In the same way that the balance can be written for the watershed at the surface
ID: 118841 • Letter: I
Question
In the same way that the balance can be written for the watershed at the surface based on storage and precipitation rate, evaporation rate and discharge (S, P, E and Q), a water balance equation can be defined for the “air-shed” above the same land area. This control volume extends the top-of-atmosphere where there is no vertical exchange of water vapor. The convergence of water vapor from the sides of the air shed is due to the transport of specific humidity q by the wind vector across the column.
Write the water balance equations for the watershed and the overlying air shed.
Take the long-term average of the balance equations across many full seasonal cycles. How do the vapor convergence and the river discharge relate?
Explanation / Answer
Water, within the watershed is existed because of precipitation, surface runoff, groundwater and evaporation. It is a closed system, so the principle of conservation of mass with an equation can be applied as this tells how much water is present in each of these storages.
Precipitation and any groundwater flowing inside the watershed is an input and surface runoff, evaporation and any groundwater flowing out is an ouput. This is shown by an equation below:Here P=precipitation, GW= groundwater, E=evaporation, and Q=runoff. Equation 2 is the regional water balance equation. Let us assume that for a watershed the groundwater change is negligible. And there is no storage in the system. By this a simplified way is estimated and the amount of runoff could be expected by giving a certain amount of precipitation and evaporation.
After rain, water infiltrates into the ground and replenish our groundwater supply, or it is evaporated, returning to the atmosphere. Some amount of the water flows into rivers and streams and discharges into oceans or reservoirs. We call it runoff because it "runs off" the land. Most runoff starts in streams, flows into rivers and eventually empties into the ocean. If the level of rains are very high, then there will be a lot of runoff as this amount of runoff is too much for a riverbed to carry, because of this water will rise up over the riverbanks and a situation of flood would be there.
The overlying airshed water balance equation is described as,
where, = precipitable water ,,= column storage of liquid and solid water, = vertically-integrated two-dimensional vapor flux, = vertically-integrated two-dimensional water flux in the liquid and solid phases, = evapotranspiration and = precipitation. The term = horizontal divergence. is the vapor flux vector, and the components are directed towards east and north;
Here = specific humidity, = wind velocity E-W, = wind velocity N-S = gravitational acceleration, = pressure at the point, and =pressure at ground surface. Assuming that the earth is a sphere which has radius of water vapor flux convergence is computed.
The water content in the atmosphere in the solid and liquid phases is negligible, so the equation (1) is simplified as:
For the estimation of the water balance in a river basin atmospheric vapour flux convergence is introduced. The global distribution of vapour flux convergence, - H · Q is estimated by using the Medium-Range Weather Forecasts global analysis data for the period 1980-1988. By the use of atmospheric water balance, the annual mean - H · Q can be interpreted as the precipitation minus evaporation. The estimated - H · Q is compared with the observed discharge data. As the mean annual values are not identical, but their seasonal change corresponds very well. The four year mean - H · Q is also compared with the climatological runoff of nearly 70 for e.g. large rivers. The multi-annual mean runoff is calculated from the Global Runoff data set and used for the comparison. Generally, the global runoff estimation is done by using the conventional hydrological water balance and annual freshwater transport is estimated by atmospheric water balance combined with geographical information. The results show that the same order of freshwater is supplied to the ocean from both the atmosphere and the surrounding continents through rivers.