cost_function: Multi-objective optimality-based cost function

In oscarperezpriego/ETpartitioning: Partitioning of eddy covariance ET into flux components

Description

Cost function to be implemented in an optimization routine of the ETpartitioning package (see Perez-Priego et al., 2018).

Usage

cost_function(par, data, ColPhotos, ColPhotos_unc, ColH, ColVPD, ColTair,
  ColPair, ColQ, ColCa, ColUstar, ColWS, ColSW_in, Chi_o, WUE_o)

Arguments

par	A vector containing 4 parameters (a1,Do,To,beta)
data	Data.frame or matrix containing all required variables.
ColPhotos	Column name of numeric vector containing time series of photosynthesis data (umol CO2 m-2 s-1).
ColPhotos_unc	Column name of numeric vector containing time series of photosynthesis uncertainties (umol CO2 m-2 s-1).
ColH	Column name of numeric vector containing time series of sensible heat flux (W m-2).
ColVPD	Column name of numeric vector containing time series of vapor pressure deficit (hPa).
ColTair	Column name of numeric vector containing time series of air temperature (deg C).
ColPair	Column name of numeric vector containing time series of atmospheric pressure (kPa).
ColQ	Column name of numeric vector containing time series of photosynthetic active radiation (umol m-2 s-1).
ColCa	Column name of numeric vector containing time series of atmospheric CO2 concentration (umol Co2 mol air-1).
ColUstar	Column name of numeric vector containing time series of wind friction velocity (m s-1).
ColWS	Column name of numeric vector containing time series of wind velocity (m s-1).
ColSW_in	Column name of numeric vector containing time series of incoming short-wave radiation (W m-2).
Chi_o	Long-term effective chi
WUE_o	Long-term effective WUE

Details

the multi-objective function is defined as:

OF <- sum((photos-photosy_mod)/photos_unc)^2)/n + phi

where phi invokes optimality theory by minimizing the following term

phi <- (sum(transpiration_mod)/sum(photos_mod)*WUE_o

Value

a numeric value:

OF	the summed cost to minimize both the mismatch between observed and modeled Photos and the unit cost of transpiration

Note

The 4 model parameters (a1, Do, Topt and beta, see Perez-Priego et al., 2018) are estimated using a multi-constraint Markov Chain Monte Carlo (MCMC).The objective function (OF) is to find those numerical solutions that minimize not only the mismatch between observed and modeled Photos but also the unit cost of transpiration by introducing a conditional factor demand (phi), which invokes the optimality hypothesis. The phi term is to be defined as the integrated cost of transpiration (i.e. transpiration_mod/photos_mod) over a time period (5 days) normalized by a factor describing the long-term effective water use efficiency (WUE_o).

References

Perez-Priego, O., G. Katul, M. Reichstein et al. Partitioning eddy covariance water flux components using physiological and micrometeorological approaches, Journal of Geophysical Research: Biogeosciences. In press

Reichstein, M., et al. (2005), On the separation of net ecosystem exchange into assimilation and ecosystem respiration: review and improved algorithm, Global Change Biology, 11(9), 1424-1439.

Examples

 ## Selecting a single day (e.g. 15-05-2011)
 tmp <-  EddySample[ EddySample$TIMESTAMP_START>  201105150000,]
 tmp <-  tmp[tmp$TIMESTAMP_START<  201105160000,]
 ## Defining parameter values
 par <- c(200, 0.2, 25, 0.6)

cost_function(
 data=tmp
 ,par=par
 ,ColPhotos="GPP_NT_VUT_MEAN"
 ,ColPhotos_unc ="NEE_VUT_USTAR50_JOINTUNC"
 ,ColH="H_F_MDS"
 ,ColVPD="VPD_F"
 ,ColTair="TA_F"
 ,ColPair="PA_F"
 ,ColQ="PPFD_IN"
 ,ColCa="CO2_F_MDS"
 ,ColUstar="USTAR"
 ,ColWS="WS_F"
 ,ColSW_in="SW_IN_F"
 ,Chi_o = 0.88
 ,WUE_o = 24.25
)

oscarperezpriego/ETpartitioning documentation built on June 4, 2019, 12:13 a.m.