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  • View in gallery

    Locations of NDBC buoys used in the model validation.

  • View in gallery

    (bottom to top) Monthly time series of the measured (black) and predicted (NAH, red; WNA, green) spectral peak periods, significant wave heights, wind speeds, and wind directions at buoy 41002, September 2005.

  • View in gallery

    Best tracks and GFDL model tracks for Hurricanes Maria, Nate, and Ophelia.

  • View in gallery

    (top) Wave steepness (for HS > 2 m) and (bottom) blended wind fields (m s−1) while Hurricanes Maria, Nate, and Ophelia coexisted. (bottom) From east to west, Hurricanes Maria, Nate, and Ophelia. Reference arrow at bottom of panels represents 10 m s−1 wind speed (bottom), and 10-s peak wave period (top).

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    Best tracks and GFDL model tracks for Hurricanes Katrina, Rita, and Wilma.

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    (a) (top two panels) Buoy measurements (black) and time history and (bottom four panels) error statistics of the NAH- (red) and WNA- (blue) predicted Hs and U10 for Hurricanes Katrina at buoy 42040. (b)–(d) As in (a), but for Hurricanes: Ophelia at buoy 41002, Rita at buoy 42001, and Wilma at Buoy 42056.

  • View in gallery

    (a) Error statistics: and linear trends in NAH- (blue) and WNA- (red) predicted Hs for all tropical cyclones at all buoy sites. Dash lines show the mean values: (top) (left) RMSE (right) BIAS; (middle) (left) COR and (right) SI; and (bottom) slope parameters (left) a and (right) b. (b) As in (a), but for U10.

  • View in gallery

    (a) (top) Scatterplots of the peak Hs and (bottom) the associated spectral Tp for (left) NAH and (right) WNA for the Atlantic basin. Legend at bottom: W, Wilma; O, Ophelia; K, Katrina; R, Rita; followed by buoy ID number. (b) Time lag of the normalized BIAS of (top) the peak Hs and the associated Tp predicted by the (left) NAH and (right) WNA models for the Atlantic basin. In each panel, center lines represent the mean and the outer lines represent the standard deviation. Symbols and colors are as in (a).

  • View in gallery

    As in Fig. 8, but for the Gulf of Mexico–Caribbean Sea.

  • View in gallery

    A comparison of (top) wind and (bottom) wave fields predicted by (left) WNA and (right) NAH for Hurricane Katrina, 1200 UTC 29 Sep.

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Performance of NCEP Regional Wave Models in Predicting Peak Sea States during the 2005 North Atlantic Hurricane Season

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  • 1 NOAA/NCEP/Environmental Modeling Center/Marine Modeling and Analysis Branch, Camp Springs, Maryland
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Abstract

Unprecedented numbers of tropical cyclones occurred in the North Atlantic Ocean and the Gulf of Mexico in 2005. This provides a unique opportunity to evaluate the performance of two operational regional wave forecasting models at the National Centers for Environmental Prediction (NCEP). This study validates model predictions of the tropical cyclone–generated maximum significant wave height, simultaneous spectral peak wave period, and the time of occurrence against available buoy measurements from the National Data Buoy Center (NDBC). The models used are third-generation operational wave models: the Western North Atlantic wave model (WNA) and the North Atlantic Hurricane wave model (NAH). These two models have identical model physics, spatial resolutions, and domains, with the latter model using specialized hurricane wind forcing. Both models provided consistent estimates of the maximum wave height and period, with random errors of typically less than 25%, and timing errors of typically less than 5 h. Compared to these random errors, systematic model biases are negligible, with a typical negative model bias of 5%. It appears that higher wave model resolutions are needed to fully utilize the specialized hurricane wind forcing, and it is shown that present routine wave observations are inadequate to accurately validate hurricane wave models.

Corresponding author address: Yung Y. Chao, NCEP/EMC/MMAB, 5200 Auth Rd., Camp Springs, MD 20746. Email: yung.chao@noaa.gov

Abstract

Unprecedented numbers of tropical cyclones occurred in the North Atlantic Ocean and the Gulf of Mexico in 2005. This provides a unique opportunity to evaluate the performance of two operational regional wave forecasting models at the National Centers for Environmental Prediction (NCEP). This study validates model predictions of the tropical cyclone–generated maximum significant wave height, simultaneous spectral peak wave period, and the time of occurrence against available buoy measurements from the National Data Buoy Center (NDBC). The models used are third-generation operational wave models: the Western North Atlantic wave model (WNA) and the North Atlantic Hurricane wave model (NAH). These two models have identical model physics, spatial resolutions, and domains, with the latter model using specialized hurricane wind forcing. Both models provided consistent estimates of the maximum wave height and period, with random errors of typically less than 25%, and timing errors of typically less than 5 h. Compared to these random errors, systematic model biases are negligible, with a typical negative model bias of 5%. It appears that higher wave model resolutions are needed to fully utilize the specialized hurricane wind forcing, and it is shown that present routine wave observations are inadequate to accurately validate hurricane wave models.

Corresponding author address: Yung Y. Chao, NCEP/EMC/MMAB, 5200 Auth Rd., Camp Springs, MD 20746. Email: yung.chao@noaa.gov

1. Introduction

The Atlantic hurricane season of 2005 was extraordinary not only for its early beginning and late ending (May–December) but also for the number and the intensity of tropical cyclones. According to the National Climatic Data Center (NCDC 2006), there was a record of 27 named tropical cyclones, of which 15 were hurricanes. Among these storms, seven were major hurricanes of category 3 or higher (i.e., hurricanes Dennis, Emily, Katrina, Maria, Rita, Wilma, and Beta). Four of them reached category 5 (Emily, Katrina, Rita, and Wilma), in which Hurricane Katrina was the most intense and destructive land-falling hurricane on record for the Atlantic basin. Many of these tropical cyclones have created high waves disastrous to the coastal areas and offshore marine activities (in particular, oil exploration and production). Extensive measurements of wind and wave conditions made by the National Data Buoy Center (NDBC) provide an excellent opportunity to validate the National Centers for Environmental Prediction (NCEP) operational regional wave models.

There are two operational regional wave models that forecast sea states over the western North Atlantic Ocean domain at NCEP. These are the Western North Atlantic wave model (WNA) and the North Atlantic Hurricane wave model (NAH) (Chao et al. 2003a,b, 2005). They are part of the National Oceanic and Atmosphere Administration’s global wave forecasting suite, NOAA WAVEWATCH III (NWW3; Tolman 2002a; Tolman et al. 2002). The performance of the forecast guidance produced by the WNA and NAH models for sea states generated by Hurricane Isabel has been reviewed by, for instance, Tolman et al. (2005). The main purpose of the present study is to assess the accuracy of these two wave models regarding the maximum significant wave height, the associated spectral peak wave period, and the time of occurrence for each storm event at a given buoy location. The model results used here are taken from the monthly hindcast data produced by NCEP. They represent operational hindcast model data consistent with the operational real-time products of NCEP and do not include any additional tuning or model modifications.

2. Models and data

Wave model data are generated by two operational regional wave models (WNA and NAH). These two models have identical model physics, spatial resolutions, and domains. The domain covers an area of 0°–50°N, and 30°–98°W, involving the North Atlantic basin, the Gulf of Mexico and the Caribbean Sea. The grid resolution is 0.25° × 0.25° in latitude and longitude. Both models obtain boundary data from NCEP’s global wave model, which has a resolution of 1.00° × 1.25° in latitude and longitude. The model physics consist of the default model settings of WAVEWATCH III version 2.22, as described in detail in Tolman (2002b). The difference between the two models lies in their input winds. The WNA model is driven solely with wind obtained from the NCEP Global Forecast System (GFS) atmospheric model, previously known as the Medium-Range Forecast (MRF) or Aviation (AVN) model (Caplan et al. 1997). For the NAH model, high-resolution wind fields generated hourly at NCEP by the Geophysical Fluid Dynamics Laboratory (GFDL) hurricane model are blended into the GFS wind field. For the 2005 hurricane season, the GFS model’s horizontal resolution is T382, approximately 30 km, and the vertical resolution is 64 layers (see the history of upgrades to GFS online at http://www.emc.ncep.noaa.gov/modelinfo/). The lowest atmospheric level is at a pressure of 997.3 hPa. Since the GFDL hurricane prediction model became operational at NCEP in 1995, it has undergone substantial modifications and improvements (Bender et al. 2007). The 2005 GFDL model has a movable three-nest grid configuration. The horizontal resolution of the outermost nest is ½°, covering an area of 75° × 75° in latitude–longitude. The size of the inner finer mesh is ⅙°, covering an area of 11° × 11° in latitude–longitude. The finest center core mesh size is , covering an area of 5° × 5° aligned to a single storm center. The number of vertical levels in the GFDL model is 42. The lowest sigma level is 996 hPa.

The 2005 GFS model provides forecast wind fields at 3-h intervals for the first 180 h and then at lower spatial and temporal resolutions for up to 16 days for each operational cycle run. The GFDL model, on the other hand, provides forecast wind fields hourly up to 126 h only. To blend with GFDL wind fields, hourly GFS wind fields are generated by interpolation. The required wind field to be used in the wave models is at a 10-m height. Thus, the lowest sigma-level winds given by the GFS and GFDL models are converted to 10-m heights before blending and interpolating to a uniform 0.25° × 0.25° wave model grid. The blending scheme is described in detail in Chao et al. (2005). The wave models operationally run four cycles per day. Each cycle generates a 6-h hindcast that precedes the actually forecasts. The forecasts extend up to 180 and 126 h for the WNA and NAH models, respectively. In this study only hindcast wave data are used. It should be noted that the term “hindcast” used in this paper has a slightly different connotation from the conventional (engineering) definition. Wave hindcasts in the WNA model driven exclusively with GFS winds are generated using 3-hourly analyses from GFS’s Global Data Assimilation System (GDAS; see e.g., Caplan et al. 1997) for a 6-h period preceding the current cycle’s UTC time stamp and are used to provide initial conditions for the wave model real-time forecast. Unlike the GFS, the GFDL model does not include a data assimilation system for the initialization of the model forecast. Thus, the NAH model hindcasts are generated using the GFS analysis winds blended with GFDL forecast winds for the 0–4-h range from the previous cycle (−6 to −2-h range in the current cycle). Wind input for NAH at the −1-h time of the current cycle is obtained by interpolating the −2-h winds with the blended GFS–GFDL 0-h nowcast. Although this may seemingly lead to lower quality winds being used for the NAH model hindcast, the higher-resolution winds available from the GFDL short-range forecast (0–6 h) may compensate for deficiencies in the lower-resolution GFS–GDAS analyses.

Quality controlled wave data for model validation were obtained from the NDBC Web site (http://www.ndbc.noaa.gov/historical_data.shtm). Figure 1 shows the locations of all operational NDBC buoys that provide measured data used in the present study. The results of predictions made by the NAH and WNA wave models on the grid points surrounding these locations are interpolated to these locations for validation. In the present study, hourly data obtained from buoy measurements and model output, including the wind speed at 10 m above the mean sea level, the wind direction, the significant wave height, and the spectral peak wave period, are used. The spectral peak wave period is the wave period that corresponds to the frequency bin of maximum wave energy in the wave spectrum. In addition, the significant wave steepness fields are calculated from the NAH model for the significant wave heights greater than 2 m. The significant wave steepness is defined here as the ratio of the significant wave height to the wavelength associated with the spectral peak wave period. Since only a limited amount of wave data obtained from altimeters is available for the present study, they are not included.

3. Identification of the peak significant wave height associated with a tropical cyclone

In this study, we assume that waves appearing at a buoy location must have the significant wave height in a continuous record, peaking up to greater than 2 m in order to be considered as being caused by a tropical cyclone. Furthermore, we assume that the submarine bottom effects on wave height, such as wave refraction and bottom friction, can be ignored in water with a depth of greater than 200 m. Consequently, we may use wave data obtained for buoy stations from such locations for storm identification. The procedures used to identify a storm that causes the significant wave height to peak up to a maximum (hereafter called the peak significant wave height) at a given buoy location at a specific time are best described by example. We use data for buoy station 41002 off the Atlantic coast in deep water (depth of 3316 m) during September 2005 for illustration. The example is particularly interesting because of three hurricanes coexisting over the North Atlantic Ocean at one time.

Figure 2 shows hourly time series of observed and predicted wave and wind conditions for September 2005. The plots include the spectral peak wave period, the significant wave height, the wind speed at 10 m above the mean sea level, and the wind direction. There are two significant wave height peaks shown in the second panel from the bottom in Fig. 2. For buoy measurement, the first peak appears at 1300 UTC 6 September and the second peak appears at 2300 UTC 10 September. For the NAH model, the first peak appears at 1600 UTC 6 September and the second peak appears at 0000 UTC 11 September. And for the WNA model, the first peak is at 1500 UTC 6 September and the second peak is at 2300 UTC 10 September. For this example, the significant wave height peaks predicted by the WNA model occur an hour earlier than the peaks predicted by the NAH model. It should be noted that we are interested in the quantity of the spectral peak wave period of the wave spectrum, from which the calculated significant wave height appears to be a peak in the time series. These two quantities are “simultaneous” in time. We are not interested in correlating the significant wave height maximum of the significant wave height time series with the maximum value of the spectral peak wave period time series. The occurrence of a peak on the spectral peak wave period time series is not necessarily associated with (or related to) the considered peak on the significant wave height time series.

Five named hurricanes appeared one after another in the western North Atlantic Basin during September 2005. Three of these storms existed when peaks in the significant wave height occurred at buoy station 41002. They are Hurricane Maria (category 3) during 1–10 September, Hurricane Nate (category 1) during 5–10 September, and Hurricane Ophelia (category 1) during 6–18 September. Figure 3 shows the track positions of the GFDL hurricane model at 6-h intervals. The best tracks (the verified tracks) for these hurricanes are also plotted at 6-h intervals based on data available from the National Hurricane Center (NHC) archive of the 2005 Atlantic hurricane season. The date of the best-track position at 0000 UTC is indicated along the path. The development of a storm’s intensity along the track is indicated by segments of different colors and line types. They might involve a tropical low/wave (LO/WV), subtropical depression (SD), subtropical storm (SS), extratropical system (EX), tropical depression (TD), tropical storm (TS), or hurricane (HU). It can be observed from Fig. 3 that the GFDL hurricane model tracks are virtually the same as the best tracks. This is because data for the initialization of the GFDL model is derived from the result of data assimilation (involving the use of observed data) for the GFS model initialization processes (i.e., in the hindcast model).

To determine which one of these hurricanes causes the significant wave height to reach a maximum, the following steps have been taken. We begin with the construction of the wind fields and the wave steepness fields covering the life cycle of tropical cyclone under study. Figure 4 is an example showing the patterns of the wind (bottom panel) and wave steepness (top panel) fields when three hurricanes coexist over the North Atlantic Basin. The shaded wave steepness contours are given only for the region where the significant wave height is greater than 2 m. Within the shaded area, the hurricane wind bars and the direction of the spectral peak wave period are presented. The direction of the spectral peak period is considered to be the representative wave direction.

We then visually examine sequential plots of the vector wind field and model-derived significant wave steepness patterns. We first observe the pattern orientation and the extent of the wind and wave steepness fields to see if they are moving toward the buoy location (The animation of the significant wave steepness fields at 3-h intervals is very helpful.) If these fields indeed move toward and eventually cover the buoy location, we then examine whether the directional variation of the wind and wave inside the shaded wave steepness areas is consistent with the time series of the wind and wave direction at the buoy location as shown in Fig. 2. It is a tedious, time-consuming, trial-and-error process. But in this manner, the storm that causes the wave height to peak up to a maximum at the given location and time can be identified eventually. For the case of buoy station 41002 during September 2005, it is found that the first wave height peak shown in Fig. 2 is identified to be caused by Hurricane Nate and the second wave height peak is identified to be caused by Hurricane Ophelia.

The same procedure is applied to all of the tropical cyclones that occurred during 2005 for all of the available deep-water buoy stations. Table 1 list the names of the tropical cyclones and the deep-water buoy locations where the significant wave heights peak at more that 2 m are observed and/or modeled. A total of 14 storms (among 28 for the whole 2005 hurricane season) are identified to have a peak significant greater than 2 m at one or more than one of 14 deep-water buoys. For buoy stations in shoaling waters (buoy stations in the water depths less than or equal to 200 m), the peak conditions associated with a specific storm event are inferred from nearby deep-water buoy stations. Detailed one-to-one comparisons of the significant wave height, peak period, and the time of occurrence between buoy measurements and model predictions are given in appendixes A and B for the Atlantic basin and the Gulf of Mexico, respectively. In these appendixes, 16 additional shoaling water buoy sites are included.

4. Model performance

As previously mentioned, our main objective in this study is to evaluate the performance of the WNA and NAH models for the western North Atlantic basin and the Gulf of Mexico–Caribbean Sea, respectively, in predicting the tropical cyclone–generated maximum significant wave height, simultaneous spectral peak wave period, and the time of occurrence during the 2005 hurricane season. These two regions are considered separately because the Gulf of Mexico–Caribbean Sea is a semi-enclosed basin while the Atlantic basin is an open ocean. The accuracy of prediction for the two regions might differ due to different geographic constrains on the characteristics of tropical cyclone–induced wind waves. The section is divided to two subsections. Section 4a evaluates the wind speed and the significant wave height predictions for each tropical storm against available buoy observations for 5 days around the evolution of the peak significant wave height. Section 4b then evaluate specifically the performance of the models in predicting the peak significant wave height, the simultaneous wave period, and the time of occurrence.

a. 5-day statistics around the significant wave height peak

We begin with an evaluation of modeled wind speeds and significant wave heights against buoy measurements for four selected storms over a 5-day time span around the significant wave height peaks. The selected storms are three category 5 hurricanes (Katrina, Rita, and Wilma) and a category 1 hurricane (Ophelia). Hurricane Ophelia never made landfall but because of its slow movement along the East Coast coastline, it produced sustained high waves for several days (see Fig. 3 for the track of Hurricane Ophelia). Each buoy selected represents the site where the maximum significant wave height peak of the corresponding hurricane was recorded among all of the buoys. Although rather subjective, the selected 5-day time span is assumed to be sufficient to see the rise and fall of the significant wave height around the peak. For each selected storm and buoy site, a total of 120 hourly data points are involved. Figure 5 exhibits the tracks of three category 5 hurricanes. Figures 6a to 6d present the time histories and scatterplots of the wind speeds at 10-m height above the mean seawater level (U10) and the significant height (Hs) caused by Hurricane Katrina at buoy 42040 and Hurricane Rita at buoy 42001 in the Gulf of Mexico, Hurricane Wilma at buoy 42056 in the Caribbean Sea, and Hurricane Ophelia at buoy 41002 in the North Atlantic Basin. Also shown in these figures are the root-mean-square error (RMSE), mean bias (BIAS), correlation coefficient (COR), scatter index (SI), and the linear trend, including the slope and the intersection with an axis. The scatter index is defined as the root-mean-square error normalized by the mean observation.

It can be seen from the time series plots shown in Fig. 6a that for Hurricane Katrina at buoy 42040 during the time period of 0000 UTC 27 August–2300 UTC 31 August, the U10 of WNA and NAH are both overpredicted for most of time, especially for WNA near the peak. However, WNA make a much better overall prediction of Hs than NAH, particularly near the peak. The NAH-predicted Hs values are much lower than the measured results. For Hurricane Ophelia at buoy 41002, as shown in Fig. 6b, the slowly moving feature of the hurricane appears in a relatively long duration of U10 at around 20 m s−1 and Hs of around 6 m for almost 2 days. Again, U10 is overpredicted, and Hs is underpredicted by both models. Note that there are six missing data points in the model predictions. Figure 6c shows the “worst” wind input associated with Hurricane Rita for the WNA and NAH wave models. As shown in the time evolution of Hurricane Rita, there is a sharp drop in the wind speed. As shown in Fig. 5, the center of Hurricane Rita is in the proximity of the buoy 42001 at about 0000 UTC 23 September. The modeled winds tend to indicate the conditions near the eye of the hurricane, with a rapid change in the wind direction; the wind blows counterclockwise from NNE to NW, to W then to S, within a 5-h period (The time history of the wind directional variations is not shown.) In spite of the substantial discrepancy in the modeled wind speed in comparison with the buoy-measured results, the predicted Hs seems to behave fairly well, underscoring that the modeled Hs’s respond to wind speed variations, but do so much more slowly and less dramatically. The results of the NAH and WNA predictions for Hurricane Wilma at buoy 42056, which is located in the Caribbean Sea, are shown in Fig. 6d. As shown in Fig. 6d, the WNA model overpredicts U10 and Hs around the peak but predicts quite consistently with the observations in the ascending and descending stages. On the other hand, the NAH model predicts the peak Hs near the same height as measured but the time of occurrence is much earlier than was measured even though the modeled maximum wind speed is consistent with the measurement in time and in magnitude. During the descending stage, both U10 and Hs are considerably underpredicted. The scatterplots shown in Fig. 6d reveals quantitatively that the NAH-modeled U10 and Hs are substantially underpredicted and have negative BIAS, large RMSE, large SI, and low COR, while the linear trend for the WNA-modeled U10 and Hs indicates that both are overpredicted but are fairly good in the statistical quantities.

The statistical evaluation of NAH and WNA for the four selected hurricanes at the selected buoys described above has been extended to all selected tropical cyclones and buoys based on the procedure described previously. Figures 7a and 7b summarize the results for Hs and U10, respectively. They are constructed based on data given in appendixes C and D of this paper. The vertical axes for in Figs. 7a and 7b represent one of the statistical quantities described previously [i.e., RMSE, BIAS, COR, SI, and the a (slope) and b (intersection) terms of the linear trend]. The horizontal axes labeled as “all (buoys–storms)” represent the event numbers assigned to the combination of a buoy and identified tropical storms. The event number is assigned according to the combination of the ascending order for the buoy ID number and the alphabetic order for the storm names, beginning with the Atlantic basin followed by the Gulf of Mexico–Caribbean Sea. Thus, the event numbers 1–19 are for the Atlantic basin; for example, 1–3 represent 41001 for Maria, Ophelia, and Wilma, and 17–19 represent 44004 for Maria, Ophelia, and Wilma. The event numbers 20–55 are for the Gulf of Mexico–Caribbean Sea; for example, 20–27 represent 42001 for Arlene, Cindy, Dennis, Emily, Katrina, Rita, Stan, and Wilma, and 54–55 represent 42057 for Wilma and Beta (Hurricane Beta is an exception, as it does not follow the alphabetic order). In each panel, values corresponding to NAH and WNA modeled are shown in blue and red, respectively. The dash lines indicate the mean. Also given in the panels are the mode and the standard deviation (std) of the dataset. The mode in statistics is not necessarily unique, but if it is considered in conjunction with the mean, it can capture important information about what is the value that is most likely to be expected in a discrete dataset. Based on graphs shown in Figs. 6 and 7, the following observations might be made:

  1. There are hardly distinct differences visually in the resulting statistics for the Atlantic basin [(case 1) (19)] of the horizontal axis) and the Gulf of Mexico regime [(case 20) (55)] from NAH or WNA modeled Hs or U10.
  2. In considering the mean and the mode values given for each of the statistical quantities, both the NAH and WNA models show the following results:
    • (a) For Hs, the RMSE is about 0.5 m, BIAS is less than 0.1 m, COR is higher than 0.9, and SI is less than 0.2 (20%). The slope of the linear regression line (the a term) is slightly less than 0.95, and the intersection (the b term) is around 0.1 m, indicating that the models tends to underpredict Hs slightly.
    • (b) For U10, the RMSE is around 2 m s−1, BIAS is near zero but with opposite sign on values for the mode, COR is only slightly above 0.80, and the SI is around 20%. The slope of the linear regression line (a) is nearly 1.0, and the intersection (b) is closer to 1.0 m s−1, indicating the tendency of only slight overprediction of the wind speed.
  3. WNA performs comparably to or better than NAH in the overall statistical results.
  4. There are a substantial number of outlying points that deviate beyond one standard deviation from the mean in each statistical quantity. No attempt is made to get rid of those extreme values in this paper.
  5. The present study clearly shows that the complexity of the hurricane wind and wave fields such that the validation of model performance for one storm event at limited buoys sites is not necessarily applicable to another storm event. An in-depth investigation of the models’ performance for each storm scenario regarding the causes of success or failure is important for the improvement of our modeling methodology but is beyond the scope of the present study.

b. Statistics for the peak significant wave height and the associated wave period

A major concern in an operational wave forecasting system is the ability to forecast the possible maximum wave height and the time of occurrence at a given location associated with a given tropical cyclone. The present section evaluates the deviations of the NAH and WNA modeled peak significant wave heights (hereafter, the peak Hs) and the associated spectral peak wave periods (hereafter Tp) and the times of occurrence against buoy measurements.

Figure 8a, containing four panels, depicts the scatterplots of the NAH and WNA modeled peak Hs and Tp for all North Atlantic tropical cyclones, as shown by the asterisk symbol. The database is given in appendix A. In addition, the peak Hs and Tp associated with the hurricanes of particular interest at various buoy sites are plotted with different symbols. In addition, the overall error statistics including root-mean-square error, bias, correlation coefficient, and scatter index, along with the linear trend for all storms and buoys involved, are also presented. Figure 8b shows the normalized bias (difference) between the model predictions and buoy measurements of the peak Hs and Tp as a function of the time lag (difference) in occurrence. The bias is normalized with the buoy measurements and is expressed in percentiles on the vertical axis. The time lag is expressed in hours on the horizontal axis: a negative (or positive) time lag means that the predictions are earlier (or later) than actually observed. The central line in each graph represents the mean value of the labeled quantity, while the outer two lines represent one standard deviation from the mean. Similar graphs for the Gulf of Mexico–Caribbean Sea are depicted in Figs. 9a and 9b based on the dataset given in appendix D.

The scatterplots of the peak Hs for the NAH and WNA models are shown in the top rows of Fig. 8a for the Atlantic basin and in Fig. 9a for the Gulf of Mexico. The plots indicate that the WNA model predictions are slightly better than the NAH model predictions in both the Atlantic basin and the Gulf of Mexico–Caribbean Sea (based on the slope of the regression line). Both models underpredict the peak significant wave height for the Atlantic basin, but predict the wave height for the Gulf of Mexico-Caribbean Sea reasonably well. Furthermore, for both models, the correlation between observations and the model predictions in the Gulf of Mexico–Caribbean Sea region is better than that in the Atlantic basin. The scatterplots of Tp for the NAH and WNA models (bottom rows in Fig. 8a for the Atlantic and Fig. 9a for the Gulf regions) show results similar to those for the peak Hs. However, Tp has greater bias and a lesser correlation coefficient than does the peak Hs. This is consistent with typical wave model validation results for the spectral peak wave period (Bidlot et al. 2002; Tolman et al. 2005).

The plots of the predicted peak Hs (and Tp) against the predicted time of occurrence for the NAH and WNA models are shown in Fig. 8b for the Atlantic basin and in Fig. 9b for the Gulf of Mexico–Caribbean Sea. As can be observed from the top rows in Figs. 8b and 9b, the normalized bias of the peak Hs is mainly within ±20% but may reach ±30% of the observed value for the Atlantic basin and ±40% for the Gulf of Mexico–Caribbean Sea. The plus sign indicates overprediction while the minus sign indicates underprediction. The mean bias of the peak Hs for both models is approximately −5%. The normalized bias of Tp for both models (bottoms rows in Figs. 8b and 9b) shows similar results to those for the normalized bias of the peak Hs. Thus, the errors are dominated by the model uncertainty (random errors), with the mean bias being comparatively small (less than 5%). The time lag of the model-predicted peak Hs (and the simultaneous Tp) spread considerably, although it was mostly clustered within ±5 h of the observed peak. On average, both the NAH and WNA models are slightly behind (positive in time lag, on the order of 1–2 h) in predicting the peak Hs and Tp in the Atlantic basin. However, in the Gulf of Mexico–Caribbean Sea, NAH is slightly ahead (negative in time lag) in contrast to WNA, which is on target in time. Note that the observation accuracy of the timing of the peaks is known to be ±1 h.

5. Discussion

Both the WNA and NAH wave models are capable of providing useful forecast guidance for hurricane-generated waves, with a potential accuracy in the peak significant wave heights that deviates from the observations by roughly 30% within 5 h of the observed time of these maxima. The associated mean biases are much smaller (typically 5%), in comparison to the corresponding random model error. We consider wave model “hindcasts” only in this study. Hence, it should be emphasized that the present results merely identify the potential accuracy of the wave model prediction within the framework of the real-time operational environment. It is anticipated that the accuracy of hurricane-associated extreme wave forecasts will be similar depending strongly on the results of the track and wind intensity forecasts of the tropical cyclones that might have occurred. For instance, forecast errors for wave models for Hurricane Isabel in 2003 are discussed in detail in Tolman et al. (2005).

Considering the problems involved with providing accurate hurricane wind nowcasts and forecasts, the method of blending GFS and GFDL model wind fields for the NAH model becomes a subject of concern. In previous hurricane seasons, the NAH model in general has outperformed the WNA model (see Chao et al. 2005). However, for the 2005 season, the models behaved similarly, with arguably better behavior for the WNA model. Within this context, it is important to realize that the wind-blending algorithm was developed almost a decade ago. At that time GFS, previously known as the Medium-Range (MRF) and Aviation (AVN) models, had a grid resolution of about 50 km, which was too coarse to resolve the wind field structure associated with a relatively small hurricane vortex. Thus, the blending algorithm was initiated to incorporate the GFDL hurricane model and take advantage of its high-resolution inner mesh of about 15 km (Chao and Tolman 2000; Chao and Tolman 2001). Since then, has GFS undergone various improvements; among these enhancements was a change in grid resolution to about 30 km in 2005. As a result, GFS was able to provide improved wind forecasts near the hurricane core. More importantly, the resolution of the GFS is now comparable to the resolution of the wave models. Conversely, the resolution of the GFDL model winds is much higher than the resolution of the wave models, and hence the wave models no longer make optimal use of the resolution of the hurricane wind models. It therefore appears to be necessary to increase the spatial resolution of the (hurricane) wave models to effectively use the increased resolution of the hurricane wind models. For this reason, it is necessary to upgrade the hurricane wave model to utilize hurricane winds at or near the native resolution of the hurricane wind fields.

Another reason for the apparently comparable behavior of the WNA and NAH wave models may be the sparsity and a corresponding lack of representativeness of the validation data. This is illustrated in Fig. 10 with results for Hurricane Katrina near landfall at 1200 UTC 29 September. (The hurricane track and the time history of the wind and wave data at buoy station 42040 near the track are shown in Figs. 5 and 6a, respectively.) The top panels in Fig. 10 show the wind fields of the WNA and NAH models. Both models have nearly identical tracks, with the centers of the maximum wind shifted by 10–20 km. The NAH winds are more intense with reasonable spatial scales, but are shifted too much to the shallow waters (west). The WNA winds have lower speeds but larger spatial scales. This produces good wind results at the only relevant observation location (buoy 42040), although the wind fields as a whole are less realistic than the NAH wind fields (Chao et al. 2005; Tolman et al. 2005). The corresponding wave height fields (bottom panels in Fig. 10) are also shifted between the models, due to the similar track but different spatial scales of the wind fields. If only buoy data at buoy 42040 were considered, one could easily come to the conclusion that the WNA model is far superior (Fig. 6a). With only the buoy in view in Fig. 10, there is clearly insufficient information to rigorously validate the hurricane wave models, unless the hurricane track is close to the buoys (see Chao et al. 2005; Tolman et al. 2005 for case studies). It therefore appears essential to have routine on-demand wave observations during hurricanes, as was available for Hurricane Bonnie from a Scanning Radar Altimeter (Alves et al. 2004; Wright et al. 2001), to systematically address the accuracy of the hurricane wave models.

Note that the model resolution in 2005 was insufficient to resolve this coastline, and therefore the results from buoy 42007 cannot be expected to be very accurate. Furthermore, wave heights in the shallow waters behind the Chandeleur Islands are obviously unrealistic due to the lack of shallow-water physics in the model and due to the fact that the spatial resolution is too poor to introduce these islands as obstructions. For the 2007 model implementation, the coastal resolution in this area is greatly improved, and surf zone physics (depth-induced breaking) were added to the model (Chawla et al. 2007; Tolman 2008).

6. Conclusions

In this study, we validate NCEP’s operational Western North Atlantic regional wave model (WNA) and North Atlantic Hurricane wave model (NAH) against NDBC buoy measurements for more than 20 tropical cyclones (including three category 5 hurricanes) for the 2005 hurricane season. The parameters evaluated include the maximum significant wave height, the corresponding spectral peak period, and the time of occurrence induced by each individual tropical cyclone. The results show that the deviations of the model-predicted wave heights and periods from buoy measurements are essentially within 20% and 30%, respectively, and that the time lags (behind or ahead of observation) on the occurrence of peak wave height are within the 5-h range for both models. Both models show similar patterns of behavior, with model uncertainty dominating the mean model bias, which is typically approximately 5%. Considering that these are operational model results produced in near–real time with no case-specific tuning of the wave models or the wind fields, the biases of both models can be considered to be rather good. Clearly, the model presents useful results for real-time forecasting, but also leaves room for improvement. The similar patterns of behavior in the WNA and NAH models suggests that the hurricane wave model (NAH) no longer optimally uses the higher resolution of the hurricane wind model, suggesting that the spatial resolution of the hurricane wave model needs to be increased to be comparable to that of the hurricane wind model. Note that, generally, better validation of hurricane wave models is greatly hampered by the lack of wave observations with suitable spatial coverage.

The NAH and WNA, as is the case with many other existing third-generation (3G) models, are essentially developed and validated on extratropical wind-forcing regimes characterized with slowly varying wind fields in space and time. The application of such a model in a real-time operational environment for tropical cyclones that are characterized by the rapidly varying extreme surface wind fields along the moving storm track faces various obstacles and uncertainties. The sparsity of measured data is just one of these potential problem areas. We would like to stress that the models are intended as operational models for real-time forecasting. Even if there is insufficient data to do a rigorous statistical analysis of bias versus uncertainty, it appears obvious to us from the present study that a human forecaster using these model data to do his or her work will have to expect the model’s uncertainty to be the main problem with the guidance, and that adding a systematic bias correction to the model guidance is a minor correction compared to this uncertainty. Hence, we cannot, based on the sparsity of the data, do an in-depth statistical analysis, but, from the perspective of these being operational forecast models, we do feel confident saying that the biases of the model are small compared to the general uncertainty.

Acknowledgments

The authors thank Janna O’Connor, Arun Chawla, Robert Grumbine, and the anonymous reviewers for their valuable comments and suggestions on our drafts of this manuscript.

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APPENDIX A

The Peak Significant Wave Heights (Hs), Simultaneous Spectral Peak Periods (Tp), Times of Occurrence, and Associated Cyclone Names for the Atlantic Basin

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APPENDIX B

The Peak Significant Wave Heights (Hs), Simultaneous Spectral Peak Periods (Tp), Times of Occurrence, and Associated Cyclone Names for the Gulf of Mexico–Caribbean Sea

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APPENDIX C

The 5-Day Error Statistics for NAH and WNA Modeled Significant Wave Heights (Hs, m) for All Available Tropical Cyclones at All Available Buoys

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APPENDIX D

The 5-Day Error Statistics for NAH and WNA Modeled Wind Speeds at 10-m Height (U10, m s−1) for All Available Tropical Cyclones at All Available Buoys

i1520-0434-25-5-1543-td01

Fig. 1.
Fig. 1.

Locations of NDBC buoys used in the model validation.

Citation: Weather and Forecasting 25, 5; 10.1175/2010WAF2222309.1

Fig. 2.
Fig. 2.

(bottom to top) Monthly time series of the measured (black) and predicted (NAH, red; WNA, green) spectral peak periods, significant wave heights, wind speeds, and wind directions at buoy 41002, September 2005.

Citation: Weather and Forecasting 25, 5; 10.1175/2010WAF2222309.1

Fig. 3.
Fig. 3.

Best tracks and GFDL model tracks for Hurricanes Maria, Nate, and Ophelia.

Citation: Weather and Forecasting 25, 5; 10.1175/2010WAF2222309.1

Fig. 4.
Fig. 4.

(top) Wave steepness (for HS > 2 m) and (bottom) blended wind fields (m s−1) while Hurricanes Maria, Nate, and Ophelia coexisted. (bottom) From east to west, Hurricanes Maria, Nate, and Ophelia. Reference arrow at bottom of panels represents 10 m s−1 wind speed (bottom), and 10-s peak wave period (top).

Citation: Weather and Forecasting 25, 5; 10.1175/2010WAF2222309.1

Fig. 5.
Fig. 5.

Best tracks and GFDL model tracks for Hurricanes Katrina, Rita, and Wilma.

Citation: Weather and Forecasting 25, 5; 10.1175/2010WAF2222309.1

Fig. 6.
Fig. 6.

(a) (top two panels) Buoy measurements (black) and time history and (bottom four panels) error statistics of the NAH- (red) and WNA- (blue) predicted Hs and U10 for Hurricanes Katrina at buoy 42040. (b)–(d) As in (a), but for Hurricanes: Ophelia at buoy 41002, Rita at buoy 42001, and Wilma at Buoy 42056.

Citation: Weather and Forecasting 25, 5; 10.1175/2010WAF2222309.1

Fig. 7.
Fig. 7.

(a) Error statistics: and linear trends in NAH- (blue) and WNA- (red) predicted Hs for all tropical cyclones at all buoy sites. Dash lines show the mean values: (top) (left) RMSE (right) BIAS; (middle) (left) COR and (right) SI; and (bottom) slope parameters (left) a and (right) b. (b) As in (a), but for U10.

Citation: Weather and Forecasting 25, 5; 10.1175/2010WAF2222309.1

Fig. 8.
Fig. 8.

(a) (top) Scatterplots of the peak Hs and (bottom) the associated spectral Tp for (left) NAH and (right) WNA for the Atlantic basin. Legend at bottom: W, Wilma; O, Ophelia; K, Katrina; R, Rita; followed by buoy ID number. (b) Time lag of the normalized BIAS of (top) the peak Hs and the associated Tp predicted by the (left) NAH and (right) WNA models for the Atlantic basin. In each panel, center lines represent the mean and the outer lines represent the standard deviation. Symbols and colors are as in (a).

Citation: Weather and Forecasting 25, 5; 10.1175/2010WAF2222309.1

Fig. 9.
Fig. 9.

As in Fig. 8, but for the Gulf of Mexico–Caribbean Sea.

Citation: Weather and Forecasting 25, 5; 10.1175/2010WAF2222309.1

Fig. 10.
Fig. 10.

A comparison of (top) wind and (bottom) wave fields predicted by (left) WNA and (right) NAH for Hurricane Katrina, 1200 UTC 29 Sep.

Citation: Weather and Forecasting 25, 5; 10.1175/2010WAF2222309.1

Table 1.

List of tropical cyclones for the wave model validation study.

Table 1.

* Marine Modeling and Analysis Branch Contribution Number 283.

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