1. Introduction
Surface winds—both wind speed and vector wind components—are fields of fundamental climatic importance. The character of surface winds profoundly influences (and is influenced by) surface exchanges of momentum, energy, and matter (e.g., Garratt 1992). Furthermore, these fields are of interest in their own right, particularly with regard to the characterization of wind power density (e.g., Archer and Jacobson 2005) and wind extremes (e.g., Gastineau and Soden 2009). While numerical weather prediction (NWP) models and global climate models (GCMs) display skill in simulating and predicting the synoptic-scale and larger features of the atmosphere (e.g., Randall et al. 2007), the skill of these models is considerably lower for smaller-scale quantities. In particular, surface winds are influenced by small-scale features (such as local topography and thermal contrasts) and processes not represented (or not represented well) in these models. Prediction of local conditions requires a second level of modeling: large-scale NWP or GCM predictions must be downscaled.
Distinct approaches to downscaling exist. Dynamical downscaling uses NWP or GCM predictions as boundary conditions to drive higher-resolution simulations using regional climate models (RCMs) or mesoscale models (MMs). While this approach has the advantage of being physically based, the still finite resolution of the downscaling model may not capture features or processes that exercise important control over local winds. Furthermore, this approach is expensive (both computationally and in terms of human effort). In contrast, statistical downscaling connects large-scale (NWP or GCM scale) to small-scale (local) variability through statistical prediction models (e.g., Benestad et al. 2008). While this approach is fundamentally empirical (although physical reasoning does enter through the choice of large-scale predictor fields), and can only be applied to locations where observations have been taken for a sufficiently long time to establish the statistical relationship (in contrast to dynamical downscaling), it is site specific and relatively inexpensive to implement. Furthermore, the use of statistical downscaling circumvents the need to correct for the biases of two physical models. Purely dynamical or purely statistical approaches can be considered as end members of a continuum, between which exist downscaling models that combine dynamical and empirical approaches (e.g., Troen and Petersen 1989; Landberg and Watson 1994; De Rooy and Kok 2004; Howard and Clark 2007).
This study considers the statistical downscaling of surface winds (both wind speed and vector wind components) on monthly time scales in the subarctic northeast Pacific Ocean off of the west coast of Canada. Both monthly average quantities and submonthly variability are considered. Merryfield et al. (2009) investigated the downscaling of the annual cycle of monthly mean vector winds in this region; the present study considers the predictability of month-to-month deviations from the annual cycle. Surface observations are taken from eight buoys (three far offshore and five near offshore, a subset of those considered by Merryfield et al.), the positions of which are illustrated in Fig. 1. We will focus on December–February (DJF) winds from 1989 through 2008. This study has three primary goals:
to characterize the spatial scales (horizontal and vertical) on which predictive information regarding surface wind variability is carried,
to assess the differences in predictability between wind speed and vector wind components, and
to investigate the sensitivity of prediction skill to the time scale of the predictor fields.
Locations of the buoys considered in this study. For those buoys that changed location during the period 1989–2008, the mean location is shown.
Citation: Journal of Climate 25, 5; 10.1175/2011JCLI4089.1
By design, this study uses the simplest possible statistical model to relate buoy winds to the large-scale circulation: multiple linear regression of surface wind statistics with predictors taken from indices of the large-scale flow (as in Kaas et al. 1996; De Rooy and Kok 2004; Pryor et al. 2005; Klink 2007; Cheng et al. 2008; St. George and Wolfe 2009; Goubanova et al. 2011). Other studies have used much more complex statistical models, such as neural networks (e.g., Landberg and Watson 1994; Sailor et al. 2000) or random forests (e.g., Davy et al. 2010); have built the statistical analyses around a classification of large-scale flows into “weather regimes” through clustering (e.g., Bogardi and Matyasovszky 1996; Gutiérrez et al. 2004; Najac et al. 2009; Salameh et al. 2009; Cassou et al. 2011; Minvielle et al. 2011) or classification and regression trees (CART) (e.g., Faucher et al. 1999; Sailor et al. 2008); or have used explicitly probabilistic approaches (e.g., Michelangeli et al. 2009; Thorarinsdottir and Gneiting, 2010; Sloughter et al. 2010). Multiple linear regression is simple to implement and (with appropriate cross-validation) produces statistically robust prediction models. The number of data points within any individual season available for building the statistical models is small (20 years of three months at each buoy, less missing and bad data), and it is expected that more sophisticated statistical models would be more prone to overfitting. For such small datasets, simple linear models can have the same predictive skill as more complex nonlinear models (e.g., Landberg and Watson 1994; Tang et al. 2000). The possibility remains that more complex statistical models could carry greater predictive skill; as such, the results of the present study should be interpreted as representing a lower bound on the statistical predictability of historical winds in this region.
The subarctic northeast Pacific off of western Canada is an oceanographically important area, characterized by a strong seasonal reversal in the coastal circulation (upwelling in summer, downwelling in winter) and straddling the bifurcation point of the North Pacific Current. The region is important economically and societally as a transportation corridor and supports major fisheries. For these reasons alone, the downscaling of surface winds in this area is of interest. The downscaling of sea surface winds is also of interest as an ideal “model problem.” Winds over land display complex variability, influenced by local topographic and roughness features and by diurnally varying boundary layer and mesoscale thermal processes (e.g., Pryor et al. 2005; Howard and Clark 2007; Pinard et al. 2009; Salameh et al. 2009; He et al. 2010; Curry et al. 2012; van der Kamp et al. 2012; Monahan et al. 2011). In contrast, away from coastlines, diurnal variability in sea surface winds is weak (in the extratropics) and topographic influences are absent. Mesoscale thermal circulations generated by sea surface temperature gradients associated with fronts and eddies do exist, but these are themselves dynamic features that do not exercise a fixed influence on local winds. These considerations suggest that that the connection between small-scale sea surface winds and the large-scale circulation should be both simpler and stronger than that over land. In fact, it will be demonstrated that there are, nevertheless, complexities to this relationship.
This study will make use of the following notation. Surface quantities measured at the buoys will be represented in lowercase: zonal wind vector component u, meridional component υ, and wind speed w = (u2 + υ2)1/2. Large-scale quantities will be denoted in uppercase: zonal wind U, meridional wind V, wind speed W, and temperature T. Monthly time-scale means and standard deviations of a variable x will be denoted as mean(x) and std(x). The buoy data and observations of large-scale flow are described in section 2. A detailed case study of surface wind downscaling at buoy 46036 (Fig. 1) is presented in section 3, followed by a comparison of predictive skill between the various buoys in section 4. A summary discussion and conclusions follow in section 5.
2. Data
Hourly reports of 10-min-averaged wind speed and direction data (measured at an altitude of approximately 5 m) from eight Navy Oceanographic Meteorological Automatic Device (NOMAD) buoys off the west coast of Canada (Fig. 1) were obtained from Fisheries and Oceans Canada Integrated Science Data Management (downloaded from www.meds-sdmm.dfo-mpo.gc.ca/isdm-gdsi/waves-vagues/index-eng.htm). These data were then averaged to produce daily and monthly averaged zonal wind, meridional wind, and wind speed. The duration of these data varied between buoys (Table 1). When available, 20 years of DJF data from 1 January 1989 to 31 December 2008 were used in the downscaling calculations. These buoy data contain a number of missing observations and erroneous data. Illustrative of this fact is that monthly values of std(w) at buoy 46036 take a small number of anomalously small (<1 m s−1) and large (>5 m s−1) values (Fig. 2). Data from these months were excluded from the monthly downscaling calculations. While these thresholds were selected subjectively, the results presented in this study are not qualitatively sensitive to reasonable changes in their values. Table 1 lists the number of “good” data points (for both monthly and daily averages) for DJF at each of these buoys. A detailed description of the buoys and their instrumentation is presented in AXYS Environmental Consulting Ltd. (1996).
Locations and observation durations of the buoys considered in this study. Locations of some buoys changed slightly during the period 1989–2008; for these cases, the mean position is given. Number N of “good” data points in DJF that were not rejected and can enter the regression analyses are given for monthly and daily data in the sixth and seventh columns. Following Merryfield et al. 2009), the first three of these buoys are described as being “far offshore” while the remaining five buoys are “near offshore.”
Time series of the raw estimates of monthly wind speed standard deviations at buoy 46036. Gaps indicate missing data.The horizontal lines at 1 and 5 m s−1 indicate the upper and lower thresholds used to identify bad data.
Citation: Journal of Climate 25, 5; 10.1175/2011JCLI4089.1
Large-scale circulation data (zonal wind U, meridional wind V, and temperature T) were obtained from the National Centers for Environmental Prediction (NCEP) North American Regional Reanalysis (NARR) (Mesinger et al. 2006). These data are available eight times daily at 29 pressure levels (from 1000 to 100 hPa) from 1 January 1979 to 31 July 2009 on an approximately 32 km × 32 km grid over the North American domain. Wind speed fields W were computed from the zonal and meridional wind component fields. For the downscaling calculation, these data were averaged to daily and monthly time scales. These data were downloaded from the U.S. National Oceanic and Atmospheric Administration Earth System Research Laboratory (ESRL) Physical Sciences Division (PSD) (at www.esrl.noaa.gov/psd).
3. Downscaling surface winds: A case study of buoy 46036
We begin our analysis of the statistical relationship between surface winds and large-scale predictors with a detailed investigation of the winds at buoy 46036 (Fig. 1). This far-offshore buoy was selected for detailed examination precisely because there is no reason to expect that it is in any way special. In fact, as we will discuss in section 4, the main features of the predictability of surface winds at this buoy are common to the other buoys in the domain (for the most part). The strength of statistical relationships will be measured by the correlation coefficient r or its square (r2, corresponding to the fraction of variance explained by the linear model).
a. Monthly mean correlation fields
To assess the horizontal and vertical scales of statistical relationships between monthly mean wind variability at buoy 46036 and the large-scale flow at the surface and aloft, correlation fields of monthly mean u, υ, and w with large-scale U, V, W, and T were computed. The correlation maps at 1000 and 500 hPa for mean(u) and mean(w) are displayed in Figs. 3 and 4. The monthly mean zonal winds at the buoy are strongly correlated with zonal winds at the surface and in the midtroposphere: positive correlations are found locally, while negative values are found to the south. This observed correlation pattern is consistent with surface zonal wind changes dominated by meridional displacements of the eddy-driven jet (although other aspects of jet variability can project onto this pattern; cf. Monahan and Fyfe 2006). The domain of strongly positive (squared) correlations with r2 > 0.5 extends from the surface to the upper troposphere, while that of the strongly negative correlations extends only to the midtroposphere (Fig. 5, left panel). Importantly, predictive information for monthly mean surface zonal winds is carried on horizontal and vertical scales that are potentially predictable by global-scale models. While correlations with the other fields considered are smaller, each of meridional wind, wind speed, and temperature also carry predictive information for the surface zonal wind on these large scales.
Correlation maps of monthly-mean zonal wind at buoy 46036 with monthly mean reanalysis variables at 1000 hPa and 500 hPa: zonal wind (first row), meridional wind (second row), wind speed (third row), and temperature (fourth row). The position of the buoy is indicated by the white circle. White boxes in the first row panels denote the domain used for the EOF decomposition of large-scale predictor fields.
Citation: Journal of Climate 25, 5; 10.1175/2011JCLI4089.1
As in Fig. 3 but for correlations of monthly -mean wind speed at buoy 46036 with the large-scale fields.
Citation: Journal of Climate 25, 5; 10.1175/2011JCLI4089.1
Vertical structure of monthly mean DJF correlation fields at buoy 46036: (left) surface zonal wind with reanalysis zonal wind aloft and (right) surface wind speed with reanalysis wind speed. Within the contours the correlation r2 values are in excess of 0.5 for the zonal wind component and of 0.25 for the wind speed. The red contours denote regions of positive correlation, and blue contours regions of negative correlation. The solid black circle indicates the location of buoy 46036.
Citation: Journal of Climate 25, 5; 10.1175/2011JCLI4089.1
The correlation fields for monthly mean meridional wind at buoy 46036 (not shown) display comparably strong correlations and large-scale features as those of mean(u) (with, of course, different patterns). In contrast, while the correlation fields between monthly mean surface wind speed at the buoy and reanalysis fields are characterized by features of comparably large scale, the absolute correlation values are much smaller than for surface monthly mean zonal winds. The domain over which the squared correlation with reanalysis monthly mean wind speeds satisfies r2 > 0.25 extends to the upper troposphere but with a horizontal extent that is smaller for comparable fields in the zonal and meridional winds (Fig. 5, right panel). For the winds at this buoy, the correlations between monthly-mean vector wind components and the large-scale flow are much stronger than those for monthly mean wind speed.
b. Prediction using monthly time-scale predictors
The existence of large-scale (both horizontal and vertical) correlations between reanalysis data and surface buoy observations on monthly time scales suggests that local wind variations are potentially predictable from the flow aloft. However, the raw large-scale atmospheric fields cannot be used for practical predictions of monthly time-scale wind variability at the buoy. Regressing a surface wind quantity on any one of the large-scale fields over the domain illustrated in, for example, Figure 3, would require the estimation of O(105) regression coefficients (one for each grid point in the domain) from N = 60 observations (20 winters of three months each). Even coarser-resolution representations of these fields (from, e.g., global-scale reanalysis products) would yield O(102 − 103) individual gridpoint predictors. The construction of robust predictive models requires the distillation of these high-dimensional fields into a much smaller number of representative indices characterizing the dominant features of large-scale variability. This was done by the calculation of combined empirical orthogonal functions (EOFs) of large-scale DJF U, V, W, and T at each pressure level. First, EOFs of each field individually were computed using singular value decomposition (SVD), resulting in 60 pairs of EOF spatial patterns and projection principal component (PC) time series. The PC time series for each field were then normalized (and nondimensionalized) by the square root of the spatial-mean variance of the field. Because large-scale variability is not independent among zonal wind, meridional wind, wind speed, and temperature, there will be redundant information carried in these four fields. To most efficiently repackage the information carried in these fields, the four normalized sets of 60 PC time series were concatenated into a single 240-dimensional vector time series that was itself subject to an EOF analysis. The resulting PC time series express the variance within and across these fields in an optimally efficient manner [although they may not have any individual dynamical or kinematic significance, e.g., Monahan et al. (2009)]. In particular, the leading PCs carry the most variance within and between these fields. Furthermore, the fact that the predictors are mutually uncorrelated improves the parsimony of the statistical prediction model and reduces the likelihood of overfitting. The normalization of the individual fields is important to ensure that they each enter the second EOF analysis on an equal footing (and do not depend on the units chosen to measure the fields).
This EOF analysis was carried out not on the entire reanalysis domain, but rather on the smaller domain indicated in the upper panels of Fig. 3. This domain was selected to capture those regions of the large-scale flow most strongly correlated with the surface wind fluctuations while excluding regions of low correlations with extraneous variability that could degrade the predictive skill of the downscaling. In fact, the skill of the statistical predictions was found to be largely insensitive to reasonable changes to the boundaries of this domain.
The number M of leading PC time series from this decomposition will be used as the predictors in linear regression predictions of surface wind variability at the buoy. To avoid artificially inflated estimates of predictability resulting from overfitting the statistical model, a cross-validation strategy is employed (e.g., von Storch and Zwiers 1999). The prediction of variability in any particular year was made using a regression model with parameters estimated from the other 19 years of data. For example, prediction of the first year was carried out using regression parameters estimated using data from year 2 through 20. Similarly, the regression model for predicting year 2 was obtained from year 1 and from year 3 through 20. While there is some autocorrelation of the wind statistics on interannual time scales, the cross-validation strategy is able to account for the larger part of the serial dependence associated with autocorrelation on intra-annual scales.
Cross-validated predictions of monthly mean zonal wind, meridional wind, and wind speed were made using M = 4 combined EOF predictors from each pressure level. Submonthly standard deviations of zonal and meridional wind were also predicted. The square of the correlation coefficient between the observed and predicted time series for each of mean(u), mean(υ), mean(w), std(u), and std(υ) is plotted in Fig. 6 as a function of the pressure level of the predictor fields. Both mean(u) and mean(υ) are predicted well by the large-scale flow across the depth of the troposphere, with most r2 values exceeding 0.5 up to 300 hPa. In contrast, none of mean(w), std(u), or std(υ) are predicted well, with r2 values not exceeding 0.15 for predictors at any pressure level (and generally being much lower). Prediction skills are not substantially changed with modest increases or decreases in the number of predictor PCs used. When M is increased beyond 6 or 7, the prediction skill starts to degrade as the model becomes overfit.
Vertical structure of the cross-validated DJF prediction correlation skill r2 at buoy 46036, from monthly time-scale predictors computed independently at each pressure level in the reanalysis data: monthly mean buoy zonal wind (solid black line), monthly mean buoy meridional wind (dashed black line), monthly mean buoy wind speed (solid gray line), monthly buoy zonal wind standard deviation (gray dashed line), and monthly buoy meridional wind standard deviation (dotted–dashed line).
Citation: Journal of Climate 25, 5; 10.1175/2011JCLI4089.1
Raw correlation maps, such as those presented in Figs. 3 and 4, provide useful baselines against which the predictive skill of the regression models can be assessed. The maximum raw r2 values at individual reanalysis grid points (not shown) are generally roughly equal to or smaller than those of the regression-based predictions. This result indicates that predictive information is being carried on scales larger than those of individual grid points, as well as across predictor fields.
The standard empirical parametric model of the wind speed probability density function (pdf) is the Weibull distribution (e.g., Pryor et al. 2005; Monahan 2006; He et al. 2010; Monahan et al. 2011). This pdf is characterized by two parameters: the scale parameter (closely related to the mean) and the shape parameter (uniquely related to the skewness). Cross-validated predictions of the Weibull scale and shape parameters displayed low prediction skill r2 values (not shown) that are comparable to those of mean(w). Consistent with the results presented in Curry et al. (2012), a statistical downscaling approach using monthly time-scale predictors can show little skill in predicting the parameters of the wind speed probability distribution.
c. An idealized model of the wind speed pdf
Why should it be the case that, while the monthly mean vector wind components are reasonably well-predicted, the monthly mean wind speed has almost no predictability? We will address this question using an idealized model of the vector wind probability distribution that allows explicit computations of the mean wind speed to be made in terms of the statistics of the vector wind components.
Given the values of 
Monthly mean DJF wind speeds at buoy 46036 from observations and as modeled by the Gaussian vector wind model Eq. (9): (a) modeled wind speed from observed monthly varying means and standard deviations of u and υ, (b) modeled wind speed with observed 
Citation: Journal of Climate 25, 5; 10.1175/2011JCLI4089.1
The number of parameters needed to predict 
(left) Mean wind speed 
Citation: Journal of Climate 25, 5; 10.1175/2011JCLI4089.1
The predictions summarized in Fig. 6 demonstrate that, while the large-scale monthly-mean flow predicts 
d. Prediction using daily time-scale predictors
Using monthly time-scale predictors, the predictability of mean(u) and mean(υ) at buoy 46036 from the large-scale flow is much greater than that of mean(w) because the monthly standard deviations of the vector wind components are themselves not well predicted. To circumvent the need to predict std(u) and std(υ) at all, we now consider the predictability of daily averaged winds at buoy 46036 from daily time-scale predictors. Daily averaged PC time series of the large-scale reanalysis data, obtained over the same region and for the same time period as the monthly averaged PCs, were used as predictors of daily mean surface zonal wind, meridional wind, and wind speed. Daily data from those months excluded as a result of bad or missing data (section 2) were also excluded from these calculations; no further quality control of daily data was carried out. Because northeast Pacific surface wind fluctuations decorrelate on a time scale of roughly one day (e.g., Monahan and Culina 2011), the daily averaged winds have a number of statistical degrees of freedom at least an order of magnitude larger than that of the monthly averaged winds. Consequently, we expect that a larger number of predictors can be robustly included in the linear regression models. A larger number of predictors may in fact be needed for skillful predictions: correlation maps of daily mean surface wind fluctuations with large-scale reanalysis data (not shown) demonstrate that, while the correlation magnitudes are similar to those of monthly averaged quantities, the spatial scales are smaller. More EOF modes are potentially needed to reproduce these smaller structures in which potential predicability resides.
The vertical structures of cross-validated r2 prediction skill for daily averaged zonal wind, meridional wind, and wind speed at buoy 46036 are displayed in Fig. 9. These predictions were made with M = 75 PC time series as predictors, cross validated by predicting daily wind fluctuations within a given year using a statistical model estimated with data from the other years. Using lower-tropospheric predictors, the wind speed prediction is almost as skillful as those of the zonal and merdional components. The prediction r2 values for each of u, υ, and w decrease as predictors are taken from higher in the atmosphere. The prediction skill for wind speed drops off with altitude more rapidly than for the vector wind components, which have r2 values in excess of 0.6 for predictors as high aloft as 400 hPa.
(left) Vertical structure of cross-validated r2 prediction skill of daily mean DJF zonal wind (solid black line), meridional wind (dashed black line), and wind speed (solid gray line) at buoy 46036. (right) As in Fig. 6 but for monthly averages and standard deviations of predicted daily averaged winds. For both of these, 75 PC predictor time series were used.
Citation: Journal of Climate 25, 5; 10.1175/2011JCLI4089.1
A much larger number of predictor EOFs was used to predict daily mean fluctuations than was used to predict monthly-mean fluctuations. The prediction skill for each of daily mean zonal wind, meridional wind, and wind speed initially increases rapidly with the number of PC predictors used (Fig. 10) before saturating. Because these are cross-validated prediction skills, the change in r2 with M is not monotonic. For the daily mean vector wind components, increases in prediction skill are modest beyond M ≃ 20, while for wind speed the prediction skill starts saturating only around M ≃ 50.
Dependence of cross-validated r2 prediction skill on the number of principal components of 700-hPa reanalysis data used in the regression model at buoy 46036 for (left) daily mean predicted and (right) monthly average of daily predicted zonal wind (solid black line), meridional wind (dashed black line), and wind speed (gray solid line). Also included in the right panel are r2 predictions of monthly time-scale std(u) and std(υ).
Citation: Journal of Climate 25, 5; 10.1175/2011JCLI4089.1
At buoy 46036, the prediction of winds on daily time scales also improves the predictions of monthly-mean winds. These monthly time-scale predictions were obtained by monthly averaging the daily time-scale predictions. While predictive skills of the monthly averaged daily predictions of the zonal wind components (Fig. 9) are similar to those obtained directly from regression models using monthly averaged predictors, the monthly fluctuations in wind speed are much better predicted. Consistent with this result is an increase (albeit modest) in predictive skill for the monthly standard deviations of zonal and meridional winds. The predictability of these monthly averaged quantities saturates with increasing number M of predictor PCs more rapidly than that of daily winds (Fig. 10): for zonal and meridional winds, predictability increases rapidly for the leading few PC time series and grows much more slowly after that, while the r2 for wind speed fluctuates around a constant value for M ≃ 10. The predictability of std(u) and std(υ) takes a local maximum at about 20 PC predictor time series, beyond which it decreases slightly while fluctuating.
4. Downscaling surface winds: Other buoys
Predictions of monthly-mean zonal and meridional winds and wind speed, as well as of the submonthly std(u) and std(υ), were made at the seven other buoys in the domain in the same manner as they were for buoy 46036. Vertical profiles of the cross-validated r2 prediction skill demonstrate that at all buoys the monthly-mean vector wind components are more predictable than the mean wind speed (Fig. 11). This predictability does not depend strongly on the altitude of the predictors (within the troposphere). At some buoys, mean(w) does demonstrate some modest predictability (e.g., 46814 and 46132) in association with some (very slight) predictability of std(u) and std(υ). However, the modest predictability of std(u) at buoy 46207 is not accompanied by a corresponding predictability of mean(w). The values of θ at all eight buoys (not shown) are generally small, falling in the range for which 
As in Fig. 6 but for all buoys considered.
Citation: Journal of Climate 25, 5; 10.1175/2011JCLI4089.1
The dependences on predictor altitude of the prediction skills of daily-average zonal wind, meridional wind, and wind speed at the various buoys are similar to those at buoy 46036 (Fig. 12). Fluctuations in all three of these quantities are more predictable on daily time scales than on monthly time scales, and this predictability declines gradually with altitude above about 800 hPa. In general, the daily average vector winds have higher predictability than wind speed. There are also commonalities among the buoys in the predictability of monthly statistics (mean and standard deviations) computed from the daily predictions (Fig. 13). The r2 values for each of the predicted zonal wind, meridional wind, and wind speed decrease when monthly averages are taken. However, the predictability of mean(w) is generally greater for monthly averages of daily predictions than for direct predictions of monthly averaged quantities, as is the predictability of each of std(u) and std(υ).
As in the first panel of Fig. 9 but for all buoys considered.
Citation: Journal of Climate 25, 5; 10.1175/2011JCLI4089.1
As in the second panel of Fig. 9 but for all buoys considered.
Citation: Journal of Climate 25, 5; 10.1175/2011JCLI4089.1
While the predictability of winds at these eight buoys share in common the same essential features, there are differences between buoys. In particular, buoy 46004 stands out as consistently displaying anomalously low r2 values. There is nothing particular about the location of buoy 46004 to suggest that the relation of wind fluctuations at this buoy should be substantially different than those of other nearby buoys. Estimates of prediction r2 at all buoys considered are subject to sampling variability, which could contribute to the anomalous nature of buoy 46004. Furthermore, although obviously bad data were removed from the buoy time series, some spurious observations may remain. On average, these bad data would be expected to reduce estimates of r2 prediction skills relative to their true values. Given the particularly large differences in predictability of all wind variables between buoy 46004 and the other buoys, we hypothesize that this buoy is characterized by a relatively large number of bad data. The results of Faucher et al. (1999) similarly identify buoy 46004 as anomalous.
Overall, despite differences between buoys, there is a broad consistency in the predictability of wind fluctuations. Monthly-mean predictors generally display high skill in predicting monthly-mean vector wind quantities and considerably less skill in predicting vector wind variability or mean speeds. For each of u, υ, and w predictive skill with daily predictors is higher than for monthly predictors; when daily predictions are averaged to monthly scales, monthly mean wind speeds and vector-wind-component standard deviations are better predicted than by monthly mean predictors. These results may not hold for surface winds at all locations, but they are broadly representative of the DJF winds in the subarctic northeast Pacific off the west coast of Canada.
5. Discussion and conclusions
Surface winds (both vector winds and wind speed) are geophysical fields of first-order importance. Surface winds strongly influence (and are influenced by) the character of turbulence in the boundary layer and thereby influence surface fluxes (e.g., Garratt 1992). Furthermore, the large-scale extraction of the energy carried in low-level winds has the potential to help offset the use of carbon-based energy sources (e.g., Archer and Jacobson 2005); therefore, it is important to understand this potential resource. Global-scale climate models and weather prediction models are able to represent processes and phenomena on the scales of tens to hundreds of kilometers and larger, but are less skillful in representing variability on the smaller scales that exercise important controls on surface winds. Small-scale, local predictions of surface wind variability must be downscaled from larger-scale predictions. Uses of such downscaled winds include the investigation of past climate variability (e.g., Kaas et al. 1996; Faucher et al. 1999; Klink 2007; Minvielle et al. 2011; Curry et al. 2012; van der Kamp et al. 2012), short-term wind forecasts (e.g., De Rooy and Kok 2004; Howard and Clark 2007; Salameh et al. 2009; Sloughter et al. 2010; Thorarinsdottir and Gneiting 2010), and future climate changes (e.g., Pryor et al. 2005; Merryfield et al. 2009; Goubanova et al. 2011).
This study has addressed some basic questions regarding the predictability of monthly time-scale surface winds from the large-scale flow with a particular focus on winds measured at eight buoys in the subarctic northeast Pacific Ocean off the west coast of Canada. In particular, the goals of this study were to (i) assess the horizontal and vertical scales on which predictive information is carried, (ii) compare the prediction of vector and scalar wind quantities, and (iii) compare the predictive skill of monthly averaged and daily averaged predictors. The following conclusions were obtained.
In general, monthly mean vector wind components are better predicted than monthly mean wind speed or submonthly time-scale vector wind standard deviations (using either daily or monthly time-scale predictors). The large-scale flow carries predictive information regarding monthly mean vector wind components on horizontal scales that are well resolved by GCMs and NWP models; the horizontal spatial scales for mean wind speeds are considerably smaller. There is no evidence of a systematic variation with predictor altitude throughout the troposphere of predictive skill for monthly averaged quantities.
The difference in predictability between monthly mean vector wind components and monthly mean wind speed can be understood in the context of an idealized model of the vector wind pdf. Modeling the zonal and meridional wind components as uncorrelated with a bivariate Gaussian distribution demonstrated that accurate prediction of mean wind speeds required accurate predictions of the standard deviations of the vector wind components. In this interpretation, the failure of monthly mean predictors to accurately predict monthly mean wind speeds can be attributed to their failure to predict these measures of submonthly vector wind variability. This analysis also predicts a state dependence for this sensitivity of mean wind speed on vector wind standard deviation: the particularly strong dependence is seen to be a consequence of the relatively small value of the ratio of the magnitude of the monthly-mean vector wind amplitude to the vector wind standard deviation. Locations for which the ratio is larger should display a correspondingly weaker sensitivity of mean(w) to std(u) and std(υ).
The r2 prediction skill of daily wind variability (both vector wind and wind speed) from daily large-scale predictors is generally larger than that of monthly averaged wind variability from monthly averaged predictors. Furthermore, when the daily predictions are averaged to monthly time scales, the prediction skill of mean(w) is generally higher than that obtained using monthly averaged predictors. To a more modest extent, this fact is also true for std(u) and std(υ).
For the region under consideration, monthly mean vector wind quantities are generally well predicted on scales in the flow that should be well resolved by GCMs or NWP models. In contrast, monthly mean wind speeds are not well predicted. While predictability of mean(w) is enhanced by averaging daily predictions, it is still smaller in general than the predictability of mean(u) or mean(υ). The subarctic northeast Pacific is apparently not a region in which a probabilistic downscaling methodology, such as that of Pryor et al. (2005) (in which the Weibull shape and scale parameters are downscaled), would successfully predict month-to-month variations in the wind speed pdf. The idealized probabilistic model considered here suggests that at other locations, where the amplitude of the mean vector wind is larger (relative to its variability) than in this region, the monthly scale wind speed statistics may be more successfully predicted. This predictability of mean(w) would also be enhanced in regions where std(u) and std(υ) are more predictable (or by finding better large-scale predictors of these quantities). We note that there is empirical evidence that the large-scale flow carries some predictive information for mean(w) in other locations [e.g., the Canadian prairies, St. George and Wolfe (2009)]; whether this is because the winds in such regions are in the large θ regime of Fig. 8 or because local std(u) and std(υ) are more predictable is an interesting direction of future study.
The idealized model of the wind speed pdf was based on the assumption that the vector wind fluctuations are uncorrelated bivariate Gaussian. In fact, sea surface vector winds display strong and systematic non-Gaussian behavior over much of the ocean (Monahan 2004, 2006) such that the higher order moments (skewness and kurtosis) can be predicted from the lower order moments. The near-Gaussian structure of vector wind fluctuations in the subarctic northeast Pacific is the exception rather than the rule. It would be interesting to determine how these deviations from Gaussianity influence the dependence of 
This study has focused on the downscaling of surface winds in the Northern Hemisphere wintertime. Further analyses (van der Kamp et al. 2012) suggest that the predictability of monthly mean surface winds (both vector and wind speed) at these buoys is generally comparable in autumn and lower in spring and summer. A more detailed analysis of the seasonality of predictability is another interesting direction of future study.
The quality control to which the buoy data considered in this study were subjected was by construction very simple. Homogenized data exist for these buoys (Faucher et al. 1999); these data are inappropriate for the present analysis, as large-scale reanalysis products were used in the homogenization process. The fact that the various buoys considered (with one single exception) display similar magnitudes and structures of predictability suggests that, while these observations may include some bad data, these are not significantly biasing the results. In fact, the one exception (buoy 46004) can be seen to prove the rule, as its singularly anomalous behavior is most likely the result of bad data.
We purposefully made use in this study of the simplest statistical model for downscaling local wind variations from those of the large-scale flow: multiple linear regression. It is, of course, possible that more sophisticated techniques could result in higher estimates of predictability. Furthermore, it is possible that other predictors (e.g., monthly standard deviations of large-scale variables, or variables representing moist and radiative processes in the boundary layer) could improve the predictions. Such predictors, of course, may not be well simulated by NWP models or GCMs, and their use in downscaling may be of little practical utility. With these caveats in mind, the results presented in this study should be interpreted as representing a lower bound on the predictability of historical surface winds in the subarctic northeast Pacific. How well this predictability of historical surface winds relates to the predictability of future surface winds using statistical downscaling of course depends on the stationarity of the statistical relationship between large-scale predictors and local winds.
As the demand increases for finescale weather forecasts and climate change predictions, so increases the need for estimates of how robustly these quantities can be predicted through downscaling approaches. This study has suggested reasons for some optimism (for mean vector winds) and some pessimism (for mean wind speeds) regarding our ability to predict monthly time-scale surface wind variability (at least in regions such as the subarctic northeast Pacific). The consideration of idealized probabilistic models of the vector wind pdf has suggested it may be possible to make some a priori determination of the predictability of mean wind speeds at a particular location, based on the statistics of the vector winds. A diagnosis of the utility of such an approach, involving a detailed consideration of different regions and different seasons, will be the subject of future studies.
Acknowledgments
This work was greatly assisted by helpful conversations with and comments from Kyla Bishop, Gerd Buerger, Aaron Culver, Charles Curry, Yanping He, Dave Rodenhuis, and Derek van der Kamp. This manuscript was also improved by helpful comments from two anonymous reviewers. The author gratefully acknowledges financial support from the Natural Sciences and Engineering Research Council of Canada.
REFERENCES
Abramowitz, M., and I. A. Stegun, Eds., 1972: Handbook of Mathematical Functions: With Formulas, Graphs, and Mathematical Tables. 9th ed. Dover Publications, 1046 pp.
Archer, C. L., and M. Z. Jacobson, 2005: Evaluation of global wind power. J. Geophys. Res., 110, D12110, doi:10.1029/2004JD005.
AXYS Environmental Consulting Ltd, 1996: Meteorological and oceanographic measurements from Canadian weather buoys: A review of sensors, data reduction, transmission, quality control and archival methods. AXYS Environmental Consulting Rep. SP-70, 57 pp. [Available at http://www.meds-sdmm.dfo-mpo.gc.ca/isdm-gdsi/waves-vagues/Odasbuoys/odasbuoys-eng.htm.]
Benestad, R. E., I. Hanssen-Bauer, and D. Chen, 2008: Empirical-Statistical Downscaling. World Scientific, 228 pp.
Bogardi, I., and I. Matyasovszky, 1996: Estimating daily wind speed under climate change. Sol. Energy, 57, 239–248.
Cakmur, R. V., R. L. Miller, and O. Torres, 2004: Incorporating the effect of small-scale circulations upon dust emission in an atmospheric general circulation model. J. Geophys. Res., 109, D07201, doi:10.1029/2003JD004067.
Cassou, C., M. Minvielle, L. Terray, and C. Périgaud, 2011: A statistical–dynamical scheme for reconstructing ocean forcing in the Atlantic. Part I: Weather regimes as predictors for ocean surface variables. Climate Dyn., 36, 19–39, doi:10.1007/s00382-010-0781-7.
Cheng, C. S., G. Li, Q. Li, and H. Auld, 2008: Statistical downscaling of hourly and daily climate scenarios for various meteorological variables in south-central Canada. Theor. Appl. Climatol., 91, 129–147, doi:10.1007/s00704-007-0302-8.
Curry, C. L., D. van der Kamp, and A. H. Monahan, 2012: Statistical downscaling of historical monthly mean winds over a coastal region of complex terrain. I: Predicting wind speed. Climate Dyn., doi:10.1007/s00382-011-1173-3, in press.
Davy, R. J., M. J. Woods, C. J. Russell, and P. A. Coppin, 2010: Statistical downscaling of wind variability from meteorological fields. Bound.-Layer Meteor., 135, 161–175.
De Rooy, W. C., and K. Kok, 2004: A combined physical–statistical approach for the downscaling of model wind speed. Wea. Forecasting, 19, 485–495.
Faucher, M., W. R. Burrows, and L. Pandolfo, 1999: Empirical-statistical reconstruction of surface marine winds along the western coast of Canada. Climate Res., 11, 173–190.
Garratt, J., 1992: The Atmospheric Boundary Layer. Cambridge University Press, 316 pp.
Gastineau, G., and B. J. Soden, 2009: Model projected changes of extreme wind events in response to global warming. Geophys. Res. Lett., 36, L10810, doi:10.1029/2009GL037500.
Goubanova, K., V. Echevin, B. Dewitte, F. Codron, K. Takahashi, P. Terray, and M. Vrac, 2011: Statistical downscaling of sea-surface wind over the Peru–Chile upwelling region: Diagnosing the impact of climate change from the IPSL-CM4 model. Climate Dyn., 36, 1365–1378, doi:10.1007/s00382-010-0824-0.
Gutiérrez, J., A. Cofiño, R. Cano, and M. Rodríguez, 2004: Clustering methods for statistical downscaling in short-range weather forecasts. Mon. Wea. Rev., 132, 2169–2183.
He, Y., A. H. Monahan, C. G. Jones, A. Dai, S. Biner, D. Caya, and K. Winger, 2010: Probability distributions of land surface wind speeds over North America. J. Geophys. Res., 115, D04103, doi:10.1029/2008JD010708.
Howard, T., and P. Clark, 2007: Correction and downscaling of NWP wind speed forecasts. Meteor. Appl., 14, 105–116.
Kaas, E., T.-S. Li, and T. Schmith, 1996: Statistical hindcast of wind climatology in the North Atlantic and northwestern European region. Climate Res., 7, 97–110.
Klink, K., 2007: Atmospheric circulation effects on wind speed variability at turbine height. J. Appl. Meteor. Climatol., 46, 445–456.
Landberg, L., and S. J. Watson, 1994: Short-term prediction of local wind conditions. Bound.-Layer Meteor., 70, 171–195.
Merryfield, W. J., B. Pal, and M. G. G. Foreman, 2009: Projected future changes in surface marine winds off the west coast of Canada. J. Geophys. Res., 114, C06008, doi:10.1029/2008JC005123.
Mesinger, F., and Coauthors, 2006: North American Regional Reanalysis. Bull. Amer. Meteor. Soc., 87, 343–360.
Michelangeli, P.-A., M. Vrac, and H. Loukos, 2009: Probabilistic downscaling approaches: Application to wind cumulative distribution functions. Geophys. Res. Lett., 36, L11708, doi: 10.1029/2009GL038401.
Minvielle, M., C. Cassou, R. Bourdallé-Badie, L. Terray, and J. Najac, 2011: A statistical–dynamical scheme for reconstructing ocean forcing in the Atlantic. Part II: Methodology, validation and application to high-resolution ocean models. Climate Dyn., 36, 401–417, doi: 10.1007/s00382-010-0761-y.
Monahan, A. H., 2004: A simple model for the skewness of global sea surface winds. J. Atmos. Sci., 61, 2037–2049.
Monahan, A. H., 2006: The probability distribution of sea surface wind speeds. Part I: Theory and SeaWinds observations. J. Climate, 19, 497–520.
Monahan, A. H., 2007: Empirical models of the probability distribution of sea surface wind speeds. J. Climate, 20, 5798–5814.
Monahan, A. H., and J. C. Fyfe, 2006: On the nature of zonal jet EOFs. J. Climate, 19, 6409–6424.
Monahan, A. H., and J. Culina, 2011: Stochastic averaging of idealized climate models. J. Climate, 24, 3068–3088.
Monahan, A. H., J. C. Fyfe, M. H. Ambaum, D. B. Stephenson, and G. R. North, 2009: Empirical orthogonal functions: The medium is the message. J. Climate, 22, 6501–6514.
Monahan, A. H., Y. He, N. McFarlane, and A. Dai, 2011: The probability distribution of land surface wind speeds. J. Climate, 24, 3892–3909.
Najac, J., J. Boé, and L. Terray, 2009: A multi-model ensemble approach for assessment of climate change impact on surface winds in France. Climate Dyn., 32, 615–634.
Pinard, J.-P., R. Benoit, and J. D. Wilson, 2009: Mesoscale wind climate modelling in steep mountains. Atmos.–Ocean, 47, 63–78.
Pryor, S., J. Schoof, and R. Barthelmie, 2005: Empirical downscaling of wind speed probability distributions. J. Geophys. Res., 110, D19109, doi:10.1029/2005JD005899.
Randall, D., and Coauthors, 2007: Climate models and their evaluation. Climate Change 2007: The Physical Science Basis, S. Solomon et al., Eds., Cambridge University Press, 589–662.
Sailor, D. J., T. Hu, X. Li, and J. N. Rosen, 2000: A neural network approach to local downscaling of GCM output for assessing wind power implications of climate change. Renewable Energy, 19, 359–378.
Sailor, D. J., M. Smith, and M. Hart, 2008: Climate change implications for wind power resources in the northwest United States. Renewable Energy, 33, 2393–2406.
Salameh, T., P. Drobinski, M. Vrac, and P. Naveau, 2009: Statistical downscaling of near-surface wind over complex terrain in southern France. Meteor. Atmos. Phys., 103, 253–265.
Sloughter, J. M., T. Gneiting, and A. E. Raftery, 2010: Probabilistic wind speed forecasting using ensembles and Bayesian model averaging. J. Amer. Stat. Assoc., 105, 25–35. doi:10.1198/jasa.2009.ap08615.
St. George, S., and S. A. Wolfe, 2009: El Niño stills winter winds across the southern Canadian prairies. Geophys. Res. Lett., 36, L23806, doi:10.1029/2009GL041282.
Tang, B., W. W. Hsieh, A. H. Monahan, and F. T. Tangang, 2000: Skill comparisons between neural networks and canonical correlation analysis in predicting the equatorial Pacific sea surface temperatures. J. Climate, 13, 287–293.
Thorarinsdottir, T. L., and T. Gneiting, 2010: Probabilistic forecasts of wind speed: Ensemble model output statistics using heteroscedastic censored regression. J. Roy. Stat. Soc., 173A, 371–388.
Troen, I., and E. L. Petersen, 1989: European Wind Atlas. Risø National Laboratory, 656 pp.
van der Kamp, D., C. Curry, and A. H. Monahan, 2012: Statistical downscaling of historical monthly mean winds over a coastal region of complex terrain. II: Predicting wind components. Climate Dyn., doi:10.1007/s00382-011-1175-1, in press.
von Storch, H., and F. W. Zwiers, 1999: Statistical Analysis in Climate Research. Cambridge University Press, 484 pp.