Regional analysis of streamflow drought: a case study in southwestern Iran

Droughts are complex natural hazards that, to a varying degree, affect some parts of the world every year. The range of drought impacts is related to drought occurring in different stages of the hydrological cycle and usually different types of droughts such as meteorological, agricultural, hydrological, and socio-economical are the most distinguished types. Hydrological drought includes streamflow and groundwater droughts. In this paper, streamflow drought was analyzed using the method of truncation level (at 70 % level) by daily discharges at 54 stations in southwestern Iran. Frequency analysis was carried out for annual maximum series of drought deficit volume and duration. 35 factors such as physiographic, climatic, geologic and vegetation were studied to carry out the regional analysis. According to conclusions of factor analysis, the six most effective factors include watershed area, the sum rain from December to February, the percentage of area with NDVI <0.1, the percentage of convex area, drainage density and the minimum of watershed elevation, explained 89.2 % of variance. The homogenous regions were determined by cluster analysis and discriminate function analysis. The suitable multivariate regression models were ascertained and evaluated for hydrological drought deficit volume with 2 years return period. The significance level of models was 0.01. The conclusion showed that the watershed area is the most effective factor that has a high correlation with drought deficit volume. Moreover, drought duration was not a suitable index for regional analysis.

soil moisture deficit, which may reduce agricultural production and increase the probability of forest fires. It can further develop into a streamflow drought defined as the deficit in surface water and groundwater, reducing water supply for drinking, irrigation, industrial and hydropower needs. A discussion of different drought definitions can be found in [3] and [20].
The truncation level method defines droughts as periods during which the streamflow is below a certain truncation level [21]. This drought event definition fulfils the above criteria and is selected for this study. This method has been used for point drought analysis in some previous researches (e.g. [24] - [12]- [18]- [4]- [16]).
Regional analysis of droughts can be performed via studying spatial patterns of point drought or alternatively studying regional characteristics of the drought [17]- [19]- [6]- [7]- [23]. Hisdal and Tallaksen [9] estimated the regional streamflow drought characteristics by truncation level, Empirical Orthogonal Functions (EOF) and Kriging method interpolation. Another method for regional analysis is studying effects of climatic, physiographic, geologic and vegetation on hydrologic indices. Nathan and McMahon [14] regional analyzed the low flow in 184 catchments by multivariate regression, cluster analysis and principle component analysis (PCA) in Australia. Nutzmann and May [15] provided a model to determinate river discharge and indicated that streamflow drought is controlled by base flow and groundwater level. Longobardi and Villani [13] studied the effects of climatic, topographic, geologic and soil properties on base flow index (BFI) as a characteristic of low flow and concluded that geologic factor exerted highest impact on BFI.
In the present study regional streamflow drought characteristics are analyzed. A drought event definition applicable to stream flow time series, and of direct relevance to the water industry and to environmental demands, is adopted.  [11]. The daily discharge series of 54 hydrometric stations was included in this study. These data were made available by Iranian Water Resource Management Organization. Fig. 1 shows the geographic location of the study area in relation to the country Iran as well as stream flow stations.

A. Threshold Level Method
The threshold level method introduced by Yevjevich [21] based on theory of runs defines droughts as periods during which the water supply is lower than the current water demand. Yevjevich [22] later simplified this method by applying a constant demand that was represented by a threshold level, α Q , thus droughts are defined as periods during which the stream flow is below the threshold level.
Based on the run theory a run is the period between two consecutive crossings of the truncation level and it delineates a drought event. The run length then explains the duration of the drought event and the run sum describes the cumulative deficit volume. The drought characteristics include deficit volume or severity, i V , duration, i d and the start of drought i t as illustrated in Fig. 2. The threshold level should represent the lower boundary to "normal" condition and is set to a percentile of the daily flow duration curve (FDC), e.g. the 70-percentile flow ( 70 Q ), which represents that flow exceeded 70 percent of the time.
Minor droughts have short duration and small deficit volume and should be reduced in an extreme value analysis. Dependent droughts can occur during long-term periods of low discharge when divide the period of low discharge into several drought events. There are three different pooling procedures; moving verage (MA), sequent peak algorithm (SPA) and the inter event time criterion (IT-Criterion). They were compared and discussed in [19]- [8]- [4].
Based of IT-Criterion two dependent droughts are pooled if they occur less than a critical number of days, c t , apart, i.e.
The duration of pooled drought is defined from the starting (first) day of the first pooled event to the last day of the last pooled event.
respectively. In references [19] and [4] recommend that day t c 5 = . The pooled drought deficit volume of the pooled events is as follows: The minor droughts are excluded when their deficit volume is smaller than a certain coefficient (%) multiple by maximum observed deficit volume ( ). The value of α must be from 0.5 to 1%. ( )

B. Frequency Analysis
Where t Z is the number of drought events and ) Pr( k Z t = is the probability of k events during the time interval [4]. The Nizowka software is used for extraction and analysis of droughts [10]. Gamma, Weibull, Log-Normal, Johnson, Gumbel and Generalized Pareto, fit to series of deficit volume and duration by applying the method of maximum likelihood. Also, the Pascal and Poisson distributions applied for the event numbers. 2 χ -goodness of fit test was used to examine different distributions at 0.05 significance level [5] . The return period of drought characteristics (deficit volume and duration) calculated by: ( ) C. Regional Analysis Regional analysis is a method to estimate the hydrological characteristics of ungauged basins with no data. The relation between dependent and independent variables is established by multivariate regression models.
Dependent variables include hydrological indices and characteristics such as flow duration quantiles, floods of different return periods, low flow and hydrological drought indices. Independent variables may involve geological, physiographic, climatic and land cover factors. In this research, some 35 independent variables which were included for the study of regional hydrological drought are main river slope, main river length, watershed length, watershed slope, mean elevation, watershed perimeter, watershed area, total length of rivers, minimum elevation, drainage density, percent of concave area, steady or convex areas, percent of area under snow melt line in different months (March, April, and May), percent of areas in different aspects (including flat, northwest, north, northeast, east, southeast, south, southwest, and west), percent of area with various ranges of NDVI ( <0.1, 0.1-0.25, 0.25-0.4, and >0.4), average annual rainfall, cumulative rainfall depth in December-February, December-March, December-April, and December-May periods.
Factor analysis attempts to identify factors that explain the formation of correlations within a set of observed variables. Varimax rotation and principal component methods were used in this research.
Cluster analysis was used to grouping the watersheds into homogenous classes. Hierarchic method starts with the calculation matrix of distances between individuals. Each individual first forms a group with one number. The groups that are 'close' together are merged. Several ways to define 'close' include nearest neighbors, furthest neighbor linkage, group average linkage and Ward's method. Ward's method with squared Euclidean distances was used in this study.
By discriminate function analysis, it is possible to separate two or more groups of individuals, given measurement of several variables related to these individuals. An approach to discriminate is based on Mahalanobis distances. The Mahalanobis distances of individuals to group centers can then be calculated and each individual can be allocated to the group that it is closest to. Another method is canonical discriminate functions that involve taking a linear combination of variables for separating groups. Second method employed in this study.
A regression model predicts the value of a dependent variable with one or more independent variables. In this research, independent variables are geological, physiographic, climatic, and land cover factors. Dependent variables are hydrological drought indexes including drought deficit volume and duration.
Step wise regression is a technique for choosing the variables to be included in a multiple regression model.

IV. RESULTS
In each one of the 54 hydrometric stations in the study area, drought periods were determined based on 70% threshold level. Frequency analysis on annual maximum series of duration and deficit volume was performed. Suitable distribution wasn't found for five stations. Thus, the number of stations was decreased to 49 for further analysis. In most stations, the most sever and longest droughts occurred during 2000-2003 period. For the regional analysis, deficit volume and duration of 2-year return period were determined as the regional model dependent variables "Figs. 3 and 4".   Performing factor analysis on 35 factors mentioned earlier, these first components with eigen value greater than one In the next step, the first six components were rotated by Varimax method. The results showed that watershed area, total rainfall depth from December to February, the percentage of watershed area with NDVI<0.1, the percentage of convex areas, drainage density, and minimum elevation had the highest correlation with the first six components. In order to determine hydrologically homogenous regions, the hierarchical cluster analysis was applied and the method of furthest neighbor yielded best results. The homogenous watersheds were determined based on maximum Euclidean distance of 12.
The discriminate analysis showed that watershed area, percentage of watershed area with NDVI<0.1, and the percentage of convex areas were the main discriminative variables between groups The map of hydrologically homogenous regions is shown in Fig. 5.
At this stage, the stepwise regression analysis was carried out with six independent variables, and two dependent variables, i.e. deficit volume and drought duration. The GLS 1 method was applied in order to determine the model parameters. No suitable relation was found for drought duration in homogenous regions. Hence, only deficit volume regional regression models were established. Coefficient of determination (R 2 ) and standard error (Se) was calculated and the best model was selected with a significance level of α=0.01, as shown in Table I.
All regional models in homogenous regions were significant in 0.01 level and had acceptable R 2 with low standard error. The value of R 2 for all models in homogenous regions was higher than that of models for the whole region.
By applying multivariate regression method, suitable 2-year deficit volume models were derived at 0.01 significance level individual homogeneous regions as well as the entire region. The deficit volume models involved watershed area and total rainfall depth from December to February. Chalise et al. [2] also found that the average annual rainfall is the most effective factor on stream flow in Himalaya. While [15] concluded that the hydrological drought in Germany was controlled by base flow and downfall of groundwater level. The main conclusions of this study as follows: • The deficit volume and duration regional maps confirmed meaningful differences between northern and southern portions as well as upstream and downstream watersheds. • The 2-year deficit volume regional models in the majority of homogenous regions were dependent on watershed area and total rainfall depth from December to February. • No regional model could be established for hydrological drought duration due to no fit of statistical distributions on drought duration. 1 Generalized Least Squares