Influence of size of rainfall events on water-driven processes - I. Water budget of wheat crops in south-eastern Australia

Power laws relating the number of events N(s) and their sizes s, i.e. N (s) similar to s(-tau), are widespread in natural and social systems. Two hypotheses were tested: (1) power laws can be used to characterise rainfall patterns irrespective of the amount, seasonality, and rainfall mechanisms; and (2) crop water budget components favoured by large rainfall events, i.e. runoff and drainage, are negatively associated with tau, whereas soil evaporation, which is favoured by small rainfall events, is positively associated with tau. Hypothesis 1 was tested using long-term records of daily rainfall in 114 geographically widespread Australian locations from 12 to 43degreesS, and from 115 to 154degreesE, with median annual rainfall from 113 to 3437 mm, and Walsh and Lawler's seasonality index from 0.07 (very equable rainfall regime) to 1.1 (most rain in 3 months or less). Coefficients of determination of the linear regression between log-transformed number and size of rainfall events ranged from 0.90 to 0.98 (P < 0.0001). A single value of tau described well the rainfall patterns in 50 out of the 114 locations, whereas some degree of curvilinearity suggested that a multidimensional model would be more suitable in the other locations. Hypothesis 2 was tested in a factorial modelling experiment combining 44 years and 39 southern Australian locations in a latitudinal band (33-36 degrees S) between 134 and 147 degrees E. Simulated water budget components of wheat crops on a sandy loam soil included runoff (R), drainage beyond the root-zone (D), and evapotranspiration (ET) and its components. Seasonal rainfall (range from 176 to 381 mm) and tau (range from 2.84 to 3.76) were unrelated. Simulated ET, R, and D increased, and the soil evaporation: ET ratio (E/ET) decreased with increasing rainfall. For a given amount of seasonal rainfall, processes favoured by large rainfall events, including runoff and drainage, were more frequent and more intense in locations with smaller tau, whereas E/ET increased with larger tau. Despite some limitations, power laws provided a statistical description of rainfall patterns that is agronomically meaningful, with parameter tau t accounting for the effect of size of rainfall events on the fate of water in crops.