On the Characteristic Height Scales of the Hurricane Boundary Layer

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JUN A. ZHANG Rosenstiel School of Marine and Atmospheric Science, University of Miami, and NOAA/AOML/Hurricane Research Division, Miami, Florida

ROBERT F. ROGERS NOAA/AOML/Hurricane Research Division, Miami, Florida

DAVID S. NOLAN Rosenstiel School of Marine and Atmospheric Science, University of Miami, Miami, Florida

FRANK D. MARKS JR. NOAA/AOML/Hurricane Research Division, Miami, Florida

(Manuscript received 26 October 2010, in ﬁnal form 9 March 2011)

ABSTRACT

In this study, data from 794 GPS dropsondes deployed by research aircraft in 13 hurricanes are analyzed to study the characteristic height scales of the hurricane boundary layer. The height scales are defined in a variety of ways: the height of the maximum total wind speed, the inflow layer depth, and the mixed layer depth. The height of the maximum wind speed and the inflow layer depth are referred to as the dynamical boundary layer heights, while the mixed layer depth is referred to as the thermodynamical boundary layer height. The data analyses show that there is a clear separation of the thermodynamical and dynamical boundary layer heights. Consistent with previous studies on the boundary layer structure in individual storms, the dynamical boundary layer height is found to decrease with decreasing radius to the storm center. The thermodynamic boundary layer height, which is much shallower than the dynamical boundary layer height, is also found to decrease with decreasing radius to the storm center. The results also suggest that using the traditional critical Richardson number method to determine the boundary layer height may not accurately reproduce the height scale of the hurricane boundary layer. These different height scales reveal the complexity of the hurricane boundary layer structure that should be captured in hurricane model simulations.

1. Introduction (PBL) parameterization schemes (e.g., Braun and Tao 2000; Nolan et al. 2009a,b; Smith and Thomsen 2010). The boundary layer is known to play an important role Understanding of the hurricane boundary layer structure in the energy transport processes of a hurricane, regulating has become increasingly important in the ongoing effort the radial and vertical distributions of momentum and toward developing high-resolution numerical models to enthalpy that are closely related to storm development improve hurricane intensity forecasts (e.g., Marks and Shay and intensiﬁcation (e.g., Ooyama 1969; Emanuel 1986; 1998; Rogers et al. 2006; Chen et al. 2007; Davis et al. 2008). Wroe and Barnes 2003; Smith et al. 2008; Rotunno et al. In many PBL schemes used in full-physics numerical 2009; Smith and Montgomery 2010). Numerical studies models, one of the crucial elements is the determination of have shown that the simulated hurricane intensity is very the atmospheric boundary layer height (H), because it is sensitive to the selection of planetary boundary layer coupled with the maintenance of low-level clouds and energy transport from the surface layer to the boundary layer above (e.g., Troen and Mahrt 1986; Hong and Pan Corresponding author address: Dr. Jun Zhang, Rosenstiel School of Marine and Atmospheric Science, University of Miami, 4600 1996; Vogelezang and Holtslag 1996; Beljaars and Viterbo Rickenbacker Cswy., Miami, FL 33149. 1998; Noh et al. 2003). The boundary layer height is also E-mail: [email protected] a key variable that regulates the vertical distribution of

DOI: 10.1175/MWR-D-10-05017.1

Ó 2011 American Meteorological Society Unauthenticated | Downloaded 09/30/21 09:25 PM UTC 2524 MONTHLY WEATHER REVIEW VOLUME 139 turbulent fluxes and helps determine where turbulent has been used in previous studies investigating the hurri- fluxes tend to become negligible (Stull 1988). cane inner-core structure (Jorgensen 1984; Frank 1977a,b, Despite the importance in defining the boundary layer 1984), boundary layer structure (Franklin et al. 2003; top in hurricane models, there has been no consensus on Powell et al. 2003), and surface layer air–sea thermal what should define this top in the hurricane research com- structure (Cione et al. 2000). The advantage of the com- munity. In the slab model used in the seminal theoretical posite analysis is that it provides a general picture and hurricane model of Emanuel (1986), a constant boundary characterization of the fields that are investigated. In this layer height is used. Early boundary layer studies (e.g., case, we intend to improve our understanding of the Powell 1990; Anthes and Chang 1978) adopted a thermo- mean boundary layer structure in hurricanes in terms of dynamic definition of the boundary layer, characterized by the boundary layer height. The most important drawback the layer in which the potential temperature or virtual to compositing is that it tends to smooth the data from potential temperature is appreciably well mixed. The ther- a large number of storms that may not be similar (Frank modynamic definition is mainly based on one observa- 1977a). The success of a compositing analysis depends on tional study of the boundary layer of Tropical Storm Eloise the similarity of the events studied. For this purpose, only (1975) by Moss and Merceret (1976), who found that mo- sondes in storms of at least hurricane intensity (.64 kt; mentum fluxes tend to become near zero near the top 1 kt = 0.5144 m s21) are used in the analysis. of the mixed layer defined using the potential tempera- The data are grouped as a function of the radius to ture profile, similar to the vertical flux profile in a typi- the storm center (r) that is normalized by the radius of cal tropical boundary layer over the ocean. Bryan and the maximum wind speed (RMW; i.e., r* 5 r/RMW). The Rotunno (2009) define the top of the boundary layer to be center positions have been determined using the flight the height of the maximum wind usually around 1 km. level to fix the storm center using the algorithm de- Kepert and Wang (2001, see their Fig. 2) show that the veloped by Willoughby and Chelmow (1982). Values of stress divergence becomes small near the height of the RMW are mainly determined using the Doppler radar maximum wind or azimuthal jet, similar to Bryan and data from the tangential winds at 2 km. When there are Rotunno’s result. Smith et al. (2009) adopt another dy- no radar data available, the RMW is determined from the namical definition, considering the strong inflow layer as flight level data. When compositing the data, the radial the boundary layer because of the frictional disruption of bin width is 0.2r* for the inner core (r* , 2), and it is 0.4r* the gradient wind balance near the surface (see their Fig. 6). for the outer part. The data are also bin averaged verti- The purpose of this paper is to use observational data cally at 10-m resolution. The final averaged data are also from multiple hurricanes to examine the structure of the smoothed using a simple 1–2–1 filter both vertically and hurricane boundary layer. We focus on investigating the horizontally, repeated 5 times. characteristic height scales of the hurricane boundary b. Data coverage and quality control layer through analyses of 794 global positioning system (GPS) dropsonde data collected by National Oceanic The dropsonde data used in this study were collected and Atmospheric Administration (NOAA) research by a total of 106 NOAA research flights in 13 hurricanes aircraft in 13 hurricanes. As part of NOAA’s Hurricane (Table 1). A detailed description of the instrumentation Forecast Improvement Project (HFIP), this work also related to the dropsonde can be found in Hock and builds a dataset that can be used to evaluate the repre- Franklin (1999). The fall speed of a sonde is 12–14 m s21, sentation of boundary layer structure in model simula- while the typical sampling rate is 2 Hz, providing mea- tions. Section 2 describes the data sources and analysis surements with 6–7 m of separation in the vertical on method, and includes a detailed description of how dif- average. The dropsonde gives measurements of air tem- ferent hurricane boundary layer heights are defined. In perature, relative humidity, pressure, and horizontal section 3, we present the results by comparing different and vertical wind speed. Typical measurement errors boundary layer height scales determined using our data for pressure, temperature, and relative humidity are to those from previous studies. Section 4 summarizes the 1.0 hPa, 0.28C, and 5%, respectively (Hock and Franklin results and discusses future work. 1999). The accuracy of the horizontal wind speed measurements is 2.0 m s21 and ,0.5 m s21 for the vertical winds with approximately 0.2 m s21 precision. The 2. Data and methodology dropsonde data have been processed and quality controlled using the EDITSONDE software developed by a. Analysis method the Hurricane Research Division (Franklin et al. 2003). The dropsonde data are analyzed and grouped within Data from 2231 GPS dropsondes have been processed a composite framework. The composite analysis technique and analyzed. However, only 794 of these that have

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TABLE 1. Storm information and number of sondes.

Storm intensity Storm Year range (kt) No. of sondes Erika 1997 83–110 40 Bonnie 1998 68–93 76 Georges 1998 66–78 39 Mitch 1998 145–155 28 Bret 1999 75–90 33 Dennis 1999 65–72 7 Floyd 1999 80–110 40 Fabian 2003 68–120 131 Isabel 2003 85–140 162 Frances 2004 68–83 62 Ivan 2004 65–135 123 Dennis 2005 65–70 7 Katrina 2005 68–100 46

continuous measurements of wind speed, temperature, and humidity from the flight level to the surface (10 m) FIG. 1. Plot of the distribution of the dropsonde locations (gray circles) and the storm centers (black dots). in mature storms are used in the final analysis. Table 1 summarizes the storm information and numbers of sondes used in this work. The intensity range of each flux. However, direct measurements of turbulent fluxes storm is also included in Table 1, showing that all of the in the high-wind hurricane boundary layer have been storms were of at least category 1 intensity on the Saffir– scarce. Until now, there have been only two studies that Simpson scale at the time of the analyses, according to have presented vertical profiles of turbulent fluxes in the National Hurricane Center’s best track. The ma- tropical cyclones. Moss (1978) presented a case study of jority of the data are from category 1 and 2 storms, while Tropical Storm Eloise (1975) showing the momentum a quarter of the data are from category 4 and 5 storms. flux profile from one stepped descent period of an air- The sonde locations and the storm centers are plotted craft. Zhang et al. (2009) presented vertical profiles of in Fig. 1, demonstrating a broad geographic area of cov- directly measured fluxes in the hurricane boundary layer erage of storms used in the composite analysis described below. Figure 2 shows the data coverage relative to the storm center. The dropsondes are nearly evenly distrib- uted in the azimuth. Figure 2 also shows that a majority of sondes were dropped near the radius of maximum wind speed (r* 5 1). Figure 3 shows that the number of sondes decreases as a function of distance away from r* 5 1. The peak number of sondes (.80) is located between r* 5 0.5 and 1.2, while the number drops to ;40 between r* 5 2 and 3 and ;25 between r* 5 3 and 5. Figure 3b indicates that most of the sondes were dropped near the eyewall region where the RMW is approximately 40 km. c. Defining characteristic boundary layer height scales Traditionally, the boundary layer is defined as the part of the troposphere that is directly influenced by the presence of the earth’s surface, and responds to surface forcing with a time scale of about an hour or less (Stull 1988). Taking this definition, the boundary layer height represents the height where turbulent fluxes become negligible, often taken in numerical models as the height FIG. 2. Plot of the azimuthal coverage of the dropsonde data where the momentum flux is nearly 5% of the surface relative to the storm center.

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and centrifugal forces. Here, we define the inflow layer as the layer that is directly induced by surface friction, ex- cluding the midlevel (above 2 km) weak inflow arising from a balanced response to heating. After testing different methods, such as taking the height where the radial wind velocity is either 0 or 22ms21 as the inflow layer top, we take the height where the radial velocity is

10% of the peak inflow as the inflow layer depth (hinfl). This definition gives consistent results when we composite the data by different hurricane intensity groups. Note that to estimate the inflow layer depth using the dropsonde data, the wind is first rotated into the radial and tangential wind components before compositing. In numerical models, including hurricane models, the bulk Richardson number has been widely used to determine the boundary layer height in PBL parameterization schemes (e.g., Troen and Mahrt 1986; Vogelezang and Holtslag 1996; Bender et al. 2007; Noh et al. 2003). For FIG. 3. Number of dropsondes (a) as a function of the radius to instance, the bulk Richardson number method has been the storm center normalized by the radius of maximum wind speed and (b) as a function of the radius to the storm center. used in both the local and nonlocal schemes in the fifth- generation National Center for Atmospheric Research– Pennsylvania State University (NCAR–Penn State) between the rainbands of four intense hurricanes. Fur- Mesoscale Model (MM5) and the Weather Research and thermore, indirect derivation of the momentum fluxes has Forecasting (WRF) model, such as the Medium-Range been confined to the surface layer below 200 m (Powell Forecast (MRF) and Yonsei University (YSU) schemes. et al. 2003). Thus, at the present time it is not possible to A detailed explanation of such schemes is given in Nolan determine the boundary layer height using its traditional et al. (2009a,b). The bulk Richardson number (Rib)rep- definition, which relies on turbulent flux data. resents the ratio of buoyancy to shear forcing, which are Alternatively, observational data such as vertical sound- responsible for reducing and generating turbulence, re- ings have been widely used to determine the boundary spectively. This ratio can be defined as layer height. For a nearly neutral or convective boundary (g/u )(u 2 u )(H 2 z ) layer, a common method is to define the boundary layer Ri 5 ys ys ys s , (1) height as the mixed layer depth based on the virtual po- b 2 (UH 2 Us) tential temperature profile. The mixed layer depth is often taken as the base of the inversion layer or stable layer in a where Rib is the Richardson number between an atmo- typical tropical boundary layer over the ocean (e.g., Barnes spheric level zs and the boundary layer top H, uy is the et al. 1980; Nicholls and Readings 1979; Yin and Albrecht virtual potential temperature, and subscripts s and H

2000; Johnson et al. 2001; Zeng et al. 2004). Here, we de- represents the levels of zs and H. A critical Rib is usually termine the mixed layer depth from this definition, that is, used to define the top of the boundary layer. A range of as the nearly constant virtual potential temperature (uy) critical Rib that defines the boundary layer top has been layer. We take the top of the mixed layer to be defined as used in previous studies, mostly varying between 0.25 and being where uy increases by 0.5 K from its mean value in 0.5 (e.g., Hanna 1969; Wetzel 1982; Mahrt 1981; Troen the lowest 150 m (Anthes and Chang 1978). We also esti- and Mahrt 1986; Holtslag et al. 1995). Using the drop- mate the mixed layer depth using the method given by sonde data, we calculate the bulk Richardson number as Zeng et al. (2004), who defined it as the lowest level where a function of height. 21 duy/dz $ 3Kkm . In terms of dynamics and/or kinematics, the height of 3. Results the maximum wind speed (hvmax) can be used to define the boundary layer height (e.g., Bryan and Rotunno The normalized-radius-height representation of the 2009). Another dynamical height scale of the hurricane total wind speed is shown in Fig. 4. A wind maximum boundary layer is the inflow layer depth (e.g., Smith known as the boundary layer jet is located around r* 5 1 et al. 2009). The boundary layer inflow is driven by an and z 5 500 m. This wind maximum or ‘‘azimuthal jet’’ imbalance between the pressure gradient and the Coriolis has been recognized in many previous studies in both

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FIG. 4. Composite analysis result of the total wind speed (in ms21) as a function of altitude and the normalized radius to the storm center. The black dashed line depicts the height of the maximum wind speed varying with radius. The contour interval is 2 ms21. The thick black lines are the 40 and 50 m s21 contours. individual and mean wind profiles (e.g., Kepert 2006a,b; Bell and Montgomery 2008; Schwendike and Kepert FIG. 5. Composite analysis result of (a) the relative tangential 2008; Franklin et al. 2003; Powell et al. 2003). The hur- and (b) radial wind velocity as a function of altitude and the nor- ricane boundary layer jet is one of the distinct features malized radius to the storm center. The thick black lines in (a) are the 40 and 50 m s21 contours and the black dashed line depicts the that is different from a typical boundary layer in non- height of the maximum wind speed varying with radius. The thick hurricane conditions. Figure 4 shows a broad wind max- black line in (b) depicts the inflow layer height defined as the height imum between 200- and 1000-m altitude, consistent with where the radial wind speed is 10% of the peak inflow. In (b), the analysis of Franklin et al. (2003), which used much negative values are contoured in dashed lines. The white dashed less data than were employed in this study. Outside the line in (b) represents the zero contour, and the black 3 represents the location of the maximum tangential wind speed. eyewall, the wind maximum occurs at a higher altitude (;1–1.5 km). Below the wind maximum, the wind speed tends to decrease logarithmically with decreasing height, This pattern of behavior for the boundary layer flow ap- especially below 200 m. This structure is similar to that pears to be evident even when we composite the data by obtained from idealized numerical simulations of the different storm intensities (to be discussed later). Mod- hurricane boundary layer (e.g., Eliassen and Lystad 1977; eling studies (e.g., Kepert and Wang 2001; Nolan et al. Kepert 2001; Kepert and Wang 2001; Nolan 2005; Foster 2009b) have also shown that the wind maximum occurs 2009; Kepert 2010a). within the inflow layer, in agreement with our analysis. Figures 5a and 5b, respectively, show the tangential (Vt) From the composite mean r*–z profiles of Vt and Vr,itis and radial (Vr) wind velocities as a function of r* and al- evident that the inflow layer depth and the height of the titude. The tangential wind speed maximum at the core is maximum wind speed both tend to decrease with de- located between 400 and 1300 m, which is similar to but creasing radius, especially near the core. slightly higher than that of the total wind speed. Again, The r*–z plot of the virtual potential temperature (uy)is below the low-level jet, the tangential wind speed tends to shown in Fig. 6, depicting a well-mixed layer roughly be- decrease nearly logarithmically. The radial inflow is stron- low 500 m beyond r* 5 3. The mixed layer depth (zi) gest at 150 m above the sea surface, decreasing gradually decreases to about 250 m near the eyewall. The decrease with height. Above 1500 m at r* 5 1, a pronounced outflow of the mixed layer depth with decreasing radius is also jet is evident. It is interesting to note that the depth of the showninFig.7,wherezi is defined using the method inflow layer (defined by where Vr equals 10% of the peak mentioned in section 2. There is no inversion layer as in a inflow) is above the height of the maximum tangential wind typical tropical boundary layer where there is a sub- speed. We found that the tangential wind maximum is lo- sidence (e.g., Nicholls 1985; Albrecht et al. 1985). The cated at the height where Vr is 25% of the peak inflow. hurricane boundary layer basically contains a mixed layer,

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FIG. 6. Composite analysis result of the virtual potential temperature (in K) as a function of altitude and the normalized radius to the storm center. The thick black lines are the 305- and 310-K FIG. 8. Composite analysis result of the lapse rate of the virtual contours. The contour interval is 0.5 K. potential temperature (in K km21) as a function of altitude and the normalized radius to the storm center. The thick black line denotes 21 a transition layer, and a stable layer (e.g., Powell 1990; the constant contour of duy /dz 5 3Kkm . Barnes 2008). The magnitude of uy generally increases 21 with decreasing radius, with the warm core clearly evident the mixed layer depth is where duy/dz $ 3Kkm fol- inside r* 5 1.5. The mixed layer depth in the outer core lowing Zeng et al. (2004), it is very close to that deﬁned (i.e., r* . 2) is very similar to that in a typical tropical using our constant uy deﬁnition, as mentioned earlier boundary layer over the ocean (e.g., Nicholls and LeMone (Fig. 7), which is found again to decrease with decreasing 1980; Barnes et al. 1980; Albrecht et al. 1985). The inner- radius. core mixed layer is much shallower. Figure 8 shows the The bulk Richardson number is calculated using Eq. lapserateofu as a function of r and altitude. Note that y * (1) and is shown in Fig. 9 as a function of r* and height. If we used dz 5 10 m when we computed the lapse rate. If Rib 5 0.25 is taken as the top of the boundary layer (solid black line in Fig. 10), it generally lies between the mixed

FIG. 7. Composite analysis result of the differences in the virtual potential temperature (in K) at each level and the mean value of FIG. 9. Composite analysis result of the bulk Richardson number the lowest 150-m data as a function of altitude and the normalized (Ri) as a function of altitude and the normalized radius to the storm radius to the storm center. The thick black line denotes the con- center. The thick black line denotes the constant contour of Ri with stant contour with a value of 0.5 K. a value of 0.25.

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FIG. 10. Composite analysis results of the (left) tangential and (right) radial wind velocities normalized by the peak values as a function of altitude and the normalized radius to the storm center, for category (top) 1–5, (middle) 1–3, and (bottom) 4–5 storms. The black dashed line in the right panels depicts the height of the maximum wind speed varying with radius. The thick black line in the left panels depicts the inflow layer height defined as the height where the radial wind speed is 10% of the peak inflow. The black 3 in the left panels represents the location of the maximum tangential wind speed. The contour interval in the left panels is 10% and it is 5% in the right panels. The total number of sondes used in group cat 1–3 is 513 and that in group cat 4–5 is 277. layer depth and the inflow layer depth. However, this group cat 4–5 hereafter). In group cat 1–3, the data are depth increases with decreasing radius, in contrast to the mainly from category 1 and 2 storms. In group cat 4–5, the depths defined by zi, hvmax,andhinfl. This indicates that sondes were mainly dropped at locations r* , 1.5 and using the Richardson number method may not capture below 2 km. Figure 10 shows a comparison of the com- the correct radial variation of the boundary layer depth. posites of Vt and Vr between groups cat 1–3 and cat 4–5, As mentioned earlier, the data used to generate the as well as the whole dataset. For comparison purpose, we plots of axisymmetric low-level kinematic and thermo- have also normalized Vt and Vr by their peak values. As dynamic structure are from multiple storms ranging from expected, the peak mean values of Vt and Vr, labeled in categories 1 to 5. To assess the variability between stron- the header of each panel in Fig. 10, are found to increase ger and weaker storms, we group the data by storm in- with increasing storm intensity. The height of the maxi- tensity before the composite analysis, by dividing the data mum Vt isfoundtobewithintheinflowlayer,whichis into two groups: one using sondes in storms with intensity located at the height of the 25% peak inflow for all the ,120 kt (i.e., category 1–3 storms, referred to as group cat intensity groups. 1–3 hereafter), and the other using sondes in storms with Figure 10 also indicates that there is almost no dif- intensity .120 kt (i.e., category 4–5 storms, referred to as ference in the inflow layer depth and height of maximum

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Vt between group cat 1–3 and the whole dataset (Fig. 5). such as the height of the maximum wind speed (hvmax), However, the inflow layer depth in group cat 4–5 is higher the inflow layer depth (hinfl), and the mixed layer depth than that in group cat 1–3 as well as the whole dataset in (zi), as a function of normalized distance (r* 5 r/RMW). the inner-core region, while it is lower in the outer region. Here, each height scale is based on the composite At first thought, this inflow layer height difference may be analysis results discussed above. Also shown in Fig. 12 is due to the differences in the numbers of storms and sondes the boundary layer depth estimated using the critical used in the composites. However, we found that both bulk Richardson number method (Fig. 9). The results groups cat 1–3 and 4–5 have more than 200 sondes with show a clear separation between the dynamical and good spatial coverage in the inner-core region. We be- thermodynamical boundary layer heights (Fig. 12). lieve the result is robust, especially for the region within Zhang et al. (2009) has highlighted this difference in the r* , 1.5. According to theoretical scaling arguments (e.g., outer-core region. They showed that turbulent mo- Kepert 2001), the boundary layer depth is scaled as a mentum fluxes are near zero, not at the top of the mixed function of the square root of the vertical eddy diffusivity layer, but at a height that is close to the depth of the divided by inertial stability. It is conceivable that in stron- inflow layer. The separation of the dynamical and ther- ger hurricanes the vertical eddy diffusivity is larger due modynamical boundary layer height scales was also ev- to increased turbulence in the boundary layer (Zhang ident in the numerical simulations of Nolan et al. et al. 2011). The data in group cat 4–5 are mainly from (2009a) and in an observational study of Hurricane Hurricanes Mitch (1998), Isabel (2003), and Ivan (2004), Isabel (2003) given by Montgomery et al. (2006, see their which are large storms, in which the inertial stability would Fig. 4). While the Zhang et al. observations are constrained not be greater than that for group cat 1–3. It is possible that to a nearly rain-free region between outer rainbands with these two factors make the boundary layer height higher in mean surface wind speeds less than 30 m s21, this finding group cat 4–5. Note that there may be a difference in the highlights the limitation of a thermodynamic definition of inertial stability between the inner core and the outer the hurricane boundary layer. When advocating that the vortex in a storm (e.g., Kepert 2006b). thermodynamic definition is not suitable for the hurricane Another interesting feature we noticed in Fig. 10 is that boundary layer, Kepert (2010a) argued that turbulence is the depth of the strong inflow layer increases (to some predominately shear generated and the height scale is extent) with decreasing radius for the group cat 4–5 storms determined by dynamics, not thermodynamics. at radius of roughly r* 5 1.5–3.0. In this region, the slope of In addition, all three height scales (hvmax, hinfl,andzi) the 10% peak inflow contour in the middle panel of Fig. 10 tend to decrease with decreasing radius to the storm is upward, while in the bottom panel the slope is down- center, in particular, in the inner-core region. It is found ward. Since there is a much smaller sample of data for that hvmax decreases more than the other two height outside r* 5 1.5 than inside r* 5 1.5 for group cat 4–5, the scales. There is a tendency toward a leveling off of the trend of increasing inflow layer height with decreasing three height scales in the outer-core region (r* . 3.5). The 1 radius beyond 1.5r* may not be conclusive. We recom- subsidence warming is likely the reason the boundary mend that more dropsondes should be released in the layer depth is reduced at large radius (e.g., Kepert 2010b). outer-core region in future field programs, especially for The decreases in hvmax and hinfl have been recognized in strong hurricanes. previous studies of individual storms (e.g., Kepert 2006a,b; Although there is an apparent difference in inflow layer Schwendike and Kepert 2008; Sitkowski and Barnes 2009). depth by storm intensity, there is little difference in the These decreases are consistent with the scaling-height ar- mixed layer depth by storm intensity, as seen in Fig. 11. gument according to theories of rotating boundary layers The inner-core region of the stronger storms (group cat (Eliassen 1971; Carrier 1971; Montgomery et al. 2001; 4–5) is warmer, however. Kepert 2001; Kepert and Wang 2001; Nolan 2005; Foster 2009; Kepert 2010a,b). We also found that the heights of both the maximum wind speed and the tangential wind 4. Discussion and conclusions speed are within the inflow layer. The height of the tan-

Characteristic height scales of the hurricane boundary gential wind speed (Vt) is located at the height where the layer are analyzed using a large quantity of dropsonde radial wind speed (Vr) is 25% of the peak inflow. This data from 13 hurricanes. Figure 12 is a schematic dia- feature appears to be independent of storm intensity. gram that summarizes the characteristic height scales From its traditional definition the mixed layer depth is found to decrease with decreasing radius from the storm center, especially near the core. Schneider and Barnes 1 Previous P3 flights have focused on dropping sondes in the (2005) showed that the lifting condensation level (LCL) eyewall region. decreased with decreasing radius in Hurricane Bonnie

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FIG. 11. Composite analysis result of the (left) virtual potential temperature and (right) difference of the virtual potential temperature at each level and the mean value of the lowest 150-m data, as a function of altitude and the normalized radius to the storm center, for category (top) 1–5, (middle) 1–3, and (bottom) 4–5 storms. The black lines in the left panels are the 305- and 310-K contours. The black dashed line in the right panels depicts the constant contour with a value of 0.5 K. The contour interval is 0.5 K for all the panels.

(1998), consistent with this result. Previous studies of the boundary layer depth is constrained by the increasing tropical boundary layer near squall lines or hurricane rotational stability toward the center. Certainly, further rainbands have shown that the mixed layer is usually analysis is required to conﬁrm the above hypotheses. shallower due to convective downdrafts that transport dry The boundary layer depth estimated using the critical and cool air to the low-level boundary layer (Zipser 1977; Richardson number method is found to behave differ- Betts and Simpson 1987; Powell 1990; Barnes and Powell ently from all the above-mentioned three height scales

1995). However, the traditional boundary layer entrain- (i.e., hvmax, hinfl, zi), in that the depth increases toward the ment processes may not be at work in the eyewall, because eyewall. This indicates that using the Richardson number the flow there is nearly saturated, which tends to prevent method to estimate the boundary layer depth may not downdrafts from bringing appreciably drier air to the produce the correct pattern of behavior in numerical boundary layer. It is possible that the increase in pre- models. cipitation and sea spray toward the storm center may be Notwithstanding the variability of different boundary responsible for the decrease of the mixed layer depth. It is layer height scales, it is thought that the inflow layer depth also possible that the mixed layer depth is controlled by, or represents the top of the hurricane boundary layer better related to, boundary layer dynamics, in that the entire than does the thermodynamic boundary layer depth.

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FIG. 12. Schematic diagram of the characteristic height scales of the hurricane boundary

layer. The height scales are based on the composite analysis of the dropsonde data. The hinﬂ is the inﬂow layer depth (red dashed line), zi is the mixed layer depth (green dashed–dotted line), and hvmax is the height of the maximum wind speed (blue dotted line). The solid black line represents the height where the bulk Richardson number is equal to 0.25.

Direct flux measurements in the outer-core regions of turbulent fluxes are different properties. The former rep- hurricanes suggest the turbulent flux transport mainly resents the turbulence intensity, which is derived from the occurs in the inflow layer (Zhang et al. 2009). The budgets variance of the flow, while the latter represents the vertical and discussion presented by Kepert and Wang (2001) and transports, which depends on the covariance of the fields. Kepert (2010a) support the statement that the momen- Zhuetal.(2010)pointedoutthatthemechanismsfor tum flux occurs mainly in the inflow layer. In his numer- generating TKE and fluxes by different types of turbulent ical simulations, Kepert (2010a) also showed that the eddies are different in the hurricane surface layer. From momentum flux is a significant part of the dynamics of the the turbulent variance profiles shown by Zhang et al. layer of outflow immediately above the inflow and sug- (2009), one can also deduce that while the turbulent fluxes gested that it is therefore appropriate to include at least tend to become zero near the top of the inflow layer, the part of this layer in the boundary layer. turbulent intensity or TKE does not vanish. We note that defining the boundary layer top as the To accurately identify the top of the hurricane boundary inflow layer depth presents its own problems, in that real layer, we believe it will be required to measure turbulent storms may have highly asymmetric inflow layers. The fluxes near the top of the inflow layer. Fortunately, tur- flow can be outward relative to the storm center near the bulence sensors that have been successfully used during the surface in a moving storm, as seen for example in Hurri- Coupled Boundary Layer Air–Sea Transfer (CBLAST) cane Frederic, given by Powell (1982, see his Fig. 6). hurricane experiment (Black et al. 2007; Drennan et al. Modeling studies also show weaker inflow, or occasionally 2007; French et al. 2007; Zhang et al. 2008) are still on outflow,ontheleftsideofmovingstorms(e.g.,Kepert board the NOAA P3 aircraft. It has been planned in 2010a; Nolan et al. 2009b), consistent with theoretical HRD’s annual hurricane field project to conduct flux arguments given by Kepert (2001). measurements near the top of the inflow layer (Rogers A recent observational study by Lorsolo et al. (2010) et al. 2010, 96–100). Such an experiment would also help showed that the turbulent kinetic energy (TKE) estimated quantify entrainment processes near the top of the from Doppler radar data in the eyewall region can extend boundary layer that are crucial to close the energy budget up to the top of the troposphere. The elevated levels of (Barnes and Powell 1995; Wroe and Barnes 2003). TKE in the eyewall suggest that it is difficult to precisely The results presented in this study should be useful for define the boundary layer in the hurricane inner core evaluating numerical simulations for hurricane prediction. using a turbulence argument, as discussed by Smith and Future work will involve adding more dropsonde data to Montgomery (2010). However, we note that TKE and the database. Emphasis will be placed on the investigation

Unauthenticated | Downloaded 09/30/21 09:25 PM UTC AUGUST 2011 Z H A N G E T A L . 2533 of the asymmetric boundary layer structure, and possible Carrier, G. F., 1971: Swirling flow boundary layers. J. Fluid Mech., structural differences between weakening, quasi-steady, 49, 133–144. and intensifying storms. Chen,S.S.,J.F.Price,W.Zhao,M.A.Donelan,andE.J.Walsh,2007: The CBLAST-Hurricane Program and the next-generation fully coupled atmosphere–wave–ocean models for hurri- Acknowledgments. This work was supported by the cane research and prediction. Bull. Amer. Meteor. Soc., 88, NOAA Hurricane Forecast Improvement Project (HFIP). 311–317. We gratefully acknowledge all the scientists who were Cione, J. J., P. G. Blasck, and S. H. Houston, 2000: Surface ob- involved in the Hurricane Research Division’s field pro- servations in the hurricane environment. Mon. Wea. Rev., 128, 1550–1561. gram collecting the data. We appreciate the efforts of Davis, C., and Coauthors, 2008: Prediction of landfalling hurri- all the scientists and students who helped with post- canes with the Advanced Hurricane WRF model. Mon. Wea. processing the sonde data used in this work. Without their Rev., 136, 1990–2005. efforts, this work would not have been possible. In par- Drennan, W. M., J. A. Zhang, J. R. French, C. McCormick, and ticular, we are grateful to Kathryn Sellwood for putting P. G. Black, 2007: Turbulent fluxes in the hurricane boundary the dropsonde data together. We acknowledge Eric layer. Part II: Latent heat fluxes. J. Atmos. Sci., 64, 1103– 1115. Uhlhorn, Joe Cione, Sylvie Lorsolo, Mike Montgomery, Eliassen, A., 1971: On the Ekman layer in a circular vortex. J. Meteor. Peter Black, and Mark Powell for valuable discussions. We Soc. Japan, 49, 784–789. appreciate the efforts of Jeff Kepert, Gary Barnes, and an ——, and M. Lystad, 1977: The Ekman layer of a circular vortex. A anonymous reviewer in reviewing our paper and providing numerical and theoretical study. Geophys. Norv., 7, 1–16. comments that led to substantial improvements. We also Emanuel, K. A., 1986: An air–sea interaction theory for tropical cyclones. Part I: Steady-state maintenance. J. Atmos. Sci., 43, thank the editor, George Bryan, for providing valuable 585–605. suggestions to improve this paper. Foster, R. C., 2009: Boundary-layer similarity under an axisymmetric, gradient wind vortex. Bound.-Layer Meteor., 131, 321–344. REFERENCES Frank, W. M., 1977a: The structure and energetics of the trop- Albrecht, B. A., R. S. Penc, and W. H. Schubert, 1985: An obser- ical cyclone I. Storm structure. Mon. Wea. Rev., 105, 1119– vational study of cloud-topped mixed layers. J. Atmos. Sci., 42, 1135. 800–822. ——, 1977b: The structure and energetics of the tropical cyclone II. Anthes, R. A., and S. W. Chang, 1978: Response of the hurricane Dynamics and energetics. Mon. Wea. Rev., 105, 1136–1150. boundary layer to changes of sea surface temperature in ——, 1984: A composite analysis of the core of a mature hurricane. a numerical model. J. Atmos. Sci., 35, 1240–1255. Mon. Wea. Rev., 112, 2401–2420. Barnes, G. M., 2008: Atypical thermodynamic profiles in hurri- Franklin, J. L., M. L. Black, and K. Valde, 2003: GPS dropwind- canes. Mon. Wea. Rev., 136, 631–643. sonde wind profiles in hurricanes and their operational im- ——, and M. D. Powell, 1995: Evolution of the inflow boundary layer plications. Wea. Forecasting, 18, 32–44. of Hurricane Gilbert (1988). Mon. Wea. Rev., 123, 2348–2368. French, J. R., W. M. Drennan, J. A. Zhang, and P. G. Black, 2007: ——, G. D. Emmitt, B. Brummer, M. A. LeMone, and S. Nicholls, Turbulent fluxes in the hurricane boundary layer. Part I: 1980: The structure of a fair weather boundary layer based on Momentum flux. J. Atmos. Sci., 64, 1089–1102. the results of several measurement strategies. Mon. Wea. Rev., Hanna, S. R., 1969: The thickness of the planetary boundary layer. 108, 349–364. Atmos. Environ., 3, 519–536. Beljaars, A. C. M., and P. Viterbo, 1998: Role of the boundary layer Hock, T. F., and J. L. Franklin, 1999: The NCAR GPS dropwind- in a numerical weather prediction model. Clear and Cloudy sonde. Bull. Amer. Meteor. Soc., 80, 407–420. Boundary Layers, A. A. M. Holtslag and P. G. Duynkerke, Eds., Holtslag, A. A. M., E. van Meijgaard, and W. C. de Rooij, 1995: A Royal Netherlands Academy of Arts and Sciences, 287–304. comparison of boundary layer diffusion schemes in unstable Bell, M. M., and M. T. Montgomery, 2008: Observed structure, conditions over land. Bound.-Layer Meteor., 76, 69–95. evolution, and intensity of category five Hurricane Isabel (2003) Hong, S. Y., and H. L. Pan, 1996: Nonlocal boundary layer vertical from 12 to 14 September. Mon. Wea. Rev., 136, 2023–2036. diffusion in a medium-range forecast model. Mon. Wea. Rev., Bender, M. A., I. Ginis, R. Tuleya, B. Thomas, and T. Marchok, 2007: 124, 2322–2339. The operational GFDL hurricane–ocean prediction system and Johnson,R.H.,P.E.Ciesielski,andJ.A.Cotturone,2001: a summary of its performance. Mon. Wea. Rev., 135, 3965–3989. Multiscale variability of the atmospheric mixed layer over Betts, A. K., and J. Simpson, 1987: Thermodynamic budget diagram the western Pacific warm pool. J. Atmos. Sci., 58, 2729– for the hurricane subcloud layer. J. Atmos. Sci., 44, 842–848. 2750. Black, P. G., and Coauthors, 2007: Air–sea exchange in hurricanes: Jorgensen, D. P., 1984: Mesoscale and convective scale character- Synthesis of observations from the Coupled Boundary Layer Air- istics of mature hurricanes. Part I: General observations by Sea Transfer experiment. Bull. Amer. Meteor. Soc., 88, 357–374. research aircraft. J. Atmos. Sci., 41, 1268–1285. Braun, S. A., and W.-K. Tao, 2000: Sensitivity of high-resolution Kepert, J. D., 2001: The dynamics of boundary layer jets within the simulations of Hurricane Bob (1991) to planetary boundary tropical cyclone core. Part I: Linear theory. J. Atmos. Sci., 58, layer parameterizations. Mon. Wea. Rev., 128, 3941–3961. 2469–2484. Bryan, G. H., and R. Rotunno, 2009: The maximum intensity of ——, 2006a: Observed boundary layer wind structure and balance tropical cyclones in axisymmetry numerical model simula- in the Hurricane core. Part I: Hurricane Georges. J. Atmos. tions. Mon. Wea. Rev., 137, 1770–1789. Sci., 63, 2169–2193.

Unauthenticated | Downloaded 09/30/21 09:25 PM UTC 2534 MONTHLY WEATHER REVIEW VOLUME 139

——, 2006b: Observed boundary layer wind structure and balance Ooyama, K. V., 1969: Numerical simulation of the life cycle of in the Hurricane core. Part II: Hurricane Mitch. J. Atmos. Sci., tropical cyclones. J. Atmos. Sci., 26, 3–40. 63, 2194–2211. Powell, M. D., 1982: The transition of the Hurricane Frederic ——, 2010a: Slab- and height-resolving models of the tropical cy- boundary-layer wind field from the open Gulf of Mexico to clone boundary layer. Part I: Comparing the simulations. landfall. Mon. Wea. Rev., 110, 1912–1932. Quart. J. Roy. Meteor. Soc., 136A, 1686–1699, doi:10.1002/ ——, 1990: Boundary layer structure and dynamics in outer hur- qj.667. ricane rainbands. Part II: Downdraft modification and mixed ——, 2010b: Slab- and height-resolving models of the tropical layer recovery. Mon. Wea. Rev., 118, 918–938. cyclone boundary layer. Part II: Why the simulations differ. ——, P. J. Vickery, and T. A. Reinhold, 2003: Reduced drag co- Quart. J. Roy. Meteor. Soc., 136A, 1700–1711, doi:10.1002/ efficient for high wind speeds in tropical cyclones. Nature, 422, qj.685. 279–283. ——, and Y. Wang, 2001: The dynamics of boundary layer jets Rogers, R. F., and Coauthors, 2006: The Intensity Forecasting within the tropical cyclone core. Part II: Nonlinear enhance- Experiment: A NOAA multiyear field program for improving ment. J. Atmos. Sci., 58, 2485–2501. tropical cyclone intensity forecasts. Bull. Amer. Meteor. Soc., Lorsolo, S., J. A. Zhang, F. D. Marks, and J. Gamache, 2010: 87, 1523–1537. Estimation and mapping of hurricane turbulent energy using ——, and Coauthors, 2010: The 2010 Hurricane Field Program airborne Doppler measurements. Mon. Wea. Rev., 138, 3656– Plan. NOAA/AOML, 104 pp. [Available online at http:// 3670. www.aoml.noaa.gov/hrd/HFP2010/HFP2010_part1.pdf.] Mahrt, L., 1981: Modeling the depth of the stable boundary layer. Rotunno, R., Y. Chen, W. Wang, C. Davis, J. Dudhia, and G. J. Bound.-Layer Meteor., 21, 3–19. Holland, 2009: Large-eddy simulation of an idealized tropical Marks, F. D., Jr., and L. K. Shay, 1998: Landfalling tropical cy- cyclone. Bull. Amer. Meteor. Soc., 90, 1783–1788. clones: Forecast problems and associated research opportu- Schneider, R., and G. M. Barnes, 2005: Low-level kinematic, ther- nities. Bull. Amer. Meteor. Soc., 79, 305–323. modynamic, and reflectivity fields associated with Hurricane Montgomery, M. T., H. D. Snell, and Z. Yang, 2001: Axisymmetric Bonnie (1998) at landfall. Mon. Wea. Rev., 133, 3243–3259. spindown dynamics of hurricane-like vortices. J. Atmos. Sci., Schwendike, J., and J. D. Kepert, 2008: The boundary layer winds 58, 421–435. in Hurricanes Danielle (1998) and Isabel (2003). Mon. Wea. ——, M. M. Bell, S. Aberson, and M. Black, 2006: Hurricane Isabel Rev., 136, 3168–3192. (2003): New insights into the physics of intense storms. Part I: Sitkowski, M., and G. M. Barnes, 2009: Low-level thermodynamic, Mean vortex structure and maximum intensity estimate. Bull. kinematic, and reflectivity fields of Hurricane Guillermo (1997) Amer. Meteor. Soc., 87, 1335–1347. during rapid intensification. Mon. Wea. Rev., 137, 645–663. Moss, M. S., 1978: Low-level turbulence structure in the vicinity of Smith, R. K., and M. T. Montgomery, 2010: Hurricane boundary- a hurricane. Mon. Wea. Rev., 106, 841–849. layer theory. Quart. J. Roy. Meteor. Soc., 136A, 1665–1670, ——, and F. J. Merceret, 1976: A note on several low-layer fea- doi:10.1002/qj.679. tures of Hurricane Eloise (1975). Mon. Wea. Rev., 104, ——, and G. L. Thomsen, 2010: Dependence of tropical-cyclone 967–971. intensification on the boundary layer representation in a nu- Nicholls, S., 1985: Aircraft observations of the Ekman layer during merical model. Quart. J. Roy. Meteor. Soc., 136A, 1671–1685, the Joint Air–Sea Interaction experiment. Quart. J. Roy. doi:10.1002/qj.687. Meteor. Soc., 111, 391–426. ——, M. T. Montgomery, and S. Vogl, 2008: A critique of Emanuel’s ——, and C. J. Readings, 1979: Aircraft observations of the structure hurricane model and potential intensity theory. Quart. J. Roy. on the lower boundary layer over the sea. Quart. J. Roy. Meteor. Meteor. Soc., 134, 551–561. Soc., 105, 785–802. ——, ——, and S. V. Nguyen, 2009: Tropical cyclone spinup re- ——, and M. A. LeMone, 1980: The fair weather boundary layer visited. Quart. J. Roy. Meteor. Soc., 135, 1321–1335. in GATE: The relationship of subcloud fluxes and structure Stull, R. B., 1988: An Introduction to Boundary Layer Meteorology. to the distribution and enhancement of cumulus clouds. Kluwer Academic, 666 pp. J. Atmos. Sci., 37, 2051–2067. Troen, I., and L. Mahrt, 1986: A simple model of the atmospheric Noh, Y., W. G. Cheon, S. Y. Hong, and S. Raasch, 2003: Im- boundary layer: Sensitivity to surface evaporation. Bound.- provement of the K-profile model for the planetary boundary Layer Meteor., 37, 129–148. layer based on large eddy simulation data. Bound.-Layer Vogelezang, D. H. P., and A. A. M. Holtslag, 1996: Evaluation and Meteor., 107, 421–427. model impacts of alternative boundary-layer height formula- Nolan, D. S., 2005: Instabilities in hurricane-like boundary layers. tions. Bound.-Layer Meteor., 81, 245–269. Dyn. Atmos. Oceans, 40, 209–236. Wetzel, P. J., 1982: Toward parameterization of the stable ——, J. A. Zhang, and D. P. Stern, 2009a: Evaluation of planetary boundary layer. J. Appl. Meteor., 21, 7–13. boundary layer parameterizations in tropical cyclones by Willoughby, H. E., and M. Chelmow, 1982: Objective de- comparison of in situ data and high-resolution simulations of termination of hurricane tracks from aircraft observations. Hurricane Isabel (2003). Part I: Initialization, maximum Mon. Wea. Rev., 110, 1298–1305. winds, and outer-core boundary layer structure. Mon. Wea. Wroe, D. R., and G. M. Barnes, 2003: Inflow layer energetics of Rev., 137, 3651–3674. Hurricane Bonnie (1998) near landfall. Mon. Wea. Rev., 131, ——, D. P. Stern, and J. A. Zhang, 2009b: Evaluation of plan- 1600–1612. etary boundary layer parameterizations in tropical cyclones Yin, B., and B. Albrecht, 2000: Spatial variability of atmospheric by comparison of in situ data and high-resolution simula- boundary layer structure over the eastern equatorial Pacific. tions of Hurricane Isabel (2003). Part II: Inner-core J. Climate, 13, 1574–1592. boundary layer and eyewall structure. Mon. Wea. Rev., 137, Zeng, X., M. A. Bruke, M. Zhou, C. Fairall, N. A. Bond, and D. H. 3675–3698. Lenschow, 2004: Marine atmospheric boundary layer height

Unauthenticated | Downloaded 09/30/21 09:25 PM UTC AUGUST 2011 Z H A N G E T A L . 2535

over the eastern Paciﬁc: Data analysis and model evaluation. ——, F. D. Marks, M. T. Montgomery, and S. Lorsolo, 2011: An J. Climate, 17, 4159–4170. estimation of turbulent characteristics in the low-level region Zhang, J. A., P. G. Black, J. R. French, and W. M. Drennan, 2008: of intense Hurricanes Allen (1980) and Hugo (1989). Mon. First direct measurements of enthalpy ﬂux in the hurricane Wea. Rev., 139, 1447–1462. boundary layer: The CBLAST results. Geophys. Res. Lett., 35, Zhu, P., J. A. Zhang, and F. J. Masters, 2010: Wavelet analysis L14813, doi:10.1029/2008GL034374. of turbulence in the hurricane surface layer during landfalls. ——, W. M. Drennan, P. G. Black, and J. R. French, 2009: J. Atmos. Sci., 67, 3793–3805. Turbulence structure of the hurricane boundary layer Zipser, E. J., 1977: Mesoscale and convective-scale downdrafts as between the outer rainbands. J. Atmos. Sci., 66, 2455– distinct components of squall line circulation. Mon. Wea. Rev., 2467. 105, 1568–1589.

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