AERMOD Tech Guide
4.1.3 Profiles of the Potential Temperature Gradient in the Interface
Ignoring the shallow superadiabatic surface layer, the potential temperature gradient in the well mixed CBL is taken to be zero. The gradient in the stable interfacial layer just above the mixed layer is taken from the morning temperature sounding. This gradient is an important factor in determining the potential for buoyant plume penetration into and above that layer. Above the interfacial layer, the gradient is typically constant and slightly stable. These three layers (well mixed, interfacial, and stable layer aloft) in the CBL have d/dz computed in AERMOD as
where zi is taken from eq. (27).
Although the interfacial layer depth varies with time, we fixed it at 500 m for these calculations to insure that a sufficient layer of the morning sounding is sampled. This avoids unrealistic kinks often present in these data. The constant value of 0.005 above the interfacial layer is suggested by Hanna and Chang (1991). Using the morning sounding to compute the interfacial temperature gradient assumes that as the mixed layer grows throughout the day, the temperature profile in the layer above zi changes little from that of the morning sounding. Of course, this assumes that I there is neither significant subsidence nor cold or warm air advection occurring in that layer. Field measurements (e.g., Clark et al., 1971) of observed profiles throughout the day lend support to this approach. These data point out the relative invariance of upper level temperature profiles even during periods of intense surface heating.
For the SBL and in the absence of measurements, the potential temperature gradient is calculated as
In the SBL if d/dz measurements are available below100m and above zo , then *p is calculated from eq. (31) using the value of d/dz at the lowest measurement level and zTref replaced by the Tref height of the d/dz measurements. The upper limit of 100 meters for the vertical temperature gradient measurements is consistent with that imposed by AERMET for wind speed and temperature reference data used to determine similarity theory parameters such as the friction velocity and the Monin-Obukhov length. Similarly, the lower limit of zo for the vertical o temperature gradient measurements is consistent with that imposed for reference temperature data. If no measurements of d_/dz are available, in that height range, then is assumed to be *p equal to * (the cloud cover parameterized temperature scale eq. (24) used in AERMET to estimate nighttime heat flux) and is calculated by combining Eqs. (8) and (25). * is not used in the CBL.
Figure 4 shows the inverse height dependency of d/dz in the SBL. To create this curve we assumed that: Zim =100m; and therefore, Zi =100m; L=10m; u*=.124, which is consistent with mixing height of 100m; Ttref =293 K; and therefore based on eq. (18) * =0.115 k/m. These ref o o parameter values were chosen to represent a strongly stable boundary layer. Below 2m /dz is persisted downward from its value of 0.228 ¬įK/m at 2m. Above 100m d/dz is allow to decay o exponentially with height.
For all z, d/dz is limited to a minimum of 0.002 K/m (Paine and Kendall, 1993). Eq. (31) is taken from Businger et al. (1971). Eq. (32) is from Stull (1988) and Van Ulden and Holtslag (1985). The constant of 0.44 within the exponential term of eq. (32) is inferred from typical profiles within the Wangara experiment (Andre and Mahrt, 1982).
When measurements of d/dz are available, eqs. (31) and (32) are applied in a slightly different way. Between measurements we interpolate. Above the highest measurement level the d/dz profile is extrapolated from the value at that height while maintaining the shape as defined by eq. (31) and eq. (32). When extrapolating below the lowest measurement height eq. (31) is first solved for * (using the d/dz measurement at that lowest height). The d/dz profile is * extrapolated down from the lowest measurement height while maintaining the shape as defined by eq. (31)