Water Balance of Lakes
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WATER BALANCE OF LAKES Lars Bengtsson Department of Water Resources Engineering, Lund University, Lund, Sweden
Description The most basic in river basin hydrology is the water balance – and so it is for lakes. Most lakes have outflows, but some of the most famous lakes of the world are terminal lakes with no outflow, for example, the Caspian Sea, Lake Chad, and the Dead Sea. The water level in the overflowing lakes is rather stable, while the water level in the terminal lakes varies with the climate. In some lakes with small upstream catchment, the inflow to the lake is dominated by the precipitation on the lake, but usually inflow rivers are the dominating source of inflow to a lake. Some lakes only have subsurface inflow, but in most lakes, the most important inflow is from rivers. There also exist kettle lakes, which are part of the groundwater system with only subsurface inflow and outflow. The water balance of a lake is dVOl dh ¼ AðhÞ dt dt ¼ Qin Qout ðhÞ þ Qgwin Qgwout þ ðP EÞAðhÞ VOL is the lake volume, A is the surface area which varies with the lake level, Q is surface flow, Qgw is subsurface flow with different index for inflows and outflows, P is precipitation on the lake surface, and E is evaporation from the lake. There is seldom any groundwater seepage out of a lake. Groundwater inflow is significant when
there are springs or when the lake is situated on the border of an esker. The natural river outflow is a function of the lake level above the outlet sill. If there is subsurface outflow, this subsurface outflow only very minor depends on the lake level. When the surface area and the outflow are known functions of the lake level, the lake level variation can be determined from the water balance. Most often the precipitation on the lake and the evaporation are nonsignificant compared to the inflows and outflows, so the water balance is simply AðhÞ
dh ¼ Qin Qout ðhÞ dt
Solving this equation with a short time step is called lake routing. The lake level and, from that, the outflow are determined. In a lake with outflow, the lake level, h, is usually given as the level above the outlet sill. A lake with no outflow is a terminal lake and situated downstream in a closed basin, endorheic basin. Such a lake is a sink to most pollutants. The water is usually salty. Water leaves the lake only by evaporation. The water balance is AðhÞ
dh ¼ Qin þ ðP EÞ AðhÞ dt
The steady-state lake level area is then Alake ¼
Qin EP
The inflow is the basin precipitation – the evapotranspiration losses over the upstream basin – eventual water withdrawals. The lake is the lower part of a basin. If this endorheic basin including the lake has the area Abasin,
L. Bengtsson, R.W. Herschy, R.W. Fairbridge (eds.), Encyclopedia of Lakes and Reservoirs, DOI 10.1007/978-1-4020-4410-6, # Springer Science+Business Media B.V. 2012
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WATER BALANCE OF THE LAURENTIAN GREAT LAKES
the specific basin runoff is q, and if the lake has the variable surface area Alake, then the part of the basin which constitutes the terminal lak
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