The Effects of Annual Storage and Random Potential Evapotranspiration on the One-dimensional Annual Water Balance

Abstract

An analysis is presented leading to the incorporation of storage terms into an existing first-order dynamic water balance. Annual change in storage in the unsaturated zone of an idealized soil column is included through the addition of one characteristic vegetal parameter, the estimated depth of the root zone. This defines the storage volume in the unsaturated zone. Annual change in storage in the saturated zone of the soil column is accounted for by assuming the dynamic linkage between percolation to the groundwater table and discharge from the groundwater reservoir to behave as a linear reservoir. The storage coefficient of this reservoir must be determined from streamflow data. The effect on the frequency of annual basin yield of annual change in storage is tested for two contrasting climates. In both test cases, the model is found to reduce the unexplained variance of the basic model without storage mechanisms. A simplified analysis is conducted to determine the effect on the frequency of the annual basin yield of a randomly varying rate of annual average potential evaporation. A modified Penman equation is used to derive an approximate relationship for the annual average rate of potential evaporation. A cdf is derived for the annual basin yield from a Gamma distribution for annual point precipitation and a double exponential distribution for the annual average rate of potential evaporation. A linearized version of the water balance model indicates for two contrasting climates that a random rate of potential evaporation has little effect on the variance of the annual basin yield. This is interpreted as a justification for considering the rate of potential evaporation to be constant when modeling the water balance on a seasonal basis.