Doing Hydrology Backward to Estimate Mountain Precipitation Patterns from Streamflow

Precipitation in mountain watersheds, whether falling as rain or snow, is critical for human water supply and ecosystems across the western United States and elsewhere worldwide. However, precipitation is difficult to measure accurately over these watersheds, due in part to its strong spatial variability which is not captured well by the very sparse network of gauges located at high altitudes. In fact, the vast majority of precipitation gauges are located at low elevations and those at higher elevations may have accuracy problems due to the difficulty of maintaining them during the snow season. As a result, predictions which rely on measurements of precipitation over a large area, such as flood forecasts and runoff volume forecasts for water supply, often suffer from serious errors. However, streamflow measurements are made more frequently in mountainous areas. These measurements indirectly reflect precipitation through snow accumulation and runoff, respectively. Therefore, we propose a method to improve estimates of precipitation in mountain watersheds by using observations of snow and streamflow to correct errors in the precipitation gauge record.

We examine watersheds in the Sierra Nevada mountain range, where the orographic effect enhances precipitation and supplies many California river systems. The long-term orographic precipitation gradient is fairly well understood, but year-to-year variations in the precipitation distribution between high- and low- elevation stations have been observed, and these variations impact the accuracy of streamflow forecasts. We use streamflow observations to estimate basin-averaged annual precipitation for three Yosemite National Park watersheds. The basins are located in the High Sierra and contain steep, granitic valleys and peaks; their climate features heavy winter snowfall and relatively dry, sunny summers. Thus, these basins are an ideal testbed for inferring precipitation from streamflow, because snowmelt and rain tend to exit the steep, impervious basins quickly.

We assume that errors in streamflow observations are small in comparison with those in precipitation measurements. Thus, given our observations of streamflow, we can assess the likelihood of the precipitation observations being representative of the basin. This approach makes use of the statistical axiom known as Bayes' Theorem, which calculates an event's likelihood given that we have observed another related event. In this context, we use streamflow as the “known” event and then estimate the most likely precipitation amount that we would expect to generate the runoff.

To do this, we need to understand something about the basins' rainfall-runoff response, which means that we need a hydrologic simulation model of the basin. We apply a conceptually-simple model of snowpack, soil water storage and runoff, in order to determine how the basin translates rainfall and snowmelt into streamflow. Then, we use a Markov Chain Monte Carlo routine to sample the rainfall probability density function (PDF), which is the relatively likelihoods of different amounts of precipitation. The updated PDF provides an improved estimate of basin-average precipitation and its confidence bounds, as compared to the uncertain gauge record alone.

We first test whether precipitation inferred from streamflow could identify the basins' climatological, area-averaged precipitation. Long-term average precipitation should be the most robust characteristic of a basin, since unusual storms and evapotranspiration events should average out over a period of many years. We test the period 1981-2006, when reliable daily low-altitude meteorological and streamflow records were available. We find that the Hetch Hetchy and upper and lower Merced basins have similar basin-mean precipitation values, at 1520, 1410 and 1460 mm per year, respectively. However, the Cherry-Eleanor basin is much wetter, with an inferred precipitation rate of 1880 mm per year. This suggests a precipitation maximum in the northern end of the region.

In order to check whether our results match other estimates of basin-average precipitation for this area, we make use of the PRISM (Parameter Estimation on Independent Slopes Method) 4km 1981-2010 precipitation dataset. While our method agrees fairly well with PRISM for the Hetch Hetchy and Merced basins, it does not for the Cherry-Eleanor basin. Here, PRISM finds that the basin receives 1400 mm per year, or 25 percent less than our estimate. To investigate further, we use a simple mass-balance check on the basins. Assuming that one third of the basin's precipitation is evapotranspired, we can generate another estimate of basin-mean precipitation for the Cherry-Eleanor basin. We estimate 1885 mm per year of precipitation using this method, which is much closer to our estimate than to PRISM.

Water managers noted a particular difference between the snowpack patterns of water years 2005 and 2006. While both years had above-average snowpack statewide, the spatial pattern of snow appeared to be very different between the two. In particular, the snowpack water equivalent (SWE) was greater at Gin Flat than at Tuolumne Meadows in 2005, while the opposite was true in 2006. This pattern also appears in streamflow records. We test our method by inferring basin-averaged precipitation in both the Hetch Hetchy and Merced basins in 2005, and again in 2006. We find that in 2005, the Merced basin had slightly more precipitation than Hetch Hetchy, but that in 2006, the Hetch Hetchy basin received more. Our results corroborate the independent snow measurements, suggesting that the inferred precipitation is a robust estimate.

The results indicate that it is possible to infer precipitation patterns over a watershed from seasonal streamflow quantities and timing. Many stream gauge records are available for the Southern Sierra Nevada, a region of very high-elevation basins stretching from Yosemite to Mt. Whitney. Precipitation gauges are very sparse here, and so the stream gauges will allow us to create a substantially more robust spatial map of precipitation patterns at the annual scale. Each basin, in effect, can act as a very large precipitation gauge, providing retrospective information about precipitation falling in the watershed. For weather forecasters and water resource managers, annual scale spatial deviations from precipitation climatology are currently difficult to identify. This problem is particularly true, and particularly important, in the high-elevation basins of the western United States. Our approach could help identify storm patterns that lead to such deviations, and thus improve future forecasts.