Precipitation Parameters of Stochastic Climate Models for a Changing Climate

Abstract

Changing climate can impact erosion directly by increasing or decreasing the rainfall depth and intensity and indirectly by influencing the vegetative cover on landscapes. Stochastic climate models are increasingly being used to allow the assessment of erosion to be done using ensemble statistics. Precipitation is mostly widely represented by first determining the state of the day is wet or dry using discrete transitional probabilities and then, for a wet day, determining the precipitation depth. The parameters for stochastic models are based on the statistical analysis of observed data for the current conditions. Simple methods to modify these stochastic parameters under different climate scenarios are desired to easily simulate their impact on erosion. Modifying parameters for precipitation depth needs to be considered carefully because changes in depth can be achieved by varying the statistics of daily precipitation, by changing the number of wet days, or by a combination of these statistics. A framework for modifying the precipitation depth for new climate conditions is developed in the study. In addition to the stochastic climate parameters related to the moments of probability density functions and transitional probabilities under the current conditions, the proposed framework requires the user to specify the fractional changes in the total precipitation depth and the mean daily precipitation depth. Relationships are developed to determine indirectly the proper number of wet days from transitional probabilities for a first-order Markov chain. These relationships are dependent on a user-specified parameter of the ratio of the mean number of wet-wet day sequences of the current and new climate conditions. The sequence of wet-wet days is important in modeling soil erosion. The framework is applied to 80 years of precipitation data for Stillwater, OK. The implications of assuming no change in the wet-wet-day ratio with new climate conditions is compared to the results obtained assuming a ratio equal to the fractional change in the mean number of wet days. If the new climate condition corresponds to an increase in the number of wet days, the assumption of an unchanged ration corresponds to new storm patterns that develop more often on dry days and dissipate more rapidly on wet days. The opposite trend occurs if the new climate condition corresponds to a decrease in the number of dry day. Under this scenario, storm patterns tend to dissipate more slowly resulting, on average, in more frequent consecutive days with precipitation. A wet-wet day ratio equal to the fractional change in the mean number of wet days corresponds to no change between the current and new climate conditions of the transitional probability of wet-given- wet-day. This result suggests that the persistence of storm systems do not change under the new climate conditions. The proposed framework is useful and easy to implement in stochastic climate models.