REgional Drought Identification Module REDIM - Gruppo Risorse ...

the null hypothesis that the population correlation coefficient ρ = 0, the test statistic t c iscomputed as:t cr ⋅ N − 2=21−rwhere r is the sample correlation coefficient and N the sample size. The null hypothesis isrejected on the basis of a two-tailed test at significance level α if t c≥ t −α N 2)where( N 2)1−/ 2−( 1 / 2−tαis the value drawn from a Student’s t distribution with N-2 degrees offreedom and non exceedence probability (1-α/2). Typical values of α are 10, 5 , 2.5 and 1percent.The Kendall τ-test (also termed rank correlation test) is applied by computing for aseries x t (t=1, 2, .., n) the number p of pairs of observations (x t ,x j ) (with j>t) for which x j >x t(Kottegoda, 1980). Under the null hypothesis of random series, the statistic:where:zcτ ==4 pNτvarτ( N −1)2varτ=9N−1( 2N + 5)( N − 1)converges rapidly to a standard normal distribution as N increases. Therefore, the nullhypothesis is rejected with a significance level α if |z c |>z t1-α/2 where z t1-α/2 is a standardnormal variable corresponding to a non exceedence probability (1-α/2).The turning point test is based on counting in a series x t (t=1,2 ….N) the number ofturning points m , i.e. for each t=2, 3 …, N-1, the values for which x t is larger than x t-1 andx t+1 or x t is smaller than x t-1 and x t+1 (Kottegoda, 1980).Under the null hypothesis the series is assumed random and it can be shown that thestatistic:with:zc =[ m−E( m)]var( m)4

variable are known. This possibility is not limited to relatively simple cases where timedependence of consecutive values can be neglected, but also when a Markov chainstructure is assumed for the underlying variable (Cancelliere et al., 1998; Fernandez andSalas, 1999). Furthermore, procedures to assess the return period of droughts definedaccording to the run method have been derived recently (Fernandez and Salas, 1999; Shiauand Shen, 2001; Bonaccorso et al., 2003; Cancelliere and Salas, 2004), thus making themethod an ideal candidate to perform drought risk analysis.3.2 Drought identification at siteGiven a discrete time series h(i), i=1, 2,… n and a truncation level h o , it is possible toidentify positive and negative deviations according to the sign of the difference betweenthe observed values of the variable and the fixed threshold.Then, a run is defined as a sequence of intervals characterized by deviations with thesame sign preceded and followed by at least one interval with deviation of the oppositesign. Negative deviations are usually referred as deficit, whereas the corresponding run istermed as negative run or drought.By analyzing a given drought s, it is possible to identify the following characteristics:• drought duration L(s), defined as the number of consecutive intervals where thevariable remains below the threshold;• accumulated deficit D(s), defined as the sum of the negative deviations, extended tothe whole drought duration;• drought intensity of ID(s), defined as the ratio between cumulated deficit and duration.More precisely, by letting d(i) be the deficit in the interval i:d(i) = [h 0 – h(i)]⋅ I[h(i)] where I[h(i)] = 1 if h(i) < h oI[h(i)] = 0 ifh(i) ≥ h o• the duration of the drought s is given by:L(s) = i f – i i + 1where i f and i i are such that: d(i) > 0 for i i ≤i≤ i f and d(i i - 1)=0, d(i f +1) = 0 ;• the accumulated deficit can be expressed by:7

h 0 (k) – h(i,k)>0Then, it is assumed that the deficit at each site is extended to an influence area aroundthe observation station, which, for example, can be estimated by Thiessen polygonsmethod. Such area S(k) is usually expressed in terms of the total area under investigationas:A(k)=S(k)/S tot .where the total area S tot is obviously:KStot= ∑ S(k)k = 1By fixing the areal threshold A crit , again expressed as a fraction of the total area, twoindices can be computed, namely:• the areal coverage of deficit A d (i) :where:II[ h(i,k)] = 1 if h(i,k)< h0(k)[ h(i,k)] = 0 if h(i,k)≥ h (k)0A ( i)=dK∑k=1I[ h(i,k)]A(k)• the areal deficit d(i) in the interval i:d( i )K= ∑k = 1[ h ( k ) − h( i,k )] ⋅ I[ h( i,k )]0d( i )= 0A( k )ififA ( i ) ≥dA ( i ) 0 for i i (r) ≤i≤ i f (r) and d[i i (r) – 1]=0, d[i f (r) + 1]=0• the cumulated areal deficit is computed as:9

period of multiyear droughts, it is necessary to consider both drought duration andaccumulated deficit (or duration and intensity), since in this case it is not possible toidentify an unique time unit (trial) with respect to which the probability of a criticaldrought can be expressed, as one can usually do in flood frequency analysis. Thus, theusual formula T=1/P[A], where P[A] is the exceedence probability with respect to a criticalevent A, e.g. a variable value greater than a fixed one, cannot be adopted.Shiau and Shen, (2001) have developed an analytical expression for return period ofdroughts with accumulated deficit greater than a given value. Other authors have extendedsuch formulation to the more general case of different combinations of duration andaccumulated deficit or intensity (Cancelliere et al., 2003; Gonzales and Valdes, 2003), orto the case of droughts identified on periodic series, such as monthly precipitation orstreamflows (Cancelliere and Salas, 2004). With reference to the generic critical droughtevent A identified on stationary (annual) and serially independent series, the return periodcan be written as:T =1p p101P[ A]where p 1 is the probability of observing a surplus (i.e. P[h(i)>h 0 ]), while p 0 =1- p 1 . In thecase of Markov serial dependence, the above equation modifies as:T=pp01+01pp10101P[ A]where p 01 represents the transition probability of observing a surplus at time i given that adeficit occurred at time i-1, while p 10 represents the transition probability of observing adeficit at time i given that a surplus occurred at time i-1.For analyzing the return period of droughts and the associated risks we need to specifythe drought event A under consideration. For instance, one may consider only the durationof a drought regardless of the accumulated deficit (or drought intensity) or vice-versa, orboth duration and accumulated deficit (or drought intensity).In Table I, a list of possible drought events and related occurrence probabilities arereported (Bonaccorso et al., 2003, Cancelliere et al., 2003). Such probabilities have beenderived by considering drought accumulated deficit, as well as drought accumulated deficitconditioned on drought duration, gamma distributed with parameters, respectively, r 1 ,β 1and r 2 ,β 2 . In the table, the symbol G refers to the incomplete gamma function (Abramowitzand Stegun, 1970).13

Table I. Occurrence probabilities of critical drought eventsDrough eventFormulal −11) A = {L d = l c (l c =1,2,…)} [ ] ( )P Ldc= l = f ( L = l ) = p − pc−12) A = {L d ≥ l c (l c =1,2,…)} P [ L ≥ l ] = ( 1−p ) l3) A = {D>d c } P[ Dcdc]dcc∞> =∫fdcD1cc1 ⋅ 1(⎡ ⎛⎢ ⎜dcz )d z = − r⎢1 G1 ,⎣ ⎝ β11x⎞⎤⎟⎥⎠⎥⎦4) A = {D>d c andL d = l c (l c =1,2,…)}5) A = {D>d c andL d ≥ l c (l c =1,2,…)}∞−1[ , ] ( , )d 1 ⎜cl, ⎟cd L = l = f z l z = − G r ⋅ p ( − p )P Dc> c d c ∫dc∞ ∞⎡D , ⎢ ⎜ 2 ⎟⎥1 1c Ldcβ2⎢⎣⎛⎝d ⎞⎤[ ] ⎜cl> d , L ≥ l = f ( z,l)dz = 1−G r , ⎟ ⋅ p ( − p )P Dccdc∫∑d l=lcc⎡⎠⎥⎦∞⎛ d ⎞D ∑⎢⎟⎥c , Ld⎜ 2 1 1l=l ⎢ ⎝ β2⎠⎥c⎣⎤⎦1−11The parameters of the probability distributions of drought characteristics can bedetermined according to a non parametric approach, as functions of the sample mean andvariance of single deficit D t and drought duration L d according to the following theoreticalequations:r12 2E[ Ld] E[ Dt][ L2] Var[ D ] + E[ D ] Var[ L ]= andEdt2[ Dt][ D ]ttEr2 = lc⋅andVardβ1E=2[ Ld] Var[ Dt] + E[ Dt] Var[ Ld]E[ L ] E[ D ]β = 2VarEd[ Dt][ D ]ttAlternatively, the same parameters can be derived as a function of the probabilitydistribution of the underlying hydrological variable and of the threshold level adopted fordrought identification. In particular, in Table II and Table III the parameters of the gammadistribution of D and D|L d are reported, by assuming the underlying variable h(i) normal,lognormal and gamma distributed respectively and the threshold level parametrized as follows(Yevjevich, 1967):x( 1 − )0 = μx− ασ x = μxαCvwith μ x , σ x e C v respectively the mean, the standard deviation and the coefficient ofvariation of h(i).14

funcţionarea consiliilor ştiinţifice specializate şi a comisiilor deexperţi în domeniu, recunoaşterea şi echivalarea gradelor ştiinţifice,titlurilor ştiinţifice şi ştiinţifico-didactice, obţinute de cetăţeniiRepublicii Moldova peste hotare;avizarea planului de înmatriculare la studii prin doctorat şipostdoctorat;aprobarea condiţiilor privind abilitarea instituţiilor de cercetareşi de învăţământ superior cu dreptul de organizare a învăţământuluipostuniversitar specializat (masterat, rezidenţiat, secundariat clinic);racordarea sistemului de pregătire şi atestare a cadrelorştiinţifice al ţării la sistemele similare ale ţărilor avansate;asigurarea recunoaşterii şi echivalării gradelor ştiinţifice şititlurilor ştiinţifice şi ştiinţifico-didactice obţinute de către cetăţeniiRepublicii Moldova în alte ţări;menţinerea în stare funcţională a unei baze de date privindpotenţialul de cadre ştiinţifice şi ştiinţifico-didactice al republicii şidinamica acestuia.CSA - o instituţie în perpetuă reformareFiind o structură ce ţine de ştiinţă, CSA a conştientizat faptul căea însăşi este o instituţie care în permanenţă trebuie să semodernizeze (reformeze, restructureze), odată cu acumularea de noicunoştinţe sau cu schimbarea paradigmelor ştiinţei. Aşadar, CSA îşicompleta/revizuia în continuu atribuţiile, îşi aprofunda şi diversificarelaţiile cu organizaţiile din sfera ştiinţei şi inovării, perfecţionadiplomele, atestatele şi certificatele pe care le elibera, tipiza şireducea numărul formularelor utilizate.O nouă etapă a Comisiei Superioare de Atestare începe în 2004(după aproximativ 10 ani de activitate), când se reformează înConsiliul Naţional pentru Acreditare şi Atestare (CNAA),extinzându-şi preocupările şi asumându-şi noi obligaţii. ActivitateaCNAA se axează de acum pe trei direcţii generale:15

4. Drought analysis through the Standardized Precipitation Index (SPI)4.1 OverviewAmong the several proposed indices for drought monitoring, the StandardizedPrecipitation Index (SPI) has found widespread application (McKee et al., 1993; Heim,2000; Wilhite et al., 2000; Rossi and Cancelliere, 2002).Unlike other drought indices, the computation of the SPI only requires the availabilityof monthly precipitation series. The main advantages of the SPI are (i) its standardizednature, which makes it particularly suited to compare drought conditions among differenttime periods and regions with different climatic conditions, and (ii) the possibility toconsider different aggregation time scale for drought analysis, which allows to take intoaccount all the possible drought impacts and the related affected components of thehydrological cycle. The aggregation time scale should be properly selected according to theaim of the study: i.e., from few months for studies oriented to analyse agricultural droughts(as the soil water content is affected by reduction in precipitation on a short time period),till one year or more for hydrological droughts (since streamflow, ground water, and watervolumes stored in the reservoirs are mainly affected by precipitation anomalies over a longtime scale).Table IV reports the drought classification based on SPI values adopted by the USNational Drought Mitigation Center (NDMC, http://www.ndmc.unl.edu).Table IV. Drought classification according to the National Drought Mitigation CenterSPIClass≥ 2.00Extremely wetDa 1.50 a 1.99 Very wetDa 1.00 a 1.49 Moderately wetDa -0.99 a 0.99 Near normalDa -1.00 a -1.49 Moderately dryDa -1.50 a -1.99 Very dry≤-2.00Extremely dryIn the following sections, a description of the procedure based on the application ofSPI for drought identification either at site and at a regional scale is presented.16

4.2 Drought identification at siteThe Standardized Precipitation Index is based on an equi-probability transformationof accumulated monthly precipitation observed at a given site into a standard normalvariable. In practice, computation of the index requires: (i) fitting a probability distributionto monthly precipitation series aggregated at a specific time scale k (e.g. k= 3, 6, 12, 24months, etc.), (ii) computing the non-exceedence probability related to such accumulatedvalues, and (iii) defining the corresponding normal standardized quantiles as the SPI series.In Figure 3 a scheme of the procedure for drought identification at site based on SPIcomputation is described.Figure 3. SPI computation schemeMcKee et al. (1993) has assumed accumulated precipitation gamma distributed andused maximum likelihood method to estimate the parameters of the distribution. Thegamma cumulative distribution function is defined as:where:α>0 is the shape parameterβ>0 is the scale parameterΓ∞F( x)=αβ Γα −1− y( α ) y e dy is the gamma function.=∫0x1 t / βte( ) ∫ α −1−αThe maximum likelihood solutions for parameters estimation provide (Thom, 1966):0dt) α =1 ⎛ 4 ⎞⎜ ⎟1+1+A4A⎝ 3 ⎠17

where:x i is the monthly rainfall;ˆ xβ =ˆ αN∑xii=1A = ln( x)− with N equal to the number of rainfall observations.NSince the gamma probability distribution is undefined for x=0 and a rainfall distributionmay contain zeros, the cumulative distribution function becomes:H ( x)= q + (1 − q)F(x)where q is the probability of 0 rainfall values. Thus, if M is the number of zeros in arainfall series aggregated at a time scale k, the probability q can be estimated as M/N. Thecumulative distribution function is finally transformed to the standard normal variable Z,which is the value of the SPI.4.3 Regional drought analysisA regional drought analysis can be carried out based on the SPI values computed fora given month i and a given aggregation time scale k at different sites.In particular, a similar approach adopted for the regional run method (see section 3.3)can be considered. More specifically, once that the SPI series for a fixed aggregation timescale k are computed at several sites, local drought conditions at each site p and at eachmonth i can be identified if SPI (i, p, k) < SPI th , where SPI th is a fixed value of SPIconsidered as a threshold level for drought identification.Drought conditions detected at each site p can be extended to influence areas S(p) (orpolygons) around the rainfall stations, so that a drought areal coverage A d (i) for eachmonth i can be determined by summing polygons corresponding to the stations affected bydrought according to the observed SPI values:where:AdP() i = I[ SPI( i, p,k)] A( p)∑p=118

AII( p)S=S( p)TOT[ SPI( i, p,k)] = 1 if SPI( i, p,k)< 0[ SPI( i, p,k)] = 0 if SPI( i, p,k) ≥ 0Finally, the drought areal coverage A d (i) is compared to a fixed areal threshold A cri ,representing the value of the area above which a regional drought is considered to occur. IfA d (i) is greater than or equal to A cri , then a regional SPI series for the consideredaggregation time scale, is computed based on the areal rainfall h areal obtained as theweighted rainfall mean with respect to the polygons of the stations under droughtconditions, namely:where:k∑ − 1j=0( i,k) = h ( i − j)areal−( i,k) = Φ [ H ( X ( i.k ))]SPI areal1X is the k-months aggregated areal rainfall series at month I;harealT() i = h( i p) A( p)( X ( i k))∑p=1, is the areal rainfall value at month i computed on the basis of thecontemporary rainfall values at the T sites for whichSPI (i, p, k) < SPI th ;H , is the exceedence probability of X(i,k) assumed gamma distributed;Φ −1 () ⋅ is the standard normal quantile corresponding to ( X ( i k))H , .Further, for each drought r:• the regional drought duration L(r) is defined as:L(r) = i f (r) - i i (r)+1where i f and i i are such that:SPI(i)< SPI th for i i (r) ≤i≤ i f (r) and SPI [i i (r) – 1] ≥ SPI th 0, SPI[i f (r) + 1] ≥ SPI th .• the mean areal coverage of drought can be computed as:i fAD ( r)= ∑ Ad(i) / L(r)i=ii19

Again as in the case of at site analysis, the above characteristics can be furtheranalyzed by taking the average and by considering their minimum and maximum values, inorder to characterize the whole period of observations.5. Description of the software5.1 OverviewThe package REDIM is an user friendly software which allows to perform drought analysison hydrological series both at a site and over a region using the method of run and the SPIindex. In addition, it allows to test statistically for the existence of non-stationarities in atime series, whose presence would lead to misleading drought analyses. The software,written in Visual Basic, runs under Windows platforms, and is structured as a succession ofdialog boxes which guide the user throughout the analysis of stationarity and droughtidentification and characterization steps. The main features of REDIM can be listed asfollows:• Data files are in MS Access format, which allows flexibility and compatibility withexisting databases, as well as Windows based programs such as spreadsheets, wordprocessors, etc..;• The Data Import function allows to create automatically MS Access database files fromexisting ASCII text files, thus avoiding tedious database creation processes;• Different aggregation time scales can be used (monthly, three months and yearly), withthe possibility to select the initial month of aggregation in order to take into accountwater years;• Testing for stationarity in hydrological series is carried out by means of six differentstatistical tests namely: Student’s t-test for linear trend, Kendall’s τ or rank correlationtest and turning point test, Mann-Withney rank-sum test for detecting the homogeneityof the series, F test for detecting change in variance, and t test for detecting change inmean;• Identification and characterization of drought is performed by means of run method orthe Standardize Precipitation Index.• Return period of at site drought characteristics is computed;• Graphical output of results allows to easily identify droughts on a given time series,and/or region.20

• Text reports is produced in MsWord format, to facilitate the merging of the outputswith other existing documents.In what follows a more detailed description of REDIM features is reported.5.2 Software configurationRedim allows to configure its main parameters which are then automatically stored to beretrieved every time the software starts. By selecting “Configure” from the “Setting” menu,the dialog box reported in Figure 4 appears.Figure 4. Configure dialog boxThe dialog box contains two tabs, one for general settings, the other one for setting thedefault path of database files. The “General” tab, allows to set the pathnames for MSAccess and MS Excel programs. The “Database Library” tab allows to define the pathwhere the hydrological databases are stored.The “Configure” dialog box appears automatically when the software is run for the firsttime after installation. Afterwards, the parameters can be changed at any time, according tothe user’s need.21

Figure 6. Main dialog boxThe user is prompted to select the type of analysis to perform and the typology ofhydrological data. Note that regional drought analysis can be performed only withprecipitation data. After selecting “Analysis of stationarity” and the hydrological variable,by clicking next the dialog box in Figure 7 appears:23

Figure 7. Aggregation time scale selection dialog boxThis dialog box allows to select the aggregation time scale for the analysis.Note that for the analysis of stationarity only annual (calendar or water year) and threemonths scales are present. Also, it should be pointed out that at the three months scale, theanalysis is performed only on the trimester starting at the month selected by the user. Inother words, suppose the user selects Trimester and initial month March. The analysis willbe performed on the series constructed by summing the variable of March+April+May forthe first year, March+April+May for the second year and so on. This allows to comparetrend features of different seasons of the year. By choosing instead the Year time scale, theanalyzed series is obtained by summing over 12 months the values, starting at the selectedmonth. For example, if the interest lies in analyzing data for the water year starting inOctober, the Year scale and October initial month should be selected. After clicking Next,the user is prompted to enter the pathname of the datafile, while as usual the Browse buttoncan be used to facilitate this task. The following two dialog boxes, which are accessed byclicking Next, prompt the user to enter the initial and final year of the analysis, as well asthe type of tests to perform and the significance level. Then, the dialog box showing theresults of the selected tests appears (Figure 8 and 9):24

Figure 8. Tests for trend detecting results dialog box25

Figure 9. Tests for trend detecting change in variance and mean results dialog boxIn particular the tab "Tests-Detection of trend" (Figure 8) reports the results of theapplication of the Student’s t-test for linear trend, Kendall’s τ or rank correlation test andof the turning point test while the tab "Tests-Detection of changes in variance and mean"shows the results of the Mann-Withney rank-sum test for detecting the homogeneity of theseries, F test for detecting change in variance, and t test for detecting change in mean. Foreach test, the intermediate results, as well as the test outcome are reported. For theexplanation of the symbols please refer to chapter 2 of the present document. Note that foreach test a green label will appear if the hypothesis is accepted, otherwise the label colorwill be red.By clicking on the “Plot” command button the form containing the plot of hydrologicalvariable time series and the trend line appears (Figure 10).26

Figure 10. Hydrological variable time series and the trend line5.5 Drought analysis at a site based on run-methodAfter selecting drought analysis at site, the run method for drought identification and thetype of hydrological variable in the main dialog box, the user is prompted to select theaggregation time scale (monthly, three months and yearly) and the initial month ofaggregation. For yearly analysis the user can also select the checkbox for the evaluation ofdrought return period.Note that for drought analysis (either regional or at site), aggregation at the three monthstime scales is carried out differently than in the case of analysis of stationarity. Indeed inthe present case, the series obtained by aggregating at three months is simply thesuccession of trimesters starting at the selected initial month. For example, if the userselect three months and initial month April, the aggregated series will be the obtained bysumming variables values of April+May+June, July+August+September, and so on. Thusthe resulting series will be in general periodic. After selecting the aggregation time scalethe user must specify the data file and the initial/final year of the analysis, as for theanalysis of stationarity case. Then dialog box in Figure 11 appears:27

Figure 11. Drought analysis options dialog boxSuch dialog box contains three sub-dialog boxes or tabs: Selected data, Statistics andOptions (which is the one shown). Each tab can be accessed by simply clicking on thename. The Selected data displays the aggregated data used for the analysis and is mainlyused for checking that the analyzed data is the correct one. The Statistics tab shows themain statistics of the analyzed series such as mean, standard deviations, etc.. The Optiontab (shown above) allows to select the threshold level as well as the options to computereturn period (only yearly time scale). Note that a sample quantile corresponding to afrequency level 50% is (by definition) the median. Regarding the return period evaluationthe user can select either the non-parametric approach or the parametric approach tocompute the parameters of the gamma distribution for accumulated deficit (please refer topar. 3.4 for the details). In the former case (non parametric), such parameters will becomputed from the sample moments of the single deficit identified on the series. In thelatter case (parametric), the parameters of the gamma will be estimated by assuming anormal, log normal or gamma distribution for the underlying hydrological series. In thiscase, the user is prompted to select the appropriate distribution. After clicking Next, thedrought analysis results dialog box appears (Figure 12).28

Figure 12. Results of at site drought analysisAgain three tabs are present. The Drought characteristics tab (shown above) contains thenumber of identified droughts, a detailed list of their characteristics, as well as their mean,max and min values. Furthermore (only yearly time scale), for each drought, the returnperiod corresponding to different combinations of drought characteristics is also shown.Note that by clicking on the appropriate Sort by buttons it is possible to show the list sortedin descending order according to the selected characteristic. By clicking on Save Reportbutton, it is possible to save a report file. The Generic information tab contains plots of thethresholds, while the Plots tab shows a graph of the analyzed series, of the threshold andred/blue values indicating whether the interval is deficit or surplus respectively (Figure13). Droughts can be easily identified as a consecutive series of red values preceded andfollowed by at least one blue value.29

Figure 13. Hydrological variable time series5.6 Regional drought analysis based on extended run-methodThe first steps for performing regional drought analysis are basically the same as in thecase of at site analysis. Regional drought analysis can be performed only on precipitationdata. After selecting the type of analysis in the main dialog box and the aggregation timescale, the dialog box in Figure 14 appears.30

Figure 14. Selection of precipitation stations for regional drought analysisBy clicking on the data file on the left box the user can select the hydrological stations tobe used for the analysis. The two buttons on the right allow to remove stations from theselection. Once the stations have been selected, the user can save the station list to beretrieved ad at later time by clicking on the button with the disk symbol. To reload thestation list, the user must click on the "Station list" check button in the upper part of thedialog box and select the file.Note that the file shown are located in the directory specified in the Setting dialog box atinstallation. If necessary, the user can change such directory by accessing the Setting menuany time.By clicking next a dialog box appears prompting for the total area of the region of interestand for the influence areas of each station, expressed as a percentage of the total area. Byclicking Next, the areas expressed in km 2 appear, as well as the common period ofobservation. The time span to be analyzed can be changed at this stage if needed. Byclicking Next again, the dialog box in Figure 15 appears.31

Figure 15. Regional drought analysis options dialog boxNote that the user must provide the areal threshold expressed as a percentage of the totalarea. As in the case of at site analysis, the Option tab allows to select the threshold, theStatistics show the threshold values and the Selected data allows to check that the analyzeddata is correct. Again, the median can be selected as a threshold by assuming a samplequantile corresponding to a frequency level 50%. By clicking Next, the drought analysisresults appear (Figure 16).32

Figure 16. Regional drought analysis resultsThe windows has three tabs. The tables tab (shown above) contains the number ofidentified droughts, a detailed list of their characteristics, as well as their mean, max andmin values. Note that the by clicking on the appropriate Sort by buttons it is possible to listthe results sorted in descending order according to the selected characteristic. By clickingon Save Report button, it is possible to save a report text file which can be visualized orprinted by using any text editors such as Notepad. The Plots tab shows the areal coverageand cumulated deficit plots. An example of such plots is reported in Figure 17. TheGeneric Information tab contains plots of the thresholds and other information, such as thetotal number of periods and the extensions of the critical area.33

Figure 17. Example of regional drought identification5.7 Drought analysis at site through SPI indexAfter selecting drought analysis at site, the SPI index method for drought identificationand the type of hydrological variable in the main dialog box, the user is prompted tospecify the data file and then a dialog box containing the original data and the statistic isshowed. By clicking on the “Next” button the dialog box showed in Figure 18 appears.34

Figure 18. SPI analysis at site results.Such dialog box contains five sub-dialog box or tabs which show the results of the analysisfor five different aggregation scales. Each tab contains a table with the identification ofdrought period with SPI < -1.00 and a table with mean and minimum value of the SPIindex and the duration for different classes. By changing the aggregation scale and clickingon the “Evaluate” button the analysis is repeated for the new aggregation scale. By clickingon the “Plot” button the graphical representation of the SPI time series appears. Byclicking on the “Table” button the graphical representation of the SPI time seriesdisappears and the table results appears again. By clicking on Save Report button, it ispossible to save a report file showing the results of the aggregation time scales selected inthe dialog-box showed in Figure 19.35

Figure 19. Selection of the aggregation scales5.8 Regional drought analysis through SPI indexAfter selecting the type of analysis in the main dialog box, and selecting the precipitationstation and their influence area as showed in paragraph 4.6 the dialog box showed inFigure 20 appears.Figure 20. Selected data, statistics and selection of threshold dialog box.36

This dialog box contains two tabs: the former contains the selected data, the latter thestatistics of the selected data on a monthly scale. The last one contains also two combo-boxfor the selection of the areal and SPI thresholds for the identification of regional drought .By clicking on the “Next” button the dialog box showed in Figure 21 appears.Figure 21. Regional drought identification through SPI index.Such dialog box contains five sub-dialog box or tabs which show the results of the analysisfor five different aggregation scale. Each tab shows two tables. The former contains adetailed list of the drought period characteristics, the latter contains the mean, maximumand minimum values of duration, SPI index and the drought areal coverage. By changingthe aggregation scale and clicking on the “Evaluate” button the analysis is repeated for thenew aggregation scale. By clicking on the “Plot” button the graphical representation of theSPI time series appears showing the areal coverage and SPI index evaluates by taking intoaccount the areal hydrological variable computed by considering only the sites for wich theSPI values are below the fixed threshold. An example of such plots is reported in Figure22. By clicking on the “Table” button the graphical representation of the SPI time seriesdisappears and the table results appears again. By clicking on Save Report button, it ispossible to save a report file of the aggregation time scales selected in the dialog-boxshowed in Figure 19.37

Figure 22. Regional drought identification through SPI index – graphical results.5.9 Graphical outputWhenever the user clicks the “Save report” button, different graphics are automaticallycreated by Redim, according to the type of analysis. Such plots are automaticallyembedded in a RTF document.38

6. ReferencesAbramowitz, M., Stegun, I.A. (eds.), (1970). Handbook of Mathematical Functions withFormulas, Graphs, and Mathematical Tables, U.S. Department of Commerce.Ben-Zvi, A., (1987), Indices of hydrological drought in Israel, J. of Hydrology, 92.Bonaccorso, B., Cancelliere, A., Rossi, G., (2003). An analytical formulation of returnperiod of drought severity, Stochastic Environmental Research and Risk Assessment,publ. no. 17, pp. 157-174Cancelliere, A. and Salas, J. D., (2004). Drought length properties for periodic-stochastichydrological data." Water Resources Research, 10(2).Cancelliere, A., Bonaccorso, B., Rossi, G., Salas, J.D., (2003). On the probabilisticcharacterization of drought events. In Proceedings of 23th Annual AmericanGeophysical Union Hydrology Days, Fort Collins, Colorado, USA, March 31 - April2, pp. 33-44.Cancelliere A., A. Ancarani, G. Rossi, (1995), Identification of drought periods onstreamflow series at different time scales, in Tsiourtis, N. X. (ed.) Proc. of the EWRASymposium on Water Resources Management under Drought or Water ShortageConditions, Nicosia, Cyprus, 14-18 March 1995, Balkema, Rotterdam.Cancelliere A., A. Ancarani, G. Rossi, (1998), Distribuzioni di probabilità dellecaratteristiche di siccità. Atti del XXVI Convegno di Idraulica e CostruzioniIdrauliche, Catania 9-12 settembre, CUECM, Catania.Clausen, B., C. P. Pearson, (1995), Regional frequency analysis of annual maximumstreamflow drought, J. of Hydrology, 173.Dracup, J. A., K. S. Lie, E. D. Paulson, (1980), On the definition of droughts, WaterResources Research, 16(2).Helsel, D. R., and R. M. Hirsch, (1992). Statistical methods in water resources, Elsevier,Amsterdam.Kottegoda, N.T., (1980), Stochastic Water Resources Technology, The Macmillan Press,London.Maidment, D. R., (ed.), (1993). Handbook of Hydrology, McGraw-Hill Inc., New York.Rodrigues, R., M.A. Santos, F.N. Correia, (1993), Appropriate time resolution forstochastic drought analysis, in: J. D. Salas, R. Harboe, and J. Marco-Segura (eds.),Stochastic Hydrology and its Use in Water Resources Systems Simulation andOptimization, Kluwer, Netherland.39

Rossi G., et al., (1992), On regional drought estimation and analysis, Water ResourcesManagement, 6.Rossi, G., Cancelliere, A., (2003). At-site and regional drought identification by REDIMmodel, in G. Rossi, et al. (eds), Tools for drought mitigation in Mediterraneanregions, Kluwer Academic Publishing, Dordrecht, pp. 37-57.Thom, H.C., (1966), Some Methods of climatological analysis, World MeteorogicalOrganization Note no. 81, World Meteorogical Organization, pp. 1-53.Wilcoxon, F. (1945). Individual Comparisons by Ranking Methods. Biometrics 1, 80-83.Yevjevich, V., (1967). An objective approach to definitions and investigations ofcontinental hydrologic drought, Hydrology paper n. 23, Colorado State University,Fort Collins, Colorado.Yevjevich V., L. Da Cunha, E. Vlachos (eds.), (1983), Coping with Droughts, WaterResources Publications, Littleton, Colorado.Zelenhasic E., A. Salvai, (1987), A method of streamflow drought analysis, WaterResources Research, 23(1).40

7. Appendix A: MS Access data file formatThe generic database file must contain at least one of the following tables:• rain• deflussi (streamflows)• rese (spring yield)Each table contains the monthly observations in a row (year) by column( month) layoutand has the following record structure:• Field 1: Anno year of observation• Field 2: Mese1 January observation• Field 3: Mese2 February observation• :::• Field 13: Mese12 December observation• Field 14: Gener The first two record of this field must contain the units and thestation name respectively• Field 15: Area Empty. Kept for compatibility with other softwareNote that it is important that the first month of observation is January, otherwise thecomputation of the water year by Redim might be incorrect.41

8. Appendix B: text data file formatThe text file to be used in the Data Import function must contain the monthly observationsin a row (year) by column (month) layout. Data must be separated by at least one space andthe decimal separator must be the dot (.). The first two line must contain the units and thename of the station.An example of text file containing 20 years of monthly precipitation data is reportedhereafter.Cerami, [mm]1921 62.8 41.9 139.4 71.9 43.6 118.3 51 40 100.7 93.9 81.1 94.41922 242 105 47 20 36 0 0 0 22 38 65 991923 124 105 97 78 0 22 23 48 48 18 96 1791924 97 112 79 32 0 26 16 0 0 152 59 781925 15 53 56 63 98 0 0 4 63 121 107 651926 48 5 52 84 36 71 7 0 80 20 75 921927 68 45 14 78 88 2 0 60 15 192 357 2141928 122 81 247 123 0 0 1 3 43 41 18 1121929 63 40 28 7 78 10 3 23 13 79 57 751930 142 301 31 23 34 6 30 0 67 62 38 511931 222 244 79 41 24 3 9 0 23 16 87 1551932 5 77 177 35 1 2 2 0 57 36 290 541933 54 98 52 49 2 31 16 145 54 13 137 3231934 147 67 47 76 14 23 0 0 36 120 138 1101935 212 57 250 0 9 0 132 20 38 70 207 881936 17 89 11 61 20 106 0 81 90 86 136 1931937 20 83 29 64 63 24 5 0 85 93 153 1621938 100 56 32 67 66 12 7 19 33 210 108 1601939 56 92 98 60 73 40 0 9 135 36 79 1061940 187 28 34 86 62 22 0 5 13 108 14 97Again, please note that it is important that the first month of observation is January,otherwise the computation of the water year by Redim might be incorrect. Also no extralines should be inserted before the station name or after the last year as this might causeunpredictable results.42

9. Appendix C: computation of sample quantilesWith reference to a series x t (t=1,2 ….n) and to a frequency level F, the sample quantile x Fis computed by letting i=F*(n+1), i1=int(i), i2=i1+1 where int(.) is the integer part of theargument. Then:x F =x i1 +(x i2 -x i1 )*(i-i1)43