ROUGH-ZO User’s Guide

The program ROUGH-ZO calculates the surface roughness length, zo, and the displacement length, d, of an industrial or urban site using equations presented in the AIChE book by Hanna and Britter (2002). The inputs required by the program are the site’s ratio of frontal area to lot area, f, the ratio of plan area to lot area, p, and the mean obstacle height, Hr. These input parameters have to be previously estimated by the user, who can calculate them directly from the geometric characteristics of the roughness elements, or using approximate estimates found in textbooks (e.g., Hanna and Britter, 2002), or using software such as the programs ROUGH-GEOMETRY (distributed with ROUGH-ZO) or ROUGH (Petersen and Parce, 1994).

Equations used by ROUGH-ZO

The program ROUGH-ZO has four alternate equations for estimating zo:

1)The equations recommended by Hanna and Britter (2002):

zo = f Hr for f < 0.15

zo = 0.15 Hrfor f > 0.15

2)The equation recommended by Macdonald et al. (1998):

zo = (1-(d/Hr))exp(-(0.5(CD/2)(1-(d/Hr)f)-0.5) Hr, with d/Hr = 1 + K-p (p - 1),

with the following values for the parameters:  = 1, CD = 1.2,  = 0.4, and K = 4 (tuned for staggered arrays of identical cubes).

3)The equation recommended by Hanna and Britter (2002) as a rule of thumb, in case of no information is available on the frontal area and the plan area:

zo = 0.1 Hr

4)The Lettau (1969) equation:

zo = 0.5 f Hr

The program also calculates two alternate estimates of the displacement length, d, as given in the following equations:

1) The equations recommended by Hanna and Britter (2002):

d = 3f Hr for f < 0.05

d = [0.15 + 5.5(f – 0.05)] Hr for 0.05 < f < 0.15

d = [0.7 + 0.35(f – 0.15)] Hr for 0.15 < f <1.0

d = [0.7 + 0.35(1 – 0.15)] Hr for f > 1

5)The equation recommended by Macdonald et al. (1998):

d = [1 + K-p (p - 1)] Hr, with K = 4.

Example of a ROUGH-ZO run

We reproduce here the sequence of prompts and responses that are obtained when running ROUGH-ZO. In this example, the user wants to estimate the roughness length, zo, and the displacement length, d, of a site with average obstacle height Hr = 9 meters, ratio of frontal area to lot area f = 0.12, and ratio of plan area to lot area p = 0.22.

C:> rough-zo[enter]

Input average obstacles height Hr (m) : 9[enter]

Input normalized frontal area lambda_f: 0.12[enter]

Input normalized plan area lambda_p : 0.22[enter]

Hanna and Britter (2002) Zo = 1.08 meters

Macdonald et al. (1998) Zo = 0.69 meters

Zo = 0.1 Hr = 0.90 meters

Lettau (1969) Zo = 0.54 meters

Hanna and Britter (2002) d = 4.82 meters

Macdonald et al. (1998) d = 3.94 meters

References

Hanna, S.R. and Britter, R.E., 2002: Wind Flow and Vapor Cloud Dispersion at Industrial and Urban Sites. AIChE/CCPS, 345 East 47th St., New York, NY10017, 171 pages.

Lettau, H., 1969: Note on aerodynamic roughness parameter estimation on the basis of roughness element description. J. Appl. Meteorol., 8, 828-832.

Macdonald, R.W., R.F. Griffiths and D.J. Hall, 1998: An improved method for the estimation of surface roughness of obstacle arrays. Atmos. Environ., 32, 1857-1864.

Petersen, R.L. and D.K. Parce, 1994: Development and testing of methods for estimating surface roughness length at refineries. CCP Project 92-0890, CPP, Ft. Collins, CO 80524.

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