3.1 Energy Balance in the PBL

The fluxes of heat and momentum drive the growth and structure of the PBL. To properly

characterize the PBL, one first needs a good estimate of the surface sensible heat flux (H) which

depends on the net radiation (Rn) and surface characteristics such as the available surface

moisture (described in the form of the Bowen ratio (Bo)). In the CBL, a simple energy balance

approach, as in Oke (1978), is used to derive the expression, used in AERMET, to calculate the

sensible heat flux, H. We begin with the following simple characterization of the energy balance

in the PBL:

where H is the sensible heat flux, 8E is the latent heat flux, G is the soil heat flux, and Rn is the

net radiation. To arrive at an estimate of H simple parameterizations are made for the soil and

latent heat flux terms; that is, G R , and , respectively. Substituting these n = 01. λE H Bo =

expressions into eq. (1) the expression for surface heat flux becomes,

3.1.1 NET RADIATION

If measured values for Rn are not available, the net radiation is estimated from the

insolation and the thermal radiation balance at the ground following the method of Holtslag and

van Ulden (1983) as

where c1 = 5.31x10-13 W m-2 K-6, c2 = 60 W m-2, c3 = 0.12, FSB is the Stefin Boltzman Constant

(5.67x10-8 Wm-2K-4), Tref is the ambient air temperature at the reference height for temperature

and Rn is the net radiation. The albedo is calculated as r{ϕ} = r ′ + (1r ) exp(aϕ + b) , where

a = −0.1 , b = − 05(1r ) , and Note, braces, {}, are used throughout this 2 . r ′ = r{ϕ = 90o}.

report to denote the functional form of variables.

Solar radiation, R, corrected for cloud cover, is taken from Kasten and Czeplak (1980) as

where n is the fractional cloud cover and Ro is the clear sky insolation which is calculated as

R ( ) , and N is the solar elevation angle (tp and t are the o = 990 sinϕ 30 =

⎛ +

⎝ ⎜

⎠ ⎟

ϕ{t } ϕ{t} p

2

previous and present hours, respectively) (1975) . Note that when observations of cloud cover

are unavailable a value of 0.5 is assumed in eq. (3) and measurements of solar radiation are

required.

3.1.2 TRANSITION BETWEEN THE CBL AND SBL

When the PBL transitions from convective to stable conditions the heat flux changes sign

from a positive to a negative value. At the point of transition the heat flux must therefore vanish,

implying that the net radiation is equal to zero. By setting Ro equal to zero in eq. (3), and solving

for sin N, the critical solar elevation angle Ncrit ,corresponding to the transition point between the

CBL and the SBL can be determined from

 

 

 

 

n951 - n952 - n953 - n954 - n955 - n956 - n957 - n958 - n959 - n960 - n961 - n962 - n963 - n964 - n965 - n966 - n967 - n968 - n969 - n970 - n971 - n972 - n973 - n974 - n975 - n976 - n977 - n978 - n979 - n980 - n881 - n982 - n983 - n984 - n985 - n986 - n987 - n988 - n989 - n990 - n991 - n992 - n993 - n994 - n995 - n996 - n997 - n998 - n999 - n1000

 

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