Inferring Mountain Basin Precipitation from Streamflow Observations Using Bayesian Model Calibration

Estimating basin-mean precipitation in complex terrain is difficult due to uncertainty in precipitation gauges' topographical representativeness relative to the basin and undercatch. Inadequate distribution with elevation and spatial density can lead to large estimation errors in basin-mean precipitation. Streamflow offers additional information about the water balance of the basin with which to estimate precipitation. We applied a methodology for inferring basin-mean precipitation from streamflow using Bayes' Theorem, and adapted this approach to snow-dominated basins in the Sierra Nevada of California. We developed and coupled a temperature-index snow model to the FUSE conceptual rainfall-runoff model. We used the BATEA (Bayesian Total Error Analysis) calibration and inference environment, which seeks to robustly calibrate hydrologic models by using streamflow to estimate representativeness errors in the observed precipitation inputs and infer the correct basin-average precipitation. We inferred 1981-2006 annual average precipitation rates across a cluster of basins in and around the high country of Yosemite National Park, and compared the rates to those from approaches based on climatological precipitation patterns (PRISM). The inferred spatial patterns of precipitation showed reasonable match to PRISM, though some deviations were identified. We also investigated the precision and robustness of this approach for estimating mean annual precipitation rates. While this approach clearly identified differences in precipitation rates between basins in different climatic zones, uncertainties between +/-100 and +/-200 mm/yr were associated with the inferred precipitation rates. These were shown to be related to uncertainties in hydrologic model structure, potential evapotranspiration rates and soil storage capacities. Future work will investigate the extent to which observations of snow water content can constrain uncertainty in inferred precipitation rates.