coreModel: Calculate trajectories in backward mode.

In ChHaeni/bLSmodelR: bLSmodelR - An atmospheric dispersion model in R

Calculate trajectories in backward mode.

Description

This is the core function to calculate the (air parcel) trajectories in a backward mode (i.e. backward-in-time).

Usage

coreModel(u, v, w, zSens, ustar, L, Zo, bw, sigmaUustar, sigmaVustar, 
  kv, C0, alpha, MaxFetch)

Arguments

u	numeric vector. Instantaneous velocity of the individual air parcels at time 0 in alongwind direction (given in m/s).
v	instantaneous velocity of air parcel at time 0 in crosswind direction (given in m/s).
w	instantaneous velocity of air parcel at time 0 in vertical direction (given in m/s).
zSens	sensor height in m above ground level.
ustar	friction velocity in m/s.
L	Obukhov length in m.
Zo	roughness length in m.
bw	parameter defining the vertical profile of the variance in the vertical velocity component sigmaW.
sigmaUustar	variance of the alongwind velocity devided by ustar.
sigmaVustar	variance of the crosswind velocity devided by ustar.
kv	von Ka'rma'n constant (usually = 0.4).
C0	Kolmogorov constant.
alpha	Fraction of the velocity decorrelation time scale as given in Flesch et al., 2004 to choose the time increment.
MaxFetch	maximum tracking distance of trajectories (in m).

Value

A list with following items:

Traj_IDOut	ID of the corresponding trajectory. This ID is identical to the indexing position of the initial velocities u, v and w (see calculation of w'C'/E in example below).
TimeOut	Time until touchdown in seconds.
xOut	x position of touchdown.
yOut	y position of touchdown.
wTDOut	Touchdown velocity.

Author(s)

Christoph Haeni

References

Flesch, T. K., J. D. Wilson, et al. (1995). “Backward-time Lagrangian stochastic dispersion models and their application to estimate gaseous emissions.” Journal of Applied Meteorology 34(6): 1320-1332.

Flesch, T. K., J. D. Wilson, et al. (2004). “Deducing ground-to-air emissions from observed trace gas concentrations: A field trial.” Journal of Applied Meteorology 43(3): 487-502.

See Also

runbLS, bLSmodelR-package.

Examples

## Not run: 

## set up model parameters
zSigmaWu <- 2
zSens <- 2
Ustar <- 0.25
L <- -600
Zo <- 0.001
SigmaUu <- 4.5
SigmaVu <- 4
SigmaWu <- 1.7
kv <- 0.4
alpha <- 0.02
MaxFetch <- 500
A <- 0.5

bw <- calcbw(SigmaWu, zSigmaWu/L)
SigmaWm <- calcsigmaW(Ustar, zSens/L, bw)
U <- calcU(Ustar, Zo, L, zSens, kv)
C0 <- calcC0(bw, kv)

## initial velocities
N0 <- 1000
set.seed(1234)
TDcat <- initializeCatalog(N0, Ustar, SigmaUu, SigmaVu, bw,
  zSens, L, Zo, A, alpha, MaxFetch, kv)
      
uvw <- uvw0(TDcat)

## run trajectory calculation
TDList <- coreModel(uvw[,"u0"], uvw[,"v0"], uvw[,"w0"], zSens, Ustar, 
  L, Zo, bw, SigmaUu, SigmaVu, kv, C0, alpha, MaxFetch)

## assign touchdowns to initalized Catalog:
assignCat(TDcat,TDList)

## Calculate C/E and w'C'/E ratios of entire domain with homogeneous
## emission rate:
Ci <- data.table(ID=1:N0,CE=0,u=uvw[,"u0"],v=uvw[,"v0"],w=uvw[,"w0"],key="ID")
Ci[TDcat[,sum(2/wTD),by=Traj_ID],CE:=V1]

stats <- Ci[,cbind(
  round(rbind(ce <- mean(CE),se <- sd(CE)/sqrt(N0),ce - 1.96*se,ce + 1.96*se),1),
  round(rbind(wce <- mean(w*(cs <- CE-ce)),wse <- sd(w*cs)/sqrt(N0)
  ,wce - 1.96*wse,wce + 1.96*wse),2))]

dimnames(stats) <- list(c("E(X)","SE","Lower-CI95%","Upper-CI95%"),c("C/E","w'C'/E"))
print(stats)



## look at Catalog:
TDcat
plot(TDcat,pch=20)



## End(Not run)

ChHaeni/bLSmodelR documentation built on Dec. 5, 2024, 8:47 a.m.