• Banner, M. L., , W. Chen, , E. J. Walsh, , J. B. Jensen, , S. Lee, , and C. Fandry, 1999: The Southern Ocean Waves Experiment. Part I: Overview and mean results. J. Phys. Oceanogr., 29, 21302145.

    • Search Google Scholar
    • Export Citation
  • Bender, M. A., , I. Ginis, , R. Tuleya, , B. Thomas, , and T. Marchok, 2007: The operational GFDL Coupled Hurricane–Ocean Prediction System and a summary of its performance. Mon. Wea. Rev., 135, 39653989.

    • Search Google Scholar
    • Export Citation
  • Bister, M., , and K. A. Emanuel, 1998: Dissipative heating and hurricane intensity. Meteor. Atmos. Phys., 65, 233240.

  • Black, P. G., and Coauthors, 2007: Air–sea exchange in hurricanes: Synthesis of observations from the Coupled Boundary Layer Air–Sea Transfer experiment. Bull. Amer. Meteor. Soc., 88, 357374.

    • Search Google Scholar
    • Export Citation
  • Bryan, G. H., , and R. Rotunno, 2009: The maximum intensity of tropical cyclones in axisymmetric numerical model simulations. Mon. Wea. Rev., 137, 17701789.

    • Search Google Scholar
    • Export Citation
  • Businger, S., , and J. Businger, 2001: Viscous dissipation of turbulence kinetic energy in storms. J. Atmos. Sci., 58, 37933796.

  • Davis, C., and Coauthors, 2008: Prediction of landfalling hurricanes with the Advanced Hurricane WRF model. Mon. Wea. Rev., 136, 19902005.

    • Search Google Scholar
    • Export Citation
  • Deacon, E., 1957: Wind profiles and the shearing stress—An anomaly resolved. Quart. J. Roy. Meteor. Soc., 83, 537540.

  • Donelan, M. A., , W. M. Drennan, , and K. B. Katsaros, 1997: The air–sea momentum flux in conditions of mixed wind sea and swell. J. Phys. Oceanogr., 27, 20872099.

    • Search Google Scholar
    • Export Citation
  • Donelan, M. A., , B. K. Haus, , N. Reul, , W. J. Plant, , M. Stianssnie, , H. C. Graber, , O. B. Brown, , and E. S. Saltzman, 2004: On the limiting aerodynamic roughness of the ocean in very strong winds. Geophys. Res. Lett., 31, L18306, doi:10.1029/2004GL019460.

    • Search Google Scholar
    • Export Citation
  • Drennan, W. M., , J. A. Zhang, , J. R. French, , C. McCormick, , and P. G. Black, 2007: Turbulent fluxes in the hurricane boundary layer. Part II: Latent heat fluxes. J. Atmos. Sci., 64, 11031115.

    • Search Google Scholar
    • Export Citation
  • Emanuel, K. A., 1995: Sensitivity of tropical cyclones to surface exchange coefficients and a revised steady-state model incorporating eye dynamics. J. Atmos. Sci., 52, 39693976.

    • Search Google Scholar
    • Export Citation
  • Fairall, C. W., , E. F. Bradley, , J. E. Hare, , A. A. Grachev, , and J. B. Edson, 2003: Bulk parameterization of air–sea fluxes: Updates and verification for the COARE algorithm. J. Climate, 16, 571591.

    • Search Google Scholar
    • Export Citation
  • French, J. R., , W. M. Drennan, , J. A. Zhang, , and P. G. Black, 2007: Turbulent fluxes in the hurricane boundary layer. Part I: Momentum flux. J. Atmos. Sci., 64, 10891102.

    • Search Google Scholar
    • Export Citation
  • Jin, Y., , W. T. Thompson, , S. Wang, , and C.-S. Liou, 2007: A numerical study of the effect of dissipative heating on tropical cyclone intensity. Wea. Forecasting, 22, 950966.

    • Search Google Scholar
    • Export Citation
  • Lenschow, D. H., 1970: Airplane measurements of planetary boundary layer structure. J. Appl. Meteor., 9, 874884.

  • Mahrt, L., 1998: Flux sampling errors from aircraft and towers. J. Atmos. Oceanic Technol., 15, 416429.

  • Mahrt, L., , D. Vickers, , J. Sun, , N. O. Jensen, , H. Jørgensen, , E. Pardyjak, , and H. Fernando, 2001: Determination of the surface drag coefficient. Bound.-Layer Meteor., 99, 249276.

    • Search Google Scholar
    • Export Citation
  • Makarieva, A. M., , V. G. Gorshkov, , B.-L. Li, , and A. D. Nobre, 2010: A critique of some modern applications of the Carnot heat engine concept: The dissipative heat engine cannot exist. Proc. Roy. Soc., 466A, 18931902, doi:10.1098/rspa.2009.0581.

    • Search Google Scholar
    • Export Citation
  • Marks, F. D., , and L. K. Shay, 1998: Landfalling tropical cyclones: Forecast problems and associated research opportunities. Bull. Amer. Meteor. Soc., 79, 305323.

    • Search Google Scholar
    • Export Citation
  • Masters, F. J., 2004: Measurement, modeling and simulation of ground level tropical cyclone winds. Ph.D. dissertation, University of Florida, 188 pp.

  • Masters, F. J., , H. W. Tieleman, , and J. A. Balderrama, 2010: Surface wind measurements in three Gulf Coast hurricanes of 2005. J. Wind Eng. Ind. Aerodyn., 98, 533547.

    • Search Google Scholar
    • Export Citation
  • Monin, A. S., , and A. M. Obukhov, 1954: Basic laws of turbulent mixing in the ground layer of the atmosphere. Tr. Geofiz. Inst. Akad. Nauk. SSSR, 151, 163187.

    • Search Google Scholar
    • Export Citation
  • Nicholls, S., 1985: Aircraft observations of the Ekman layer during the Joint Air–Sea Interaction Experiment. Quart. J. Roy. Meteor. Soc., 111, 391426.

    • Search Google Scholar
    • Export Citation
  • Nicholls, S., , and C. J. Readings, 1979: Aircraft observations of the structure on the lower boundary layer over the sea. Quart. J. Roy. Meteor. Soc., 105, 785802.

    • Search Google Scholar
    • Export Citation
  • Powell, M. D., , P. J. Vickery, , and T. A. Reinhold, 2003: Reduced drag coefficient for high wind speeds in tropical cyclones. Nature, 422, 279283.

    • Search Google Scholar
    • Export Citation
  • Powell, M. D., , G. Soukup, , S. Cocke, , S. Gulati, , N. Morisseau-Leroy, , S. Hamid, , N. Dorst, , and L. Axe, 2005: State of Florida hurricane loss prediction model: Atmospheric science component. J. Wind Eng. Ind. Aerodyn., 93, 651674.

    • Search Google Scholar
    • Export Citation
  • Rotunno, R., , Y. Chen, , W. Wang, , C. Davis, , J. Dudhia, , and G. J. Holland, 2009: Large-eddy simulation of an idealized tropical cyclone. Bull. Amer. Meteor. Soc., 90, 17831788.

    • Search Google Scholar
    • Export Citation
  • Smith, R. K., , and M. T. Montgomery, 2010: Hurricane boundary-layer theory. Quart. J. Roy. Meteor. Soc., 136, 16651670.

  • Smith, R. K., , M. T. Montgomery, , and S. Vogl, 2008: A critique of Emanuel’s hurricane model and potential intensity theory. Quart. J. Roy. Meteor. Soc., 134, 551561.

    • Search Google Scholar
    • Export Citation
  • Sreenivasan, K. R., 1995: On the universality of the Kolmogorov constant. Phys. Fluids, 7, 27782784.

  • Stull, R. B., 1988: An Introduction to Boundary Layer Meteorology. Kluwer Academic, 666 pp.

  • Wang, Y., 2001: An explicit simulation of tropical cyclones with a triply nested movable mesh primitive equation model—TCM3. Part I: Description of the model and control experiment. Mon. Wea. Rev., 129, 13701394.

    • Search Google Scholar
    • Export Citation
  • Zhang, D.-L., , and E. Altshuler, 1999: The effects of dissipative heating on hurricane intensity. Mon. Wea. Rev., 127, 30323038.

  • Zhang, J. A., 2010: Estimation of dissipative heating using low-level in situ aircraft observations in the hurricane boundary layer. J. Atmos. Sci., 67, 18531862.

    • Search Google Scholar
    • Export Citation
  • Zhang, J. A., , P. G. Black, , J. R. French, , and W. M. Drennan, 2008: First direct measurements of enthalpy flux in the hurricane boundary layer: the CBLAST results. Geophys. Res. Lett., 35, L14813, doi:10.1029/2008GL034374.

    • Search Google Scholar
    • Export Citation
  • Zhang, J. A., , W. M. Drennan, , P. G. Black, , and J. R. French, 2009: Turbulence structure of the hurricane boundary layer between the outer rainbands. J. Atmos. Sci., 66, 24552467.

    • Search Google Scholar
    • Export Citation
  • Zhu, P., 2008a: Impact of land surface roughness on surface winds during hurricane landfall. Quart. J. Roy. Meteor. Soc., 134, 10511057.

    • Search Google Scholar
    • Export Citation
  • Zhu, P., 2008b: A multiple scale modeling system for coastal hurricane wind damage mitigation. Nat. Hazards, 47, 577591, doi:10.1007/s11069-008-9240-8.

    • Search Google Scholar
    • Export Citation
  • Zhu, P., 2008c: Simulation and parameterization of the turbulent transport in the hurricane boundary layer by large eddies. J. Geophys. Res., 113, D17104, doi:10.1029/2007JD009643.

    • Search Google Scholar
    • Export Citation
  • Zhu, P., , J. A. Zhang, , and F. J. Masters, 2010: Wavelet analyses of turbulence in the hurricane surface layer during landfalls. J. Atmos. Sci., 67, 37933805.

    • Search Google Scholar
    • Export Citation
  • View in gallery

    Plot of the tower locations with respect to the storm tracks. The storm tracks between the two black circles present the periods of measurements. The observation period is from 1700 UTC 4 Sep to 1900 UTC 5 Sep in Hurricane Frances (2004), from 0000 to 1900 UTC 16 Sep in Hurricane Ivan (2004), and from 0000 to 1400 UTC 26 Sep in Hurricane Jeanne (2004).

  • View in gallery

    (a) Plots of momentum fluxes at 5 and 10 m as a function of 10-m wind speed, (b) comparison of the momentum fluxes at 5 and 10 m, and (c) drag coefficients as a function of 10-m wind speed. Each symbol in the plots represents a flux run with a period of 15 min. The solid line in (b) shows the 1:1 ratio, and the dashed line shows the least-squares best fit of the data. The linear regression equation and the correlation between the two estimates are also shown in (b). The black line in (c) shows the bin-averaged drag coefficients and 1 std dev with a bin width of 2 m s−1.

  • View in gallery

    Dissipative heating estimated from the BE formula and directly from the turbulent spectra plotted (a) as a function of 10-m wind speed and (b) against each other. The black dashed line in (b) denotes the least-squares best fit of the data, and the light solid line shows the 1:1 ratio. The linear regression equation and the correlation between the two estimates are also shown in (b).

  • View in gallery

    (a) Plots of shear production as a function of 10-m wind speed, (b) dissipation rate as a function of 10-m wind speed, and (c) comparison between the shear production and dissipation rate. The light solid line in (c) shows the 1:1 ratio, and the black dashed line denotes the least-squares best fit of the data. The linear regression equation and the correlation between the two estimates are also shown in (c).

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On Momentum Transport and Dissipative Heating during Hurricane Landfalls

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  • 1 Rosenstiel School of Marine and Atmospheric Science, University of Miami, and Hurricane Research Division, NOAA/AOML, Miami, Florida
  • | 2 Department of Earth and Environment, Florida International University, Miami, Florida
  • | 3 Department of Civil and Coastal Engineering, University of Florida, Gainesville, Florida
  • | 4 Hurricane Research Division, NOAA/AOML, Miami, Florida
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Abstract

Momentum transport and dissipative heating are investigated using the high-resolution (10 Hz) wind data collected by Florida Coastal Monitoring Program portable weather stations in the surface layer of three landfalling hurricanes. The momentum flux is calculated using the eddy correlation method. The drag coefficient is determined from the momentum flux and surface wind speed. The values of the momentum flux and drag coefficient are found to be generally larger than those observed over the ocean at similar wind speeds up to near hurricane strength. The rate of dissipation is determined from the wind velocity spectra. The dissipative heating is estimated using two different methods: 1) integrating the rate of dissipation in the surface layer and 2) multiplying the drag coefficient by the cubic of the surface wind speed. It is found that the second method, which has been widely used in previous theoretical and numerical studies, significantly overestimates the magnitude of dissipative heating. This finding is consistent with a recent study on estimation of the dissipative heating over the ocean using in situ aircraft observations. This study is a first attempt at estimating the magnitude of dissipative heating in landfalling hurricanes using in situ observations. The results are believed to offer useful guidance in numerical weather prediction efforts aimed at improving the forecast of hurricane intensity.

Corresponding author address: Jun Zhang, NOAA/AOML/Hurricane Research Division, 4301 Rickenbacker Causeway, Miami, FL 33149. E-mail: jun.zhang@noaa.gov

Abstract

Momentum transport and dissipative heating are investigated using the high-resolution (10 Hz) wind data collected by Florida Coastal Monitoring Program portable weather stations in the surface layer of three landfalling hurricanes. The momentum flux is calculated using the eddy correlation method. The drag coefficient is determined from the momentum flux and surface wind speed. The values of the momentum flux and drag coefficient are found to be generally larger than those observed over the ocean at similar wind speeds up to near hurricane strength. The rate of dissipation is determined from the wind velocity spectra. The dissipative heating is estimated using two different methods: 1) integrating the rate of dissipation in the surface layer and 2) multiplying the drag coefficient by the cubic of the surface wind speed. It is found that the second method, which has been widely used in previous theoretical and numerical studies, significantly overestimates the magnitude of dissipative heating. This finding is consistent with a recent study on estimation of the dissipative heating over the ocean using in situ aircraft observations. This study is a first attempt at estimating the magnitude of dissipative heating in landfalling hurricanes using in situ observations. The results are believed to offer useful guidance in numerical weather prediction efforts aimed at improving the forecast of hurricane intensity.

Corresponding author address: Jun Zhang, NOAA/AOML/Hurricane Research Division, 4301 Rickenbacker Causeway, Miami, FL 33149. E-mail: jun.zhang@noaa.gov

1. Introduction

Turbulent transport in the atmospheric boundary layer is believed to play an essential role in the maintenance and intensification of a hurricane (e.g., Emanuel 1995; Smith et al. 2008; Rotunno et al. 2009; Smith and Montgomery 2010). Properly parameterizing turbulent transport processes is also essential to modeling hurricane decay, storm surge prediction, wind damage/risk assessment, and other hurricane mitigation applications (e.g., Marks and Shay 1998; Powell et al. 2005; Zhu 2008a,b). However, the physical processes—such as air–sea/air–land exchange of momentum, heat, and moisture, and turbulent mixing throughout the boundary layer in hurricane conditions—remain poorly understood because of the lack of turbulence data.

The purpose of this paper is to investigate the momentum transport processes in the surface layer of landfalling hurricanes, using high-resolution (10 Hz) wind data collected by portable weather stations deployed by the Florida Coastal Monitoring Program (FCMP; http://fcmp.ce.ufl.edu). We focus on examining the magnitude of dissipative heating (DH) during hurricane landfalls. Bister and Emanuel (1998) first pointed out that DH, which is caused by the dissipation of kinetic energy at the air–sea interface through molecular diffusion, is a significant source of energy for hurricane intensification and is very important for the hurricane intensity theory. Since this work, DH has been included in both theoretical and numerical hurricane models (e.g., Zhang and Altshuler 1999; Jin et al. 2007; Wang 2001; Bender et al. 2007; Bryan and Rotunno 2009).

In the Bister and Emanuel (1998) study, the dissipative heating is parameterized as DH = ρCdU3 (hereafter referred to as the BE formula), where ρ, Cd, and U are air density, drag coefficient, and surface wind speed, respectively. Using the dataset collected during the Coupled Boundary Layer Air–Sea Transfer (CBLAST) experiment (Black et al. 2007; Zhang et al. 2008), Zhang (2010) made the first comprehensive evaluation of the BE formula of DH in hurricanes over the ocean, showing that the BE formula significantly overestimated DH compared to that directly computed from turbulent spectra. This overestimation likely reflects the fact that not all the kinetic energy is dissipated into heat through molecular processes. Instead, a significant proportion of kinetic energy is believed to be used for surface wave production over the ocean. Over land, where there is no wave generation, one would expect that the BE formula of DH might work well. This prospect motivates us to further evaluate the BE formula during hurricane landfall.

An outline of the remaining sections of this paper is as follows. In section 2, we give a brief description of the data and the analysis methodology. Section 3 presents the results of the data analysis. This is followed by section 4, which summarizes the main findings and discusses future work.

2. Data and analysis method

Data used in this study were collected by seven portable weather stations deployed at locations near the paths of Hurricanes Frances (2004), Ivan (2004), and Jeanne (2004) at landfall, as part of FCMP (Masters 2004). Note that FCMP was initially designed with a focus on full-scale experimental methods to quantify near-surface hurricane wind behavior and the resultant loads on residential structures. Nevertheless, the wind measurements collected during FCMP provided a unique dataset to investigate the turbulent flow in the surface layer of landfalling hurricanes. On the FCMP stations, two arrays of 3D Gill propeller anemometer (model 200–27005) were installed at 5 and 10 m that measure three-dimensional wind velocity at 10 Hz. The R. M. Young van wind monitor (model 05103V) was also installed at 10 m to measure the three-dimensional velocity. Extensive comparisons between the two systems at 10 m show consistent wind measurements under hurricane wind conditions. Detailed description of the instrumentation is given by Masters et al. (2010) and Zhu et al. (2010).

Figure 1 shows the locations of the portable weather stations with respect to the storm tracks. The observation period is from 1700 UTC 4 September to 1900 UTC 5 September in Hurricane Frances (2004), from 0000 to 1900 UTC 16 September in Hurricane Ivan (2004), and from 0000 to 1400 UTC 26 September in Hurricane Jeanne (2004). All seven towers were deployed on relatively flat terrain with open exposure within 0.5 km of the location. The local static roughness lengths estimated from the U.S. Geological Survey (USGS) land use and land cover data are less than 0.3 m for all the towers. A total of 300 h of wind data have been analyzed. The maximum 10-m wind speed measured by the tower is 33 m s−1, close to hurricane strength.

Fig. 1.
Fig. 1.

Plot of the tower locations with respect to the storm tracks. The storm tracks between the two black circles present the periods of measurements. The observation period is from 1700 UTC 4 Sep to 1900 UTC 5 Sep in Hurricane Frances (2004), from 0000 to 1900 UTC 16 Sep in Hurricane Ivan (2004), and from 0000 to 1400 UTC 26 Sep in Hurricane Jeanne (2004).

Citation: Journal of the Atmospheric Sciences 68, 6; 10.1175/JAS-D-10-05018.1

Momentum flux τ is computed through the eddy correlation method in the form of
e1
where u′, υ′, and w′ are the turbulent fluctuations of the along-wind (i.e., along the mean wind direction), crosswind, and vertical component of the wind velocity, respectively. An overbar represents a time average over a suitable amount of time. The frictional velocity is defined as . The surface drag coefficient is calculated from the frictional velocity and 10-m wind speed such that
e2

To obtain momentum flux, the time series of data were split into 15-min segments or flux runs. The time series was detrended for each time segment before the momentum flux was calculated. Data quality assurance for individual flux run includes inspection of cumulative summation of covariance and power spectra of three wind components (e.g., Mahrt 1998; French et al. 2007; Drennan et al. 2007).

Following the method used by Zhang et al. (2009) and Zhang (2010), the dissipation rate of turbulent kinetic energy (TKE) is estimated from the spectral density of the horizontal along-wind velocity component in the inertial subrange; it is given by
e3
where αu is the one-dimensional Kolmogorov constant (=0.5, Sreenivasan 1995), Suu is the power-spectral density of the horizontal along-wind speed, and f is the frequency. Although the computation of ε is sensitive to αu, it is shown by Sreenivasan (1995) that αu is a universal constant in turbulent flow and the variation of αu is generally within 20%. An example of the wind velocity spectra for a typical flux run can be found in Zhu et al. (2010; see their Fig. 1), showing that the spectra follow the Kolmogorov law at low wavenumber or high frequency (f > 0.5 Hz). This spectral behavior gives us confidence in the estimation of ε using Eq. (3).
The dissipative heating in the surface layer is then determined by integrating the dissipation rate over the layer; it can be expressed by
e4
where z1 is the depth of the surface layer and is the average of the dissipation rate over the surface layer. Equation (4) provides a direct estimate of DH, so it is referred to as the direct method hereafter.
The BE formula can be derived from Eq. (4) by applying the surface layer theory (Monin and Obukhov 1954; Businger and Businger 2001), with assumption that there is a balance between the shear production and dissipation rate (i.e., ε) in the TKE budget:
e5
where κ is the von Kármán constant (=0.4).

Typically, the surface layer is 5%–10% of the boundary layer (Stull 1988). In the air–sea interaction and boundary layer community, it is a consensus to use 10 m as the surface layer height (e.g., Mahrt et al. 2001; Fairall et al. 2003; Donelan et al. 2004; Drennan et al. 2007). It is also a standard to use 10-m exchange coefficients to parameterize surface fluxes in the surface layer schemes used in numerical weather prediction models (e.g., Bender et al. 2007; Jin et al. 2007; Davis et al. 2008). This is the reason why surface flux measurements are typically taken at 10 m, as in our study. Notwithstanding that the surface layer may be higher than 10 m in landfalling hurricanes, we use 10 m as the surface layer height in the analyses.

3. Results

Momentum fluxes as a function of 10-m wind speed calculated using Eq. (1) at two levels, 5 and 10 m, are shown in Fig. 2a. The increase of momentum flux with wind speed is consistent with previous studies for low to moderate wind speed (<15 m s−1) over land (e.g., Deacon 1957; Mahrt et al. 2001) and ocean (e.g., Donelan et al. 1997; Banner et al. 1999; Fairall et al. 2003; French et al. 2007). A comparison of momentum fluxes measured at 5 and 10 m (Fig. 2b) shows a general agreement between them. The correlation between the two estimates is γ2 = 0.7, and the maximum likelihood regression gives . This result suggests that the momentum flux is roughly constant with height, which generally agrees with Monin–Obukhov similarity theory (Monin and Obukhov 1954). The magnitude of the momentum flux is found to be larger than that observed over the ocean in the similar wind speed range (French et al. 2007), which is mostly attributed to the large surface roughness over land.

Fig. 2.
Fig. 2.

(a) Plots of momentum fluxes at 5 and 10 m as a function of 10-m wind speed, (b) comparison of the momentum fluxes at 5 and 10 m, and (c) drag coefficients as a function of 10-m wind speed. Each symbol in the plots represents a flux run with a period of 15 min. The solid line in (b) shows the 1:1 ratio, and the dashed line shows the least-squares best fit of the data. The linear regression equation and the correlation between the two estimates are also shown in (b). The black line in (c) shows the bin-averaged drag coefficients and 1 std dev with a bin width of 2 m s−1.

Citation: Journal of the Atmospheric Sciences 68, 6; 10.1175/JAS-D-10-05018.1

The drag coefficient determined from all the flux runs is shown in Fig. 2c as a function of 10-m wind speed. The values of Cd vary from 0.002 to 0.04, which are larger than those observed over the ocean in a similar range of wind speeds (e.g., Fairall et al. 2003; Powell et al. 2003; Donelan et al. 2004; French et al. 2007). This difference can again be attributed to the larger surface roughness over land than that over the ocean. Although the scatter of the data is relatively large, there is a tendency for a decrease of Cd with increasing wind speed for wind speed less than 15 m s−1. This drag coefficient behavior is in general agreement with the analysis of Mahrt et al. (2001), who attributed the decrease of Cd to the decreasing role of viscous effects and streamlining of the vegetation. Following the error analysis method described by Drennan et al. (2007) and French et al. (2007), the uncertainty in Cd is approximately 30%. The large spread of Cd is believed to be due to the variation of upwind roughness, change of wind direction, stability, and inhomogeneous turbulent flow, which will be explored in the future work.

DH is computed using the BE formula and the direct method from the turbulent spectra. When estimating DH using the direct method, we have supposed that ε is constant with height as there is an agreement in the estimates of ε at 5 and 10 m (i.e., the regression equation is , and the correlation between the two estimates is γ2 = 0.78). In previous studies, direct measurements of momentum flux and ε over land are usually taken at one altitude (i.e., 10 m above the surface) with few flux observation above or below 10 m (e.g., Mahrt et al. 2001). Our analyses are consistent with previous aircraft observations over the ocean, showing that ε is nearly constant close to the surface, while it tends to decrease with increasing height above the surface layer (e.g., Lenschow 1970; Nicholls and Readings 1979; Nicholls 1985; Zhang et al. 2009). It is thought that the uncertainty in DH using the direct method that is associated with the vertical distribution of ε is small (<30%). The overall uncertainty in DH using the direct method is thought to be approximately 50%, considering the 20% uncertainty in the estimation of ε as discussed earlier.

Figure 3a shows DH estimated using the abovementioned two methods as a function of surface wind speed, indicating a clean trend of the increase of DH with increasing wind speed. This behavior of DH is in agreement with the finding of Zhang (2010) for over-ocean conditions. Undoubtedly, more heat is generated because of the dissipation of kinetic energy at higher wind speeds. The comparison of the two calculation methods (Fig. 3b) clearly shows that the BE formula overestimates DH compared with that computed from turbulent spectra. This overestimation is nearly by an order of magnitude, as shown by the least squares best-fit regression equation: . The significant difference between the two estimates is confirmed by a t test. Similar results are obtained using the observations at 5 m (not shown).

Fig. 3.
Fig. 3.

Dissipative heating estimated from the BE formula and directly from the turbulent spectra plotted (a) as a function of 10-m wind speed and (b) against each other. The black dashed line in (b) denotes the least-squares best fit of the data, and the light solid line shows the 1:1 ratio. The linear regression equation and the correlation between the two estimates are also shown in (b).

Citation: Journal of the Atmospheric Sciences 68, 6; 10.1175/JAS-D-10-05018.1

Because the BE formula is derived from the surface layer theory assuming a simplified balance between shear production and dissipation rate in the TKE budget, the overestimation of DH by the BE formula (Fig. 3) suggests that this balance may not be at work. To confirm this, we computed the shear production and compared it with the dissipation rate directly estimated from the turbulent spectra (Fig. 4). The result shows that the shear production is substantially larger than the dissipation rate, especially for surface wind speeds greater than 10 m s−1. The imbalance between the shear production and dissipation rate is also shown by Zhang (2010) in hurricanes over the ocean for surface wind speeds greater than 20 m s−1, but in a different sense of imbalance with the rate of dissipation dominates the shear production. Unfortunately, there is no high-resolution temperature or humidity data collected during FCMP, so we could not estimate the buoyancy production term in the TKE budget. Since the turbulence in the hurricane boundary layer is mainly shear driven and the boundary layer is usually under near-neutral conditions (e.g., Drennan et al. 2007; Zhang et al. 2008), the buoyancy term in the TKE budget is expected to be small. The local change rate of TKE estimated using data from consecutive legs with similar wind speeds is found to be much smaller than the shear production. Thus, other terms such as the advection, pressure transport, and turbulent transport terms are believed to be important in the TKE budget. Zhu (2008c) computed all the terms in the TKE budget using the large-eddy simulation of Hurricane Ivan (2004) and showed that the advection term can dominate a local budget of TKE. It is thought that the unsteady and inhomogeneous turbulent flow destroys the simplified TKE balance in the hurricane surface layer.

Fig. 4.
Fig. 4.

(a) Plots of shear production as a function of 10-m wind speed, (b) dissipation rate as a function of 10-m wind speed, and (c) comparison between the shear production and dissipation rate. The light solid line in (c) shows the 1:1 ratio, and the black dashed line denotes the least-squares best fit of the data. The linear regression equation and the correlation between the two estimates are also shown in (c).

Citation: Journal of the Atmospheric Sciences 68, 6; 10.1175/JAS-D-10-05018.1

4. Summary and discussion

In this study, 10-Hz wind data collected by the FCMP portable weather stations during the landfalls of three hurricanes are analyzed to instigate the momentum transport and dissipative heating (DH) in the hurricane surface layer over land. The momentum flux is directly calculated using the eddy correlation method. The drag coefficient is determined from the momentum flux and surface wind speed. The momentum flux is found to increase with increasing wind speed, in agreement with the findings of previous studies on momentum transfer in low to moderate wind conditions. The momentum fluxes at 5 and 10 m generally agree with each other at a given wind speed. The values of momentum flux and drag coefficient are found to be generally larger than that over the ocean in the similar wind speed range from previous observational studies. There is a tendency for the drag coefficient to decrease with increasing wind speed at low to moderate wind (<15 m s−1) conditions.

We estimate DH using two different methods: 1) integrating the rate of dissipation in the surface layer and 2) multiplying the drag coefficient by the cubic of the surface wind speed. The latter method is given by Bister and Emanuel (1998) (i.e., the BE formula), which has been widely used in numerical simulations of hurricanes. Our analyses show that the BE formula significantly overestimates the magnitude of DH directly estimated from turbulent spectra. This result is consistent with a recent study by Zhang (2010), who showed that the BE formula also fails to represent the dissipative heating for over-ocean conditions.

The failure of the BE formula to represent dissipative heating can be attributed to two possible reasons. First, over the ocean the BE formula fails to consider the energy used for wave production. Second, the BE formula is derived from the simplified TKE budget assuming a balance between the shear production and dissipation rate. While this balance is a good simplification for quasi-steady and near-homogeneous conditions (i.e., Businger and Businger 2001), it oversimplifies the local TKE budget in hurricane conditions where other terms in the budget such as the advection of TKE could be important. Moreover, terms in the TKE budget can have substantial temporal and spatial variations depending on specific locations in a hurricane. The imbalance between the dominant terms, the shear production and dissipation rate, is clearly shown in our analyses.

Recently, Makarieva et al. (2010) argued that adding DH back in the thermodynamic equation appears to be against the second law of thermodynamics, contrary to the findings of both theoretical analyses and numerical simulations showing the importance of DH in the evolution of a hurricane (Bister and Emanuel 1998; Zhang and Altshuler 1999; Jin et al. 2007). Leaving aside this controversy, it is believed that a realistic representation of DH in models is critical to hurricane simulations. Our work is a first attempt at estimating the dissipative heating in landfalling hurricanes using in situ observations. We believe our results can offer useful guidance in numerical weather prediction efforts aimed at improving the forecast of hurricane intensity.

We note that one of the limitations of this study is that only wind data are available for the analyses. Thus, it is impossible for us to perform a detailed analysis of all the terms in the TKE budget. We are also unable to look into the variation of the drag coefficient as a function of stability. This limitation will be alleviated once high-resolution temperature and moisture measurements are available. Currently, the portable weather stations are to be upgraded by implementing fast-response temperature and moisture sensors. More data would be collected in the coming hurricane seasons to further investigate turbulent processes in the hurricane boundary layer during landfalls. The other limitation of our results is that the data were collected within 10 m above the surface. It is certainly true that observations of turbulent fluxes at higher altitudes than 10 m will be crucial to verify the height at which a constant flux layer may end and to determine the vertical distribution of ε in the entire atmospheric boundary layer. Such observations will require dedicated field program with robust instrumentation to survive in such a severe condition in landfalling hurricanes.

Acknowledgments

This work was partially supported by the NOAA HFIP program. JZ also acknowledges the support from the National Research Council Research Associateship Award. PZ acknowledges the support from the National Science Foundation under Grant ATM-0847332. We thank Sim Aberson and Altug Aksoy for valuable comments on the early version of the manuscript. We thank the reviewers for their valuable comments, which improved the paper.

REFERENCES

  • Banner, M. L., , W. Chen, , E. J. Walsh, , J. B. Jensen, , S. Lee, , and C. Fandry, 1999: The Southern Ocean Waves Experiment. Part I: Overview and mean results. J. Phys. Oceanogr., 29, 21302145.

    • Search Google Scholar
    • Export Citation
  • Bender, M. A., , I. Ginis, , R. Tuleya, , B. Thomas, , and T. Marchok, 2007: The operational GFDL Coupled Hurricane–Ocean Prediction System and a summary of its performance. Mon. Wea. Rev., 135, 39653989.

    • Search Google Scholar
    • Export Citation
  • Bister, M., , and K. A. Emanuel, 1998: Dissipative heating and hurricane intensity. Meteor. Atmos. Phys., 65, 233240.

  • Black, P. G., and Coauthors, 2007: Air–sea exchange in hurricanes: Synthesis of observations from the Coupled Boundary Layer Air–Sea Transfer experiment. Bull. Amer. Meteor. Soc., 88, 357374.

    • Search Google Scholar
    • Export Citation
  • Bryan, G. H., , and R. Rotunno, 2009: The maximum intensity of tropical cyclones in axisymmetric numerical model simulations. Mon. Wea. Rev., 137, 17701789.

    • Search Google Scholar
    • Export Citation
  • Businger, S., , and J. Businger, 2001: Viscous dissipation of turbulence kinetic energy in storms. J. Atmos. Sci., 58, 37933796.

  • Davis, C., and Coauthors, 2008: Prediction of landfalling hurricanes with the Advanced Hurricane WRF model. Mon. Wea. Rev., 136, 19902005.

    • Search Google Scholar
    • Export Citation
  • Deacon, E., 1957: Wind profiles and the shearing stress—An anomaly resolved. Quart. J. Roy. Meteor. Soc., 83, 537540.

  • Donelan, M. A., , W. M. Drennan, , and K. B. Katsaros, 1997: The air–sea momentum flux in conditions of mixed wind sea and swell. J. Phys. Oceanogr., 27, 20872099.

    • Search Google Scholar
    • Export Citation
  • Donelan, M. A., , B. K. Haus, , N. Reul, , W. J. Plant, , M. Stianssnie, , H. C. Graber, , O. B. Brown, , and E. S. Saltzman, 2004: On the limiting aerodynamic roughness of the ocean in very strong winds. Geophys. Res. Lett., 31, L18306, doi:10.1029/2004GL019460.

    • Search Google Scholar
    • Export Citation
  • Drennan, W. M., , J. A. Zhang, , J. R. French, , C. McCormick, , and P. G. Black, 2007: Turbulent fluxes in the hurricane boundary layer. Part II: Latent heat fluxes. J. Atmos. Sci., 64, 11031115.

    • Search Google Scholar
    • Export Citation
  • Emanuel, K. A., 1995: Sensitivity of tropical cyclones to surface exchange coefficients and a revised steady-state model incorporating eye dynamics. J. Atmos. Sci., 52, 39693976.

    • Search Google Scholar
    • Export Citation
  • Fairall, C. W., , E. F. Bradley, , J. E. Hare, , A. A. Grachev, , and J. B. Edson, 2003: Bulk parameterization of air–sea fluxes: Updates and verification for the COARE algorithm. J. Climate, 16, 571591.

    • Search Google Scholar
    • Export Citation
  • French, J. R., , W. M. Drennan, , J. A. Zhang, , and P. G. Black, 2007: Turbulent fluxes in the hurricane boundary layer. Part I: Momentum flux. J. Atmos. Sci., 64, 10891102.

    • Search Google Scholar
    • Export Citation
  • Jin, Y., , W. T. Thompson, , S. Wang, , and C.-S. Liou, 2007: A numerical study of the effect of dissipative heating on tropical cyclone intensity. Wea. Forecasting, 22, 950966.

    • Search Google Scholar
    • Export Citation
  • Lenschow, D. H., 1970: Airplane measurements of planetary boundary layer structure. J. Appl. Meteor., 9, 874884.

  • Mahrt, L., 1998: Flux sampling errors from aircraft and towers. J. Atmos. Oceanic Technol., 15, 416429.

  • Mahrt, L., , D. Vickers, , J. Sun, , N. O. Jensen, , H. Jørgensen, , E. Pardyjak, , and H. Fernando, 2001: Determination of the surface drag coefficient. Bound.-Layer Meteor., 99, 249276.

    • Search Google Scholar
    • Export Citation
  • Makarieva, A. M., , V. G. Gorshkov, , B.-L. Li, , and A. D. Nobre, 2010: A critique of some modern applications of the Carnot heat engine concept: The dissipative heat engine cannot exist. Proc. Roy. Soc., 466A, 18931902, doi:10.1098/rspa.2009.0581.

    • Search Google Scholar
    • Export Citation
  • Marks, F. D., , and L. K. Shay, 1998: Landfalling tropical cyclones: Forecast problems and associated research opportunities. Bull. Amer. Meteor. Soc., 79, 305323.

    • Search Google Scholar
    • Export Citation
  • Masters, F. J., 2004: Measurement, modeling and simulation of ground level tropical cyclone winds. Ph.D. dissertation, University of Florida, 188 pp.

  • Masters, F. J., , H. W. Tieleman, , and J. A. Balderrama, 2010: Surface wind measurements in three Gulf Coast hurricanes of 2005. J. Wind Eng. Ind. Aerodyn., 98, 533547.

    • Search Google Scholar
    • Export Citation
  • Monin, A. S., , and A. M. Obukhov, 1954: Basic laws of turbulent mixing in the ground layer of the atmosphere. Tr. Geofiz. Inst. Akad. Nauk. SSSR, 151, 163187.

    • Search Google Scholar
    • Export Citation
  • Nicholls, S., 1985: Aircraft observations of the Ekman layer during the Joint Air–Sea Interaction Experiment. Quart. J. Roy. Meteor. Soc., 111, 391426.

    • Search Google Scholar
    • Export Citation
  • Nicholls, S., , and C. J. Readings, 1979: Aircraft observations of the structure on the lower boundary layer over the sea. Quart. J. Roy. Meteor. Soc., 105, 785802.

    • Search Google Scholar
    • Export Citation
  • Powell, M. D., , P. J. Vickery, , and T. A. Reinhold, 2003: Reduced drag coefficient for high wind speeds in tropical cyclones. Nature, 422, 279283.

    • Search Google Scholar
    • Export Citation
  • Powell, M. D., , G. Soukup, , S. Cocke, , S. Gulati, , N. Morisseau-Leroy, , S. Hamid, , N. Dorst, , and L. Axe, 2005: State of Florida hurricane loss prediction model: Atmospheric science component. J. Wind Eng. Ind. Aerodyn., 93, 651674.

    • Search Google Scholar
    • Export Citation
  • Rotunno, R., , Y. Chen, , W. Wang, , C. Davis, , J. Dudhia, , and G. J. Holland, 2009: Large-eddy simulation of an idealized tropical cyclone. Bull. Amer. Meteor. Soc., 90, 17831788.

    • Search Google Scholar
    • Export Citation
  • Smith, R. K., , and M. T. Montgomery, 2010: Hurricane boundary-layer theory. Quart. J. Roy. Meteor. Soc., 136, 16651670.

  • Smith, R. K., , M. T. Montgomery, , and S. Vogl, 2008: A critique of Emanuel’s hurricane model and potential intensity theory. Quart. J. Roy. Meteor. Soc., 134, 551561.

    • Search Google Scholar
    • Export Citation
  • Sreenivasan, K. R., 1995: On the universality of the Kolmogorov constant. Phys. Fluids, 7, 27782784.

  • Stull, R. B., 1988: An Introduction to Boundary Layer Meteorology. Kluwer Academic, 666 pp.

  • Wang, Y., 2001: An explicit simulation of tropical cyclones with a triply nested movable mesh primitive equation model—TCM3. Part I: Description of the model and control experiment. Mon. Wea. Rev., 129, 13701394.

    • Search Google Scholar
    • Export Citation
  • Zhang, D.-L., , and E. Altshuler, 1999: The effects of dissipative heating on hurricane intensity. Mon. Wea. Rev., 127, 30323038.

  • Zhang, J. A., 2010: Estimation of dissipative heating using low-level in situ aircraft observations in the hurricane boundary layer. J. Atmos. Sci., 67, 18531862.

    • Search Google Scholar
    • Export Citation
  • Zhang, J. A., , P. G. Black, , J. R. French, , and W. M. Drennan, 2008: First direct measurements of enthalpy flux in the hurricane boundary layer: the CBLAST results. Geophys. Res. Lett., 35, L14813, doi:10.1029/2008GL034374.

    • Search Google Scholar
    • Export Citation
  • Zhang, J. A., , W. M. Drennan, , P. G. Black, , and J. R. French, 2009: Turbulence structure of the hurricane boundary layer between the outer rainbands. J. Atmos. Sci., 66, 24552467.

    • Search Google Scholar
    • Export Citation
  • Zhu, P., 2008a: Impact of land surface roughness on surface winds during hurricane landfall. Quart. J. Roy. Meteor. Soc., 134, 10511057.

    • Search Google Scholar
    • Export Citation
  • Zhu, P., 2008b: A multiple scale modeling system for coastal hurricane wind damage mitigation. Nat. Hazards, 47, 577591, doi:10.1007/s11069-008-9240-8.

    • Search Google Scholar
    • Export Citation
  • Zhu, P., 2008c: Simulation and parameterization of the turbulent transport in the hurricane boundary layer by large eddies. J. Geophys. Res., 113, D17104, doi:10.1029/2007JD009643.

    • Search Google Scholar
    • Export Citation
  • Zhu, P., , J. A. Zhang, , and F. J. Masters, 2010: Wavelet analyses of turbulence in the hurricane surface layer during landfalls. J. Atmos. Sci., 67, 37933805.

    • Search Google Scholar
    • Export Citation
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