The primary objective of mathematical modeling in agricultural water management is to optimize crop yield by determining the optimal allocation of water resources.

The finite element method is a numerical technique that is widely used to simulate water flow in agricultural fields. It involves dividing the field into small elements and solving the governing equations for each element.

Optimization techniques are used in agricultural water management to determine the optimal crop rotation, schedule irrigation events, and allocate water resources among different crops.

The crop water production function is a mathematical model that represents the relationship between crop yield and water availability. It is used to determine the optimal amount of water required for a given crop.

Remote sensing is used in agricultural water management to estimate crop water requirements, monitor soil moisture content, and detect water stress in crops.

Geostatistics is a mathematical technique that is used to analyze the spatial distribution of soil moisture content. It involves the use of statistical methods to estimate the values of soil moisture content at unsampled locations.

Decision support systems are used in agricultural water management to provide information to farmers about irrigation scheduling, help them make decisions about crop selection and water allocation, and optimize water use efficiency.

The HYDRUS model is a mathematical model that is used to simulate the movement of water and solutes in the soil-plant-atmosphere continuum. It is used to study the effects of irrigation, drainage, and other water management practices on crop growth and water quality.

Artificial intelligence is used in agricultural water management to develop decision support systems, automate irrigation scheduling, and detect water stress in crops.

Linear programming is a mathematical technique that is used to optimize the allocation of water resources among different crops. It involves the use of linear equations to represent the constraints and objective function.

Game theory is used in agricultural water management to analyze the behavior of farmers in water-sharing situations, develop cooperative water management strategies, and resolve conflicts over water resources.

The Saint-Venant equations are a set of mathematical equations that are used to simulate the flow of water in irrigation canals. They are based on the conservation of mass and momentum.

Economic models are used in agricultural water management to evaluate the economic benefits of irrigation projects, analyze the impact of water scarcity on agricultural production, and develop policies for water pricing and allocation.

The Penman-Monteith equation is a mathematical equation that is used to estimate the evapotranspiration rate of crops. It is based on the energy balance of the crop canopy.

Mathematical modeling is used in the design of irrigation systems to determine the optimal size and location of irrigation canals, design the layout of irrigation fields, and select the appropriate irrigation method.