Statistical methods for forecasting daily snow depths and assessing trends in inter-annual snow depth dynamics
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Statistical methods for forecasting daily snow depths and assessing trends in inter-annual snow depth dynamics Jonathan Woody1
· QiQi Lu2 · James Livsey3
Received: 1 October 2019 / Revised: 15 July 2020 / Accepted: 24 July 2020 / Published online: 25 August 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract 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. Keywords Snow depth dynamics · Snow depth forecast · Time varying parameter regression
1 Introduction This paper introduces a time-varying parameter (TVP) regression model for modeling, forecasting, and detecting seasonal trends in daily snow depths at a single location.
Handling Editor: Pierre Dutilleul. Disclaimer This report is released to inform interested parties of research and to encourage discussion. The views expressed on statistical issues are those of the authors and not those of the U.S. Census Bureau.
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Jonathan Woody [email protected]
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Department of Mathematics and Statistics, Mississippi State University, Starkville, MS 39762, USA
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Department of Statistical Sciences and Operations Research, Virginia Commonwealth University, Richmond, VA, USA
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Center for Statistical Research and Methodology, U.S. Census Bureau, Washington, DC 20233, USA
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Environmental and Ecological Statistics (2020) 27:609–628
Daily snow depths constitute a complicated and important geophysical process having both environmental and economic impacts Maurer and Bowling (2014). Indeed, negative trends in snow pack observed in some areas of the western United States have been linked to earlier maximum stream flow dates Barnett et al. (2005), Burn (1994). This may have pronounced effects on local hydrology Maurer and Bowling (2014) which is a topic of ongoing research Schaefli et al. (2013). Daily snow depth forecasts are of great interest for millions of winter sports enthusiasts, whose commerce is eagerly anticipated by many local economies. There is ongoing study aimed at numerically forecasting snowfall amounts Byun et al. (2008), Roebber et al. (2007). Numerous geophysical properties, such as snowto-liquid ratio and Snow Water Equivalents (SWE), are used to quantify the forecasted depth of individual snow fall events Alcott and Steenburgh (2010). Forecasting of daily snow
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