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Pumpa Irrigation System

Model Type
SES Library XPP model

In this case, the surface water level is modeled by a first order differential equation. There are six sections with equal area that are allocated water based on institutions that determine how long each sector receives water, and in what order. Water is allocated to a given sector by opening and closing gates along the irrigation canals. Based on these allocations, each sector maintains a crop yield depending on the amount of time that maintains their water level within the bounds of a desired water height. When a sector receives less water than is desirable, yields decrease depending on the cumulative water stress (area on the curve between actual and desired water height). Water needs for each sector depends on the stage.

Default Dynamics

(Please describe default dynamics for this model.)

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Name Initial Value Description
\(y\) - The state variable is the surface water level
\(ϕ\) - ϕ is the evapotranspiration/leakage/seepage of water from the 6 different sectors. It is assumed as
\(y3\) - -
\(y4\) - -
\(y5\) - -
\(y6\) - -
Name Default Value Description
\( ϕ\) - ϕ is the evapotranspiration/leakage/seepage of water from the 6 different sectors. It is assumed that ϕ is same for all. Hence, it is a parameter is this case.
\(A\) - A is the area of each sectors. The area do not change so it is the parameter here.
\(a3\) - -
\(a4\) - -
\(a5\) - -
\(a6\) - -
$$dy/dt = \frac{u_n - \phi_n y_n}{A_n}\r \r \r \r \r $$
$$dy_1/dt = \frac{u_B - u_1 - \phi y_1}{A_1}$$
$$dy_2/dt = \frac{u_C - u_2 - \phi y_2}{A_2}$$
$$dy_3/dt = \frac{u_2 - u_3 - \phi y_3}{A_3}$$
$$dy_4/dt = \frac{u_A - u_4 - \phi y_4}{A_4}$$
$$dy_5/dt = \frac{u_D - u_5 - \phi y_5}{A_5}$$
$$dy_6/dt = \frac{u_4 - u_6 - \phi y_6}{A_6}$$
$$\r \r \r \r 0\leq u_A \leq w - (u_B + u_C + u_D), 0\leq u_1 \leq u_B, \\\r 0\leq u_4 \leq u_A, 0\leq u_B \leq w, 0\leq u_2 \leq u_C, 0\leq u_C \leq w-(u_A + u_C + u_D)\\\r 0 \leq u_5 \leq u_D, 0 \leq u_3 \leq u_C - u_2, 0 \leq u_6 \leq u_A - u_4 \\\r 0 \leq u_D \leq w - (u_A + u_B + u_C) \\$$
pumpa_irrigation_systemsix_sections_with_equal_area_are_allocated_water_based__dubHhSe.ode
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