Abstract

Changes in the extreme annual wind speed in and around the Gulf of St. Lawrence (Canada) were investigated through a nonstationary extreme value analysis of the annual maximum 10-m wind speed obtained from the North American Regional Reanalysis (NARR) dataset as well as observed data from selected stations of Environment Canada. A generalized extreme value distribution with time-dependent location and scale parameters was used to estimate quantiles of interest as functions of time at locations where significant trend was detected. A Bayesian method, the generalized maximum likelihood approach, is implemented to estimate the parameters. The analysis yielded shape parameters very close to 0, suggesting that the distribution can be modeled using the Gumbel distribution. A similar analysis using a nonstationary Gumbel model yielded similar quantiles with narrower credibility intervals. Overall, little change was detected over the period 1979–2004. Only 7% of the investigated grids exhibited trends at the 5% significant level, and the analysis performed on the reanalysis data at locations of significant trend indicated a rise in the median extreme annual wind speed by up to 2 m s−1 per decade in the southern coastal areas with a corresponding increase in the 90% and 99% quantiles of the extreme annual wind speeds by up to 5 m s−1 per decade. Also in the northern part of the gulf and some offshore areas in the south, the 50%, 90%, and 99% quantile values of the extreme annual wind speeds are noted to drop by up to 1.5, 3, and 5 m s−1, respectively. While the directions of the changes in the annual extremes at the selected stations are similar to those of the reanalysis data at nearby grid cells, the magnitudes and significance levels of the changes are generally inconsistent. Change at the same significance level over the same period of the NARR dataset was noted only at 2 stations out of 13.

1. Introduction

For the purpose of ensuring safety of exposed structures, it is usually a requirement to estimate the extreme loads they might be subjected to during their service time. In addition to the service loads, the possible effects of extreme meteorological events should be assessed in the design of vulnerable structures. During storm activity, the extremes of low-level winds can generate huge oceanic waves and storm surges in the maritime sectors that consequently may lead to damage of marine structures and coastal erosion. This is especially the case in the Gulf of St. Lawrence area (Canada), where regular events of intense extratropical cyclones are observed mainly from autumn to spring. As suggested in the recent work of Wang et al. (2006b), the highest center of cyclone activity is located over the Canadian east coast from the Great Lakes area to the Gulf of St. Lawrence, with the highest long-term mean of cyclone deepening rate (see Wang et al. 2006b, their Fig. 4a). It is therefore worthwhile to properly assess the distribution of wind extremes and their potential changes in terms of their intensity, duration, and frequency of occurrence under climate change and the associated effects on storm surges.

Design wind loads are generally estimated using extreme value analysis of observed wind speed series in the vicinity of the proposed structure. Many studies have been done in the past on the estimation of extreme wind speeds, which were motivated by different objectives, such as selection of an appropriate statistical model (Pavia and O’Brien 1986), evaluation of efficiency of model parameter estimation techniques and uncertainty analysis (Pandey et al. 2003), dealing with small datasets (Simiu and Heckert 1996; Brabson and Palutikof 2000), extrapolation of extremes to estimate long return period values (Naess 1998), and investigating the presence of more than one distribution of the extremes (Van den Brink et al. 2004).

Extreme value analysis of wind speeds is generally performed through implementation of either of the two commonly used approaches. In the first approach, one of the distributions from the generalized extreme value (GEV) family is applied to the largest wind speed in a selected period of time. In the second approach [the peaks-over-threshold (POT) modeling approach], the generalized Pareto distribution (GPD) is applied to peaks of independent storms exceeding a sufficiently high threshold. To insure independency of the data, a certain minimum separation time is maintained between the data selected for the analysis. Gusella (1991), for instance, used a minimum separation time of 48 h. Application of the GEV to the maximum wind speed for a given period is generally used when the datasets are sufficiently long to allow fitting of the distribution function with a reasonable error margin. Because of the widespread belief that wind speed is generally modeled by the Weibull distribution (Tuller and Brett 1984; Pavia and O’Brien 1986; Barthelmie and Pryor 2003) and the fact that Weibull is one of the parent distributions of the Gumbel extremes (a special case of the GEV), Gumbel distribution has traditionally been used for analyzing wind extremes (see Palutikof et al. 1999 for the review). There are, however, some authors who suggested the use of the reverse Weibull distribution to model extreme wind speeds (Walshaw 1994; Simiu et al, 2001).

Most of the previous studies focused on analysis of extreme winds under the assumption of stationarity. However, recent studies have revealed that extremes of many weather and climate variables have been in a state of change over the last decades and that the change is likely to continue in the future (Zwiers and Kharin 1998; Houghton et al. 2001; Solomon et al. 2007; Yan et al. 2006). Therefore, it is worthwhile to verify if trends or any type of nonstationarity are present in the historical data and to adapt the analytical methods in such a way that the nonstationarities can be taken into account. This makes it possible to estimate design values in a more realistic way under the changing climate.

Recent studies have focused on the introduction of covariates in the parameters of the extreme value distribution to account for nonstationarity in the data (Katz et al. 2002; Wang et al. 2004; Kharin and Zwiers 2005). This is done by modeling one or more of the parameters as linear or nonlinear functions of the covariates on which the data show dependence. Covariate methods have also been implemented in the detection of trends in extremes. After comparing different methods of detecting trends in extreme values, Zhang et al. (2004b) came to a conclusion that methods that are based on modeling trends in the parameters of the distribution of the extremes are powerful methods of detecting statistically significant trends in the extremes.

This study is aimed at investigating the existence of trends in the extremes of historical station wind data as well as recent gridded regional reanalysis wind data [i.e., North American Regional Reanalyses (NARR) from the National Centers for Environmental Prediction (NCEP); Mesinger et al. 2006] covering the whole of North America, and performing a spatial mapping of changes in the extreme wind and their quantiles across the Gulf of St. Lawrence (located in eastern Canada; see Fig. 1). A nonstationary extreme value analysis that incorporates time as a covariate is implemented to model the distribution of the extremes in the presence of a significant trend. Spatial mapping of the changes in the extreme wind speed is done using analysis of the gridded data, while analysis of the selected station data was performed to check the consistency of the reanalysis data with the actual observations. Since the observed data are assimilated in the development of the reanalysis products, one would expect a fairly good correspondence between the NARR dataset and the observations. It should, however, be noted that there could be potential inhomogeneities in both datasets and no detailed investigation and rectification thereof was made. This could potentially introduce uncertainty in the interpretation of the results.

Fig. 1.

Location of observation stations within the Gulf of St. Lawrence.

Fig. 1.

Location of observation stations within the Gulf of St. Lawrence.

This study, nevertheless, constitutes the first usage of wind speed products from NARR over the Gulf of St. Lawrence in the investigation of the usefulness of the dataset in maritime areas of Canada. Also, one of the objectives of the present study is to analyze the veracity of changes in annual maximum wind speed in eastern Canada that are seen in the new regional reanalyses data. Hourly observations of wind speeds from thirteen Canadian weather observation sites for the period 1979–2004 are analyzed to assess the observed changes, which are then compared with the changes derived from the NARR data.

The outline of the paper is as follows: the study area and dataset used in this study are presented in section 2, followed by a description of methods of analysis within the nonstationary framework in section 3. Results obtained through the analysis are discussed in section 4. A brief summary and conclusions are given in section 5.

2. Study area and dataset

The study was performed over the Gulf of St. Lawrence (see Fig. 1), where regular storm surge events are observed. Strong wind speed events are often noted in the region in winter and early spring when there is a higher temperature gradient between land and oceanic areas, as well as with regular cold air advection over the region during the passage of meteorological synoptic storms (e.g., Gachon et al. 2001). Wind speeds of around 100 km h−1 (i.e., over 25 m s−1) are observed during this time, inducing high waves of more than 5 m. When these events are in phase with high tides and sea level rise associated with the presence of a low pressure system, they often cause coastal damages and erosion over localized sectors of the Gulf, as has been the case over the St. Lawrence estuary and around the Gaspesian Peninsula in recent years.

A dataset of 3-hourly 10-m zonal and meridional wind components of the NARR dataset on a 32-km grid for the period 1979–2004 (e.g., Mesinger et al. 2006) was obtained. These data correspond to diagnostic values at the equivalent anemometer level, computed from the wind at the lowest prognostic level of the NCEP NARR model. The depths of the lowest layer vary depending on the surface height, but for the grid points where the surface height is zero (i.e., oceanic points) it is about 20 m, which means 10 m is approximately at the middle of the lowest layer, where the model winds are calculated. Following a similar practice applied to NCEP’s global reanalysis, the 26-yr NARR retrospective production period is enriched by construction and daily execution of a system for near-real-time continuation of the NARR, known as the Regional Climate Data Assimilation System (R-CDAS). The observed winds are assimilated in the NARR, both upper air and near-surface winds.

In addition to NARR data, observed hourly 10-m wind speed data from selected stations across the Gulf were obtained from Environment Canada, with the record period varying from station to station. For the present study, a period over which less than 20% of data are missing for each year is considered and the period over which this criterion is fulfilled is shown in Table 1. The location of the stations is also shown in Fig. 1. The use of station data will also make it possible to evaluate the consistency, in terms of trends and pattern of increase/decrease, between wind reanalysis products and near-surface observations.

Table 1.

Selected wind measurement stations across the Gulf of St. Lawrence and trends in their annual maximum wind speed over the observation period (values in boldface type are significant at the 5% level).

Selected wind measurement stations across the Gulf of St. Lawrence and trends in their annual maximum wind speed over the observation period (values in boldface type are significant at the 5% level).
Selected wind measurement stations across the Gulf of St. Lawrence and trends in their annual maximum wind speed over the observation period (values in boldface type are significant at the 5% level).

3. Methods of analysis

a. Detection of nonstationarity

To investigate the presence of a significant trend in the data, a rank-based nonparametric significance trend test, the Kendall tau test (Kendall 1975), was performed on the annual maximum of both the gridded NARR and station wind speed data. Estimation of trends and their corresponding significance was performed over a common period of time between the two datasets (i.e., over 1979–2004). The estimated significance levels were verified using a resampling (permutation) technique (Good 1994). Trends are considered significant at a 5% level.

b. Nonstationary GEV analysis

Stationarity of data is a basic requirement in the classical frequency analysis, but may not be realized in atmospheric variables (e.g., Tramblay et al. 2005), particularly in the context of global climate change. Therefore, analytical methods designed to quantify extremes need to be adapted in such a way that temporal trends are taken into account.

The approach followed in this work is based on implementation of the GEV distribution with time-dependent parameters to model the distribution of annual extremes. The cumulative distribution function of the GEV is expressed as (Jenkinson 1955)

 
formula

where μ, α > 0, and κ are the location, the scale, and the shape parameters, respectively.

The value of the shape parameter determines the tail behavior of the distribution. So κ > 0 corresponds to the reverse Weibull distribution and has a bounded upper tail at x = μ + α/κ; κ < 0 corresponds to the Fréchet distribution and has a heavy unbounded upper tail; κ = 0 corresponds to the Gumbel distribution and has thin unbounded tails.

To account for nonstationarity, the location and scale parameters are assumed to change with time. In the present work, the location parameter and the logarithm of the scale parameter are modeled as polynomial functions of time. The logarithm of the scale parameter is used to ensure that its value remains positive. We started with a linear function and a higher term was added only when a significant improvement in the fit is indicated by the deviance statistic. The general form of the location and the scale parameters is therefore

 
formula
 
formula

The model parameters can classically be estimated using the maximum likelihood (ML) approach. However, when used for small sample sizes, the ML method may lead to very high quantile estimation variances and values of the shape parameters that are not physically plausible. Besides, it is difficult to verify that the ML estimator meets the desired asymptotic properties when the shape parameter is different from 0, which might lead to estimation with very high variance (Smith 1985). As an alternative, the generalized maximum likelihood (GML) approach, which is a Bayesian approach based on the maximum likelihood method with additional prior information on one or more of the parameters (Martins and Stedinger 2000; El Adlouni et al. 2007), is implemented in this work.

The GML method involves maximizing the likelihood function of the sample data given the prior distribution of some or all of the parameters, which is equivalent to maximizing the posterior distribution of the parameters conditionally to the data. This can be computed using numerical methods. Alternatively, it can be handled using the Markov chain Monte Carlo (MCMC) method, which is based on generating random samples of the parameters whose distribution approximates the posterior distribution of the parameters. In the present work, a sufficiently long chain is constructed using a single-component Metropolis–Hastings algorithm (Gilks et al. 1998). Each parameter is updated using a random walk Metropolis algorithm with a Gaussian proposal density centered at the current state of the chain. For each iteration, the conditional quantiles with a given nonexceedance probability are computed using the inverse of the cumulative distribution function of the GEV distribution with the updated parameters.

The empirical posterior distribution of the parameter vector and the distribution of the corresponding quantiles are estimated from the last part of the chain leaving out the initial part (“spinup” portion) to allow for convergence of the chain. In addition to the empirical posterior distribution, this approach allows deduction of the marginal distributions of the parameters and their characteristics. The modes of the marginal distributions are taken as the GML estimator. The approach is presented in detail in El Adlouni et al. (2007), where they evaluated its performance against the classical maximum likelihood method through a simulation study. A similar approach is used in the present study.

c. The peaks-over-threshold method

To further verify the changes in the quantiles estimated using the nonstationary GEV method, a simple stationary analysis was performed on extreme wind speed over two separate periods by dividing the NARR period into two halves. The peaks-over-threshold approach was implemented to increase the sample size for the analysis. A sufficiently large threshold was fixed and independent peaks above the threshold were selected. To ensure independence of events, a minimum of 48 h was maintained between selected events. The GPD (Pickands 1975) was then fitted to the samples using the maximum likelihood approach.

4. Results and discussion

a. Trends in the annual maximum series

For the time period 1979–2004, trend tests performed on the gridded NARR annual maximum wind speeds reveal that only 7% of the grids covering the study area exhibit trends significant to a 5% level. Grid cells showing significant increasing trends are concentrated along the coastal areas in the southern part of the gulf, while those showing significant negative trends form a band in the inland areas farther north and in some parts of the offshore area in the southeast. Figure 2 shows the trends at grids of significant change and the derived contours together with trends at the stations.

Fig. 2.

Trends in the annual maximum wind speed over the period 1979–2004 at observation stations and NARR grids where the trends are significant at the 5% level together with the derived contours.

Fig. 2.

Trends in the annual maximum wind speed over the period 1979–2004 at observation stations and NARR grids where the trends are significant at the 5% level together with the derived contours.

A similar test was performed on the annual maximum of 3-h average wind speeds at 13 stations across the study area. When the test is performed over the periods where there are enough data, eight of the stations exhibited a negative trend significant at a 5% level, while a positive trend at the same significance level was displayed at one station as shown in Table 1. However, over the NARR period (i.e., 1979–2004), only two out of the investigated thirteen stations (one in the St. Lawrence estuary and one in the eastern part of Newfoundland as shown in Fig. 2) exhibited trends at a 5% significance level. The trends at both stations are negative, but none of the NARR grids around these stations show a trend at the same significance level. The other stations, which showed nonsignificant changes, are generally surrounded by grid cells, which also showed a nonsignificant trend.

In terms of the magnitudes of the trends, although most of the stations showed trends within the range of the magnitude of the trends of the NARR values, a few stations located in the eastern part of the Gulf have shown considerably higher negative trend (up to −3 m s−1 per decade). Figure 3 shows, as an example, the moving average annual maximum wind speed (over an 11-yr window to smooth subdecadal variabilities) at one of the stations where the trend is markedly different from that of the surrounding grids [Gander International Airport (IA)] and at the nearest NARR grid cell over the last 15 yr. In addition to a significant difference in the trend magnitudes, the figure shows that the wind speed values are systematically lower in NARR data, by 3–5 m s−1, suggesting smoother estimates of the near-surface wind speed relative to observed values.

Fig. 3.

Time series of moving average (over 11-yr window) of annual maximum wind speeds at station Gander IA and the surrounding 10 nearest NARR grid cells.

Fig. 3.

Time series of moving average (over 11-yr window) of annual maximum wind speeds at station Gander IA and the surrounding 10 nearest NARR grid cells.

Different sources of uncertainty could contribute to the discrepancy between the trends and the magnitudes of the NARR and station extreme winds. One possible source is the possibility of changes in instrumentation and sites at observation stations. Metadata for some of the stations have been obtained from Environment Canada. A test for changes in the mean values of the annual extreme wind speeds at these stations has been performed using a nonparametric Wilcoxon Mann–Whitney test over the period 1979–2004. The metadata and the test results are shown in Table 2. One can see from the table that no changes that can systematically be related to changes in the observation practice have taken place on the station annual extreme wind speeds. Also, a recent work (R. Diaconesco et al. 2008, unpublished manuscript) has shown that nonhomogeneity and nonstationary values are present in instrumental records, but they are not systematically linked to the timing of the changes in observational techniques (e.g., instrumentation, site location). Nevertheless, these changes can potentially introduce some inconsistencies in the computed trends with respect to NARR data. In addition to changes in the observational techniques, the mismatch in the spatial scales of the two datasets and the difference in the sampling frequency of the data can contribute to the difference, at least in terms of the absolute magnitudes of the trends.

Table 2.

Metadata of some of the observation stations and years of analyzed changes in the mean of the annual maximum wind speed together with the corresponding significance level.

Metadata of some of the observation stations and years of analyzed changes in the mean of the annual maximum wind speed together with the corresponding significance level.
Metadata of some of the observation stations and years of analyzed changes in the mean of the annual maximum wind speed together with the corresponding significance level.

As the annual maximum values of wind speed occur mainly during winter as a consequence of higher low-level air temperature gradients between land areas and ice-free ocean (e.g., Gachon et al. 2001), the related changes in atmospheric circulation variability during that period (i.e., storm activities or sea level pressure patterns) are responsible for the main changes in wind field characteristics, but in a nonequivocal manner as they depend on storm tracks and intensity as well as their duration and frequency. A recent study by Wang et al. (2006b) using observed sea level pressure data over the 1953–2002 period (from 83 Canadian observation stations) has suggested that winter cyclone activity has shown the most significant trend when compared with other seasons. It has become significantly more frequent and stronger, which lasts longer in the lower Canadian Arctic, but less frequent and weaker in the south, especially along the southeast coast of Canada. In the latter region, cyclone activity was found to be closely related to the North Atlantic Oscillation (NAO), as the simultaneous NAO index explains about 44% (41%) of the winter (autumn) cyclone activity variance.

A different study by Wang et al. (2006a), which uses a cyclone detection/tracking algorithm from two sets of global reanalysis products [European Centre for Medium-Range Weather Forecasts (ECMWF) (Uppala 2001; Uppala et al. 2005) and NCEP (Kistler et al. 2001)], shows that most notable historical trends in cyclone activity are found to be associated with strong-cyclone activity in winter. Over the boreal extratropics, both global ECMWF and NCEP reanalyses show a significant increasing trend in January–March (JFM) strong-cyclone activity over the high-latitude North Atlantic, with a significant decreasing trend over the midlatitude North Atlantic (including the Gulf of St. Lawrence, where a distinct pattern is observed in southern and northern areas of the gulf in winter; see Wang et al. 2006a, their Fig. 2a). The JFM changes over the North Atlantic are associated with the mean position of the storm track shifting about 181 km northward.

Although only a small fraction of the investigated grids and stations have shown significant trends in the present study, a part of the changes can be explained by these changes in storm-track location and intensity, especially the shift of the most intense cyclone toward north over the recent decades. Nevertheless, more work is needed to better understand without ambiguity the spatial and temporal changes of winds and their associated storm activities using the same regional NARR dataset used in this study.

Previous studies on the analysis of cyclone activity have only focused on the use of global reanalysis products. However, regional-scale feedbacks that are not taken into account in coarse-scale reanalysis products are also important for the wind regime of a smaller area such as the present study area (see the winter effects of regional sea ice conditions on wind field patterns in Gachon et al. 2001). This makes it difficult to make a direct link between the results in the present study and those performed using coarse-scale reanalysis products. Further work is needed to establish the links between the variability of flow regimes and wind field evolution. Indeed, a trend assessment devoted specifically to cyclone activity in Canada has only been done recently in Wang et al. (2006b), although some previous studies included Canada as part of the boreal extratropics (e.g., Wang et al. 2006a; Gulev et al. 2001; Lambert 1996) or the Arctic (e.g., Zhang et al. 2004a; Serreze et al. 1997, 1993; Serreze 1995).

b. Estimation of model parameters and quantiles under nonstationarity

Applicability of the MCMC approach to estimate the nonstationary parameters of the GEV was first tested on the annual extremes at the stations that showed a significant trend by using noninformative priors for the distribution parameters. A uniform prior distribution with a very large variance was used for each parameter. As mentioned in section 3b, selection of the best trend pattern in the model parameters was performed hierarchically starting with the simplest and adding more terms of a polynomial until the deviance statistics showed no significant improvement in the fit. While a linear trend in the logarithm of the scale parameter was found to be adequate at all stations, the location parameter at some of the stations was modeled as a quadratic function of time while at the others a linear trend was found to be adequate.

Table 3 shows the estimated model parameters using both a stationary and nonstationary approach. Both the location and scale parameters generally show a decreasing trend. For a given shape parameter, a decreasing trend in both the location and scale parameters leads to a decreasing tendency in the mean value of the extremes. This is consistent with the trends in the annual extremes shown in Table 1. The estimated shape parameters at all stations were found to be very close to 0, as shown in Table 3. The values at the different stations range between −0.09 and 0.09 with the mean of the absolute values equal to 0.010. This confirms the suggestion made by many of the earlier studies that the distribution of extreme wind speeds in midlatitudes is generally modeled using the Gumbel distribution. Therefore, a similar analysis was performed on the station values using the Gumbel distribution to investigate how the uncertainty, as described by the credibility intervals (CIs) for the different quantiles, varies between the GEV and the Gumbel models. The 50%, 90%, and 99% quantile values were considered for evaluation. Although the mean estimators for all quantiles are very similar in both cases, the 95% credibility interval for the GEV distribution was found to be much wider than that of the Gumbel distribution. This is, indeed, what would be expected as more parameters are involved in the GEV and the cumulative effect of the uncertainties in their estimation would result in a higher quantile variance. As expected, the credibility intervals also consistently increase with quantiles in both models, which suggests that estimation of very rare events is associated with more uncertainty. Figure 4 shows a comparison of estimated time varying quantiles using a Gumbel and a GEV model at one of the stations (i.e., Quebec) together with the time series of the observed annual maximum and the corresponding empirical quantiles.

Table 3.

Estimates of parameters of the extreme value distribution of wind speeds at the stations (numbers in parentheses are 95% CI).

Estimates of parameters of the extreme value distribution of wind speeds at the stations (numbers in parentheses are 95% CI).
Estimates of parameters of the extreme value distribution of wind speeds at the stations (numbers in parentheses are 95% CI).
Fig. 4.

Comparison between estimated quantiles and their CIs using the nonstationary Gumbel and GEV models (station Quebec).

Fig. 4.

Comparison between estimated quantiles and their CIs using the nonstationary Gumbel and GEV models (station Quebec).

A stationary analysis was also performed on the station data using the same approach to investigate the differences in the quantile estimation. The results obtained indicate that the 95% credibility interval for the nonstationary Gumbel model at most of the stations is narrower than the corresponding confidence interval of the stationary analysis (Fig. 5, as an example at station Mont Joli, where the location parameter is a quadratic function of time). On the other hand, the opposite tendency was noted for the GEV model (Fig. 6). Because of this and the tendency of the estimated shape parameter of the GEV distribution to be close to 0, the Gumbel distribution was used for further analysis of the NARR dataset.

Fig. 5.

Comparison between quantiles estimated using a stationary and nonstationary Gumbel model with a quadratic trend in the location parameter (station Mont Joli).

Fig. 5.

Comparison between quantiles estimated using a stationary and nonstationary Gumbel model with a quadratic trend in the location parameter (station Mont Joli).

Fig. 6.

Comparison between quantiles estimated using stationary and nonstationary GEV models (station Mont Joli).

Fig. 6.

Comparison between quantiles estimated using stationary and nonstationary GEV models (station Mont Joli).

To assess the spatial variation of changes in the quantiles of the annual extreme wind speed, nonstationary Gumbel models were fitted using the GML method to the annual extreme wind speeds at each NARR grid where the annual extremes showed a trend at the 5% significance level. Figures 7 –9 show the estimated changes in the 50%, 90%, and 99% quantiles per decade, respectively.

Fig. 7.

Changes in the 50% quantile annual maximum wind speeds over the period 1979–2004 at locations where trends in the annual maximum are significant at the 5% level.

Fig. 7.

Changes in the 50% quantile annual maximum wind speeds over the period 1979–2004 at locations where trends in the annual maximum are significant at the 5% level.

Fig. 9.

As in Fig. 7, but for the 99% quantile.

Fig. 9.

As in Fig. 7, but for the 99% quantile.

As shown in section 4a, some grids in the southern coastal areas of the Gulf show an increasing trend in the annual extreme wind speeds. The quantile estimates of the GML show an increase in the 50% quantile that ranges between 0.5 and 2 m s−1 per decade. The highest changes in the 50% quantile are found in the offshore areas east of Cape Breton (Nova Scotia). Over the land surface, the changes are fairly uniform with magnitudes at most locations between 0.5 and 1 m s−1 per decade. Similarly, the 90% and 99% quantiles show an increase in the range from 0 to 5 m s−1 per decade. Unlike the changes in the 50% quantile, however, their changes show a less coherent spatial structure.

A decreasing trend in the extremes is displayed in the Newfoundland areas north of the Gulf and some parts of the offshore areas in the southeast. The changes in the 50% quantile of the annual extremes are fairly uniform throughout the locations that showed a downward trend at the 5% significance level and they range between −1.5 and 0 m s−1 per decade. The changes in the 90% and 99% quantile, on the other hand, show more variability, with some grids in the northern inland areas showing a slightly increasing tendency. But, generally, the changes in the 90% quantile range between −3 and −0.5 m s−1 per decade, while those of the 99% quantile range between −5 and −2 m s−1 per decade. The strongest decreasing changes are estimated in the southeastern offshore areas.

No significant trends were observed at the NARR grids in the neighborhood of the two stations that showed a trend at the 5% significance level in their annual extremes over the NARR period (Baie-Comeau and Gander IA). Nevertheless, the tendency of the changes at the grids is in the same direction although not significant (see Fig. 2). The estimated quantile changes at the stations are also within the range of the corresponding changes at the NARR grids where significant changes were noted.

As a further check to the pattern of the changes estimated through the nonstationary extreme value analysis, a peaks-over-threshold analysis was performed using the generalized Pareto distribution over the first and second halves of the NARR period. Figure 10 shows, as an example, the changes in the estimated 90% quantiles between the two periods. One can clearly see that the directions of the changes and the spatial variations in the relative magnitudes of the changes are generally consistent with the corresponding changes estimated using the nonstationary approach.

Fig. 10.

Differences in the 90% quantile of the peaks over threshold wind speed between 1979–91 and 1992–2004 at locations of significant trend as estimated using stationary GPD analysis separately over the two periods.

Fig. 10.

Differences in the 90% quantile of the peaks over threshold wind speed between 1979–91 and 1992–2004 at locations of significant trend as estimated using stationary GPD analysis separately over the two periods.

5. Summary and conclusions

A nonstationary extreme value analysis has been implemented to estimate quantiles of extreme wind speed and their changes against time. The application was made on 10-m wind speed data taken from the gridded NARR dataset and selected observation stations near the Gulf of St. Lawrence. The analysis was performed on those grids and stations for which a statistically significant (5% significance level) trend was detected in the annual maximum series. The implemented analytical approach was based on incorporating time as a covariate and including it in the functions defining the parameters. The GEV distribution was implemented to model the extremes with the location parameter and the logarithm of the scale parameter assumed to be polynomial functions of the covariate, i.e. the time). To reduce the risk associated with estimation of the model parameters using the maximum likelihood method when the sample size is small, the generalized maximum likelihood approach was implemented for parameter estimation. The solution was obtained using the Monte Carlo Markov chains method.

Generally, little change has been detected over the entire gulf area. Only 7% of the total number of investigated grids exhibited trends at the 5% significance level over the period 1979–2004. An increasing trend of up to 1.5 m s−1 per decade was noted at a few locations in the coastal area of the southern part of the Gulf of St. Lawrence. A negative trend of similar magnitude was also obtained at some locations in the offshore areas south of the gulf and in the inland areas to the north of the gulf. At the station scale, only 2 stations out of 13 showed significant trends over a similar period, but none of the NARR grids around them showed significant trends.

Application of the nonstationary GEV analysis to the station data yielded values of the shape parameter very close to 0 at all stations. Although no informative prior knowledge was used for the shape parameter, the result is interesting in that it suggests that the distribution is approximately Gumbel, which is a generally suggested distribution of extreme wind speed in the extratropical latitude regions. Also, application of a nonstationary Gumbel model resulted in similar quantile values with the GEV model, but with narrower credibility interval.

The nonstationary Gumbel analysis performed at locations of significant trend indicates an increase in the 50% quantile of the annual extreme by up to 2 m s−1 per decade over the period 1979–2004 at some grid cells located in the southern inland areas, mainly concentrated along the coastal area. Similarly, the 90% and 99% quantiles showed an increase by up to 5 m s−1 per decade. The downward changes in the quantiles at locations where the annual maximum series showed significant negative trend (northern inland areas and southern offshore areas) are generally comparable with the corresponding rise at locations of significant increase. However, at some of the grid cells, the higher quantiles showed a tendency to increase. This is, in fact, a result of increasing variability of the extremes despite the fall in the mean value.

The approach discussed in this paper can potentially be exploited in the estimation of design values of wind speed for vulnerable structures for future time horizons by taking into account the trends in the extremes. However, it should be noted that the time period considered in this work is relatively short to make a comprehensive assessment of the prevalent trend in the extremes and make any plausible statement about the tendency of the changes in the future. As shown through the analysis of the stations data over a time period that extends back from the period corresponding to the beginning of the NARR dataset, the trend pattern might show a considerably different direction and magnitude. A longer dataset is therefore required to detect a relatively stable trend pattern that can be useful to extrapolate the changes in the future.

Despite the fact that the present study showed very localized changes in annual extreme wind speeds at only a few locations, it would be worthwhile to establish the link between the suggested changes in extremes of wind speed and the changes in synoptic storm activities (in terms of track and intensity) over the area. This will be useful for improving our knowledge on the suggested pattern of increase–decrease of wind extremes, and their effects on coastal erosion processes. As shown in the recent work of Caires et al. (2006), in which the nonhomogeneous Poisson process has been used to model extreme values of the oceanic wave height, trends have been detected using projections of the sea level pressure by the Canadian coupled global climate model under three different forcing scenarios [also the study of Wang et al. (2006a)]. Other complementary works are under way to link the most significant oceanic waves and storm surge events with the corresponding track of intense extratropical cyclones and associated direction of strong wind speeds from NARR reanalysis products, as well as from outputs of the Canadian regional climate model. A more comprehensive trend pattern of wind extremes, their variability, and their potential changes in the future will be made possible. This can help researchers to produce more reliable climate change information for use in impact studies, especially over the Gulf of St. Lawrence where wind characteristics and their evolution may have considerable effects on human infrastructures.

Fig. 8.

As in Fig. 7, but for the 90% quantile.

Fig. 8.

As in Fig. 7, but for the 90% quantile.

Acknowledgments

The financial support provided by the Natural Sciences and Engineering Research Council of Canada (NSERC) and the OURANOS consortium is gratefully acknowledged. We acknowledge Dr. Wesley Ebisuzaki from NCEP for providing the NARR data as well as useful information. Finally, we acknowledge the useful facility of the Data Access Interface (http://gaia.ouranos.ca/local/data/DAI-e.html), jointly developed in collaboration between Environment Canada and the Global Environmental and Climate Change Centre (GEC3 from McGill University), which has strongly facilitated the access to all data.

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Footnotes

Corresponding author address: Y. Hundecha, NSERC/Hydro-Quebec Statistical Hydrology Chair, Canada Research Chair on the Estimation of Hydrological Variables, INRS-ETE, University of Quebec, 490 de la Couronne, Quebec, QC G1K 9A9, Canada. Email: yeshewatesfa.hundecha@rub.de