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Mono Lake, California: 3rd model

Model : mono3
Simile version : 3.1+
Date added : 2003-06-26
Keywords : Lake model ; Mono Lake, California ; Lumped model ; Water ;

Description

Mono Lake is a lake in the Sierra Nevada, California, that was used to supply water to Los Angeles, and is also of considerable ecological importance. This is the first of a series of models developed as a teaching exrcise to explore the effects of different policies for water extraction.

This model uses a single compartment to represent the amount of water in the lake, with inflows representing precipitation, flow in past diversion points and other sources; and flows out for evaporation and other losses (extraction).

This model differs from the first in that the surface area of the lake now depends on the volume of water in the lake, rather than being assumed to be constant.

Source: Andrew Ford (1999): Modelling the Environment, p.42

dW/dt = P+F+O-E-X
P = p*sa
E = e*sa
F = r-ex

sa = graph(W) Where:
W = water in lake
P = precipitation
F = fl = ow past diversion points
O = other flow in
E = evaporation
X = extraction
p = precipitation rate
sa = surface area
e = evaporation rate
r = sierra gauged runoff
ex = export

Diagram

Equations

Compartments:
	water in lake
	Initial value = 2228
	Comments: Amount of water in lake, KAF (thousand acre-feet)

Flows:   
	evaporation = surface_area*evaporation_rate
	Comments: thousand acre-feet/year

	flow past diversion points = sierra_gauged_runoff-export
	Comments: thousand acre-feet/year

	other in = ungauged_sierra_runoff+non_sierra_runoff+land_surface_precipitation+diversion_inflows 
	Comments: thousand acre-feet/year

	other out = evapotranspiration+exposed_lake_bottom_evaporation+net_grant_lake_evaporation+ground_water_export 
	Comments: thousand acre-feet/year

	precipitation = surface_area*precipitation_rate
	Comments: thousand acre-feet/year

Variables:
	elevation = graph(water_in_lake)

	evaporation rate = 3.75*evaporation_rate_multiplier_from_specific_gravity
	Comments: feet/year

	evaporation rate multiplier from specific gravity = graph(specific_gravity) 

	specific gravity = (water_in_lake*mass_of_fresh_water+total_dissolved_solids)/(water_in_lake*mass_of_fresh_water)

	surface area = graph(water_in_lake)
	Comments: thousand acre

Parameters:
	evapotranspiration = 13
	Comments: thousand acre-feet/year

	export = 100
	Comments: thousand acre-feet/year

	exposed lake bottom evaporation = 12
	Comments: thousand acre-feet/year

	ground water export = 7.3
	Comments: thousand acre-feet/year

	land surface precipitation = 9
	Comments: thousand acre-feet/year

	mass of fresh water = 1.359
	Comments: million tons per thousand acre-feet

	net grant lake evaporation = 1.3
	Comments: thousand acre-feet/year

	non sierra runoff = 20
	Comments: thousand acre-feet/year

	precipitation rate = 0.667
	Comments: feet/year

	sierra gauged runoff = 150
	Comments: thousand acre-feet/year

	total dissolved solids = 230
	Comments: million tons

Results

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References

Ford, A (1999) Modeling the Environment.
Island Press. p.42

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