A probabilistic approach for estimating spring discharge facing data scarcity

Since spring discharge, especially in arid and semiarid regions, varies considerably in different months of the year, a time series of spring discharge observations is needed to determine the firm yield of the spring and the amount of water allocated to different needs. Because most springs are in mountainous and inaccessible areas, long-term observational data are often unavailable. This study proposes a probabilistic method based on bivariate analysis to estimate the discharge of the Absefid spring in Iran. This method constructed the bivariate distribution of the outflows of Absefid (AS) and Gerdebisheh (GS) springs using Copula functions. For this purpose, the fit of 11 different univariate distributions to the discharge data of each spring was tested. The results revealed that the GEV and log-normal distributions best fit the discharge data of GS and AS springs, respectively. In addition, among eight different copula functions, the Joe copula function was selected to construct the bivariate distribution of the discharge data of AS and GS springs. With the help of the created bivariate distribution and assuming a certain probability level, it is possible to estimate the discharge of Absefid spring based on the discharge of Gerdebisheh spring in a particular month. The estimated values of the discharge of the Absefid spring in the period from March 1993 to August 2022 show that with a probability of 90%, the lowest discharge of this spring is 600 L per second and occurred in June 2001. Therefore, to allocate the water from this spring for drinking purposes, this discharge value can be considered as the firm yield of this source. However, the amount of allocated water from this source should be determined by considering the ecological needs of the river downstream of this spring.