Therefore, AERMET defines the point of transition between the CBL and SBL (day to

night) as the point in time when the solar elevation angle N = Ncrit. On average, for clear and

partly cloudy conditions, the transition from stable to convective conditions occurs when N

17

reaches approximately 13o; for overcast conditions Ncrit increases to about 23o (Holtslag and van

Ulden 1983).

However, if solar radiation measurements are available AERMET determines Ncrit from an

estimate of cloud cover rather than the actual observations themselves. In eq. (5) the cloud cover

(n) is replaced with an equivalent cloud cover (neq) that is calculated from eq. (4) such that

n R R .

3.2 Derived Parameters in the CBL

In this section the methods used by AERMET to calculate the PBL parameters in the

convective boundary layer are discussed. AERMET first estimates the sensible heat flux (H ),

then calculates the friction velocity (u*) and the Monin Obukhov Length (L). With H, u* and L,

AERMET can then estimate the height of the mixed layer and the convective velocity scale (w*).

3.2.1 FRICTION VELOCITY (u*) & MONIN OBUKHOV LENGTH (L) IN THE CBL

In the CBL, AERMET computes the surface friction velocity, u*, and the Monin-Obukhov

length, L, using the value of H estimated from eq. (2). Since the friction velocity and the Monin

Obukhov length depend on each other, an iterative method, similar to that used in CTDMPLUS

(Perry 1992), is used. AERMOD initializes u*, and L by assuming neutral conditions (i.e., L=4).

The final estimate of u* and L is made once convergence is reached through iterative

calculations (i.e., there is less than a 1% change between successive iterations). The expression

for u* (e.g., Panofsky and Dutton (1984)) is

where g is the acceleration of gravity, cp is the specific heat of air at constant pressure, D is the

density of air, and Tref is the ambient temperature representative of the surface layer. Then u* and

L are iteratively recalculated using eqs. (6), (7) and (8) until the value of L changes by less than

1%.

The reference heights for wind speed and temperature that are used in determining the

friction velocity and Monin-Obukhov length are optimally chosen to be representative of the

surface layer in which the similarity theory has been formulated and tested with experimental

data. Typically, a 10 m height for winds and a temperature within the range of 2 to 10 m is

chosen. However, for excessively rough sites (such as urban areas with zo can be in excess of 1

m), AERMET has a safeguard to accept wind speed reference data that range vertically between

7 zo and 100 m. Below 7 zo (roughly, the height of obstacles or vegetation), measurements are

unlikely to be representative of the general area. A similar restriction for temperature

measurements is imposed, except that temperature measurements as low as zo are permitted.

Above 100 m, the wind and temperature measurements are likely to be above the surface layer,

especially during stable conditions. Therefore, AERMET imposes an upper limit of 100 meters

for reference wind speed and temperature measurements for the purpose of computing the

similarity theory friction velocity and Monin-Obukhov length each hour. Of course, other US

EPA guidance for acceptable meteorological siting should be consulted in addition to keeping

the AERMET restrictions in mind.

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