• Andreas, E. L., 1990: Time constants for the evolution of sea spray droplets. Tellus, 42B , 481497.

  • Andreas, E. L., 1995: The temperature of evaporating sea spray droplets. J. Atmos. Sci., 52 , 852862.

  • Andreas, E. L., 1998: A new sea spray generation function for wind speeds up to 32 m s−1. J. Phys. Oceanogr., 28 , 21752184.

  • Andreas, E. L., , and J. Decosmo, 1999: Sea spray production and influence on air-sea heat and moisture fluxes over the open ocean. Air-Sea Exchange: Physics, Chemistry and Dynamics, G. L. Geernaert, Ed., Kluwer Academic, 327–362.

    • Search Google Scholar
    • Export Citation
  • Andreas, E. L., , and K. A. Emanuel, 2001: Effects of sea spray on tropical cyclone intensity. J. Atmos. Sci., 58 , 37413751.

  • Bao, J-W., , J. M. Wilczak, , J-K. Choi, , and L. H. Kantha, 2000: Numerical simulations of air–sea interaction under high wind conditions using a coupled model: A study of hurricane development. Mon. Wea. Rev., 128 , 21902210.

    • Search Google Scholar
    • Export Citation
  • Barnes, G. M., 2006: Thermodynamic structure of a hurricane’s lower cloud and subcloud layers. Preprints, 27th Conf. on Hurricanes and Tropical Meteorology, Monterey, CA, Amer. Meteor. Soc., 5C.1. [Available online at http://ams.confex.com/ams/pdfpapers/107927.pdf.].

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

  • Blanchard, D. C., 1963: The electrification of the atmosphere by particles from bubbles in the sea. Prog. Oceanogr., 1 , 71202.

  • Chen, Y., , and M. K. Yau, 2001: Spiral bands in a simulated hurricane. Part I: Vortex Rossby wave verification. J. Atmos. Sci., 58 , 21282145.

    • Search Google Scholar
    • Export Citation
  • Cione, J. J., , P. G. Black, , and S. H. Houston, 2000: Surface observations in the hurricane environment. Mon. Wea. Rev., 128 , 15501561.

    • Search Google Scholar
    • Export Citation
  • Cipriano, R. J., , and D. C. Blanchard, 1981: Bubble and aerosol spectra produced by a laboratory “breaking wave”. J. Geophys. Res., 86 , 80858092.

    • Search Google Scholar
    • Export Citation
  • Day, J. A., 1964: Production of droplets and salt nuclei by bursting of air-bubble films. Quart. J. Roy. Meteor. Soc., 90 , 498.

  • de Leeuw, G., 1990: Profiling of aerosol concentrations, particle size distributions and relative humidity in the atmospheric surface layer over the North Sea. Tellus, 42B , 342354.

    • Search Google Scholar
    • Export Citation
  • Dudhia, J., 1993: A nonhydrostatic version of the Penn State–NCAR mesoscale model: Validation tests and simulation of an Atlantic cyclone and cold front. Mon. Wea. Rev., 121 , 14931513.

    • 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., , J. D. Kepert, , and G. J. Holland, 1994: The effect of sea spray on surface energy transports over the ocean. Global Atmos. Ocean Syst., 2 , 121142.

    • Search Google Scholar
    • Export Citation
  • Garratt, J. R., 1992: The Atmospheric Boundary Layer. Cambridge University Press, 316 pp.

  • Grell, G. A., , J. Dudhia, , and D. R. Stauffer, 1995: A description of the fifth-generation Penn State/NCAR mesoscale model (MM5). NCAR Tech. Note NCAR/TN-398+STR, 122 pp.

  • Kain, J. S., , and J. M. Fritsch, 1993: Convective parameterization for mesoscale models: The Kain–Fritsch scheme. The Representation of Cumulus Convection in Numerical Models, Meteor. Monogr., No. 46, Amer. Meteor. Soc., 165–170.

    • Search Google Scholar
    • Export Citation
  • Kepert, J. D., , C. W. Fairall, , and J-W. Bao, 1999: Modelling the interaction between the atmospheric boundary layer and evaporating sea spray droplets. Air-Sea Exchange: Physics, Chemistry and Dynamics, G. L. Geernaert, Ed., Kluwer Academic, 363–410.

    • Search Google Scholar
    • Export Citation
  • Kwon, Y. C., , and W. M. Frank, 2005: Dynamic instabilities of simulated hurricane-like vortices and their impacts on the core structure of hurricanes. Part I: Dry experiments. J. Atmos. Sci., 62 , 39553973.

    • Search Google Scholar
    • Export Citation
  • Kwon, Y. C., , and W. M. Frank, 2008: Dynamic instabilities of simulated hurricane-like vortices and their impacts on the core structure of hurricanes. Part II: Moist experiments. J. Atmos. Sci., 65 , 106122.

    • Search Google Scholar
    • Export Citation
  • Lighthill, J., , G. Holland, , W. Gray, , C. Landsea, , G. Craig, , J. Evans, , Y. Kurihara, , and C. Guard, 1994: Global climate change and tropical cyclones. Bull. Amer. Meteor. Soc., 75 , 21472157.

    • Search Google Scholar
    • Export Citation
  • Monahan, E. C., , and I. G. O’Muircheartaigh, 1986: Whitecaps and the passive remote sensing of the ocean surface. Int. J. Remote Sens., 7 , 627642.

    • Search Google Scholar
    • Export Citation
  • Monahan, E. C., , and M. Lu, 1990: Acoustically relevant bubble assemblages and their dependence on meteorological parameters. IEEE J. Oceanic Eng., 15 , 340349.

    • Search Google Scholar
    • Export Citation
  • Perrie, W., , E. L. Andreas, , W. Zhang, , W. Li, , J. Gyakum, , and R. McTaggart-Cowan, 2005: Sea spray impacts on intensifying midlatitude cyclones. J. Atmos. Sci., 62 , 18671883.

    • Search Google Scholar
    • Export Citation
  • Riehl, H., 1954: Tropical Meteorology. McGraw-Hill, 392 pp.

  • Wang, Y., 1999: A triply-nested movable mesh tropical cyclone model with explicit cloud microphysics—(TCM3). BMRC Research Rep. 74, 81 pp.

  • Wang, Y., , J. D. Kepert, , and G. J. Holland, 2001: The effect of sea spray evaporation on tropical cyclone boundary layer structure and intensity. Mon. Wea. Rev., 129 , 24812500.

    • Search Google Scholar
    • Export Citation
  • Woodcock, A. H., 1972: Smaller salt particles in oceanic air and bubble behavior in the sea. J. Geophys. Res., 77 , 53165321.

  • Woolf, D. K., , P. A. Bowyer, , and E. C. Monahan, 1987: Discriminating between the film drops and jet drops produced by a simulated whitecap. J. Geophys. Res., 92 , 51425150.

    • Search Google Scholar
    • Export Citation
  • Wu, J., 1981: Evidence of sea spray produced by bursting bubbles. Science, 212 , 324326.

  • Wu, J., 1994: Bubbles in the near-surface ocean: Their various structures. J. Phys. Oceanogr., 24 , 19551965.

  • Wu, J., 2002: Jet drops produced by bubbles bursting at the surface of seawater. J. Phys. Oceanogr., 32 , 32863290.

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

  • View in gallery

    The evolution of the temperature T and radius r of a 100-μm drop with initial temperature 28°C in air with temperature 27°C and 80% relative humidity (Andreas and Emanuel 2001). The wet-bulb temperature Tw = 24.5°C is reached at t = 0.3 s. The drop temperature begins to rise at t = 100 s.

  • View in gallery

    The four-domain setup (162, 54, 18, and 6 km) used in this study to simulate the idealized hurricanes.

  • View in gallery

    Time series of the minimum sea level pressure (mb) for EXP1–EXP5.

  • View in gallery

    Time series of the 200–850-mb vertical shear for EXP1–EXP5.

  • View in gallery

    Time series of the maximum wind speed (m s−1) for EXP1–EXP5.

  • View in gallery

    The azimuthally averaged and t = 33- to 45-h time-averaged sensible heat flux terms. Plotted on the abscissa is the radius (km) and on the ordinate is the flux (W m−2). (a) The control sensible heat flux and (b)–(e) the spray sensible heat flux Qs (solid), the surface sensible heat flux (thick dashed), and the total sensible heat flux (thin dashed) for EXP2–EXP5, respectively.

  • View in gallery

    Same as Fig. 6, but for latent heat fluxes.

  • View in gallery

    (a) Azimuthally averaged and t = 33- to 45-h time-averaged temperature (K). Plotted on the abscissa is the radius (km) and on the ordinate is the height (km). (b)–(e) The T anomaly from panel (a) of EXP2–EXP5, respectively, with negative values shaded.

  • View in gallery

    Same as Fig. 8, but for the mixing ratio (g kg−1).

  • View in gallery

    Same as Fig. 8, but for wind speed (m s−1).

  • View in gallery

    The fraction of spray that evaporates as a function of radius for EXP2–EXP5. Plotted on the abscissa is the radius (km) and on the ordinate is the fraction.

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 26 26 1
PDF Downloads 21 21 3

Effects of Sea Spray on Tropical Cyclones Simulated under Idealized Conditions

View More View Less
  • 1 Department of Meteorology, The Pennsylvania State University, University Park, Pennsylvania
  • | 2 National Centers for Environmental Prediction, Camp Springs, Maryland
© Get Permissions
Full access

Abstract

Under high-wind conditions, breaking waves and whitecaps eject large numbers of sea spray droplets into the atmosphere. The spray droplets originate with the same temperature and salinity as the ocean surface and thus increase the effective surface area of the ocean in contact with the atmosphere. As a result, the spray alters the total sensible and latent heat fluxes in the near-surface layer. The spray drops in the near-surface layer also result in horizontal and vertical spray-drag effects. The mass of the spray introduces an additional drag in the vertical momentum equation and tends to stabilize the lower boundary layer (BL).

An initially axisymmetric control hurricane was created from the output of a real-data simulation of Hurricane Floyd (1999) using the nonhydrostatic fifth-generation Pennsylvania State University–National Center for Atmospheric Research Mesoscale Model (MM5, version 3.4). The subsequent simulations, however, are not axisymmetric because the mass, wind, and spray fields are allowed to develop asymmetries. While such a design does not result in an axisymmetric simulation, the mass, wind, and spray fields develop more realistic structures than in an axisymmetric simulation. Simulations of the hurricane were conducted using a version of the Fairall et al. (1994) sea spray parameterization, which includes horizontal and vertical spray-drag effects. The simulations were run using varying spray-source function intensities and with and without horizontal and vertical spray-drag effects. At present, the relationship of spray production to surface wind speed is poorly known for hurricane-force wind regimes.

Results indicate that spray modifies the hurricane structure in important but complex ways. Spray moistens the near-surface layer through increased evaporation. The effect of spray on the near-surface temperature profile depends on the amount of spray and its location in the hurricane. For moderate spray amounts, the near-surface layer warms within the high-wind region of the hurricane and cools at larger radii. For larger spray amounts, the near-surface layer warms relative to the moderate spray case.

The moderate spray simulations (both with and without drag effects) have little net effect on the hurricane intensity. However, in the heavier spray runs, the total sensible heat flux is enhanced by 200 W m−2, while the total latent heat flux is enhanced by over 150 W m−2 in the high-wind region of the storm. Horizontal spray drag decreases wind speeds between 1 and 2 m s−1, and vertical spray drag increases the stability of the lower BL. In these heavy spray runs, the effect of the enhanced spray sensible and latent heat fluxes dominates the negative spray-drag effects, and as a result, the modeled storm intensity is upward of 10 mb stronger than the control run by the end of the simulation time. This study shows that spray has the capability of significantly affecting hurricane structure, but to do so, the amount of spray ejected into the BL of the hurricane would need to lie near the upper end of the currently hypothesized spray-source functions.

Corresponding author address: Jeffrey S. Gall, The Pennsylvania State University, 503 Walker Building, University Park, PA 16802. Email: gall@meteo.psu.edu

Abstract

Under high-wind conditions, breaking waves and whitecaps eject large numbers of sea spray droplets into the atmosphere. The spray droplets originate with the same temperature and salinity as the ocean surface and thus increase the effective surface area of the ocean in contact with the atmosphere. As a result, the spray alters the total sensible and latent heat fluxes in the near-surface layer. The spray drops in the near-surface layer also result in horizontal and vertical spray-drag effects. The mass of the spray introduces an additional drag in the vertical momentum equation and tends to stabilize the lower boundary layer (BL).

An initially axisymmetric control hurricane was created from the output of a real-data simulation of Hurricane Floyd (1999) using the nonhydrostatic fifth-generation Pennsylvania State University–National Center for Atmospheric Research Mesoscale Model (MM5, version 3.4). The subsequent simulations, however, are not axisymmetric because the mass, wind, and spray fields are allowed to develop asymmetries. While such a design does not result in an axisymmetric simulation, the mass, wind, and spray fields develop more realistic structures than in an axisymmetric simulation. Simulations of the hurricane were conducted using a version of the Fairall et al. (1994) sea spray parameterization, which includes horizontal and vertical spray-drag effects. The simulations were run using varying spray-source function intensities and with and without horizontal and vertical spray-drag effects. At present, the relationship of spray production to surface wind speed is poorly known for hurricane-force wind regimes.

Results indicate that spray modifies the hurricane structure in important but complex ways. Spray moistens the near-surface layer through increased evaporation. The effect of spray on the near-surface temperature profile depends on the amount of spray and its location in the hurricane. For moderate spray amounts, the near-surface layer warms within the high-wind region of the hurricane and cools at larger radii. For larger spray amounts, the near-surface layer warms relative to the moderate spray case.

The moderate spray simulations (both with and without drag effects) have little net effect on the hurricane intensity. However, in the heavier spray runs, the total sensible heat flux is enhanced by 200 W m−2, while the total latent heat flux is enhanced by over 150 W m−2 in the high-wind region of the storm. Horizontal spray drag decreases wind speeds between 1 and 2 m s−1, and vertical spray drag increases the stability of the lower BL. In these heavy spray runs, the effect of the enhanced spray sensible and latent heat fluxes dominates the negative spray-drag effects, and as a result, the modeled storm intensity is upward of 10 mb stronger than the control run by the end of the simulation time. This study shows that spray has the capability of significantly affecting hurricane structure, but to do so, the amount of spray ejected into the BL of the hurricane would need to lie near the upper end of the currently hypothesized spray-source functions.

Corresponding author address: Jeffrey S. Gall, The Pennsylvania State University, 503 Walker Building, University Park, PA 16802. Email: gall@meteo.psu.edu

1. Introduction

a. Overview

A hurricane is a complex dynamical system whose intensity is affected by both internal processes and interactions between the storm and its environment. Many of these processes are poorly understood, and numerical models presently have little skill in forecasting the intensity change of individual storms. One external process that may affect the intensity and structure of a hurricane is sea spray. In high-wind conditions, sea spray is injected into the near-surface layer and can modify both the total sensible and latent heat fluxes as well as the near-surface momentum transport and stability. This results in modification of the surface enthalpy and momentum exchange coefficients. Because hurricanes are strongly dependent on the ratio of the exchange coefficients of enthalpy and momentum (Emanuel 1995), sea spray could play a significant role in modifying hurricane structure and intensity.

b. Properties of spray

Sea spray is created through four different mechanisms. The first method of sea spray production involves air bubbles bursting at the sea surface (e.g., Woodcock 1972; Monahan and Lu 1990; Day 1964; Andreas 1990, 1995, 1998; Wu 1994, 2002; Woolf et al. 1987; Cipriano and Blanchard 1981). Jet drops are the second type of sea spray drop and are produced through the breakup of a water jet formed by the collapse of a bubble cavity (Blanchard 1963; Wu 1981). The spray drops created by both bursting air bubbles and jets are typically less than 20 μm and are the principal component of the droplet flux spectrum below radii of 3 μm (Woolf et al. 1987; Andreas 1998; Woodcock 1972; Cipriano and Blanchard 1981). The two remaining types of spray droplets, collectively referred to as spume droplets, are produced directly from breaking waves and do not rely on air entrained by the wave. When the 10-m wind speed reaches a threshold speed in the range of 7–11 m s−1, it is strong enough to tear off some wave crests and produce airborne spray (Monahan and O’Muircheartaigh 1986; Andreas 1990). The other type of spume drops are splash droplets, which result from the curling over and breaking of waves (Kepert et al. 1999). The radii of the spume drops are typically greater than 20 μm with no definite maximum (Andreas 1998). These latter two mechanisms account for a large percentage of the net spray-mediated enthalpy flux (Kepert et al. 1999), and the drop spectrum of these spume droplets is used in current spray parameterizations (e.g., Fairall et al. 1994).

The life cycle of an individual spray drop is complex, as described in Andreas and Emanuel (2001). Once a spray drop is ejected into a near-surface layer whose temperature Ta is cooler than the sea surface temperature (SST), the drop quickly cools from the SST to Ta by transferring sensible heat to the air, as seen in Fig. 1. The drop then evaporates and cools further. Before the drop reaches its wet-bulb temperature, the amount of evaporative cooling by the drop is greater than the amount of sensible heat absorbed, as indicated by the decreasing drop temperature with time in Fig. 1. Once the drop temperature reaches its wet-bulb temperature, the evaporative cooling of the drop is equal to the amount of sensible heat absorbed, and the drop temperature remains quasi steady. This continues until the drop either completely evaporates or falls back into the sea.

Individual sea spray drops can be divided into two distinct classes: drops that completely evaporate in the air and those that are reentrant (drops that fall back into the sea before completely evaporating). In the case of the fully evaporating drops, the boundary layer (BL) air provides most of the sensible heat required to evaporate the drops. The sensible heat lost to the evaporating drops by the BL air is balanced by the latent heat of the water vapor added to the BL air. Thus, the net enthalpy flux from the ocean to the air is due to the sensible heat lost from the drops before evaporation starts. If some of the spray falls back into the sea, however, the result is a larger net enthalpy flux from sea to air relative to the completely evaporating spray drop (Andreas and Emanuel 2001).

c. Sea spray and hurricanes

Sea spray generation over the open ocean during high-wind conditions has been observed for at least 200 yr. The Beaufort scale, although qualitative and extremely crude, was the first wind-dependent spray-generation description. Riehl (1954) first proposed the idea that sea spray evaporation generated in high-wind conditions provided a large amount of the heat necessary for tropical cyclone intensification. Fairall et al. (1994) first incorporated a reasonable spray-based parameterization into a simple model of the tropical cyclone BL. The inclusion of sea spray in their crude model produced a more realistic boundary layer structure. The authors stated, however, that their results should be treated with caution because of the simplicity of the model, and they offered no concrete conclusions on the net effect of sea spray on tropical cyclone intensity. The main conclusion from their primitive model is that sea spray droplet evaporation may be important in the maintenance of the hurricane BL. Kepert et al. (1999) continued this work using a more sophisticated tropical cyclone model and concluded that although spray had little effect on the net air–sea enthalpy flux, mechanisms such as enhanced evaporation due to spray could alter the BL stratification and increase the cyclone intensity. Lighthill et al. (1994) argued, however, that reducing the surface layer temperature by spray evaporation would actually weaken tropical cyclones.

Wang et al. (2001) evaluated the effect of parameterized sea spray on the tropical cyclone BL structure and intensity using a high-resolution tropical cyclone model (TCM3) developed by Wang (1999). The authors tested two spray droplet parameterizations—the Fairall et al. (1994) scheme and the Andreas and Decosmo (1999) scheme. The numerical results from inclusion of the Fairall et al. (1994) sea spray parameterization were that the spray-air sensible heat flux was only 6% of the direct (interfacial) sensible heat flux, while the spray-air latent heat flux was 60% of the direct (interfacial) latent heat flux. The energy necessary for the evaporation of large amounts of spray was provided by significant sensible heat transfer from the BL air to the evaporating spray. This negative (air to spray) sensible heat flux was much larger in magnitude than the spray-air sensible heat flux and explains why the total sensible heat flux in their Fig. 5a is negative over all radii. The resulting negative sensible heat flux cooled the BL by as much as 1.5 K in the high-wind region of the simulated hurricane. Because the positive spray latent heat flux was larger than the negative spray sensible heat flux, the net effect of the Fairall et al. (1994) spray parameterization was to enhance the total enthalpy flux by 1.5%, which ultimately increased the maximum wind speeds by 8%. Results from the Andreas and Decosmo (1999) parameterization, however, enhanced the maximum wind speeds by 25%. Andreas and Emanuel (2001) state that Wang et al. (2001) misrepresented the Andreas and Decosmo model such that their net air–sea enthalpy flux was too large and, as a result, produced a modeled storm that was too intense.

Andreas and Emanuel (2001) demonstrated that spray is important in the transfer of both enthalpy and momentum between the air and sea in high-wind conditions. Reentrant sea spray enhances the net enthalpy flux between sea and air. Both reentrant and fully evaporating sea spray act as a momentum sink, in that they extract momentum from the near-surface layer. This effect in turn moderates the effects of the net spray enthalpy flux. The authors found that including both enthalpy and momentum effects due to spray produced model results similar to simulations with no spray effects. Bao et al. (2000) employed a coupled atmosphere–ocean modeling system to simulate air–sea interaction under high-wind conditions. Results from model simulations with and without sea spray demonstrated that the inclusion of sea spray evaporation can significantly increase a hurricane’s intensity when the part of the spray that evaporates is only a small fraction of the total spray mass. When the fraction of spray that evaporates increases, spray has a negligible effect on hurricane intensity, which agrees with the findings of Andreas and Emanuel (2001).

Perrie et al. (2005) implemented the Andreas and Decosmo (1999) spray flux algorithm into the Canadian mesoscale model (MC2) in order to investigate the effects of spray on midlatitude cyclones. The authors found that the inclusion of sea spray effects increased the model storm intensity. They also investigated the effects of spray on BL structure. It was found that the inclusion of sea spray resulted in net cooling of the near-surface layer and net warming in the upper levels of the midlatitude cyclone, while near-surface mixing ratio values increased on the order of 1 g kg−1.

There are few sea spray observations for wind speeds above 20 m s−1. Measurements of the air–sea temperature difference taken by a USSR research vessel during Typhoons Skip and Tess in November 1988 (Fairall et al. 1994) revealed that as wind speed increases, the magnitude of the air–sea temperature difference increases. It was concluded that spray evaporation could cool the BL. More recently, Cione et al. (2000) used composite analyses of marine surface observations to show that the difference between the sea surface temperature and the surface air temperature significantly increased just outside the hurricane inner core. They hypothesized that within the inner core, the large sensible heat flux is balanced by the cooling effects of evaporation and adiabatic expansion, while the cooling observed just outside the inner core was due to unsaturated convective downdrafts along with the evaporation of sea spray. Barnes (2006) analyzed dropwindsonde data from Hurricane Bonnie (1998) and drew the important conclusion that spray may be responsible for the warming of the near-surface layer, with the largest warming (1 K) occurring in the eyewall of the hurricane.

The purpose of this study is to examine the effects of sea spray on hurricane structure and intensity using a full-physics model with idealized initial conditions. Such a model was used to associate cause–effect to sea spray and to minimize the effects of other external forcings (i.e., background flow, SST). Simulations were performed with varying amounts of sea spray and with and without spray-drag effects. This study was designed to address a few key questions: What are the values of the spray fluxes for a given spray source function? For the given spray fluxes, what is the effect on the structure of the simulated hurricane and how do these additional fluxes modify the hurricane intensity? Are horizontal and vertical spray-drag effects significant, and if so, what is the net effect on hurricane structure and intensity?

Section 2 of this paper features a description of the fifth-generation Pennsylvania State University–National Center for Atmospheric Research Mesoscale Model (MM5, version 3.4), the method by which the idealized conditions were created, and gives the equations for the interfacial fluxes. Section 3 describes version 3b of the Fairall et al. (1994) spray parameterization, as well as the parameterizations for horizontal and vertical spray drag. Section 4 outlines the experimental design used for this study. Section 5 presents simulation results, and section 6 provides a discussion of the results. Section 7 offers some conclusions of the effects of sea spray on hurricane structure and intensity.

2. Model description

The nonhydrostatic MM5, version 3.4, was used in this study to simulate the effects of parameterized sea spray on a hurricane within an idealized environment. The model governing equations and other specifics to the model formulation can be found in Grell et al. (1995). The model was run in a one-way nested fashion with a coarse grid domain of 162-km horizontal resolution covering most of the Atlantic Ocean, North America, and South America; a nested 54-km grid covering the eastern half of the United States and most of the Atlantic basin; a nested 18-km grid covering the Atlantic Ocean; and a nested, high-resolution 6-km grid in the western Atlantic centered on 17°N latitude (Fig. 2). All four domains contained 31 vertical levels at σ = 1.00, 0.993, 0.980, 0.966, 0.950, 0.933, 0.913, 0.892, 0.869, 0.844, 0.816, 0.786, 0.753, 0.718, 0.680, 0.639, 0.596, 0.550, 0.501, 0.451, 0.398, 0.345, 0.290, 0.236, 0.188, 0.145, 0.108, 0.075, 0.046, 0.021, and 0.000, with a greater density of sigma layers near the surface to better resolve the atmospheric BL and effects associated with the evaporation of sea spray. The 6-km domain used a 10-s model time step, which ensured numerical stability.

The initial and lateral boundary conditions for the 162-km domain MM5 simulations were provided by the National Centers for Environmental Prediction (NCEP) 12-h Navy Operational Global Atmospheric Prediction System (NOGAPS) analysis for the time period between 0000 UTC 9 September and 0000 UTC 17 September 1999. The following procedure used to create an initially axisymmetric vortex follows from Kwon and Frank (2005) and Chen and Yau (2001). A 162-km domain (162 × 162 grid points) simulation of Hurricane Floyd (1999) was performed for 96 h starting at 0000 UTC 9 September 1999. To create the highly idealized conditions for all subsequent simulations, an axisymmetric vortex on the 162-km domain was constructed by the azimuthal averaging of the tangential wind, pressure, mixing ratio, and temperature fields at t = 96 h. To remove all environmental flow around the vortex, all variables outside of 400 km were assigned a horizontally averaged value, except for the winds, which were set to 0. Also, to reduce the noise between the axisymmetric vortex and the constant environmental field, a buffer area was set between r = 300 and 400 km. Within this region, all variables were adjusted such that they changed smoothly from the environment (r = 400) to r = 300 km. All terrain was then removed and the land mask over the entire domain was set to water at a constant SST of 29°C. After creating the axisymmetric vortex and idealized conditions, an additional 96-h simulation was performed on an f plane to generate the initial and lateral boundary conditions for the nested domain. This simulation produced a relatively well-balanced vortex, but it was not axisymmetric. A similar procedure was repeated for the 54-km domain (217 × 217), 18-km domain (223 × 223), and 6-km domain (361 × 361), except each nested domain was started 24 h later to allow ample time for the vortex to spin up. All simulations, except for the initial 96 h 162-km run, were performed under idealized conditions and began with an initially axisymmetric vortex on an f plane. The subsequent simulations, however, were not axisymmetric. Numerous one-way nested simulations were conducted so that nearly all of the noise (gravity waves) was removed by the start of the 6-km run.

The high-resolution planetary boundary layer scheme of Blackadar (Zhang and Altshuler 1999) modified with Garratt (1992) fluxes was used in all simulations. Use of the Garratt fluxes has been shown to work well in similar types of MM5 simulations (S. Chen 2003, personal communication). The Blackadar BL model is used to forecast the vertical mixing of horizontal wind (u and υ), temperature (T), and mixing ratio (qυ). The bulk surface sensible heat flux is computed using
i1520-0493-136-5-1686-e1
where cp is the specific heat of air at constant pressure, ρa is the density of air, u* is the friction velocity, Ta is the air temperature of the lowest model layer (z = 39.1 m), Ts is the sea surface temperature, and Ch is the surface thermal exchange coefficient specified by the Garratt (1992) formulation. It should be noted that Ch is not the traditional exchange coefficient because it is multiplied by u* rather than the wind speed. For this reason, the exchange coefficient is typically one order of magnitude larger (10−2) than the traditional exchange coefficient. The surface latent heat flux is computed from
i1520-0493-136-5-1686-e2
where m is the moisture availability, Lυ is the latent heat of vaporization, q(Ta) is the mixing ratio of the lowest layer, qs(Ts) is the saturation surface mixing ratio, and Ce is the surface moisture exchange coefficient specified by the Garratt (1992) formulation.

The Dudhia (1993) explicit moisture scheme was used for grid-scale precipitation. This scheme allows for ice-phase processes but does not include supercooled water in the parameterization. The Kain–Fritsch convective scheme (Kain and Fritsch 1993) was implemented for all grids, except for the 6-km domain within which convection is assumed to be resolved explicitly and no cumulus parameterization is used. The cloud radiation scheme was implemented for all domains. This parameterization accounts for longwave and shortwave radiation interactions with clouds and clear air.

The initially axisymmetric vortex on the 6-km domain was used in this study. The SST was set to 29°C and was held constant for the entire simulation. The advantages of starting with an axisymmetric, mature storm are that the effects of vertical shear are minimized, while spray effects are large because spray generation is highly dependent on near-surface wind speeds. Additionally, the wind field, and consequent spray field, is allowed to develop asymmetries, as is often the case with such storms. The main disadvantage of beginning with a mature storm whose convection is not parameterized is that the time scale for the effect of spray processes to be realized at the upper levels of the hurricane is on the order of hours. This time lag prevents the effects of spray from being felt throughout the depth of the hurricane instantaneously.

Although initializing the model with a weaker storm would allow for an examination of the effects of sea spray on changing intensity, we wanted to focus on an initially mature storm in which spray effects would be most significant and do so in a relatively steady state (i.e., relatively small intensity changes over the period of the simulation). Future work will address effects of spray on an intensifying hurricane.

3. Spray parameterization

a. Flux parameterization

Version 3b of the Fairall et al. (1994) scheme is a scaling model that considers the thermal and evaporation time responses of the spectrum of ejected droplets versus their suspension lifetimes. The two factors that control the spray-suspension time are the fall velocity of the spray drops and their vertical transport by turbulence (Bao et al. 2000). The spectrum of droplets is determined as a function of wind speed from the spray-source function. This parameter is fundamental for properly representing the effect of sea spray on air–sea exchange processes. It is defined as the number of droplets of a given radius produced at the surface per unit surface area per unit time. The input variables for the parameterization are the wind speed (m s−1), the height (m) of the lowest model layer, the sea surface temperature (°C), the air temperature (°C) of the lowest model layer, the lowest model layer relative humidity (%), the surface pressure (mb), the interfacial sensible heat flux (W m−2) from the Blackadar BL routine, the interfacial latent heat flux (W m−2) from the Blackadar BL routine, and the friction velocity (m s−1).

The Fairall et al. (1994) parameterization accounts for the following spray drop processes:

  1. the spray drop gives off sensible heat in cooling from the ocean temperature (Ts) to the air temperature (Ta);
  2. the spray drop evaporates, which results in a spray-air latent heat flux;
  3. as the drop evaporates, the drop temperature cools to what is essentially a wet-bulb temperature (Tw), and the spray drop temperature becomes lower than the temperature of the surrounding environment, which results in a negative sensible heat flux from air to spray because Tw < Ta;
  4. while the drop is evaporating, the ambient moisture field nears saturation, which decreases the saturation mixing ratio gradient between the drop and the air and causes a decrease in the spray-air latent heat flux term; and
  5. the drop is constantly releasing or absorbing sensible heat, which in turn modifies the near-surface ambient temperature and then affects the spray-air sensible heat flux.

The first three processes can be thought of as direct spray effects, while the latter two are considered indirect spray effects because they modify BL air, which in turn modifies the net spray-air sensible and latent heat fluxes. All five processes are incorporated in the Fairall et al. (1994) parameterization.

Version 3b of the Fairall et al. (1994) parameterization first calculates the raw spray droplet sensible heat flux Qs by
i1520-0493-136-5-1686-e3
where the 0.92 accounts for the loss of heat not transferred from the largest droplets, cw is the specific heat of seawater, and Mflux is the spray mass flux with units (kg m−2 s−1). The spray mass flux is calculated by
i1520-0493-136-5-1686-e4
where ζ is a model tuning parameter, ρw is the density of seawater, and Sυ is the normalized source function. The currently accepted value of ζ is 0.3, which is based on a blend of the Fairall et al. (1994) physical spray-generation model, a fit to the de Leeuw (1990) data from the Humidity Exchange Over the Sea (HEXOS), and the Andreas (1998) spray-generation function, but this parameter is poorly known for high-wind conditions. The spray-air latent heat flux is given by
i1520-0493-136-5-1686-e5
where Vflux is the potential droplet vapor flux, qs(Ta) is the saturation mixing ratio over the ocean surface, and qs(Tw) is the saturation mixing ratio at the drop wet-bulb temperature Tw and reflects the fact that the drop is at Tw over most of its suspension lifetime. The potential droplet vapor flux is given by
i1520-0493-136-5-1686-e6
where ρa is the density of air and Sυ,l is a modified version of the normalized source function, which reflects the fact that only a fraction of the initial spray drop evaporates.
The raw droplet sensible heat flux Qs is not the spray-air sensible heat flux term. Rather, it is the heat flux given off by a drop in cooling from Ts to Tw. As noted in Fig. 1, the spray sensible heat flux is composed of two processes. First, spray gives off sensible heat in cooling from Ts to Ta. Second, the spray droplet cools from Ta to Tw, and the drop absorbs sensible heat from the environment. The first process is positive because Ts > Ta. The second process is negative because the spray drop absorbs sensible heat from the surrounding environment as it evaporates (Ta > Tw). As argued previously, the sensible heat gained from the surrounding air as the drop cools from Ta to Tw is equal to the latent heat given up by the spray drop as it evaporates. Thus, the spray-air sensible heat flux can be computed by
i1520-0493-136-5-1686-e7
It should be noted that Eqs. (3) and (5) of the Fairall et al. (1994) parameterization also account for the indirect spray effects through the modification of Ta. Moistening and heating–cooling the near-surface layer causes a slight change in Ta, which in turn slightly modifies the spray flux terms.
Equations (1) and (2) are modified to reflect the additional spray flux terms. The total sensible heat flux realized in the near-surface layer is
i1520-0493-136-5-1686-e8
The total latent heat flux realized in the near-surface layer is
i1520-0493-136-5-1686-e9
The total enthalpy flux is given by
i1520-0493-136-5-1686-e10

b. Horizontal drag parameterization

The horizontal spray-drag parameterization is based on the conservation of momentum. It is assumed that sea spray has a direct impact only on the lowest level wind field, with the higher levels being modified through vertical diffusion of momentum. Before the injection of spray into the atmosphere, the momentum in the lowest level (Mi) is given by
i1520-0493-136-5-1686-e11
where ma,i is the initial mass of air in a grid box and Vi is the initial wind speed of the lowest layer. After injecting sea spray into the atmosphere, some of the momentum in the lowest model layer is transferred to the sea spray before the spray falls back to the sea. It is assumed here that the spray accelerates to the wind speed before it falls out. The momentum in the lowest level (Mf) is now
i1520-0493-136-5-1686-e12
where ma,f is the final mass of air in a grid box, ms is the total spray mass in a grid box, and Vf is the final wind speed of the lowest layer after adjusting to the injected spray. Equating (11) and (12) and solving for Vf gives
i1520-0493-136-5-1686-e13
A reasonable assumption to invoke is that ma,fma,i because the total spray mass in a grid box is much smaller than the mass of the air. Thus, (13) can be rewritten as
i1520-0493-136-5-1686-e14
The variables Vi and ma,i can be computed from standard variables used in the model. The spray mass (ms), however, is estimated from the spray mass flux, which is calculated by the Fairall et al. (1994) spray parameterization. Thus, both reentrant and fully evaporating sea spray are accounted for by using the spray mass flux to calculate ms. It should also be noted that although the mass of water vapor from the interfacial vapor flux imposes a drag on the near-surface wind as well, it was not included within the drag parameterization for the following two reasons: first, the spray mass flux is much larger than the interfacial vapor flux within the high-wind region of the storm; second, the drag coefficient used in the Blackadar boundary layer scheme has been tuned to fit empirical data, which accounts for the drag of interfacial water vapor.

To incorporate the horizontal drag effect into the model equations, u- and υ-momentum tendency terms were calculated using Vi, Vf , and the model time step (Δt). These tendency terms were then added on to the full x- and y-momentum tendency terms.

c. Vertical drag parameterization

The spray mixing ratio qspray can be computed from the output of the spray parameterization and is given by
i1520-0493-136-5-1686-e15
It was assumed that qspray = 0 everywhere, except for in the lowest model layer. The vertical momentum equation contains a vertical drag term that accounts for the mass of rainwater (qr) and cloud water (qi). The drag term in the vertical momentum equation of the MM5 was modified to account for qspray and is given by
i1520-0493-136-5-1686-e16

4. Experimental design

This study examines how parameterized sea spray modifies the behavior of a hurricane and, in particular, the structure of the hurricane BL. Several model simulations are conducted to explore the sensitivity of the results to variations in the employed parameterization, as listed in Table 1. Sensitivity tests are performed for variations in the source function strength (ζ) in the spray parameterization. This function specifies the amount of spray generated for a specific surface wind speed. The effects of sea spray drag are also explored through the methods described in the previous section. All model simulations are integrated for a 45-h period, which allows ample time for the simulated hurricane to adjust to the additional spray fluxes. The control simulation (EXP1) is run with no spray parameterization. Experiment 2 (EXP2) employs the Fairall et al. (1994) spray parameterization, with the spray-source function tuning parameter set to the recommended value of ζ = 0.3. Experiment 3 (EXP3) is the same as EXP2, except that it includes spray-drag effects. Experiments 4 (EXP4) and 5 (EXP5) are the same as EXP2 and EXP3, respectively, except that the spray-source function tuning parameter is increased by a factor of 5 (ζ = 1.5). This five-time increase in the spray-source function tuning parameter is well within the bounds of uncertainty of the spray-source function (Andreas 1998).

5. Results

a. Hurricane intensity

Figure 3 reveals two different regimes during the model integration period for EXP1. During the first 18 h, the control hurricane maintained a minimum pressure near 944 mb. Starting at t = 21 h, the storm began to weaken, which continued through the remainder of the simulation. The initial vortex used in this study is the control vortex of Kwon and Frank (2008), except that the initial vortex was spun up using the modified Garratt (1992) surface fluxes. Since the Garratt (1992) fluxes decrease the magnitude of both the sensible and latent heat fluxes relative to the unmodified surface fluxes (S. Chen 2003, personal communication), the initial sea level pressure (945 mb) of the EXP1 vortex (Fig. 3) is higher than the initial sea level pressure of the vortex (926 mb) used in Kwon and Frank (2008). Figure 3 of Kwon and Frank (2008) showed that after about t = 24 h, their simulated hurricane began to weaken, and by t = 45 h, the vortex had weakened nearly 20 mb. Kwon and Frank (2008) attributed this long-term weakening to the sudden outbreak of positive baroclinic energy conversion in the upper levels starting at t = 24 h. Also, between the start and the end of the EXP1 simulation, the vertical shear between 850 and 200 mb and averaged from r = 0 to 150 km increased by approximately 6 m s−1 (Fig. 4). The increase in vertical shear over this period was the result of the specified lateral boundary conditions created using the procedure described in Kwon and Frank (2005). Thus, the weakening of the EXP1 (control) vortex after t = 18 h is due to the outbreak of positive baroclinic energy conversion in the upper levels starting at t = 18 h (not shown) and the increase in the vertical shear over the storm.

The maximum near-surface wind speed for EXP1 exhibited a similar but more erratic pattern (Fig. 5) when compared to Fig. 3. At t = 3 h, the hurricane had a peak wind speed of 54 m s−1, which steadily decreased to 50 m s−1 by t = 18 h. The wind speed continued to decrease for the remainder of the model integration. Examination of both the minimum sea level pressure and the maximum wind speed reveals two different regimes in the control run: a quasi-steady state over the first 18 h of the EXP1 simulation followed by a decrease in intensity for the remainder of EXP1.

The time series of minimum central pressures (Fig. 3) for the moderate spray cases with no drag (EXP2) and spray drag (EXP3) were nearly identical to the control run (EXP1) until t = 30 h. The vertical shear for EXP2 and EXP3 was also very similar to EXP1 (Fig. 4). After t = 30 h, the EXP2 minimum central pressure decreased about 3 mb relative to both EXP1 and EXP3 and remained lower for the rest of the simulation. Time series plots of the maximum wind speed for EXP2 and EXP3 in Fig. 5 exhibit trends somewhat similar to those of the minimum central pressure, but they tend to be more variable. Over the first 30 h of model run time, the wind speeds of those two runs are similar, but after this time they begin to diverge. The maximum wind speed of EXP3 is consistently 3–4 m s−1 lower than both EXP1 and EXP2 after about t = 33 h.

The minimum central pressures of the idealized storms in EXP4 and EXP5 remained in a quasi-steady state over the entire simulation period, even though the vertical shear increased slightly over the simulation period (Fig. 4). In both cases, the minimum central pressure remained between 941 and 944 mb from t = 0 to 30 h. During this period, the EXP4 and EXP5 pressures were consistently 1–3 mb lower than the EXP1 simulation. Also, the EXP4 storm was slightly more intense than the EXP5 case. After t = 30 h, the control minimum central pressure increased steadily for the rest of the model integration, while the minimum central pressure of EXP4 and EXP5 increased only slightly. The time series plots of maximum near-surface wind speed (Fig. 5) for EXP4 and EXP5 are very similar to the minimum central pressure time series. Over the first 36 h, the maximum wind speed of EXP4 was consistently 1–2 m s−1 larger than the maximum wind speed of EXP5. After this time, however, they are nearly equal. By t = 45 h, the EXP5 wind speed is near 48 m s−1, while the EXP4 maximum wind speed is closer to 46 m s−1. Figures 3, 5 reveal that variations in the spray-source function (and ultimately the amount of ejected spray) cause many more significant changes in the simulated storm than does inclusion of spray-drag effects.

b. Surface fluxes

All terms comprising the total sensible heat flux (Fig. 6) and the total latent heat flux (Fig. 7) were averaged in time over the period from t = 33 to 45 h and azimuthally averaged at each radius from the hurricane center (r = 0) to r = 155 km. Because the total fluxes were instantly larger than the control fluxes, the time period over which the fluxes were averaged was chosen to allow the model ample time to adjust to the enhanced surface fluxes. It should also be noted that the center of the storm was located using the minimum sea level central pressure. The fluxes were also averaged over the radial band between r = 30 and 60 km, as seen in Tables 2 –4. This latter averaging was done to highlight the magnitude of the fluxes in the high-wind region of the storm, where the fluxes tend to be the strongest. Figures 6a, 7a show the EXP1 (control) time-averaged sensible and latent heat fluxes, as given by Eqs. (1) and (2). Both flux maxima are located in the high-wind region of the hurricane. The (30–60 km) radially averaged latent heat flux is 659.9 W m−2, and the average sensible heat flux is 139.6 W m−2 (Table 3).

Plotted in Figs. 6b–c, 7b–c are the terms comprising the total sensible and latent heat fluxes from the spray alone for EXP2 and EXP3, respectively. Both the moderate spray, no-drag case (EXP2) and the moderate spray-drag case (EXP3) are extremely similar. The magnitudes of Qs and Ql are extremely small and have radial-averaged values for EXP2 of 8.9 W m2 and 11.3 W m2 and for EXP3 of 5.6 W m−2 and 8.2 W m−2, respectively. Table 2 shows that Qs accounts for 6% of the total sensible heat flux in EXP2 and 4% of the total sensible heat flux in EXP3 in the high-wind region. The spray latent heat flux term (Ql) comprises only 2% of the total latent heat flux for EXP2 and 1% for EXP3. Both Qs and Ql are near zero outside of the high-wind region. The total latent heat flux term (Hl,tot) and the total sensible heat flux term (Hs,tot) are dominated by the interfacial (i.e., surface) flux terms in both EXP2 and EXP3. Table 3 shows that in both EXP2 and EXP3, the interfacial fluxes are slightly weaker than those of the control fluxes. In EXP2, the net effect of spray is a slight enhancement of the total sensible heat flux and there is no change in the total latent heat flux (Table 4). In EXP3, both the total sensible and latent heat fluxes are weaker than the control fluxes. All terms in the total sensible heat flux and latent heat flux equation are larger in magnitude in EXP2 than in EXP3.

In the heavy spray cases (EXP4 and EXP5), it is readily apparent that the spray flux terms comprise a much larger percentage of the total sensible and latent heat flux terms, as seen in Figs. 6d–e, 7d–e. The spray sensible heat flux and spray latent heat flux both peak in the high-wind region of the hurricane but quickly decrease as r increases past the radius of maximum winds, which is indicative of the strong dependence of spray generation on the near-surface wind speed. In EXP4 and EXP5, Qs is negative but small in magnitude, past r = 55 km. Here, Ql also decreases as the radius increases, but Ql decreases more slowly than Qs with radius. This is indicative that although Ql has a strong dependence on near-surface wind speed, the dependence is less than that of Qs. It should also be noted that Ql ≥ 0 over all r, as seen in Figs. 7d–e.

For EXP4, the high-wind-region spray sensible heat flux is 86.7 W m−2 and comprises 37% of the total sensible heat flux, while the spray latent heat flux is 87.8 W m−2 and comprises 11% of the total latent heat flux (Table 2). EXP5 exhibits slightly smaller spray flux values than EXP4. In EXP5, the high-wind-region sensible heat flux is 75.1 W m−2, which accounts for 37% of the total sensible heat flux, while the spray latent heat flux is 73.2 W m−2 and comprises 10% of the total latent heat flux. In both EXP4 and EXP5 the interfacial fluxes are only slightly modified, as seen in Table 3. In EXP4, the bulk surface sensible heat flux increased by 2% and the bulk latent heat flux increased by 4% relative to the control fluxes. In EXP5, the bulk surface sensible heat flux is 9% less than the control sensible heat flux, and the bulk surface latent heat flux is 4% smaller than the control latent heat flux.

The net effect of spray in both EXP4 and EXP5 is to enhance the total fluxes as seen in Table 4. The total latent heat flux is increased by 18% in EXP4 and by 7% in EXP5. The greater percentage enhancement, however, occurs with the total sensible heat flux, as indicated by the 67% increase in the EXP4 total sensible heat flux and the 45% increase in the EXP5 sensible heat flux relative to the control sensible heat flux.

c. Hurricane structure

Model structure variables are both azimuthally and time averaged over a 12-h period beginning at t = 33 h, as done in the previous section. The later time was selected to allow the model ample time to adjust to the additional spray fluxes. Figures 8a, 9a, 10a show rz plots of T, q, and V, respectively, for the EXP1 simulation. These control fields were subtracted from the results of the other simulations to generate anomaly fields for EXP2–EXP5. For EXP2 (Fig. 8b), a warm anomaly extends from z = 13 to 16 km and from r = 0 to 70 km. The near-surface layer contains a weak, positive temperature anomaly between about r = 10 and 65 km. At radii greater than 65 km, however, the near-surface layer in EXP2 is approximately 0.1 K cooler than the control near-surface layer. In EXP2, spray is associated with warming at the upper levels of the hurricane. Spray also modifies the near-surface layer such that locations at smaller radial distances from the hurricane center warm relative to the EXP1 near-surface layer, while locations at larger radial distances cool relative to the EXP1 near-surface layer. The final feature of note is the midlevel warming in Fig. 8b of 0.25–0.5 K from z = 2 to 6 km and from about r = 50 to 100 km.

Comparing Figs. 8b,c reveals a few differences in thermal structure between EXP2 and EXP3. First, there is no upper-level warming in EXP3. Also, the core of the storm of EXP3 features pockets of negative temperature anomaly, indicative of the slightly weaker intensity. No such structure was observed in the core of the storm for EXP2. The near-surface layer of EXP3 was also cooler than that of EXP2, and the boundary between near-surface warming and cooling shifted from r = 65 for EXP2 to r = 40 km for EXP3. The near-surface temperature anomalies in EXP3 are more strongly negative than in EXP2 at larger radii, with the largest negative anomaly of −0.5 K existing near r = 100 km. Thus, including spray-drag effects in the spray parameterization results in negative temperature anomalies in the upper levels of the hurricane and a cooler near-surface layer when compared to the EXP2 results, which is due to the decreased intensity of the EXP3 hurricane relative to the control hurricane intensity over the final 12 h of the simulation.

Figure 8d shows the temperature difference between the high spray, no-drag simulation (EXP4) and the control simulation. The first feature of interest is the near-surface layer warming between r = 0 and 115 km. Within this region, temperatures are near 0.25 K warmer than the control simulation. At r > 115 km, however, there is little change in the near-surface temperature structure. The core region of the storm experienced a slight warming, with a maximum temperature anomaly of 2.0 K, which is located at small radii and z = 15 km. There are also pockets of small negative temperature anomaly (−0.25 K) oriented diagonally from z = 2 and r = 10 to z = 6 and r = 80 km. Figure 8e is similar to Fig. 8d with three significant exceptions. The diagonally oriented area of midlevel cooling present in EXP4 has shifted to smaller radii and is approximately 0.25 K in magnitude. Midlevel cooling at z = 4 km is present between r = 80 and 125 km in EXP5, and the near-surface warming is about 0.25 K greater for EXP5 than for EXP4. For the heavy spray cases (EXP4 and EXP5), the warming in the upper levels of the hurricane is greater than in the moderate spray cases. The near-surface layers of the heavy spray cases are also warmer than in the moderate spray cases, and the radius at which the near-surface temperature anomaly nears 0 increases. Comparing EXP4 to EXP5 reveals a slightly larger vertical temperature gradient between z = 0 and 4 km for EXP5.

Figure 9b shows the mixing ratio anomaly field for EXP2 relative to the control simulation. Figure 9b shows a broad region of positive anomalies in the near-surface layer, with a maximum of 0.75 g kg−1 between r = 100 and 150 km. Directly above this maximum is an area of negative q anomaly, with a minimum value of −0.5 g kg−1. The largest q anomalies are located close to the ocean surface. In Fig. 9c, the near-surface layer positive q anomaly for EXP3 is slightly smaller than in EXP2, with a maximum of 0.50 g kg−1 near r = 150 km. At z = 3 km, however, a negative q anomaly at r = 150 km (Fig. 9c) is apparent directly above the region of positive q anomaly. No such negative q anomaly was apparent in Fig. 9b of EXP2. In both EXP2 and EXP3, the hurricane BL has moistened. The EXP2 vertical q gradient between z = 0 and 4 km is larger in magnitude when compared with EXP1, while the EXP3 vertical q gradient between z = 0 and 4 km is smaller in magnitude, on average, when compared with EXP1.

For EXP4, a positive q anomaly of 0.50 g kg−1 is located through much of the near-surface layer (Fig. 9d). There is an area of negative q anomaly at z = 1.5 km, located directly above the positive q anomaly at larger radii. In comparing Figs. 9d,e, the most significant difference is that the near-surface maximum positive q anomaly has increased to 1 g kg−1 in EXP5 and is much larger in radial extent. In summary, the positive q anomalies in the near-surface layer are larger in EXP4 and EXP5 when compared with EXP2 and EXP3 and result in larger vertical gradients of q between z = 0 and 4 km.

The difference between the time-averaged control wind speed and the EXP2 wind speed is shown in Fig. 10b. The largest positive wind speed anomalies exist in the high-wind region of the storm between the surface and z = 6 km and are on the order of 2–3 m s−1. The wind speeds in EXP3 (Fig. 10c) are generally 2– 3 m s−1 slower than the control simulation, with the largest difference occurring in the near-surface, high-wind region of the hurricane. Thus, the wind speeds in EXP2 are upward of 4 m s−1 faster in the high-wind region of the storm than in EXP3.

Figure 10d shows the largest increase in wind speed between r = 20 and 50 km for EXP4. In this case, however, the area of strong positive anomalies extends upward to z = 11 km. The maximum V anomalies in Fig. 10d are 6–8 m s−1. In comparing Fig. 10d to Fig. 10e, the wind speed anomalies for EXP5 are between 1 and 2 m s−1 slower than those of EXP4. Although the horizontal and vertical drag effects are stronger in the heavy-spray case (EXP5) than in EXP3, the wind speed differences between drag and no-drag simulations are generally smaller for the high spray cases (EXP5 versus EXP4) than for the moderate spray cases (EXP3 versus EXP2).

6. Discussion

a. Moderate spray (EXP2 and EXP3)

In the moderate spray, no-drag and drag cases (EXP2 and EXP3), the spray-air sensible heat flux (Qs) is slightly positive between 0 ≤ r ≤ 60 km and near 0 at larger radii, as seen in Figs. 6b,c. Thus, Qs is positive in the high-wind region of the storm. This indicates that the spray drop loses more sensible heat in cooling from the SST to the air temperature than it gains from evaporation. The spray-air latent heat flux (Ql) is also positive in this region because the spray drop partially evaporates. Thus, the direct effects of sea spray enhance both the total sensible and latent heat flux terms in the high-wind region.

The Qs and Ql fluxes have noticeable effects on the profiles of temperature and mixing ratio in the moderate spray cases. From Figs. 8b,c, it is evident that there is a transition from near-surface warming to near-surface cooling as the distance from the center of the storm increases. Andreas and Emanuel (2001) showed that less than 1% of the initial spray mass needs to evaporate for a spray drop to cool from its air temperature to its equilibrium temperature. A similar expression can be derived to determine the fraction of spray that is needed to evaporate to cool the near-surface layer (see the appendix). Results from the appendix show that the effect of evaporating spray on near-surface temperature is controlled by the fraction of spray that evaporates. It was concluded that approximately 1% or more of the total spray needs to evaporate to cool the near-surface air. When less than 1% of the spray evaporates, more heat is transferred from the spray to the air than is taken by the spray in response to evaporation, and the near-surface layer warms. Figure 11 displays the fraction of spray that evaporates as a function of radial distance from the center of the storm. As the distance from the storm center increases, the fraction of spray that evaporates increases. Thus, one would expect the greatest near-surface-layer warming to be located nearer the center of the storm with a transition to cooling as the radius increases. This phenomenon is observed for the moderate spray cases, as seen in Figs. 8b,c. Although the magnitudes of the positive–negative temperature anomalies differ between the two figures, the transition from near-surface warming to near-surface cooling with increasing radius occurs in both cases.

Midlevel warming on the order of 0.5 K is apparent in Fig. 8b up to z = 6 km. This warming may be the result of changes in storm intensity or, as speculated by Perrie et al. (2005), a dynamic response to the increased latent heat release associated with recondensing spray-derived vapor. More diagnostics beyond the scope of this study are needed to determine the cause of this observed warming.

Because the interfacial sensible and latent heat spray flux terms are coupled to the ambient values of air temperature and mixing ratio, modifying the background environment via Qs and Ql affects the interfacial fluxes that indirectly influence the total sensible and latent heat fluxes. The net warming and moistening of the near-surface layer decreases the interfacial surface fluxes of both latent and sensible heat fluxes (Table 3) because of the decreases in the near-surface gradients of temperature and mixing ratio. Thus, the enhancement of the total fluxes via the spray terms is opposed by the decrease in the interfacial fluxes for the moderate spray cases. For EXP2, the positive contribution of the spray sensible heat flux to the total sensible heat flux is larger than the surface sensible heat flux decrease, as seen by the increase in the total sensible heat flux given by Table 4. Conversely, the net effect of the spray on the latent heat flux in EXP2 is to decrease the total latent heat flux. Thus, the indirect effect of spray in decreasing the surface latent heat flux is stronger than the positive latent heat spray flux.

In the high-wind region of the storm, where the total flux terms are most significant, spray slightly increased the EXP2 total sensible plus latent heat flux between t = 33 and 45 h, which in turn helped to lower the storm central pressure during this period (Fig. 3) relative to EXP1. The drop in pressure resulted in increased wind speeds, and spray therefore had an indirect effect on wind speed as well in the EXP2 case.

Including spray drag in the moderate spray case (EXP3) had a small but noteworthy effect on hurricane structure and intensity. The direct effect of horizontal spray drag was to decrease the horizontal wind speed. As shown in Figs. 10b,c, the horizontal wind speed anomalies are positive for the no-drag case and negative for the spray-drag case (EXP3) in the high-wind region of the hurricane. Because the spray fluxes are highly dependent on the near-surface wind speed, a decrease in horizontal wind speed also decreases the magnitude of the spray flux terms. As shown in Table 2, the spray flux terms for EXP3 are smaller in magnitude than the spray flux terms of EXP2. In EXP3, the layer between the surface and z = 4 km has a larger vertical T gradient and smaller vertical q gradient, on average, when compared to the vertical gradients of T and q of EXP2. Because it would be expected for vertical drag to decrease the vertical mixing and ultimately increase the vertical gradients of both temperature and mixing ratio, it was concluded that vertical spray drag had little effect on the moderate spray cases (EXP2 and EXP3). To verify this, EXP3 was modified to include only horizontal spray drag. Results of the simulation (not shown) were nearly identical to the horizontal and vertical spray-drag simulation. Thus, including drag (both horizontal and vertical) in the moderate spray case ultimately decreased the simulated storm intensity. In the case of EXP3, the negative effect of horizontal spray drag on both the horizontal wind speeds and the interfacial fluxes was the primary cause for the additional weakening of the simulated hurricane relative to EXP2.

b. Heavy spray (EXP4 and EXP5)

In the strong spray simulations (EXP4 and EXP5), the spray latent heat flux term comprises close to 10% of the total latent heat flux, while the spray sensible heat flux comprises slightly less than 40% of the total sensible heat flux in the high-wind region of the hurricane (Table 2). The large spray flux terms enhance the total latent and sensible heat fluxes over most of the domain (Figs. 6d,e and 7d,e). Because the spray flux terms comprise much larger fractions of the total flux terms relative to the moderate spray cases, the effects of the spray flux terms on the ambient environment are much more pronounced. In the EXP4 simulation, the BL warming is greater than in the moderate spray cases, as evidenced by comparing Figs. 8b,d. The BL is 0.1–0.2 K warmer than in EXP2, and the transition line from BL warming to cooling is located at a larger radius. Positive temperature anomalies are present up to z = 6 km, but the midlevel warming is slightly smaller in magnitude than in EXP2. Also, the increased spray-air latent heat flux increased the total amount of spray evaporated, which consequently increased the near-surface mixing ratio, as evidenced by Fig. 9d. In the EXP4 case, the near-surface layer is 0.5 g kg−1 moister than the moderate spray cases. Thus, additional spray ejected into the BL warms and moistens the near-surface layer through the larger spray-air sensible and latent heat flux terms.

In the heavy spray, no-drag case, the surface (interfacial) latent and sensible heat fluxes are slightly larger than the control fluxes, as seen in Table 3. There are two competing factors that essentially oppose each other. First, the warming and moistening of the near-surface layer in EXP4 decreases the near-surface T and q gradients, thus acting to decrease the interfacial fluxes. However, this effect is opposed by the increase in storm intensity. As evidenced by Fig. 10d, the near-surface wind speed has increased by upward of 6 m s−1 for EXP4, and this acts to increase the interfacial fluxes because the fluxes are proportional to the near-surface wind speed. The increase in wind speed has a larger effect on the interfacial fluxes than does the warming and moistening of the near-surface layer. Hence, the net effect of spray is to increase the total fluxes in the high-wind region of the storm, as seen in Table 4. The increase in the total fluxes for EXP4 results in an increase in the simulated hurricane intensity. By the end of the model simulation, the EXP4 idealized hurricane is 8 mb stronger than the control simulation, as seen in Fig. 3. EXP4 does not experience the intensity decrease witnessed in EXP2 past t = 18 h, and the enhanced spray fluxes counteract the negative effect of vertical shear on hurricane intensity.

As in the moderate spray cases, including horizontal and vertical spray drag in the heavy spray simulation (EXP5) has a small effect on hurricane structure and intensity. Over the entire simulation, the maximum wind speed in EXP5 is generally 1–2 m s−1 slower than that of EXP4 (Fig. 5). The spray-caused decrease in wind speeds decreases the magnitude of both the spray flux and interfacial flux terms. The vertical drag decreases the mixing of warm, moist air from the surface with relatively cooler, drier air from aloft. The decrease in mixing results in larger positive T and q anomalies in the near-surface layer in EXP5 when compared to EXP4 and further decreases the magnitude of the interfacial flux terms. Both horizontal and vertical spray drags result in the hurricane in EXP5 being weaker than the EXP4 storm during most of the model integration.

c. Limitations

Two important processes were not included within the spray parameterization: the effect of spray on the surface exchange coefficients and the effect of dissipative heating on sea spray evaporation. In the Blackadar BL routine modified with Garratt (1992) fluxes, the surface exchange coefficients Ch [Eq. (1)] and Ce [Eq. (2)] are dependent on the near-surface stability. We note that to properly account for the effect of liquid spray on the BL stability, the surface exchange coefficients should also be modified. However, this is not straightforward in the Blackadar BL and the coefficients are not altered in the current paper.

It has been shown that the dissipation (friction) of turbulent kinetic energy has a first-order effect on the thermodynamics of a hurricane, as shown in Bister and Emanuel (1998) and Zhang and Altshuler (1999). This term, however, was not included within the model simulations for the following two reasons: first, model simulations were conducted with this extra heating term included within the Fairall et al. (1994) spray parameterization for EXP1, EXP2, and EXP4. Results from these simulations (not shown) show that dissipation heating had a similar effect on all simulations. Dissipation heating contributed a maximum of 200 W m−2 in the high-wind region of the storm. Although these dissipation heating rates appear to be weaker than the maximum values in Bister and Emanuel (1998), the maximum winds in EXP1–EXP5 were considerably weaker and the drag coefficient was smaller. This additional heating term increased the total sensible heat flux, which in turn led to a slightly more intense hurricane in all simulations. Second, the physical parameterizations in MM5 have been tuned to produce realistic simulations without the use of a dissipation heating term. The two processes described above are important problems that were not addressed in this study and will be the subject of future research.

7. Summary and conclusions

In summary, spray affects the structure of the hurricane. Spray moistens the near-surface layer at all radii through enhanced spray evaporation. As the amount of spray increases, the near-surface mixing ratio increases. The effect of spray on the near-surface temperature is more complex. Spray warms the near-surface layer in the high-wind region through the additional spray sensible heat flux term. At larger radii, however, the fraction of spray that evaporates increases and the spray sensible heat flux term becomes negative. This causes weak near-surface cooling at larger radii. This result is consistent with Barnes (2006) and Cione et al. (2000), as well as the theoretical work of Andreas and Emanuel (2001) and the modeling studies conducted by Bao et al. (2000). Increasing the amount of spray enhanced the spray effects on the structure of the hurricane. Heavy spray simulations produced an overall moister and warmer near-surface layer relative to the moderate spray simulations. For heavier spray amounts, a larger portion of the near-surface layer warms relative to the moderate spray cases.

The warming effects of spray are not constrained to the BL. The effects of spray on the thermal structure of the hurricane can be seen in midlevel warming extending up to z = 6 km. Further diagnostics are needed to determine if this warming is the result of a dynamic response (i.e., a secondary circulation) to accommodate the large increase in latent heating because of the recondensation of spray-derived vapor (Perrie et al. 2005) or if it is the direct result of intensity changes of the hurricane.

Moderate amounts of spray have relatively little net effect on hurricane intensity. For the moderate spray, no-drag case (EXP2), spray enhances the net enthalpy flux slightly, which results in a small intensity increase in the hurricane. In the moderate spray drag case (EXP3), however, the horizontal drag effect decreases horizontal wind speeds by a few meters per second. This in turn decreases the total surface energy fluxes and ultimately weakens the storm, such that the storm is slightly weaker than the control run by the end of the simulation. Vertical spray drag results in slight differences in the T and q structures of the hurricane but has no significant effect on hurricane intensity.

For heavy spray amounts, the spray processes become more significant. The spray sensible and latent heat fluxes are both enhanced. The resulting increase in the total sensible and latent heat fluxes increases the intensity of the hurricane relative to the control simulation. The effect of horizontal spray drag decreases the wind speeds, which decreases the total sensible and latent heat flux terms. Vertical spray drag decreases the interfacial sensible and latent heat flux terms through an increase in the near-surface values of T and q relative to the no-drag case. Thus, both horizontal and vertical spray drags decrease the total sensible and latent heat fluxes, which ultimately leads to a small decrease in storm intensity.

Results from this study indicate that hurricane structure and intensity are sensitive to the amount of sea spray ejected into the near-surface layer and, ultimately, the spray-generation function itself. It appears that sea spray produces a warmer near-surface layer at smaller radii and a cooler near-surface layer at larger radii. For the moderate amounts of spray, the enhancement of the total fluxes is minimal. When spray-drag effects are also included, the intensity of the simulated hurricane actually weakens slightly relative to the control vortex. In heavy spray simulations, spray fluxes become much larger, which enhances the total fluxes. Results suggest that the enhanced surface fluxes counteract the weakening effects of vertical shear in regards to storm intensity. Horizontal and vertical drag effects are small in comparison to the magnitude of the additional spray fluxes. In the heavy spray cases, which lie at the upper threshold of the currently accepted spray-generation function, the minimum central pressure of the simulated hurricanes is on the order of 10 mb lower than that of the moderate spray cases. Thus, to get a realistic hurricane simulation, a more precise spray-generation function is needed to determine just how much spray is ejected into the BL of the hurricane. The aforementioned results, however, pertain to a gradually weakening hurricane. The results may be much different if similar experiments were performed for an intensifying (or initially more intense) hurricane.

Acknowledgments

Insightful comments from Drs. David Stauffer, Jerry Harrington, Mark Kelly, and three anonymous reviewers improved both the ideas expressed herein and the manuscript itself. This work was supported by the National Aeronautics and Space Administration Grant NNG05GQ64G and the National Science Foundation Grant ATM-0630364. Many of the plots were generated using the Grid Analysis and Display System (GrADS), developed by the Center for Ocean–Land–Atmosphere Studies at the Institute of Global Environment and Society.

REFERENCES

  • Andreas, E. L., 1990: Time constants for the evolution of sea spray droplets. Tellus, 42B , 481497.

  • Andreas, E. L., 1995: The temperature of evaporating sea spray droplets. J. Atmos. Sci., 52 , 852862.

  • Andreas, E. L., 1998: A new sea spray generation function for wind speeds up to 32 m s−1. J. Phys. Oceanogr., 28 , 21752184.

  • Andreas, E. L., , and J. Decosmo, 1999: Sea spray production and influence on air-sea heat and moisture fluxes over the open ocean. Air-Sea Exchange: Physics, Chemistry and Dynamics, G. L. Geernaert, Ed., Kluwer Academic, 327–362.

    • Search Google Scholar
    • Export Citation
  • Andreas, E. L., , and K. A. Emanuel, 2001: Effects of sea spray on tropical cyclone intensity. J. Atmos. Sci., 58 , 37413751.

  • Bao, J-W., , J. M. Wilczak, , J-K. Choi, , and L. H. Kantha, 2000: Numerical simulations of air–sea interaction under high wind conditions using a coupled model: A study of hurricane development. Mon. Wea. Rev., 128 , 21902210.

    • Search Google Scholar
    • Export Citation
  • Barnes, G. M., 2006: Thermodynamic structure of a hurricane’s lower cloud and subcloud layers. Preprints, 27th Conf. on Hurricanes and Tropical Meteorology, Monterey, CA, Amer. Meteor. Soc., 5C.1. [Available online at http://ams.confex.com/ams/pdfpapers/107927.pdf.].

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

  • Blanchard, D. C., 1963: The electrification of the atmosphere by particles from bubbles in the sea. Prog. Oceanogr., 1 , 71202.

  • Chen, Y., , and M. K. Yau, 2001: Spiral bands in a simulated hurricane. Part I: Vortex Rossby wave verification. J. Atmos. Sci., 58 , 21282145.

    • Search Google Scholar
    • Export Citation
  • Cione, J. J., , P. G. Black, , and S. H. Houston, 2000: Surface observations in the hurricane environment. Mon. Wea. Rev., 128 , 15501561.

    • Search Google Scholar
    • Export Citation
  • Cipriano, R. J., , and D. C. Blanchard, 1981: Bubble and aerosol spectra produced by a laboratory “breaking wave”. J. Geophys. Res., 86 , 80858092.

    • Search Google Scholar
    • Export Citation
  • Day, J. A., 1964: Production of droplets and salt nuclei by bursting of air-bubble films. Quart. J. Roy. Meteor. Soc., 90 , 498.

  • de Leeuw, G., 1990: Profiling of aerosol concentrations, particle size distributions and relative humidity in the atmospheric surface layer over the North Sea. Tellus, 42B , 342354.

    • Search Google Scholar
    • Export Citation
  • Dudhia, J., 1993: A nonhydrostatic version of the Penn State–NCAR mesoscale model: Validation tests and simulation of an Atlantic cyclone and cold front. Mon. Wea. Rev., 121 , 14931513.

    • 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., , J. D. Kepert, , and G. J. Holland, 1994: The effect of sea spray on surface energy transports over the ocean. Global Atmos. Ocean Syst., 2 , 121142.

    • Search Google Scholar
    • Export Citation
  • Garratt, J. R., 1992: The Atmospheric Boundary Layer. Cambridge University Press, 316 pp.

  • Grell, G. A., , J. Dudhia, , and D. R. Stauffer, 1995: A description of the fifth-generation Penn State/NCAR mesoscale model (MM5). NCAR Tech. Note NCAR/TN-398+STR, 122 pp.

  • Kain, J. S., , and J. M. Fritsch, 1993: Convective parameterization for mesoscale models: The Kain–Fritsch scheme. The Representation of Cumulus Convection in Numerical Models, Meteor. Monogr., No. 46, Amer. Meteor. Soc., 165–170.

    • Search Google Scholar
    • Export Citation
  • Kepert, J. D., , C. W. Fairall, , and J-W. Bao, 1999: Modelling the interaction between the atmospheric boundary layer and evaporating sea spray droplets. Air-Sea Exchange: Physics, Chemistry and Dynamics, G. L. Geernaert, Ed., Kluwer Academic, 363–410.

    • Search Google Scholar
    • Export Citation
  • Kwon, Y. C., , and W. M. Frank, 2005: Dynamic instabilities of simulated hurricane-like vortices and their impacts on the core structure of hurricanes. Part I: Dry experiments. J. Atmos. Sci., 62 , 39553973.

    • Search Google Scholar
    • Export Citation
  • Kwon, Y. C., , and W. M. Frank, 2008: Dynamic instabilities of simulated hurricane-like vortices and their impacts on the core structure of hurricanes. Part II: Moist experiments. J. Atmos. Sci., 65 , 106122.

    • Search Google Scholar
    • Export Citation
  • Lighthill, J., , G. Holland, , W. Gray, , C. Landsea, , G. Craig, , J. Evans, , Y. Kurihara, , and C. Guard, 1994: Global climate change and tropical cyclones. Bull. Amer. Meteor. Soc., 75 , 21472157.

    • Search Google Scholar
    • Export Citation
  • Monahan, E. C., , and I. G. O’Muircheartaigh, 1986: Whitecaps and the passive remote sensing of the ocean surface. Int. J. Remote Sens., 7 , 627642.

    • Search Google Scholar
    • Export Citation
  • Monahan, E. C., , and M. Lu, 1990: Acoustically relevant bubble assemblages and their dependence on meteorological parameters. IEEE J. Oceanic Eng., 15 , 340349.

    • Search Google Scholar
    • Export Citation
  • Perrie, W., , E. L. Andreas, , W. Zhang, , W. Li, , J. Gyakum, , and R. McTaggart-Cowan, 2005: Sea spray impacts on intensifying midlatitude cyclones. J. Atmos. Sci., 62 , 18671883.

    • Search Google Scholar
    • Export Citation
  • Riehl, H., 1954: Tropical Meteorology. McGraw-Hill, 392 pp.

  • Wang, Y., 1999: A triply-nested movable mesh tropical cyclone model with explicit cloud microphysics—(TCM3). BMRC Research Rep. 74, 81 pp.

  • Wang, Y., , J. D. Kepert, , and G. J. Holland, 2001: The effect of sea spray evaporation on tropical cyclone boundary layer structure and intensity. Mon. Wea. Rev., 129 , 24812500.

    • Search Google Scholar
    • Export Citation
  • Woodcock, A. H., 1972: Smaller salt particles in oceanic air and bubble behavior in the sea. J. Geophys. Res., 77 , 53165321.

  • Woolf, D. K., , P. A. Bowyer, , and E. C. Monahan, 1987: Discriminating between the film drops and jet drops produced by a simulated whitecap. J. Geophys. Res., 92 , 51425150.

    • Search Google Scholar
    • Export Citation
  • Wu, J., 1981: Evidence of sea spray produced by bursting bubbles. Science, 212 , 324326.

  • Wu, J., 1994: Bubbles in the near-surface ocean: Their various structures. J. Phys. Oceanogr., 24 , 19551965.

  • Wu, J., 2002: Jet drops produced by bubbles bursting at the surface of seawater. J. Phys. Oceanogr., 32 , 32863290.

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

APPENDIX

Derivation of the Fraction of Spray

Equation (2) of Andreas and Emanuel (2001) is given by
i1520-0493-136-5-1686-ea1
where cpd is the heat capacity of dry air, md is the mass of dry air, cpv is the heat capacity at constant pressure of water vapor, mυ is the mass of water vapor, fi is the fraction of original spray mass that evaporates, δmi is the mass of spray droplets, δTa is the change in air temperature, Lυ is the latent heat of vaporization, cw is the heat capacity of liquid water, Ts is the sea surface temperature, Ta is the air temperature, and Tri is the droplet equilibrium temperature. Solving Eq. (A1) for δTa gives
i1520-0493-136-5-1686-ea2
Equation (A2) is set to 0 because we are interested in determining how much spray must evaporate for the spray to cool the near-surface layer. Setting δTa to 0 and rearranging gives
i1520-0493-136-5-1686-ea3
Because Lυcw(TaTri), Eq. (A3) can be approximately rewritten as
i1520-0493-136-5-1686-ea4
Using cw = 4186 J kg−1 K−1, Lυ = 2.5 × 106 J kg−1, and TsTri = 5 K gives fi ≈ 0.008, which is on the order of 1% and is similar to (but higher than) the fraction of mass needed for a drop with temperature Ta to cool to Tri. When the fraction of spray that evaporates is zero, spray serves to warm the air temperature by δTa. As the fraction of spray that evaporates increases, the magnitude of δTa decreases, but the sign of δTa remains positive until some critical fraction is reached (on the order of 1%). Past this point, any additional spray that evaporates serves to cool the near-surface layer (i.e., makes δTa negative).

Fig. 1.
Fig. 1.

The evolution of the temperature T and radius r of a 100-μm drop with initial temperature 28°C in air with temperature 27°C and 80% relative humidity (Andreas and Emanuel 2001). The wet-bulb temperature Tw = 24.5°C is reached at t = 0.3 s. The drop temperature begins to rise at t = 100 s.

Citation: Monthly Weather Review 136, 5; 10.1175/2007MWR2183.1

Fig. 2.
Fig. 2.

The four-domain setup (162, 54, 18, and 6 km) used in this study to simulate the idealized hurricanes.

Citation: Monthly Weather Review 136, 5; 10.1175/2007MWR2183.1

Fig. 3.
Fig. 3.

Time series of the minimum sea level pressure (mb) for EXP1–EXP5.

Citation: Monthly Weather Review 136, 5; 10.1175/2007MWR2183.1

Fig. 4.
Fig. 4.

Time series of the 200–850-mb vertical shear for EXP1–EXP5.

Citation: Monthly Weather Review 136, 5; 10.1175/2007MWR2183.1

Fig. 5.
Fig. 5.

Time series of the maximum wind speed (m s−1) for EXP1–EXP5.

Citation: Monthly Weather Review 136, 5; 10.1175/2007MWR2183.1

Fig. 6.
Fig. 6.

The azimuthally averaged and t = 33- to 45-h time-averaged sensible heat flux terms. Plotted on the abscissa is the radius (km) and on the ordinate is the flux (W m−2). (a) The control sensible heat flux and (b)–(e) the spray sensible heat flux Qs (solid), the surface sensible heat flux (thick dashed), and the total sensible heat flux (thin dashed) for EXP2–EXP5, respectively.

Citation: Monthly Weather Review 136, 5; 10.1175/2007MWR2183.1

Fig. 7.
Fig. 7.

Same as Fig. 6, but for latent heat fluxes.

Citation: Monthly Weather Review 136, 5; 10.1175/2007MWR2183.1

Fig. 8.
Fig. 8.

(a) Azimuthally averaged and t = 33- to 45-h time-averaged temperature (K). Plotted on the abscissa is the radius (km) and on the ordinate is the height (km). (b)–(e) The T anomaly from panel (a) of EXP2–EXP5, respectively, with negative values shaded.

Citation: Monthly Weather Review 136, 5; 10.1175/2007MWR2183.1

Fig. 9.
Fig. 9.

Same as Fig. 8, but for the mixing ratio (g kg−1).

Citation: Monthly Weather Review 136, 5; 10.1175/2007MWR2183.1

Fig. 10.
Fig. 10.

Same as Fig. 8, but for wind speed (m s−1).

Citation: Monthly Weather Review 136, 5; 10.1175/2007MWR2183.1

Fig. 11.
Fig. 11.

The fraction of spray that evaporates as a function of radius for EXP2–EXP5. Plotted on the abscissa is the radius (km) and on the ordinate is the fraction.

Citation: Monthly Weather Review 136, 5; 10.1175/2007MWR2183.1

Table 1.

Summary of the MM5 simulations used in this study.

Table 1.
Table 2.

The t = 33- to 45-h time-averaged and azimuthally averaged spray sensible heat flux Qs (W m−2) and the spray latent heat flux Ql (W m−2) averaged over the high-wind region (r = 30 to 60 km, inclusive). Also listed are the ratios of both Qs to the radially averaged Hs,tot and of Ql to Hl,tot.

Table 2.
Table 3.

Same as Table 2, but for interfacial fluxes Hs (W m−2) and Hl (W m−2), as well as the ratio of the bulk fluxes to the control sensible heat flux Hs,control and the control latent heat flux Hl,control.

Table 3.
Table 4.

Same as Table 3, but the total sensible heat flux Hs,tot (W m−2) and the total latent heat flux Hl,tot (W m−2) are given.

Table 4.
Save