General procedure to initialize the cyclic soil water balance by the Thornthwaite and Mather method

The original Thornthwaite and Mather method, proposed in 1955 to calculate a climatic monthly cyclic soil water balance, is frequently used as an iterative procedure due to its low input requirements and coherent estimates of water balance components. Using long term data sets to establish a characteristic water balance of a location, the initial soil water storage is generally assumed to be at field capacity at the end of the last month of the wet season, unless the climate is (semi-) arid when the soil water storage is lower than the soil water holding capacity. To close the water balance, several iterations might be necessary, which can be troublesome in many situations. For (semi-) arid climates with one dry season, Mendon a derived in 1958 an equation to quantify the soil water storage monthly at the end of the last month of the wet season, which avoids iteration procedures and closes the balance in one calculation. The cyclic daily water balance application is needed to obtain more accurate water balance output estimates. In this note, an equation to express the water storage for the case of the occurrence of more than one dry season per year is presented as a generalization of Mendon a's equation, also avoiding iteration procedures.