1. Introduction
Periodically issuing estimates of tropical cyclone (TC) intensity is a primary operational requirement for the National Hurricane Center. The intensity of a TC is determined by the maximum sustained surface wind speed, which the National Weather Service (2010) defines as “the highest one-minute average[1] (at an elevation of 10 meters with an unobstructed exposure) associated with a weather system at a particular point in time.” Forecasting this quantity accurately is of paramount importance, since storm-surge predictions that rely on the intensity form the basis for coastal emergency management preparation decisions, including evacuations. In addition, the historical Best Track intensity record (Jarvinen et al. 1984), which has an uncertainty estimated to be ±10% based on currently available observation capabilities (J. Franklin 2010, personal communication), represents a primary metric for assessing both official forecast and numerical model guidance skills. To provide hurricane intensity forecast guidance, the Statistical Hurricane Intensity Prediction Scheme (SHIPS; DeMaria and Kaplan 1994) has been developed from the correlation between the Best Track intensity value and various environmental meteorological parameters. For TC intensity analysis, in particular when aircraft reconnaissance data are not available, the Dvorak technique (Velden et al. 2006) employs a relationship between satellite-based cloud patterns and historic minimum central pressure observations, and then to the maximum surface wind speed through a pressure–wind relationship (e.g., Knaff and Zehr 2007).
Along with the storm center location, the intensity is the most important parameter used to define a TC (OFCM 2007). In contrast to the storm center, the maximum surface wind speed in a well-developed TC is not likely to be found at a definite location but rather broadly embedded somewhere within the eyewall. Theoretical and idealized models provide some insight into the expected (i.e., mean) azimuthal location (e.g., Kepert and Wang 2001; Kepert 2001; Shapiro 1983), but observations indicate that significant variability exists (Powell et al. 2009; Uhlhorn et al. 2007). Furthermore, current observation systems remain limited in their capabilities to simultaneously measure both at the required resolution and over a sufficiently large area to have confidence that the peak wind is directly observed. The two observational tools most utilized for directly measuring surface winds are the GPS dropwindsonde (Hock and Franklin 1999) and, more recently, the stepped-frequency microwave radiometer (Uhlhorn et al. 2007). Each of these instruments measures at highly specific locations relative to the vast spatial extent of the TC circulation.
Because of the limited spatial sampling of surface winds in TCs, forecasters often assume that the observed peak wind speed value is somewhat less than the true peak wind speed in the eyewall (Landsea et al. 2004), and a National Hurricane Center official intensity estimate may be somewhat higher than the highest observed wind over a flight to account for this undersampling. However, to date, the difference between observed winds and the actual peak wind in a TC has not been quantified, because of the very fact that it seems highly unlikely that the true peak wind is ever measured. A recent article by Solow (2010) recognized this observational underestimation of TC intensity as it relates to detecting interannual trends, by randomly sampling a simple analytical model. A practical result of this study was that the maximum observed wind speed could be adjusted to obtain an estimate of the true peak wind by multiplying by the factor (n + 1)/n, where n is the number of observations. However, this purely statistical approach admittedly considered neither realistic observation methods nor details about TC surface wind field structure.
Since direct surface observations with sufficient resolution are relatively scarce because of a number of factors, the only practical tool currently available to help quantify differences between observed surface winds and peak surface wind maxima is a high-resolution numerical model, which borrows from the observing system simulation experiment (OSSE; e.g., Arnold and Dey 1986) concept of a “nature run.” The obvious advantage of using a model is that information is available with sufficient resolution over a large area such that a peak wind speed can be isolated; by “observing” the model wind field, the difference between the absolute peak and observed values can be computed over a broad range of conditions.
A potential drawback of applying this methodology regards a comprehensive lack of understanding about how well peak winds are represented in numerical models. Specific questions about statistical distributions, including gust factors, spatiotemporal averaging characteristics, and qualitative representativeness of the vortex-scale circulation are relevant. Furthermore, there is no universal agreement about which physical processes are dominant at the scales commensurate with these peak winds, since processes at these scales are largely stochastic and remain wholly or partially parameterized. Peak sustained winds are generally regarded as occurring over longer periods (e.g., 1 min) than transient turbulent gusts (e.g., 3 s). However, convective eyewall features can last for several minutes and span over a few kilometers (meso-γ scale), so they may be regarded as an important contribution the maximum sustained wind, even though predicting individual convective events remains highly limited. To address these questions, simulated “observations” can be made from the model and compared with actual observations in a statistical sense to aid in understanding. As part of the work presented herein, we seek to quantify both the spatial and temporal characteristics of wind speeds in a particular numerical simulation and ultimately calibrate the simulated observations to real surface wind data obtained in TCs.
In this study, the numerical model results of Nolan et al. (2009a,b) are utilized to quantify the extent to which observed surface wind maxima underestimate the storm’s actual peak wind. The model output was generated by a 96-h simulation of Hurricane Isabel (2003) during a period when it was particularly well observed by numerous aircraft penetrations during the Office of Naval Research–sponsored Coupled Boundary Layer Air–Sea Transfer (CBLAST) field experiment (Black et al. 2007). As part of their study, Nolan et al. (2009a) analyzed time series of the 10-m wind fields from simulations using 4-, 1.33-, and 0.444-km horizontal resolutions, to determine which of these grid spacings generated winds that were the most consistent with the 1-min average wind speed. They found that at 1.33-km resolution the instantaneous wind was only slightly greater than its 1-min average, exceeding it typically by less than 2%.
In section 2, details about the numerically simulated peak winds are examined, specifically with regard to spatial- and temporal-scale characteristics. Section 3 describes the methodology for drawing simulated wind “observations” from the numerical model, including a statistically based calibration against real wind data. A set of observing system simulation experiments devised to test the undersampling hypothesis is presented in section 4, and section 5 discusses implications for the results.
2. Simulated surface wind fields
a. Model and parameterizations
For this study, synthetically generated observations of surface (10 m) and flight-level winds are obtained from a high-resolution simulation of Hurricane Isabel (2003) (Nolan et al. 2009a,b). This simulation was performed using the Weather Research and Forecasting (WRF) model version 2.2.1 (Skamarock et al. 2005). Briefly, the simulation used nested grids with 12-, 4-, and 1.33-km horizontal resolution; the inner two grids were two-way interactive and moved with the cyclone. Surface stress, fluxes, and 10-m winds were diagnosed with the Yonsei University (YSU) boundary layer scheme (Hong et al. 2006), with a modification of the drag coefficient implemented by Davis et al. (2008) based on the laboratory results of Donelan et al. (2004). Wind fields for the 4-day simulation were saved at hourly intervals, totaling 97 instantaneous snapshots. In addition, for two 30-min periods the surface wind fields were saved every 10 s, equal to the numerical integration time step on the 1.33-km domain.
This particular simulation was validated against numerous observations, such as the estimated peak winds speeds, minimum surface pressures, and detailed observational analyses of the boundary layer both outside and inside the radius of maximum winds (Rmax). To accurately assess TC observation system capabilities, this “nature run” is required to have sufficient resolution to capture small-scale phenomena that are relevant to the observed quantities of interest–—in this case, the maximum 1-min average winds. To this point, Nolan et al. (2009a) showed that the simulation explicitly resolved small-scale features in the eyewall that were responsible for significant variations of the 1-min sustained wind. Nonetheless, turbulent mixing in both the horizontal and vertical directions is highly parameterized, and the extent to which these parameterizations might be representative of smaller-scale features (such as wind gusts) is poorly understood. To assess how accurately this simulation represents extreme winds, statistical distributions of observed versus simulated surface winds within the TC eyewall are examined in a later section.
b. Time-averaging considerations
Any model with a time step shorter than the averaging period over which a peak quantity, such as wind speed, is sought will generally produce peak values greater than the time-averaged quantity. Since it is of interest to assess operationally defined TC intensity in terms of the maximum time-averaged winds, we examine a distribution of peak winds in the eyewall. As previously mentioned, model wind fields at the highest spatial resolution are available at every model time step (δt = 10 s) for two 30-min periods of the full 4-day simulation. The first period begins at 1800 UTC 12 September and the second at 0000 UTC 14 September. In Fig. 1, surface wind speed snapshots are shown at the time of the peak instantaneous wind for each of the two high-frequency output periods, according to three time averages: 0 min (i.e., instantaneous), 1 min, and 10 min. To produce the time-averaged winds, each instantaneous field is first interpolated to a storm-relative grid, and then the 30-min time series at each grid point is filtered by passing the winds through a first-order autoregressive (FOAR) low-pass filter (Merceret 1983), with coefficients chosen to obtain the correct frequency response corresponding to either 1- or 10-min averaging. The filter is applied both forward and backward in time to eliminate phase distortion. Comparison of FOAR filter results with data filtered using a simple running mean indicates that the FOAR filter yields peak values typically ~0.5% greater than using a running mean.
(left column) Instantaneous, (middle column) 1-min averaged, and (right column) 10-min averaged 10-m winds (m s−1) for two periods (top and bottom rows) of simulation in which high-frequency output was generated. Peak values for each field are indicated, and locations are marked by plus signs.
Citation: Monthly Weather Review 140, 3; 10.1175/MWR-D-11-00073.1
(left column) Instantaneous, (middle column) 1-min averaged, and (right column) 10-min averaged 10-m winds (m s−1) for two periods (top and bottom rows) of simulation in which high-frequency output was generated. Peak values for each field are indicated, and locations are marked by plus signs.
Citation: Monthly Weather Review 140, 3; 10.1175/MWR-D-11-00073.1
(left column) Instantaneous, (middle column) 1-min averaged, and (right column) 10-min averaged 10-m winds (m s−1) for two periods (top and bottom rows) of simulation in which high-frequency output was generated. Peak values for each field are indicated, and locations are marked by plus signs.
Citation: Monthly Weather Review 140, 3; 10.1175/MWR-D-11-00073.1
Quantitatively, the peak 1-min averaged wind speed is just slightly weaker than the instantaneous value, and additionally much of the qualitative finescale structure is preserved after filtering, in agreement with the conclusion of Nolan et al. (2009a). This is in contrast to the 10-min averaged winds, which in this example are around 10% less than the instantaneous peak speed, with significant smoothing of small-scale features embedded within the eyewall, although the vortex-scale structure apparently remains intact. In the example shown in Fig. 1, model winds at each time step were interpolated to a common storm-relative grid prior to filtering, but a more realistic representation of observed winds is obtained by interpolating model winds at all time steps to a fixed geographic location, analogous to an anemometer-instrumented tower or buoy. As the model storm translates and evolves, time series sampled at the highest possible frequency (0.1 Hz) are generated from a high-density field of simulated anemometers (Fig. 2). An example 30-min time series is shown in Fig. 3 for a single simulated anemometer placed at the location of the absolute peak model wind speed found during the first of the two high-frequency output periods. One- and 10-min average wind speeds are also shown. The peak instantaneous 10-m wind speed is Ui = 70.0 m s−1, which exceeds the maximum 1-min average wind speed (U1 = 68.7 m s−1) by only 1.9%. The 10-min maximum wind speed (U10 = 62.1 m s−1) is exceeded by 12.7%.
High-density simulated anemometer field and 10-m instantaneous wind speed (m s−1). This snapshot is at the time of maximum wind speed during the first high-frequency model output period, and the location of the peak is indicated by the white dot. The inner (0.8Rmax) and outer (1.2Rmax) rings identify the bounds of the annulus that defines the eyewall.
Citation: Monthly Weather Review 140, 3; 10.1175/MWR-D-11-00073.1
High-density simulated anemometer field and 10-m instantaneous wind speed (m s−1). This snapshot is at the time of maximum wind speed during the first high-frequency model output period, and the location of the peak is indicated by the white dot. The inner (0.8Rmax) and outer (1.2Rmax) rings identify the bounds of the annulus that defines the eyewall.
Citation: Monthly Weather Review 140, 3; 10.1175/MWR-D-11-00073.1
High-density simulated anemometer field and 10-m instantaneous wind speed (m s−1). This snapshot is at the time of maximum wind speed during the first high-frequency model output period, and the location of the peak is indicated by the white dot. The inner (0.8Rmax) and outer (1.2Rmax) rings identify the bounds of the annulus that defines the eyewall.
Citation: Monthly Weather Review 140, 3; 10.1175/MWR-D-11-00073.1
Simulated anemometer wind speed (m s−1) time series for a 30-min period at the gridpoint location of the peak wind identified in Fig. 2. Instantaneous wind speeds every 10 s are shown as black dots; 1- and 10-min averaged time series are plotted in red and blue, respectively.
Citation: Monthly Weather Review 140, 3; 10.1175/MWR-D-11-00073.1
Simulated anemometer wind speed (m s−1) time series for a 30-min period at the gridpoint location of the peak wind identified in Fig. 2. Instantaneous wind speeds every 10 s are shown as black dots; 1- and 10-min averaged time series are plotted in red and blue, respectively.
Citation: Monthly Weather Review 140, 3; 10.1175/MWR-D-11-00073.1
Simulated anemometer wind speed (m s−1) time series for a 30-min period at the gridpoint location of the peak wind identified in Fig. 2. Instantaneous wind speeds every 10 s are shown as black dots; 1- and 10-min averaged time series are plotted in red and blue, respectively.
Citation: Monthly Weather Review 140, 3; 10.1175/MWR-D-11-00073.1
With apparent differences in the simulated peak instantaneous wind speeds and time-averaged values, a method for converting between these quantities is developed. Ideally, an entire simulation should be available at every time step, which could then be appropriately filtered. However, since data storage limitations are currently prohibitive, functional relationships between instantaneous and averaged winds are determined from the two 30-min high-frequency output period samples. These functions are then used to convert the hourly output instantaneous wind maxima to time-averaged values for the entire simulation.
The 1-min maximum gust factor Gi,1 is plotted as a function of maximum instantaneous wind speed in Fig. 4a for all eyewall simulated anemometers. A functional relationship between the peak instantaneous value and maximum averaged value is computed by fitting a power law to the paired data, as shown by the black line in Fig. 4a. There is clear dependence of Gi,1 with increasing Ui, which is contradictory to the observed behavior of traditional gust factors (e.g., relative peak 3-s values), which have been shown to slightly decrease with wind speed (e.g., Vickery and Skerlj 2005; Krayer and Marshall 1992), or are simply taken to be a constant value (Harper et al. 2009). This further highlights the fact that peak values in the model are not generated by turbulence but by some processes that are resolved by the model.
Instantaneous to (a) 1- and (b) 10-min gust factors (Gi,T) plotted as a function of instantaneous wind speed (m s−1, blue crosses). Simulated data are within the eyewall from both high-frequency model output periods. Also shown are binned averages over 5 m s−1 bandwidths (red) and power-law best-fit regression (black).
Citation: Monthly Weather Review 140, 3; 10.1175/MWR-D-11-00073.1
Instantaneous to (a) 1- and (b) 10-min gust factors (Gi,T) plotted as a function of instantaneous wind speed (m s−1, blue crosses). Simulated data are within the eyewall from both high-frequency model output periods. Also shown are binned averages over 5 m s−1 bandwidths (red) and power-law best-fit regression (black).
Citation: Monthly Weather Review 140, 3; 10.1175/MWR-D-11-00073.1
Instantaneous to (a) 1- and (b) 10-min gust factors (Gi,T) plotted as a function of instantaneous wind speed (m s−1, blue crosses). Simulated data are within the eyewall from both high-frequency model output periods. Also shown are binned averages over 5 m s−1 bandwidths (red) and power-law best-fit regression (black).
Citation: Monthly Weather Review 140, 3; 10.1175/MWR-D-11-00073.1
The 10-min maximum wind speed gust factor Gi,10 versus Ui is shown in Fig. 4b. Average values at the highest wind speeds are found to be ~12%, again, with a strong wind speed dependence. By solving these expressions for the peak instantaneous wind speed, a peak 10- to 1-min wind speed relationship (U10/U1) is found to vary between 1 at 30 m s−1 and 0.9 at 70 m s−1. For comparison, Harper et al. (2009) recommends a constant 1- to 10-min maximum wind speed conversion of 0.93 for “at-sea” situations; this is the average ratio found here at ~64 m s−1. These 1- and 10-min gust-factor relationships are applied to model instantaneous wind maxima to convert to properly time-averaged values in the experiments performed herein. Note that these functions are not to be interpreted as universal conversion factors but simply represent a model-dependent calibration that should be required of any high-resolution model designed for operational TC intensity prediction.
c. Spatial resolution
Recent attention has been given to the simulated TC intensity response to changes in model resolution (Fierro et al. 2009; Rotunno et al. 2009; Nolan et al. 2009a,b; Hill and Lackmann 2009; Davis et al. 2008; Yau et al. 2004; Persing and Montgomery 2003; Braun and Tao 2000). Generally, as model grid spacing is decreased, finer-scale flow features are permissible, including details about convective processes. With a broader spectrum of motions explicitly resolved, the wind speed variance increases, and therefore a higher peak wind can be simulated. As an alternative, in a mesoscale model in which the effects of turbulent-scale motions are parameterized, a turbulent mixing-length scale parameter may be decreased, resulting in the same practical consequence that the simulated maximum wind speed is increased. As described by the 2D axisymmetric simulations of Bryan and Rotunno (2009), in which sensitivity to this parameter was examined, the frontal structure of the eyewall becomes less diffuse with decreased mixing-length scale, resulting in a stronger gradient. Further decrease of the assumed value may render the flow approximately inviscid, possibly resulting in unrealistically high peak wind speeds and unphysical model behavior.
Since we are primarily interested in a peak wind speed, it is required that any such model be of sufficient spatial scale to resolve the peak wind. Numerical simulations at coarse resolution (e.g., currently run global models) do not contain sufficiently strong horizontal gradients necessary for producing peak winds at the required scale, while extremely high resolutions (e.g., of the large-eddy simulation type) contain 3D eddies with attendant high-frequency fluctuations that must be filtered. A strict numerical limit for the maximum wind speed at a given horizontal Cartesian grid spacing Δ and time step δt can be found for the Courant–Friedrichs–Lewy criterion (Umax ≤ Δ/δt), but, as pointed out by Skamarock (2004), the effective model resolution is typically several times more coarse because of diffusion, either explicitly represented or implied by the numerical discretization method. The large-eddy simulation model results of Rotunno et al. (2009) found that the maximum 1-min averaged wind speed on the finest-scale grid (Δ = 62 m) lay in between the peak instantaneous winds found at Δ = 1.7 and Δ = 0.6 km resolution grids, in practical agreement with the conclusions of Nolan et al. (2009a).
d. Fourier decomposition and spatiotemporal relationships
For each hourly snapshot, wind fields are reconstructed by summing components zero through wavenumber m, and the corresponding peak wind speed is normalized by the averaged (1 or 10 min) peak wind speed of the fully composed field. As the wind field is resolved to higher wavenumbers, the peak wind speed should be expected to increase. From the 97 fields, a mean and standard deviation of peak-to-peak ratio is computed as a function of wavenumber truncation, normalized by the cutoff wavenumber computed for the field [Eq. (2)].
As shown in Fig. 5, on average, the wavenumber m = 0 azimuthal mean is 83% ± 6% of the peak 1-min average wind speed. Additionally, it is found that the peak value is fully resolved on average at m = 0.43mc, with a one-standard-deviation variation between 0.20mc and 0.56mc. Considering now the peak 10-min wind speed, the axisymmetric mean wind speed is 88% ± 6% of the maximum, and peak value is resolved at only m = 0.03mc, on average, demonstrating the large difference in spatial scale between these two operational standard quantities. Statistically, in approximately 67% of the 97 snapshots, the 10-min peak wind speed is resolved at 0.1mc. Dimensionally, for a mean Rmax = 47 km, the 1-min peak wind is fully resolved at azimuthal-wavenumber 34, while the 10-min peak wind speed is fully resolved at wavenumber 3, or greater than an order-of-magnitude difference in spatial scale.
Ratio of maximum wind speed from field truncated at wavenumber m to maximum 1-min wind speed for the fully resolved field, as a function of wavenumber normalized by the maximum wavenumber determined by Rmax. Mean (solid lines) and standard deviation (dashed lines) are computed from all 97 instantaneous hourly output wind fields.
Citation: Monthly Weather Review 140, 3; 10.1175/MWR-D-11-00073.1
Ratio of maximum wind speed from field truncated at wavenumber m to maximum 1-min wind speed for the fully resolved field, as a function of wavenumber normalized by the maximum wavenumber determined by Rmax. Mean (solid lines) and standard deviation (dashed lines) are computed from all 97 instantaneous hourly output wind fields.
Citation: Monthly Weather Review 140, 3; 10.1175/MWR-D-11-00073.1
Ratio of maximum wind speed from field truncated at wavenumber m to maximum 1-min wind speed for the fully resolved field, as a function of wavenumber normalized by the maximum wavenumber determined by Rmax. Mean (solid lines) and standard deviation (dashed lines) are computed from all 97 instantaneous hourly output wind fields.
Citation: Monthly Weather Review 140, 3; 10.1175/MWR-D-11-00073.1
3. Simulated wind observations
a. Aircraft flight pattern
To assess potential differences between observed and actual TC peak surface wind speeds, simulated observations are drawn from the numerical model described in section 2. Of particular interest are aircraft-based observations from a stepped-frequency microwave radiometer (SFMR), which is now installed on all National Oceanic and Atmospheric Administration (NOAA) WP-3D (Aberson et al. 2006) and Air Force Reserve Command WC-130J hurricane-penetrating aircraft (details available online at http://www.hurricanehunters.com/plane.html). Along with GPS dropwindsondes, the SFMR has become a primary operational tool for measuring TC surface winds and, together with observations from other data sources, may be used for analyzing storm intensity.
The typical hurricane aircraft operational reconnaissance mission contains an in-storm pattern plus transit to and from the base of operations. In well-developed TCs, the pattern is flown at the 700-mb level (~3.1-km altitude), consisting of a “figure four” (or “alpha”), which may be repeated depending on aircraft range limitations. Radial legs extend 105 n mi (196 km) from storm center, and at an aircraft ground speed of 230 kt (~120 m s−1), the in-storm pattern takes around 2.5 h to complete. The virtual flight patterns simulated here are designed to replicate this (while ignoring the transit to/from the storm), totaling four eyewall penetrations over the course of a mission. For simulation purposes, the highest wind speed value found during a flight represents the maximum observed surface wind speed. As an example, Fig. 6 shows a simulated figure-four flight track over the surface wind field, in which the aircraft enters the pattern southwest of the storm center (225° azimuth clockwise from north) and terminates southeast of center (135° azimuth). Thus, flight legs that connect radial endpoints are flown in a downwind direction. Note that the simulated wind field is not stationary over the time period of a flight but is assumed to evolve linearly between hourly instantaneous snapshots. Higher frequencies of model output—up to the rate of model integration time step–could theoretically be used. But, since the eyewall is penetrated only four times in around 2.5 h, the maximum wind along a radial leg cannot be observed at a higher frequency; therefore, simply interpolating between hourly wind fields appears adequate for purposes of simulating observed eyewall winds.
Single figure-four (or alpha) flight pattern superimposed on a surface wind field snapshot (m s−1). Aircraft symbols identify initial and final points of the pattern.
Citation: Monthly Weather Review 140, 3; 10.1175/MWR-D-11-00073.1
Single figure-four (or alpha) flight pattern superimposed on a surface wind field snapshot (m s−1). Aircraft symbols identify initial and final points of the pattern.
Citation: Monthly Weather Review 140, 3; 10.1175/MWR-D-11-00073.1
Single figure-four (or alpha) flight pattern superimposed on a surface wind field snapshot (m s−1). Aircraft symbols identify initial and final points of the pattern.
Citation: Monthly Weather Review 140, 3; 10.1175/MWR-D-11-00073.1
b. SFMR footprint averaging
The SFMR (Uhlhorn et al. 2007) measures nadir-incidence brightness temperature at six C-band channels, from which surface wind speed and path-integrated rain rate are retrieved via least squares inversion using a geophysical model. Radiation is collected over a finite area that depends inversely on both antenna size and electromagnetic frequency. For the SFMR antenna’s diameter, the half-power (−3 dB) beamwidth (HPBW) varies from 20°–28° from the highest-to-lowest (7.1–4.7 GHz) frequency channels. At the operational flight altitude, the mean HPBW footprint projected onto the sea surface is ~1.3 km in diameter (Fig. 7a).
(a) SFMR antenna pattern at the sea surface from an operational flight altitude of 3.1 km for each channel and mean frequency; and (b) SFMR footprint for the mean frequency projected onto the model surface wind field (m s−1). In (b), crosses are at locations separated by a distance equivalent to 10 s along the flight track. Half-power and 1% power footprints are indicated by solid and dashed circles, respectively. Wind vector arrows begin at every grid point on the inner domain (1.33 km).
Citation: Monthly Weather Review 140, 3; 10.1175/MWR-D-11-00073.1
(a) SFMR antenna pattern at the sea surface from an operational flight altitude of 3.1 km for each channel and mean frequency; and (b) SFMR footprint for the mean frequency projected onto the model surface wind field (m s−1). In (b), crosses are at locations separated by a distance equivalent to 10 s along the flight track. Half-power and 1% power footprints are indicated by solid and dashed circles, respectively. Wind vector arrows begin at every grid point on the inner domain (1.33 km).
Citation: Monthly Weather Review 140, 3; 10.1175/MWR-D-11-00073.1
(a) SFMR antenna pattern at the sea surface from an operational flight altitude of 3.1 km for each channel and mean frequency; and (b) SFMR footprint for the mean frequency projected onto the model surface wind field (m s−1). In (b), crosses are at locations separated by a distance equivalent to 10 s along the flight track. Half-power and 1% power footprints are indicated by solid and dashed circles, respectively. Wind vector arrows begin at every grid point on the inner domain (1.33 km).
Citation: Monthly Weather Review 140, 3; 10.1175/MWR-D-11-00073.1
The normalized power of the antenna pattern determines the weighting of surface wind speed at model grid points within a radial distance from the nadir point equivalent to 1% of the peak power at the mean SFMR frequency (~2.8 km diametrically as indicated by Fig. 7a). Grid points outside the 1% equivalent radial distance are excluded, so a single simulated SFMR “observation” is composed of a weighted average of approximately 3–5 model grid point wind speed values (Fig. 7b). Real SFMR wind speeds are available once per second, and, according to operational practice, 10 s of data are averaged along the flight track to produce a wind speed equivalent to a 1-min average value at a fixed point by considering the relationship between aircraft sampling volume and averaging period (Powell et al. 1991). A 10-s phase-preserving FOAR filter is applied to the simulated 1-Hz measurements in order to replicate this quantity. Comparisons with results computed using a simple moving-average filter, as is typically applied for operations, indicate negligible difference. The single SFMR “observed” wind speed therefore consists of a temporally and spatially weighted average of 7–9 model grid point values.
c. Flight-level winds
Although not a direct measure of TC surface winds, flight-level wind speeds have nevertheless assumed a prominent role as a tool for estimating surface wind speeds through use of extrapolation methods (e.g., Powell et al. 2009; Franklin et al. 2003). That these measurements have been documented to a far greater extent than direct surface observations makes them a solid basis for evaluating simulated TC structure, at least above the boundary layer. Synthetic flight-level winds from simulated flights are obtained by sampling from the full 4D numerical model wind field.
At each simulated aircraft “time step” (1 s), the two-dimensional horizontal wind field at 700 mb is computed by linear time interpolation between hourly numerical model snapshots and linear vertical interpolation between adjacent model “pressure-sigma” surfaces. The flight-level wind speed at the aircraft location is then simply computed by horizontal bilinear interpolation. As for the simulated SFMR surface wind speeds, a 10-s low-pass filter is applied to the 1-Hz wind measurements. A time series of simulated flight-level and SFMR surface wind speeds for a single mission consisting of two figure-four patterns (hence, eight eyewall penetrations) is shown in Fig. 8. A qualitative comparison between surface and flight-level wind speeds indicates that several commonly observed features are well represented in the numerical model: the peak surface wind speed in the eyewall is typically 80%–90% of the peak value at the 700-mb flight level along the same radial (Powell et al. 2009); the surface peak is generally displaced radially inward of the peak flight-level location, indicative of eyewall tilt (Stern and Nolan 2009); and surface–to–flight-level wind speed ratios at Rmax vary azimuthally around the eyewall, which indicates that asymmetries at the surface and flight level are not in phase (Powell et al. 2009; Rogers and Uhlhorn 2008; Kepert and Wang 2001). One artifact of note, however, is a discontinuity found outside the eyewall, which corresponds to the transition between inner and intermediate nests, an example of which is identified by the arrow in Fig. 8. Because these discontinuities are found outside the eyewall and away from peak wind speed locations, they are of little concern for this work.
Time series of simulated flight-level (blue) and SFMR surface (red) wind speeds (m s−1) for a single flight. The arrow identifies an example of the resulting discontinuity between the inner and intermediate grid nests.
Citation: Monthly Weather Review 140, 3; 10.1175/MWR-D-11-00073.1
Time series of simulated flight-level (blue) and SFMR surface (red) wind speeds (m s−1) for a single flight. The arrow identifies an example of the resulting discontinuity between the inner and intermediate grid nests.
Citation: Monthly Weather Review 140, 3; 10.1175/MWR-D-11-00073.1
Time series of simulated flight-level (blue) and SFMR surface (red) wind speeds (m s−1) for a single flight. The arrow identifies an example of the resulting discontinuity between the inner and intermediate grid nests.
Citation: Monthly Weather Review 140, 3; 10.1175/MWR-D-11-00073.1
d. Calibration against real observations
While many qualitative features of tropical cyclones appear well captured in high-resolution simulations, it remains an outstanding question whether the most intense winds are accurately represented. Since the 10-m wind exists within the boundary layer where turbulent fluxes dominate, parameterization of these processes will impact the simulated winds. With the far-reaching implications for forecasting intensity, it is imperative to understand how well numerical models represent maximum winds. Unfortunately, high-frequency, near-surface wind observations in extreme winds in an unobstructed marine environment remain relatively rare because of the obvious difficulties in obtaining data in these conditions. However, an extensive database of SFMR surface wind speeds can be compared with model-simulated winds to help understand their respective statistical distributions. Differences in the model distributions from those observed are then corrected by matching to the distributions of real surface wind observations. As a result, simulated surface wind observations are statistically similar to real SFMR surface winds and can be directly compared to model wind maxima in our experiments with a high degree of confidence.
From 12 yr (1998–2010) of observations from NOAA WP-3D missions in which SFMR surface wind data were obtained, the highest wind speeds for each radial pass through a particular storm’s eyewall are found. As an example, observed SFMR surface winds U from NOAA flights in Hurricane Isabel (2003) and Hurricane Rita (2005) are plotted as a function of storm motion direction-relative azimuth angle (Fig. 9). The Isabel flight consisted of a single figure-four pattern, while the flight in Rita contained repeated figure fours. Using a single (repeated) figure-four pattern, the highest wind speed was found for each of four (eight) eyewall penetrations, and from these measurements, the mean plus wavenumber-1 asymmetric wind speed (Um=0+1) is estimated using least squares regression. This low-wavenumber reference is chosen since it is the highest unambiguously resolved azimuthal structure observed using a figure-four pattern. Wind speed anomalies U′ are computed by subtracting the harmonic fit from observed maxima along each radial. Only cases in which the observed highest wind speed was >32 m s−1 are considered, totaling 117 flights. Single figure-four and repeated figure-four cases are examined separately.
Real observed peak SFMR surface wind speeds (m s−1) as a function of storm motion direction-relative azimuth angle for each radial pass through the eyewall of Hurricanes (a) Isabel on 13 Sep 2003 and (b) Rita on 22 Sep 2005. Also shown are mean plus wavenumber-1 asymmetry (Um=0+1) fit to the observations via least squares. In (a), a figure-four pattern was flown to provide four highest winds in the eyewall, and in (b), a repeated figure-four pattern was flown, yielding eight measurements.
Citation: Monthly Weather Review 140, 3; 10.1175/MWR-D-11-00073.1
Real observed peak SFMR surface wind speeds (m s−1) as a function of storm motion direction-relative azimuth angle for each radial pass through the eyewall of Hurricanes (a) Isabel on 13 Sep 2003 and (b) Rita on 22 Sep 2005. Also shown are mean plus wavenumber-1 asymmetry (Um=0+1) fit to the observations via least squares. In (a), a figure-four pattern was flown to provide four highest winds in the eyewall, and in (b), a repeated figure-four pattern was flown, yielding eight measurements.
Citation: Monthly Weather Review 140, 3; 10.1175/MWR-D-11-00073.1
Real observed peak SFMR surface wind speeds (m s−1) as a function of storm motion direction-relative azimuth angle for each radial pass through the eyewall of Hurricanes (a) Isabel on 13 Sep 2003 and (b) Rita on 22 Sep 2005. Also shown are mean plus wavenumber-1 asymmetry (Um=0+1) fit to the observations via least squares. In (a), a figure-four pattern was flown to provide four highest winds in the eyewall, and in (b), a repeated figure-four pattern was flown, yielding eight measurements.
Citation: Monthly Weather Review 140, 3; 10.1175/MWR-D-11-00073.1
This methodology is extended to the model-simulated “observations”. Figure 10 shows histograms of wind speed anomalies U′ as defined above for real SFMR observations (Figs. 10a,c), simulated SFMR observations (Figs. 10b,d), and cumulative distributions of these anomalies (Figs. 10c,f). Clearly the model-simulated wind observations overall provide a reasonable statistical representation of the distribution of SFMR winds, especially for the single figure-four cases, where a two-sided Kolmogorov–Smirnov (K–S) test (Massey 1951) of the distributions indicates no significant difference. Some differences are found for the repeated figure-four cases, and in Fig. 10f we find a divergence in the cumulative distribution functions (CDFs) at the spectral tails (|U′| > 2.5 m s−1). The simulated wind anomalies are apparently more narrowly distributed as compared to the real SFMR surface wind data, and a method for correcting this difference is developed.
Histograms of (a),(d) SFMR-observed and (b),(e) SFMR simulated wind speed anomalies (m s−1), and (c),(f) cumulative distributions of anomalies. (a)–(c) Single figure-four patterns; (d)–(f) repeated figure-four patterns. Anomalies (U′) are defined as maximum winds speeds along each radial minus the mean plus wavenumber-1 asymmetry (U − Um=0+1) for an individual flight. In (a),(b),(d), and (f), dashed lines are Gaussian distributions for the indicated sample standard deviations.
Citation: Monthly Weather Review 140, 3; 10.1175/MWR-D-11-00073.1
Histograms of (a),(d) SFMR-observed and (b),(e) SFMR simulated wind speed anomalies (m s−1), and (c),(f) cumulative distributions of anomalies. (a)–(c) Single figure-four patterns; (d)–(f) repeated figure-four patterns. Anomalies (U′) are defined as maximum winds speeds along each radial minus the mean plus wavenumber-1 asymmetry (U − Um=0+1) for an individual flight. In (a),(b),(d), and (f), dashed lines are Gaussian distributions for the indicated sample standard deviations.
Citation: Monthly Weather Review 140, 3; 10.1175/MWR-D-11-00073.1
Histograms of (a),(d) SFMR-observed and (b),(e) SFMR simulated wind speed anomalies (m s−1), and (c),(f) cumulative distributions of anomalies. (a)–(c) Single figure-four patterns; (d)–(f) repeated figure-four patterns. Anomalies (U′) are defined as maximum winds speeds along each radial minus the mean plus wavenumber-1 asymmetry (U − Um=0+1) for an individual flight. In (a),(b),(d), and (f), dashed lines are Gaussian distributions for the indicated sample standard deviations.
Citation: Monthly Weather Review 140, 3; 10.1175/MWR-D-11-00073.1
We focus exclusively on the repeated figure-four observations and simulations in the following. To isolate the positive portion of the histogram tail, only anomalies at the maximum observed wind speed 
(a)–(c) Same as Figs. 10d–f, but only for the anomaly at the maximum observed wind speed value (m s−1) over a single flight.
Citation: Monthly Weather Review 140, 3; 10.1175/MWR-D-11-00073.1
(a)–(c) Same as Figs. 10d–f, but only for the anomaly at the maximum observed wind speed value (m s−1) over a single flight.
Citation: Monthly Weather Review 140, 3; 10.1175/MWR-D-11-00073.1
(a)–(c) Same as Figs. 10d–f, but only for the anomaly at the maximum observed wind speed value (m s−1) over a single flight.
Citation: Monthly Weather Review 140, 3; 10.1175/MWR-D-11-00073.1
Matched probabilities for simulated vs observed maximum SFMR wind speed anomalies (m s−1) for repeated figure-four flights. Quantile levels are from 5% to 95%, in 5% increments. Also shown is a linear best-fit regression line, which is applied to correct simulated surface wind observation maxima.
Citation: Monthly Weather Review 140, 3; 10.1175/MWR-D-11-00073.1
Matched probabilities for simulated vs observed maximum SFMR wind speed anomalies (m s−1) for repeated figure-four flights. Quantile levels are from 5% to 95%, in 5% increments. Also shown is a linear best-fit regression line, which is applied to correct simulated surface wind observation maxima.
Citation: Monthly Weather Review 140, 3; 10.1175/MWR-D-11-00073.1
Matched probabilities for simulated vs observed maximum SFMR wind speed anomalies (m s−1) for repeated figure-four flights. Quantile levels are from 5% to 95%, in 5% increments. Also shown is a linear best-fit regression line, which is applied to correct simulated surface wind observation maxima.
Citation: Monthly Weather Review 140, 3; 10.1175/MWR-D-11-00073.1
To summarize, calibrating simulated surface wind observations for our experiments is performed as follows: 1) for each simulated flight, the highest wind U along each radial leg is found; 2) the mean plus wavenumber-1 asymmetry (Um=0+1) is fit to these wind maxima; 3) the anomaly at the highest observed wind 
4. Experiments
a. Figure-four control experiment
To test the hypothesis that observed and true TC peak surface winds differ, maximum simulated SFMR surface wind speeds are found for each flight and compared to the maximum model wind speed anywhere in the storm. A control experiment is designed to simulate, insofar as possible, standard operational hurricane reconnaissance missions. As described in section 3, a standard mission contains a single figure-four pattern that flies along orthogonal tracks, radially inbound and outbound from the storm center. This pattern may be repeated on a single flight if range limitations allow.
A simulated pattern begins at an initial point located 105 n mi (196 km) radially from the storm center and at a cardinal (N, S, E, or W) or ordinal (NE, SE, SW, NW) azimuth. The radial leg proceeds inbound toward the moving storm center and outbound to a point on the opposite side of the storm. The aircraft then flies to a point 90° and 105 n mi downwind, and turns toward the center for a second radial traverse across the storm. An aircraft ground speed of 230 kt (~120 m s−1) is assumed, which is roughly typical for both the WP-3D and WC-130J aircraft, and a pattern takes around 2.5 h to complete. Storm-center fixes are tied to 6-h synoptic times (0000, 0600, 1200, 1800 UTC), so the simulated in-storm pattern begins 1.25 h before each synoptic time. Over the 4-day period of the numerical model simulation, 15 individual missions are executed.
Because the pattern orientation depends primarily on the relative location of storm to the aircraft base, the initial point may vary. Since the peak wind speed location is not stationary, it is impossible to know a priori how to orient the pattern to optimize observations. To simulate the variability in the highest wind speed measurement due to this uncertainty, a single pattern is initiated at eight equally spaced azimuth angles around the storm (0°–315° in 45° increments). The resulting highest wind observation representing a single flight is the average of the eight highest values, with attendant 95% confidence limits on the mean. As each of the 15 missions is repeated eight times, the control experiment consists of a total of 15 × 8 = 120 simulated flights.
For each of the 97 one-hourly surface wind fields, the peak value is found and converted to a maximum 1-min average using the function in Fig. 4a, plotted as a time series by the solid red line in Fig. 13. Notice that early in the simulation, there is an artifact balance-adjustment period that results in relatively large fluctuations in the peak 1-min wind speed. An approximate Best Track intensity is indicated by a 6-h running mean of the model’s peak 1-min wind speed (blue line in Fig. 13). Since we are comparing simulated maximum-wind observations with the 6-h running mean of the peak 1-min wind that filters these large initial wind speed variations, this model artifact does not appear to influence results. For each flight, a maximum “observed” wind speed is found (Fig. 13, green line) and compared to the model 1-min averaged peak wind speed at the time of observation.
Figure-four pattern control experiment results, plotted as wind speed (m s−1) time series over the full 96-h simulation period. Red curve is maximum model value at each hour, blue curve is a running 6-h average, green curve is maximum (mean and 95% confidence interval) “observed” wind speed for each simulated flight, and black curve is maximum of eight simulated flights initiated at the same time but at varying azimuths. The large variations in peak 1-min wind speed early in the simulation period are a result of model spinup and adjustment.
Citation: Monthly Weather Review 140, 3; 10.1175/MWR-D-11-00073.1
Figure-four pattern control experiment results, plotted as wind speed (m s−1) time series over the full 96-h simulation period. Red curve is maximum model value at each hour, blue curve is a running 6-h average, green curve is maximum (mean and 95% confidence interval) “observed” wind speed for each simulated flight, and black curve is maximum of eight simulated flights initiated at the same time but at varying azimuths. The large variations in peak 1-min wind speed early in the simulation period are a result of model spinup and adjustment.
Citation: Monthly Weather Review 140, 3; 10.1175/MWR-D-11-00073.1
Figure-four pattern control experiment results, plotted as wind speed (m s−1) time series over the full 96-h simulation period. Red curve is maximum model value at each hour, blue curve is a running 6-h average, green curve is maximum (mean and 95% confidence interval) “observed” wind speed for each simulated flight, and black curve is maximum of eight simulated flights initiated at the same time but at varying azimuths. The large variations in peak 1-min wind speed early in the simulation period are a result of model spinup and adjustment.
Citation: Monthly Weather Review 140, 3; 10.1175/MWR-D-11-00073.1
The highest “observed” wind speed is found to be, with 95% confidence, 8.5% ± 1.5% (5.5 ± 0.9 m s−1) weaker than the maximum 1-min averaged wind speed, suggesting that the sampling pattern is highly unlikely to encounter the storm’s peak winds. Under the most favorable juxtaposition of flight pattern and peak wind locations, the best (i.e., minimum) expected underestimate is 3.7% ± 1.5%, which has a ⅛ (12.5%) probability of occurring on any single flight, as indicated by the black line in Fig. 13. Over the entire simulation, these highest “observed” winds are not found to equal or exceed the 6-h running mean of the maximum 1-min wind in any case.
b. Repeated figure-four experiment
As previously discussed, a single figure-four flight pattern may be repeated if aircraft range limitations are not prohibitive. After completing the first figure-four, the aircraft then proceeds to a point 90° downwind and executes a second figure-four pattern with radials along the same azimuths as the first full pattern, although not in the same chronological sequence. This pattern takes around 5.6 h to complete and penetrates the eyewall eight times over a flight. Based on the argument by Solow (2010), more observations of winds in the eyewall suggest the potential for decreasing the difference between the highest observed wind and the maximum 1-min wind anywhere in the storm. Based on the calibration procedure developed in section 3d, the highest simulated wind found for a single flight is slightly adjusted to account for distribution bias relative to actual surface wind observations. As for the control experiment, each pattern is initiated at eight azimuths around the storm to yield statistics.
Compared to a running mean of the maximum 1-min wind, the highest wind observed over a mission is 7.8% ± 1.2% weaker, which is only slightly lower than for the single figure-four experiment, and this difference is not statistically significant. Also, 2 out of the 120 total simulated missions (1.7%) find the highest wind equal to or greater than a 6-h running mean of the peak 1-min wind. Though the number of wind observations in the eyewall over a single flight has increased by repeating the pattern, the storm’s evolution over the flight period apparently diminishes the impact that adding observations might have if the storm were perfectly steady over the same period.
c. Rotated figure-four experiment
Though not standard operational reconnaissance practice, often NOAA WP-3D research flights will fly a modified “rotated figure-four” pattern, in which the second figure four is flown rotated 45° downwind of the first. As opposed to the repeated figure four, eight different radials from the storm center are sampled, with a corresponding factor-of-2 increase in azimuthal resolution and a potentially smaller underestimate relative to the maximum wind in the storm based on the results in Fig. 5. However, since a storm is constantly (and possibly rapidly) evolving, it is not sampled synoptically, so it is not clear that this enhanced resolution yields an improvement in the low bias found for the repeated figure-four case.
The rotated figure-four pattern experiment is otherwise identical to the control, as it consists of the same 120 simulated flights, with only the second of two figure-fours modified (Fig. 14). Compared to the repeated figure-four control experiment flights, these flights are of slightly less duration because of the shorter downwind leg when rotating. Experimental results indicate only marginal difference from the standard operational single figure-four pattern, with the mean underestimate of the 1-min maximum wind reduced by only 0.6% to 7.2% ± 0.9%. Also, the best possible underestimate, due to the aircraft fortuitously intercepting a greater wind, is now 2.6% ± 1.5%. There are other observationally based motivations for flying such a modified pattern (e.g., enhancing Doppler radar–derived 3D wind coverage), but it is not apparent that such an advantage exists for SFMR-derived surface wind measurements. On the other hand, fortunately this pattern apparently does not further worsen the underestimate. Additionally, for operational purposes, highest observed winds from two concurrent flights each using a different flight pattern should not be expected to differ significantly.
Example rotated figure-four experimental flight pattern superimposed on surface wind field (m s−1). Aircraft symbols identify initial and final points of the pattern.
Citation: Monthly Weather Review 140, 3; 10.1175/MWR-D-11-00073.1
Example rotated figure-four experimental flight pattern superimposed on surface wind field (m s−1). Aircraft symbols identify initial and final points of the pattern.
Citation: Monthly Weather Review 140, 3; 10.1175/MWR-D-11-00073.1
Example rotated figure-four experimental flight pattern superimposed on surface wind field (m s−1). Aircraft symbols identify initial and final points of the pattern.
Citation: Monthly Weather Review 140, 3; 10.1175/MWR-D-11-00073.1
d. 10-min peak wind
The World Meteorological Organization has adopted a 10-min peak wind for defining TC intensity, and most of the world’s operational forecast centers outside of the United States adhere to this reference. In this context, the 1-min sustained wind speed may be interpreted as a gust, while the 10-min mean wind is more representative of the vortex-scale circulation, as it represents a correspondingly larger spatial scale, as demonstrated in section 2. Figure 4b showed the relationship between model peak wind speeds and 10-min mean wind speeds from simulated anemometer records. The functional relationship is applied to the peak winds at each hourly snapshot for comparison with the highest “observed” surface winds from the simulated single figure-four control experiment. Peak model surface wind speed values, which are between 60 and 70 m s−1 over the simulated period, are reduced by 6%–12% to equivalent 10-min maximum winds.
Figure 15 shows the wind time series for the control experiment, but in this case compared to maximum 10-min wind speeds. The broader spatial azimuthal scale represented by the 10-min wind is reflected in the results here, which indicate that the average underestimate relative to the maximum wind is now only 1.5% ± 1.7% and is therefore not signficantly different. The maximum-of-maximum observed surface wind [with ⅛ (12.5%) probability of measuring] exceeds the 10-min value, with an average overestimate of 3.6% ± 1.6%. Based on these results, the highest observed wind over a reconnaissance mission would not appear to require much adjustment to arrive at a maximum 10-min value. Perhaps more importantly, the azimuthal wind structure at Rmax responsible for supporting the peak 10-min wind is apparently sufficiently resolved with this sampling methodology.
As in Fig. 13, but for 10-min peak wind speeds (m s−1).
Citation: Monthly Weather Review 140, 3; 10.1175/MWR-D-11-00073.1
As in Fig. 13, but for 10-min peak wind speeds (m s−1).
Citation: Monthly Weather Review 140, 3; 10.1175/MWR-D-11-00073.1
As in Fig. 13, but for 10-min peak wind speeds (m s−1).
Citation: Monthly Weather Review 140, 3; 10.1175/MWR-D-11-00073.1
Table 1 summarizes experimental results in terms of percentage underestimate of the maximum wind.
Summary statistics for the simulation experiments. Averaging period (min) is for the maximum sustained wind anywhere in the storm. Underestimates are differences (%) between the highest observed and maximum sustained surface wind speeds. Minimum underestimate has a 12.5% probability of occurrence.
e. Probability of experiencing peak winds
Based on the simulation experiments performed here it is evident that the peak 1-min maximum surface wind speed is excessively difficult to observe, even with targeted platforms such as reconnaissance aircraft. Because of this limitation, we ask how this peak wind generally relates to winds throughout the entire eyewall. One answer to this question could be provided by examining the likelihood of a location within the eyewall actually experiencing some percentage of this maximum wind speed.
For each of the 97 hourly surface wind fields, the cumulative distribution of relative peak winds in the eyewall is computed to estimate how much of the eyewall area (annulus between 0.8 and 1.2Rmax) experiences some percentage of the maximum 1- or 10-min surface wind speed. From all snapshots, means and standard deviations of wind speeds normalized by the peak value are computed. Both the 1- and 10-min peak wind speed are considered (Fig. 16). Based on these distributions, only around 5% of the eyewall experiences winds greater than 90% of the peak 1-min value, on average. Expressed in dimensional terms, if the maximum 1-min wind speed is 70 m s−1, the wind speed over 95% of the eyewall is not be expected to exceed 63 m s−1. For the 10-min wind, around 15%–20% of the eyewall experiences winds greater than 90% of the peak value, while the instantaneous wind speed exceeds the peak 10-min wind for only about 2% of the eyewall area. Statistically, in only 2.5% of the cases (i.e., +2σ) is the maximum instantaneous wind speed at least 20% greater than the peak 10-min value.
Cumulative distribution of simulated eyewall instantaneous wind speeds normalized by peak 1-min (red) and 10-min (black) averaged wind speeds. Means (solid lines) and standard deviations (dashed lines) are computed from the 97 hourly surface wind fields.
Citation: Monthly Weather Review 140, 3; 10.1175/MWR-D-11-00073.1
Cumulative distribution of simulated eyewall instantaneous wind speeds normalized by peak 1-min (red) and 10-min (black) averaged wind speeds. Means (solid lines) and standard deviations (dashed lines) are computed from the 97 hourly surface wind fields.
Citation: Monthly Weather Review 140, 3; 10.1175/MWR-D-11-00073.1
Cumulative distribution of simulated eyewall instantaneous wind speeds normalized by peak 1-min (red) and 10-min (black) averaged wind speeds. Means (solid lines) and standard deviations (dashed lines) are computed from the 97 hourly surface wind fields.
Citation: Monthly Weather Review 140, 3; 10.1175/MWR-D-11-00073.1
5. Conclusions
The experimental results here suggest that the maximum observed surface wind measured by an SFMR-equipped aircraft typically underestimates the TC maximum 1-min sustained wind speed. For a major hurricane, such as the Isabel case examined here, this difference is around 7%–10%, on average. This result, subject to the ability of the model to simulate real surface wind speed features corresponding to the proper time and space scales, supports the operational practice that assumes that the maximum surface wind is rarely directly observed, implying that an increase over the highest observed wind speed is necessary to accurately estimate the maximum 1-min sustained wind and, therefore, TC intensity.
A novel procedure for calibrating a model simulation to proper temporal averages and statistical distributions of observed TC peak winds has been developed. The methodology consists of converting instantaneous winds within the eyewall to averaged maximum values by low-pass filtering simulated high-frequency anemometer time series and, second, matching statistical distributions of simulated and observed surface wind data. These specific relationships could only be expected to hold for an identical combination of model options, as changes to one or several of these options would result in a different relationship; for example, increasing the horizontal mixing-length scale would expectedly weaken the model’s peak wind speed. Such calibration should be required of any numerical model designed to simulate a TC’s intensity in order to both provide operationally consistent intensity estimates, as well as make meaningful model intercomparisons.
TC intensity prediction is evolving to a point where high-resolution numerical models will be increasingly utilized when making operational forecasts. Recently, the question about predictability of flow at convective scales (order kilometers) was addressed by Nguyen et al. (2008), who concluded that there is a degree of randomness that renders any single prediction of the maximum wind speed at such scales highly uncertain. From an ensemble of high-resolution simulations, the ensemble mean was shown to smooth large instantaneous excursions in the simulated maximum wind speed. In essence, the operational TC intensity analysis process allows for similar smoothing of these high-frequency oscillations by considering data simultaneously from various observational sources (occasionally described as a “blend”). With the large number of model configurations now available (resolution, physics, initializations, coupling, etc.), it is imperative that details about how models behave at these scales be thoroughly understood before making substantial use of them.
The tropical cyclone Best Track database contains the official historical intensity record and therefore represents the definitive metric for evaluating numerical forecast guidance accuracy. Best Track intensity analyses are also subjective combinations of observations from possibly several sources and have an associated uncertainty that is estimated to be ±10% based on currently available observation capabilities (J. Franklin 2010, personal communication). These errors should be considered when assessing numerical TC intensity predictions, as it is unreasonable to expect a model forecast to be more accurate. Future work should involve comparing numerical intensity predictions as derived from various simulated data sources in a consistent, calibrated, spatiotemporal framework.
Acknowledgments
The authors thank Drs. Frank Marks, Altug Aksoy, and Mark Powell, who provided insightful comments on preliminary versions of the manuscript. Mark Powell’s suggestions regarding gust-factor interpretation have been particularly helpful. In addition, Specialists at the National Hurricane Center have provided both motivation and highly valuable feedback during the course of this project, and we thank NHC Hurricane Specialist Unit Branch Chief James Franklin for providing a thorough review of the article. Special thanks to Brad Klotz for processing of recent SFMR wind data. Finally, we thank two anonymous reviewers for their helpful comments and suggestions to improve the manuscript. D. Nolan was supported in part by the National Ocean and Atmospheric Administration through a grant to the Cooperative Institute for Marine and Atmospheric Studies at the University of Miami.
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We interpret this to imply that the terms “sustained” and “averaged” are interchangeable, and therefore should be taken as such throughout this article.
Nevertheless, the term “gust factor” has entered the wind engineering and meteorological vernacular, whether or not the wind measurements consist primarily of turbulence. Based on the discussion in Harper et al. (2009), the highest 1-min wind speed relative to a 10-min wind speed is considered a “gust,” even though the 1-min wind may filter much of the turbulent fluctuations.
