Above here, the behavior of
density as a function of temperature approached normal again, because the difference in volume between ordered and disordered states began to drop.
The corresponding working quasilinear wave equation for the barotropic azonal stream
function Ψm ′
of the forced waves with m = 6, 7, and 8 (m waves) with nonzero right - hand side (forcing + eddy friction) yields (34) u˜ ∂ ∂ x (∂ 2Ψm ′ ∂ x2 + ∂ 2Ψm ′ ∂ y2) + β˜ ∂ Ψm ′ ∂ x = 2Ω sin ϕ cos2 ϕT˜u˜ ∂ Tm ′ ∂ x − 2Ω sin ϕcos2 ϕHκu˜ ∂ hor, m ∂ x − (kha2 + kzH2)(∂ 2Ψm ′ ∂ x2 + ∂ 2Ψm ′ ∂ y2), [S3] where x = aλ and y = a ln -LSB-(1 + sin ϕ) / cos ϕ] are the coordinates
of the Mercator projection
of Earth's sphere, with λ
as the longitude, H is the characteristic value
of the atmospheric
density vertical scale, T˜ is a constant reference
temperature at the EBL, Tm ′ is the m component
of azonal
temperature at this level, u˜ = u ¯ / cos ϕ, κ is the ratio
of the zonally averaged module
of the geostrophic wind at the top
of the PBL to that at the EBL (53), hor, m is the m component
of the large - scale orography height, and kh and kz are the horizontal and vertical eddy diffusion coefficients.
If you can't reach the answer by considering Equation 8 itself, consider the lead - up to it, where Velasco et al point out that the state
density as a
function of both velocity and altitude (Equation 5) is not the product
of state
density as a
function of altitude alone (Equation 6) and state
density of a
function of velocity alone (Equation 7)--
as it would be if
temperature were independent
of altitude.
Perhaps the fire frequency was a
function of population
density, cultural practices innovations, or other human - based factors that had nothing to do with
temperature, such
as war, peace, displacement, entrenchment, food preference shifts, food availability changes, evolution in customs, advances in ecological knowledge, population growth, etc..