Modeling daily average stream temperature from air temperature and watershed area

Habitat restoration efforts within watersheds require spatial and temporal estimates of water temperature for aquatic species especially species that migrate within watersheds at different life stages. Monitoring programs are not able to fully sample all aquatic environments within watersheds under the extreme conditions that determine long-term habitat viability. Under these circumstances a combination of selective monitoring and modeling are required for predicting future geospatial and temporal conditions. This study describes a model that is broadly applicable to different watersheds while using readily available regional air temperature data. Daily water temperature data from thirty-eight gauges with drainage areas from 2 km² to 2000 km² in the Sonoma Valley, Napa Valley, and Russian River Valley in California were used to develop, calibrate, and test a stream temperature model. Air temperature data from seven NOAA gauges provided the daily maximum and minimum air temperatures. The model was developed and calibrated using five years of data from the Sonoma Valley at ten water temperature gauges and a NOAA air temperature gauge. The daily average stream temperatures within this watershed were bounded by the preceding maximum and minimum air temperatures with smaller upstream watersheds being more dependent on the minimum air temperature than maximum air temperature. The model assumed a linear dependence on maximum and minimum air temperature with a weighting factor dependent on upstream area determined by error minimization using observed data. Fitted minimum air temperature weighting factors were consistent over all five years of data for each gauge, and they ranged from 0.75 for upstream drainage areas less than 2 km² to 0.45 for upstream drainage areas greater than 100 km². For the calibration data sets within the Sonoma Valley, the average error between the model estimated daily water temperature and the observed water temperature data ranged from 0.7 °C to 1.5 °C for the different gauges. To test the model, the average water temperature was estimated at the six locations within the Sonoma Valley not used in the calibration. For each water temperature record, the prior area dependent weighting factor was used. Regional maximum and minimum air temperature data were then used to estimate the average stream water temperature over the period of recorded water temperature. The average error between model-estimated and observed water temperature for the additional locations in the Sonoma Valley ranged from 0.7 °C to 3.5 °C. The model estimated water temperature for gauges with upstream drainage area less than 50 km² had average error between estimated and observed water temperature less than 1.7 °C. When upstream drainage area was greater than 50 km², the average error increased up to 3.5°C for some gauge locations. The model could also estimate water temperature in streams in other basins using the same area-dependent weighting factor. For eighteen gauges in the Napa Valley to the east , the average error between estimated and observed water temperature ranged from 0.7 °C to 1.9 °C, while for four gauges in the Russian River Valley to the northwest, the average error ranged from 1.2 °C to 3.2 °C. We speculate the area-dependent weighting factor reflects the temperature of groundwater contributions to stream flow.