entropy
Article Spatio-Temporal Evolution Analysis of Drought Based on Cloud Transformation Algorithm over Northern Anhui Province
Xia Bai 1,2, Yimin Wang 1,*, Juliang Jin 3, Shaowei Ning 3, Yanfang Wang 2 and Chengguo Wu 3 1 State Key Laboratory of Eco-Hydraulics in Northwest Arid Region, Xi’an University of Technology, Xi’an 710048, China; [email protected] 2 School of Civil and Hydraulic Engineering, Bengbu University, Bengbu 233030, China; [email protected] 3 School of Civil Engineering, Hefei University of Technology, Hefei 230009, China; [email protected] (J.J.); [email protected] (S.N.); [email protected] (C.W.) * Correspondence: [email protected]; Tel.: +86-13679279030
Received: 31 October 2019; Accepted: 13 January 2020; Published: 16 January 2020
Abstract: Drought is one of the most typical and serious natural disasters, which occurs frequently in most of mainland China, and it is crucial to explore the evolution characteristics of drought for developing effective schemes and strategies of drought disaster risk management. Based on the application of Cloud theory in the drought evolution research field, the cloud transformation algorithm, and the conception zooming coupling model was proposed to re-fit the distribution pattern of SPI instead of the Pearson-III distribution. Then the spatio-temporal evolution features of drought were further summarized utilizing the cloud characteristics, average, entropy, and hyper-entropy. Lastly, the application results in Northern Anhui province revealed that the drought condition was the most serious during the period from 1957 to 1970 with the SPI12 index in 49 months being less than 0.5 and 12 months with an extreme drought level. The overall drought intensity varied with − the highest certainty level but lowest stability level in winter, but this was opposite in the summer. Moreover, drought hazard would be more significantly intensified along the elevation of latitude in Northern Anhui province. The overall drought hazard in Suzhou and Huaibei were the most serious, which is followed by Bozhou, Bengbu, and Fuyang. Drought intensity in Huainan was the lightest. The exploration results of drought evolution analysis were reasonable and reliable, which would supply an effective decision-making basis for establishing drought risk management strategies.
Keywords: drought evolution analysis; uncertainty; entropy; cloud transformation algorithm; conceptual zooming; Northern Anhui province
1. Introduction Drought is an extreme climate event. The conceptual definition of drought mainly focuses on the essential characteristics of a drought process while the descriptive definition of drought is primarily linked with the occurrence, recognition, and evolution of the drought event [1]. Overall, drought can be defined as a random environmental disaster and is mainly characterized with a water deficit, which has a critical and far-reaching impact on agriculture, social economy, and ecosystem, and has attracted more attention from meteorologists and hydrologists [1,2]. In recent years, with the influence of global climate change, extreme climate events occur more frequently, and the frequency and intensity of drought also present an evident increasing trend [1–3]. Spatio-temporal evolution characteristics of drought is a primary factor that leads to the disequilibrium distribution of regional water resources availability, which will, conversely, have a great impact on regional water resources development, utilization, and an ecological environment [2,4–6]. Therefore, the understanding of spatio-temporal
Entropy 2020, 22, 106; doi:10.3390/e22010106 www.mdpi.com/journal/entropy Entropy 2020, 22, 106 2 of 15 distribution characteristics of drought is of significant importance for exploring the evolution features of drought and then establishing feasible and effective drought disaster regulation strategies. To date, the most widely-applied research method of drought evolution trend mainly focuses on the stochastic process and statistical related theory. Drought evolution characteristics is usually described by various indicators [4,6–9], and plenty of research and investigation involving the causing factors, distribution, and evolution features of drought from the perspective of hydrological, meteorological, and remote sensing have been carried out around the world. For instance, T. B. McKee et al. (1993) proposed a Standard Precipitation Index (SPI) to describe the variation characteristics of drought and flood disasters from different time scales [10]. Y. Zhang et al. (2008) discussed drought and flood variation characteristics during the pre-flood season by the mathematical statistics method based on the daily precipitation data from 1958 to 2004 in Huanan Station [11]. W. H. Huang et al. (2010) analyzed the ratio of the station number with drought to the total station number from annual and seasonal scales based on a calculated SPI value, which revealed that the impact of drought on agricultural production would be more serious in Southern China [12]. Y. L. Ren et al. (2013) analyzed drought evolution characteristics based on SPI from a monthly scale using the monthly precipitation data from 1961 to 2009 from 137 hydrological stations in Northwest China [13]. Based on the above, it can be seen that an existing drought indicator can be effectively applied to describe drought evolution features from a specific perspective. However, how to construct a comprehensive drought indicator to capture the hydrologic and meteorological uncertainties is still a challenge for drought risk assessment research [14,15]. Moreover, the key of exploration of drought variation characteristics can be focused on the recognition and quantification of uncertainties throughout the drought evolution process by an integrated drought indicator. Cloud model related theory, as a reliable tool of mathematical transformation from conceptual qualitative description to its quantitative computation, has been widely applied in many fields, including image recognition, intelligent modeling, big data analysis, and more [16,17]. Concerning complicated uncertainties throughout the drought variation process and the systematic analysis approaches themselves, the primary motivation of this manuscript is to explore the spatio-temporal evolution characteristics of drought by transforming the calculated SPI series data into qualitative concepts of Gaussian cloud distribution, and then realizing the soft division of drought grade conceptual clouds through the Cloud Transformation Algorithm (CTA) and the Conception Zooming method. Ultimately, the proposed approach was applied in the case study analysis in the Anhui province of China to testify its reliability and effectiveness, and can be further extended to provide a new research idea of the drought process analysis.
2. Introduction of Drought in Northern Anhui Province As indicated in Figure1, the Northern Anhui province, located in the hinterland of East China and North of Huai River with longitude between 114◦580 and 18◦100 and latitude between 32◦450 and 34◦350, has jurisdiction over six cities including Suzhou, Bozhou and Bengbu and 17 counties including Dangshan, Lingbi, and Huaiyuan. The Northern Anhui province is mainly plain with a total area of 36,694 km2, a natural slope between 0.13% and 0.83%, and an average altitude between 20 m and 40 m. In addition, the Northern Anhui province is located in the transition zone between the north subtropical humid climate and half of the moist monsoon climate. The annual average precipitation is between 770 mm to 950 mm, but varies significantly both from spatial and temporal scales, which presents an increasing trend from north to south. Moreover, the annual average precipitation during the flood season from June to September accounts for 70% to the total mainly with the form of rainstorm, which is beneficial for the occurrence of waterlogging in the flood season and drought in the non-flood season. Water shortage is also serious in the North Anhui province with the annual average water resources availability of 12.87 billion m3, which is half of the provincial level and even below 0.75 of the average national level. Compared with the surface water resources availability, the ground water resources are abundant, and the ratio for surface and ground water resources is approaching 1: 1 in the North Anhui province. Entropy 2020, 22, 106 3 of 15 Entropy 2020, 22, x FOR PEER REVIEW 3 of 15
FigureFigure 1.1.Geographical Geographical locationlocation ofof thethe NorthernNorthern AnhuiAnhui provinceprovince in in China. China.
ForFor thethe dualdual influencesinfluences ofof precipitationprecipitation andand geomorphicgeomorphic factors,factors, thethe NorthernNorthern AnhuiAnhui provinceprovince isis oneone ofof thethe mostmost vulnerablevulnerable areasareas susufferingffering fromfrom drought-relateddrought-related disasters, disasters, according according to to thethe historicalhistorical statisticsstatistics andand nationalnational standardstandard ofof meteorologicalmeteorological droughtdrought classificationclassification criteriacriteria [[5,6].5,6]. AA totaltotal ofof 109109 droughtsdroughts occurredoccurred duringduring 500500 yearsyears fromfrom 14501450 toto 19491949 withwith anan occurringoccurring frequencyfrequency ofof aboutabout 44 years,years, andand anotheranother 3636 autumnautumn droughtsdroughts occurred during 64 years after after the the foundation foundation of of PRC, PRC, in in which which 5 5years years had extremeextreme droughts droughts and and 14 years14 years had extraordinaryhad extraordinary droughts. droughts. Furthermore, Furthermore, drought durationdrought induration Northern in Northern Anhui province Anhui isprovince long, and is long, frequently and frequently follows with follows waterlogging. with waterlogging. Thus, it isThus, evident it is thatevident drought that drought is the most is the common most common and heavily and damagedheavily damaged natural disastersnatural disasters in the Northern in the Northern Anhui province,Anhui province, and drought and evolution drought characteristicevolution characteristic analysis is urgent analysis and fundamentalis urgent and for fundamental carrying out risk for comprehensivecarrying out risk management comprehensive of drought management disaster. of drought disaster. 3. Methodologies 3. Methodologies 3.1. Standardized Precipitation Index (SPI) 3.1. Standardized Precipitation Index (SPI) The drought indicator is an effective tool to explore the variation characteristics of the drought The drought indicator is an effective tool to explore the variation characteristics of the drought evolution process, which is also a crucial tool to measure the influence of drought to a regional evolution process, which is also a crucial tool to measure the influence of drought to a regional socio- socio-economic system [18]. The Standardized Precipitation Index (SPI) is a typical meteorological economic system [18]. The Standardized Precipitation Index (SPI) is a typical meteorological drought drought indicator, which has an ability to reveal statistical distribution rules of precipitation by indicator, which has an ability to reveal statistical distribution rules of precipitation by meteorological meteorological theory, and then derive the magnitude, intensity, and duration of the drought theory, and then derive the magnitude, intensity, and duration of the drought process [18,19]. The process [18,19]. The SPI was initially proposed and applied to evaluate the drought evolution SPI was initially proposed and applied to evaluate the drought evolution in Colorado State by Mckee in Colorado State by Mckee in 2002 [10,20], and now is accepted by the World Meteorological in 2002 [10,20], and now is accepted by the World Meteorological Organization as the reference Organizationdrought index as for the effective reference drought drought monitoring index for and effective evaluation drought [21]. monitoring The SPI computation and evaluation is done [21 by]. Thefitting SPI historical computation precipitation is done by data fitting to historical a Gamma precipitation probability data distribution to a Gamma function probability for a specific distribution time functionperiod and for location. a specific The time detailed period calculation and location. procedures The detailed of SPI calculation can be described procedures as follows of SPI [21,22]. can be describedStep as1: followsSuppose [21 ,the22]. precipitation data series of a specific time period satisfies Gamma distribution.Step 1: Suppose Then its the probability precipitation distribution data series function of a specific can be time denoted period as satisfies Equation Gamma (1). distribution. Then its probability distribution function can be denoted as Equation (1). −x 1 α − gx()= x1 e β βαα Γ (1) 1 ()α 1 x/β g(x) = x − e − (1) βαΓ(α) where α and β are the shape and scale parameters, respectively, which satisfy α > 0 and β > 0, and usually can be estimated using the maximum likelihood method, as follows. 1 α=(114/3)++A (2) 4A
Entropy 2020, 22, 106 4 of 15 where α and β are the shape and scale parameters, respectively, which satisfy α > 0 and β > 0, and usually can be estimated using the maximum likelihood method, as follows.
1 p α = (1 + 1 + 4A/3) (2) 4A
β = x/α (3) Pn ln(xi) i=1 A= ln(x) (4) − n where parameter n and x are the length and average of precipitation data series, respectively. Based on the parameter calibration, the cumulative possibility of precipitation x not exceeding a specific value x0 in a given time scale can be determined as follows.
Z x Z x 1 αˆ 1 x/βˆ G(x x ) = g(x)dx = x e − dx (5) < 0 αˆ − 0 0 β Γ(αˆ)
Step 2: the definition in Equation (5) is not valid when precipitation x equals 0. Thus, the cumulative possibility G(x < x0) should be modified as follows.
H(x) = q + (1 q) G(x) (6) − · where q is the possibility when precipitation x equals 0, which can be obtained by q = m/n, and parameter m is the sample number with precipitation x equal to 0. Step 3: Normal standardization processing. Through numerical integration computation, the calculated cumulative probability H(x) can be transformed to a standard normal distribution to yield SPI, which can be denoted as follows [22,23].
2 c0+c1 t+c2 t · 2 · 3 (0 3.2. Forward Normal Cloud Algorithm (FNCA) Proposed by Chinese scholar D. Y. Li, the Cloud model is an effective mathematical cognitive tool to describe the transforming mechanism of uncertainty from a qualitative concept to its corresponding quantitative expression utilizing three parameters including average, entropy, and hyper-entropy [16]. The mathematical definition of cloud drop and its certainty degree can be explained as follows [16,24]. Suppose U is a universal set denoted by precise data, and C is the qualitative concept related to U. If randomly generated data x (x U) is related to concept C, then the membership degree of ∈ random data x belonging to concept C is named as a certainty degree [16,24]. Specifically, let C(Ex, En, He) be a qualitative concept C related to precise set U and described by average Ex, entropy En, and hyper-entropy He in which average Ex denotes the most representative sample data of concept C, and can be adopted to reveal the concentration condition of samples. Entropy En is related to the uncertainty of sample distribution and reflects both the random dispersing degree of cloud drops and acceptable range of concept C. Hyper-entropy He is the uncertainty degree of entropy, which reflects the concentration condition of samples under a certain deviation condition [16]. Thereby, if the distribution of variable x satisfies x N(Ex, En 2) and En0 N(En, He2), then the distribution of variable ∈ 0 ∈ Entropy 2020, 22, 106 5 of 15 Entropy 2020, 22, x FOR PEER REVIEW 5 of 15 x within set U is defined as one-dimensional normal cloud, and data point [x0, µ0(x)] is defined as the C Ex En clouddefined drop as the [16 cloud,24]. Figure drop [16,24].2 illustrates Figure the 2 distributionillustrates the of distribution cloud , which of cloud satisfies C, which= satisfies1.5, = Ex0.5, = He and1.5, En == 0.5,0.1. and He = 0.1. Figure 2. Distribution of a qualitative concept cloud C(1.5, 0.5, 0.1). In practice,practice, thethe most most widely widely applied applied form form of Cloudof Cloud theory theory are forwardare forward and backwardand backward normal normal cloud algorithms.cloud algorithms. The forward The forward normal normal cloud algorithm cloud algori (FNCA)thm explores(FNCA) theexplores sample the distribution sample distribution basing on determinedbasing on determined cloud characteristic cloud characteristic parameters Ex parameters, En, and He Ex, while, En, theand backward He, while normal the backward cloud algorithm normal (BNCA)cloud algorithm is opposite, (BNCA) which is is opposite primarily, which applied is primarily to estimate applied the cloud to estimate characteristic the cloud parameters characteristicEx, En, andparametersHe in terms Ex, ofEn a, statisticaland He in perspective terms of a [ 16statistical,25]. The perspective procedure of [16,25]. one-dimensional The procedure FNCA of can one- be describeddimensional as follows.FNCA can be described as follows. 2 2 StepStep 1: randomly randomly generate generate no normallyrmally distributed distributed variable variable EnEn′0,, which which satisfies satisfies EnEn′0~~NN(En(En, ,HeHe).). 2 2 StepStep 2: randomly randomly generate generate no normallyrmally distributed distributed variable variable xxii,, which which satisfies satisfies xx~~NN((ExEx, ,EnEn′0).). StepStep 3: calculate thethe certaintycertainty degreedegreeµ μof of data datax xbelonging belonging to to the the concept conceptC throughC through Equation Equation (9). (9). (x Ex)2 2 µ= exp()xEx−− (9) μ − 2 = exp -2(En0)2 (9) 2(En ') Step 4: repeat step 1 to step 3 until generating N cloud drops, and then the cloud distribution of conceptStepC 4:can repeat be obtained. step 1 to step 3 until generating N cloud drops, and then the cloud distribution of concept C can be obtained. 3.3. Cloud Transformation Algorithm (CTA) and Conception Zooming 3.3. Cloud Transformation Algorithm (CTA) and Conception Zooming The precondition for the application of BNCA and FNCA assumes all given samples belong to one specificThe precondition qualitative for concept, the application which will of restrictBNCA theand explorationFNCA assumes of more all given possible samples properties belong and to knowledgeone specific relatedqualitative to the concept, sample which distribution will restri [16ct]. the It has exploration been testified of more that possible the curve properties fitting error and canknowledge be reduced related clearly to the by sample dividing distribution the overall [16]. probability It has been density testified function that the into curve the fitting combination error can of severalbe reduced normal clearly distributions by dividing [16 the,17 overall]. The probability cloud transformation density function algorithm into the (CTA), combination as an effective of several tool ofnormal probability distributions statistical [16,17]. analysis, The is cloud capable transformation of transforming algorithm overall probability (CTA), as densityan effective function tool into of theprobability integration statistical of multiple analysis, Gaussian is capable cloud of distribution,transforming which overall can probability be applied density for the function generation into and the divisionintegration of aof complicated multiple Gaussian concept cloud [16,17 distribution,,26]. CTA can which be interpreted can be applied as the for exploration the generation of concept and attributesdivision of from a complicated its actual sampleconcept distribution [16,17,26]. CTA in a morecan be refined interpreted scale [as26 ].the In exploration other words, of theconcept data sampleattributes with from higher its actual frequency sample will distribution also have a higher in a more contribution refined toscale the [26]. qualitative In other concept. words, Therefore, the data thesample local with maximum higher of datafrequency frequency will distributionalso have cana hi begher regarded contribution as the center to the of aqualitative qualitative concept. concept (expectationTherefore, the value local of maximum concept cloud). of data Then, frequency we substract distribution the corresponding can be regarded sample as the in thecenter original of a samplequalitative distribution concept and(expectation calculate value the next of localconcep maximum.t cloud). Then, Lastly, we we substract repeat the the above corresponding procedures untilsample the in frequency the original of the sample remained distribution data sample and calculate is below athe specific next local threshold maximum. [17,26]. Lastly, Considering we repeat the droughtthe above evolution procedures process until can the alsofrequency be described of the throughremained SPI, data the sample CTA method is below based a specific on peak threshold theory was[17,26]. introduced Considering in the the drought drought spatio-temporal evolution proces evolutions can researchalso be fielddescribed in this through study [16 SPI,,17]. the CTA methodOne based of the on key peak issues theory when was introduced applying the in CTAthe drought method spatio-temporal for curve fitting evolution is the determination research field in this study [16,17]. of entropy values Eni. After the determination of average Exi, the difference frequency value δ One of the key issues when applying the CTA method for curve fitting is the determination of entropy values Eni. After the determination of average Exi, the difference frequency value δ between Exi and the remaining probability density peak can be obtained, if the difference value δ is larger than the specific threshold μ. Then average data Exi′ with the shortest distance to Exi can be obtained, and Entropy 2020, 22, 106 6 of 15 between Exi and the remaining probability density peak can be obtained, if the difference value δ is larger than the specific threshold µ. Then average data Exi0 with the shortest distance to Exi can be obtained, and the corresponding entropy Eni and hyper-entropy Hei can be determined according to the sample distribution within the interval [Exi-fabs(Exi0-Exi), Exi-fabs(Exi0-Exi)] through the BNCA method [27,28]. In addition, to better fit the probability distribution curve of SPI, the entropy Eni corresponding to a different conceptual cloud also need to be adjusted slightly [28]. Generally, because of not considering the relationship between different cloud distribution patterns, the initial conceptual cloud distribution derived from the CTA method is rough, which might lead to the presentence of a closely distributed cloud pattern or “blank area” [16,17,26]. Thereby, the initial conceptual cloud distribution derived from the CTA method need to be further improved by the zooming process. Conceptual cloud zooming is frequently accomplished by merging the neighboring cloud distribution patterns to simplify the cloud transformation results [16]. Considering the influence of the amplitude coefficient for different conceptual cloud distribution, the two neighboring cloud distribution patterns can be merged based on their intersecting level [29,30]. Suppose the two neighboring cloud distributions can be denoted as C1(Ex1, En1, He1) and C2(Ex2, En2, He2), and their expectation curves intersect at point A(xd, yd). Then the truncation entropy En10 and En20 can be determined as follows [17,29,30]. Z x 1 d 2 2 (x Ex1) /(2En1 ) En10 = r1e− − dx (10) √2π −∞ Z + 2 2 1 ∞ (x Ex2) /(2En2 ) En20 = r2e− − dx (11) √2π xd where r1 and r2 are the amplitude coefficients of cloud distribution C1 and C2, respectively, and the final characteristic values of emerged cloud distribution can be obtained as follows [17,29]. Ex1 En0 + Ex2 En0 Ex = · 1 · 2 (12) 3 + En10 En20 En10 En20 En3 = + (13) r1 r2 He1 En0 + He2 En0 He = · 1 · 2 (14) 3 + En10 En20 Furthermore, the amplitude coefficients r3 of emerged cloud distribution can be obtained as follows. En10 + En20 r3 = (15) En3 3.4. Analysis Framework of this Manuscript The primary innovation of this study is to explore the spatial-temporal distribution features of drought in the Northern Anhui province from seasonal scale through re-fitting the distribution pattern of the SPI index via a cloud transformation algorithm instead of Pearson-III distribution. Thus, in the first section, the approaches applied in this paper were briefly introduced. In the second section, based on the frequency analysis of historical SPI series, the initial cloud characteristic parameters were determined. Then, concerning the similarity of different cloud patterns, the ultimate cloud distribution modes were obtained by conception zooming and merging, which were applied to reveal the spatial-temporal distribution features of drought. Thus, the analyzing framework of this manuscript can be illustrated in Figure3. Entropy 2020, 22, 106 7 of 15 EntropyEntropy 20202020,, 2222,, xx FORFOR PEERPEER REVIEWREVIEW 77 ofof 1515 Figure 3. Framework of drought evolution characteristic analysis of this study. FigureFigure 3.3. FrameworkFramework ofof droughtdrought evolutionevolution characcharacteristicteristic analysisanalysis ofof thisthis study.study. 4. Results and Discussion 4.4. ResultsResults andand DiscussionDiscussion Frequently, the SPI index can be applied to monitor the occurrence of drought, and drought Frequently, the SPI index can be applied to monitor the occurrence of drought, and drought will will resultFrequently, in disaster the SPI when index it occurscan be applied intensively to moni andtor extensively the occurrence in denselyof drought, populated and drought areas will [31 ]. result in disaster when it occurs intensively and extensively in densely populated areas [31]. The Theresult overall in disaster variation when trend it ofoccurs SPI series intensively from one-month,and extensively three-month, in densely and populated 12-month areas time [31]. scales The for overall variation trend of SPI series from one-month, three-month, and 12-month time scales for the theoverall Northern variation Anhui trend province of SPI through series from 1957 one-mont to 2010 wash, three-month, illustrated inand Figure 12-month4. time scales for the NorthernNorthern AnhuiAnhui provinceprovince throughthrough 19571957 toto 20102010 waswas illustratedillustrated inin FigureFigure 4.4. 44 SPI1SPI1 SPI3SPI3 SPI12SPI12 22 0 SPI 0 SPI -2-2 -4-4 1957 1961 1965 1969 1973 1977 1981 1985 1989 1993 1997 2001 2005 2009 1957 1961 1965 1969 1973 1977 1981 1985 1989 1993 1997 2001 2005 2009 Figure 4. Variation of SPI series for different time scales in Northern Anhui province, 1957-2010. FigureFigure 4.4. VariationVariation ofof SPISPI seriesseries forfor differentdifferent timetime scalesscales inin NorthernNorthern AnhuiAnhui province,province, 1957-2010.1957-2010. It can be revealed from Figure4 that, (1) influenced by short-term precipitation events, the SPI1 ItIt cancan bebe revealedrevealed fromfrom FigureFigure 44 that,that, (1)(1) influeinfluencednced byby short-termshort-term precipitationprecipitation events,events, thethe SPI1SPI1 series fluctuated significantly through 1957 to 2010, which was applied as the data basis to derive a seriesseries fluctuatedfluctuated significantlysignificantly throughthrough 19571957 toto 20102010,, whichwhich waswas appliedapplied asas thethe datadata basisbasis toto derivederive aa diffdifferentdifferenterent drought droughtdrought conceptual conceptualconceptual cloud, cloud,cloud, and andand then thenthen further furthefurtherr exploreexplore thethe spatialspatial spatial evolutionevolution evolution characteristicscharacteristics characteristics ofof of droughtdroughtdrought in inin this thisthis study. study.study. (2) (2)(2) Concerning ConcerningConcerning the thethe consideration considerationconsideration ofof precipitationprecipitation precipitation inin in thethe the previousprevious previous threethree three months,months, months, thethethe variation variationvariation of SPI3ofof SPI3SPI3 series seriesseries was waswas relevant relevantrelevant with withwith agricultural agriculturalagricultural drought droughtdrought [19 [19,22].[19,22].,22]. The TheThe SPI12 SPI12SPI12 series seriesseries revealed revealedrevealed the overallthethe overalloverall yearly yearlyyearly variation variationvariation trend trendtrend of drought ofof droughtdrought and waterlogging-relatedandand wawaterlogging-relatedterlogging-related disasters. disasters.disasters. Therefore, Therefore,Therefore, the thethe SPI3 SPI3SPI3 and SPI12andand series SPI12SPI12 were seriesseries applied werewere appliedapplied to explore toto exploreexplore the temporal thethe temptemp evolutionoraloral evolutionevolution characteristics characteristicscharacteristics of drought ofof droughtdrought from seasonal fromfrom andseasonalseasonal yearly scalesandand yearlyyearly in this scalesscales study. inin thisthis study.study. 4.1.4.1.4.1. Temporal TemporalTemporal Variation VariationVariation Analysis AnalysisAnalysis of ofof Drought DroughtDrought 4.1.1.4.1.1.4.1.1. Yearly YearlyYearly Variation VariationVariation Characteristics CharacteristicsCharacteristics Analysis AnalysisAnalysis AsAsAs indicated indicatedindicated by bybySPI SPISPI series seriesseries in inin Figure FigureFigure4 4,,4, the thethe drought droughtdrought evolutionevolutionevolution in thethe NorthernNorthern Northern AnhuiAnhui Anhui provinceprovince province presentedpresentedpresented a slight aa slightslight decreasing decreasingdecreasing trend trendtrend from fromfrom 1957 19571957 to toto 2010. 20102010.. If If dividingdividing droughtdrought drought intensityintensity intensity intointo into fourfour four gradesgrades grades including light, moderate, severe, and extreme drought based on the indicator threshold of SPI12 Entropy 2020, 22, 106 8 of 15 Entropy 2020, 22, x FOR PEER REVIEW 8 of 15 proposed in meteorological drought classification criteria [5,6], the statistical result of drought duration ofincluding different light, grades moderate, on a monthly severe, scale and inextreme the Northern drought Anhuibased provinceon the indicator for each thresholdperiod wasof SPI12 shown inproposed Table1. in meteorological drought classification criteria [5,6], the statistical result of drought duration of different grades on a monthly scale in the Northern Anhui province for each period was shown Tablein Table 1. Statistical 1. result of drought duration in the Northern Anhui province (unit: month). Level 1957–1970 1971–1980 1981–1990 1991–2000 2001–2010 Table 1. Statistical result of drought duration in the Northern Anhui province (unit: month). Light Drought 29 15 20 18 19 ModerateLevel Drought 1957–1970 7 1971–1980 11 1981–1990 14 1991–2000 22 2001–2010 1 LightSevere Drought Drought 29 1 615 120 818 719 ModerateExtreme DroughtDrought 127 211 014 022 0 1 SevereTotal Drought 491 346 351 488 277 Extreme Drought 12 2 0 0 0 Specifically,Total it can be indicated 49 from Table1 34that, (1) the drought35 condition48 was the most27 serious from 1957 to 1970 in the Northern Anhui province in which a total of 49 months with SPI12 less than Specifically, it can be indicated from Table 1 that, (1) the drought condition was the most serious 0.5 and 12 months with an extreme drought level. The extreme drought duration was from August in − from 1957 to 1970 in the Northern Anhui province in which a total of 49 months with SPI12 less than 1966-0.5 to and July 12 in months 1967. (2)with The an drought extreme situationdrought leve in thel. The Northern extreme Anhui drought province duration was was relieved from August from 1971 toin 1980, 1966 but to July the numberin 1967. (2) of The severe drought drought situation months in the increased Northern from Anhui one province from 1957 was to relieved 1970 to sixfrom from 19711971 to to 1980. 1980, (3) but The the drought number evolutionof severe drought trend from mont 1981hs increased to 1990 in from the Northernone from 1957 Anhui to province1970 to six was approximatelyfrom 1971 to 1980. consistent (3) The withdrought the evolution period from trend 1971 from to 1981 1980. to The1990 droughtin the Northern situation Anhui was province intensified fromwas 1991approximately to 2000, but consistent mainly presented with the withperiod a lightfrom drought 1971 to (18 1980. months) The drought and a moderate situation drought was (22intensified months). from (4) The1991 droughtto 2000, but situation mainly inpresente the Northernd with a light Anhui drought province (18 months) was much and relieveda moderate from 2001drought to 2010. (22 Themonths). total (4) 49 monthsThe drought of drought situation occurred, in the Northern but primarily Anhui presentedprovince was a light much drought relieved level (19from months). 2001 to (5) 2010. The The statistical total 49 resultmonths of of drought drought occurrence occurred, but in primarily Northern presented Anhui province a light drought from 1957 tolevel 2010 (19 was months). consistent (5) The with statistical historical result records of drought [32], which occurrence verified in theNorthern adaptability Anhui andprovince reliability from of 1957 to 2010 was consistent with historical records [32], which verified the adaptability and reliability applying the SPI drought index in drought recognition and distribution exploration to a large extent. of applying the SPI drought index in drought recognition and distribution exploration to a large 4.1.2.extent. Seasonal Variation Characteristics Analysis 4.1.2.Considering Seasonal Variation the impact Characteristics of precipitation Analysis during the previous three months, the SPI3 series can be adopted to analyze the seasonal distribution features of drought. Therefore, the SPI3 characteristic Considering the impact of precipitation during the previous three months, the SPI3 series can be valueadopted of spring, to analyze summer, the seasonal autumn, distribution and winter features were obtained of drought. by the Therefore, SPI3 of May,the SPI3 August, characteristic November, andvalue next of Februaryspring, summer, separately, autumn, and and then winter the SPI3were seriesobtained from by the a seasonal SPI3 of May, scale August, for diff erentNovember, cities in theand Northern next February Anhui separately, province and can then be constructed.the SPI3 series Infrom addition, a seasonal the scale cloud for theorydifferent was cities applied in the to furtherNorthern discuss Anhui the province certainty can and be stability constructed. of seasonal In addition, distribution the cloud of droughttheory was in which applied the to average further Ex representeddiscuss the the certainty overall intensityand stability of drought. of seasonal Entropy distributionEn revealed of drought the certainty in which level the of theaverage determined Ex droughtrepresented intensity, the overall and hyper-entropy intensity of Hedrought.indicated Entropy the stabilityEn revealed level the about certainty the variation level of trend the of droughtdetermined intensity. drought The intensity, higher of and the entropyhyper-entropy and hyper-entropy He indicated the values, stability the morelevel about scattering the variation distributed oftrend cloud of drops, drought and intensity. the higher The uncertainty higher of the level entr ofopy the and cloud hyper-entropy distribution values, pattern. the more scattering distributed of cloud drops, and the higher uncertainty level of the cloud distribution pattern. Thereby, based on the determination of cloud characteristic values for seasonal SPI3 series, Thereby, based on the determination of cloud characteristic values for seasonal SPI3 series, the the corresponding cloud distribution pattern can be obtained through the FNCA approach. Table2 and corresponding cloud distribution pattern can be obtained through the FNCA approach. Table 2 and FiguresFigures5– 5–1010 illustrated illustrated the the seasonal seasonal cloudcloud characteristiccharacteristic values values and and correspon correspondingding cloud cloud distribution distribution pattern,pattern, respectively, respectively, for for di differentfferent cities cities inin thethe NorthernNorthern Anhui province. province. (a) (b) (c) (d) FigureFigure 5. 5.Cloud Cloud distributiondistribution of SPI3 in in Huaibei, Huaibei, (a (a) )spring, spring, (b ()b summer,) summer, (c) ( cautumn,) autumn, and and (d) ( winter.d) winter. Entropy 2020, 22, 106 9 of 15 Table 2. Cloud characteristic values of SPI3 series for different seasons in the Northern Anhui province. Huaibei Bozhou Suzhou Season Ex En He Ex En He Ex En He Spring 0.0045 0.9826 0.2278 0.0003 1.0035 0.1104 0.0029 0.9947 0.1768 − − Summer 0.0010 0.9846 0.2221 0.0022 0.9854 0.2176 0.0004 1.0301 0.1635 − − Autumn 0.0020 1.0201 0.2372 0.0033 0.9976 0.1598 0.0027 1.0288 0.2393 Winter 0.0198 0.9621 0.2742 0.0066 1.0404 0.2738 0.0027 0.9868 0.2484 − − − Bengbu Fuyang Huainan Season Ex En He Ex En He Ex En He Spring 0.0003 1.0484 0.1279 0.0053 0.9700 0.2260 0.0026 0.9689 0.2852 Summer 0.0017 1.0041 0.1061 0.0007 1.0112 0.1385 0.0014 0.9944 0.1754 Autumn 0.0017 0.9854 0.2208 0.0073 0.9657 0.2108 0.0001 0.9956 0.1674 − Winter 0.0170 0.9838 0.2317 0.0227 1.0195 0.2169 0.0177 1.0241 0.3200 − − − Entropy 2020,, 22,, xx FORFOR PEERPEER REVIEWREVIEW 9 of 15 ((a)) ((b)) ((c)) ((d)) FigureFigure 6. 6.Cloud Cloud distributiondistribution of SPI3 SPI3 in in Bozhou, Bozhou, (a ()a) )spring,spring, spring, ((b ())b summer,summer,) summer, ((c)) ( cautumn,autumn,) autumn, andand and ((d)) ( winter.winter.d) winter. ((a)) ((b)) ((c)) ((d)) FigureFigure 7. 7.Cloud Cloud distributiondistribution of SPI3SPI3 inin in Suzhou,Suzhou, Suzhou, ((a (a)) )spring,spring, spring, ((b ())b summer;summer;) summer; ((c)) ( cautumn,autumn,) autumn, andand and ((d)) ( winter.winter.d) winter. ((a)) ((b)) ((c)) ((d)) FigureFigure 8. 8.Cloud Cloud distributiondistribution of SPI3 SPI3 in in Bengbu, Bengbu, (a ()a) )spring,spring, spring, ((b ())b summer,summer,) summer, ((c)) ( cautumn,autumn,) autumn, andand and ((d)) ( winter.winter.d) winter. ((a)) ((b)) ((c)) ((d)) Figure 9. Cloud distribution of SPI3 in Fuyang, (a) spring, (b) summer, (c) autumn, and (d) winter. FigureFigure 9. 9.Cloud Cloud distributiondistribution of SPI3 SPI3 in in Fuyang, Fuyang, (a ()a) )spring,spring, spring, ((b ())b summer,summer,) summer, ((c)) ( cautumn,autumn,) autumn, andand and ((d)) ( winter.winter.d) winter. ((a)) ((b)) ((c)) ((d)) Figure 10. Cloud distribution of SPI3 in Huainan, (a)) spring,spring, ((b)) summer,summer, ((c)) autumn,autumn, andand ((d)) winter.winter. Entropy 2020, 22, x FOR PEER REVIEW 9 of 15 (a) (b) (c) (d) Figure 6. Cloud distribution of SPI3 in Bozhou, (a) spring, (b) summer, (c) autumn, and (d) winter. (a) (b) (c) (d) Figure 7. Cloud distribution of SPI3 in Suzhou, (a) spring, (b) summer; (c) autumn, and (d) winter. (a) (b) (c) (d) Figure 8. Cloud distribution of SPI3 in Bengbu, (a) spring, (b) summer, (c) autumn, and (d) winter. Entropy 2020, 22(,a 106) (b) (c) (d) 10 of 15 Figure 9. Cloud distribution of SPI3 in Fuyang, (a) spring, (b) summer, (c) autumn, and (d) winter. (a) (b) (c) (d) FigureFigure 10. 10.Cloud Cloud distribution distribution ofof SPI3 in Huainan, Huainan, (a ()a )spring, spring, (b ()b summer,) summer, (c) (autumn,c) autumn, andand (d) winter. (d) winter. From Table2 and Figures5–10 , the temporal variation features of drought from a seasonal scale for different cities in the Northern Anhui province can be summarized as follows. Huaibei • The sorting result from high to low by the entropy values of seasonal SPI3 cloud distribution in Huaibei city was autumn, summer, spring, and winter. The sorting result by hyper-entropy values was winter, autumn, spring, and summer. Thus, it was evident that the fuzziness of drought distribution in autumn and summer was higher than that of spring and winter. In other words, the certainty of drought distribution in the winter was the highest in the Huaibei city. Moreover, the cloud layers indicating drought distribution in winter and autumn were much thicker than that in the spring and summer, and the stability of drought intensity and the variation trend in the summertime was the highest. Bozhou • The sorting result from high to low by the entropy values of seasonal SPI3 cloud distribution in Bozhou city was winter, spring, autumn, and summer, and the sorting result by hyper-entropy values was winter, summer, autumn, and spring. Thus, it was evident that the certainty level of drought distribution in the summer was the highest in Bozhou city. Furthermore, the stability of drought intensity and possible future variation trend in the spring was the highest. Suzhou • The sorting result from high to low by the entropy values of seasonal SPI3 cloud distribution in Suzhou city was the summer, autumn, spring, and winter, and the sorting result by hyper-entropy values was consistent with that of Huaibei city. Therefore, it was clear that the certainty level of drought distribution in the winter was the highest in Suzhou city. Moreover, the stability level of drought intensity and the future variation trend was consistent with that of the Huaibei city. Bengbu • The sorting result from high to low by the entropy values of seasonal SPI3 cloud distribution in Bengbu city was the spring, summer, autumn, and winter, which was exactly opposite with the sorting result by hyper-entropy values. Thus, it could be revealed that the uncertainty level of drought intensity and a possible evolution trend in the spring was the highest than during other seasons in Bengbu city. Fuyang • The sorting result from high to low by the entropy values of seasonal SPI3 cloud distribution in Fuyang city was winter, summer, spring, and autumn, and the sorting result by hyper-entropy values was spring, winter, autumn, and summer. Thus, it was evident that the uncertainty level of drought distribution in the winter was the highest, while the stability of a future variation trend of drought in the summer was the highest in Fuyang city. Entropy 2020, 22, 106 11 of 15 Entropy 2020, 22, x FOR PEER REVIEW 11 of 15 Huainan •• Huainan TheThe sorting sorting result result from from high high to to low low by by the the entrop entropyy values values of ofseasonal seasonal SPI3 SPI3 cloud cloud distribution distribution in Huainanin Huainan city city was was winter, winter, autumn, autumn, spring, spring, and and summer, summer, and and the the sorting sorting result result by by hyper-entropy hyper-entropy valuesvalues was was winter, winter, spring, summer, and autumn. Thus, Thus, it it could could be be indicated indicated that that the the fuzziness fuzziness and and randomnessrandomness levels levels of of drought drought distribution distribution and and future future possible possible evolution evolution trend trend in in winter winter was was the the highesthighest in in Huainan Huainan city. city. ItIt could could be be revealed revealed that that the the temporal variation variation characteristics characteristics of of drought drought distribution distribution in in cities cities ofof Huaibei, Huaibei, Suzhou, Suzhou, and and Bengbu Bengbu were were consistent consistent with with each each other, other, with with the the highest highest certainty certainty level level of of droughtdrought intensity distributiondistribution butbut lowest lowest stability stability level level of of drought drought evolution evolution trend trend in winter.in winter. This This was wasexactly exactly opposite opposite with thatwith of that summer. of summer. The possible The possible reasons causingreasons thecausing above the distribution above distribution features of featuresdrought of were drought that Huaibei,were that Suzhou, Huaibei, and Suzhou, Bengbu and cities Bengbu located cities in located the eastern in the part eastern of Anhui part of province, Anhui province,with little with but stable little annualbut stable precipitation annual precipitatio influencedn byinfluenced a monsoon by climate, a monsoon which climate, led to thewhich stable led and to theconsistent stable and seasonal consistent distribution seasonal characteristics distribution characteristics of drought. of drought. 4.2. Spatial Variation Characteristics Analysis of Drought 4.2. Spatial Variation Characteristics Analysis of Drought The cloud transformation algorithm (CTA) and conception zooming coupling approach was The cloud transformation algorithm (CTA) and conception zooming coupling approach was introduced to explore the spatial evolution characteristics of drought through re-fitting the distribution introduced to explore the spatial evolution characteristics of drought through re-fitting the pattern of SPI3 series instead of Pearson-III distribution in this study. Concerning the similarity of distribution pattern of SPI3 series instead of Pearson-III distribution in this study. Concerning the the calculation process for different cities in the Northern Anhui province, the detailed determination similarity of the calculation process for different cities in the Northern Anhui province, the detailed procedures for cloud distribution characteristic values of drought through CTA and a conception determination procedures for cloud distribution characteristic values of drought through CTA and a zooming coupling approach in Huaibei city was illustrated as follows, which can be further applied in conception zooming coupling approach in Huaibei city was illustrated as follows, which can be other cities of the Northern Anhui province. further applied in other cities of the Northern Anhui province. • Determination of Conceptual Cloud Parameters • Determination of Conceptual Cloud Parameters AccordingAccording to to the the procedures procedures of of CTA CTA and concep conceptiontion zooming coupling approach approach indicated indicated in in sectionSection 3.33.3,, first,first, the the calculated calculated SPI3 SPI3 series series was applied was applied to determine to determine the probability the probability density distribution density distributionhistogram of histogram drought, which of drought, was shown which in was Figure sh own11a. Then,in Figure supposing 11a. Then, the thresholdsupposing values the thresholdδ1 and δ2 valuesequaled δ1 to and 0.1 andδ2 equaled 0.01, respectively, to 0.1 and which 0.01, respectively, were used to controlwhich thewere occurrence used to control frequency the of occurrence remaining frequencycloud drops, of andremaining the four cloud initial drops, conceptual and the cloud four distributions initial conceptual of drought cloud were distributions obtained throughof drought the wereCTA obtained method, asthrough indicated the inCTA Figure method, 11b. as Lastly, indicate thed ultimate in Figure three 11b. cloud Lastly, distribution the ultimate of three drought cloud for distributiondifferent drought of drought intensity for levels different could drought be derived inte throughnsity levels a subtle could adjustment be derived of through entropy valuesa subtle of adjustmentinitial drought of entropy cloud distribution values of initial and drought a merging cloud process, distribution which were and a illustrated merging process, in Figure which 11c. were illustrated in Figure 11c. (a) (b) (c) FigureFigure 11.11. DeterminationDetermination process process of cloudof cloud distribution distribution of drought of drought by CTA by in CTA Huaibei in city,Huaibei (a) probability city, (a) probabilitydensity histogram, density histogram, (b) initial conceptual (b) initial conceptual cloud distribution, cloud distribution, and (c) final and cloud (c) final distribution cloud distribution of drought. of drought. Similarly, the conceptual cloud distribution for different drought intensity in other cities of the NorthernSimilarly, Anhui the provinceconceptual could cloud be distribution derived by for applying different CTA drought and conception intensity in zooming other cities coupling of the Northernapproach, Anhui and the province cloud characteristiccould be derived parameters by applying and corresponding CTA and conception drought zooming cloud distribution coupling approach,patterns were and indicatedthe cloud in characteristic Table3 and Figure parameters 12. and corresponding drought cloud distribution patterns were indicated in Table 4 and Figure 12. Entropy 2020, 22, 106 12 of 15 Table 3. Cloud characteristic parameters of drought in the Northern Anhui province. Huaibei Bozhou Suzhou Value C1 C2 C3 C1 C2 C3 C4 C5 C6 C1 C2 C3 C4 C5 Ex 1.36 0.14 1.17 1.68 1.11 0.54 0.01 0.60 1.55 1.40 0.86 0.02 0.84 1.53 − − − − − − − En 0.36 0.75 0.42 0.20 0.23 0.33 0.41 0.41 0.30 0.36 0.24 0.51 0.34 0.25 He 0.06 0.09 0.07 0.03 0.04 0.06 0.04 0.07 0.05 0.06 0.05 0.09 0.06 0.03 Bengbu Fuyang Huainan Value C1 C2 C3 C4 C1 C2 C3 C4 C1 C2 C3 Ex 1.51 0.09 0.67 1.46 1.52 0.83 0.01 1.01 0.81 0.08 0.88 − − − − − − En 0.36 0.56 0.35 0.25 0.19 0.35 0.47 0.36 0.41 0.42 0.43 He 0.06 0.05 0.06 0.04 0.03 0.06 0.08 0.03 0.07 0.07 0.04 Entropy 2020, 22, x FOR PEER REVIEW 12 of 15 (a) (b) (c) (d) (e) FigureFigure 12. 12. ConceptualConceptual cloud cloud distribution distribution of dr ofought drought in Northern in Northern Anhui Anhui province, province, (a) Bozhou, (a) Bozhou, (b) Suzhou,(b) Suzhou, (c) Bengbu, (c) Bengbu, (d) Fuyang, (d) Fuyang, and and(e) Huainan. (e) Huainan. EvolutionTable Trend 4. Cloud Analysis characteristic of Concept parameters Cloud of for dr Droughtought in the Northern Anhui province. • For the consistencyHuaibei with seasonal variationBozhou characteristics analysis of drought Suzhou in Section 4.1.2, Value the averageC1 Ex, entropyC2 CEn3 , andC1 hyper-entropyC2 C3 He wereC4 alsoC5 appliedC6 toC present1 C2 the overallC3 intensityC4 C5 of droughtEx − and1.36 its0.14 derived 1.17 certainty −1.68 level−1.11 and−0.54 evolution 0.01 stability0.60 1.55 level. −1.40 Additionally, −0.86 −0.02 according 0.84 to1.53 the En 0.36 0.75 0.42 0.20 0.23 0.33 0.41 0.41 0.30 0.36 0.24 0.51 0.34 0.25 division standard of the drought hazard based on the SPI index [22,33], the conceptual grade cloud He 0.06 0.09 0.07 0.03 0.04 0.06 0.04 0.07 0.05 0.06 0.05 0.09 0.06 0.03 distribution of droughtBengbu for different cities in theFuyang Northern Anhui provinceHuainan under the same restrictions Value of cloud transformationC1 C2 C principles3 C4 andC1 conceptualC2 zoomingC3 C4 thresholdC1 values,C2 whichC3 could be obtained asEx indicated −1.51in Figures−0.09 0.6711 and 1.46 12 . It− can1.52 be− evidently0.83 0.01 summarized1.01 −0.81 from−0.08 the two0.88 figures that: En 0.36 0.56 0.35 0.25 0.19 0.35 0.47 0.36 0.41 0.42 0.43 (1) moderate grade cloud C1( 1.36, 0.36, 0.06) of drought occurred in Huaibei city, light, moderate, He 0.06 0.05 0.06 0.04 − 0.03 0.06 0.08 0.03 0.07 0.07 0.04 and severe grades cloud C ( 0.54, 0.33, 0.06), C ( 1.11, 0.23, 0.04), and C ( 1.68, 0.20, 0.03) occurred in 3 − 2 − 1 − Bozhou city, respectively, light and moderate grades cloud C ( 0.86, 0.24, 0.05) and C ( 1.40, 0.36, 0.06) • Evolution Trend Analysis of Concept Cloud for Drought2 − 1 − of drought occurred in Suzhou city, respectively, severe grade cloud C ( 1.51, 0.36, 0.06) of drought 1 − occurredFor the in Bengbuconsistency city, lightwith andseasonal severe variation grades cloudcharacteristicsC ( 0.83, analysis 0.35, 0.06) of and droughtC ( 1.52, in section 0.19, 0.03) 4.1.2, of 2 − 1 − thedrought average occurred Ex, entropy in Fuyang En, and city, hyper-entropy respectively, andHe were light also grade applied cloudC1( to present0.81,0.41, the overall 0.07) of intensity drought − ofoccurred drought in and the its Huainan derived city. certainty level and evolution stability level. Additionally, according to the division(2) Amongstandard cities of the with drought the occurrence hazard based of a light on the grade SPI cloud index of [22,33], drought the (Bozhou, conceptual Suzhou, grade Fuyang, cloud distributionand Huainan), of drought the certainty for different of determined cities in drought the Northern intensity Anhui and stabilityprovince of under the corresponding the same restrictions drought ofevolution cloud transformation trend in Suzhou principles city was theand highest, concep whichtual zooming was the opposite threshold of Huainanvalues, which city. could be obtained as indicated in Figure 11 and Figure 12. It can be evidently summarized from the two figures that: (1) moderate grade cloud C1(−1.36, 0.36, 0.06) of drought occurred in Huaibei city, light, moderate, and severe grades cloud C3(−0.54, 0.33, 0.06), C2(−1.11, 0.23, 0.04), and C1(−1.68, 0.20, 0.03) occurred in Bozhou city, respectively, light and moderate grades cloud C2(−0.86, 0.24, 0.05) and C1(−1.40, 0.36, 0.06) of drought occurred in Suzhou city, respectively, severe grade cloud C1(−1.51, 0.36, 0.06) of drought occurred in Bengbu city, light and severe grades cloud C2(−0.83, 0.35, 0.06) and C1(−1.52, 0.19, 0.03) of drought occurred in Fuyang city, respectively, and light grade cloudC1(−0.81, 0.41, 0.07) of drought occurred in the Huainan city. (2) Among cities with the occurrence of a light grade cloud of drought (Bozhou, Suzhou, Fuyang, and Huainan), the certainty of determined drought intensity and stability of the corresponding drought evolution trend in Suzhou city was the highest, which was the opposite of Huainan city. Entropy 2020, 22, 106 13 of 15 (3) Among cities with the occurrence of a moderate grade cloud of drought (Huaibei, Bozhou, and Suzhou), the certainty of determined drought intensity and stability of corresponding drought evolution trend in Buzhou city was the highest, which was opposite that in Huaibei city as well. (4) Among cities with the occurrence of extreme grade cloud of drought (Bozhou Bengbu and Fuyang), the certainty of determined drought intensity and stability of the corresponding drought evolution trend in Fuyang city was the highest, which was also opposite that in Bengbu city. Therefore, the drought hazard will be more intensified significantly along with the elevation of latitude in Northern Anhui province, not only for overall drought intensity at present but also for the evolution trend in the future. The overall drought hazard in Suzhou and Huaibei were the most serious followed by Bozhou, Bengbu, and Fuyang. Drought intensity in Huainan was the lightest. 5. Conclusions For the influence of the monsoon climate, the northern Anhui province is one of the most typical regions with a large amount of drought-related disaster loss every year in mainland China. The purpose of this study is to explore the spatial-temporal distribution features of drought in the Northern Anhui province from both yearly and seasonal scales. The application results of the cloud transformation algorithm and conceptual zooming coupling model in the Northern Anhui province indicated that (1) the drought situation varying from 1957 to 1970 was the most serious during the study period, in which 12 months belong to an extreme drought level. (2) During the period from 1957 to 2010, the evolution trend of drought intensity varied with the highest certainty level but lowest stability level in the winter, but this was exactly opposite of that in the summer. (3) The overall drought intensity in Suzhou and Huaibei were the most serious from 1957 to 2010, which is followed by Bozhou, Bengbu, and Fuyang, and drought intensity in Huainan was the lightest. Thus, it can be deduced that the drought hazard would present a more severe trend with the elevation of latitude in the Northern Anhui province in the future. All in all, compared with previous work, the primary innovation of the manuscript is to essentially explore the spatio-temporal evolution characteristics of drought by transforming drought indicator series into multiple qualitative concepts of Gaussian cloud distribution based on the Cloud Transformation Algorithm (CTA) and Conception Zooming method. However, the reasonable computation of cloud characteristic parameters and the understanding of its transformation mechanism from a traditional interval threshold are crucial for systematic analysis, which is now inconclusive. Furthermore, drought is a complex natural phenomenon with randomness and uncertainties. How to further explore its natural evolution characteristics through comprehensive indicators integrating hydrological, meteorological, and underlying surface information is still a big challenge, which is exactly the foundation to realize the strategical planning research of drought risk management. Author Contributions: Conceptualization, X.B. and Y.W. Methodology, Y.W. and J.J. Software, X.B. Validation, S.N. and C.W. Formal analysis, X.B. Investigation, Y.W. Resources, X.B. Data curation, X.B. Writing—original draft preparation, X.B. Writing—review and editing, S.N. and C.W. Visualization, X.B. Supervision, Y.W. Project administration, S.N. and Y.W. Funding acquisition, S.N. and Y.W. All authors have read and agreed to the published version of the manuscript. Funding: The National Key Research and Development Program of China under Grant No. 2017YFC1502405, National Nature Science Foundation of China under Grant No. 51709071, Key Research and Development Program of Shandong Province of China under Grant No. 2017GSF20101, and the Natural Science Research Project of Bengbu University under Grant No. 2017ZR21 funded this research. Conflicts of Interest: The authors declare no conflict of interest. References 1. Mishra, A.K.; Singh, V.P. A review of drought concepts. J. Hydrol. 2010, 391, 202–216. [CrossRef] 2. Hoerling, M.; Schubert, S.; Mo, K. An Interpretation of the Origins of the 2012 Central Great Plains Drought. NOAA Drought Task Force; NOAA: Silver Spring, MD, USA, 2013. 3. Zhang, J.; Chen, G.Y.; Yang,W.F.Summary of advancement of drought study at home and abroad. YangtzeRiver 2011, 42, 65–69. Entropy 2020, 22, 106 14 of 15 4. Xu, J.J.; Yang, D.W. 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