An overview on water balance models: mathematical-conceptual water balance models for watershed

Water consumption has been rising during the last five decades across the globe because of population growth, higher standard of living, and economic development. Water resources limitations in Iran has led to the emergence of sustainable water resource management. To deal with the complex and interlinked water challenges, we need knowledge about the quantity and quality of water in the watersheds through water balance investigation. Evaluating available water resources is a prerequisite step in the water resources management to avoid adverse environmental impacts. Water balance investigations, as a tool for quantitative evaluation of water resources, is a prerequisite step in water resources management process. However, we have faced to some problems with water balance calculations such as: it is costly and time-consuming to provide reliable data for a large area and the estimation methods of water balance components rely on the methods that would not be appropriate for Iran's meteorological, hydrological and hydrogeological conditions. For example, in many cases, the empirical methods and mathematical models used in Iran were developed in other countries with different climates.

Water balance models have been developed over multiple timescales (hourly, daily, monthly and yearly) and different spatial resolutions and varying degrees of complexity. Water balance models were first developed in the 1940s by Thornthwaite. With the increasing use of water balance models to address hydrological problems, a considerable amount of efforts has been devoted to the development of such models and techniques. A variety of models have been considered, ranging from relatively complex conceptual models to complex physical based models. Previous studies showed that using conceptual water balance models rather than process-based models or data-driven models have some advantages. Process-based models require high resolution, in both space and time, data and data-driven models may not remain valid in changed climatic conditions. Therefore, we focus on distributed and semi-distributed mathematical conceptual models. After evaluation different models, we introduce and classify some models that have relative advantages for being applied in Iran. These models have at least one of the following properties: they are conceptual models, some of them have been used for different regions, and some of them have been used for dry and semi-arid areas, and they use a simple method for water balance calculation, or their code, software or graphical interface are available freely.

To choose and modify an appropriate water balance model for Iran's watersheds, we should consider a simpler one especially when there are usually uncertainties about the model parameters and input data due to sparse data and lack of knowledge about the natural systems. We investigated different models especially models that have a fewer number of parameters for calibration and consider hydrological spatial variability in a water basin. Considering these facts, it seems the model developed by Portoghese et al. could be a good choice for the most arid and semiarid regions in Iran, after necessary corrections and modifications. The modified model was successfully implemented in different watersheds in Razavi Khorasan province. The model results, such as runoff, actual evapotranspiration, and deep percolation were in agreement with other studies, and consistent with the basin hydrological process.