Latent heat is released or absorbed in the atmosphere as a result of phase changes of water (i.e., gas to liquid, gas to solid, liquid to solid, or vice versa). These phase changes involve processes of condensation, evaporation of cloud water and rainwater, freezing of raindrops and cloud water, melting of cloud ice, snow and graupel/hail, as well as deposition and sublimation of cloud ice (Tao et al., 2006). Riehl and Malkus (1958) emphasize that the latent heat is the primary fuel source of a tropical convective heat engine. Emanuel (1999) studied thermodynamic controls of a hurricane intensity, identifying three important factors for the evolution of the hurricane intensity: a storm’s initial intensity, the thermodynamic state of the atmosphere, and a heat exchange with the oceanic upper layer. Generally, the release of latent heat from the transformation of different hydrometeors is an important energy source for typhoons. Zhang and Kieu (2006) show that the release of the latent heat in the eyewall plays an important role in divergence aloft and convergence below the hurricane eye. Wu et al. (2009) also show that diabatic heating is a key factor to eyewall development in tropical cyclones. It is estimated that a tropical cyclone releases heat energy at a rate of 0.60×10¹⁵ W (2×10¹⁸ J/h), assuming that an average hurricane produces 1.5 cm/d of rain inside a circle of radius 665 km (Gray, 1981). Another value of the latent heat release of 0.88×10¹⁵ W was calculated by Adler and Rodgers (1977). From special sensor microwave/imager (SSM/I), Wang et al. (2008) indicate that the mean total latent heat released from a developing tropical disturbance is larger than for a non-developing tropical disturbance.

The latent heat is an energy released or absorbed during a constant-temperature process with phase changes. These phase changes involve phase of cloud water, rainwater, cloud ice, snow and graupel, etc. Latent heating (LH) cannot be directly measured using current technologies (Tao et al., 2006). Moreover, there has been no dependable method for observing the global distribution of diabatic heating. This is particularly true over ocean areas, because of the lack of adequate conventional data sets. However, the diabatic heating can be derived using a residual method (called a diagnostic budget) based on vertical profiles of temperature and three-dimensional wind fields, available from widespread rawinsonde networks (Yanai et al., 1973; Johnson, 1984; Houze, 1997). Fortunately, satellite measurements from the Tropical Rainfall Measuring Mission (TRMM) provide a more reliable method for detecting the LH. Thus, the LH can be estimated using data from SSM/I. In fact, several investigators (Olson et al., 1999; Tao et al., 1993; Yang and Smith, 1999) have successfully used this method. However, the TRMM microwave imager (TMI), launched in 1997, has a finer spatial resolution than the SSM/I. Thus, the LH is now retrieved from cloud-resolving models (CRMs), supported by the TRMM rainfall products (Kummerow et al., 2001).

Although there is lots of research on tropical cyclones, few studies have examined inner-core energy conversions because of the lack of high-resolution data. To calculate the LH, research efforts have focused almost exclusively on TRMM satellite retrieval. Moreover, there are a few studies using numerical simulations to determine LH calculations (Hogsett and Zhang, 2009; Sui et al., 1994). In this study, we aimed at understanding more about the LH structure during a typhoon evolution. Specifically, this would enable us to calculate typhoon LH using the microphysical LH budgets from the Weather Research and Forecasting (WRF) single-moment six-Class (WSM6) microphysical scheme (Hong et al., 2009). To study the LH structure of a typhoon core, the WRF model with the WSM6 cloud microphysical scheme was used to simulate Typhoon Molave. Here, emphasis was placed on revealing the LH structure and processes occurring within this typhoon, through the calculation of LH rates of various cloud microphysical processes. Our detailed analysis of Typhoon Molave is presented here as a case study.

Typhoon Molave began as a tropical depression that originated east of the Philippines at 00:00 UTC on 15 July 2009. Moving northwestward, it was upgraded to a tropical storm, east of the Philippines at 06:00 UTC on 16 July. It strengthened to become a typhoon over the South China Sea, tracking west-northwest from 17:00 UTC to 18:00 UTC on 17 July. It reached its peak intensity at 18:00 UTC, with maximum surface winds of 33 m/s and central pressure of 975 hPa. Typhoon Molave made landfall on Shenzhen City, China. Subsequently, it weakened rapidly, and was downgraded to a tropical depression at 06:00 UTC on 19 July, before dissipating 6 h later over southern China.

In this study, the advanced research WRF (ARW) dynamical core (Version 3.2) (Skamarock et al., 2005) was used to simulate Typhoon Molave. The ARW 3.2 solves the fully compressible, non-hydrostatic Euler equations of motion in flux with terrain, following sigma coordinates. Our simulation was carried out on an Arakawa C-grid with triple-nested domains (D01, D02, and D03). A Mercator map projection with horizontal grid spacing of 18, 6, and 2 km was configured for the WSM6 simulation (Fig. 1). Domain D01 is the outermost mesh domain, with its center located at 19°N and 119°E, and a grid spacing of 18 km; it was set up to simulate the large-scale environmental field of the typhoon. The intermediate domain, D02, was used to simulate mesoscale features of the typhoon evolution; it has a grid spacing of 6 km. The fine domain, D03, was designed for detailed analysis of small-scale structures and microphysical processes of the typhoon; it has a grid spacing of 2 km. From the ground surface to the top layer, there were 28 vertical levels defined within the WRF model. The following parameterizations were activated for all three domains: the WSM6 cloud microphysics scheme, based on Hong and Lim (2006); the Yonsei University boundary layer parameterization, which accounts for local and nonlocal mixing (Hong et al., 2006); the Dudhia short wave parameterization (1989); and the rapid radiative transfer model (RRTM) long-wave parameterization (Mlawer et al., 1997). The Betts-Miller-Janjic cumulus parameterization scheme (Betts, 1986; Janjić, 1994) was used in Domains D01 and D02. Meanwhile, no cumulus parameterization scheme was used in Domain D03 (Molinari and Dudek, 1992; Lin et al., 2011), because convection is assumed to be resolved reasonably well by the explicit microphysical parameterization scheme. The initial and boundary conditions were interpolated horizontally for the coarse model resolution (with a grid spacing 18 km), and vertically to 28 levels using the US National Center for Environmental Prediction (NCEP) final reanalysis (FNL) data (http://dss.ucar.edu/datasets/ds083.2). The FNL data sets are compiled at 6 h interval, with a horizontal grid resolution of 1°×1°. Surface and rawinsonde conventional observation data were incorporated into our analysis using a Cressman-type analysis technology (Benjamin and Seaman, 1985). QuikSCAT/ NCEP blended ocean winds data were also accessed from Colorado Research Associates (5.0) (http://dss.ucar.edu/datasets/ ds744.4), and incorporated using the standard MM5 (mesoscale model; developed by the Pennsylvania State University and the National Center for Atmospheric Research) initialization procedure. A bogus vortex with a maximum velocity of 60 m/s and a maximum radius of 190 km (Low-Nam and Davis, 2001; Fong et al., 2001) was inserted into Domain D01. Initial conditions for Domains D02 and D03 were obtained from interpolation of Domain D01 values. For Domains D01 and D02, the WSM6 experiment was initialized at 00:00 UTC on 18 July, and was integrated for 36 h. Over the integration time, the best track of Typhoon Molave was located in Domain D02. In Domain D03, integration was preformed from 00:00 UTC on 18 July to 00:00 UTC on 19 July.

This study introduces a new method for determining the latent heat using numerical simulations, which calculate LH rates for various microphysical processes. This is a markedly different approach from previous studies using the TRMM satellite retrieval.

Our comparison of the latent heat determined from the simulation versus the TRMM observations shows a similar overall structure, although specific values are different. The highest LH rate for the TRMM data is observed from 4 to 5 km, which is lower than the 8 km height obtained in the simulation. The total LH mainly originates from the condensation LH below the zero degree isotherm, and the deposition LH above it. Cloud microphysical processes related to graupel played a major role in our simulation. In our case study simulation of Typhoon Molave, we assessed the dominant contributors to the LH of various cloud microphysical processes. The positive contributors were mainly condensation of cloud water, deposition of cloud ice, deposition of snow, initiation of cloud ice crystals, deposition of graupel, and accretion of cloud water by graupel. The negative LH contributors were mainly evaporation of cloud water, evaporation of rain, sublimation of snow, sublimation of graupel, melting of graupel, and sublimation of cloud ice.

The authors thank the National Supercomputing Center in Guangzhou for providing the use of super-computers. We are grateful to the National Center for Atmospheric Research (NCAR) Mesoscale and Microscale Meteorology Division: http://www. mmm.ucar.edu/wrf/users, which is responsible for the WRF model. The National Centers for Environmental Prediction final (NCEP-FNL) global tropospheric analysis data for this paper are available at http://rda.ucar.edu/datasets/ds083.2.