Using Mixed Models to Determine the Contribution of Land Use and Geology Formation in Erosion and Sediment Yield: A Case Study of Tange Bostanak Watershed in Fars province, Iran

Introduction Many catchment erosion studies focus on formation and land use as the primary source of sediment. It is important to improve information on sediment sources, especially in large catchments and sediment source information which can support catchment management decisions. Erosion control projects need to be understood as the relative contributions of different sediment sources from catchments. Fingerprinting methods identify soil erosion sources where geologic variations or different land uses span watershed boundaries. Sediment fingerprinting studies often rely on the collection of sediment from different sources within a catchment. Few studies have focused on using the Hughes mixed model to identify sediment sources. This model can quickly process a large number of samples from the main samples based on Monte Carlo simulation. The main objectives of this research were to determine the contribution of sediment sources by applying a fingerprinting mixing model in a Tange Bostanak drainage catchment. Material and Methods. Case Study Our study area was located in the Tange Bostanak catchment (30°16′ to 30°25′ N and 52°03′ to 52°13′ E),in the Southern Zagros Mountains, 80 km Northwest of Shiraz, Iran. The drainage area of the Tange Bostanak catchment is 81.73 km2. Sediment source samples were collected throughout the study catchment from each of the three principal source types (cultivated land, pasture, forest, gardens and also six formations in catchment). 43 representative samples were collected from these potential sources at different locations within the study catchment. Samples were initially oven-dried to 40 °C in order to remove the bias associated with the grain-size effects, only the <63 μm soil and sediment fraction, obtained by dry sieving, was taken for tracer analysis. To discriminate sediment sources, two stages were performed to confirm the discrimination of the potential sediment sources within each land use and six formations. The first step was based on the use of the Kruskal–Wallis H-test to discriminate the potential sources by the fingerprint properties. Stepwise multivariate discriminant function analysis (DFA) was applied to identify the optimum combination of the tracers passing the Kruskal–Wallis H-test for maximizing the discrimination between the potential sources. The multivariate mixed model involves minimizing the sum of squares of residuals between the predicted tracer values for each source in the sediment samples and those observed, which is an optimization problem. A Monte Carlo mixed model was used to predict the relative contribution of each of the sources. The Hughes mixed model was used for both the geochemical and radionuclide tracing. In the mixed model, individual sample concentrations were denoted by Ci,j,k, where i=source index (i=1, …, I; I=3 for erosion sources and I=4 for rock type sources), j=sample number index (j=1,…, J; J is 10 for both the geochemical and radionuclide tracing) and each sample has k constituent concentrations (k=1, …, K; K=2 for radionuclide tracing and K=9 for geochemical tracing). For each Monte Carlo iteration (l) and for each source (i), j is randomly selected and Ci,j,k,l is used to calculate source-weighted composite concentrations: Eq.1 Where l=1,…, 1000 and ρˆi is the proportion contributed from each sediment type source. The relative contribution of each erosion type source, ρˆj must meet the following constraints: For each geochemical property/radionuclide tracer, the average concentration of C is calculated over 1000 iterations using: Eq.2 The best estimate of the relative contribution (ρˆi) of each erosion type/rock type was determined by minimizing the sum of squares of the deviations of the concentration calculated in Eq. (2) from the measured geochemical property/radionuclide tracer concentration of the deposit (Cd): Eq.3 Also, the genetic algorithm, local optimization and Monte Carlo simulation were used to solve the following equation. Results and Discussion C, N, Cu, Ti, Si and Sr were identified by the Kruskal–Wallis test to discriminate the potential sediment sources in land use and Nd, Si, C, N, Ti and Nd144/Nd143 were identified by the Kruskal–Wallis test to discriminate the potential sediment sources in the formations. In stepwise multivariate discriminant function analysis, four tracers(C, Cu, Si, Ti) were capable of correctly distinguishing the land use source type. Four tracers (Nd143/144, Cu, Si, Ti) verified the ability to discriminate between geology information source categories. The results on geology information showed that the mean relative contributions related to the areas of Asmary (84.51%) and Quaternary (5.37%) were highest, respectively in Local optimization with 99.94 GOF index. For land uses, the results showed that the GOF index with 97.84 associated with GA optimization were the greatest. The relative contributions related to the areas of range lands (63.04%) and forest (31.81%) were the highest, respectively. Pabedeh Gorpi and Bakhtyari information with 0.24 and 0.27 were the lowest relative importance; also cultivation and forest land uses with 0.022 and 0.55 were the lowest relative importance, respectively. This study suggested that the future sediment fingerprinting studies use models that combine the best explanatory parameters provided by the Hughes (relying on iterations involving all data, and not only their mean values) models with the optimization using genetic algorithms to best predict the relative contribution of sediment sources. Comparing the applications in this catchment, the Hughes mixed model appears a more robust method in Tange Bostanak catchment using the GA optimization method.