RAINFALL-RUNOFF-EROSION MODELING

Abstract

The watershed response in terms of its runoff and sediment yield is the net result of its complex interaction between the climatological and physiographical characteristics. These factors are responsible for the spatial and temporal variability of the watershed responses. Therefore, in the present study, attempts have been made to solve the runoff mechanics of a watershed which influences theprocess of soil erosion and transportation of eroded material. To start with, a detailed survey of the published works relating to rainfall7runoff-erosion process has been carried out. The modeling of this process was carried out through two major components viz., flow dynamics and soil erosion dynamics. The soil erosion process in the watershed is extensively dependent on the flow processes due to occurrence of severe storms. Therefore, in this research, an attempt was made to systematically develop an event based rainfall-runoff and rainfall-runoff -erosion model for the watershed. Flow Dynamics Model The well accepted kinematic wave (KW) equations were used as governing equations for the computation of flow dynamics parameters such as flow depth, discharges, and velocities in the overland plane as well as in the channel. To account for the infiltration process, two-term Philip's model was used for which the parameters (i.e. infiltration sorptivity and gravitational infiltration rate) were estimated based on soil properties viz., initial soil moisture, effective porosity, pore size distribution index and saturated hydraulic conductivity. The modified form of KWequationswas arrived at for the overland flow after introducing the temporal variation of overland resistances. The KW parameters i.e. a and m are capable to account for the physiographic parameters, flow characteristics as well as the roughness parameter. In all, the overland roughness is the most sensitive parameter in KW based modeling. However, the vegetative resistance varies with the depth of flows or the degree of submergence. Keeping this (iii) fact in mind, for overland flow computations the KW model was modified by introducing the concept of temporal variations of overland resistances. For this purpose, to account for the temporal variations ofoverland resistances, coupled analytical and conceptual relationships was proposed and is given as follows. »(t) =nm-{2timm/[3hmh(t)m-h(tn Jot h(t) < tim »(0 =nm , for h(t) > tim In the above relationships, tin and corresponding nm become characteristics of a particular watershed for its physiography, soil surface and vegetation. Utilizing the concept ofopen-book physiographic model, the governing partial differential equations of flow dynamics expressed through modified form ofKW equations were solved by using the two forms ofexplicit finite difference approximation with Courant's number as a stability criterion for appropriate initial and boundary conditions. The applicability ofthe proposed flow dynamics model was initially tested onto three Indian watersheds (i.e. Nagwa, Karso and Mansara) and one US watershed (i.e. W-7 watershed). The drainage area of these watersheds ranged from 1.60 km2 to 92.46 km2. Using the data of these four watersheds and available twenty storm events, the runoff hydrographs were computed and compared with the observed hydrographs. To test the efficacy of the temporally varied overland roughnesses in the overland flow computations, the runoff responses were also computed byusing the constant overland roughness. These responses were compared with the response obtained by using the temporally varied overland roughness. Analysis of the results show that the computed hydrographs with variable overland roughnesess gives better agreement with the observed one in comparison to those which were computed using the constant overland roughnesses. The flow parameters so arrived at served as input to the erosion model. Soil Erosion Model Through flow dynamics the flow depth, velocity fields and flow discharges on the land surface as well as in the channels were obtained. These variables were used as hydrologic input to the erosion dynamics, for the computations of sediment flow rate and sediment yield. The (iv) upland erosion model was used to provide equations for the erosion dynamics inthe watersheds. The central themeof modeling upland erosion lies with the fact that sediment load is controlled by the interaction between the availability of sediment to be transported and the transport capacity of the flow. The total availability of soil to be transported was computed as a function of rainfall as well as for the shear stress induced due to flow using the auxiliary equations derived from the parameters of the universal soil loss equation (USLE). Again, the governing equation of erosion dynamics along with their auxiliary equations was solved simultaneously with the flow dynamics equations using the two forms of explicit finite difference numerical solution using the appropriate initial and boundary conditions. The applicability ofthe proposed rainfall-runoff-erosion model was tested onto the data of six watersheds having drainage areas ranging from 0.335 km2 to 92.46 km2. In all, the thirty five storm events were used in the analysis. The storm event data from these watersheds were randomly divided into two sets viz., the calibration set and verification set. During the calibration process, the model parameters were fixed up on the basis of best fit criteria between the observed and computed responses (i.e. hydrographs and sedimentographs). The calibrated values of the parameters were averaged for the particular watershed and used as model parameters for the verification of the model. Using the open-book physiographic model and appropriate initial and boundary conditions, the governing equations were solved for the data of all the six watersheds and responses at the outlets were computed and compared with the observed one. From the comparison of the responses and further analyses of the results, it may be remarked that the efforts made in interconnecting the flow dynamics and erosion dynamics have given satisfactory results for the complex situations. Extension of the proposed Model to Ungauged Watersheds The findings of the flow dynamics and erosion dynamics model have also been used to develop suitable relationships for estimation of hydrographs and sedimentographs for ungauged watersheds. The proposed extended model for ungauged watersheds gave satisfactory match withthe observed responses for all the six watersheds whichwere considered to be ungauged. (v) Concludingly, it may be remarked that the efforts made in interconnecting the flow dynamics and the erosion dynamics have given satisfactory results for the complex situations. It may have the limitations which are inbuilt in solving the mathematical formulations of both the processes. However, considering the totality of the picture, the solutions obtained seem to be quite satisfactory. Thesis Layout The present thesis describes the author's attempt to systematically study rainfall-runofferosion process involved in natural watersheds. A chapter-wise brief account of the work followed by statement ofthe problem discussed in the Chapter-1 is given as follows. In Chapter 2, relevant literatures relating to the approaches followed in the dissertation pertaining to flow dynamics and soil erosion dynamics of the watershed have been presented. The details of the study areas and availability of the hydro-climatic data of all the six watersheds have been presented in Chapter 3. The Chapter 4 presents a detailed description of themodel formulations ofthe flow dynamics. This includes the infiltration approach; incorporation ofthe concept of temporal variations of overland resistances; and numerical solution for the flow dynamics with initial and boundary conditions applied. This chapter includes the applicability ofthe proposed KW model onto four watersheds for computing runoff hydrographs. The Chapter 5 demonstrates the mathematical formulation for the erosion dynamics with their auxiliary equations of detachment and transport processes. This chapter also includes the numerical solution with initial and boundary conditions, and application of the model onto four India watersheds and two watersheds of USA. Extension of the proposed rainfall-runoff-erosion model for ungauged watersheds has been dealt with in the Chapter 6. In the last chapter i.e. Chapter 7, the summary and conclusions have been presented.