Calculate the maximum height of rise based on Brigs (1975), the height is calculated using different formulations depending on stability and wind conditions.
plumeRise(df, imax = 10, ermax = 1/100, Hmax = TRUE, verbose = TRUE)data.frame with the input, rise (m) and effective higt (m)
data.frame with micrometeorological and emission data
maximum number of iteractions
maximum error
use weil limit for plume rise, see details
display additional information
a data.frame with effective height of emissions for pointSource function
The input data.frame must contains the folloging colluns:
- z: height of the emission (m)
- r: source raius (m)
- Ve: emission velocity (m/s)
- Te: emission temperature (K)
- ws: wind speed (m/s)
- Temp: ambient temperature (K)
- h: height of the Atmospheric Boundary Layer-ABL (m)
- L: Monin-Obuhkov Lench (m)
- dtdz: lapse ration of potential temperature, used only for stable ABL (K/m)
- Ustar: atriction velocity, used only for neutral ABL (m/s)
- Wstar: scale of convectie velocity, used only for convective ABL (m/s)
Addcitionaly some combination of ws, Wstar and Ustar can produce inacurate results, Weil (1979) propose a geometric limit of 0.62 * (h - Hs) for the rise value.
The plume rise formulas are from Brigs (1975):"Brigs, G. A. Plume rise predictions, Lectures on Air Pollution and Environmental Impact Analyses. Amer. Meteor. Soc. p. 59-111, 1975." and Arya 1999: "Arya, S.P., 1999, Air Pollution Meteorology and Dispersion, Oxford University Press, New York, 310 p."
The limits are from Weil (1979): "WEIL, J.C. Assessmet of plume rise and dispersion models using LIDAR data, PPSP-MP-24. Prepared by Environmental Center, Martin Marietta Corporation, for Maryland Department of Natural Resources. 1979."
The example is data from a chimney of the Candiota thermoelectric powerplant from Arabage et al (2006) "Arabage, M. C.; Degrazia, G. A.; Moraes O. L. Simulação euleriana da dispersão local da pluma de poluente atmosférico de Candiota-RS. Revista Brasileira de Meteorologia, v.21, n.2, p. 153-160, 2006."
candiota <- matrix(c(150,1,20,420,3.11,273.15 + 3.16,200,-34.86,3.11,0.33,
150,1,20,420,3.81,273.15 + 4.69,300,-34.83,3.81,0.40,
150,1,20,420,3.23,273.15 + 5.53,400,-24.43,3.23,0.48,
150,1,20,420,3.47,273.15 + 6.41,500,-15.15,3.48,0.52,
150,1,20,420,3.37,273.15 + 6.35,600, -8.85,3.37,2.30,
150,1,20,420,3.69,273.15 + 5.93,800,-10.08,3.69,2.80,
150,1,20,420,3.59,273.15 + 6.08,800, -7.23,3.49,1.57,
150,1,20,420,4.14,273.15 + 6.53,900,-28.12,4.14,0.97),
ncol = 10, byrow = TRUE)
candiota <- data.frame(candiota)
names(candiota) <- c("z","r","Ve","Te","ws","Temp","h","L","Ustar","Wstar")
row.names(candiota) <- c("08:00","09:00",paste(10:15,":00",sep=""))
candiota <- plumeRise(candiota,Hmax = TRUE)
#> convective, h/L = -5.7372346528973
#> using weil max= 31
#> convective, h/L = -8.61326442721792
#> strong convective, h/L = -16.3733115022513
#> using weil max= 155
#> strong convective, h/L = -33.003300330033
#> using weil max= 217
#> strong convective, h/L = -67.7966101694915
#> strong convective, h/L = -79.3650793650794
#> strong convective, h/L = -110.650069156293
#> strong convective, h/L = -32.0056899004267
print(candiota)
#> z r Ve Te ws Temp h L Ustar Wstar rise He
#> 08:00 150 1 20 420 3.11 276.31 200 -34.86 3.11 0.33 31.0000 181.0000
#> 09:00 150 1 20 420 3.81 277.84 300 -34.83 3.81 0.40 41.5831 191.5831
#> 10:00 150 1 20 420 3.23 278.68 400 -24.43 3.23 0.48 155.0000 305.0000
#> 11:00 150 1 20 420 3.47 279.56 500 -15.15 3.48 0.52 217.0000 367.0000
#> 12:00 150 1 20 420 3.37 279.50 600 -8.85 3.37 2.30 121.4376 271.4376
#> 13:00 150 1 20 420 3.69 279.08 800 -10.08 3.69 2.80 102.0828 252.0828
#> 14:00 150 1 20 420 3.59 279.23 800 -7.23 3.49 1.57 207.6558 357.6558
#> 15:00 150 1 20 420 4.14 279.68 900 -28.12 4.14 0.97 355.4518 505.4518