Statistical methods for forecasting daily snow depths and assessing trends in inter-annual snow depth dynamics

This paper introduces a time-varying parameter regression model for modeling, forecasting, and assessing inter-annual trends in daily snow depths. The time-varying parameter regression is written in a simple state-space representation and forecasted using a Kalman filter. The recursive Kalman filter algorithm updates the time-varying parameter sequentially when a new data point becomes available and is a flexible forecasting technique. The proposed method is applied to a time series of daily snow depth observations recorded over a 103 year period at a station in Napoleon, North Dakota. The forecasts of the final ten years of data perform well when compared to the actual daily snow depths. Inter-annual snow depth trends indicate an increase in mid-winter snow depths followed by an earlier spring ablation.