MODELLING OF RAINFALL GENERATED RUNOFF AND SEDIMENT YIELD

Abstract

Rainfall-runoff-sediment yield modeling is integral to water resources planning, development and management, flood control, environmental impact assessment, erosion and sediment control, water quality modeling and watershed management. A multitude of models are available in hydrologic literature to address the issues related with the runoff and sediment yield modeling. The Soil Conservation Service Curve Number (SCS-CN) method is one of the popular event-based models widely used for estimation of direct runoff for a given storm rainfall event from small watersheds. The method has witnessed myriad applications including those which were not originally intended. Similarly, the synthetic unit hydrograph (SUH) methods are widely used for estimating design flood for ungauged catchments, and for partial data availability conditions. The SUH methods are of paramount importance for developing countries, for majority of the small basins are ungauged. The sediment graph models are particularly used for estimation of time distributed sediment yield and play a significant role in water quality modeling and effectiveness of watershed management programmes. The increased awareness of environmental quality and an efficient control of non-point source pollution have further increased the need for sediment graph models. The present study is undertaken to explore the new/modified or improved versions of SCS-CN method, SUH methods, and sediment graph models on a more sound hydrological perception and a stronger mathematical foundation to perform their prescribed tasks successfully and efficiently. Revised Soil Moisture Accounting Procedure in SCS-CN Methodology Recent past has witnessed various improvements/modifications to the existing SCSCN methodology. Based on certain issues, however, a need of further improvement has been felt for better results. The soil moisture accounting (SMA) procedure that lies behind the SCS-CN methodology is one of them. Introduced by Williams and LaSeur (1976), SMA procedure was employed by Mishra et al. (2004a) to address the variability due to antecedent rainfall and associated soil moisture amount in terms of antecedent moisture condition (AMC). Based on SMA procedure, Michel et al. (2005) proposed a renewed SCS-CN methodology to overcome the inconsistencies associated with the existing SCS-CN method, including the incorrect parameterization. However, the proposed methodology contains some structural inconsistencies from SMA view point. Specifically, it relies on the existing SCSCN method, which lacks SMA accountability in the basic proportionality concept or C =Sr concept (Mishra and Singh, 2003a), where C is the runoff coefficent, Sr is the degree of saturation. Secondly, the methodology does not have any expression for estimation of initial soil moisture Vo and threshold soil moisture or intrinsic parameter Sa. Hence, the present study revisits the existing SCS-CN method for its underlying SMA procedure and provides simple expressions for Vo and Sa. This revision led to the development of revised version of the Michel et al. model, named as SMA inspired event-based SCS-CN model. Based on the revised SMA procedure, the present study also proposes SMA inspired continuous SCS-CN model parallel to continuous model of Michel et al. The performance of SMA inspired event-based SCS-CN model, event model of Michel et al., and the existing SCS-CN method has been evaluated by applying them to event rainfall-runoff data of 35 small watersheds of United States. In these applications, the proposed SMA inspired event-based model performs the best, and the existing SCS-CN method performs poorest of all. Further, the performance of SMA inspired continuous SCSCN model and continuous model of Michel et al. is evaluated by applying both to daily rainfall-runoff data of Hemavati watershed (India). Based on Nash and Sutcliffe (NS) (1970) efficiency criterion, both the models perform equally well for continuous hydrologic simulation; the proposed model however performs marginally better than the Michel et al. model. Extended Hybrid Model for Synthetic Unit Hydrograph (SUH) Derivation The unavailablity or partial availability of the required rainfall-runoff data in quality and quantity largely initiated the development of SUH methods. However, the efforts still continue for development of new/improved models for synthetic unit hydrograph (SUH) derivation. For example, Bhunya et al. (2005) proposed a hybrid model (HM) for SUH derivation. Though the proposed HM model can be taken as an improvement over the widely used Nash (1957) model, it also has few concerns, which require to be attended for a credible ii application. First it ignores the concept of translation, which is essential for describing a dynamic system, and secondly it lacks in its generality. The present study proposes a conceptually sound and theoretically improved extended hybrid model (EHM) by introducing the concept of translation. The proposed EHM model explicitly considers the cascaded approach of Nash (1957) and the hybrid approach of Bhunya et al. (2005) for SUH derivation. The study also proposes a general expression for EHM model. Both EHM and HM models are applied to the short-term data of five catchments (small to medium) ranging from 21 km2 to 452.25 km2. It is found that the quantitative performance of EHM model in terms of standard error (STDER) and relative error (RE) enhances upon the HM model for the larger catchments. The Nash model performs poorer than both EHM and HM models. Further, a structural diagnosis of the general expression of EHM shows that HM and Nash models are the only specific cases of the earlier one. Chi-square and Frechet Distributions for SUH derivation The probability distribution functions (pdfs) as synthetic unit hydrograph (SUH) is a well accepted technique among the hydrologists. Probably, the similarity between pdf of a distribution with area under the pdf curve to be unity and a conventional unit hydrograph are the two important features of a pdf useful for SUH derivation. The present study explores the potential of one-parameter Chi-square and two-parameter Frechet distributions for SUH derivation using Horton order ratios (Rodriguez-Iturbe and Valdes, 1979) in comparison to widely used two-parameter Gamma distribution (2PGD) model (Rosso, 1984). Analytical methods are proposed for parameter estimation of the two distributions. Using random generation scheme, the suitability of proposed analytical methods is checked, and it is found that the proposed analytical methods can be used successfully for their intended task. Further, an attempt has been made to search for the possible similarity among the three pdfs, viz., one parameter Chi-square distribution (CSD), two-parameter Frechet distribution (2PFD), and two-parameter Gamma distribution (2PGD). The three pdfs are applied to two Indian catchments for limited data availability conditions. The results show that SUHs obtained by one parameter CSD and 2PFD are well comparable with those obtained by 2PGD model. iii SCS-CN Method Based Sediment Graph Models The conceptual sediment graph models are popular for estimation of time distribution of sediment yield (sediment graph computation) as well as the total sediment yield due to a particular storm event from a catchment. The present study attempts to develop new conceptual sediment graph models based on three popular and extensively used models/methods (here termed as sub-models), viz., Nash-based IUSG (Nash, 1957), SCS-CN method, and Power law (Novotny and Olem, 1994). Four sediment graph models (SGM1 - SGM4), corresponding to four different cases are proposed. For SGM1, both the initial soil moisture Vo and initial abstraction Ia are assumed to be zero, i.e. Vo = 0 and la= 0. For SGM2, Vo = 0, but Ia 0; For SGM3, Vo t 0 and Ia=0; and for SGM4, Vo t 0 and Ia # 0. The proposed sediment graph models take due consideration to the major runoff and, in turn, the sediment yield producing watershed characteristics such as soil type, land use, hydrologic condition, antecedent moisture, and rainfall characteristics. On the basis of number of parameters, SGM1 is the simplest one, and SGM4 the most complex sediment graph model. The proposed sediment models are applied to the observed short-term sediment yield data of Nagwan watershed. Goodness-of-fit (G0F) results show that the proposed sediment graph models matched closely with the observed sediment graphs and the total sediment yield computed by them is in close agreement with the observed sediment yield for the three storm events. The results indicate that both components of hydrologic cycle affect both the sediment graph derivation and sediment yield computation, and the proposed models are most sensitive to the exponent of the Power law, f3, than the other parameters. The workability of simplest SGM1 model is further evaluated using the short-term sediment yield data of Ramganga catchment. The resulting higher values of model efficiencies and lower values of RE of peak sediment flow rate (4, and total sediment yield Q, further supports the suitability of the proposed sediment graph model for computation of time distributed sediment yield and total sediment yield as well. Keywords: SCS-CN method, Soil moisture accounting, Synthetic unit hydrograph, Probability distribution function, Sediment graph, Rainfall-runoff-sediment yield. iv