flux {flux}

Estimate gas flux rates using non-steady-state closed chamber data

Description

flux is a convenience wrapper for the other two functions that should be suitable for most users. It can be used to estimate gas fluxes for all three commonly measured greenhouse gases (CO_2, CH_4, N_2O) at once or separately.

Usage

flux(x, var.par, co2ntrol = list(leak = TRUE, relay = FALSE), 
min.allowed = 3, max.nrmse = 0.1, nrmse.lim = 0.2, r2.qual = 0.8, 
range.lim = 30, out.unit = "auto", elementar = FALSE, 
hardflag = list(range = TRUE), asterisks = TRUE)

flux.odae(dat, var.par, min.allowed = 3, max.nrmse = 0.1, rl = NULL)

flux.conv(fl.dat, ghg = "CH4", r2.qual = 0.8, nrmse.lim = 0.2, 
out.unit = "auto", elementar = FALSE, hardflag = list(range = TRUE))

Arguments

x

A list of data tables as returned by chop. Each table contains data for one chamber measurement. Required are at least the columns specified in the argument var.par (see also Example).

var.par

A named list specifying the variables and parameters that are used in the estimation process and variables that should be handed through the function so that they are easily available for further analysis. Some of the names are obligatory (time, volume, area, t.air, p.air, and two or more that specify the gas column and the gas quality column), others are optional. See details and examples.

ghg

Character string identifying the greenhouse gas for which concentration measurements are handled. Can be "CH4", "N2O" or "CO2". Defaults to "CH4". This argument determines the molar weight that is used in the flux calculation with gflux, the input unit (ppb or ppm), and the ambient concentration of the gas that is added to the diagnostic plots plotted with plot.fluss and used for the determination of the number of measurements below ambient (nomba).

co2ntrol

Options for estimating fluxes with CO_2 control. In this case outliers and the slope of the CO_2 concentration measurements influence the estimated flux rate of the other greenhouse gases (N_2O and CH_4; see Details). By default, CO_2 correction is switched off.

min.allowed

Integer giving the minimum number of concentration measurements allowed during the estimation of one single flux. Can be any number between 3 and the number of concentration measurements during one chamber placement.

max.nrmse

Numeric giving the maximum acceptable normalized root mean square error for configurations with higher numbers of concentration measurements than specified in min.allowed. Numeric value between 0 and 1. Defaults to 0.1. Above that value lower numbers of concentration measurements down to min.allowed are considered. See details. In flux max.nrmse can also be given as a named list with three items giving the maximum acceptable nrmse per gas. See examples.

nrmse.lim

Numeric between 0 and 1 (defaults to 0.2) giving the main quality parameter for the model fit, the maximum acceptable normalized root mean square error. If the best fit for one chamber measurement exceeds this value, the function reports FALSE in the nrmse.f quality flag. See details and value. In flux nrmse.lim can also be given as a named list with three items giving the nrmse.lim per gas. See examples.

range.lim

The minimum detectable range of the concentration measurements during one chamber placement. Has to be either a single numerical value, a numeric vector with the same length as x giving different range limits for each chamber placement (for instance obtained by flux.calib) or a character string naming the column in x that contains range limit data. If this column is named "rl" (the default when the range limits are attached to the data by flux.calib) flux automatically detects it. Note, that setting range.lim != NULL overrides the auto detected range limits.

The acceptable range limit depends on the accuracy of the concentration measurements. When the range of the concentration measurements is smaller than the repeatability range of the measurement device (e.g., a gas chromatograph) one cannot tell real increase in concentration from random fluctuation. Therefore, if the range of the concentration measurements during one chamber placement is < range.lim, the range.flag is set to FALSE (0). See details. In flux range.lim can also be given as a named list with three items giving the maximum acceptable range limits per gas. See examples.

r2.qual

Numeric giving the limit of minimum acceptable r2 as an alternative quality parameter describing the model fit. Can be between 0 and 1 (0.8 by default). If a model r2 is below the setting the r2 quality flag is reported FALSE (0). In flux r2.qual can also be given as a named list with three items giving the acceptable r2.qualities per gas. See examples.

out.unit

Character string determining the output unit of the flux rate mass part. Character string. The default "auto" tries to find a unit that ranges the output value between 0.01 and 10. Possible output units are "ng", "mug", "mg", or "g". "mug" stands for "\mug" because non-ascii characters are not allowed in functions.

elementar

When the fluxes are wanted as element values set elementar = TRUE. Defaults to FALSE.

hardflag

Named list that controls which of the quality flags are to be hard flagged (the value is changed according to the quality flag). range.lim is hard flagged by default. So when the range of the actual concentration values for a chamber measurement is smaller than the set range limit a zero flux is returned. When a flux estimation does not meet the quality requirements of any other hard-flagged quality parameter flux returns NA. For changing a quality parameter to a hard flag just provide its name (without quotation marks) and set it to TRUE. Possible parameters to chose as hard or soft flag are nrmse, range, and r2. Further the number of measurements below ambient (nomba) can be hardflagged by setting nomba = [0…nc] with nc = number of concentration measurements during one chamber placement. See examples.

asterisks

Logical. If TRUE, p-values are given as asterisks.

dat

One data table for one chamber placement. See x and var.par for details.

rl

Specifies range.lim in the low level function flux.odae. As with range.lim several options are allowed. Defaults to NULL. In this case, the function looks for a column rl in dat. If it can't find a column rl, the value is set to 0 and a warning is returned; if it does exist dat$rl is always taken. If rl is a character string the function looks for a column of that name in dat, if rl is a numeric value, this value is taken as the range limit. See examples.

fl.dat

An object with the same structure as returned by flux.odae. See details and value.

Details

Typically it will be most convenient to use flux on objects returned by chop (i.e. on lists of data tables that contain all necessary data per chamber measurement including supporting information). flux simply wraps flux.odae and flux.conv applied on lists of chamber measurement data tables into one function. Thus, the data of a one day field campaign or a year of chamber measurements can easily be handled by simply running two functions (chop and flux) consecutively to estimate ghg fluxes for all three common ghg gases. See example.

Probably the most important argument is var.par. It specifies the variables (by referring to the names of the data columns) from x and parameters (fixed values that are constant for all chamber placements) that are used for the flux estimations. For simple handling it is expecting a named list.

For flux the obligatory list items are: One item that refers to a column in x containing ghg concentrations (see next paragraph for details); time – chamber closing time in minutes; volume – chamber volume during placement (in cbm); area – chamber area (in sqm); t.air – air temperature inside chamber during concentration measurements (in °C); p.air – air pressure during concentration measurements (in Pa).

The list items that are used to specify the ghg for which flux estimation is carried out have to be specified by using the named list items CH4 – CH_4 concentrations; CH4.gcq – CH_4 GC quality flag; CO2 – CO_2 concentrations; CO2.gcq – CO_2 GC quality flag; N2O – N_2O concentrations; N2O.gcq – N_2O GC quality flag. Fluxes are estimated for all ghg for which concentration data are given. Thus, at least one ghg should be specified. GC quality flags are optional. If you don't provide a reference to a column in x the function assumes that all GC measurements were OK.

All these list items can either be given as a variable (name of a column in x) or as a fixed parameter (a numeric value). This makes no sense for the ghgs and time, but in many cases chamber volume and area will be constant across measurements. Another likely candidate for a fixed parameter is p.air because air pressure is often not logged during chamber measurements. All additional list items should be of type ‘variable‘ and refer to further columns in x if you want those data handed through the function and be part of the result tables (for having all data in one place for further analyses). You are free to choose appropriate names. Fixed parameters will not be relayed.

If the flux estimation is carried out in two steps it will typically be carried out on a list structure as returned by chop. Therefore, it is used within a lapply call. For details see examples. However, the functions flux.odae and flux.conv are designed to be carried out on single data tables (data.frame) per chamber measurement.

First flux.odae is run. It simply tries to find the best model fit for the series of concentration measurements that are given in dat. This data.frame has to consist of five columns that give (in that order): gas concentration, closing time of the chamber in minutes, gas concentration quality flag, chamber volume, temperature within the chamber headspace during measurements (may change during chamber placement). See example data.

At the moment the optimization bases on linear regression. All possible models with n (= total number of concentration measurements per chamber placement) to min.allowed number of concentration measurements are fitted and the best fit is evaluated in a stepwise procedure. The normalized root mean square error is used as the quality criterion for the outlier detection and elimination procedure. All model fits with a nrmse <= max.nrmse are extracted and ranked according to the number of concentration measurements (decreasing) and to the nrmse (increasing). The first ranked model is stored along with the original data table and some other information. Therefore a model with e.g. a nrmse of 0.081 constructed from 5 concentration measurements wins against a model with a nrmse of 0.07 with only 4 concentration measurements. This reflects the idea that models with nrmse <= max.nrmse already represent a sufficient fit and do not have "outliers" that must be eliminated.

In case no model has a nrmse <= max.nrmse, the models are simply ranked according to their nrmse and the model with the lowest nrmse wins and is stored. In that way outliers are detected and exluded. flux.odae returns a complex object that contains most of the necessary information for the flux.conv function and also carries information that is later needed for the plot functions (plot.flux and plot.fluss).

The flux calculation is then carried out with the function flux.conv. It takes the object returned by flux.odae and additional information (chamber area, gas species, several quality settings and in- as well as output units) and calculates the flux rates. Further several quality checks (r2 check, range check, nrmse check, nomba check; for details see Value) are carried out and quality flags are reported along with the fluxes in the output. It is best when all quality flags are returned TRUE. Depending on the application quality requirements might vary. Therefore, per default the function reports soft quality flags (despite for range). However, this can be changed via hardflag.

The idea behind co2ntrol in flux is that the CO_2 concentration measurements might serve as a further check on the integrity of the chamber measuremnt in the field. When co2ntrol is set, the function first carries out an outlier procedure on the CO_2 concentration data (the respective columns have to be in x of course). Further, the slope of the CO_2 concentration change over time is checked. When it is negative, chamber leakage is assumed and a respective quality flag (leak.flag) is reported FALSE. The leak.flag cannot be hard flagged.

Value

flux returns a complex object of class fluxes that is a 3 entry list. When the object is printed to the console only the second entry is displayed in a modified form that is meant to maximize information display with small footprint for easy inspection. A table is printed to the console with three columns per gas. The first contains the quality flags (e.g. "111.02"). The order is: nrmse.f, r2.f, range.f, nomba.f, leak.f. The first three are considered more important, and if they are '1' everything is fine. The first flag behind the full stop just gives the number of measurements below ambient, while the second is '2' when co2ntrol was switched off, '0' when leaking occurred, and '1' when no leaking occurred.

The data.frame with the estimated flux rates contains all data needed for further analysis. The columns represent the entries in fluss of the single chamber measurements (including quality flags, see below) plus naming information according to the settings in the nmes argument of chop. export provides a simple way to export the results. The first entry is itself a list of lists and data tables. It is called flux.res and is comprised of objects that are returned by flux.conv per ghg. Each first level entry in these lists contains the information for one chamber measurement. It is named according to the nmes-setting in chop and contains the elements fluss (which is itself a list with the elements given below), fl.dat (equals the object returned by flux.odae; see below), and unit which provides information on the output mass unit of the flux rate that is handed over to the function plot.fluss and to the table output.

The elements of fluss:

ghg

Character. The gas species for which the flux has been estimated.

flux

Numeric. Calculated flux rate in mass unit per m2 and hour.

r2

The R^2 of the best fitted model that has been used for flux caclulation.

nrmse

The NRMSE of the best fitted model that has been used for flux caclulation.

r2.f

Logical. R^2 quality flag telling whether the R^2 quality setting given in r2.qual is fulfilled.

range.f

Logical. Range quality flag telling whether the range of the concentration measurements exceeded the quality range of the measurement device that has been specified in range.lim.

nrmse.f

Logical. NRMSE quality flag telling whether the NRMSE quality setting given in nrmse.lim is fulfilled (i.e. if the NRMSE of the best model <= nrmse.lim).

nomba.f

Integer. Reports the number of measurements below ambient. The ambient concentrations are set to be 392.6 ppm (CO_2), 1874 ppb (CH_4), and 324 ppb (N_2O) (taken from Mace Head Ireland (N_2O, CH_4) and global average (CO_2) obtained from http://cdiac.ornl.gov/pns/current_ghg.html as of August 16th, 2013).

leak.f

Logical. When co2ntrol was applied with leak = TRUE, possible chamber leakage as represented by decreasing CO_2 concentrations over time is shown by a FALSE (0).

The elements of fl.dat that is also the object returned by flux.odae are:

lm4flux

Complex object. The best fitting model as reported by lm. It builds the basis for the calculation of the flux rate via flux.conv.

row.select

Integer vector giving the indices of the rows of the data table that have been used to construct the best fitting model. This information is later used in the plotting functions plot.flux and plot.fluss.

orig.dat

data.frame with the original data provided according to arguments x and columns.

out.dat

Data to be handed through. Per default area and volume of the chamber are relayed but these values are not part of the table output whereas all additionally relayed data are part of the table output.

Author(s)

Gerald Jurasinski <[e-mail]>, Franziska Koebsch <[e-mail]>, Ulrike Hagemann <[e-mail]>, Anke Günther <[e-mail]>

References

Nakano T (2004) A comparison of regression methods for estimating soil-atmosphere diffusion gas fluxes by a closed-chamber technique. Soil Biology and Biochemistry 36: 107-113.

Forbrich I, Kutzbach L, Hormann A, Wilmking M (2010) A comparison of linear and exponential regression for estimating diffusive CH4 fluxes by closed-chambers in peatlands. Soil Biology and Biochemistry 42: 507-515.

See Also

chop, flux.calib, gflux, plot.fluss

Examples

## load example data
data(tt.pre)

## extract field concentration measurements
gcd <- tt.pre[tt.pre$sampletype_a=="P",]

## partition the data into data tables per chamber measurement
# then do the partitioning
gcd.parts <- chop(gcd, factors = c("date", "spot", "veg"), 
nmes = c("date", "veg", "spot"))

## calculate flux rates for methane
# first define a global CH4 range limit
CH4.lim <- 30
# do the flux rate estimation (it will often be best to define
# var.par separately, note that p.air is given as a parameter)
vp.CH4 <- list(CH4 = "CH4ppb", time = "time_min", CH4.gcq = "CH4Code", 
volume = "cham_vol", t.air = "temp_dC", area = "cham_area", p.air = 101325)
flux.CH4 <- flux(gcd.parts, var.par = vp.CH4)
# look at the results table
flux.CH4

# extracting range limits from the calibration gas measurements
# and attaching them to gcd.parts. first get the calibration gas
# measurements from tt.pre (changing the date because it is in 
# a strange format and has to be the same as the dates in gcd.parts)
cgm <- tt.pre[tt.pre$sampletype_a=="E",c("date_gc", "CH4ppb", "CH4Code", 
"CO2ppm", "CO2Code", "N2Oppb", "N2OCode")]
names(cgm)[1] <- "date"
cgm$date <- "2011-03-16"
# now we can do the flux.calib
gcd.parts.cal <- flux.calib(gcd.parts, columns = c("date", "CH4ppb"), 
calib = cgm, format="%Y-%m-%d", window=48, buffer=1100, attach=TRUE)
# do the flux rate estimation (we use the same var.par as before)
flux.CH4 <- flux(gcd.parts.cal, var.par=vp.CH4, co2ntrol = NULL, 
range.lim=NULL)
# look at the results table
flux.CH4
# export the results to the working directory
wd <- getwd()
export(flux.CH4, file=paste(wd, "/flux.CH4.txt", sep=""))

## plot the concentration-change-with-time-plots as kind of diagnostic
plot(flux.CH4, dims = c(3,6))

## do the flux rate estimation whilst using CO2 concentrations to
## control for possible chamber leakage
flux.CH4.b <- flux(gcd.parts, var.par=vp.CH4)
# look at the results table
flux.CH4.b
# plot the concentration-change-with-time-plots as kind of diagnostic
plot(flux.CH4.b, dims = c(3,6))

## do the flux rate estimation whilst using CO2 concentrations to
## control for outliers and possible chamber leakage
flux.CH4.c <- flux(gcd.parts, var.par=vp.CH4, co2ntrol = list(leak = TRUE, 
relay = FALSE))
# look at the results table
flux.CH4.c
# plot the concentration-change-with-time-plots as kind of diagnostic
plot(flux.CH4.c, dims = c(3,6))