Average: Average flux footprint
In FREddyPro: Post-Processing EddyPro Full Output File

Description Usage Arguments Value Note Author(s) References Examples

Calculate the average flux footprint from an array of half hourly turbulance data using Kormann and Meixner 2001 model.

1 2	Average(fetch = 500, height = 3, grid = 200, speed, direction, uStar, zol, sigmaV, weights = NULL)

`fetch`	The upwind distance over which you want the calculation domain to extend. Note that the footprint will be normalized to that domain so footprints that extend well beyond the domain will be overrepresented in
`height`	The z-d height of the flux system
`grid`	The total calculation grid size. The default is 200 which would mean the footprint would be represented in a 200x200 array corresponding to dimensions of two times the fetch on each side of the grid.
`speed`	An N length array of wind speeds at the flux system
`direction`	An N length array of wind directions at the flux system
`uStar`	An N length array of friction velocities
`zol`	An N length array of Monin Ohbukov stability parameters
`sigmaV`	An N length array of standard deviations of the cross-stream wind component
`weights`	A dictionary of N length arrays footprint weighting values. This is an optional input

Output is a list object with a 3 elements including:

Probability: the array holding the footprint probabilities Fpn: the array holding the grid point distance north of the flux system Fpe: the array holding the grid point distance east of the flux system WeightedProbability: the array holding the weighted footprint probabilities

This code impliments the footprint model of Kormann and Meixner 'An Analytical Footprint Model For Non-Neutral Stratification' , Boundary-Layer Meteorology, 2001, v99, Issue 2, pp 207-224

Modifications have been added to determine the footprint for a two-dimensional area surrounding the flux tower. Calculations can be done for a single flux footprint, or an average of weighted or non-weighted footprints.

This code was written by Robert Clement, (robert.clement@ed.ac.uk)

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

Original author: Robert Clement, University of Edinburgh. R adaptation: Georgios Xenakis, Forest Research

Kormann, R., and Meixner, F.X. (2001). An analytical footprint model for non-neutral stratification, Boundary-Layer Meteorology. 99, 207-224.

## Load the data
data(fluxes)

## Clean fluxes
fluxes=cleanFluxes(fluxes,sdCor=TRUE,sdTimes=3,timesList=3,distCor=TRUE,
                   thresholdList=list(H=c(-100,1000),LE=c(-100,1000)))

## Use data without NA values
fluxes_noNA<-fluxes[which(!is.na(fluxes$L)),]

## Displacement height
d=17.42

## Calculate z
fluxes_noNA$z=(fluxes_noNA$X.z.d..L*fluxes_noNA$L)+d

## Calculate zol
fluxes_noNA$zol=fluxes_noNA$z/fluxes_noNA$L

## Calculate average footprint
footprint=Average(fetch=500,height=33,grid=200,fluxes_noNA$wind_speed[180:183],
fluxes_noNA$wind_dir[180:183],fluxes_noNA$u.[180:183],fluxes_noNA$zol[180:183],
sqrt(fluxes_noNA$v_var[180:183]))

## You can also use the plot.footprint function of FREddyPro to plot the result
plotFootprint(footprint)