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The formula of groundwater level during current time step h(t) and its derivation are shown below (Figure 12 ). In this figure, P is percolation (assumed to be constant during a time step), qs is downward seepage to deep groundwater, qd is drainage to Open Water. All these water flows can get positive as well as negative values, negative meaning flow in the other direction. In Urbanwb all relevant levels are relative to the surface level, where the unit (m-SL) means meter below surface level.
Figure 12 Groundwater level h(t) calculation
The basic applied formula is:
Seepage: Drainage: Drainage Continuity: Continuity:
Substitution results in:
Initial condition:
Example (check):
h(t) = 1 m –MV; PP = 1.5 m –MV; H = 2 m –MV; c = 1000 d; w = 50 d :
qs = (2 – 1) / 1000 = 0.001 m/d = 1 mm/d (downward)
qd = (1.5 – 1) / 50 = 0.01 m/d = 10 mm/d (outflow)
Two options for seepage are available.
In option 1 the seepage is dependent of the difference between the variable groundwater level and a user defined constant hydraulic head of the deep groundwater (H) over a hydraulic resistance (c) of the layer in-between.
In option 2 the seepage is defined as a constant water flow.
Important note: all parameters in these formulas are in meters and days. For different time step sizes water flows expressed in meter per time step need to be adapted.
Option 1. Seepage is groundwater level dependent
Substitution in continuity equation results in:
Rewritten:
Solving:
Initial condition:
Resulting in:
Drainage (qd) and seepage (qs) are automatically calculated in depth per day, because the sizes of both flow resistances (w and c) are expressed in days.
Percolation (P) is expressed in depth per time step, hence must be divided by the time step size (t [d])
Option 2. Seepage is constant
Substitution in continuity equation results in:
Rewritten:
Solving:
Initial condition:
Resulting in:
Drainage (qd) is automatically calculated in depth per day, because the size of the flow resistances (w) is expressed in day.
Seepage (qs) is defined as a constant flow, expressed in depth per day.
Percolation (P) is expressed in depth per time step, hence must be divided by the time step size (t [d])
2.6.1 Assumptions
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