The impact of Coriolis approximations on the environmental sensitivity of idealized extratropical cyclones

Abstract

The precise influence of climate change on extratropical cyclone genesis and evolution is an important (but as yet unsolved) problem, given their physical and economic impact on a large portion of the planet’s population. However, extratropical cyclones are also affected by the competing influences of forcing mechanisms at a wide range of spatial scales, complicating the problem. While the advent of idealized numerical modeling has allowed great strides in addressing these complications and achieving some qualitative consensus in the literature, there is still some quantitative disagreement about response magnitude and where local maxima and minima in the response may be located. Thus, the advantages inherent in the variety of idealized numerical modeling methods used to address this problem are also a drawback, as it can be difficult to draw one-to-one comparisons across experiments. Although the effects of particular model architecture choices such as microphysical and cumulus schemes are well-documented, others are less understood. In this study, we examine the role of Coriolis approximations by comparing a new set of ETC sensitivity experiments using a linear β-plane approximation to an existing set of extratropical sensitivity experiments using a constant f-plane approximation. ETCs within the new β-plane experiment are found to generally decrease in strength with temperature, as measured by both minimum sea level pressure and maximum eddy kinetic energy (EKE). A small increase in EKE is observed at the warmest temperatures, likely due to diabatic influences disrupting flow within the warm conveyor belt. While seemingly contradictory to the previous f-plane results, the two experiments are instead found to be qualitatively similar upon further inspection, with an offset of approximately 8 K. This offset is primarily due to the Coriolis approximations, although the initial stability profile (affected by the Coriolis approximation) has a marginal influence.

Appendix: Model initialization equations

1.1 Initial flow field

As the flow is initiated in a purely zonal orientation, we need only worry about initiating the u-component of the wind, and consider changes only in the latitudinal direction, j, and height, k. Our wind profile takes the functional form:

$$u\left( {j,k} \right) = U_{0} *F\left( j \right)*G\left( k \right)$$

(A1)

U₀, the speed at the jet maximum, is set to 45 m/s. F(j) and G(k) are functions for the variation with latitudinal direction and height, respectively:

$$\begin{aligned} & F\left( j \right) = \sin (\pi *\sin \left( {lat\left( j \right)^{2} } \right)^{3} {\text{and }}\\ & G\left( k \right) = \frac{zz\left( k \right)}{{z_{t} }}*e^{{ - \frac{1}{2}\left( {\frac{zz\left( k \right)}{{z_{t} }}} \right)^{2} + \frac{1}{2}}} \end{aligned}$$

(A2–A3)

The latitude of the selected row of grid points is specified by lat(j), zz(k) is the height of level k, and z_t equals 13 km in these simulations. F(j) is chosen following PE2007, which itself attempts to mimic Thorncroft et al. (1993). G(k) also follows PE2007, which follows a latitude dependence from Simmons and Hoskins (1977). Together these profiles produce a reasonable jet shape, with wind velocity at the surface initialized at 0 m/s.

1.2 Initial temperature field

Finally, we complete the balanced temperature field at initialization. Again, following the appendix of PE2007, we can arrive at a temperature formulation as follows:

$$T\left( {j,k} \right) = T_{r} \left( k \right) - T_{c} \left( {j,k} \right)$$

(A4)

The formulation depends on a reference temperature profile valid at the southern boundary, T_r:

$$T_{r} \left( k \right) = T_{0} + \frac{{\varGamma_{0} }}{{\left( {z_{t} + z\left( k \right)^{ - \alpha } } \right)^{1/\alpha } }}$$

(A5)

and utilizes a correction factor of T_c to iteratively bring the temperature field into balance with the wind field:

$$\begin{aligned} T_{c} \left( {j,k} \right) & = T_{c} \left( {j - 1,k} \right) + \left( {\frac{du}{dz}\left( {j,k} \right) + \frac{du}{dz}\left( {j - 1,k} \right)} \right)\\ &\quad*\frac{1}{2}\Delta y*\frac{H}{R}*f, {\text{for}}\, j > 1 \end{aligned}$$

(A6)

where H is the scale height of the atmosphere, set to 7500 m, and R is the gas constant of dry air, 287 J kg⁻¹ K⁻¹. At j = 1, the southern boundary of the domain, T_c is set equal to 0 and the temperature is equal to the reference value. T_c includes the change in jet speed $\left( {\frac{{{\text{d}}u}}{{{\text{d}}z}}} \right)$, meridional grid spacing used within the model ($\Delta y$), and the Coriolis parameter f.

1.3 Moisture initialization

After the dry initialization is complete, moisture is then added; and as in B2013, the initial relative humidity profile is given by:

$$RH = RH_{0} *\left\{ {\begin{array}{ll} {\left( {1 - 0.85*\frac{Z}{{Z_{t} }}} \right)} & \,{for\,Z < Z_{t} } \\ {0.15} & \,{for\,Z > Z_{t} } \\ \end{array} } \right.$$

For all experiments, the surface relative humidity (RH₀), is set to 80%, and the moisture scale height (Z_t) is set to 12 km.