## 1. Introduction

Population growth and the influx of wealth along the U.S. coastline have been highlighted as the cause for large economic losses incurred during tropical cyclone (TC) landfalls (Pielke et al. 2008). Wind engineers, operational meteorologists, and TC wind hazard modelers are constantly assessing building codes, forecast practices, and model parameterizations, in an effort to mitigate the loss of life and property. Proper examination of the horizontal and vertical structure of the tropical cyclone boundary layer (TCBL) at landfall can provide wind engineers, operational meteorologists, and TC wind hazard modelers with useful information regarding relationships between TCBL structures (e.g., low-level wind maxima) and surface wind characteristics overland to improve building codes, warnings, and simulated wind footprints for TC-prone regions (Giammanco et al. 2012; Hirth et al. 2012; Giammanco et al. 2013).

Previous studies have analyzed surface wind measurements obtained by reconnaissance aircraft (Powell 1980, 1982, 1987; Powell and Black 1990; Powell et al. 1991, 1996), global positioning system (GPS) dropwindsondes (Sparks and Huang 2001; Sparks 2003; Franklin et al. 2003; Powell et al. 2003; Dunion et al. 2003; Kepert 2006a,b; Schwendike and Kepert 2008), and Stepped Frequency Microwave Radiometer (SFMR) measurement systems (Uhlhorn et al. 2007; Powell et al. 2009). The National Hurricane Center (NHC) has applied wind speed reduction factors (WSRFs), which are ratios of maximum 1-min sustained speeds at 10 m above ground level (AGL) over “unobstructed” exposure to reference mean wind speeds measured at flight level to classify TC strength. These WSRFs vary anywhere between 0.6 and 0.7 in the outer vortex storm region and between 0.8 and 1.0 in the eyewall storm region (Kepert 2001; Kepert and Wang 2001; Franklin et al. 2003; Kepert 2006a,b; Schwendike and Kepert 2008) and are susceptible to large errors due to the outward slope of the radius of maximum wind (RMW) with increasing height (Powell et al. 2009).

Three SFMR-based regression methods have been developed to predict slant-maximum reduction factors *F*_{rmx} based on flight-level input data (Powell et al. 2009). The predicted *F*_{rmx} values are then used to estimate maximum surface wind speeds along radial flight legs in TCs over water. The primary advantage of the SFMR-based regression methods over reduction factors *F*_{r} used by Franklin et al. (2003) is *F*_{rmx} effectively captures the maximum surface wind along the sloping RMW during a radial flight leg, whereas GPS dropwindsondes may completely miss the maximum surface wind speed along the sloping RMW during a radial flight leg because of the launch location and trajectory (Powell et al. 2009). Since the SFMR directly measures the maximum surface wind speed along the sloping RMW during a radial flight leg, the SFMR-based regression methods developed in Powell et al. (2009) have been implemented in H*Wind and can be used in the absence of SFMR data to retrospectively evaluate maximum storm intensities. Unfortunately, overwater empirical wind speed relationships are not applicable over land and research regarding the proper adjustment of TCBL lower-tropospheric winds to represent near-surface wind conditions in landfalling TCs is scarce as a result of a limited amount of collocated observations available for comparison.

Dobos et al. (1995) used hourly radar wind profiler observations and both surface-sustained and gust wind speeds to formulate relationships for a single weather station at Kadena Air Base along the west coast of Okinawa, Japan. Surface-sustained and gust-to-radar wind profiler wind speed ratios (WSRs) were evaluated against linear regression models for several different altitudes and layers. Results from the comparison showed that a linear regression model that uses a 600–1800-m-layer average wind speed to predict surface-sustained and gust wind speeds explains 80% of the variance in the prediction and is more accurate than a simple WSR.

Amano et al. (1999) compared sonic anemometer and Doppler sonic detection and ranging (sodar) wind speed measurements for three typhoons in Okinawa. Good agreement was found between the two measurement systems, but heavy rainfall and surface structures disrupted the agreement for specific wind approach angles. Power law fits were evaluated for 10-min-averaged Doppler sodar wind speed profiles and it was observed that the theoretical profile failed to describe the mean profile for smaller storm radii, because of the variable nature of the TC low-level wind speed maximum with respect to storm radius.

Giammanco et al. (2012) applied a logarithmic fit to the lower 300 m of the modified VAD wind speed profiles generated at the Slidell, Louisiana (KLIX), Weather Surveillance Radar-1988 Doppler (WSR-88D) system during the landfall of Hurricane Katrina (2005) to estimate velocity–azimuth display (VAD) 10-m mean wind speeds. A comparison with a Texas Tech University (TTU) 10-m tower deployed in the VAD domain was made, and the wind speed record was segmented using various averaging times centered on the VAD data collection time period. The authors computed the smallest mean error between the two wind speed measurements (−1.2 m s^{−1}) using a 10-min-averaging window and determined that the log law underpredicted the 10-m mean wind speed measured by the TTU tower.

The coastal network of National Weather Service WSR-88Ds provides operational coverage during landfalling TCs; however, there currently is no methodology in place to estimate near-surface winds in landfalling TCs from elevated WSR-88D radial velocity measurements. Previous studies that have examined overland adjustments of TCBL winds to the near surface (i.e., 10 m) at landfall using Doppler radar wind profilers, sodars, or WSR-88Ds (Dobos et al. 1995; Amano et al. 1999; Giammanco et al. 2012) have been conducted for a limited number of sites with collocated volumetric and in situ measurement platforms. The proposed methodologies and conclusions from these studies have not been validated at other sites, which limits their application to the broader operational community. Thus, in an effort to develop a new methodology and empirical relationships that relates TCBL winds to near-surface wind conditions at landfall, a large and diverse WSR-88D VAD wind profile database was constructed and compared to collocated Automated Surface Observing System (ASOS) standardized mean and nonstandardized (i.e., not corrected for height, terrain, and averaging time) gust wind speed conditions.

## 2. Data and methodologies

### a. WSR-88D level-II data

U.S. landfall events were identified during the years of WSR-88D operation prior to 2012 using past track seasonal maps from NHC. Once candidate events were identified, WSR-88D level-II data files were obtained from the National Climatic Data Center [NCDC; now National Centers for Environmental Information (NCEI)] for the duration of each NHC best-track file. Level-II data files were preferred over VADs in level-III data files because the vertical resolution of the level-III VAD wind profiles was too coarse to develop meaningful empirical relationships with ASOS wind measurements. The 0.5° base reflectivity plan position indicators (PPIs) stored in each level-II data file were viewed using the NCDC Weather and Climate Toolkit to determine whether or not TC storm centers moved within 150 km of WSR-88D sites selected for analysis (Giammanco et al. 2012). For events that moved within 150 km of WSR-88D sites, the analysis periods were subjectively defined by the first and last primary rainband passages over each WSR-88D site using the 0.5° base reflectivity PPIs.

WSR-88D level-II data files were converted to Network Common Data Form (NetCDF) using the ldm2netcdf algorithm contained in the Warning Decision Support System–Integrated Information (WDSS-II) suite (Lakshmanan et al. 2007). WSR-88D metadata and base moments were extracted from the NetCDF files and both azimuth and Doppler radial velocity measurements were paired together to construct VADs for each elevation angle, range gate from 3 to 5 km, and WSR-88D site. A custom script was developed to objectively screen a total of 1 915 164 VADs for Doppler radial velocity aliasing (The MathWorks 2015; Krupar 2015). Aliased Doppler radial velocities represent particle radial velocities that exceed the Nyquist velocity *V*_{max} of the WSR-88D and are interpreted as folds with opposite sign offset by multiples of 2*V*_{max}. Velocity aliasing must be corrected in order to effectively compute horizontal wind speed profiles in landfalling TCs.

### b. Refined VAD technique

^{−1}),

*R*

^{2}greater than 90% (Giammanco et al. 2012). For VADs with a sample size less than 200 and

*R*

^{2}greater than 90%, a sine fit was applied to the data with the same iteration and

*R*

^{2}constraints (Lorsolo 2006). Fitting constraints were employed in order to reduce overfitting and produce more reliable estimates of the VAD horizontal wind speed and direction.

Giammanco et al. (2013) used 11 height bins between 50 and 1500 m with an approximate vertical resolution of 100 m below 700 m to construct VAD horizontal wind profiles. In an attempt to improve upon the vertical height binning scheme used by Giammanco et al. (2013), a sensitivity test was performed to determine the smallest vertical height bin resolution that could be used to generate vertical wind profiles over a 3–5-km annulus. Based on the results of the sensitivity test, the best-performing vertical height binning scheme employed 50-m vertical resolution below 400 m, 75-m vertical resolution between 400 and 700 m, and 100-m vertical resolution above 700 m. The new vertical height binning scheme represented an improvement over the vertical height binning scheme employed by Giammanco et al. (2013) because of an increase in the vertical resolution below 100 m and was used to vertically bin all of the quality controlled VAD wind measurements.

Residuals from the Fourier and sine fits were also binned vertically with the newly developed vertical height binning scheme and the root-mean-square error (RMSE) was computed for each vertical height bin. A chi-square goodness-of-fit hypothesis test was performed within each vertical height bin to determine if a random RMSE originated from a lognormal distribution. The null hypothesis was not rejected at the 5% significance level for height bins above 100 m and below 1400 m. This result indicated that a random RMSE would come from a lognormal distribution, except at altitudes below 100 m and above 1400 m. The vertical height bins below 100 m and above 1400 m were rejected by the chi-square goodness-of-fit test because they lacked a sufficient number of residuals to adequately assess the distribution of the RMSEs. The RMSE mean departures were about 1.5 m s^{−1} through the 100–1400-m depth, which is half the value estimated by Giammanco et al. (2012) and Giammanco et al. (2013). The standard deviation for each vertical height bin did not significantly increase with height, but was larger in the lowest and highest bins due to sample size differences. Using the normal probability rule (Milton and Arnold 2003), the upper bound of the 99.7% probability statement suggests that an error estimate of 3 m s^{−1} is approximately the upper bound error expected with increasing height, which was speculated by Giammanco et al. (2012) and Giammanco et al. (2013).

### c. ASOS wind and roughness length data

Historically, very few observational studies have addressed the relationship between TCBL lower-tropospheric winds measured by single-Doppler radars and surface anemometers at landfall (Giammanco et al. 2012). To examine this relationship, ASOS 10-m wind measurements archived in the NCDC electronic land-based station database (DSI-6405) were retrieved and merged with VAD horizontal wind speed profiles. The ASOS 10-m wind data consisted of 2-min running averages and maximum 5-s block averages measured over the previous minute, prior to 2007 and a maximum 3-s running average from 2007 to the present (NWS 2003). A total of 22 comparisons between seven different ASOS and VAD measurement sites during landfalling TCs from 2000 to 2012 were identified (Fig. 1) and used to construct a unique mean wind speed comparative dataset (Table 1). Eleven of the 22 comparisons from 2007 to 2012 were extracted from the aforementioned comparative dataset, in order to keep the gust duration consistent in accordance with ASCE (2010) and construct a unique maximum 3-s gust comparative dataset.

A summary of TC landfall events, measurement sites, dates, time periods, and volume coverage patterns (VCPs) used in the comparative database.

A large database of ASOS roughness length

Mean and median ASOS

The RMSE and mean absolute error (MAE) were computed to assess the average difference between the Lombardo mean and Powell *z*_{0} estimates are lower than the differences between the Powell and Lombardo median ASOS *z*_{0} estimates for all ASOS sites except KJAX and Lake Charles, Louisiana (KLCH). The largest average differences were observed by the ASOS at Slidell, Louisiana (KASD), where the lower limit imposed by Powell et al. (2004) and the small sector count sizes likely led to larger average differences. Further examination of the Lombardo mean and median

Lombardo

### d. Data reduction and standardization

A data reduction and quality control methodology was developed to remove erroneous ASOS 10-m wind data and VAD horizontal wind speed profiles. ASOS 10-m measurement sites were restricted to a distance separation of 10 km from nearby WSR-88Ds to satisfy the assumption that there were no horizontal inhomogeneities in the wind field over the 10-km separation distance (Powell and Black 1990). VAD horizontal wind profiles associated with the eye and reflectivity gradient on the inner edge of the eyewall were removed to eliminate the influence of curved flow (Giammanco 2010). ASOS 2-min running averages and maximum 3-s gust wind speeds were screened for continuity and outliers were flagged and removed using an approach consistent with Masters et al. (2010).

Vertically binned VAD horizontal wind profiles were manually screened on an event-by-event basis for poor wind estimates, fragmented profiles, and time gaps. Erroneous VAD wind estimates represent poor Fourier and sine fits and were removed to eliminate potential bias in any relationships formed between the two measurement platforms. Fragmented VAD horizontal wind profiles also contribute to potential bias in the VAD layer average wind speeds and were removed. Time gaps identified during VAD analysis periods were removed using a one-dimensional median filter, which ultimately helped remove discontinuities between radar volumes.

## 3. Overland near-surface wind speed estimation

Before comparisons and empirical relationships were formed between the ASOS and VAD wind speed measurements, it was important to first identify what averaging time windows and VAD wind speed measurements could be used to predict the ASOS 10-m standardized mean and nonstandardized maximum 3-s gust wind speeds. The correlation coefficient *R* was used to assess the correlation between ASOS 10-m standardized mean wind speeds, 24-layer average VAD wind speeds, and six moving averaging time windows (defined by 1, 2, 3, 4, 6, and 12 continuous VAD volumes, where one volume takes approximately 5 min to complete on average). As the depth of the VAD layer average wind speed increased, the magnitude of *R* decreased (not shown). Improvements in *R* with respect to increasing the averaging time window were not dramatic. At most sites, the 0–200-m layer average VAD wind speed resulted in the highest *R* compared to individual vertically binned VAD wind speed measurements below 250 m. Since *R* was greater than or equal to 0.83 using a moving averaging time window defined by two continuous VAD volumes, it was determined that the ASOS 10-m standardized mean wind speed averaged over two continuous VAD volumes could be estimated reliably using a VAD 0–200-m layer average wind speed estimate averaged over the same time window.

Powell et al. (2003) argued that the 0–500-m mean boundary layer (MBL) wind speed effectively represented a source of momentum for gusts impacting the surface. To test this hypothesis, VAD 0–500-m MBL wind speeds were computed for each moving averaging time window and were compared against the ASOS 10-m nonstandardized maximum 3-s gust wind speed within each respective averaging time window. As the averaging time window increased, the percentage of ASOS 10-m nonstandardized maximum 3-s gusts that exceeded the VAD 0–500-m MBL wind speed also increased. The result was expected given that the magnitude of the VAD 0–500-m MBL wind speed decreases with an increasing averaging time window. Also, improvements in *R* with respect to increasing the averaging time window were not dramatic. It was determined that the ASOS 10-m nonstandardized maximum 3-s gust wind speed computed over two continuous VAD volumes could be estimated reliably using a VAD 0–500-m MBL wind speed estimate averaged over the same time window.

ASOS 10-m maximum 3-s gusts measured over two continuous VAD volumes were also compared with the maximum wind speed contained in each VAD horizontal wind profile to test the hypothesis offered by Giammanco et al. (2012) and Giammanco et al. (2013) that the VAD maximum wind speed represents the upper bound of the surface gust magnitude. The distribution of the ASOS 10-m nonstandardized maximum 3-s gust-to-VAD maximum wind speed ratios was then examined to determine how often the ASOS 10-m nonstandardized maximum 3-s gusts exceeded the VAD wind maxima (not shown). Based on the distribution of the ASOS 10-m nonstandardized maximum 3-s gust-to-VAD wind maximum wind speed ratios, 0.16% of 3160 ASOS 10-m nonstandardized maximum 3-s gusts measured exceeded the VAD maximum horizontal wind speed. The magnitude of the ASOS 10-m nonstandardized maximum 3-s gust exceedance of the VAD maximum wind speed measured over two continuous VAD volumes ranged from 0.15 to 1.20 m s^{−1}. This result validated the hypothesis put forward by Giammanco et al. (2012) and Giammanco et al. (2013).

### a. Log law

Surface-layer observations in TCs over water have shown that the mean wind varies logarithmically with height in neutral atmospheric boundary layer conditions over a depth of 0–300 m (Franklin et al. 2003; Powell et al. 2003; Vickery et al. 2009; Giammanco et al. 2012; Giammanco et al. 2013). Similarly, over land, the variation of the mean wind through the surface layer of TCs has been described using the log law (Giammanco et al. 2012; Donaher et al. 2013) since mechanically generated turbulence is more pronounced than buoyancy-driven turbulence, due to enhanced cloud cover and faster mean wind speeds. To determine how well the log law predicts the ASOS 10-m standardized mean wind speed averaged over two continuous VAD volumes, averaged VAD wind speed profiles were plotted on a semilog *y* axis. Log-law fits were applied over a 0–300-m depth or through the height of the VAD low-level wind maximum, if it was observed at or below 300 m (Giammanco et al. 2012). Goodness-of-fit statistics were computed for each profile and the mean *R*^{2} was 0.954. Fits that did not explain at least 95% of the variation in the VAD mean wind speed profile fitting depth were disregarded (51.2% of 6029 possible VAD profiles were disregarded). The VAD 10-m mean wind speed was extrapolated from the log-law fits that met the *R*^{2} criteria to evaluate mean wind speed prediction errors (Table 3).

Log-law 10-m standardized mean wind speed prediction error summary statistics listed by landfall event in chronological order.

Based on the error summary statistics provided in Table 3, all of the mean errors are negative, meaning that the log-law-estimated 10-m mean wind speeds are much smaller than the observed ASOS 10-m standardized mean wind speeds. The lowest 10-m mean wind speed average predication errors were associated with KBRO, KBYX, and KLCH, which ranged in magnitude from −15.81 to −1.30 m s^{−1} and qualitatively had smoother surface terrain conditions relative to the other WSR-88D sites evaluated. Thus, the log law is not an appropriate methodology to use to estimate near-surface winds in the TCBL. The results were expected given that the VAD wind speeds were not adjusted to represent a standard exposure, internal boundary layer (IBL) processes were likely buried within the Fourier and sine fits, and VAD wind speed information below 50 m was unavailable (Giammanco et al. 2012; Donaher et al. 2013). When convective rainbands propagated through the VAD annulus or if VAD low-level wind maxima were observed within VAD wind speed profiles, the slope of the surface-layer portion of the VAD horizontal wind profile became flatter compared to the remainder of the profiles. The elevated wind maximum made it difficult for the log law to capture the VAD low-level wind speeds, which Giammanco et al. (2012) postulated could potentially lead to poor estimates of the VAD wind speed in the lowest height bin.

### b. Power law

In contrast to the log law, the power law is an empirical wind profile model that is applicable to all altitudes at and below the gradient wind speed height. The power law also comes in two forms: one representing the mean wind profile and the other the peak wind profile. The only difference between the forms of the power law for computing the mean and peak wind profiles is the reference wind speeds used to compute either a mean or gust power-law exponent. Similar to the log law, when observations are collected at multiple heights AGL, the mean power-law exponent can be estimated by fitting a linear curve to the log–log plot of measurement height versus mean wind speed. To obtain the mean exponent, the inverse of the slope of the log–log plot is computed. Depending on what the underlying exposure is and what height range is being considered, the mean exponent will vary when matched with the log-law profile (Holmes 2007).

The power law was evaluated at each WSR-88D site over the same VAD data collection time period and vertical depths as the log law. Goodness-of-fit statistics were computed for each profile and the mean *R*^{2} was 0.946. Fits that did not explain at least 95% of the variation in the VAD mean wind speed were disregarded. The VAD 10-m mean wind speed was extrapolated from power-law fits that met the *R*^{2} criteria to evaluate mean wind speed prediction errors for each storm and site (Table 4). Based on the error summary statistics provided in Table 4, all of the mean errors are again negative, meaning that the power-law-estimated ASOS 10-m standardized mean wind speeds are much smaller than the observed ASOS 10-m standardized mean wind speeds. However, in comparison to the log-law mean wind speed mean prediction errors in Table 3, the power-law mean wind speed mean prediction errors are much smaller. The smaller mean prediction errors were attributed to not using the friction velocity and roughness length associated with the log-law fit to predict ASOS 10-m standardized mean wind speeds. The lowest mean wind speed prediction errors were again associated with KBRO, KBYX, and KLCH. When convective rainbands propagated through the VAD annulus or if VAD low-level wind maxima were observed, the slope of the power-law profile also became flatter compared to the remaining profiles. Similar reasoning for the log law’s inability to predict the ASOS 10-m standardized mean wind speed also applies to the power law.

Power-law 10-m standardized mean wind speed prediction error summary statistics listed by landfall event in chronological order.

### c. Wind speed ratios

Ratios of surface-to-TCBL lower-tropospheric winds have been used throughout the historical literature to adjust TCBL lower-tropospheric wind speed estimates to represent near-surface wind conditions in TCs both over water (Schwerdt et al. 1979; Batts et al. 1980; Powell 1980; Georgiou 1985; Powell and Black 1990; Vickery et al. 2000a,b; Sparks and Huang 2001; Franklin et al. 2003; Powell et al. 2003, 2005; Kepert 2006a,b; Schwendike and Kepert 2008; Powell et al. 2009; Vickery et al. 2009) and land (Schwerdt et al. 1979; Batts et al. 1980; Georgiou 1985; Dobos et al. 1995; Sparks and Huang 2001; Sparks 2003). A variety of instrument platforms, altitudes, and averaging times have been used to generate WSRs, making it difficult to compare them universally. Thus, unique WSRs were computed using the following wind speed measurements:

ASOS 10-m standardized mean wind speed to the VAD 0–200-m mean wind speed and

ASOS 10-m nonstandardized maximum 3-s gust wind speed to the VAD 0–500-m MBL wind speed.

Normal probability plots for each WSR-88D site were constructed to isolate the influence associated with the effective

WSR-88D site-specific normal probability plots comparing ASOS 10-m standardized mean-to-VAD 0–200-m layer average wind speed ratios to a Gaussian distribution (black dashed line).

Citation: Weather and Forecasting 31, 4; 10.1175/WAF-D-15-0162.1

WSR-88D site-specific normal probability plots comparing ASOS 10-m standardized mean-to-VAD 0–200-m layer average wind speed ratios to a Gaussian distribution (black dashed line).

Citation: Weather and Forecasting 31, 4; 10.1175/WAF-D-15-0162.1

WSR-88D site-specific normal probability plots comparing ASOS 10-m standardized mean-to-VAD 0–200-m layer average wind speed ratios to a Gaussian distribution (black dashed line).

Citation: Weather and Forecasting 31, 4; 10.1175/WAF-D-15-0162.1

ASOS 10-m standardized mean-to-VAD 0–200-m layer average wind speed ratio summary statistics stratified by measurement site.

Using the site-relative mean WSRs, predictions of the ASOS 10-m standardized mean wind speed were made for each TC landfall event. Mean wind speed biases were added back into the mean wind speed predictions before computing the mean wind speed prediction error summary statistics, which are shown in Table 6. The mean wind speed prediction errors were within ±1.5 m s^{−1} with standard deviations less than +2.5 m s^{−1}. Only 5.25% of 5618 ASOS 10-m standardized mean wind speed values fell outside the ±3 m s^{−1} upper bound error associated with the predicted ASOS 10-m standardized mean wind speed estimates (error bound based on VAD residual analysis).

ASOS 10-m standardized mean wind speed prediction error summary statistics for the mean wind speed ratio method. Prediction error summary statistics are listed by landfall event and measurement site in chronological order.

In contrast to the WSR analysis conducted for the ASOS 10-m standardized mean wind speed measurements, normal probability plots were not constructed for ASOS 10-m nonstandardized maximum 3-s gust WSRs, since peak wind speeds are not expected to follow a normal distribution. Also, the gust WSRs were not segregated by measurement site, since the short-duration peak gusts are expected to compare well in variable surface exposure (Masters et al. 2010). Both a normal and logistic probability density function (PDF) were fit to the gust WSR distribution based on a qualitative assessment of the gust WSR distribution, in order to determine the likelihood that a random gust WSR originated from either PDF (Fig. 3). To statistically determine whether or not a gust WSR originated from either a normal or logistic PDF, a one-sample Kolmogorov–Smirnov test was conducted at the 5% significance level. Based on the results of the one-sample Kolmogorov–Smirnov test, a random gust WSR can be modeled using a logistic PDF. The mean and standard deviation of the gust WSRs based on a logistic PDF are 0.7310 and 0.0692, respectively.

Probability histogram of ASOS 10-m nonstandardized maximum 3-s gust-to-VAD 0–500-m MBL wind speed ratios. Normal (light gray) and logistic (dark gray) PDFs are fit to the gust wind speed ratio probability histogram.

Citation: Weather and Forecasting 31, 4; 10.1175/WAF-D-15-0162.1

Probability histogram of ASOS 10-m nonstandardized maximum 3-s gust-to-VAD 0–500-m MBL wind speed ratios. Normal (light gray) and logistic (dark gray) PDFs are fit to the gust wind speed ratio probability histogram.

Citation: Weather and Forecasting 31, 4; 10.1175/WAF-D-15-0162.1

Probability histogram of ASOS 10-m nonstandardized maximum 3-s gust-to-VAD 0–500-m MBL wind speed ratios. Normal (light gray) and logistic (dark gray) PDFs are fit to the gust wind speed ratio probability histogram.

Citation: Weather and Forecasting 31, 4; 10.1175/WAF-D-15-0162.1

The mean gust WSR based on a logistic PDF was used to predict ASOS 10-m nonstandardized maximum 3-s gust wind speeds. A gust wind speed bias of −0.12 m s^{−1} was computed and added back into the gust wind speed predictions before computing prediction error summary statistics. A scatterplot of the predicted versus observed ASOS 10-m nonstandardized maximum 3-s gust wind speeds, as well as the residuals from the best fit are shown in Fig. 4. The mean absolute percentage error (MAPE) was computed to represent the accuracy of the prediction method as a percentage. Based on 2948 estimates of the 0–500-m mean wind speed, the average gust WSR was able to predict the ASOS 10-m nonstandardized maximum 3-s gust wind speed with an accuracy of 15.07%. The residuals appear to be randomly distributed about the zero line; however, as shown in Fig. 2, the tails of the predicted versus observed ASOS 10-m nonstandardized maximum 3-s gust wind speeds are not modeled well using the gust WSR method. Gust wind speed prediction errors for each TC landfall event that had ASOS 10-m nonstandardized maximum 3-s gust wind speed measurements ranged from −1.25 to +3.25 m s^{−1} and the standard deviations were less than +2.85 m s^{−1} (Table 7). The larger mean errors noted for some landfall events in Table 7 are believed to be associated with storm decay effects, storm-relative positional differences, and the lack of inclusion of higher surface gust wind speeds (>30 m s^{−1}) to further interrogate the nonlinear behavior of the gusts.

(top) Scatterplot of predicted vs observed ASOS 10-m nonstandardized maximum 3-s gust wind speeds computed using the gust wind speed ratio method. The black dashed line represents the 1:1 reference line and the red line the linear best fit (*Y* = *mX* + *b*) to the data, respectively, where *Y* and *X* are the predicted and observed ASOS 10-m nonstandardized maximum 3-s gust wind speeds. (bottom) Scatterplot of the residuals from the linear best fit vs the observed ASOS 10-m nonstandardized maximum 3-s gust wind speed about the zero line (red).

Citation: Weather and Forecasting 31, 4; 10.1175/WAF-D-15-0162.1

(top) Scatterplot of predicted vs observed ASOS 10-m nonstandardized maximum 3-s gust wind speeds computed using the gust wind speed ratio method. The black dashed line represents the 1:1 reference line and the red line the linear best fit (*Y* = *mX* + *b*) to the data, respectively, where *Y* and *X* are the predicted and observed ASOS 10-m nonstandardized maximum 3-s gust wind speeds. (bottom) Scatterplot of the residuals from the linear best fit vs the observed ASOS 10-m nonstandardized maximum 3-s gust wind speed about the zero line (red).

Citation: Weather and Forecasting 31, 4; 10.1175/WAF-D-15-0162.1

(top) Scatterplot of predicted vs observed ASOS 10-m nonstandardized maximum 3-s gust wind speeds computed using the gust wind speed ratio method. The black dashed line represents the 1:1 reference line and the red line the linear best fit (*Y* = *mX* + *b*) to the data, respectively, where *Y* and *X* are the predicted and observed ASOS 10-m nonstandardized maximum 3-s gust wind speeds. (bottom) Scatterplot of the residuals from the linear best fit vs the observed ASOS 10-m nonstandardized maximum 3-s gust wind speed about the zero line (red).

Citation: Weather and Forecasting 31, 4; 10.1175/WAF-D-15-0162.1

ASOS 10-m nonstandardized maximum 3-s gust wind speed ratio prediction error summary statistics for the gust wind speed ratio method. Prediction error summary statistics are listed by landfall event and measurement site in chronological order.

### d. Curve fitting with linear regression

WSR-88D site-specific scatterplots of the ASOS 10-m standardized mean wind speed vs VAD 0–200-m layer average wind speed. The red line represents the 1:1 reference line.

Citation: Weather and Forecasting 31, 4; 10.1175/WAF-D-15-0162.1

WSR-88D site-specific scatterplots of the ASOS 10-m standardized mean wind speed vs VAD 0–200-m layer average wind speed. The red line represents the 1:1 reference line.

Citation: Weather and Forecasting 31, 4; 10.1175/WAF-D-15-0162.1

WSR-88D site-specific scatterplots of the ASOS 10-m standardized mean wind speed vs VAD 0–200-m layer average wind speed. The red line represents the 1:1 reference line.

Citation: Weather and Forecasting 31, 4; 10.1175/WAF-D-15-0162.1

Using the scatterplots shown in Fig. 5 to drive which approach was employed to explain the variation in the ASOS 10-m standardized mean wind speed variation based on the ^{−1} and were not factored into the final predicted ASOS 10-m standardized mean wind speed before computing landfall event-specific prediction error summary statistics (Table 10). Based on the mean error wind speed summary statistics in Table 10, mean wind speed errors were within ±1.5 m s^{−1} with standard deviations of less than 1.59 m s^{−1}. Only 2.35% of 5618 ASOS 10-m standardized mean wind speed values fell outside the ±3 m s^{−1} error bound associated with the VAD wind speed measurement.

Goodness-of-fit summary statistics for ASOS–WSR-88D site-specific linear regression. The general form of the measurement-site-specific linear regression equations is *y* = (*p*_{1} × *x*) + *p*_{2}, where *x* is the VAD 0–200-m layer average wind speed, *y* is the ASOS 10-m standardized mean wind speed, and CI is confidence interval

Goodness-of-fit summary statistics for ASOS–WSR-88D second-degree polynomial linear regression. The general form of the second-degree polynomial linear regression equation is *y* = (*p*_{1} × *x*^{2}) + (*p*_{2} × *x*) + *p*_{3}, where *x* is the VAD 0–200-m layer average wind speed, and *y* is the ASOS 10-m standardized mean wind speed.

ASOS 10-m standardized mean wind speed prediction error summary statistics using ASOS–WSR-88D event-specific linear regression equations. Prediction error summary statistics are listed by landfall event and measurement site in chronological order.

An additional sensitivity analysis was carried out to examine how the linear regression coefficients varied with respect to each storm at each ASOS site evaluated in this study. The storm-specific linear regression coefficients and fit statistics are shown in Table 11. In comparison to the WSR-88D site-specific coefficients (excluding KEYW since a second-degree polynomial fit was employed), it is apparent that some storms dominate the site-relative sample. For example, Fay (2008) makes up approximately 82% of the total number of ASOS–VAD comparisons at KJAX. Also of note is that the individual storm regression coefficients tend to fall outside the 95% confidence interval of the WSR-88D site-relative regression coefficients (e.g., TC Gordon 2000 at KJAX), which is likely due to complex IBLs, decay and intensification processes not captured well by the site-relative models, and storm positional sampling differences.

Goodness-of-fit summary statistics for ASOS 10-m standardized mean wind speed vs VAD 0–200-m layer average wind speed storm-specific linear regression. The general form of the storm-specific linear regression equations is *y* = (*p*_{1} × *x*) + *p*_{2}, where *x* is the VAD 0–200-m layer average wind speed, and *y* is the ASOS 10-m standardized mean wind speed.

*m*= 0.8651 [95% confidence interval (0.8510, 0.8792)], and intercept

*b*= −2.5546 [95% confidence interval (−2.8469, −2.2623)]. The linear regression model explained approximately 83% of the variation in the ASOS 10-m nonstandardized maximum 3-s gust wind speed (see Fig. 6). The residuals from the linear regression model appear to be randomly scattered about the zero line in Fig. 6, which lends credence to the choice of model used to predict the ASOS 10-m nonstandardized maximum 3-s gust wind speed.

(top) Scatterplot of predicted vs VAD 0–500-m MBL wind speeds. The dashed black line is the 1:1 reference line and the red line the linear best fit (*Y* = *mX* + *b*) to the data, respectively, where *Y* is the ASOS 10-m nonstandardized maximum 3-s gust wind speed and *X* is the VAD 0–500-m MBL wind speed. (bottom) Scatterplot of the residuals from the linear best fit vs VAD 0–500-m MBL wind speed about the zero line (red).

Citation: Weather and Forecasting 31, 4; 10.1175/WAF-D-15-0162.1

(top) Scatterplot of predicted vs VAD 0–500-m MBL wind speeds. The dashed black line is the 1:1 reference line and the red line the linear best fit (*Y* = *mX* + *b*) to the data, respectively, where *Y* is the ASOS 10-m nonstandardized maximum 3-s gust wind speed and *X* is the VAD 0–500-m MBL wind speed. (bottom) Scatterplot of the residuals from the linear best fit vs VAD 0–500-m MBL wind speed about the zero line (red).

Citation: Weather and Forecasting 31, 4; 10.1175/WAF-D-15-0162.1

(top) Scatterplot of predicted vs VAD 0–500-m MBL wind speeds. The dashed black line is the 1:1 reference line and the red line the linear best fit (*Y* = *mX* + *b*) to the data, respectively, where *Y* is the ASOS 10-m nonstandardized maximum 3-s gust wind speed and *X* is the VAD 0–500-m MBL wind speed. (bottom) Scatterplot of the residuals from the linear best fit vs VAD 0–500-m MBL wind speed about the zero line (red).

Citation: Weather and Forecasting 31, 4; 10.1175/WAF-D-15-0162.1

The mean bias was very close to 0 m s^{−1} in magnitude and was not factored into the final predicted ASOS 10-m nonstandardized maximum 3-s gust wind speed. A scatterplot of the predicted versus observed ASOS 10-m nonstandardized maximum 3-s gust wind speeds was generated (Fig. 7), and the MAPE was computed to determine the accuracy of Eq. (7). In comparison to the gust WSR method, the MAPE for Eq. (7) was 1.07% smaller (14.00%) and explained the same amount of variation (i.e., *R*^{2}) in the ASOS 10-m nonstandardized maximum 3-s gust wind speed as the gust WSR method. TC landfall event-specific ASOS 10-m nonstandardized maximum 3-s gust wind speed prediction error summary statistics were computed in a manner similar to Table 7 and are displayed in Table 12. Based on the gust wind speed prediction error summary statistics, the average gust wind speed errors ranged from −1.59 to +3.37 m s^{−1} with standard deviations less than 2.39 m s^{−1}. The average gust wind speed errors were, in general, larger than those associated with the gust WSR method; however, the standard deviations were smaller for the linear regression method. The standard deviation for the ASOS 10-m nonstandardized maximum 3-s gust wind speed prediction error in most storms is believed to be high because of the large WSR-88D antenna displacement heights, the storm decay/intensification process, and the inclusion of complex IBLs and low-level wind speed maxima that all potentially modulate the low-level portion of the VAD horizontal wind profile.

(top) Scatterplot of predicted vs observed ASOS 10-m nonstandardized maximum 3-s gust wind speeds computed using linear regression. The black dashed line represents the 1:1 reference line and the red line the linear best fit (*Y* = *mX* + *b*) to the data, respectively, where *Y* and *X* are the predicted and observed ASOS 10-m nonstandardized maximum 3-s gust wind speeds. (bottom) Scatterplot of the residuals from the linear best fit vs observed ASOS 10-m nonstandardized maximum 3-s gust wind speed about the zero line (red).

Citation: Weather and Forecasting 31, 4; 10.1175/WAF-D-15-0162.1

(top) Scatterplot of predicted vs observed ASOS 10-m nonstandardized maximum 3-s gust wind speeds computed using linear regression. The black dashed line represents the 1:1 reference line and the red line the linear best fit (*Y* = *mX* + *b*) to the data, respectively, where *Y* and *X* are the predicted and observed ASOS 10-m nonstandardized maximum 3-s gust wind speeds. (bottom) Scatterplot of the residuals from the linear best fit vs observed ASOS 10-m nonstandardized maximum 3-s gust wind speed about the zero line (red).

Citation: Weather and Forecasting 31, 4; 10.1175/WAF-D-15-0162.1

(top) Scatterplot of predicted vs observed ASOS 10-m nonstandardized maximum 3-s gust wind speeds computed using linear regression. The black dashed line represents the 1:1 reference line and the red line the linear best fit (*Y* = *mX* + *b*) to the data, respectively, where *Y* and *X* are the predicted and observed ASOS 10-m nonstandardized maximum 3-s gust wind speeds. (bottom) Scatterplot of the residuals from the linear best fit vs observed ASOS 10-m nonstandardized maximum 3-s gust wind speed about the zero line (red).

Citation: Weather and Forecasting 31, 4; 10.1175/WAF-D-15-0162.1

ASOS 10-m nonstandardized maximum 3-s gust wind speed prediction error summary statistics using linear regression. Prediction error summary statistics are listed by landfall event and measurement site in chronological order.

A similar sensitivity analysis to Table 11 was conducted to examine how the linear regression coefficient for the ASOS 10-m nonstandardized maximum 3-s gust wind speed versus 0–500-m MBL wind speed model varied from storm to storm. Results from the analysis are shown in Table 13. In comparison to the universal regression equation formulated [Eq. (7)], 8 of the 11 storm-specific regression coefficients deviated from the confidence intervals established for the coefficients used in Eq. (7). For example, TC Gustav (2008) at KLIX has a slope value that is 0.2965 larger than the universal slope value and an intercept that is 9.1521 smaller than the universal intercept. Gustav weakened quickly leading up to landfall, and the antenna of the KLIX WSR-88D site sits approximately 55 m AGL. This example is one of several others demonstrating that even though Eq. (7) explains 83% of the variation in the ASOS 10-m nonstandardized maximum 3-s gusts, significant storm-to-storm and site-to-site variability will be exhibited and difficult to account for with a universal model.

Goodness-of-fit summary statistics for ASOS 10-m maximum 3-s gust wind speed vs VAD 0–500-m MBL wind speed storm-specific linear regression. The general form of the storm-specific linear regression equations is *y* = (*p*_{1} × *x*) + *p*_{2}, where *x* is the VAD 0–500-m layer average wind speed, and *y* is the ASOS 10-m nonstandardized maximum 3-s gust wind speed.

## 4. Summary and conclusions

The primary goal of this study was to formulate an appropriate methodology and empirical relationships for estimating overland near-surface wind conditions during landfalling TCs using VAD TCBL lower-tropospheric wind speed measurements. Improvements in surface wind estimation during TC landfalls begin with a keen understanding of the relationship between TCBL lower-tropospheric winds and the near-surface wind field. A refined VAD technique was used to generate VAD horizontal wind profiles in landfalling TCs during the 1995–2012 Atlantic hurricane seasons. VAD horizontal wind profiles from 17 landfalling TCs were matched with available ASOS 10-m wind data that were averaged and standardized to represent either open or marine exposure.

ASOS 10-m nonstandardized maximum 3-s gust wind speeds measured over two continuous VAD volumes rarely exceeded the magnitude of the VAD 0–500-m MBL wind, thus, validating the theory put forth by Powell et al. (2003) that the 0–500-m MBL wind speed represents a source of momentum available for transport to the surface in the form of a gust. Giammanco et al. (2012) hypothesized that the maximum VAD wind speed was likely the upper-bound threshold of the expected gust at the surface. Comparisons of the ASOS 10-m nonstandardized maximum 3-s gust to the maximum VAD wind speed revealed that the former rarely exceeded the maximum VAD wind speed, thus, validating the hypothesis put forward by Giammanco et al. (2012) and Giammanco et al. (2013).

Four methods including the log law, power law, mean/gust WSR method, and curve fitting with linear regression/polynomial fitting were individually evaluated to determine which method most accurately predicted standardized (nonstandardized) ASOS 10-m mean (gust) surface wind conditions in landfalling TCs. Results from the evaluation revealed that both the log- and power-law relationships failed to estimate the ASOS 10-m standardized mean wind speed reliably when assuming neutral atmospheric boundary layer conditions. WSR-88D site-specific regression models with nonzero intercepts explained anywhere from 69% to 97% of the variation in the ASOS 10-m standardized mean wind speed and were more accurate than the log law, power law, and WSRs. The nonzero intercepts in the WSR-88D site-specific regression equations were believed to capture more variation in the ASOS 10-m standardized mean wind speed and isolate the WSR-88D antenna displacement and effective *R*^{2} values associated with the regression equations developed by Dobos et al. (1995) were smaller in magnitude than most of the *R*^{2} values computed in this study.

Despite the larger *R*^{2} values and smaller mean prediction errors, the WSR-88D site-specific regression-based equations developed in this study had limitations. At some sites, one landfall event dominated the wind data used to formulate a regression-based equation. Moreover, some sites sampled a predominant side of the landfalling TCs (i.e., left semicircle). The lack of a large storm sample size and diversity in storm regions sampled validates the need to continue generating VAD wind profiles in future landfalling TCs using the proposed methodology, in order to enhance the established empirical wind speed relationships between ASOS 10-m standardized mean and nonstandardized maximum 3-s gust wind speeds, as well as to formulate new relationships at sites not examined in this study.

Another challenge encountered in this study was how difficult and nearly impossible it was to classify the effective

It was also difficult to assess the sensitivity of the WSR-88D site-specific regression-based equations to changes in storm-relative azimuth and radius, given the 10-km radius-of-influence constraint imposed on each measurement site and the truncated VAD annulus used to generate horizontal wind profiles. One potential avenue for exploring the sensitivity of the WSR-88D site-specific regression-based equations to changes in storm-relative azimuth or radius could involve reconstructing historical landfalling TC wind fields using the Weather Research and Forecasting (WRF) Model. Hundreds of landfall scenarios (and comparison points) at different locations in space could be generated and validated with available historical in situ observations to establish ground truth with the simulated WRF wind fields and examine how well the empirical relationships perform. With more simulated landfall scenarios or additional (realistic) landfalls, changes in the WSR-88D site-specific regression coefficients could be monitored relative to changes in storm-relative azimuth and radius to improve the coefficients generated in this study.

To extend the application of the regression-based models developed in this study to distances farther away from the WSR-88Ds, future studies should focus on the collection of smaller-scale dual-Doppler research radar wind measurements in landfalling TCs over a finer-scale grid of standardized surface wind measurements. The current configuration of the WSR-88D network does not afford the opportunity to conduct meaningful dual-Doppler wind field comparisons with near-surface observations because of the large separation distances between the Doppler radar systems. Mobile research radar measurements could be adjusted using a similar regression-based approach that might lead to the generation of 2D near-surface wind maps in landfalling TCs. The 2D near-surface wind maps could be leveraged for near-real-time use to improve building codes, warnings, and poststorm analyses. Similar work has already been conducted by Kosiba et al. (2013), who mapped 10-m winds during the landfall of Hurricane Rita (2005) by adjusting 2D dual-Doppler wind speeds collected by the Doppler on Wheels (DOWs).

## Acknowledgments

The authors of this study would like to acknowledge Risk Management Solutions and State Farm for providing funding for this research, as well as the National Oceanic and Atmospheric Administration’s NCDC for maintaining and freely offering ASOS and WSR-88D data for use in this study. A special thank you is extended by the authors to Dr. Franklin Lombardo from the University of Illinois at Urbana–Champaign for providing his ASOS roughness length database to conduct standardization and both Mr. Colton Ancell and Mr. Tanli Sun for their assistance in performing quality control of the level-II radial velocity measurements used to generate the VAD wind speed profiles during their undergraduate research experiences at Texas Tech University. Finally, the authors thank the anonymous reviewers for their constructive criticism, which ultimately enhanced the quality of this manuscript.

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