Modeling bulk density and snow water equivalent using daily snow depth observations

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Bulk density is a fundamental property of snow relating its depth and mass. Previously, two simple models of bulk density (depending on snow depth, date, and location) have been developed to convert snow depth observations to snow water equivalent (SWE) estimates. However, these models were not intended for application at the daily time step. We develop a new model of bulk density for the daily time step and demonstrate its improved skill over the existing models. Snow depth and density are negatively correlated at short (10 days) timescales while positively correlated at longer (90 days) timescales. We separate these scales of variability by modeling smoothed, daily snow depth (long timescales) and the observed positive and negative anomalies from the smoothed time series (short timescales) as separate terms. A climatology of fit is also included as a predictor variable. Over half a million daily observations of depth and SWE at 345 snowpack telemetry (SNOTEL) sites are used to fit models and evaluate their performance. For each location, we train the three models to the neighboring stations within 70 km, transfer the parameters to the location to be modeled, and evaluate modeled time series against the observations at that site. Our model exhibits improved statistics and qualitatively more-realistic behavior at the daily time step when sufficient local training data are available. We reduce density root mean square error (RMSE) by 9.9 and 4.5% compared to previous models while increasing R<sup>2</sup> from 0.46 to 0.52 to 0.56 across models. Focusing on the 21-day window around peak SWE in each water year, our model reduces density RMSE by 24 and 17.4% relative to the previous models, with R<sup>2</sup> increasing from 0.55 to 0.58 to 0.71 across models. Removing the challenge of parameter transfer over the full observational record increases R<sup>2</sup> scores for both the existing and new models, but the gain is greatest for the new model (R<sup>2</sup> = 0.75). Our model shows general improvement over existing models when data are more frequent than once every 5 days and at least 3 stations are available for training.




McCreight, J. L., & Small, E. E. (2014). Modeling bulk density and snow water equivalent using daily snow depth observations. Cryosphere, 8(2), 521–536.

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