[1] This paper introduces a stochastic storage model capable of assessing trends in daily snow depth series. The model allows for seasonal features, which permits the analysis of daily data. Breakpoint times, which occur when the observing station changes location or instrumentation, are shown to greatly influence estimated trend margins and are accounted for in this analysis. The model is fitted by numerically minimizing a sum of squares of daily prediction errors. Standard errors for the model parameters, useful in making trend inferences, are presented. The methods are illustrated in the analysis of a century of daily snow depth observations from Napoleon, North Dakota. The results here show that snow depths are significantly declining at Napoleon, with spring ablation occurring earlier, and that breakpoint features are very influential in deriving realistic trend estimates.

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The statistician often needs to test whether or not a time series has a seasonal first moment. The problem often arises in environmental series, where most time‐ordered data display some type of periodic structure. This paper reviews the problem, proposing new statistics in both the time and frequency domains. Our new time domain statistic has an analysis of variance form that is based on the one‐step‐ahead prediction errors of the series. This statistic inherits the classic traits of the F‐distribution arising in one‐way analysis of variance tests, is easy to use, and is asymptotically equivalent to the likelihood ratio test. The statistics asymptotic distribution is quantified when time series parameters are estimated. In the frequency domain, a statistic modifying Fisher's classical test for a sinusoidal mean superimposed on independent and identically distributed Gaussian noise is devised. The performance and comparison of these statistics are studied via simulation. Implementation of the methods merely requires sample means, autocovariances, and periodograms of the series. Application to a data set of monthly temperatures from Tuscaloosa, Alabama, is given. Copyright © 2016 John Wiley & Sons, Ltd.

This paper develops methods to estimate a long‐term trend in a daily snow depth record. The methods use a storage equation model for the daily snow depths that allows for seasonality, support set features (snow depths cannot be negative), correlation, and mean level shift changepoint features. Changepoints can occur in snow processes whenever observing stations move or station instrumentation is changed; they are critical features to consider when estimating a long‐term trend. A likelihood objective function is developed for the storage model and is used to estimate model parameters. Genetic algorithms are used to optimize a minimum descriptive length model selection criterion that estimates the changepoint numbers and locations. The methods are applied in the analysis of a daily series recorded near Warm Lake, Idaho, from 1948 to 2009.

This article presents a study of the ground thermal regime recorded at 11 stations in the North Dakota Agricultural Network. Particular focus is placed on detecting trends in the annual ground freeze process portion of the ground thermal regime's daily temperature signature. A multivariate storage model from queuing theory is t to a quantity of estimated daily depths of frozen soil. Statistical inference on a trend parameter is obtained by minimizing a weighted sum of squares of a sequence of daily one-stepahead predictions. Standard errors for the trend estimates are presented. It is shown that the daily quantity of frozen ground experienced at these 11 sites exhibited a negative trend over the observation period.

Several attempts to assess regional snow depth trends have been previously made. These studies estimate trends by applying various statistical methods to snow depths, new snowfalls, or their climatological proxies such as snow water equivalents. In most of these studies, inhomogeneities (changepoints) were not accounted for in the analysis. Changepoint features can dramatically influence trend inferences from climate time series. The purpose of this paper is to present a detailed statistical methodology to estimate trends of a time series of daily snow depths that account for changepoint features. The methods are illustrated in the analysis of a daily snow depth data set from North America.

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