Roy W. Koch

Surface Climate and Streamflow Variability in the Western United States and Their Relationship to Large‐Scale Circulation Indices

A statistical analysis was undertaken to determine the nature and magnitude of the relationship of precipitation, temperature and streamflow in the western United States to large-scale atmospheric circulation patterns. The Southern Oscillation Index (SOI) was used as an indicator of the El Nino/Southern Oscillation (ENSO) and the PNA index as an indicator of the Pacific//North America pattern. These indices were correlated with surface climate data and split sample analyses were conducted to determine climate response during the extreme phases of each index. October–March precipitation was shown to be most strongly correlated with SOI averaged over the July–November period. The analysis showed that there are two centers of opposite association with the SOI. During low values of the SOI (ENSO events) precipitation is low in the Pacific northwest and high in the desert southwest. Correlations between SOI and temperature were greatest in the Pacific northwest. The split sample analysis also revealed statistically significant differences in precipitation occurring during extremes of the SOI. The PNA pattern was related to precipitation and temperature over a concurrent time period. Especially strong associations were noted in the Pacific northwest for both precipitation and temperature. Streamflow showed associations with SOI similar to precipitation.

A stochastic differential equation approach to soil moisture

The dynamics of water within the unsaturated root zone of the soil are represented by a pair of stochastic differential equations (SDEs), one representing the so-called “surplus” state of the moisture and the other the “deficit” condition. The inputs to the model are the climatically controlled random infiltration events and evapotranspiration which are modeled as a compound Poisson process and a Wiener (Brownian motion) process, respectively.The solutions to these SDEs are not in “close-form” but sample functions are obtained by numerical integration. The moment properties of the soil moisture evolution process have also been derived analytically including the mean, variance, covariance and autocorrelation functions.To illustrate the model, climatic parameters representing the “surplus” and “deficit” cases and properties of clay loam soil have been used to numerically derived the corresponding sample functions. With proper selection of all the parameters, physically realistic sample trajectories can be obtained for the model.