1. Introduction
Analog-based methods using information of past observations, reanalysis, and numerical weather prediction (NWP) have been explored for various forecast fields. These methods have been applied to general circulation models (Radinović 1975; van den Dool 1989, 1994, 2007; Gao et al. 2006; Ren and Chou 2007), forecasting of summer monsoon subseasonal variability (Xavier and Goswami 2007), Southern Oscillation index (Drosdowsky 1994), mesoscale forecasts (Carter and Keislar 2000), temperature (Bergen and Harnack 1982; Livezey and Barnston 1988; Toth 1989), wind speed (Klausner et al. 2009), and precipitation prediction (Hamill and Whitaker 2006; Panziera et al. 2011; Toth 1989). Recently, Delle Monache et al. (2011) proposed a method to capture similarity between current and past forecasts for analog–space Kalman filter (ANKF) and weighted analogs (AN). Their analog-based technique is used for deterministic and probabilistic predictions of a range of parameters, including 1) atmospheric variables (e.g., wind speed, temperature, and relative humidity; Delle Monache et al. 2011, 2013; Mahoney et al. 2012; Nagarajan et al. 2015; Eckel and Delle Monache 2016); 2) improvement for surface particulate matter (PM2.5) forecasts (Djalalova et al. 2015; Delle Monache 2017); 3) wind power forecasts (Alessandrini et al. 2015a; Junk et al. 2015a; Davò et al. 2016); 4) solar power prediction (Alessandrini et al. 2015b; Davò et al. 2016); 5) assessment of the economic impact of deterministic and probabilistic wind power forecast (Alessandrini et al. 2014); 6) reconstruction of historical wind speed data for wind resource estimates (Vanvyve et al. 2015; Zhang et al. 2015) and precipitation (Keller et al. 2017); 7) calibration of ensemble forecasts using ensemble model output statistics (EMOS; Junk et al. 2015b); 8) gridded probabilistic forecasts (Sperati et al. 2017); and 9) prediction of tropical cyclone intensity (Alessandrini et al. 2018).
The analog ensemble algorithm (AnEn; Delle Monache et al. 2013) searches for the best-matching past forecasts (analogs) to the current forecast at specific locations and forecast lead times. Single or multiple physical predictors from deterministic model predictions are used in the analog metric to find the best-matching analogs. The AnEn performance can be improved by selecting appropriate predictor combinations. For example, Delle Monache et al. (2013) found that a set of wind speed and direction, 2-m temperature, and surface pressure is reasonable for wind speed prediction, but better results in terms of error and correlation can be obtained if pressure is not included in the selected predictors. Junk et al. (2015a) explored predictor-weighting techniques to assign unequal weights to the predictors, resulting in improved results, as also shown by Alessandrini et al. (2015b). Although the weight term of the analog metric has been included in the initial study (Delle Monache et al. 2011), most of the studies (Delle Monache et al. 2011, 2013; Mahoney et al. 2012; Alessandrini et al. 2014; Nagarajan et al. 2015; Djalalova et al. 2015; Alessandrini et al. 2015a; Vanvyve et al. 2015; Zhang et al. 2015; Eckel and Delle Monache 2016) have not attempted to find optimal weights for the predictors (i.e., all weights are set to 1). Also, in previous studies, only a single deterministic forecast or a mean of ensemble predictions has been used to generate analogs. Table 1 outlines some of the AnEn applications that researchers have implemented so far and the one used in this work.
Previous studies on AnEn (2011–17). Acronyms are as follows: Global Environmental Multiscale model (GEM); Community Multiscale Air Quality model (CMAQ); Kalman filter in analog space (KFAS, or ANKF); Kalman-filtered AnEn mean (KFAN); European Centre for Medium-Range Weather Forecasts (ECMWF) Ensemble Prediction System (EPS); ECMWF high-resolution (HRES); North American Mesoscale Forecast System (NAM); Rapid Update Cycle (RUC); mean, maximum, and minimum values and standard deviation (MMMS); hybrid ensemble (HyEn); Consortium for Small-Scale Modeling (COSMO) reanalysis at 6-km horizontal grid spacing (COSMO REA6); and Hurricane WRF (HWRF).
In this study, two NWP models and observations are combined to postprocess predicted wind speed during storms, such as those that had significant impacts on infrastructure and the environment. For the first time, AnEn uses multiple predictors from two atmospheric modeling systems [the Weather Research and Forecasting (WRF) Model and the Regional Atmospheric Modeling System–Integrated Community Limited Area Modeling System (RAMS–ICLAMS)] with a predictor-weighting technique (Junk et al. 2015a; Alessandrini et al. 2015b). The approach in this work aims to improve the prediction of wind speed associated with a storm. The latter is the main driving force behind tree damages in the northeast United States, and it results in interruptions in the electric power grid that can last from hours to days, depending on storm severity. The correlation between storm severity and power outages has been investigated in recent studies and has motivated new ways to improve weather prediction accuracy (Yang et al. 2017; Wanik et al. 2015, 2017; He et al. 2017). Additionally, the performance of AnEn for high-impact tropical storms such as Irene (2011) and Sandy (2012) is investigated through the application of a bias-corrected analog ensemble (BCAnEn) to further improve the prediction. The paper is structured as follows. Section 2 describes the model configuration and observations; section 3 provides details about the methodology for AnEn and BCAnEn; section 4 contains a discussion on the results; and major findings are summarized in section 5.
2. Atmospheric modeling systems and observations
The storm set is composed of 146 storms over the years 2005–16 and includes thunderstorms, extratropical storms, and two major tropical storms (Irene and Sandy). The storms are selected based on the impacts caused to the environment and electric power network in the northeast United States [from 20 to >15 000 power outages defined as locations that require manual intervention to restore power (Wanik et al. 2015); data provided from Eversource Energy]. In the storm database, 18 occurred during spring, 43 during summer, 30 in the fall, and 55 during winter. Hourly wind speed NWP forecasts for the selected storms are simulated using two mesoscale meteorological modeling systems: the WRF Model (WRF-ARW version 3.4.1; referred to as WRF; Skamarock et al. 2008) and the RAMS–ICLAMS (referred to as ICLAMS; Cotton et al. 2003; Solomos et al. 2011). For each storm, WRF and ICLAMS are initialized 12–24 h before the peak of the storm defined by the strongest wind speed (for thunderstorms, we use 12 h). The selection of the simulation start time also reflects the timing of the first power outage report running in the Eversource network (Wanik et al. 2015). The duration of the simulation encapsulates the event by placing the peak of the storm approximately in the middle of the timeline.
Both models are configured with three nests with horizontal grid spacing of 18 (outer domain), 6 (inner-intermediate domain), and 2 km (inner domain). The innermost domain is the focus area in this study (Figs. 1a,b). The National Centers for Environmental Prediction (NCEP) Global Forecast System (1° × 1°, 6-hourly intervals) analyses (NCEP/NWS/NOAA/DOC 2007) and the GFS Final Analysis (1° × 1°, 6-hourly intervals) data (NCEP/NWS/NOAA/DOC 2000) are used to initialize WRF and ICLAMS, respectively. For each storm, the two models produce hourly outputs for a maximum lead time of 61 h.
Model domains (the inner rectangle box indicates the fine model domain) from (a) WRF and (b) RAMS–ICLAMS; (c) NCEP/NWS/NOAA stations over the northeast United States (circles) and elevation (shaded area).
Citation: Monthly Weather Review 146, 12; 10.1175/MWR-D-17-0198.1
WRF utilizes the Thompson scheme for cloud microphysics (Thompson et al. 2008); Grell 3D scheme for convective parameterization (Grell and Dévényi 2002); Goddard for shortwave radiation (Chou and Suarez 1994); Rapid Radiative Transfer Model (RRTM) for longwave radiation (Mlawer et al. 1997); Noah for land surface scheme (Tewari et al. 2004); and the Yonsei scheme for the planetary boundary layer (PBL; Hong et al. 2006). ICLAMS uses a two-moment bulk microphysics scheme (Walko et al. 1995; Meyers et al. 1997) with an explicit cloud droplet activation (Nenes and Seinfeld 2003; Fountoukis and Nenes 2005); Kain–Fritsch cumulus parameterization for convective parameterization; RRTM for shortwave/longwave radiation (Mlawer et al. 1997); Land Ecosystem–Atmosphere Feedback version 3 (LEAF-3; Walko et al. 2000) as surface–atmosphere interaction scheme; and Mellor–Yamada scheme for PBL (Mellor and Yamada 1982). Detailed information regarding the WRF and ICLAMS configuration is summarized in Table 2. All WRF and ICLAMS predicted storms are based on retrospective simulations.
WRF and ICLAMS configuration.
Observations comprise hourly 10-m AGL wind speed from 80 meteorological terminal aviation routine weather report (METAR) stations in the northeast United States (Fig. 1c). Model outputs are interpolated to the METAR station locations with bilinear interpolation using four neighboring grid points. In addition, METAR observations for wind direction and temperature are used to evaluate model performance.
3. Methodology
a. Analog ensemble
The AnEn is formed with observations that correspond to past forecasts, which better match the current forecast and are referred to as analog forecasts. The following are the main steps of the algorithm: 1) at each station location and lead time, the best analog forecasts are selected based on the analog metric defined below, which quantifies the degree of analogy between the current forecast, for which AnEn is being generated, and forecasts available in the training dataset (the training dataset comprises available storms in the database and the selection of analogs depends on the lead time); and 2) observations corresponding to the best analog forecasts form the members of AnEn (Fig. 2).
A schematic diagram of the three phases to implement the AnEn technique.
Citation: Monthly Weather Review 146, 12; 10.1175/MWR-D-17-0198.1
Three model variables are used as parameters to select the best single-model analog sets from past forecasts: wind speed (WSPD), wind direction (WDIR), and temperature (TEMP). All parameters combined (i.e., three from WRF and three from ICLAMS) are used to select the combined-model analog set. An analog predictor-weight optimization is implemented for each station given the weight constraint 
AnEn and BCAnEn predictor weights for 80 stations (bar: median, box: interquartile range, whiskers: range, and error bars: minimum and maximum).
Citation: Monthly Weather Review 146, 12; 10.1175/MWR-D-17-0198.1
b. Bias-corrected analog ensemble
A bias-correction scheme is applied to improve the AnEn performance for wind speed (S. Alessandrini et al. 2017, meeting presentation). The AnEn introduces a conditional negative bias when predicting high wind events of the forecast probability density function (PDF). This underestimation increases as the predicted event is rarer. This error is found to be dependent on the difference between the mean of the past analog forecasts and the current forecast. The approach used in this work is the simplest among those proposed by S. Alessandrini et al. (2017, meeting presentation). An adjustment factor is added to each AnEn member, which are past observations corresponding to past analog forecasts. This method is applied under the assumption that a linear relationship between predicted and observed wind speed holds when predictions are in the right tail of the PDF. This has been verified by fitting a linear regression with predicted wind speed as the response variable and the observed wind speed as the explanatory variable.
The optimal weights change after the application of bias correction (Fig. 3). Specifically, the weights of WDIR increase for all AnEn implementations: the median values are 0.4 for BCAnEnWRF, 0.5 for BCAnEnICLAMS, and 0.3 for both WRF and ICLAMS. We speculate that the latter can be explained by the fact that high wind conditions, which are better predicted with the bias correction, are associated with specific wind directions.
c. Sensitivity of the analog ensemble size and length of the training set
The AnEn forecast is constructed by observations that match the past forecast analogs. AnEn forecasts are created for each individual model. That from WRF predictors is referred to as AnEnWRF; that from ICLAMS predictors is referred to as AnEnICLAMS; and that for both models combined is referred to as AnEnDUAL (Table 3 presents the variables included in each AnEn model). The AnEn is verified using leave-one-out cross validation (LOOCV), where a single storm is held out and the remaining storms compose the training set. The training dataset used in this study is restricted to past storms based on the need to improve wind speed prediction when a storm is imminent and does not include daily weather forecasts. We cannot speculate on the analog forecast performance when applied to daily weather forecasts, but in that case, the training dataset would have to include a wider range of meteorological conditions and not, like in this case, only past storms selected for their intensity.
Predictor combinations for AnEn and BCAnEn.
A sensitivity analysis is conducted to define the AnEn size (phase 1 in Fig. 2). Multiple AnEn forecasts are created with 1, 3, 5, 7, 10, 15, 20, 25, and 30 members using Eq. (1) and weights 
To identify an optimal number of training storms, AnEnDUAL and BCAnEnDUAL are implemented using an increasing number of randomly selected storms (20, 40, 60, 80, 120, 140, and 145). The comparison of RMSE for the raw models (WRF and ICLAMS), AnEnDUAL, and BCAnEnDUAL computed with all available pairs of observations and predictions for each season shows that AnEnDUAL starts to outperform ICLAMS in RMSE reduction when 60–80 storms are included in the training dataset (Figs. S1–S3 in the online supplemental material). BCAnEnDUAL exhibits significant RMSE reduction with only 20 training storms when compared to ICLAMS. Although all AnEn models produce the best results in terms of the global RMSE (Fig. S1) when using 145 storms for all seasons, the trend reaches a plateau after using 140 training storms to an almost constant value. Thus, the number of training storms to improve wind speed prediction should be at least 140 for all models to be comparable. We opted to use the maximum available training storms to get the best error reduction possible.
d. Data processing and evaluation
The first 6 h of the simulations are treated as the model spinup time and are discarded from the analysis. Zero and missing values for hourly wind speed observations are not included as modeled–observed pairs to generate AnEn (zero observed wind speed is predominantly wind speed below the instrument’s threshold; by discarding those values, we avoid including a nonrealistic model bias in the analysis). Since we focus on an improvement of raw deterministic forecasts from WRF and ICLAMS, only deterministic verification scores are used in this study. WRF and ICLAMS serve as baselines to compare with the ensemble mean of AnEn and BCAnEn models in a deterministic framework; thus, any probabilistic scores are not considered. Statistical metrics are calculated globally (use of all available model–observation pairs), temporally (at each lead time), and spatially (for each station separately). Global error metrics are also estimated for wind direction and temperature [see Table S1; wind direction is treated using circular statistics as described by Jammalamadaka and Sengupta (2001)]. The common statistical metrics used are RMSE, mean bias (BIAS), and coefficient of determination R2. Note that the ensemble mean is used from AnEn and BCAnEn throughout the manuscript.
4. Results and discussion
a. Seasonal analysis of global and event-based error
WRF and ICLAMS winds exhibit large scatter that is caused by over-/underestimation of wind speed (density scatterplots binned by 2 m s−1 shown in Figs. 4a,b). AnEn partially improves the raw model forecasts, in that it corrects the WRF and ICLAMS overestimations of wind speeds higher than 20 m s−1 and increases the density of correctly predicted wind speeds across the 1:1 regression line. However, the AnEn results show that it penalizes accurate forecasts of high wind speeds, as underestimation of winds larger than 20 m s−1 situated along the diagonal is introduced (Figs. 4c–e). BCAnEn alleviates this underestimation problem of high wind speed with respect to AnEn (Figs. 4f–h; BCAnEnWRF, BCAnEnICLAMS, BCAnEnDUAL).
Density scatterplots of observed and modeled 10-m wind speed binned by 2 m s−1 intervals for (a) WRF, (b) ICLAMS, (c)–(e) AnEn, and (f)–(h) BCAnEn models (146 storms).
Citation: Monthly Weather Review 146, 12; 10.1175/MWR-D-17-0198.1
Errors in the prediction in terms of RMSE and BIAS are estimated across seasons and wind categories to further assess the improvements gained by AnEn and BCAnEn (Figs. 5, 6). The four wind categories include light breeze (group 1), moderate breeze (group 2), strong breeze (group 3), and gale/storm (group 4), following the World Meteorological Organization (WMO) classification (Table 4). RMSE values of models in groups 1 and 2 are lower than those in groups 3 and 4 in all seasons because the error metrics are proportional to the wind speed magnitude. This is also the main reason that for lower wind speed, AnEn and BCAnEn do not show noticeable RMSE reduction relative to the raw models since the error is already small (e.g., group 1 in Fig. 5). For all seasons and groups, the best AnEn performance is obtained when applied to both models, as in AnEnDUAL and BCAnEnDUAL, with the exception of group 1 (light breeze; 0.0 < observed wind speed ≤ 3.1 m s−1), where all models behave similarly with small errors and biases. AnEn reduces the RMSE for group 2 (moderate breeze: 3.1 < observed ≤ 8.2 m s−1) and group 3 (strong breeze: 8.2 < observed < 13.9 m s−1) with the biases almost zero for all models. The results clearly demonstrate that BCAnEn outperforms AnEn with improvements of RMSE and BIAS values for strong breeze/gale/storm (groups 3 and 4: 8.2 m s−1 < observed wind speed). Among the three BCAnEn implementations, the most skillful is BCAnEnDUAL, with reduced RMSEs for all seasons when compared to raw models (group 3: 20%–38% of WRF, 22%–25% of ICLAMS; group 4: 13%–27% of WRF, 15%–22% of ICLAMS).
Seasonal RMSE calculated by observed 10-m wind speeds classified in four groups as described in Table 4. The number of model–observation pairs is indicated for each group.
Citation: Monthly Weather Review 146, 12; 10.1175/MWR-D-17-0198.1
As in Fig. 5, but for seasonal BIAS.
Citation: Monthly Weather Review 146, 12; 10.1175/MWR-D-17-0198.1
Wind speed classification. (Source: NOAA, Beaufort wind scale; http://www.spc.noaa.gov/faq/tornado/beaufort.html.)
Since high wind speed storms are the main focus of this study, the models’ performance is also assessed for wind speed during the observed storm peak at each station (i.e., the maximum value of wind speed for each storm and location; Figs. 7, 8). BCAnEnDUAL is consistently performing best across all seasons, with summer being the only exception, where performance is similar to AnEnWRF and BCAnEnWRF. In the summer, the models exhibit lower forecast errors in terms of storm peaks when compared to errors in the other seasons because summer wind speeds are lower. About 98% of low wind speeds in groups 1 and 2 (Table 4) are observed during summer.
Seasonal RMSE calculated with 10-m wind speeds during the observed storm peaks (maximum wind speed).
Citation: Monthly Weather Review 146, 12; 10.1175/MWR-D-17-0198.1
As in Fig. 7, but for seasonal BIAS.
Citation: Monthly Weather Review 146, 12; 10.1175/MWR-D-17-0198.1
The AnEn skill depends on the raw model’s ability to estimate the observations (Nagarajan et al. 2015). In this regard, AnEn and BCAnEn take advantage of the WRF and ICLAMS independent estimates in searching for analogs. Furthermore, from the previous discussion, it is evident that BCAnEn using dual predictors is the best-performing method for the prediction of high wind speeds associated with extreme storms (Figs. 5–8). Thus, in the analysis that follows, the forecast skill is compared among WRF, ICLAMS, and BCAnEnDUAL.
Errors calculated individually for each storm and season reveal the main differences between raw model outputs and the BCAnEn method (Fig. 9). WRF exhibits higher RMSE values than ICLAMS for most of the storms, with the exception of summer. Regardless of the different performances of the two raw models, BCAnEnDUAL reduces their RMSE and BIAS over all seasons. BCAnEnDUAL achieves RMSE improvements for all storms in the range of 9%–42% and 1%–29% when compared to WRF and ICLAMS, respectively. In addition, BCAnEnDUAL reduces the RMSE values for Irene to 1.73 m s−1 (28 August 2011; 24% and 20% reduction for WRF and ICLAMS, respectively) and Sandy to 1.93 m s−1 (29 October 2012; 27% and 24% reduction for WRF and ICLAMS, respectively). On the contrary, AnEnDUAL does not reduce the error for the two tropical storms (not shown in Fig. 9).
RMSE and BIAS of WRF, ICLAMS, and BCAnEnDUAL for storms in each season. The modeled box-and-whisker plots include 18 (spring), 43 (summer), 30 (fall), and 55 (winter) storms. RMSE and BIAS calculated with all data available for individual storms.
Citation: Monthly Weather Review 146, 12; 10.1175/MWR-D-17-0198.1
WRF has a negative bias for 88% of the storms, ranging from −1.55 to −0.01 m s−1, with biased predictions being especially predominant in winter (Fig. 9). ICLAMS performs better than WRF in terms of bias (−0.52 m s−1 for WRF and −0.19 m s−1 for ICLAMS), but a noticeable positive BIAS for ICLAMS greater than 0.9 m s−1 is evident for several storms (e.g., 25 October 2005 and 1 and 17 December 2015; not shown in Fig. 9). BIAS is almost entirely removed for most of the storms with BCAnEnDUAL, having an average BIAS value of 0.03 m s−1. BCAnEnDUAL also brings the median BIAS among all seasons closer to zero, compared to the raw models (spring: −0.06; summer: −0.01; fall: 0.16; and winter: 0.01 m s−1; Fig. 9). The results for the event-based analysis discussed in this section indicate that BCAnEnDUAL is indeed able to significantly reduce the error of raw forecast for individual storms. The behavior of BCAnEnDUAL in terms of errors for the two extreme cases of Tropical Storms Irene and Sandy is analyzed in detail in section 4c.
b. Seasonal analysis of temporal and spatial error
In this section, the temporal and spatial variation of the errors are discussed at each forecast lead time and station and analyzed separately for each season. Figure 10 shows the temporal variation of RMSE, BIAS, and R2 for WRF (blue), ICLAMS (red), BCAnEnDUAL (purple), and HyEnBC (orange) (each error metric is calculated using all available model–observation pairs for the specified lead time). Temporal RMSE values feature similar patterns among the three predictions with peaks between the 20th and 30th lead times. This is because RMSE peaks correspond to maximum wind speed, where the magnitude of the variable and, thus, its error, is higher. The start and end times of the simulation are selected as such that they encapsulate the entire storm duration, having the peak of the storm approximately in the middle of the forecast timeline. Compared to WRF and ICLAMS, BCAnEnDUAL and HyEnBC show error reductions across all forecast lead times in the range of 9%–30% (spring), 8%–25% (summer), 6%–32% (fall), and 14%–36% (winter). Additionally, seasonal RMSE peaks are consistently reduced by both AnEn applications, with percentage improvements in the range of 13%–32%, compared to raw models across the four seasons. Nonoverlapping bootstrapped intervals (95%) provide confidence that results are significantly different for all RMSE values for BCAnEnDUAL and HyEnBC (not shown).
Temporal variation of R2, RMSE, and BIAS for WRF (blue), ICLAMS (red), BCAnEnDUAL (purple), and HyEnBC (orange) for each season. The HyEnBC is constructed by the best five analog ensemble members selected separately from BCAnEnWRF and BCAnEnICLAMS. Statistical metrics use all available observed–modeled pairs at a given lead time.
Citation: Monthly Weather Review 146, 12; 10.1175/MWR-D-17-0198.1
BCAnEnDUAL provides a nearly constant-in-time BIAS around zero, whereas WRF and ICLAMS BIAS values fluctuate over forecast lead times. WRF has negative BIAS for most forecast lead times in all seasons. During winter, WRF wind speeds show a stronger negative BIAS, compared to the other seasons, but nevertheless BCAnEnDUAL removes the BIAS of the raw forecasts. The correlation of determination R2 also indicates the improvements succeeded with BCAnEnDUAL, compared to individual raw models WRF and ICLAMS (Fig. 10). It is noteworthy that BCAnEnDUAL and HyEnBC exhibit similar skill in terms of R2, RMSE, and BIAS for all seasons.
AnEn forecast variability is compared to observed and raw model variability using the standard deviation of observed and predicted wind speed at a given forecast lead time (shown in Fig. S5). AnEnDUAL forecast variability is lower than the observed variability across forecast lead times, but BCAnEnDUAL gets closer to the observations and similar to ICLAMS. To see how that translates in time series of wind speed, we randomly selected four stations and plotted observed and modeled wind speeds for Hurricane Sandy (Fig. S6). This gives an indication of the temporal variability during a storm and how it is depicted by all models. It is clear that AnEnDUAL underestimates wind speed maxima during these extreme events, but BCAnEnDUAL brings them closer to the observed ones. Last, maximum values of observed and predicted wind speeds for each station and lead time are shown in Fig. S7. Consistent with the results shown in the manuscript (Figs. 7, 8), all models show underestimations of maximum wind speed when compared to the observations. However, AnEnDUAL and BCAnEnDUAL exhibit similar variability with the raw models and closer to the observed variability.
The spatial distribution of RMSE and BIAS analyzed for 80 stations in the northeast United States for the four seasons is shown by geographical maps of the area of interest (Figs. 11, 12). Each colored circle represents the value of the statistical metric calculated with observations for each station and season using all available data pairs. Consistent with the results reported earlier, BCAnEnDUAL is effective at reducing the RMSE, compared to raw models (third row in Fig. 11). BCAnEnDUAL achieves average RMSE reduction (i.e., spatially averaged RMSE) in the range of 18%–30% and 15%–18% for WRF and ICLAMS, respectively, across the four seasons. In the summer period, the models exhibit lower RMSE values, explained by the fact that over that period, the metric is computed with a greater percentage of low wind speeds than the other seasons, and this is also shown in the event-based and temporal RMSE analyses (Figs. 7–10).
Spatial distribution of seasonal RMSE for WRF, ICLAMS, and BCAnEnDUAL. The topography is denoted with the gray-shaded area. Statistical metrics use all available data for each station.
Citation: Monthly Weather Review 146, 12; 10.1175/MWR-D-17-0198.1
As in Fig. 11, but for spatial distribution of seasonal BIAS.
Citation: Monthly Weather Review 146, 12; 10.1175/MWR-D-17-0198.1
BCAnEnDUAL removes the BIAS of raw models for most of the stations, indicated by the whiter colors in Fig. 12. WRF consistently exhibits negative bias values, similar to temporal BIAS results for 47 (spring), 34 (summer), 38 (fall), and 53 (winter) stations (BIAS < −0.5 m s−1). For BCAnEnDUAL, 21%–79% stations have a BIAS in the range of −0.1 to 0.1 m s−1 over the four seasons (WRF: 1%–10% stations; ICLAMS: 5%–11% stations). Overall, BCAnEnDUAL is shown to be an effective method to reduce RMSE and BIAS spatially and temporally.
c. Analysis of model performances for Tropical Storms Irene and Sandy
The bias-correction scheme applied to AnEn is successful in significantly reducing the error of the raw models, according to the analysis presented in the previous sections. Here, we analyze the AnEn performance for two tropical storms (Irene and Sandy) to investigate how much improvement can be obtained with AnEnDUAL, BCAnEnDUAL, and HyEnBC. Tropical Storms Irene and Sandy have resulted in significant impacts for the northeast United States (power network interruptions, critical infrastructure damages, and coastal area flooding), which is the main reason for focusing on improving wind speed prediction for these storms using AnEn.
BCAnEnDUAL is an effective method for reducing the peak RMSE values, compared to AnEnDUAL (38% and 39% RMSE reduction for Irene and Sandy, respectively). The peak RMSE generally coincides with the storm peak (9–13-h forecast lead time for Irene and 20–28 h for Sandy), and the error reduction is statistically significant for 7-, 11-, and 13-h forecast lead times for Irene, and 18 and 20 h for Sandy (shown in Figs. 13a,b). The RMSE peaks produced by the 10 members of AnEnDUAL are in the range of 3.7–5.0 and 5.3–6.8 m s−1 for Irene and Sandy, which are higher than the BCAnEnDUAL members (Irene: 2.7–3.6 m s−1; Sandy: 3.9–4.7 m s−1; not shown in Figs. 13a,b). The AnEnDUAL members are biased (shown in Fig. S4), which elucidates why the ensemble mean is not improving the prediction for Irene and Sandy. This suggests that the bias-correction method is necessary to address AnEnDUAL’s notable underestimation of rarely observed wind speed, as indicated by the temporal BIAS of the ensemble mean for the two tropical storms (Figs. 13c,d).
Temporal variation of (a),(b) RMSE and (c),(d) BIAS for WRF (blue), ICLAMS (red), AnEn (orange), BCAnEnDUAL (purple), HyEn (green), and HyEnBC (black) for Irene and Sandy. Statistical metrics use all available observed–modeled pairs at a given lead time.
Citation: Monthly Weather Review 146, 12; 10.1175/MWR-D-17-0198.1
The biggest impact of BCAnEnDUAL is the significant RMSE reduction at the storm peak. The overall BIAS for Irene is not significantly different from the two raw models (Fig. 13c), while for Sandy, it is significantly different for the first 10 h (Fig. 13d). BCAnEnDUAL performs better than AnEnDUAL not only for the temporal, but also for the spatial errors. Out of the 80 available stations, AnEnDUAL decreases the RMSE for 33 and 38 stations for Irene and 31 and 36 stations for Sandy, compared to WRF and ICLAMS, whereas BCAnEnDUAL achieves improvements at double the number of stations (Irene: 64 for WRF and 69 for ICLAMS; Sandy: 69 for WRF and 65 for ICLAMS; Fig. 14).
Spatial distribution of RMSE and BIAS of WRF, ICLAMS, AnEnDUAL and BCAnEnDUAL, HyEn, and HyEnBC for Irene and Sandy. Topography is denoted with the gray-shaded area. Statistical metrics use all available data for each station.
Citation: Monthly Weather Review 146, 12; 10.1175/MWR-D-17-0198.1
BCAnEnDUAL shows positive BIAS values across some stations but also achieves greater bias reduction when compared to WRF, ICLAMS, and AnEnDUAL for Irene and Sandy. BCAnEnDUAL has 49 (Irene) and 47 (Sandy) stations in the BIAS range of −0.5 to 0.5 m s−1, compared to 32 (Irene) and 19 (Sandy) for WRF, 25 (Irene) and 14 (Sandy) for ICLAMS, and 36 (Irene) and 26 (Sandy) for AnEnDUAL. This demonstrates that BCAnEnDUAL effectively improved the bias for most stations when compared to the other models.
Given the BCAnEnDUAL’s computational cost for weight optimization using six predictors, there is interest in looking at the performance of HyEn, selecting five analogs from each NWP member, and constructing the 10 ensemble members to assess how different HyEn and BCAnEnDUAL are for the two tropical storms. For Irene and Sandy, two HyEn models constructed by the best five analog ensemble members for each model (from AnEnWRF and AnEnICLAMS is referred to as HyEn; from BCAnEnWRF and BCAnEnICLAMS is referred to as HyEnBC) are evaluated against AnEnDUAL and BCAnEnDUAL.
Although HyEnBC employs the analog ensemble members from two different BCAnEn models, HyEn (green) and AnEnDUAL (orange), and HyEnBC (black) and BCAnEnDUAL (purple) models are almost identical in terms of their performance for RMSE and BIAS across all forecast hours (Fig. 13). The improvements of RMSE and BIAS are not achieved by HyEn in predicting Irene and Sandy because the members of AnEnWRF and AnEnICLAMS are biased (see Fig. S4). However, HyEnBC and BCAnEnDUAL improve wind speed prediction of Irene and Sandy with similar RMSE and BIAS over forecast lead times (Fig. 13). For the spatial distribution of the error metrics analyzed for 80 stations, both AnEnDUAL and HyEn models and both BCAnEnDUAL and HyEnBC models show similar spatial patterns with regard to RMSE and BIAS for each station (Fig. 14). The decrease in RMSE and BIAS for HyEnBC model is significant and useful to improve the performance of WRF and ICLAMS. This indicates that a hybrid AnEn method is effective at producing improved prediction of wind speed for two tropical storms when employing the members from two BCAnEn models.
5. Summary
This study presents a new implementation of the analog ensemble (AnEn) and a bias-corrected analog ensemble (BCAnEn) for improving wind speed prediction of extreme storms that have impacted the northeast United States during a 12-yr period (2005–16). The novelty of the presented approach is the use of two NWP models (WRF and ICLAMS) simultaneously to provide multiple predictors to the AnEn, as well as the implementation to extreme storms where high wind speeds have significant impacts on the infrastructure and the environment. Optimal analogs for AnEn and BCAnEn are searched using multiple predictors from WRF, ICLAMS, and a combination of both models (DUAL), given optimized weights that are found by minimizing the root-mean-square error (RMSE).
A leave-one-out cross validation (LOOCV) is implemented to build the training dataset and to apply and evaluate AnEn and BCAnEn for each storm. Both AnEn and BCAnEn are most efficient for wind speed prediction improvements when using dual predictors from the two NWP models (six atmospheric variables/predictors; AnEnDUAL and BCAnEnDUAL). The seasonal statistical metrics for four wind speed classification groups indicate that the inclusion of all six, rather than three, predictors from WRF or ICLAMS is beneficial for error reduction. For strong wind associated with rare events, AnEn does not reduce the largest errors, which instead is accomplished with BCAnEn. For the gale/storm group, BCAnEn reduces the seasonal RMSE of WRF and ICLAMS by 13%–27% and 15%–22%, respectively. BCAnEn reduces the RMSE also for individual storms by an amount ranging between 9% and 42% for WRF and 1% and 29% for ICLAMS.
Results from the spatial and temporal error analysis indicate that BCAnEn consistently produces significantly lower RMSE than WRF and ICLAMS at all forecast lead times. Similar results are achieved by BCAnEn also for individual stations, indicated by the spatially averaged RMSE reduction of raw models in the range of 18%–30% (WRF) and 15%–18% (ICLAMS) across all seasons.
Performances of AnEn and BCAnEn (using six predictors) for Irene and Sandy differ substantially. The temporal and spatial analysis of RMSE and BIAS for BCAnEn shows that the bias-correction scheme applied to AnEn offers benefits for the two tropical storms, which are characterized by winds significantly higher than the other storms included in this study. Consequently, the improvements obtained by BCAnEn for Irene and Sandy are shown with average RMSE reductions of around 22% for Irene and 26% for Sandy with respect to the raw models, and the most significant benefit is that the error is reduced for the peak wind speed associated with each storm. The hybrid AnEn approach (HyEnBC) is also proven to have similar skill with BCAnEn, with the advantage of a lower computational burden since the optimization is done on fewer predictors and separately for each NWP.
Overall, AnEn is proven a successful technique to improve wind speed predictions for extreme storms in the northeast United States. The results in this study highlight that using dual-model predictors and a bias-correction scheme results in high-quality AnEn-based deterministic forecasts. A future implementation of this technique involves error correction of wind speed during real-time forecast of storms, given the advantage of using past storm forecasts and matching observations to build the analogs in the domain of interest.
Acknowledgments
The work was supported by Eversource Energy through a research grant awarded by the Eversource Energy Center at the University of Connecticut and by the Graduate Visitor program of the Advanced Study Program of National Center for Atmospheric Research.
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