ارزیابی روابط کمی خشکسالی های هواشناسی و هیدرولوژیکی با استفاده از رژیم نرمال ماهانه(مطالعه موردی: حوضه صوفی چای)

Climate change with population growth makes the water resources an important issue in Iran. Drought is an abnormal dry period which lasted for a long time. Frequency analysis of drought and prediction of drought deficit volume (drought severity) for a determined period and return period are the most important issues in drought studies. Frequency analysis is a technique of fitting a probability distribution to a series of observations for providing the probabilities of future occurrences. Also, this technique is the statistical analysis of series that have a suitable probability distribution. Inappropriate temporal and spatial distribution of rainfall exacerbate water resources management problems in addition to rainfall deficit. We can consider drought as an inappropriate temporal distribution of rainfall, So we feel the necessity of drought studies in different aspects. There are various studies for meteorological, hydrological and agricultural droughts but it seems we have not any specific research about relationship between intensity and duration frequency of both meteorological and hydrological droughts. Therefore, the purpose of this study is to determine a consolidated statistical indicator based on meteorological and hydrological droughts in regional scale.
This drought study is described in Soufi-Chai basin with 265 km2 in East Azerbaijan which is located in northwestern Iran. The monthly flow and precipitation data of Soufi-Chai's stations was used. The observed data consists of 40 years (480 months) period between 1970 and 2011. Then the monthly precipitation data have been classified by using Thiessen Polygon for meteorological droughts and the monthly flow data of Tazeh-Kand station in outlet was considered for hydrological droughts. In order to extract the amount of drought periods for both flow and precipitation, monthly normal regime method was applied. Monthly normal series show a long-term average for each month of a year that presents monthly normal regime for a normal year. Anomaly series for both flow and precipitation data were made by subtracting flow and precipitation data from monthly normal series. In fact, we considered monthly normal series as base level and amounts under this level (negative amounts) introduced as dry periods. Then these droughts was converted to the volume deficits that showed by duration one month, two months, …and up to twelve months. In order to fit suitable distribution and extract IDF (Intensity- Duration- Frequency) curves, frequency analysis upon volume deficit was done by using statistical distribution methods. In this study, SMADA software was used for frequency analysis. In this work, root mean square error (RMSE) were used to assess different distributions. For various return periods (2, 3, 5, 10, 25, 50, 100 and 200) the precipitation and flow drought volume deficits were calculated by using Normal and Pearson type III distributions. We eliminated temporal factor and only based on various return periods for extracting a model which shows a relationship between both meteorological and hydrological droughts. At first, a statistical model was obtained separately for each drought and then a new index was created by eliminating temporal factor as below:

This index is an exponentially equation which only related to return period. For investigating performance of this index, correlation coefficient (R) was used. R values had high amounts that shows a desirable result for this equation. This index is so important in reservoirs and dam management.
As a result of this study, we considered average amount as a management line, so that, drought will be the precipitation or flow under the average. The meteorological and hydrological drought graphs show that in most years, hydrological drought has not occurred in those months which have meteorological drought, because of some reasons such as delay in snow melting. So hydrological droughts have occurred in few months later. Therefore, it takes time to affect different elements of hydrologic system like river, reservoirs and underground waters by precipitation deficit. A comparison between IDF curves showed that hydrological droughts take place with more intensity rather than meteorological droughts. Then forecasting hydrological droughts by meteorological droughts done by frequency analyzing. The results showed that Normal distribution has the least root mean square error (RMSE) for precipitation volume deficits in duration from one month to nine, respectively: (1.07, 1.950, 2.043, 1.917, 1.924, 1.981, 2.641, 3.515, 5.489) and Pearson type ? for flow volume deficits (1.179, 2, 2.663, 3.101, 3.508, 3.812, 4.321, 4.828, 5.029). By using these statistical distributions, severity- duration- frequency curves were extracted and an appropriate mathematical equation based on correlation coefficient and also the least error has been selected. Then the relationship between meteorological and hydrological droughts was earned exponentially independent of time and only based on frequency. The results of this study are very noteworthy for droughts management.