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  • Author or Editor: Xiaolan L. Wang x
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Xiaolan L. Wang

Abstract

This study proposes an empirical approach to account for lag-1 autocorrelation in detecting mean shifts in time series of white or red (first-order autoregressive) Gaussian noise using the penalized maximal t test or the penalized maximal F test. This empirical approach is embedded in a stepwise testing algorithm, so that the new algorithms can be used to detect single or multiple changepoints in a time series. The detection power of the new algorithms is analyzed through Monte Carlo simulations. It has been shown that the new algorithms work very well and fast in detecting single or multiple changepoints. Examples of their application to real climate data series (surface pressure and wind speed) are presented. An open-source software package (in R and FORTRAN) for implementing the algorithms, along with a user manual, has been developed and made available online free of charge.

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Xiaolan L. Wang
,
Hanfeng Chen
,
Yuehua Wu
,
Yang Feng
, and
Qiang Pu

Abstract

This study integrates a Box–Cox power transformation procedure into a common trend two-phase regression-model-based test (the extended version of the penalized maximal F test, or “PMFred,” algorithm) for detecting changepoints to make the test applicable to non-Gaussian data series, such as nonzero daily precipitation amounts or wind speeds. The detection-power aspects of the transformed method (transPMFred) are assessed by a simulation study that shows that this new algorithm is much better than the corresponding untransformed method for non-Gaussian data; the transformation procedure can increase the hit rate by up to ∼70%. Examples of application of this new transPMFred algorithm to detect shifts in real daily precipitation series are provided using nonzero daily precipitation series recorded at a few stations across Canada that represent very different precipitation regimes. The detected changepoints are in good agreement with documented times of changes for all of the example series. This study clarifies that it is essential for homogenization of daily precipitation data series to test the nonzero precipitation amount series and the frequency series of precipitation occurrence (or nonoccurrence), separately. The new transPMFred can be used to test the series of nonzero daily precipitation (which are non Gaussian and positive), and the existing PMFred algorithm can be used to test the frequency series. A software package for using the transPMFred algorithm to detect shifts in nonzero daily precipitation amounts has been developed and made freely available online, along with a quantile-matching (QM) algorithm for adjusting shifts in nonzero daily precipitation series, which is applicable to all positive data. In addition, a similar QM algorithm has also been developed for adjusting Gaussian data such as temperatures. It is noticed that frequency discontinuities are often inevitable because of changes in the measuring precision of precipitation, and that they could complicate the detection of shifts in nonzero daily precipitation data series and void any attempt to homogenize the series. In this case, one must account for all frequency discontinuities before attempting to adjust the measured amounts. This study also proposes approaches to account for detected frequency discontinuities, for example, to fill in the missed measurements of small precipitation or the missed reports of trace precipitation. It stresses the importance of testing the homogeneity of the frequency series of reported zero precipitation and of various small precipitation events, along with testing the series of daily precipitation amounts that are larger than a small threshold value, varying the threshold over a set of small values that reflect changes in measuring precision over time.

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Hui Wan
,
Xiaolan L. Wang
, and
Val R. Swail

Abstract

In this study a comprehensive quality assurance (QA) system, which includes the hydrostatic check combined with a statistical homogeneity test, is designed and applied to hourly pressure records (for 1953–2002) from 761 Canadian stations, to produce a high-quality database of hourly station and sea level pressures for various climate studies. The main principles of the QA system are described in detail, followed by a brief emphasis on the error correction algorithms. The general performance of the QA system and the main problems in the Canadian historical hourly pressure database are discussed and illustrated through various examples. The results show that there are serious systematic errors (i.e., sudden changes in the mean, or mean shifts) in the Canadian hourly pressure database, which are caused either by the use of incorrect station elevation values in the reduction of barometer readings to station or sea level pressure values (e.g., the “50-ft rule” or station relocation without updates to the station elevation), by transposing/swapping station and sea level pressure values, or by mistakes made in the archive data ingestion or data recording/digitization processes (e.g., use of a wrong base number). Random errors also exist and are mainly due to the transposition of two digits or miscoding of one or two digits. These errors must be corrected before the data are used in various climate studies, especially climate change–related studies.

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Xiaolan L. Wang
,
Qiuzi H. Wen
, and
Yuehua Wu

Abstract

In this paper, a penalized maximal t test (PMT) is proposed for detecting undocumented mean shifts in climate data series. PMT takes the relative position of each candidate changepoint into account, to diminish the effect of unequal sample sizes on the power of detection. Monte Carlo simulation studies are conducted to evaluate the performance of PMT, in comparison with the most popularly used method, the standard normal homogeneity test (SNHT). An application of the two methods to atmospheric pressure series recorded at a Canadian site is also presented. It is shown that the false-alarm rate of PMT is very close to the specified level of significance and is evenly distributed across all candidate changepoints, whereas that of SNHT can be up to 10 times the specified level for points near the ends of series and much lower for the middle points. In comparison with SNHT, therefore, PMT has higher power for detecting all changepoints that are not too close to the ends of series and lower power for detecting changepoints that are near the ends of series. On average, however, PMT has significantly higher power of detection. The smaller the shift magnitude Δ is relative to the noise standard deviation σ, the greater is the improvement of PMT over SNHT. The improvement in hit rate can be as much as 14%–25% for detecting small shifts (Δ < σ) regardless of time series length and up to 5% for detecting medium shifts (Δ = σ–1.5σ) in time series of length N < 100. For all detectable shift sizes, the largest improvement is always obtained when N < 100, which is of great practical importance, because most annual climate data series are of length N < 100.

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Jaxk Reeves
,
Jien Chen
,
Xiaolan L. Wang
,
Robert Lund
, and
Qi Qi Lu

Abstract

This review article enumerates, categorizes, and compares many of the methods that have been proposed to detect undocumented changepoints in climate data series. The methods examined include the standard normal homogeneity (SNH) test, Wilcoxon’s nonparametric test, two-phase regression (TPR) procedures, inhomogeneity tests, information criteria procedures, and various variants thereof. All of these methods have been proposed in the climate literature to detect undocumented changepoints, but heretofore there has been little formal comparison of the techniques on either real or simulated climate series. This study seeks to unify the topic, showing clearly the fundamental differences among the assumptions made by each procedure and providing guidelines for which procedures work best in different situations. It is shown that the common trend TPR and Sawa’s Bayes criteria procedures seem optimal for most climate time series, whereas the SNH procedure and its nonparametric variant are probably best when trend and periodic effects can be diminished by using homogeneous reference series. Two applications to annual mean temperature series are given. Directions for future research are discussed.

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Heather MacDonald
,
Daniel W. McKenney
,
Xiaolan L. Wang
,
John Pedlar
,
Pia Papadopol
,
Kevin Lawrence
,
Yang Feng
, and
Michael F. Hutchinson

Abstract

This study presents spatial models (i.e., thin-plate spatially continuous spline surfaces) of adjusted precipitation for Canada at daily, pentad (5 day), and monthly time scales from 1900 to 2015. The input data include manual observations from 3346 stations that were adjusted previously to correct for snow water equivalent (SWE) conversion and various gauge-related issues. In addition to the 42 331 models for daily total precipitation and 1392 monthly total precipitation models, 8395 pentad models were developed for the first time, depicting mean precipitation for 73 pentads annually. For much of Canada, mapped precipitation values from this study were higher than those from the corresponding unadjusted models (i.e., models fitted to the unadjusted data), reflecting predominantly the effects of the adjustments to the input data. Error estimates compared favorably to the corresponding unadjusted models. For example, root generalized cross-validation (GCV) estimate (a measure of predictive error) at the daily time scale was 3.6 mm on average for the 1960–2003 period as compared with 3.7 mm for the unadjusted models over the same period. There was a dry bias in the predictions relative to recorded values of between 1% and 6.7% of the average precipitations amounts for all time scales. Mean absolute predictive errors of the daily, pentad, and monthly models were 2.5 mm (52.7%), 0.9 mm (37.4%), and 11.2 mm (19.3%), respectively. In general, the model skill was closely tied to the density of the station network. The current adjusted models are available in grid form at ~2–10-km resolutions.

Open access