MODELING OF SURFACE RUNOFF FROM NATURAL WATERSHEDS WITH VARIED ROUGHNESS

Abstract

Many hydrologists, researchers from India as well as from abroad have worked and reported their research findings on various aspects of surface hydrology particularly with a view to obtain design parameters and to evolve practices relating to engineering aspects of application of the science of hydrology. However, off late focus has considerably shifted to field conditions / practices responsible for influencing the responses in surface hydrology. These efforts in the tropical climates mostly centered towards establishing the role of vegetation, not only for reducing the runoff but some times also for inducing the surface runoff in certain situations like better water harvesting to meet the requirement of water shortages. Keeping these factors in view, it was proposed to carry out an in-depth study of the effective overland roughness and its role in influencing the runoff process on the tropical watersheds of India. Also the related works of previous researchers have been duly summarized in the dissertation. DATA USED AND MODEL APPLIED Efforts were made to collect the required data from different organizations. The hydrological data pertaining to the six watersheds of varying sizes (1.2 - 9246 ha) for a total number of 43 storm events could be procured. These watersheds were located in different agro-climatic zones in different parts of India. The KW theory has become a well accepted tool for studying the role of different physiographic factors on to the overland flows as well as on to the surface runoff responses at the outlet of the watersheds. A brief description of the KW theory has been presented along with the details of the mathematical treatment for solving the Saint Venant's equations characterizing the surface flows. An open book type physiographic model has been applied and finite difference numerical solutions based on explicit methods have been worked out. Results of detailed sensitivity analysis revealed that the effective overland roughness happens to be the most sensitive parameter followed by the overland slope and the shape of the watersheds (i.e. L:B ratio). Keeping this in view further detailed analysis were carried out by adopting a synthetic watershed of 100 ha in size with constant and prolonged application of input iv rainfall excess rate of 20 mm/hr under different sets of uniform roughness parameters. The S-hydrographs so developed were differed significantly and greater influence of overland roughness was detected. Subsequently, the exercise was repeated on the six natural watersheds for uniform inputs. The KW outputs in the form of S-hydrographs failed to match the S-hydrographs derived from the unit pulse response theory. Rather, the later intercepted with the S-hydrographs obtained with the KW theory for different effective overland roughness values at different points. This suggested further in-depth study on time varied nature of roughness. TEMPORAL VARIATIONS IN EFFECTIVE OVERLAND ROUGHNESS PARAMETER The interaction of the vegetation with the developing and the receding overland flow depths has been investigated by following the trial and error procedures through automatic optimization. The values of the effective overland roughnesses were obtained to reproduce the watershed responses at its outlet for a complete match with the observed one. The constraint pertaining to the Froude number ( Fr < 2 ) was imposed at successive time steps. This also resulted in keeping the Kinematic wave number always within the safe and acceptable limits (i.e. > 50). The rainfall excess function was obtained from the gross rainfall using the conventional phi-index approach. For this analysis 27 storm events were randomly selected, out of the total 43, and were analyzed in details for deriving various flow parameters. The outputs with regard to the time varied overland flow parameters viz. verland flow depths, overland flow velocities, Reynolds number, effective overland roughness etc. were studied in details. The real time variations of these flow parameters suggested somewhat similar patterns over all the six watersheds adopted in the present research work. From this analysis the relationships were synthesized in between the effective overland roughnesses with overland flow depths as well as the overland flow Reynolds number (Re = Vjhj/v). Logical conclusions have been drawn from the relationships of overland roughness and Reynolds number for the three main time segments of hydrographs (i)0-»hmax (ii) peak segment (iii) receding hj. The effective overland roughness (nj) and the corresponding overland flow depths (hj), produced hysterisis loops suggesting different trends ofrelationship between hj and nj for the rising and the recession periods of overland flow depths. A single pooled set of optimized hj-rij values for h-rising (i.e. for 0->hmax) was derived by pooling individual set of optimized values of hj and nj for different storm events on a particular watershed. Simillarly another pooled set was generated for h-falling periods (i.e. for hmnx->end of runoff). The same exercise was performed on each of the six watersheds, in order lo generate regression relationships in the form of non linear power functions termed herein as Direct Runoff Hydrograph (DRH) based roughness prediction equations and given as under: n-j =a,(/iy)p' for h-rising period (0->hmax) 6.2(a) rij =a2 {h^1 for h-falling period (O^end of runoff) 6.2 (b) Where, nj is temporally varied overland roughness at jth time step, hj is corresponding mean overland flow depth in mm at jth time step, a\ &a2 are coefficients and pi &p2 are exponents of the above cited roughness prediction equations. Sets of synthetic parameters aua2, pi, and p2 were developed for all the six watersheds and the same were utilized for validation purposes. The simulations performed by using these equations gave encouraging results. The DRH simulations results for 43 storm events on six watersheds have been sucessfully demonstrated proving the applicability of the equations developed. These results indicate that the time variability of the effective overland roughness need to be considered while simulating the watershed responses through KW modeling approach. APPLICATION TO UNGAUGED WATERSHEDS The above mentioned concepts of temporally varied effective overland roughness have also been successfully extended to the ungauged watersheds for computing the runoff in the following two ways: (i) To generate the DRH based roughness prediction equations for use in ungauged watershed conditions (ii) Use of SCS Synthetic hydrograph for developing alternate roughness prediction equations In the first approach the numerical coefficients (ctj , a2) and exponents (p,, p2) of DRH based roughness prediction equations ( Eq. 6.2 a and Eq.6.2 b) were correlated with measureable physiographic parameters like drainage area and VI watershed slope, in ordexr to develope following regression models to compute the values of cti, cx2, pi, and p2 on ungauged watersheds. (a) For the period 0->hmax a, = 1/(2.145*A+11.656) (7.2) Pi = l/(-1.049*S+1.142) (7.3) (b) For the period hmax->0 ct2=l/(2.124*A + 8.707) (7.4) p2 = 0.783 - 0.421*S - (0.000043/(S2) ( 7.5 ) Where, A is watershed area in Sq. Km. and S is average overland slope in m/m. This made it possible to compute the values of cci, a2, Pi, and p2 any of the watersheds under study . Thus knowing these synthetic parameters for the watershed the time varied effective roughnesses can be easily estimated . Application of these relationships produced runoff responses which matched reasonably well with the observed ones for all the watersheds. However simulation results for only two watersheds i.e. W8 (smallest in size) and Nagwan (biggest in size) are included here. Application of above cited first approach required certain number of observed DRH events to generate basic value of cti, oc2, Pi, and p2. However in Indian tropical conditions most of the watersheds do not have provision for runoff gauging. Keeping this in mind vin the second approach, possibilities are explored to use and judge the applicability of synthetic unit hydrographs for developing certain simple and alternate roughness prediction equations for completely ungauged watersheds where not a single observed DRH event is available. In general two types of synthetic unit hydrographs are commonly used viz. the Snyder's UH and SCS synthetic UH. Out of these the later was considered more applicable looking into its basic positive features. Watershed B719 was adopted for application of this second approach considering it as totally ungauged watershed. A synthetic unit hydrograph was developed using the standard SCS method. For the same unit duration, unit responses of different rainfall excess depths were computed in the form of direct runoff hydrographs considering the system to be linear. For each hydrograh ordinate the effective overland roughnesses were computed by trial and error while running the KW model through the computer given in Appendix 1 (b). VII The optimized values of hj and nj for each hydrograph were segmented into two parts viz. 0 ->hmax and hmax -»0. All the data corresponding to the period 0->hmax was pooled for developing a regression equation. Similar procedure was adopted for the period hmax ->0. For watershed B719 these relationships were found to be linear and given as under : nj = -0.01 + 0.01798 hj (for 0 -* hmax) (*].6) nj = -0.00776 +0.0125 hj (for hmax ^ 0) (1-7) By incorporating the above equations for computing the time varied overland roughnesses, the kinematic wave responses were simulated for a few storms on this watershed and found to match reasonably well with the observed hydrographs. Thus, through this dissertation, a sincere effort has been initiated towards a nearly unexplored research field of temporal variations in effective roughness parameters but much need to be done through future studies.