NDFE.fit {gasfluxes}

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