A comparative study of the role of the Saharan air layer in the evolution of two disparate Atlantic tropical cyclones using WRF model simulations and energetics calculations

Abstract

The Weather Research and Forecasting (WRF) Model 5-day simulations of Major Hurricane Julia (2010) and Tropical Storm Florence (2012), both of which developed from African easterly waves, are used to conduct a complete energetics study to explain why one storm became a major hurricane while the other weakened to a wave. The disparate intensity outcomes are caused by significant differences in the energetics of the two systems that emerge in their storm stages due to differences in the impact of the Saharan air layer (SAL). In their wave stages both waves exhibit a convectively driven energy production cycle, in which the regions of positive barotropic and baroclinic energy conversion and of diabatic heating and rainfall are all superimposed. Convection induces barotropic instability which then enhances the baroclinic overturning through a resonance of the two instabilities, which together produce the eddy kinetic energy. Diabatic heating in the convection generates eddy available potential energy which, along with the eddy kinetic energy, defines the total eddy energy of the system. Florence loses the convectively driven energy production cycle in the storm stage and begins to weaken, while Julia maintains this cycle and becomes a major hurricane. The disruption of the convection in Florence is due to the drying, stabilizing, and vertical shearing effects of an expansive SAL to the north of the storm, effects not present in the Julia case. Consideration is given to the different effects of the SAL on 6–10 day waves (Florence wave) versus 3–5 day waves (Julia wave).

Appendix: Energetics equations

$$K_{\text{Z}} = \int\limits_{p1}^{p2} {\frac{{\overline{{\left[ u \right]^{2} + \left[ v \right]^{2} }} }}{2g}} {\text{d}}p$$

(3)

$$A_{\text{Z}} = \int\limits_{p1}^{p2} {\frac{{\overline{{\left[ T \right]^{*2} }} }}{{2\overline{\sigma } }}{\text{d}}p}$$

(4)

$$C_{\text{Z}} = - \int\limits_{p1}^{p2} {\frac{R}{p}} \overline{{\left[ \omega \right]^{*} \left[ T \right]^{*} }} \frac{{{\text{d}}p}}{g}$$

(5)

$$K_{\text{E}} = \int\limits_{p1}^{p2} {\overline{{\frac{{\left[ {u^{{{\prime }2}} + v^{{{\prime }2}} } \right]}}{2g}}} {\text{d}}p}$$

(6)

$$A_{\text{E}} = \int\limits_{p1}^{p2} {\frac{{\overline{{\left[ {T^{{{\prime }2}} } \right]}} }}{{2\overline{\sigma } }}{\text{d}}p}$$

(7)

$$\begin{aligned} {\text{C}}_{\text{k}} = {\text{C}}_{\text{k1}} + {\text{C}}_{\text{k2}} + {\text{C}}_{\text{k3}} + {\text{C}}_{\text{k4}} \hfill \\ \quad = - \int\limits_{p1}^{p2} {\overline{{\left[ {u^{{\prime }} v^{{\prime }} } \right]\frac{\partial \left[ u \right]}{\partial y}}} } \frac{{{\text{d}}p}}{g} - \int\limits_{p1}^{p2} {\overline{{\left[ {u^{{\prime }} \omega^{{\prime }} } \right]\frac{\partial \left[ u \right]}{\partial p}}} } \frac{{{\text{d}}p}}{g} - \int\limits_{p1}^{p2} {\overline{{\left[ {v^{{{\prime }2}} } \right]\frac{\partial \left[ v \right]}{\partial y}}} \frac{{{\text{d}}p}}{g}} - \int\limits_{p1}^{p1} {\overline{{\left[ {v^{{\prime }} \omega^{{\prime }} } \right]\frac{\partial \left[ v \right]}{\partial p}}} } \frac{{{\text{d}}p}}{g} \hfill \\ \end{aligned}$$

(8)

$$C_{\text{pk}} = - \int\limits_{p1}^{p2} {\frac{R}{p}} \overline{{\left[ {\omega^{{\prime }} T^{{\prime }} } \right]}} \frac{{{\text{d}}p}}{g}$$

(9)

$$\begin{aligned} {\text{C}}_{\text{A}} = {\text{C}}_{\text{A1}} + {\text{C}}_{\text{A2}} \hfill \\ \quad = - \int\limits_{p1}^{p2} {\overline{{\frac{{\left[ {v^{{\prime }} T^{{\prime }} } \right]}}{{\overline{\sigma } }}\frac{\partial \left[ T \right]}{\partial y}}} } {\text{d}}p - \int\limits_{p1}^{p2} {\overline{{\frac{{\left[ {\omega^{{\prime }} T^{{\prime }} } \right]}}{{\overline{\sigma } }}\frac{{\partial \left[ T \right]^{*} }}{\partial p}}} {\text{d}}p} \hfill \\ \end{aligned}$$

(10)

$$G_{\text{E}} = \int\limits_{p1}^{p2} {\frac{{\overline{{\left[ {T^{{\prime }} Q^{{\prime }} } \right]}} }}{{\overline{\sigma } c_{p} }}} {\text{d}}p$$

(11)

$$D_{\text{E}} = - \int\limits_{p1}^{p2} {\overline{{\left[ {u^{{\prime }} F_{x}^{{\prime }} + v^{{\prime }} F_{y}^{{\prime }} } \right]}} } \frac{{{\text{d}}p}}{g}$$

(12)

$$K_{{{\text{EB}}}} = \frac{1}{{L_{x} }}\int\limits_{{p1}}^{{p2}} {\left[ {\left( {\frac{{\overline{{u\left( {u^{{{\prime }2}} + v^{{{\prime }2}} } \right)}} }}{{2g}}} \right)_{{x1}} - \left( {\frac{{\overline{{u\left( {u^{{{\prime }2}} + v^{{{\prime }2}} } \right)}} }}{{2g}}} \right)_{{x2}} } \right]} {\text{d}}p + \frac{1}{{L_{y} }}\int\limits_{{p1}}^{{p2}} {\left( {\left[ {\frac{{v(u^{{{\prime }2}} + v^{{{\prime }2}} )}}{{2g}}} \right]_{{y1}} - \left[ {\frac{{v(u^{{{\prime }2}} + v^{{{\prime }2}} }}{{2g}}} \right]_{{y2}} } \right)} {\text{d}}p + \left( {\left[ {\frac{{\overline{{\omega \left( {u^{{{\prime }2}} + v^{{{\prime }2}} } \right)}} }}{{2g}}} \right]_{{p1}} - \left[ {\frac{{\overline{{\omega \left( {u^{{{\prime }2}} + v^{{{\prime }2}} } \right)}} }}{{2g}}} \right]_{{p2}} } \right)$$

(13)

$$\Phi_{\text{EB}} = \frac{1}{{L_{x} }}\int\limits_{p1}^{p2} {\left( {\left( {\overline{{u^{{\prime }} \phi^{{\prime }} }} } \right)_{x1} - \left( {\overline{{u^{{\prime }} \phi^{{\prime }} }} } \right)_{x2} } \right)} \frac{{{\text{d}}p}}{g} + \frac{1}{{L_{y} }}\int\limits_{p1}^{p2} {\left( {\left[ {v^{{\prime }} \phi^{{\prime }} } \right]_{y1} - \left[ {v^{{\prime }} \phi^{{\prime }} } \right]_{y2} } \right)} \frac{{{\text{d}}p}}{g} + \frac{1}{g}\left( {\overline{{\left[ {\phi^{{\prime }} \omega^{{\prime }} } \right]}}_{p1} - \overline{{\left[ {\phi^{{\prime }} \omega^{{\prime }} } \right]}}_{p2} } \right)$$

(14)

$$\begin{aligned} A_{{{\text{EB}}}} & = \frac{1}{{L_{x} }}\int\limits_{{p1}}^{{p2}} {\left( {\left( {\overline{{\frac{{uT^{{\prime 2}} }}{{2\bar{\sigma }}}}} } \right)_{{x1}} - \left( {\overline{{\frac{{uT^{{\prime 2}} }}{{2\bar{\sigma }}}}} } \right)_{{x2}} } \right)} {\text{d}}p \\ & \quad + \frac{1}{{L_{y} }}\int\limits_{{p1}}^{{p2}} {\left( {\left( {\frac{{\left[ {vT^{{\prime 2}} } \right]}}{{2\bar{\sigma }}}} \right)_{{y1}} - \left( {\frac{{\left[ {vT^{{\prime 2}} } \right]}}{{2\bar{\sigma }}}} \right)_{{y2}} } \right)} {\text{d}}p \\ & \quad + \left( {\left( {\overline{{\frac{{\left[ {\omega T^{{\prime 2}} } \right]}}{{2\bar{\sigma }}}}} } \right)_{{p1}} - \left( {\overline{{\frac{{\left[ {\omega T^{{\prime 2}} } \right]}}{{2\bar{\sigma }}}}} } \right)_{{p2}} } \right) \\ \end{aligned}$$

(15)

[()] represents a zonal mean and $\overline{{\left[ {\left( {} \right)} \right]}}$ represents a meridional mean of the zonal mean. Primes indicate deviations from the zonal mean, and asterisks indicate deviations from the area mean. The relationships are $\left( {} \right) = \left[ {\left( {} \right)} \right] + \left( {} \right)^{{\prime }}$ and $\left[ {\left( {} \right)} \right] = \overline{{\left[ {\left( {} \right)} \right]}} + \left( {} \right)^{*}$. Vaiables not mentioned in the text: K _Z is zonal kinetic energy, A _Z is zonal available potential energy, C _Z represents conversions between the two.

Following are the definitions of variables:

u :

Zonal wind component, positive to the east

v :

Meridional wind component, positive o the north

ω :

Vertical pressure velocity

T :

Temperature

p :

Pressure

F _x :

Friction in the zonal direction

F _y :

Friction in the meridional direction

Q :

Diabatic heating

ϕ :

Geopotential

$\overline{\sigma }$ :

Mean static stability (gc ⁻¹ _p $\overline{\left[ T \right]}$ - gpR ⁻¹ $\partial \overline{\left[ T \right]}$ ∂ p ⁻¹)

c _p :

specific heat at constant pressure

R :

Specific gas constant for dry air

g :

Gravitational acceleration

x :

Zonal coordinate, positive to east

y :

Meridional coordinate, positive to north

L _x :

Zonal distance for the domain

L _y :

Meridional distance for the domain