24 The Urban Heat Island
Each of the nonradiative exchanges are functions of a vertical gradient (Δ) of a
relevant property and a means of exchange:
(2.6a)
(2.6b)
(2.6c)
In the case of Q
G, the flux is regulated by the gradient in substrate tempera-
ture (∆
Tsub, K m
− 1
) and the conductivity (k) of the soil material. The convective
fluxes, Q
H and QE, are regulated by the gradients in air temperature, ∆
Ta (K m
− 1
),
and water vapor, ∆ ρv (kg m
− 1
), and the respective eddy conductivities, K H and K V.
The eddy conductivity terms are shorthand expressions for complex convective
processes that mix the atmosphere and account for the effect of both wind and
atmospheric stability.
Fig. 2.4 presents the typical diurnal patterns for the radiative (Fig. 2.4A) and non-
radiative (Fig. 2.4B) fluxes over a grassland surface under clear and calm conditions.
At night, the ground cools by radiation (Q
∗
< 0) and this loss is compensated for by
the transfer of energy from the substrate (Q G < 0) and from the overlying air toward
the surface ((Q H + QE) < 0). Similarly, during the daytime the ground is heated by ra-
diation and energy is transferred to the atmosphere and the substrate, warming the substrate and near-surface air and increasing its vapor content. Note that the diurnal patterns of exchanges are not symmetrical as they depend on the relevant gradients (ΔT
sub, ΔTa, and Δρ v) and transfer terms (k, KH, and KV), each of which will change
in response to the respective energy exchanges (Q
G, QH, and QE).
After sunrise, Q* increases and becomes positive. Initially, this energy is pref-
erentially channeled into the substrate (Q
G), while the response of the convective
exchanges (Q
H and QE) lags. QG reaches a peak before noon and declines in the after-
noon, becoming negative before sunset. By comparison, Q
H and QE peak after noon
before declining and becoming zero or negative after sunset. The offset between the conductive and convective fluxes can be attributed to the behavior of the substrate and near-surface atmosphere, respectively. In the morning hours, the substrate is cool and ∆
Tsub is large; by comparison, the atmosphere is stable so although ΔT a (Δρ v) may
be large, K
H (KV) is weak. By noon, the substrate has been warmed and, although the
surface continues to warm, ∆
Tsub has been reduced and QG is lowered. As the surface
warms, it heats the overlying air, which becomes progressively less stable (more tur-
bulent) making mixing easier. The turbulent fluxes (Q
H and QE) increase during the
late morning and early afternoon. As the surface cools in late afternoon, the intensity of turbulence weakens, the fluxes diminish and become negative after sunset. Note that in Fig. 2.4, Q
E
> QH for much of the daytime indicating that for a surface where
water is readily available, Q* is preferentially channeled into the evaporation of water through plants (referred to as evapotranspiration). A useful measure of the relative roles of these two fluxes is the Bowen ratio (β), which is simply the ratio Q
H/QE; if
β
< 1, e β > 1, heating dominates.
Qf Tk
Gs ub
∆≈λ,
Qf TK
Ha H
∆≈λ,
Qf K
Ev V
∆≈λμ,