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’s highest 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.