precipitation precipitation and its variability was stud studiedied above through four single continuouscontinuous decade decades.s. The The regional regional average average DAP DAP and and DAMDI DAMDI general generallyly reduced reduced first first and increased later,later, and patterns varied towards towards the the irregular irregular mainly mainly due due to to interference interference from from the the shift shift in in values over the summit and NW regions. The The DAMDI DAMDI has has a a barely barely changed mean, a slightly decreased minimum, and and an increased increased maximum. T Thehe statistics statistics all all increase increase in in the the DAP, DAP, and the greatest rate in thethe mean of DAP emergedemerged inin thethe lastlast decade,decade, later later than than the the extremes extremes of of 1997–2006. 1997–2006. The The distribution distribution is isdistinguishable, distinguishable, which which means means that that the the nature nature of of precipitation precipitation is diis ffdifferenterent from from its its variability. variability.

4.3. Implication of Precipitation and Its Variability 4.3. Implication of Precipitation and Its Variability 4.3.1. Long-Term Precipitation Variation Characteristics 4.3.1. Long-Term Precipitation Variation Characteristics The AP series shows a significantly increased trend during 1979–2015, and the monotonic trends The AP series shows a significantly increased trend during 1979–2015, and the monotonic trends of AP reversed from downwards to upwards gradually over the SRYR from the end of the last century of AP reversed from downwards to upwards gradually over the SRYR from the end of the last century to the beginning of this century. The increase in the MP in May contributes the main changes in AP, to the beginning of this century. The increase in the MP in May contributes the main changes in AP, and May should be the start of the wet season, instead of the traditional season between June–September. and May should be the start of the wet season, instead of the traditional season between June– May has a great share of AP, it accounts for about 11.6%, while the other months in the dry season September. May has a great share of AP, it accounts for about 11.6%, while the other months in the accounted for no more than 6.5%; during 1979–2015, the proportion of MP in May is comparable dry season accounted for no more than 6.5%; during 1979–2015, the proportion of MP in May is to that of MP during June–September, which ranges from 15.3% to 20.6% (see Figure5). Moreover, comparable to that of MP during June–September, which ranges from 15.3% to 20.6% (see Figure 5). the magnitude of LMDI in May is much less than that in other months in the dry season, the value is Moreover, the magnitude of LMDI in May is much less than that in other months in the dry season, around 0.1 during May–September, and in the other months, all are above 0.2 (see Figure3). That is to the value is around 0.1 during May–September, and in the other months, all are above 0.2 (see Figure say that, during the study period, the MP in May, as well as its variability, is close to the value of the 3). That is to say that, during the study period, the MP in May, as well as its variability, is close to the traditional wet season, thus May should be classified as a wet season. MP in May is the only month in value of the traditional wet season, thus May should be classified as a wet season. MP in May is the the wet season in sync with AP and the significantly increasing trend during 1979–2015 on the basin only month in the wet season in sync with AP and the significantly increasing trend during 1979– scale, according to the M–K test (see Figure5). Additionally, the spatial distribution of LMDI in May is 2015 on the basin scale, according to the M–K test (see Figure 5). Additionally, the spatial distribution conformed to that of AP, dividing the basin into two halves based on a value, which for MP in May is of LMDI in May is conformed to that of AP, dividing the basin into two halves based on a value, 0.1m within the range 0.03–0.29 and for AP is 0.02, within 0.01–0.10, with NW over the value and SE which for MP in May is 0.1m within the range 0.03–0.29 and for AP is 0.02, within 0.01–0.10, with NW under it (see Figure 11). Overall, the wet season begins from May to September over the SRYR during over the value and SE under it (see Figure 11). Overall, the wet season begins from May to September 1979–2015, and the changes in AP series mainly attributes to the variation in May. over the SRYR during 1979–2015, and the changes in AP series mainly attributes to the variation in May.

Water 2020, 12, 2486 15 of 20 Water 2020, 12, x 15 of 20

Figure 11. 11. SpatialSpatial distribution distribution of LMDI of LMDI for AP for (a ) AP and (a MP) and in May MP (b in) during May ( 1979–2015,b) during with 1979 a–2015, dividing with line. a dividing line. LMDI of the AP series indicated an unevenly distributed hydrologic budget over the SRYR, and theLMDI changes of the in AP the series Northern indicated edge an and unevenly the summit distributed M are more hydrologic concentrated budget and over prominent the SRYR, on and an annualthe changes basis, in see the Figure Northern4. There edge are and high the LMDI summit regions M coveringare more withconcentrated a significantly and prominent increasing trend.on an Theannual overlap basis, region see Figure means 4. onThere the oneare handhigh LMDI that it regions has a non-uniformed covering with moisturea significant supplyly increasing annually, andtrend. on The the other, overlap the regioncasual inputmeans of on precipitation the one hand generally that becameit has a abundantnon-uniformed in amount. moisture That is supply to say, theannually, long-term and precipitationon the other, in the the casual most NWinput area of precipitation is both scarce generally in amount became and sparse abundant in distribution in amount. on anThat annual is to say, time the scale. long The-term summit precipitation M neighborhood in the most is aNW typical area overlap is both area,scarce which in amount is involved and sparse in the waterin distribution circle during on an the annual last two time decades, scale. The by summit disturbing M neighborhood the original stair-step is a typical shape overlap in Figure area,9. which is involveThe variationd in the water of DAP circle among during decades the last indicates two decades, that the by nature disturbing of precipitation the original has stair been-step disturbed shape andin Figure affected 9. by global climate change during the study period. Warming is a key feature of the globalThe climate variation change of DAPin the among Tibetan decades Plateau. indicates For the unique that the permafrost nature of ecosystem precipitation in the hasSRYR, been soildisturbed freezing and and affected thawing by global is highly climate depend change on temperature,during the stu thusdy period the region. Warming is very is vulnerablea key feature to warming.of the global The climate freeze-thaw change process in the Tibetan in the SRYR Plateau. has For drawn the unique lots of attentionpermafrost worldwide ecosystem [25 in]. the Thawing SRYR, ofsoil soil freezing is accompanied and thawing with is moisture highly depend transfer on and temperature, heat exchange, thus therefore the region releasing is very watervulnerable into the to dynamicwarming. hydrologic The freeze- cycle.thaw process The regional in the meanSRYR temperaturehas drawn lots of of the attention SRYR is worldwide2.5 ◦C, and [25 the]. Thawing climate 1 − inclinationof soil is accompanied rate was 6.7 with◦C (100a) moisture− during trans 1979–2015.fer and heat The exchange, whole region therefore shows releas a temperature-raisinging water into the trend,dynamic and hydrologic except for cycle the small. The arearegional in the mean NW temperature corner, it is significantof the SRYR during is −2.5 this °C,period, and the which climate is showninclination in Figure rate was 12a. 6.7 The °C regional (100a)−1 meanduring temperature 1979–2015. isThe above whole 0 ◦ Cregion during shows May–September, a temperature according-raising totrend, the distributionand except for ofthe the average small area value in ofthe monthly NW corner, temperatures it is significant in Figure during 12b, andthis theperi raisingod, which trend is isshown significant in Figure every 12a month. The regional during mean the period. temperature Warming is above and 0 human °C during construction May–September, is threatening according the glaciersto the distribution and permafrost, of the the average water value used toof bemonthly on hold temperature in ice was thoughts in Figure to be 12b now, and releasing the raising gradually trend intois significant the local every hydrological month during cycle. the Another period. impact Warming of rising and human temperatures construction lies in is the threatening precipitation the transformation.glaciers and permafrost, Due to the the low water temperature used to be andon hold dramatic in ice dailywas thought temperature to be dinowfferences, releasing precipitation gradually into the local hydrological cycle. Another impact of rising temperatures lies in the precipitation transformation. Due to the low temperature and dramatic daily temperature differences,

Water 2020, 12, 2486 16 of 20 Water 2020, 12, x 16 of 20 isprecipitation mostly in the is most formly of in hailstorms, the form of and hailstorm warmings, and helps warming in solid-to-liquid helps in solid changes.-to-liquid Thus chang physicales. Thus state changesphysical relatedstate change to warmings related is to another warming reason is another for the highreason LMDI. for the high LMDI.

(a) Spatial distribution of annual temperature

(b) Regional mean monthly temperature

Figure 12. The average annual ( a) and monthly ( b) air temperature and the M–KM–K test statistic during 1979–20151979–2015 inin thethe SRYR.SRYR.

The reason for the variation in precipitation could also be drawn from the spatial and temporal distribution of inter-annualinter-annual amounts amounts andand variability. variability. Given Given that that the the main moisture source of precipitation is is th thee summer summer monsoon, monsoon, the the big big leap leap in inminimum minimum DAP DAP of 71 of mm 71 mm at the at h theeadwater headwater NW NWcorne cornerr between between the decadesthe decades before before and and after after 1997 1997 in inFigure Figure 99 implies implies that that moisture was was further further transmitted.transmitted. There were three regions concentrated with a significant significant increasing trend over the SRYR at two stages after 1997, the central and upper regions during 1997–20061997–2006 in Figure9 9c,c, andand thethe lowerlower SE region around the inlet ofof thethe summersummer monsoonmonsoon duringduring thethe lastlast decadedecade inin FigureFigure9 9d.d. FromFrom thethe perspective of a summer monsoon, the increasing trend in the central and upper regions supported the monsoon enhancement firstfirst and then the increaseincrease in the lower region forecasts the enhancement persistence. From thethe perspectiveperspective of of the the freeze-thaw freeze-thaw process, process, the the central central and and upper upper regions regions including including the summitthe summit M are M the are permafrost the permafrost areas, and areas, the andlower the region lower is the region seasonal is the frozen seasonal area, frozenboth concentrated area, both withconcentrated the effects with of thaws.the effects Thus of thethaws. water Thus vapor the couldwater bevapor from could the release be from of the the release freeze-thaw of the process. freeze- Maythaw contributesprocess. May the contributes main changes the inmai then increasechanges ofin AP.the Zhang,increase et of al. AP. [26 ]Zhang, uncovered et al. that[26]the uncovered wetting trendthat the over wetting the TP trend in May over has the resulted TP in May directly has result fromed the directly earlier from onset the of theearlier South onset Asian of the summer South monsoonAsian summer since monsoonthe late 1970s since and the is late associated 1970s and with is associated the phase withtransition the phase of Inter transiti decadalon of Pacific Inter Oscillationdecadal Pacific around Oscillation the late around 1990s, the and late that 1990s, the South and that Asian the South summer Asian monsoon summer explains monsoon 95% explains of the increase95% of the in increase the total in amount the total of precipitationamount of precipitation in May. The in results May. The in this results study in support this study this support conclusion. this Highconclusion. LMDI High for MP LMDI in May for MP is in in the May NW is part,in the and NW May part, has and three May regions has three with regions significant with significant increasing trends—theincreasing trend SE corner,s—the theSE Middlecorner, the region Middle and NWregion corner, and NW in Figure corner,6c. in According Figure 6c to. According the route ofto thethe summerroute of the monsoon summer in monsoon the SRYR, in thesethe SRYR regions, these could regions represent could represent the inlet, the barriers inlet, andbarriers hard-to-reach and hard- to-reach destinations. As is well-known, summer monsoons have a lower entrance in the SE corner, and mainly travel along the south edge before the rising high altitude block their way, and then climb

Water 2020, 12, 2486 17 of 20 destinations. As is well-known, summer monsoons have a lower entrance in the SE corner, and mainly travelWater 20 along20, 12, x the south edge before the rising high altitude block their way, and then climb up17 and of 20 spread out while losing moisture [27]. That is to say, the increasing precipitation in May could hint at theup earlyand spread onset ofout a while summer losing monsoon. moisture [27]. That is to say, the increasing precipitation in May could hint at the early onset of a summer monsoon. 4.3.2. Throughout-the-Year Moisture Supply 4.3.2. Throughout-the-Year Moisture Supply The AMDI calculates the uniformity of the apportionment of AP and reflects the moisture persistenceThe A withinMDI calculates a year at the a fixed uniformity location. of High the apportionment AMDI indicates of an AP unsustainable and reflects water the moisture supply, whilepersistence low AMDI within indicates a year at a relativelya fixed location. more stable High moisture AMDI indicates supply. The an unsustainable origin of precipitation water supply, could bewhile water low vapor AMDI transportation indicates a relatively and local more evapotranspiration, stable moisture and supply thus. theThe supply origin couldof precipitation be from outside could orbe fromwater a local vapor cycle. transport Figureation7 displays and local the evapotranspiration distribution of AMDI, and and thus the the variation supply trend; could for be easy from interpretation,outside or from the a informationlocal cycle. Figure is combined 7 displays with the a land distribution cover map of inAMDI Figure and 13 the. Extensive variation di trendfferences; for existeasy among interpretation, the distinctive the information underlying is surfaces, combined and with three a regionsland cover disturb map the in continuity Figure 13. of Extensive contour lines,differences due to exist a relatively among low the AMDI distinctive compared underlying with the surface neighborhood,s, and three marked regions with disturba, b and thec .continu Regionitya isof in contour the Maduo lines, country due to a [ 28relatively], which low has theAMDI nickname compared “thousand-lakes with the neighborhood, country”, withmarked one with third a of, b theand area c. Region being wetland;a is in the Region Maduob iscountry around [28 the], which summit has M, the the nickname highest point “thous inand the-lake basin,s country covered”, withwith permanentone third of snow the area and being glaciers; wetland Region; Regionc is the b is Zoige around Plateau the summit Wetland, M, the the mainhighest grazing point place.in the Regionbasin, covera anded Region with cpermanentare both covered snow and with glaciers wetland;; Region abundant c is waterthe Zoige reserves Plateau and Wetland, evaporation the helpsmain ingrazing the supply place. and Region offers a aand low Region AMDI. c Regionare bothb usedcover toed be with scarcely wetland involved; abundant in the water local reserve exchanges and of waterevaporation and energy, helps but in the it was supply slightly and interruptedoffers a lowby AMDI the active. Region hydrological b used to be cycle, scarcely which involved could be in thethe explanationlocal exchange for itsof water low AMDI. and energy, but it was slightly interrupted by the active hydrological cycle, which could be the explanation for its low AMDI.

Figure 13. Land cover map combined with the information in Figure 7, the isolines of the mean value Figure 13. Land cover map combined with the information in Figure7, the isolines of the mean value of of AMDI during 1979–2015 and the areas with AMDI significant trends over the SRYR, and three AMDI during 1979–2015 and the areas with AMDI significant trends over the SRYR, and three regions regions with typical underlying surface, marked with a, b and c. with typical underlying surface, marked with a, b and c.

ToTo betterbetter understandunderstand thethe variationvariation ofof AMDI,AMDI, especiallyespecially thethe fourfour regionsregions withwith significantsignificant trendstrends duringduring 1979–2015, 1979–2015, local local environment environment should should be be involved. involved. Firstly, Firstly, the the Zoige Zoige Plateau Plateau Wetland Wetland is the is only the regiononly region located locate in thed in SE the part, SE with part the, with largest the largest increasing increasing area among area theamong four. the It isfour. the mostIt is the famous most grazingfamous placegrazing over place the SRYR,over the since SRYR, its lower since altitude its lower makes altitude it easier makes to accessit easier and to warmeraccess and to protectwarmer the to animalsprotect inthe the animals cold dry in season.the cold However, dry season. it is However, suffering from it is asuffering continuous from shrinking a continuous problem shrinking related toproblem over-grazing related andto over rodent-grazing damage, and rodent as well damage, as climate as well change as climate [29]. The change degradation [29]. The could degradation be the reasoncould thatbe the there reason is damage that there in the is sustainable damage in water the sustainable supply, which water is supportedsupply, whic by Figuresh is supported9c and 10 byc duringFigures 1997–2006, 9c and 10c when during the 1997 DAP–2006, did notwhen significantly the DAP did vary not and significantly the DAMDI var hady and an increasingthe DAMDI trend. had an increasing trend. Secondly, the summit M neighborhood has a decreasing trend, which means that the supply tends to be perennial. Considering the altitude, a monsoon could barely disturb the water income in this region. The water transformed from a solid state is more likely to be the main source of the local cycle, and the low and raising temperature could guarantee that the supply would be slow and stable. DAP increases during 1997–2006 in Figure 9c, and the decreasing trend in DAMDI,

Water 2020, 12, 2486 18 of 20

Secondly, the summit M neighborhood has a decreasing trend, which means that the supply tends to be perennial. Considering the altitude, a monsoon could barely disturb the water income in this region. The water transformed from a solid state is more likely to be the main source of the local cycle, and the low and raising temperature could guarantee that the supply would be slow and stable. DAP increases during 1997–2006 in Figure9c, and the decreasing trend in DAMDI, appears afterwards in Figure 10d, when temperatures are higher. Thirdly, the decreasing trend in the headwater NW corner could be a mixed result of more water transfer from the summer monsoon and snow and permafrost thaws, together with warming, giving a more perennial supply. This deduction could be supported with the increasing DAP in Figure9c and the decreasing DAMDI in Figure 10c during 1997–2006 over the corner. Lastly, the region between the headwater NW corner and the summit M is part of the North Slope in the Bayan Har Mountain, which could most easily be influenced by the enhanced southwest monsoon, thus resulting in a more concentrated supply. The scale jumps in DAP between Figure9c,d, meanwhile DAMDI generally remainsing over the region could serve as a proof. Another noticeable point in the DAP and DAMDI from the last decade is the SE wetlands at the neighborhood of Grid 46, where DAP increases and DAMDI decreases. This means that the local water supply tends to be perennial under the condition of wetting. This could be the joint effect of global climate change and ecological and environmental protection directed by the government. It is near the inlet of a summer monsoon, and is downstream of the mountainous regions, and thus more water vapor would be from enhanced monsoon and runoff due to the freeze-thaw process. If the increase is mainly contributed by monsoon, there would be a bigger DAMDI for temporal supply. Runoff could offer a relatively long-lasting supply of water only if the underlying surface has the storage capacity. Due to long-term over-grazing, the wetlands in the SRYR have experienced a severe shrinking period, as herd livestock is the dominating economic activity for local residents. The number of sheep has reduced by 71.7% since 1990 in the Maduo country, and large-scale ecological immigration has been implemented by the government [30]. This fact offers us some inspiration for how to deal with the impact of global environmental change.

5. Conclusions In order to investigate the spatio-temporal distribution of variability of long-term and intra-annual precipitation, the marginal disorder index based on entropy theory was calculated respectively for annual, monthly and daily series. The reasons for variation of precipitation and its apportionment variability were analyzed, and the main conclusion were as follows: (1) The AP series shows a significantly increasing trend during 1979–2015 measured by the M–K test and the inclination rate is 2.7 mm a 1, with a reverse in climate trend from warm-dry · − to warm-wet. Wetting is mainly attributed to the growing impact of global climate change, in particular the enhanced southwest monsoon and a warming-induced freeze-thaw process, with summer monsoons making the biggest contribution. (2) The arrival of the summer monsoon was advanced, which makes May the beginning of the wet season, and the increase in the MP in May contributes to the main changes in AP. There are four quantitative pieces of evidence to support this view. The proportion of MP in AP during May–September ranges between 11.6–20.6%, while in the other months it is no higher than 6.5%; the average LMDI during May–September is about 0.1, the other months are all above 0.2; the MP in May is the only month during May–September in sync with the significantly incrasing AP trend during 1979–2015; the spatial distribution of LMDI in May is conformed with that of the AP, dividing the basin in half based on a value, which for MP in May is 0.1 within the range 0.03–0.29 and for AP is 0.02 within 0.01–0.10, with NW over the value and SE under it. (3) The variability of the throughout-the-year precipitation apportionment based on daily precipitation is measured by AMDI. The long-term AMDI time series ranges between 1.52–1.93 during 1979–2015, and no significant trend was detected during 1979–2006. The multi-year average AMDI roughly increased with latitude in space, with a range of 1.46–2.17. The Zoige Water 2020, 12, 2486 19 of 20

Plateau Wetland (wetlands on the SE), the Maduo country (wetlands on the West) and the summit M (peak of the SRYR) is more uniform than the neighborhood by about 0.1 in AMDI, as a result of a relatively perennial local water supply. (4) The increase in precipitation amounts were concentrated in the period after 1997, especially in the decade of 1997–2006, according to a segmented study. During 1979–2006, the mean, minimum and maximum regional averages of AP reached their biggest rising rate, as 9.8 mm a 1, · − 12.0 mm a 1 and 15.3 mm a 1, respectively. The big increase in the minimum is a remarkable · − · − feature in wetting. Meanwhile, the intra-annual apportionment variability slightly increased in 1 1 the mean and the maximum, and decreased in the minimum, the rate is 0.008 a− , 0.009 a− and 0.003 a 1, successively. − − (5) From a spatial distribution perspective, the increase in AP after 1997 was concentrated on the NW high-altitude areas first and then the lower southern corner. AP in the summit M changed from 390 mm to 680 mm during 1997–2006, and the southern corner was raised by about 50 mm in AP during the last decade. The degradation problem drove the moisture supply on the Zoige Plateau Wetland towards non-uniformity mainly during 1997–2006, when its AMDI raised from 1.4 to 1.7; the supply on the summit M and the headwater NW corner varied towards perennial with the AMDI dropping from 1.8/2.0 to 1.5/1.8, respectively, and part of the North Slope in the Bayan Har Mountain towards temporary, as the AMDI increased from 1.4 to 1.6, due to the single or combined effect of enhanced monsoon and/or a freeze-thaw process after 1997.

Author Contributions: Conceptualization, H.G.; data curation, H.G., Z.Y. and J.L.; formal analysis, H.G.; funding acquisition, Z.Y., G.L. and X.F.; investigation, H.G. and Q.J.; methodology, H.G.; project administration, Z.Y.; resources, Z.Y., Q.J. and Y.H.; software, H.G. and J.L.; supervision, G.L.; validation, Y.H.; visualization, H.G.; writing—review and editing, H.G. All authors have read and agreed to the published version of the manuscript. Funding: This work was supported by the National Key R&D Program of China (Grant Nos. 2018YFC1508205, 2016YFC0402710, 2018YFC1508001); the National Natural Science Foundation of China (Grant Nos. 51479061, 51539003, 41761134090, 51709046); National Science Funds for Creative Research Groups of China (No. 51421006) and the Special Fund of State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering (Grant No. 20185043812, 20185044012). Conflicts of Interest: The authors declare no conflict of interest.

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