Estimation and Mapping of Hurricane Turbulent Energy Using ...

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MONTHLY WEATHER REVIEW

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Estimation and Mapping of Hurricane Turbulent Energy Using Airborne Doppler Measurements SYLVIE LORSOLO AND JUN A. ZHANG Cooperative Institute for Marine and Atmospheric Studies, Rosenstiel School of Marine and Atmospheric Science, University of Miami, Miami, Florida

FRANK MARKS JR. AND JOHN GAMACHE Hurricane Research Division, NOAA/AOML, Miami, Florida (Manuscript received 3 August 2009, in final form 13 November 2009) ABSTRACT Hurricane turbulent kinetic energy (TKE) was computed using airborne Doppler measurements from the NOAA WP-3D tail radars, and TKE data were retrieved for a variety of storms at different stages of their life cycle. The geometry of the radar analysis coupled with the relatively small beam resolution at ranges ,8 km allowed for the estimation of subkilometer turbulent processes. Two-dimensional profiles of TKE were constructed and revealed that the strongest turbulence was generally located in convective regions, such as the eyewall, with magnitudes often exceeding 15 m2 s22 and in the boundary layer with values of 5–10 m2 s22 in the lowest kilometer. A correlation analysis showed that the strong turbulence was generally associated with strong horizontal shear of vertical and radial wind components in the eyewall and strong vertical shear of horizontal wind in the boundary layer. Mean vertical profiles of TKE decrease sharply above the hurricane boundary layer and level off at low magnitude for all regions outside the radius of maximum wind. The quality of the retrieval method was evaluated and showed very good agreement with TKE values directly calculated from the three-dimensional wind components of in situ measurements. The method presented here provides a unique opportunity to assess hurricane turbulence throughout the storm, especially in high-wind regions, and can be applied on extensive datasets of past and future airborne hurricane penetrations.

1. Introduction One of the main challenges of hurricane research is to better understand the processes that influence hurricane intensity change that could ultimately lead to improved intensity forecasts. Among the various parameters believed to affect hurricane intensity change are air–sea interaction and turbulent energy transport within the hurricane boundary layer (HBL; Malkus and Riehl 1960; Emanuel 1986, 1995). Because turbulent kinetic energy (TKE) is directly related to the energy transport through the boundary layer (BL; Stull 1988), it is important to better estimate TKE and the TKE budget, which will help identify the HBL processes that generate turbulence and affect hurricane intensity.

Corresponding author address: Sylvie Lorsolo, NOAA/AOML, 4301 Rickenbacker Causeway, Miami, FL 33149-1097. E-mail: [email protected] DOI: 10.1175/2010MWR3183.1 Ó 2010 American Meteorological Society

In numerical weather prediction models, the aforementioned factors affecting hurricane intensity are represented by BL parameterization, which has significant impacts on model results (e.g., Anthes and Chang 1978; Braun and Tao 2000; Moon et al. 2007). Among the various parameterization schemes, TKE closure schemes have been used for BL studies (e.g., Holt and Raman 1988) and were found to have advantages for mesoscale models (e.g., Huang and Raman 1991). More and more hurricane modeling studies are including TKE schemes based on the formulation of Mellor and Yamada (1982), where TKE and dissipation rate are prognostic variables, increasing the necessity of an accurate estimation of these turbulent parameters. Studies are conducted to evaluate numerical intensity forecasts, BL parameterization, and reasons for inaccuracies (e.g., Braun and Tao 2000; Hill and Lackmann 2009); one of the reasons often stated is the lack of observational turbulence data hindering the understanding of the physical processes for better BL parameterization.

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To remedy the BL parameterization problem and to better understand the turbulent processes at play, more observations are needed. Comprehensive observational datasets are critical to evaluate the different turbulent parameters of the TKE scheme output, such as TKE and dissipation rate and diffusivity. Field projects focusing on hurricane low-level turbulence have been of crucial importance for many years. An early study from Merceret (1976) examined turbulent microstructures of Hurricane Caroline (1975), providing valuable turbulence data in the HBL. One of the findings of the Merceret (1976) study was able to establish that below cloud base, the horizontal wind field at small scales is inertial and that the dissipation rate is log-normally distributed. Later, Moss (1978) conducted research using observational data to study the turbulent properties of the HBL and compared them with results from the Deardoff parameterization scheme. More recently, in an effort to obtain more observational data in the HBL, Powell et al. (2003) gathered and analyzed data from 331 dropsonde profiles, providing unprecedented drag coefficient data for a better surface layer parameterization. From 2002 to 2004, the Coupled Boundary Layers Air–Sea Transfer (CBLAST) experiment (Black et al. 2007) acquired very low-level HBL data to improve our understanding of HBL turbulence and provided unique flux measurements in hurricane conditions (French et al. 2007; Drennan et al. 2007; Zhang et al. 2008). Although these measurements have helped improve our understanding of hurricane turbulence, datasets are still quite limited and not available in extreme wind situations (.30 m s21). Moreover, the available in situ data are point measurements and do not allow for a more global assessment of turbulent energy throughout the storm. Among issues not well understood about the HBL turbulent flow are the role and the importance of organized turbulent eddies in the HBL. Numerous studies have shown the existence of various small-scale turbulent features (Zhang et al. 2008; Lorsolo et al. 2008; Morrison et al. 2005; Gall et al. 1998; Wurman and Winslow 1998) and have argued a potential impact of these turbulent processes on vertical fluxes and therefore hurricane intensity change (Zhang et al. 2008; Zhu 2008; Foster 2005; Morrison et al. 2005). Zhang et al. (2008) was able to document the enhanced surface fluxes caused by HBL eddies using observational studies. However, given the small dataset available and the location of the measurements (rain-free environment and relatively low wind ,30 m s21), there are still a lot of uncertainties concerning the impact of these features on hurricane intensity change, prompting a need for more observational data of hurricane turbulence. The spatial limitation and the difficulty in acquiring direct measurement of HBL

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turbulence have led to the investigation of other means to study low-level turbulence. Doppler radar measurements have been increasingly used to study hurricane structure, as they generally provide data over a large portion of the storms. For more than 25 years, airborne radars have collected valuable data in the outskirts as well as in the inner core of tropical storms (e.g., Jorgensen et al. 1983; Marks 2003). Onboard the National Oceanic and Atmospheric Administration (NOAA) WP-3D aircraft, the tail (TA) Doppler radar has been able to record reflectivity and wind data and has allowed for the retrieval of the full three-dimensional wind field of numerous hurricanes (Marks and Houze 1984, 1987; Marks et al. 1992). The implementations of the fore–aft scanning technique (FAST; Gamache et al. 1995; Jorgensen et al. 1996) and new variational (Gamache 1997; Reasor et al. 2009) and automatic retrieval methods (available online at http://www.nhc.noaa.gov/jht/20032005reports/DOPLRgamache_JHTfinalreport.pdf) have enabled the retrieval of very accurate high-resolution wind data throughout hurricanes. Comparison of the retrieved winds with in situ data has shown very good agreement and was used for in-depth studies of mesoscale phenomena within hurricanes (Marks et al. 1992; Gamache et al. 1995; Reasor et al. 2000, 2005, 2009). Reasor et al. (2009) utilized a new variational method to retrieve high-resolution winds and was able to resolve mesoscale and convective-scale processes. Aberson et al. (2006) showed that radar data analyzed using this method could resolve some characteristics associated with smallscale features embedded in the three-dimensional eyewall circulation. Extending the use of airborne Doppler measurements to estimate hurricane turbulent energy could provide a unique opportunity to map turbulence throughout tropical cyclones. Lothon et al. (2005) successfully retrieved turbulent parameters using airborne Doppler measurements in a drizzling marine boundary layer, using a W-band radar with two pointing angles and the aircraft flying circle legs at multiple altitudes. Although the NOAA tail radar is X band and the aircraft track is at a fixed altitude on a relatively straight path, various look angles provided by FAST strategy along with the high resolution of the beam and the subsequent analysis make the Doppler data from hurricane penetrations an appealing candidate for turbulent energy estimation. The objective of this study is to introduce a new method to assess the distribution of the turbulent energy in a hurricane using airborne Doppler measurements. This unique method will not only allow the investigation of turbulence through a tropical cyclone, including the HBL in extreme winds, but also, given the appropriate resolution, could help clarify the impact that features

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such as HBL linear features or mesovortices have on turbulent energy and energy transport. Moreover, this method would help provide valuable turbulence data in the upper levels, which are very important to optimize higher-altitude flights, such as those conducted by the NOAA G-IV that can encounter turbulence (Rogers et al. 2002).

2. Methodology Data from both NOAA WP-3D TA radars were used for this study. For decades the NOAA TA radars have been collecting Doppler measurements during hurricane penetrations, and a large dataset is thus available for comprehensive studies using radar measurements (Lee et al. 2003; Marks 2003). Both TA instruments are X-band radars and have overall similar characteristics (Jorgensen et al. 1983; Lee et al. 2003), although the antenna mechanisms are different (Gamache et al. 1995). All the data utilized here were collected using the FAST strategy with the same settings and therefore generally have the same resolution. The range resolution was set at 150 m, and the cross-scan and along-scan half-power beamwidth are 1.358 and 1.98, respectively. Gamache et al. (1995) stated early in their paper that FAST was inappropriate for radial penetrations, although in their

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conclusions they clarify that hurricane radial penetrations using FAST should produce analyses with nearly equivalent accuracies to downwind penetrations, except for gaps resulting from rapid changes in aircraft heading within the eyewall. The larger temporal evolution required by a single plane flying two perpendicular flight legs results in much higher errors than incorporating FAST into one single radial leg. By allowing the two aircraft to be launched in alternating missions around the clock, the use of the one-aircraft FAST has greatly increased the frequency with which the hurricane core can be probed, resulting in many more cases for this study. After removing the aircraft motion, the Doppler radial velocities Vr are a combination of all three components of the wind, defined as follows: V r 5 u sinb cosu 1 y cosb cosu 1 (w 1 V t ) sinu, (1) where u, y, and w are the wind components; Vt is the mean terminal fall velocity; and b and u are the earthrelative azimuthal and elevation angles, respectively. All angle conversions follow the method described by Lee et al. (1994). Given that Reynolds averaging (Stull 1988) allows each component of the wind to be expressed as the sum of a mean and turbulent part, (1) can be rewritten as

V r 5 [u sinb cosu 1 y cosb cosu 1 (w 1 V t ) sinu] 1 [u9sinb cosu 1 y9cosb cosu 1 (w9 1 V9t ) sinu], (I) (II)

where the overbar and prime variables represent the mean and turbulent parts, respectively. It is assumed that (I) is the mean Doppler radial velocity V r and (II) represents the turbulent part of the Doppler radial velocity V9r. Analysis of the variation of Vt showed root-mean-square (rms) values ,1 m s21; therefore, the turbulent component of the terminal fall velocity was considered negligible. Since the mean TKE is defined as TKE 5 0.5(u92 1 y92 1 w92 ) and V9r is a combination of the turbulent components of the wind, it is hypothesized that the mean squared perturbation V9r 2 over a grid cell containing various Doppler measurements is a good approximation of the TKE. The TKE can then be estimated as the variance s2V about the r mean of all the Vr within the grid cell as follows: s2V 5 R

1 1 (V V R )2 5 V 92 . N Overgrid cell R N Overgrid cell R

å

å

(3)

To estimate s2V for a given grid cell, the three mean r components of the wind have to be retrieved first. The

(2)

retrieval of the mean wind components is done using Gamache’s analysis method described in the appendix of Reasor et al. (2009). The algorithm is similar to a method of Gao et al. (1999) to retrieve the three-dimensional wind from a dual-Doppler array. Data from the aft and fore scans are treated as if generated by two independent radars. The method is a variational analysis aiming at simultaneously minimizing the following: 1) the difference between the projection of wind analysis on the Doppler radials and the original Doppler radial velocities; 2) the three-dimensional mass divergence (analestic approximation); 3) the second derivative in all three directions, as well as cross derivatives; (this is a smoother and should be given a relatively low weight); and 4) the difference between vertical wind at vertical boundaries and wind-analysis vertical wind. A full description of the method is given in Reasor et al. (2009).

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FIG. 1. Description of the radar-retrieved TKE method.

Here, instead of a three-dimensional domain, the analysis was performed on a two-dimensional domain along the flight track, from grid cells with a dimension of 10 km 3 1.5 km 3 0.15 km, azimuthally around the storm center, radially and vertically, respectively, as shown in Fig. 1a. One of the advantages of such an analysis is that it provides finer resolution in the vertical and radial directions, with the lowest measurement located at 150 m above sea level. Moreover, because of the large amount of radial velocity estimates in a single grid cell (.100) obtained along sufficiently independent lines of sight, the use of the anelastic continuity equation is not needed for an accurate retrieval of the three components of precipitation velocity. Elimination of this constraint limits errors introduced by the mass continuity equation through setting arbitrary boundary conditions at echo top (Jorgensen et al. 1996). Once the mean wind components are retrieved, the wind vector is then projected onto each radial velocity

measurement contained in each grid cell that entered the radar wind analysis, providing V r (az) for each azimuthal direction. This V r (az) is then subtracted from the original Doppler radial velocity measurement Vr(az) to obtain a perturbation radial velocity V9r(az). The mean V r92 is the estimated TKE contained in each grid cell. Figure 1b and (3) depict the basics of the calculation. The choice of the gridcell size of 10 km 3 1.5 km 3 0.15 km was dictated by the radar beam resolution (,350 m at 10-km range and ,175 m at 5-km range from the radar) and by the scales of the processes that need to be resolved. The geometry of the grid cells was chosen in an effort to provide a finer vertical and radial resolution while allowing enough independent estimates to be included in the wind analysis algorithm. To provide a representative mean, the choice of the 10-km crosstrack dimension was also governed by the data coverage. A smaller size would considerably limit both the vertical and the horizontal data coverage of the analyzed field.

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TABLE 1. Data processed and included in the present study. Hurricane

Center time and date

Leg

Katrina

1755 UTC 28 Aug 2005 1926 UTC 28 Aug 2005 2038 UTC 28 Aug 2005 2231 UTC 28 Aug 2005 1601 UTC 20 Sep 2005 1518 UTC 21 Sep 2005 1601 UTC 21 Sep 2005 1913 UTC 22 Sep 2005 1911 UTC 23 Sep 2005 2147 UTC 23 Sep 2005 1719 UTC 12 Sep 2003 1901 UTC 12 Sep 2003 1940 UTC 12 Sep 2003 1827 UTC 14 Sep 2003 2131 UTC 14 Sep 2003 1459 UTC 16 Sep 2003 1707 UTC 1 Sep 2004 1829 UTC 1 Sep 2004 1952 UTC 1 Sep 2004 1826 UTC 3 Sep 2004 1720 UTC 3 Sep 2003

KL1 KL2 KL3 KL4 RL1 RL2 RL3 RL4 RL5 RL6 IL1 IL2 IL3 IL4 IL5 IL6 FL1 FL2 FL3 F4 FAL1

Rita

Isabel

Frances

Fabian

For the TKE data to be meaningful, it is crucial that the method resolve turbulence associated with relevant scales of the energy spectrum. The vertical and horizontal beamwidths along with the 150-m-range bin resolution were able to provide sufficient radial and vertical

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resolution and TKE estimates over sample volumes of the order of 3 3 106 m3 at 10-km range. One of the main issues of the algorithm is that the automatic quality control algorithm tends to eliminate potentially useful data. Another issue is the presence at times of unusually high TKE values (.100 m2 s22) around the flight level, at the edges of the vertical profiles, and at the top of the profiles where the lack of reflectors affected the Doppler measurements and subsequently the radar analysis. Thus, a subsequent thresholding was implemented based on the mean of the perturbations V9r . The theory being the Reynolds-averaging approach states that V9r 5 0. Because the precipitation–motion problem is solved in a least squares sense, deviations of the data from being normally distributed will lead to a mean perturbation V9r 6¼ 0. TKE computed on grid cells for which V9r . 2 m s21 were discarded. The threshold value was set based on previous studies exhibiting rms values of approximately 2–3 m s21 for both analyzed data (Reasor et al. 2009) and radial measurements (Gamache et al. 1995). Data from Hurricanes Isabel (2003), Fabian (2003), Frances (2004), Katrina (2005), and Rita (2005) at various stages of their development were included in this study. Table 1 provides details on the dataset used. The data presented here are from both radars and a total of 20 legs were processed. Only data acquired during radial

FIG. 2. Horizontal cross section of reflectivity at 3 km MSL for Hurricane Katrina (KL1 in Table 1). The black line represents the flight track during this period.

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penetrations were processed as the automatic data quality control, and the dealiasing algorithm can only be performed when data are centered on the storm center position, resulting in the processing of only inbound or outbound legs. The algorithm was applied to the various storms, and the TKE data were mapped on twodimensional vertical profiles. Negative values on the abscissa are relative to the outbound leg, while positive values refer to the inbound leg.

3. Results a. TKE estimation Figure 2 displays a horizontal cross section of reflectivity from Hurricane Katrina (KL1 in Table 1), providing an overall perspective of the storm structure during the penetration. Figure 3 presents vertical profiles of reflectivity, tangential wind, radial wind, vertical wind, and TKE fields for Hurricane Katrina for the period presented in Fig. 2. The analysis shows that Hurricane Katrina had a well-defined eyewall similar to those seen in earlier studies (Jorgensen 1984; Marks 1985; Dodge et al. 1999; Marks and Houze 1987; Black et al. 1996) with relatively strong reflectivity in the eyewall. The radial and tangential wind fields exhibit the strongest winds in the eyewall of the inbound leg and a well-established inflow layer below 1 km on both inbound and outbound legs. As found in earlier studies (Marks and Houze 1987; Black et al. 1996; Dodge et al. 1999), the vertical wind field shows sharp horizontal gradients on the inner and outer edges of the eyewall. The TKE profile clearly depicts the highest TKE values in the eyewall region, with magnitudes up to 22 m2 s22. Aside from the eyewall, strong TKE values are located in the lowest levels in the HBL and in other relatively strong reflectivity areas as shown in Figs. 3a and 3e at ;80 km from the center on the inbound leg. Elsewhere, TKE values are ,1 m2 s22. Notice also that the strongest TKE values are located in the outbound eyewall, even though it does not exhibit the strongest winds. The analysis of all the cases shows that the correlation with horizontal and vertical gradients of vertical and radial winds was the highest, with correlation coefficients greater than 0.5, and in numerous instances exceeding 0.7. The TKE behavior displayed in Fig. 3e is common for all the analyzed legs, with magnitudes of TKE higher than 15 m2 s22 in the eyewall region in all cases. Twodimensional histograms of TKE in the annuli relative to the maximum wind (RMW) for all cases were created. For each profile the RMW was computed at each height. Figure 4 presents the contoured-frequency-by-altitude diagrams (CFADs; Yuter and Houze 1995) for TKE: (a) inside the RMW, (b) from the RMW to 20 out, 20–40,

FIG. 3. Two-dimensional profiles of (a) reflectivity (dBZ), (b) tangential wind (m s21), (c) radial wind (m s21), (d) vertical wind (m s21), and (e) TKE (m2 s22) for Hurricane Katrina (KL1 in Table 1). The cyan line indicates the position of the RMW.

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FIG. 4. Two-dimensional histograms (a) inside the RMW, (b) 20 km, (c) 20–40 km, (d) 40–60 km, and (e) 60–80 km outside the RMW for all cases.

40–60, and 60–80 km outside of RMW, respectively. Near the RMW (Figs. 4a and 4b), the distribution shows .30% of TKE values .10 m2 s22, with more than 8% with values greater than 15 m2 s22 in the HBL (less than 700 m). Further outside of the RMW, there are still a large amount of high TKE values in the HBL. More than 35% of TKE values are .5 m2 s22 in the HBL. Above the HBL, the TKE values decrease with distance from the RMW, with .40% of the TKE values ,1 m2 s22. The eyewall area is the only region with high TKE data above the HBL.

This method of estimating TKE is very effective in identifying localized enhanced turbulence. In Fig. 5a, for instance, the TKE field depicts quite well the double eyewall structure that Hurricane Rita was exhibiting at the time, with values in the outer eyewall as high as 15 m2 s22. The TKE estimates were able to clearly identify the most turbulent region of the outbound leg and showed that although the inner eyewall on the outbound leg was still stronger in terms of wind speed (Fig. 5b), the turbulence was not as active as in the new developing eyewall. In this case, the TKE was correlated with the

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FIG. 5. Two-dimensional profiles of (a) TKE (m2 s22) and (b) tangential wind (m s21) for Hurricane Rita (RL4 in Table 1).

high horizontal gradient of vertical wind because of a relatively strong updraft (not shown). Another example can be seen in Fig. 6a. The higher TKE values in Hurricane Isabel between 60 and 80 km in the inbound leg and above 6 km altitude seem to be related to ;6-km wavelength features identifiable in the vertical wind field (Fig. 6b). The features seem to display regular oscillation between updrafts and downdrafts of rather marginal intensity (6;2 m s21), which results in high TKE values (.10 m2 s22). Further investigation of these features should be conducted to identify their origin and nature. The results discussed in this section were generalized and presented in Fig. 7, which depicts the mean R–Z cross section of TKE for all considered legs, scaled by the RMW. In general the most turbulent regions are inside the RMW and in the HBL, with a well-defined structure for the HBL and a sharp decrease of TKE above. The largest mean TKE value has a magnitude of ;16 m2 s22 and is located in the inner edge of the RMW. There are some relative TKE maxima likely associated with convective features in the outer region of the storms. The two TKE maxima inside the RMW are essentially due to Hurricane Isabel, which displayed the strongest TKE in the HBL. Because in most cases there were little data in this area, high TKE estimates from

Hurricane Isabel represent most of the data in the area, hence producing the maxima. Given the TKE distribution (Figs. 4 and 7) and the strong correlation values found with gradients of radial and vertical wind, a simple conceptual model is proposed (Fig. 8). In Fig. 8, the strongest turbulence represented by the red rotating arrows is located inside the RMW, where strong horizontal shear is present because of the eyewall circulation. The other area displaying relatively strong turbulence (green rotating arrows) exists in the BL, where highly sheared regions are caused by strong vertical gradient in the radial flow. The schematic shows that hurricane turbulence is in general concentrated in specific areas of a storm (eyewall, HBL, and localized strong reflectivity areas) and is quite low elsewhere. It is anticipated that a more refined model can be developed in the future, accounting for TKE dissipation and providing better understanding of energy generation and dissipation in a storm.

b. Evaluation of the method of estimation of TKE Estimation of turbulence using Doppler measurements is potentially quite valuable in assessing turbulence over extended portions of the storms. However, more importantly, it would allow for investigation of the turbulence in the lowest portions of the storm even in

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FIG. 6. Two-dimensional profiles of (a) TKE and (b) vertical wind for Hurricane Isabel (IL2).

extreme wind speed, which has not been possible to achieve with in situ measurements. To use the TKE information in a more quantitative way, it is essential to evaluate the quality of the retrieved TKE. Qualitatively, analysis of the TKE two-dimensional profiles and the vertical mean profiles displaying higher TKE values in

highly sheared and convective regions indicates that the method provide a reasonable estimation of the TKE distribution throughout the storm. Comparison of the different profiles at different periods of a particular storm showed that the TKE retrieval was good at depicting variation in turbulence during an eyewall replacement

FIG. 7. The R–Z mean cross section of TKE for all cases, scaled on RMW.

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FIG. 8. Simple conceptual model of TKE behavior in a hurricane with respect to location.

or localized increases of turbulence not necessarily obvious from the wind or reflectivity fields (Figs. 5 and 6). However, a more quantitative assessment of the method is necessary, as the TKE computation does not include the full spectrum of the turbulent components of the wind. Thus, it is likely that the TKE could be an underestimate. Furthermore, another challenge of conducting such an analysis is to estimate the effect of the size of the swath used to retrieve the wind. The apparent averaging time is a function of the width of the analysis domain and the magnitude of the wind component along that dimension. Because of the fixed dimension of the domain perpendicular to the tangential wind, the apparent averaging time of the flow within a 10-km-wide swath decreases with increasing tangential wind. Thus, if the dimension of the swath width is not properly chosen, then the TKE data and their interpretation could be heavily influenced by the magnitude of the tangential wind. One way to test the sensitivity of the method to the averaging time is to look at the sensitivity of the TKE estimates to the magnitude of the tangential wind. Figure 9 presents a scatterplot of tangential wind versus TKE as well as the associated correlation coefficient. The scatterplot shows a weak correlation with the tangential wind, confirmed by the correlation coefficient of 0.28. Some correlation was expected, as the strongest TKE values are located in the eyewall region, where strong shear occurs. When removing the eyewall region, the correlation drops significantly (not shown here), thus confirming that the averaging time should not be a major issue for the interpretation of the TKE results. Another evidence of the weak influence of the tangential wind was shown in Fig. 5, where the strongest TKE data on the outbound leg were not correlated with the strongest tangential wind in the eyewall.

To quantitatively evaluate the TKE magnitude, TKE estimates were compared with in situ estimates from the flight-level data and data collected during the CBLAST experiment. TKE data from flight-level data were computed using the 1-Hz u, y, and w components every 1.5 km to approximately match the resolution of the radar profiles in the along-track direction. Every 1.5 km the mean of 12–15 estimates of each component was computed and then removed and the TKE was calculated. Because of the larger azimuthal extent of the swath for the Doppler data, it is expected that the data will not match perfectly; however, comparison between

FIG. 9. Scatterplot of TKE (m2 s22) vs tangential wind (m s21) for all the cases in Table 1.

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FIG. 10. Comparison of radar-retrieved TKE estimates (m2 s22) with flight-level values: (a) an example from the same leg as Fig. 4 in Hurricane Rita (RL4 in Table 1) and (b) a scatterplot for all cases in Table 1.

the two types of estimates should give a good indication of the magnitude of the retrieved TKE values. Because of the lack of estimates at—and sometimes around—the flight level, radar-retrieved TKE data were taken as close as possible to the flight level (,300 m) and averaged. Figure 10a shows an example of the comparison of flight-level data with the radar-retrieved TKE estimates for the same leg in Fig. 5 (RL4 in Table 1). The comparison shows a striking resemblance even though the methods of calculation are inherently different. Overall, the radar-retrieved TKE data have magnitudes comparable to the flight-level TKE estimates. The majority of the cases used in this study exhibit similar resemblance, with 91% of the radar-retrieved TKE values departing no more than 4 m2 s22 from the flight-level TKE. However, Fig. 10b shows that only 50% of the total variance of the radar-retrieved TKE can be explained by the relationship between the two datasets. Given some of the uncertainties involved to spatially interpolate the flight level to the radar grid points, it is likely that part of the unexplained variance is due to shortcomings of the comparison itself. Moreover, given the radar resolution and the azimuthal extent over which TKE is measured, the radar-retrieved TKE should be able to resolve more scales of motion of the energy spectrum than the 1-Hz flight-level data, which would explain some of the differences between the two methods. Given the lack of

other data sources to estimate TKE in a hurricane environment, especially in a high-wind regime, the Doppler radar gives the best source at this point. A more accurate study will be conducted in the future when 40Hz flight-level data and in situ turbulence data will be collected simultaneously with radar data. During the CBLAST field project, direct measurements of the turbulent quantities u9, y9, and w9 were collected in clear air at ;120 km from the center of Hurricanes Isabel and Fabian. TKE data from the dataset were computed and compared with the radar-retrieved TKE data for both Hurricanes Isabel and Fabian. Because the radar data do not radially extend as far as the CBLAST measurements, the comparison was made using data acquired at 65–80 km from each storm’s center. Figure 4 suggests little change of the HBL TKE distribution outside the eyewall, so comparing the two sets of data appears quite reasonable. The CBLAST TKE data presented here (Fig. 11) are a composite of data from Hurricanes Isabel and Fabian for several days and vertically binned over 150 m (French et al. 2007). Overall the vertical profiles exhibit similar behavior and magnitude, confirming that the TKE retrieval using the Doppler radar data provides reliable estimates. The radar-retrieved TKE profile presents slightly smaller magnitudes than the CBLAST profile, but the difference in magnitude between the two datasets is ,1 m2 s22, and the overlapping

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FIG. 11. Comparison of radar-retrieved TKE with CBLAST flight-level data.

of the error bars supports the agreement of the two datasets. Smaller values of the radar-retrieved TKE data were expected because of the difference in the scales of motion resolved by the two methods. The CBLAST turbulent data were acquired with fast-response instruments (40 Hz) capable of resolving a broader range of the energy spectrum (French et al. 2007; Drennan et al. 2007) and therefore capture energetic turbulent processes not resolved by the radar-retrieved turbulent data. However, the radar-retrieved TKE method incorporates volumes that sample turbulent motions over a much larger volume than a series of point estimates from time series along the flight track, which makes the method appealing for more generalized results. To provide an accurate interpretation of the TKE analysis, it is crucial to understand the scales of motion represented by the radar data. It is not practical to conduct a spectral analysis on the radar data used in each bin. Considering the results from the comparison between radar-retrieved and flight-level TKE, it is believed that the scales documented by the radar encompass the range of scales resolved by the flight-level data. Thus, it is assumed that a spectral analysis of the flight-level data would provide a good representation of some of the scales resolved by the radar method. Figure 12 is a power spectral density (PSD) plot of data over one outbound pass in Hurricane Isabel. The PSD was obtained by applying a 2-min running window on a 40-Hz wind estimate. Each data segment was first detrended and the

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resulting spectral estimates averaged together. The two parts—A and B of the PSD—represent two highenergy frequency bands with a horizontal scale very close to the scales resolved by the radar and support the argument that the method for computing TKE using airborne Doppler measurements captures the turbulent energy associated with relevant scales of motion. Zhang et al. (2008) and Lorsolo et al. (2008) show the existence of organized turbulent features of the HBL with similar scales of motion and exhibiting relatively high energy as shown in Fig. 12. In the present paper, it was possible to estimate the TKE associated with these small-scale features using Doppler measurement, confirming the importance of these features in the HBL turbulent regime. Lorsolo et al. (2008) showed that the HBL flow contains various superimposed scales of motion. In general, a method focused on documenting a specific range of wavelength would result in disregarding other wavelengths (Lorsolo et al. 2008). Here, not only is the radar method able to document the small organized turbulent features of the HBL, but it is also able to capture larger scales as shown in Fig. 6.

4. Conclusions and future work Estimating hurricane turbulence is of crucial importance for a better understanding of hurricane intensity change. Assessing hurricane turbulence especially in the BL and in extreme wind speed has always been a very challenging task, as these regions are not easily accessible by in situ instruments. In this study a promising technique is presented that provides not only an efficient way of estimating TKE using airborne Doppler measurements but also a unique mapping of the turbulent energy throughout a storm. The method proved to be very effective at assessing turbulence in regions that the in situ instruments, such as the ones used for the CBLAST experiment, cannot access. The data presented here were collected from six storms at various stages of their lifetimes. Two-dimensional profiles from the storms’ penetrations revealed that the highest turbulence was located in the eyewall, in the highly convective regions, and in the HBL. Turbulence tends to decrease sharply at the top of the boundary layer and is uniformly low at higher altitude. Analysis of the two-dimensional TKE profiles was useful in identifying smaller-scale processes and a period of reorganization of Hurricane Rita, as illustrated by larger TKE values in an area where the storm was ‘‘building’’ a second eyewall, which was not easily identified from the other fields. The method was able to retrieve TKE estimates in very good agreement with in situ measurements. Comparison with flight-level data showed that the method

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FIG. 12. PSD of 40-Hz flight-level data from Hurricane Isabel.

was able to capture TKE variations even of a few meters squared per second squared and that there was a slight, though expected, underestimation. This new method of estimating TKE is essential to assessing TKE throughout large portions of the storm, particularly in the low levels and for evaluating numerical parameterization. TKE produced from a simulation of Hurricane Ivan conducted by Zhu (2008) shows much larger TKE values than either radar-retrieved or CBLAST TKE estimates, illustrating how important turbulent observational data are to model evaluations. Although the radar-retrieved TKE data cannot separate all three components of the wind, it is not likely that the method alone results in such differences in magnitude. The differences from Zhu (2008) might be attributed to a combined effect of the underestimation of the present method, but they are much more likely caused by the fact that the simulation is conducted over land with enhanced mechanical shear and surface roughness and in the presence of small-scale turbulent features, which were documented to be very energetic.

Understanding and evaluating the results from the hurricane models is one of the reasons why estimating turbulence using observational data is so important and why the method described here could prove to be a useful tool, as it not only provides a good estimation of the turbulence but also does so throughout the storms and for an extended number of cases. Assessing TKE data over land is one of the goals for future work. The technique described is not constrained to the TA radars and could be extended to ground-based radar or wind data from other remote sensing instruments with finer resolution. It will be possible to assess the turbulent energy generated by small-scale linear features often documented over land using ground-based radars (Lorsolo et al. 2008; Morrison et al. 2005; Wurman and Winslow 1998). Given additional information, such as surface wind and thermodynamic information, an accurate assessment of the TKE in the HBL could help retrieve other important parameters, such as eddy diffusivity and dissipation, necessary to evaluate model parameterization

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