RAINFALL-RUN0FF-SED1MENT YIELD MODELLING OF MOUNTAINOUS WATERSHEDS

Abstract

Rainfall-runoff-sediment yield modelling being highly complex, dynamic, and non-linear, exhibits temporal and spatial variability and comprises several physical processes. Varying in complexity from lumped empirical to physically based space and time-distributed, several models are available in literature to model runoff and subsequent soil erosion/sediment yield. Although physically based models have proven very useful as a research tool but are o f limited use in field, especially in developing countries like India as they require large amount o f data. However, search is still continuing for developing new and simple model. In the present research work, an attempt is therefore made to explore new/modified or improved techniques to model major components o f the rainfallrunoff- sediment yield process in a more sound theoretical and mathematical environment. However, in the mean time, sim plicity o f model structure, practical u tility in terms o f data requirement as well as easiness in use, and parsimony in data, time, and funds are central to the present study. The present research investigates a few an important components o f process o f the hydrological cycle, specifically the process o f rainfall-runoff-sediment yield including evapotranspiration, runoff, soil erosion, and sediment yield. Evapotranspiration (ET), a major component o f the hydrologic cycle, is important for planning, design, and operation o f irrigation systems. Most o f the hydrologic, watermanagement, and crop-growth models also require an accurate estimate o f potential evapotranspiration (PET) for its reliable application (Parmele 1972; Skaggs 1982). A common procedure for estimating ET is to first estimate potential evapotranspiration (PET). Further, crop coefficients, which depend on the crop characteristics and local conditions, are used to convert PET to ET. Secondly, runoff is an important component of hydrologic cycle and quantitatively second major component, after evapotranspiration, o f the cycle; The runoff is o f prime importance for the hydrologist at both field and at large scales. A t the field scale, the runoff is used in planning and design o f soil conservation practices, irrigation water management, wetland restoration, and water table management. However, at large scale, it is o f major concern in flood forecasting, floodplain management, design o f hydro-power projects, and water supply studies. Furthermore, soil erosion, normally resulting from rainfall and consequent runoff is a serious problem affecting the soil, land, and water which are essential resources for any civilization. Soil erosion either as on-site erosion or off-site erosion is equally important for the society. On-site erosion (sediment source) is important for the rural population especially the farmer community in terms o f removal o f fertile top soil layer which ultim ately hampers the agricultural production. However, the off-site erosion (sediment sink areas) is o f interest to the society at large i.e. in multi-purpose reservoir preservation, flood protection, and water quality.control (Garen et al., 1999). CN-PET Relationship Derivation Evapotranspiration is a major component o f the catchment water balance and potential evapotranspiration (PET) data therefore forms a key to rainfall-runoff models. As far as concerned to surface water, PET is required for water availability, estimation o f daily, weekly, and monthly flows for multipurpose reservoir operation, design (frequency) flows, scheduling o f irrigation project, and flood forecasting. Long-term changes in PET can affect the hydrologic processes as w ell as the performance o f agricultural crops. Several PET estimation methods based on temperature, radiation, and their combination have been developed over the last 50 years in different parts o f the world but none can be recommended as the best one for any area or any season in terms o f its accuracy and profitability. Furthermore, different researchers (Buransh, 1995; Fowler, 2002 Andreassian et al. 2004; Morton, 1994) have criticized the performance o f complex PET methods, and raised the question “ Is the temporal PET, derived from complex PET methods, suitable in rainfall-runoff modelling?” In the present research work, nine commonly used PET methods (one based on temperature, two based on radiation, and six combination based) were employed for estimation o f duration-dependent long-term mean PET on a large set o f hydrometeorological data from three catchments o f Narmada river basin, located in Central India. Significant variations (up to 42%) among the estimated PET values by different methods were observed. Therefore, care should be taken in selection o f an appropriate PET estimation method. Furthermore, the performance o f different commonly used PET methods was compared w ith Penman-Monteith method, a standard method recommended by FAO-56. Following the usual statistical criteria, temperature based Hargreeves method was found most suitable (Root Mean Square Error — 0.2) for PET estimation o f Narmada river basin. The performance o f radiation-based Priestley-Taylor (RMSE=4.71), and Turc methods (RMSE=3.90) was also found to be satisfactory. The Soil Conservation Service Curve Number (SCS-CN) method, though empirical, has increasingly gained wide recognition as a practical tool for solving wide range o f hydrologic problems involving the rainfall-runoff process because o f its overwhelming sim plicity. In the present study, interrelationship o f CN and PET was also investigated. This interrelationship was derived from the coupling o f SCS-CN concept and M intz and Walker (1993) equations (for the root-zone soil moisture (W) and evapotranspiration (ET)). The water balance equation and proportionality hypothesis o f SCS-CN method invoked SCS-CN parameter S to be expressible in terms o f the maximum possible evaporable depth or PET, described in power form as: PET = aSf or more generalized as ET = aSp. Consequently, long term mean PET values o f duration ranges from 1-day to 30-day for seven watersheds o f India were correlated with the runoff curve numbers derived for the respective durations from observed rainfall-runoff data, following the Mishra et al. (2008) procedure. The correlation exhibited a strong power relationship with coefficient o f determination (R ) values in the range (0.96, 0.99). Such a relationship invokes determination o f PET from the available CN values, and therefore, may be quite useful in field applications. Probability Distribution-Based SUH derivation The use o f probability distribution functions (pdf) for derivation o f synthetic unit hydrograph (SUH) is gaining acceptance among the hydrologists due to sim ilarity in typical shape and unit area enveloped by a pdf curve. The present study explores, first time in hydrology, the potential o f two-Parameter Inverse Gamma Distribution (2PIGD) for SUH derivation using geomorphological parmeters i.e., Horton’s ratio. The performance o f 2PIGD was compared with the most popular flexible and accurate two- Parameter W eibull Distribution (2PWD) and conventional two-Parameter Nash Gamma Model (2PNGM) (Rosso, 1984). When applied to the data from two Himalayan watersheds from India, the performance o f 2PIGD found superior to the 2PWD and 2PNGM based on statistical as well as visual criteria. Using 2PIGD and geomorphological parameters o f Ramganga watershed, a simple regression model for peak flow rate (Qp = 17.149 v + 0.1361, R2=0.99), and time to peak flow (Tp = 29.535 v '1, R2 =1) for known value o f dynamic flow velocity (v) were developed. Such a simple linear relationship can be o f importance for the field engineers as well as hydraulic engineers for design o f hydraulic structures and development o f flood prediction and warning systems. Lag Time Based GIUH Derivation Linking o f hydrological response o f a catchment w ith the geomorphologic characteristics has been o f paramount research interest for last three decades. The Instantaneous U nit Hydrograph (IU H ) theory, popularly known as geomorphologic IU H (or G IUH) o f Rodriguez-Iturbe et al. (1979) and further refinement by Gupta et al (1980), became more promising for ungauged catchments or data deficient catchments. Consequently, Rosso (1984) derived Nash parameters ‘n’ and ‘k ’ in terms o f Horton’s ratio and a dynamic velocity parameter using power regression and derived the complete shape o f the unit hydrograph. However, estimation o f dynamic velocity itse lf is an ambiguous task and involves great subjectivity in routine applications. In the present study, using the basic G IUH governing equations (Rodriguez-Iturbe et al., 1979 and Rosso, 1984), a revised G IUH model based on watershed lag time concept has been proposed. The proposed approach is more pragmatic than the older one due to replacement o f dynamic velocity by lag time o f the watershed. The resulting high value o f coefficient o f efficiency and low values o f relative error in peak estimation o f direct runoff hydrograph for eight single-peaked isolated storms o f two h illy watersheds indicated the suitability o f the proposed lag time-based G IUH approach. The model outcome was better than the result o f kinematic-wave based G IUH approach (Kumar & Kumar, 2008). For estimation o f Horton’ s ratio the realistic drainage network was extracted using the M elton concept in GIS environment. Moreover, the proposed approach can be extended for an ungauged watershed, and UHs derived from variable lag time may be helpful to quantify the effect o f urbanization and land use changes on water resources, for the lag time is the finger print o f the watershed. Development of RBFANN-Based Runoff Model A rtific ia l Neural Network (ANN ) is a technique which comprises o f both linear and non-linear concepts in model building and is capable o f handling the problem which is dynamic and even not clearly defined. Radial Basis Function A rtific ia l Neural Network (RBFANN) is a specific type o f AN N recently used by a number o f researchers in hydrological modelling. The RBFANN network model is motivated by the locally tuned response. Owing to this ability, the networks are easily trained by using a sufficiently large data set. In the present research, an RBFANN model was developed based on kmeans clustering algorithm to model the daily rainfall-runoff process. The training o f RBFANN network can be split into an unsupervised part and a supervised part. Unsupervised training techniques are relatively fast. Clustering algorithm k-means is used for unsupervised learning in function layer. Gradient descent algorithm is used for supervised learning part in output layer. Different network parameters such as learning rate in function layer (ALR), learning rate in output layer (ALRG), and number o f iterations are optimized using the data o f calibration period for three Himalayan watersheds, Naula, Chaukhutia, and Ramganga. The model network weights are calibrated using five years seasonal (June- September) rainfall-runoff data. Then model performance was evaluated by two unknown data sets, cross-validation and verification. The Nash efficiency o f proposed RBFANN was satisfactory and it was 86.28%, 84.91%, and 86.81% in calibration, cross-validation, and verification, respectively. As such, the efficiency was consistent during all three periods in case o f Naula watershed. However, the model efficiency was good and consistent in cross-validation and verification with efficiencies o f 84.76%, and 84.59%, respectively, and satisfactory in calibration (efficiency = 77.48%) for Chaukhutia watershed. In case o f Ramganga watershed, the model performed well in calibration (76%) and cross-validation (77.68%), and it was however reasonable (68.25%) in , verification. Overall, the model efficiency was excellent in error convergence due to . adopting k-means cluster algorithm, and there was no need to go beyond 1 0 0 0 iterations. However, the higher network achieves the desired performance w ithin 500 iterations. The model is very sensitive to learning rate in function layer (ALR), but not to learning rate in output layer (ALRG). Development of a Spatially Distributed Sediment Yield Model It is well known that onsite erosion reduces the soil quality due to removal o f nutrient rich top soil layer and also reduced the water holding capacity o f many soils. Therefore, in developing countries like India, where rural population is more than 65% and land is the identity o f the people, assessment o f erosion focuses mainly on the on-site effects o f erosion. To this end, a spatially distributed sediment yield model was developed in GIS environment (ERDAS 8.5 and ArcGIS 9.3) which is capable to identify the sediment source and sink areas w ithin the catchment. Transport capacity and gross soil erosion maps were generated by overlaying different thematic maps according to their equations. In the transport capacity map, the ridges and the flatter areas near the channel, generally cultivated (viz., south-west direction o f Chaukhutia gauging site) are the areas possessing low transport capacity. However, transport capacity is high in channels and v steep head water areas especially where the slope plane curvature is convex in nature. Employing transport capacity maps alongwith gross soil erosion (GSE), a programme was developed in Interactive Data Language (ID L ) to route the sediment form ridge pixel to the outlet o f the watershed by follow ing the hydrological drainage path. The programme compares the gross soil erosion (total soil ready to move out o f particular pixel) and transport capacity o f the flo w in that pixel, i f transport capacity is equal or greater than gross soil erosion then entire eroded soil w ill be transported to the next pixel. However, I f the transport capacity o f any pixel is less than total soil ready to move out o f a particular pixel, the tools w ill assign the difference between transport capacity and the total soil ready to move out, as amount o f sediment deposited in that pixel. Such maps exhibit sediment rate at a particular cell in spatial domain, and the value at the outlet cell indicate the sediment outflow from the entire watershed. Lumped as w ell as spatial accuracy o f the model was checked by comparing the model output w ith the observed sediment data at the outlet and three upstream gauging sites and theses are found to be w ithin lim it. Further, the spatial distribution ability o f the model was improved by incorporating the variable rainfall erosivity map. By overlaying the gross soil erosion and deposition maps, net erosion/deposition maps were generated. Theses are o f importance in soil erosion inventory and site selection for a multipurpose reservoir. Keywords: AN N, ArcGIS, GIUH, Horton’s ratio, Inverse gamma distribution, Lag time, Penman-Monteith, Potential evapotranspiration, Probability density function, RBFANN, SCS curve number, Soil erosion, SRTM, SUH, Spatially distributed sediment yield model, Transport capacity, USLE, W eibull distribution.