1. Introduction
Energy for the genesis and development of tropical cyclones (TCs) is essentially supplied by heat and moisture from the tropical oceans. Energy exchange at the air–sea interface, as discussed for example in Black et al. (2007), is one of the three major physical processes governing hurricane intensity change, together with 1) environmental interactions with surrounding large-scale circulations and 2) internal dynamics such as eyewall replacement cycles and cloud microphysics. Precise representation of the air–sea energy exchange is crucial for TC forecasting and, particularly, for prediction of intensity and structure change, with the latter on occasions further affecting the track. It is thus important to represent the air–sea exchanges as best we can. Furthermore, the coherent relationship between the air–sea interaction and the internal dynamics during hurricane intensity change remains mostly unexplained, and so a better representation of the surface processes will help us to understand TC development in an integrated way.
The energy exchanges are composed of momentum, sensible heat, and latent heat (moisture) fluxes. Over water, a “bulk” exchange parameterization is commonly applied in numerical modeling to compute the fluxes in TC models. The fluxes are parameterized as being proportional to exchange coefficients and the differences in wind, temperature, and moisture between the surface and lowest model level in the boundary layer (e.g., Fairall et al. 2003). The exchange coefficient for momentum flux, or drag coefficient, plays a role not only in parameterization for the momentum flux but also for the heat exchanges, because the turbulent heat exchanges also rely on near-surface wind shear. The drag coefficient over water was initially based upon the Charnock relation with a constant Charnock parameter (Charnock 1955). However, based on the analysis of results from field programs, a constant Charnock parameter is questionable. Wu (1980) has reviewed the derivation of the Charnock parameter and obtained values with a large range from 0.012 to 0.035 at moderate (>5 m s−1) to strong wind speeds. Fairall et al. (2003) recommended a relationship between the Charnock parameter and the 10-m near-surface wind speed in neutral conditions. This was termed the COARE3.0 (Coupled Ocean–Atmosphere Response Experiment; e.g., Fairall et al. 2003) expression and was based upon analysis of large sets of data from field programs. They also pointed out that the variation of the Charnock parameter with wind speed still remains uncertain. Although the Charnock parameter has been related to ocean wave age, as functions of the ratio of the wave phase speed at the peak of the spectrum and either the friction velocity or the 10-m neutral wind speed U10N (Drennan et al. 2005; Donelan 1982), Fairall et al. (2003) pointed out that there is still a lack of consensus on the relationship in the wave stress community. Andreas et al. (2012) endorsed a correlation between the surface friction velocity and U10N, which is equivalent to a correlation between a variable Charnock parameter and the winds, using data for winds up to 24 m s−1. At very high wind speeds near the hurricane eyewall (>40 m s−1), Powell et al. (2003) obtained a declining drag coefficient with increasing near-surface winds using global positioning system (GPS) sondes. Focusing on the hurricane component of the Coupled Boundary Layers Air–Sea Transfer experiment (CBLAST), Black et al. (2007) also obtained a declining drag coefficient even when the winds were greater than 25 m s−1 (their Fig. 5). Based on a laboratory experiment, Donelan et al. (2004) suggested that the coefficient tends to level off when the winds are greater than 35 m s−1. Bell et al. (2012) obtained a declining or nonincreasing drag coefficient when the winds were greater than 60 m s−1. The latter study computed quite scattered values of the coefficient by deducing the momentum and enthalpy fluxes via absolute angular momentum and total energy budgets. Although the methodology and data used to obtain the coefficient at very high wind speeds are problematic, the mechanisms behind the phenomena have been discussed. For instance, Powell et al. (2003) speculate that sea foam and sea spray generated by wave breaking and wind tearing the breaking wave chest prevent the underlying sea surface from being dragged by the wind. Physical models were being set up to illustrate and simulate the phenomena (e.g., Liu et al. 2012; Makin 2005).
At high winds, the concept of a thermal roughness length for sensible and latent heat fluxes is no longer fully valid. At low winds, heat and water vapor at the air–sea interface are transferred by molecular diffusion across an interfacial sublayer (e.g., Garratt 1994, p. 89), which is then defined as the interfacial route. As one of several physical mechanisms proposed, a cyclic growth and destruction pattern of the interfacial sublayer accounts for the introduction of the thermal roughness length (Liu and Businger 1975). At higher winds (>10 m s−1), heat and water vapor transfers also occur at the surface of the spray droplets, which have been blown up through the interfacial sublayer, which is then defined as the spray route for heat and water vapor exchanges (e.g., Andreas et al. 2008). Parameterizations for the spray route have been developed by Andreas et al. (2008), Andreas (2010), Fairall et al. (1994), Fairall et al. (2009), Kepert et al. (1999), and Bao et al. (2011).
Using two spray route inclusion schemes, Wang et al. (2001) made a simulation of a TC and analyzed the influence on the TC boundary layer structure. Bao et al. (2000) used an air–sea coupled model that included wave and spray models to make a study of TC development. Neither of the studies made simulations of real TCs. These studies were essentially for research purposes; the feasibility of the application of a sea spray parameterization to operational tropical cyclone models is thus yet to be fully investigated.
Through theoretical considerations, Emanuel (1986) proposed that air–sea sensible and latent heat fluxes are more critical in developing and maintaining a TC than the ambient air instability. Emanuel (1986, 1995), with further revision to the theory, suggested a relationship between the maximum tangential wind speed averaged over the subcloud layer and the ratio of enthalpy to momentum exchange coefficients for a steady-state TC, based on the balance between radial entropy advection and surface entropy flux over the inner region of a TC in quasi-equilibrium. This leads to a constraint on the ratio of the coefficients for TC conditions. How the ratio behaves with the new surface exchange parameterization is one of the issues addressed in this study. Our preliminary results indicate some consistency with the theoretical predictions. The focus of this study is on the revised parameterizations and their impact on TC predictions, and particularly rapid intensification (RI). A summary of TC studies on structure and intensity can be found in Wang and Wu (2004). In addition, we will discuss other aspects of RI in the text.
In summary, in high winds, the parameterizations for each of the momentum and heat exchanges at the air–sea interface are quite different from the conventional bulk exchange algorithms, as evidenced from various observational studies. Clearly, it is of great significance to the TC numerical weather prediction (NWP) and air–sea exchange research communities that a spray route inclusion scheme be applied to operational TC forecast systems. Documenting its potential impact on TC track, intensity, and internal dynamics—especially the intensification process—is then of theoretical and practical interest. We have thus investigated the impact of a new parameterization on TC forecasts in the current Australia TC model.
The manuscript is organized as follows. Section 2 summarizes the parameterizations for air–sea exchanges, which comprise a conventional bulk algorithm, a spray route inclusion scheme at high wind speeds, and a surface-wind-dependent Charnock relation. Section 3 briefly describes a TC model that has been applied to evaluate the new scheme. Section 4 offers a discussion on the TC track and intensity evaluations and provides an illustrative example of a TC rapid intensification case with some detailed diagnostics. Section 5 provides our conclusions.
2. Air–sea exchange parameterization
a. Bulk air–sea exchange parameterization in the UM
b. The BFK sea spray parameterization scheme for air–sea heat and moisture exchanges
The spray route inclusion scheme is based on a series of studies reported upon in Bao et al. (2011), Fairall et al. (1994), and Kepert et al. (1999). That work led to a method we call the BFK scheme, although in fact it is also based or related other works such as Andreas and Emanuel (2001) and Andreas (1992). We briefly describe the scheme in this section. The scheme consists of the parameterization of sea-spray-modulated heat and moisture fluxes at the air–sea interface. To use the scheme, we also introduce an expression for the dependence of the Charnock parameter on the 10-m wind speed in neutral conditions, and in turn the formulation of the surface roughness length over water [Eq. (3)]. We describe this expression in section 2c.
c. Revised Charnock relation
As discussed in the introduction, it has been recognized that a constant value of the Charnock parameter α does not adequately describe the observations from many datasets. Determining the sea surface wind stress over the open sea for a large range of surface wind speeds (6–26 m s−1), Yelland and Taylor (1996) concluded that α monotonically increases from 0.011 to 0.017 with increasing wind speed, using an inertial dissipation method (e.g., Fairall and Larsen 1986). Fairall et al. (2003) derived a similar relation, COARE3.0, upon a large survey of field program results, but also pointed out that the dependence of the Charnock parameter on wind speed remains uncertain. They attribute the uncertainty upon Yelland et al.’s (1998) reanalyses on the results reported in Yelland and Taylor (1996). Yelland et al. (1998) no longer support the increase in α after revising with corrections to the mean winds and the measurement heights in their experiment. However, results from Andreas et al. (2012), who included more data from field programs conducted during recent years, are consistent with a variable Charnock parameter, dependent on U10, as indicated equivalently by the correlation between u* and U10N.
For high winds, a constant Charnock parameter independent of surface wind speed leads to large biases in the drag coefficient, compared with observations. The constant Charnock parameter leads to an approximately linear increment in the drag coefficient with increasing surface winds [Eq. (2a)]. Powell et al. (2003) found that the drag coefficient even decreased with increasing wind speed above 40 m s−1 in tropical cyclones, based on analysis of 331 GPS sonde wind profiles in 15 tropical cyclones. Those authors attributed the causes for the small roughness length to helical rolls/foams in very high winds. French et al. (2007) also found a decrease in the drag coefficient at high speeds using direct aircraft measurements. Their results do not match with extrapolation of the empirical forms from Smith (1980) and Large and Pond (1982), whose results increase almost linearly with increasing wind speeds.
Comparison of coefficients for momentum exchange parameterization for (a) Charnock parameters and (b) surface exchange coefficients, as a function of 10-m neutral wind speed. The form used in this study (SPY) is in comparison with COARE3.0 (Fairall et al. 2003; Powell et al. 2003; Large and Pond 1982; French et al. 2007; Donelan et al. 2004; Bell et al. 2012; Andreas et al. 2012) and CTL (the UM model; Lock 2007). Note that in both (a) and (b) the COARE3.0 curve is overlapped with the SPY curve at U10N < 18 m s−1 and with the CTL curve at U10N > 18 m s−1.
Citation: Weather and Forecasting 32, 3; 10.1175/WAF-D-15-0109.1
3. ACCESS-TC
The Australian Community Climate and Earth-System Simulator (ACCESS; Puri et al. 2013) is an implementation at the Australian Bureau of Meteorology of the full Met Office Numerical Modeling System of the United Kingdom (e.g., Gregory and Rowntree 1990; Wilson and Ballard 1999; Webster et al. 2003; Davies et al. 2005; Rawlins et al. 2007). ACCESS-TC, its configuration for operational TC forecasting, has been adapted for operational and research applications on tropical cyclones. Table 1 lists the major features of ACCESS-TC (Davidson et al. 2014). The base system runs at a resolution of 0.11° and 50 levels. The domain is relocatable and nested in coarser-resolution ACCESS forecasts. Initialization consists of five cycles of four-dimensional variational data assimilation (4DVAR) over 24 h prior to the initial time and forecasts to 72 h are made. Vortex specification or a TC bogus is applied, without which initial conditions usually contain a weak and misplaced circulation. Significant effort has been devoted to building physically based, synthetic inner-core structures, validated using historical dropsonde data and surface analyses from the Atlantic. Based on estimates of central pressure and storm size, vortex specification is used to filter the analyzed circulation from the original analysis, construct the inner core of the storm, locate it to the observed position, and merge it with the large-scale analysis at outer radii.
Major components of ACCESS-TC.
Using all available conventional observations and only synthetic surface pressure observations from the idealized vortex to correct the initial location and structure of the storm, 4DVAR builds a balanced, intense 3D vortex with maximum wind at the radius of maximum wind and with a well-developed secondary circulation. The TC domain is one-way nested in the ACCESS global model (Puri et al. 2013). Operational estimates of TC characteristics (location, surface center pressure, and size) are derived from standard observational data and satellite image interpretation. Mean track and intensity errors for the Australian region and northwest Pacific storms have been encouraging, as are results from operational runs at the Australian National Meteorological and Oceanographic Centre. The system became fully operational in November 2011. A detailed description of the system is contained in Davidson et al. (2014).
4. Results and discussion
The revised parameterization acts in a clearly different way in simulating the fluxes from the conventional scheme. With the distinguishing acronym of SPY (spray in combination with reduced drag in high wind speeds) and CTL (control) for the two parameterizations, Fig. 2 shows an example of exchange coefficients and fluxes along with the neutral 10-m surface wind in conditions when the sea surface is 2°C warmer than the 2-m air temperature and the relative humidity is 80% near the surface. The exchange coefficients are shown in Fig. 2a. Note for the revised parameterization that CH,SPY and CQ,SPY do not appear as a single coefficient in the formulations based on the computed fluxes from Eq. (5) for the spray route inclusion scheme. They are equivalent to the exchange coefficients that are computed with the conventional bulk formulas in Eqs. (1b) and (1c) with the heat fluxes computed from the spray route inclusion model [Eq. (5)] and the prescribed values of the difference between the near-surface air and the surface temperature, as well as the near-surface air relative humidity. Also note that for the original bulk scheme the thermal exchange coefficients for the sensible heat, latent heat, and enthalpy fluxes are equal (CH,CTL = CQ,CTL = CK,CTL) as a thermal roughness length formulation is used for both the sensible and latent heat fluxes [Eq. (4)]. When winds are below 15 m s−1, the thermal exchange coefficients (CH, CQ, CK) for the spray route inclusion scheme are not greatly different from their counterparts for the bulk scheme. When winds become high, CQ,SPY becomes increasingly larger while CH,SPY becomes increasingly smaller. The dipping of CH,SPY with increasing winds above about 20 m s−1 is presumably due to the cooling effect of the sea spray on the near-surface air [Eq. (5)]. Consequently, the ratio between the enthalpy exchange coefficient and drag coefficient (CK/CD) shows great departures between the two parameterizations for winds greater than 20 m s−1. Results for CK/CD,SPY show increasing values along with the increasing winds when they are greater than 25 m s−1, while CK/CD,CTL keeps the decreasing trend. Andreas (2011) also indicates a similar large ratio using their spray model under more diverse conditions (his Fig. 3). Equivalent to the variable Charnock parameter, the friction velocity starts to be increasingly different from the original bulk formulation when winds are larger than 30 m s−1 (Fig. 2c), in agreement with the observations of Powell et al. (2003). In accordance with the difference in the exchange coefficients, as shown in Fig. 2d, the differences in the sensible and latent heat fluxes between the two schemes becomes progressively larger as winds become greater than 25 m s−1, and the difference of their sum or enthalpy flux is comparably small. That is, for the new scheme, the moisture flux is larger and the sensible flux is smaller than for the original scheme, but the enthalpy flux remains similar.
The formulated exchange coefficients and fluxes for the SPY and CTL formulations: (a) CD (×10−3), CH (×10−3), CQ (×10−3), and CK (×10−3) exchange coefficients; (b) CK/CD; (c) U* (m s−1); and (d) SH, LH, and enthalpy flux SH + LH (W m−2).
Citation: Weather and Forecasting 32, 3; 10.1175/WAF-D-15-0109.1
The revised air–sea exchange parameterization schemes are thus applied in ACCESS-TC, together with the original scheme to make simulations. Table 2 shows the selected four TCs for which a total of 13 forecasts were performed for each of the two schemes. Each forecast runs for 72 h. Among the four TCs, two (Fanapi and Songda) occurred over the northwest Pacific Ocean: one (Yasi) to the northeast of Australia over the Pacific Ocean and another (Carlos) to the northwest of Australia over the eastern Indian Ocean. This represents an important geographical diversity. Two TCs (Fanapi and Songda) intensified before landfall, one (Yasi) intensified and decayed, and one (Carlos) was nearly steady with offshore movement. Figures 3 and 4 show examples of the track and intensity forecasts from each TC. Note that each figure shows the model domain. For all TCs, their major movement and curvature are well simulated with both the CTL and SPY tests. This can be attributed to the well-forecast environmental steering flow and, to a lesser extent, the vortex structure. The track errors show the differences between CTL and SPY tests and do not display large or systematic differences from these examples, although we will discuss the statistics further. The central pressures (CPs) more closely correspond with the estimates in the SPY tests than in the CTL tests for the intensification of Yasi, Fanapi, and Songda. For Carlos, which was near steady in intensity with movement away from the coast, the forecasts are similar. It is worth noting that excessive development or intensification is not a characteristic of the new scheme, even though it does represent somewhat larger latent heat fluxes.
Descriptions of TC case studies.
Observed and 72-h forecast tracks and central pressures for TCs Yasi and Fanapi from (a),(c) CTL and (b),(d) SPY forecasts.
Citation: Weather and Forecasting 32, 3; 10.1175/WAF-D-15-0109.1
Observed and 72-h forecast tracks and central pressures for TCs Songda and Carlos from (a),(c) CTL and (b),(d) SPY forecasts.
Citation: Weather and Forecasting 32, 3; 10.1175/WAF-D-15-0109.1
a. Statistical analysis of predicted TC tracks and intensities
Statistically, over all of the 72-h forecasts, for both parameterizations, the average predicted track shows very similar mean errors (MEs) prior to 48 h, but the results are very marginally worse with the SPY scheme compared with the CTL scheme (Fig. 5a). The average initial position errors for both schemes are near 30 km, and the ME increases with increasing forecast time, generally in a consistent way, but the results are slightly better than the ACCESS-TC mean statistics (Davidson et al. 2014). The overall ME is 80 km for the CTL runs and 92 km for the SPY runs. These are not significant differences. The spray scheme makes clear improvements to the prediction of CP. As shown in Fig. 5b, both the MEs and root-mean-square errors (RMSEs) from the SPY tests are clearly reduced at almost all forecast times. The overall MEs and RMSEs are 13.8 and 20.5 hPa, respectively, for the CTL tests and 8.7 and 14.5 hPa for the SPY tests. This represents an improvement of 37% in ME and 29% in RMSE from the SPY runs in comparison with the CTL runs, with very small changes in the track forecasts. It is noted that for this limited sample large biases exist in the high intensities, which mainly occur in the shorter forecast times, and small biases exist in the weak intensities, which mainly occur in the longer forecast times. This leads to a decreasing error along the increasing forecast time shown in Fig. 5b.
Mean forecast biases against forecast time. (a) Mean track and (b) CP using CTL and SPY.
Citation: Weather and Forecasting 32, 3; 10.1175/WAF-D-15-0109.1
Beyond a certain TC intensity, the improvement in CP predictions becomes evident with the spray inclusion scheme. The CP mean biases are plotted against the observed CPs in Fig. 6a. As we might expect, when CPs are lower than 955 hPa, MEs and RMSEs are clearly reduced in the SPY tests. When CPs are higher than 970 hPa, values of the MEs and RMSEs are very similar to their counterparts from the CTL tests. As discussed for the situation in Fig. 2a, the sea-spray-affected enthalpy exchange coefficient and declining drag coefficient only become active for wind speeds greater than approximately 20 and 30 m s−1. This further demonstrates that the SPY scheme does not simply make stronger CP predictions. Improvement is also seen in the initialized TC circulations. As shown in Fig. 6b, the initial individual CPs for each run are also closer to the estimates using the spray scheme. For the control runs, the ME averaged over the initial pressures of all the forecasts is 17.6 hPa and the RMSE is 23.4 hPa. The values are reduced to 12.3 and 15.3 hPa, respectively, for the SPY runs, or 30% and 35% reductions from the CTL statistics. As described in section 3, ACCESS-TC employs the use of synthetic surface pressure observations from a carefully constructed idealized vortex, and a five-cycle 4DVAR initialization to generate a TC structure (Davidson et al. 2014). This dynamic process also is affected by the changes in the surface exchanges induced by the parameterization changes, which has a positive influence on generating a better representation of the real structure.
(a) CP bias against observed CP. (b) Initial CP bias against observed CP.
Citation: Weather and Forecasting 32, 3; 10.1175/WAF-D-15-0109.1
The correlation between CP and the tangential wind maximum (VM) is generally summarized in the empirical relation of Dvorak (1975) over different ocean basins. Accordingly, corresponding to the improvement in CP predictions, comparison between the SPY and CTL tests shows clear increases in VMs obtained from the SPY tests for intensities greater than approximately 32 m s−1. The increases are of the order of 8 m s−1 for maximum winds of 50 m s−1. This represents a 16% improvement from the SPY tests (Fig. 7).
Graph of VMCTL vs VMSPY − VMCTL.
Citation: Weather and Forecasting 32, 3; 10.1175/WAF-D-15-0109.1
b. Analysis of a rapid intensification case
To investigate the relationship between air–sea exchanges and the internal processes of TC intensity and structure changes, we choose TC Yasi (2011) as a detailed case study. We analyze the 72-h simulations for Yasi initialized at 1200 UTC 30 January 2011 with both the CTL and SPY configurations. Figure 8a shows the TC structure and intensity changes, which are represented by time series of CP, VM, the radius of the maximum wind (RMW), and the radii of the 64-, 50-, and 34-kt wind (R64, R50, and R34, respectively; 1 kt = 0.51 m s−1). The track forecast is also shown in Figs. 8b and 8c. During the first 48 h, CP dips 33 hPa in the CTL test and 45 hPa in the SPY test. The latter represents the estimated pressure drop of 47 hPa more closely. The maximum wind increases during the forecast by roughly 20 m s−1 from the CTL test and 32 m s−1 from the SPY test. Kaplan and DeMaria (2003) define RI as a 24-h increase in the maximum sustained wind of 30 kt (15.4 m s−1). RI has proven to be especially difficult for operational forecasting (Elsberry et al. 2007). The new scheme has thus forecast the RI more satisfactorily. Also shown in Fig. 8a are the predicted TC size parameters from both schemes, represented here by R34, but also by R50 and R64. There is little difference in these parameters from the CTL and SPY forecasts. In addition, RMW is slightly smaller during most of the forecast with the SPY scheme, while the evolution is similar. Note that initially CP and VM values from both of the tests are quite similar. A relatively smaller inner-core structure develops from the SPY test, as indicated by the smaller RMW and R34. An inner-core contraction and TC intensification are clearly seen in the relation between VM and RMW. The TC size parameters, R34 from the two schemes, are basically the same, and so the TC size is almost unaffected by the new parameterization, even though the intensities are quite different. The forecast tracks from both the schemes are comparable with the observed curved track, which basically follows the environmental flow (Figs. 8b and 8c). As expected, the largest differences between the CTL and SPY experiments will be over the inner-core (approximately a radius of 100 km) where high wind speeds mean that the revised parameterizations will be active.
RI case: (a) Time series of simulated CP, inner-core parameters of VM and RMW, and outer-ring wind radius R34, using CTL and SPY. The best-estimated CP is indicated with an open circle. (b),(c) Observed and 72-h forecast tracks from CTL and SPY, respectively.
Citation: Weather and Forecasting 32, 3; 10.1175/WAF-D-15-0109.1
1) The air–sea surface exchange coefficients, surface fluxes, and near-surface simulations
We have derived azimuthally averaged coefficients of CD and CK from the model outputs to describe the difference between the two schemes. The coefficients are derived from the surface stress, sensible and latent heat fluxes, and the vertical gradient of the wind speed, temperature, and humidity. Detailed procedures are also referred to in the appendix of Bao et al. (2011). As shown in Fig. 9 from the 72-h forecast of the case, the model-derived drag and enthalpy exchange coefficients generally preserve the patterns shown earlier in Fig. 2 for the theoretical formulation for a specific condition. As shown in Figs. 9a and 9b, when surface winds are under around 20 m s−1, CD increases linearly with surface wind speed in both schemes. When the winds are greater than 20 m s−1, the drag coefficients for the two schemes begin to differ. The CD results for the SPY test slightly increase with the increasing winds, level off around 35 m s−1, and then decrease with the stronger winds. The exchange coefficients for enthalpy fluxes for the SPY test are lower than those for the CTL test, and both slightly increase with increasing winds. The ratios between CK and CD for the two schemes thus show different patterns. A nearly linearly decreasing trend between CK/CD is maintained with increasing winds for the CTL test, while such a trend becomes linearly increasing with increasing winds beyond 25 m s−1 for the SPY test. There is some sensitivity to the tangential wind calculation from the center-finding algorithm, especially for the low wind speeds. The large fluctuations in the coefficients and the ratios at winds below 20 m s−1 are due mainly to the uncertainty of the mean wind speed at these relatively low speeds.
Model-derived exchange coefficients and their ratios: (a),(b) CD, (c),(d) CK, and (e),(f) CK/CD, versus mean tangential wind at 10-m height. Shown are (left) CTL and (right) SPY surface exchange schemes.
Citation: Weather and Forecasting 32, 3; 10.1175/WAF-D-15-0109.1
Emanuel (1986, 1995) suggested a relationship between the maximum tangential wind speed averaged over the subcloud layer and the ratio of enthalpy to momentum exchange coefficients for a TC in quasi-equilibrium. As shown in his Fig. 1 (Emanuel 1995) the ratio increases nearly linearly with an increasing maximum wind at high winds. With the SPY test, the ratio in Figs. 2b and 9f agrees quite well with Emanuel’s theory.
Simulated surface variables and fluxes are displayed in pairs for the CTL and SPY tests in Fig. 10. Although the maximum 10-m tangential winds reach much higher values during the SPY test than during the CTL test (cf. Figs. 10a and 10b), the maximum surface friction velocities U* for the SPY test do not show much higher values than the CTL (cf. Figs. 10c and 10d), given that at high winds a relatively low surface stress is achieved from the SPY scheme compared to that from the CTL scheme (Fig. 2c). That is, alternatively, for the same stress between the TC atmosphere and the water surface, higher winds are simulated with the new scheme. A somewhat broad region of sensible and latent heat fluxes occurs in the CTL run, especially prior to the intensification process (t < 30 h) (cf. Figs. 10e and 10f, as well as Figs. 10f, 10g, and 10h). The sensible heat flux is higher in the SPY run than the CTL run with its maximum between 55 and 60 h for both the runs (Figs. 10e,f). We note that the sensible heat flux is still higher in SPY than CTL. This is mainly because of the effect of larger surface winds in SPY than CTL. The latent heat flux is higher and occurs earlier with the maximum in the SPY run than the CTL run (Figs. 10g,h). Their sum, the time evolution of the enthalpy flux (cf. Figs. 10i and 10j), resembles that of the latent heat flux as it is the major contributor to the enthalpy flux. It is noted that there are clearly two enthalpy flux maxima from the SPY tests (Fig. 10j) between 30 and 40 h, and between 55 and 60 h, that correspond to the two sea level pressure minima in the TC eye (Fig. 10l). For CTL, there are a series of enthalpy flux maxima (Fig. 10i) and no clear dual surface level pressure (SLP) minima at the simulated center (Fig. 10k). These dual peaks are also represented in the surface wind for the SPY run (Fig. 10b). Two such CP minima during the TC evolution are also seen in the observations around 24 and 60 h (Fig. 8a), although the timings are biased between the SPY simulations and the observations. This finding suggests that the TC underwent two cycles of intensification over the ocean during the 60 h from the beginning of the simulation time, and that the SPY run, with the revised air–sea exchange scheme, better captures the two cycles. The near-surface meteorological fields and their evolution are thus changed with the revised scheme in a way that seems more consistent with the observed TC intensity change.
Radius–time Hovmöller diagrams of azimuthal means of (a),(b) U10m (m s−1), (c),(d) U* (m s−1), (e),(f) SH (W m−2), (g),(h) LH (W m−2), (i),(j) enthalpy flux SH + LH (W m−2), and (k),(l) SLP (hPa) for TC Yasi from base time 1800 UTC 30 Jan 2011. Shown for each pair are (left) CTL and (right) SPY runs.
Citation: Weather and Forecasting 32, 3; 10.1175/WAF-D-15-0109.1
We also plot the near-surface temperature and specific humidity in Fig. 11. Compared with the CTL test, a relatively cold and dry core is initialized with the SPY test, which consistently increases its temperature and humidity during the forecast hours, while the former roughly retains its temperature and humidity (Figs. 11a,b and Figs. 11c,d, respectively). There is still some cooling for the near-surface air, although it is not as strong as in the inner core, because the revised parameterization has only a weak effect at low winds.
Hovmöller diagrams of azimuthal means of near-surface model level (a),(b) temperature (°C) and (c),(d) relative humidity (%) for TC Yasi from base time 1200 UTC 30 Jan 2011. Shown for each pair are (left) CTL and (right) SPY runs.
Citation: Weather and Forecasting 32, 3; 10.1175/WAF-D-15-0109.1
2) Impact on TC inner-core (eye and eyewall) structure change
Although the pressure drop between the eye center and eyewall accounts for less than half of the drop between the eye center and the environment (Willoughby 1998), the difference in SLP falls between the two tests during the RI occurs mainly in the vicinity of the TC eye and near the eyewall. As shown in Fig. 12 (shading), the differences mainly occur within a radius of 100 km of the center. The difference reaches 10 hPa in the center during the time between 30 and 60 h. Outside the radius of 100 km, the difference is within 2 hPa. Correspondingly, as shown by the contours in Fig. 12, the difference in the surface tangential winds also occurs mostly within a radius of 100 km of the center. The differences are around or more than 20 m s−1 near the eyewall during the time between 30 and 60 h. Outside the radius of 100 km, the difference is within 2 m s−1.
Radius–time cross section of SLP (hPa) difference (shaded) and the near-surface tangential wind (black contours) between the CTL and SPY tests.
Citation: Weather and Forecasting 32, 3; 10.1175/WAF-D-15-0109.1
Radius–time section of 
Citation: Weather and Forecasting 32, 3; 10.1175/WAF-D-15-0109.1
Cancelation of contributors to the divergence in the TC eye from (a),(b) the radial wind and (c),(d) vertical motion for (left) CTL and (right) SPY in Eq. (10b). The units are m s−1.
Citation: Weather and Forecasting 32, 3; 10.1175/WAF-D-15-0109.1
We investigate the inner-core thermal and kinetic changes during the simulated RI of Yasi with control and spray scheme tests. Fig. 15 displays the evolution of vertical structures of thermal and dynamical variables. The model does not simulate a clear inversion layer, as indicated in Willoughby (1998). There are high vertical gradients in potential temperature θ around 6–7 km during the forecast RI (Figs. 15a,b), which could be contributed to by large condensational heating at that height (Figs. 15e,f). A major distinguishing feature between the CTL and SPY forecasts is that strong subsidence occurs earlier in the eye during RI from the SPY forecast (Figs. 15c,d). Below 4 km, both of the tests predict a moist layer (RH > 90%) roughly below 1 km while a dry layer (RH < 80%) is approximately centered at 2.5 km. Between these two experiments, the SPY test predicts a thicker moist layer and a relatively less dry upper layer compared to CTL. Subsidence of air aloft is believed to be the source of the warming and drying of the eye air (Willoughby 1998). In the TC eye, an initially less stable stratification in the layer between about 10 and 16 km is seen in the SPY test (cf. Figs. 15b and 15a). This may allow less inhibition to earlier subsidence between 20 and 40 h in the SPY test while it is at 30–50 h in the CTL test (cf. Figs. 15d and 15c). Consequentially, dry air (RH < 50%) begins to dominate the upper layer (>10 km) during earlier simulation times (Figs. 15e,d,f). Both of the tests show that pseudoequivalent potential temperature θe decreases, then increases with height, and reaches a minimum at around 4 km (Figs. 15g,h). Compared with the CTL result, the SPY test predicts weaker vertical gradients of θe, due to the relatively high moisture in the low atmosphere. That is, conditional instability is still present but weaker in the SPY run, possibly because of the more active convection creating a more stable environment.
Time–height cross sections of (a),(b) θ (K), (c),(d) w (m s−1), (e),(f) RH (%), and (g),(h) θe (K) in the TC eye with the CTL and SPY tests.
Citation: Weather and Forecasting 32, 3; 10.1175/WAF-D-15-0109.1
In the eye and eyewall region, the new parameterization of the surface exchange leads to some changes to the thermal structure in the low atmosphere. Figure 16 shows the time evolution of the thermal structure in the low atmosphere (<2.5 km). Compared with the CTL results, the SPY test shows a slightly cooler and moister lower layer (Figs. 16a,b and 16c,d). This is also discussed in Wang et al. (2001), who indicate that some observational evidence may support the real existence of the phenomena (Cione et al. 2000). Both of the tests exhibit a shallow mixing layer (<300 m) near the surface that is defined by a near-constant potential temperature and unsaturated layer (RH < 90%) (Figs. 16c,d and 16e,f). This structure seems consistent with the observational studies of Willoughby (1998) and Barnes and Fuentes (2010).
Time–height cross sections in the lower atmosphere of (a),(b) T (°C), (c),(d) RH (%), and (e),(f) θ (K) in the TC eye with the CTL and SPY tests.
Citation: Weather and Forecasting 32, 3; 10.1175/WAF-D-15-0109.1
Theoretical and observational evidence (e.g., Rogers et al. 2013; Vigh and Schubert 2009; Schubert and Hack 1982) suggests that during intensification convection is located on the inside of Rmax, defined as radius of maximum azimuthal-mean tangential wind, where the inertial stability is high and convective heating can act efficiently to create the surface pressure fall. The overlap between regions of ascent and large inertial stability {
Radius–height azimuthal mean fields at 36 h: (top) I2 (shaded; ×10−7 s−2), tangential wind (black contours, m s−1) and w (red contour; m s−1); (middle) divergence (shaded; ×10−3 s−1), tangential wind (black contours; m s−1), and agradient wind (red contours; m s−1); and (bottom) θe (shaded; K), radial wind (black contours; m s−1), and T (red contours; °C) for (a),(c),(d) CTL and (b),(e),(f) SPY tests.
Citation: Weather and Forecasting 32, 3; 10.1175/WAF-D-15-0109.1
As in Fig. 17, but the radius–height azimuthal-mean fields at 60 h.
Citation: Weather and Forecasting 32, 3; 10.1175/WAF-D-15-0109.1
Studies show that notable differences in the radial profile of relative vorticity (RV) exist between storms undergoing RI and storms that are steady state (SS). Rogers et al. (2013), from a statistical survey of airborne Doppler observations of TCs, conclude that there is a ringlike structure for RI with maximum magnitude of RV within Rmax between 0.3 Rmax and 0.6 Rmax, while for SS such maxima are much closer to the eye center with higher RV in the eye (their Fig. 4b). Nguyen et al. (2011), from a numerical study, described a similar dual appearance of a monopole structure with maximum vorticity near the center of the circulation, and a ringlike structure with maximum vorticity at some radius from the center. Other studies also show that the differences in RV profiles are closely related to the TC development status (e.g., Kossin and Eastin 2001). Such differences in the RV profiles are also notable from our simulations between the CTL and SPY tests. As shown in Fig. 19, for SPY, during the early hours the maximum vorticity is located at the center of the circulation (monopole structure) and is evolving toward a ringlike structure. As RI further develops, a strong ringlike RV structure occurs by 36 h. RV then becomes weaker near the eyewall and stronger near the eye center when the simulated TC becomes nearly steady (the lines on 48 and 60 h, respectively). For CTL, a slow but steady intensification in the later hours (36, 48, and 60 h) maintains the ringlike RV profiles.
Radial distributions of RV (10−3 s−1) around 2-km height for the (a) CTL and (b) SPY tests at different forecast hours.
Citation: Weather and Forecasting 32, 3; 10.1175/WAF-D-15-0109.1
The above results suggest that both reduced drag and a sea spray parameterization may be needed to simulate TC intensification, consistent with previous studies (e.g., Nguyen et al. 2011; Kossin and Eastin 2001; Montgomery et al. 2014; Smith et al. 2009). The revised scheme appears to simulate these processes better and also better represents the evolution to a steady-state TC.
3) Analysis of rapid intensification based on the MPI framework
We calculated CAPE, VMPI, and the components of VMPI and illustrate them in Fig. 20. As shown in Fig. 20a, both the VMPI,1 and VMPI,2 results are quite similar, and the maximum boundary layer–averaged tangential winds Vm,B from both the CTL and SPY tests start to intensify at the beginning of the model simulations and maintain a similar pace until hour 24, when VMPI results for both of the tests are much larger than their corresponding Vm,B results. During the period, both Vm,B and VMPI in the SPY test are consistently larger than their counterparts in the CTL test. After hour 24, the difference between the SPY and CTL VMPI values becomes large, as does Vm,B, until around hour 39, when both VMPI and Vm,B start to become steady. After hour 39, when Vm,B reaches steady state, the difference between VMPI and Vm,B becomes smaller, yet VMPI is still larger than Vm,B for both of the tests. The matches between MPI and numerical simulations have been studied by Wang and Xu (2010). The above description suggests, but does not demonstrate, that the MPI tangential wind guides and bounds the model-simulated tangential wind from its rapid intensification to its steady state.
Time series of VMPI and components contributing to its formation: (a) Vm,B, VMPI,1, and VMPI,2. Components constituting the VMPI expressions in Eqs. (11a) and (11b) are (b) Tt and Ts, (c) CK/CD, (d) θe,s* and θb, and (e) CAPEs and CAPEb. (f) Ratios from SPY to CTL tests of (Ts − Tt)/(Ts/Tt), CK/CD, lnθe,s* − lnθb, and CAPEs − CAPEb.
Citation: Weather and Forecasting 32, 3; 10.1175/WAF-D-15-0109.1
We decompose the components in Eqs. (11b) and (11c) to investigate their contributions to VMPI. We plot CK/CD, Tt and Ts, 
We would attribute the smaller CAPEb in SPY than CTL to the cooler near-surface air in the SPY test (cf. Figs. 16a and 16b), as a result of the spray evaporation cooling. Although the larger CAPEb in the CTL could potentially be associated with enhanced convection, the actual larger vertical motion and tangential wind in SPY compared with CTL (cf. Figs. 13a and 13b; see also Fig. 20a) are also influenced by the air–sea interaction processes, which are represented by the MPI theory through its components in Eqs. (11b) and (11c).
5. Conclusions
A revised parameterization for modifying air–sea momentum, sensible heat, and moisture exchanges at high wind speeds has been implemented in the current Australian numerical weather prediction system for tropical cyclones (ACCESS-TC). The parameterization is composed of a sea spray route inclusion scheme for sensible heat and moisture fluxes and a variable Charnock parameter algorithm for momentum roughness length. At high winds of approximately greater than 18 m s−1, the latter not only greatly impacts the parameterization of surface momentum flux but also influences the parameterization of heat and moisture fluxes. The sea spray scheme is adapted from a series of studies summarized in Bao et al. (2011), Fairall et al. (1994), and Kepert et al. (1999), referred to as the BFK model, and is applied in conjunction with the variable Charnock parameter that varies with the 10-m wind speed in neutral conditions. Such a revised air–sea exchange parameterization behaves differently in comparison with the conventional bulk algorithm. At high winds, it has a relatively lower surface stress, enhanced sensible and latent heat fluxes (as well as enthalpy flux), and makes a cooler but moister near-surface layer. Preliminary results suggest the ratio CK/CD becomes high with increasingly high winds, which is in general agreement with the theoretical prediction of Emanuel (1986, 1995) for a steady-state tropical cyclone.
For the small number of TC predictions around Australia and the west Pacific conducted so far, the revised air–sea exchange parameterization enhances the predictability of TC intensity, while still mostly maintaining the skill of the track forecasts. In comparison with the bulk algorithm, it enhances the initialized TC circulation during 4DVAR and improves predictions of TC intensity, even for a near steady-state storm.
A rapid intensification case study indicates that the revised parameterization affects the evolution of rapid intensification. Both forecasts represent major features of TC inner-core structure change described in previous studies. A nearly saturated layer with a height of less than 1 km is separated from the surface by a shallow unsaturated mixing layer for both tests. In comparison with the control test using the conventional scheme, the test with the revised scheme predicts a relatively moister and thicker layer above the shallow mixing layer. A more weakly vertically stratified pseudo–potential temperature from the spray route inclusion test seems less inhibiting for subsidence in the eye, which is important to the surface pressure fall. Ultimately, the revised surface fluxes influence the behavior of the eyewall convection, and this in turn appears to influence the behavior of the eyewall and subsidence in the eye. Such behaviors include radial and temporal pulsations of vertical and radial motion in the eye during the RI process.
Regardless of the clear difference in the parameterized surface fluxes in the two simulations, the simulated inner-core structures characterizing rapid intensification and steady-state conditions are basically the same between the two simulations. Both of the simulations represent the positions of inertial instability and vertical motion relative to the radius of the azimuth-mean maximum wind, and the radial divergence and agradient wind in the layer near the surface. The shapes of the radial profiles of mean relative vorticity are also consistent between the two simulations for both RI and SS. The coherence of the structure change between the schemes implies that it is the TC inner-core dynamics that determines the TC development, while the changes in the surface exchanges modulate the course of the TC development.
Within the framework of Emanuel’s MPI theory, the differences between the original and revised air–sea exchange parameterization schemes are characterized mostly by the differences in the ratio between enthalpy and momentum exchange coefficients and the differences in near-surface atmospheric thermal properties. These results lead to the differences between the MPI tangential wind speeds.
Acknowledgments
This research was partially supported by the National Oceanographic Partnership Program (NOPP) and the U.S. Office of Naval Research (ONR) under Award N000141010139.
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