Analytical Solution of the Transport Equation for Exponentially Decreasing Initial Concentration in Shallow Water Table Condition in an Irrigated Field
Ram Pal *
Krishi Vigyan Kendra, Madhepura, Bihar Agricultural University, Sabour, Bahalpur, Bihar- 852113, India.
M. Imtiyaz
Department of Soil, Water, Land Engineering and Management, College of Agricultural, Engineering and Technology, Allahabad Agricultural Institute, Deemed University, Allahabad-7, Uttar Pradesh, India.
H. C. Sharma
Department of Irrigation and Drainage Engineering, College of Technology G.B. Pant University of Agriculture and Technology, Pantnagar-263145, U.S. Nagar, Uttaranchal, India.
*Author to whom correspondence should be addressed.
Abstract
Most of the agricultural activities are limited for the depth of 15 – 20 cm and rest soil remain enact for long periods which inhibits the microbial activities below this depths and create an initial concentration of nutrients exponentially decreasing with depth. An attempt has been made to develop analytical models for time-dependent nitrification/ denitrification and depth-dependent absorption of urea fertilizer in high water table conditions with fertigation. Laplace transformation method was used to solve the unsteady-state advection-dispersion equation. The analytical solutions that can be derived by this method assist understanding of the movement of fertilizer in irrigated fields. The developed models were validated with the experimental results. They were closely predicting the fertilizer movement in one-dimension soil medium. The little deviation of result from observed values may be due to change of dispersion coefficient and velocity with moisture content. Here these parameters were assumed as constant throughout the time under consideration. Models developed for constant degradation rate is predicting very close to observe values which shows that the soil under study has no depth-dependent degradation. The developed models may be helpful for the planning of drain design, nutrient management and assessment of potential hazards to groundwater in agricultural fields by the knowledge of exact transport parameters and boundary conditions universally.
Keywords: Transport equation, initial concentration, shallow water, irrigated field.