Analysis and Modeling of the Relationship between Monthly Discharge and Geomorphometric Characteristics (Case Study: Kashafrood Watershed)

Predicting and obtaining information about stream flows is vital for many practical applications such as water allocation, long-term planning, catchment management operation, flood forecasting, optimization of hydropower production, designing hydraulic structures, and so on. On these accounts, experts have always attempted to accurately estimate river flows and provide contributions to the existing methods. It is possible to establish a relationship between discharges of catchments based on sufficient statistics and their geometry characteristics by using regional analysis and multivariate regression in a relatively homogeneous region in order to estimate discharges of the catchments without statistics or with insufficient statistics in that region. Owing to the need for a better modeling of water discharges in terms of seasonal variations, the present study tried to regionally estimate the monthly mean, minimum, and maximum discharges in Kashfarud Watershed based on geomorphometric variables in order to: (1) examine the possibility of scientific and useful generalization of surface water quantity in the whole watershed and (2) identify and determine important geomorphometric factors influencing the water discharge variations of Kashfarud sub-watersheds. Kashfarud as a vital flow in this region, including Mashhad plain, has played an important role in supplying water to the inhabitants of Mashhad metropolis and other surrounding cities such as Chenaran and Torqabeh. Besides, extensive engineering facilities, such as Golestan, Torogh, Kardeh, and Ardak dams, have been built on the tributaries of this river. 

The research was grounded upon statistical analysis, including correlation and regression tests. For this study, we made use of monthly average (low, medium, high) discharge data and resolution of 30-m DEM. The discharge data were measured in 10-gauge stations of 10 sub-watersheds over 20 year (1997-2017). In this regard, we considered the monthly discharge values ​​of 10 stations located in 10 sub-basins during the water years of 1997-2016. The research proceeded as follows: after selecting the common statistical period, we calculated the monthly average flows recorded in the stations over 20 years. Next, 2 months with the highest and lowest flows were selected in each station. Also, we considered the values ​​of the two selected months besides the average monthly discharges in the stations (average of 12 months) as the dependent variables. Afterwards, we embarked upon to calculate the independent geomorphometric variables (16 variables), which were determined by using DEM in the GIS environment. The independent variables included perimeter, area, minimum elevation, average elevation, maximum elevation, elevation range, average slope, maximum slope, main stream slope,  main stream length, total stream length, drainage density, Schumm’s roughness index, Gravilius coefficient, elongation, and concentration time. After calculating the values ​​of the 3 dependent and 16 independent variables for each station, we tested them based on a two-way correlation to find out which variables had a significant relationship by means of the correlation matrix. The significance level of the correlation relationships was ≤0.05. Finally, we  presented an estimate model of the dependent variables via the independent variables. This was done based on the dependent and independent variables that had significant correlation relationships.  

The results of the correlation analysis showed no significant relationships between the minimum monthly discharges and the independent variables.  This was probably due to the dryness condition and small variance in the low monthly discharge rates among the sub-watersheds. In contrast, significant relationships were obtained among the monthly mean and maximum discharges and 6 geomorphometric variables including the average elevation, maximum elevation, elevation range, average slope, drainage density, and roughness ratio. The correlation coefficients of all significant relationships were above 0.6, indicating a close and strong relationship between these variables. The direct correlation of altitude, slope, and roughness with monthly mean and maximum discharges indicated that on the one hand, the monthly discharges of the sub-watersheds were strongly dependent on the altitude variables dominating the other environmental factors while on the other hand, the roughness intensity and active dynamics associated with the variables of altitude played an important role in water flowing and transporting from upstream to downstream of the catchments so that the speed of hydrological responses of the catchments increased by the rise of roughness severity. In contrast, the negative correlation between the drainage density and the dependent variables was unexpected and probably associated with hydroclimatic conditions indicating characteristics of the dry and geologic conditions, permeability of some formations, and presence of joints and fissures in the rocks. The predictive regression models of the monthly mean and maximum discharges had good accuracies and efficiencies and could explain 80 and 90% of variances of the monthly average and maximum discharges, respectively. 

Modeling the spatial variations of discharges in watersheds requires consideration of hydrological limit values both daily and seasonally, along with normal and average values. By adopting such an approach, the present study aimed at modeling monthly water discharges in Kashfarud sub-watersheds based on geomorphometric variables. The multivariate regression analysis among the independent variables including the average and maximum monthly flows and 16 independent geomorphometric variables revealed that the regression models could be obtained through the variables of average elevation, maximum elevation, elevation range, average slope, drainage density, and roughness ratio. These factors could explain the major parts of variance of the independent variables. It is possible to generalize the monthly mean and maximum discharges achieved in this study to other sub-watersheds through the resulting models with respect to the low estimation errors and high accuracies. However, generalization the monthly minimum discharges is not possible due to the lack of a significant correlation between this variable and geomorphometric variables. It is necessary to estimate the monthly minimum discharges in Kashfarud Watershed by reconstructing and converting the data or extending other predictive models. Reliable estimations of low water discharges provide us with information about water supply for the environment and water quality management for sustainability of healthy ecosystems. Also, owing to the role of small mountain catchments in the occurrence of peak flows, prioritization of watershed management measures in such catchments is incumbent to reduce the risk of floods.