NDFE.fit: NDFE fit

In gasfluxes: Greenhouse Gas Flux Calculation from Chamber Measurements

NDFE fit

Description

Fit the the non-steady-state diffusive flux extimator model using the Golub-Pereyra algorithm for partially linear least-squares models.

Usage

NDFE.fit(
  t,
  C,
  A = 1,
  V,
  serie = "",
  k = log(0.01),
  verbose = TRUE,
  plot = FALSE,
  maxiter = 100,
  ...
)

Arguments

t	time values (usually in hours)
C	concentration values
A	area covered by the chamber
V	effective volume of the chamber
serie	id of the flux measurement
k	starting value for nls function
verbose	logical, TRUE prints message after each flux calculation
plot	logical, mainly intended for use in gasfluxes
maxiter	see nls.control
...	further parameters, currently none

Details

The NDFE model (Livingston et al., 2006) is C(t)=C_0+f_0\tau \frac{A}{V}\left [\frac{2}{\sqrt{\textup{pi}}}\sqrt{t/\tau}+e^{t/\tau}\textup{erfc}(\sqrt{t/\tau})-1\right ]. To ensure the lower bound \tau > 0, the substituion \tau = e^k is used. The resulting reparameterized model is then fit using nls with algorithm = "plinear".

Note that according to the reference the model is not valid for negative fluxes. Warning: This function does not check if fluxes are positive. It's left to the user to handle negative fluxes.

The default starting value k = log(\tau) assumes that time is in hours. If you use a different time unit, you should adjust it accordingly.

Note that nls is used internally and thus this function should not be used with artificial "zero-residual" data.

Value

A list of

f0	flux estimate
f0.se	standard error of flux estimate
f0.p	p-value of flux estimate
C0, tau	other parameters of the NDFE model
AIC	Akaike information criterion
AICc	Akaike information criterion with small sample correction
RSE	residual standard error (sigma from summary.nls)
diagnostics	error or warning messages

References

Livingston, G.P., Hutchinson, G.L., Spartalian, K., 2006. Trace gas emission in chambers: A non-steady-state diffusion model. Soil Sci. Soc. Am. J. 70(5), 1459-1469.

Examples

#a single fit
t <- c(0, 1/3, 2/3, 1)
C <- c(320, 340, 355, 362)
print(fit <- NDFE.fit(t, C, 1, 0.3, "a"))
plot(C ~ t)
curve({fit$C0+fit$f0*fit$tau*1/0.3*(2/sqrt(pi)*sqrt(x/fit$tau)+
      exp(x/fit$tau)*erfc(sqrt(x/fit$tau))-1)}, 
      from = 0, to = 1, add = TRUE)
#note that the flux estimate is very uncertain because 
#there are no data points in the region of high curvature

gasfluxes documentation built on Sept. 11, 2024, 6:09 p.m.