Statistical assessments are performed for the 8 runs concatenated into one dataset. Surface pressure has more scatter than maximum sustained one-minute winds (Vmax), hence the analysis is performed on Vmax. All variables are available in 3-h segments. SST, sensible heat flux, latent heat flux, Convective Available Potential Energy (CAPE), surface relative humidity, and surface dewpoint temperature are determined at the radius of maximum winds (Rmax) in compass 30-deg directions, and averaged using the 12 points. Filtered wind shear and precipitable water are determined at the 100-, 200-, 300-, 400-, and 500-km radii in compass 90-deg directions, and averaged using the 20 points. Wind shear is computed as the vectorial wind difference between 200- and 850-mb pressure levels.
Linear correlation results show Vmax is correlated to SST with a variance explained of 59-61%, but higher correlations exist for the fluxes with a variance explained of 72-80%. However, the intensification cycle (defined as ΔVmax over a 24-h period) is mostly linearly correlated to CAPE with r=0.7 and variance explained of 49%. Generally, other correlations are either low for Vmax, low for ΔVmax, or highly correlated with CAPE or sensible heat flux (multicollinearity).
Moreover, when a sigmoidal correlation relationship (“s-curve pattern”) is computed for sensible heat flux versus Vmax, r=0.94 and the variance explained is 88%. Hence, for a favorable environmental environment in this HWRF environment of 8 cases, the TC slowly develops as it approaches the warm pool with a correspondence to heat flux, intensifies in response to a “CAPE boost” as it begins moving over SST of 27.5-28.5°C with an intensity change linearly proportional to CAPE, then approaches steady-state as CAPE is reduced partially due to the developing warm-core aloft. A simple model that uses an empirically derived heat flux sigmoidal equation and linear CAPE equation explains 75% of the variance. Implications of this concept towards understanding intensity change, facilitating Maximum Potential Intensity theory, and possible utilization in statistical intensity schemes such as SHIPS, LGEM, and the Rapid Intensification Index will be briefly discussed.
Wind shear calculations required removing the vortex influence of Edouard, which was a large storm. Using the traditional 2-3-4-2-5-6-7-2-8-9-2 Kurihara filter failed, but was remedied by expanding to a 2-3-4-2-5-6-7-2-8-9-2-10-11-2-12-13-2-3-2 filter. A response function analysis of both filters shows the new scheme is more suitable for higher-resolution models, as Kurihara originally tuned his scheme for a coarse model to remove ten-degree features. An interesting necessity is the need for an intermittent 2Δx pass or the scheme becomes unstable — a property not discussed in Kurihara’s original paper. As many more passes are required for the new technique, additional modifications to remove 3-5Δx noise may be required. Ultimately, as model resolution continues to improve, the original Kurihara scheme will become ineffective, and we will discuss necessary steps to remedy this problem.