This vignette introduces the gasfluxes package to calculate soil
greenhouse gas fluxes from static chamber measurements. The package
offers different models for measured concentration-time relationships
from static chambers within the function `gasfluxes`

- “linear”
- “robust linear”
- “HMR” (see Pedersen et al., 2010)
- “original HMR” (the implementation according to Pedersen et al. 2010 in the HMR package)
- “NDFE”

and offers the function `selectfluxes`

to use selection
algorithms that combine the different models appropriately

- “RF2011” described in Leiber-Sauheitl et al. (2014)
- “RF2011new” same as RF2011 but with improved fitting function for HMR and based on corrected calculation of p-values
- “kappa.max” described in Hüppi et al. (2018)

The input data.frame or data.table can be imported easily from a CSV file (e.g., as exported by Excel):

```
library(data.table)
#adjust path (see help("setwd")) and file name as appropriate
fluxMeas <- fread("fluxmeas.csv")
#here we use two flux measurements from the file as an example
fluxMeas <- fluxMeas[ID %in% c("ID6","ID11")]
fluxMeas
#> ID V A time C
#> <char> <num> <int> <num> <num>
#> 1: ID6 0.535125 1 0.0000000 0.3241982
#> 2: ID6 0.535125 1 0.3333333 0.3838311
#> 3: ID6 0.535125 1 0.6666667 0.3623941
#> 4: ID6 0.535125 1 1.0000000 0.5067303
#> 5: ID11 0.550000 1 0.0000000 0.3337777
#> 6: ID11 0.550000 1 0.3333333 0.4410218
#> 7: ID11 0.550000 1 0.6666667 0.5080499
#> 8: ID11 0.550000 1 1.0000000 0.5417371
```

The `ID`

column must be a unique identifier for each flux
measurement, hence the same value for all the concentration-time points
that belong to the same flux. Column `V`

stands for the
chamber volume, `A`

for the chamber area, `time`

for the elapsed time after chamber closure and `C`

is the
concentration of the measured species (CO_{2}, N_{2}O,
CH_{4} etc.)

Units of the output fluxes depend on input units. It’s recommended to
use [V] = m^{3}, [A] = m^{2}, [time] = h, [C] = [mass or
mol]/m^{3}, which results in [f0] = [mass or
mol]/m^{2}/h. Since all algorithms only use V/A, A can be input
as 1 and V as the chamber height.

The following features of the input will be checked for sanity:

- if specified columns exist
(
`ID`

,`V`

,`A`

,`time`

,`C`

) - if input is numeric
- if there are any NA’s
- non-unique values in
`V`

or`A`

per chamber and if time is sorted and time values are unique - only positive input is allowed

`gasfluxes`

functionIf the input dataframe has the appropriate format, plug it into the function to calculate the fluxes:

```
library(gasfluxes)
flux.results <- gasfluxes(fluxMeas, method = c("linear","robust linear", "HMR"), plot = TRUE)
#> ID6: lm fit successful
#> ID6: rlm fit successful
#> ID6: HMR fit failed
#> ID11: lm fit successful
#> ID11: rlm fit successful
#> ID11: HMR fit successful
flux.results
#> ID linear.f0 linear.f0.se linear.f0.p linear.C0 linear.AIC linear.AICc
#> <char> <num> <num> <num> <num> <num> <num>
#> 1: ID6 0.0844683 0.03531910 0.13923269 0.3153645 -9.516839 Inf
#> 2: ID11 0.1139995 0.01920685 0.02723196 0.3525107 -14.609437 Inf
#> linear.RSE linear.r linear.diagnostics robust.linear.f0 robust.linear.f0.se
#> <num> <num> <char> <num> <num>
#> 1: 0.04919468 0.8607673 0.09719292 0.002805431
#> 2: 0.02602898 0.9727680 0.11399952 0.019206850
#> robust.linear.f0.p robust.linear.C0 robust.linear.weights
#> <num> <num> <char>
#> 1: 0.0006741157 0.3232908 1|1|0.033|1
#> 2: 0.0272319550 0.3525107 1|1|1|1
#> robust.linear.diagnostics HMR.f0 HMR.f0.se HMR.f0.p HMR.kappa HMR.phi
#> <char> <num> <num> <num> <num> <num>
#> 1: NA NA NA NA NA
#> 2: 0.2332107 0.01194175 0.03257022 1.628399 0.593832
#> HMR.AIC HMR.AICc HMR.RSE
#> <num> <num> <num>
#> 1: NA NA NA
#> 2: -33.15832 NA 0.002821234
#> HMR.diagnostics
#> <char>
#> 1: Missing value or an infinity produced when evaluating the model
#> 2:
```

The output of `gasfluxes`

contains the estimate of the
initial flux (`f0`

) for each method chosen
(`linear`

, `robust linear`

and `HMR`

in
this case) including statistical parameters of the fits:

- the standard error
`se`

`p-value`

- estimated concentration at time zero
`C0`

- Akaike Information Citerion
- Akaike Information Citerion corrected for finite sample size
`AICc`

(needs more than four points per flux) - the residual standard error
`RSE`

- for linear regression the
`R`

value is shown (not squared!) - Diagnostic information about the fit
- estimated parameters depending on the fit (note
`HMR.kappa`

will be used in the decision scheme`kappa.max`

)

For the improved HMR fitting function the starting value
`k_HMR`

= log(1.5) is used by default. This is appropriate
for hourly values. If you change the input i.e. by providing your
measurement time in seconds use `k_HMR = log(1.5/3600)`

.

It is possible to have more than one ID column in the input file. For
instance, it is often convenient to use a `plot_ID`

and a
`date`

column by specifying the column names, e.g.,
`gasfluxes(fluxMeas, .id = c("plot_ID", "date"), method = c("linear","robust linear", "HMR"))`

.

###Graphical output

By default and with `plot = TRUE`

the flux calcuation
function plots a figure for each chamber flux that is stored in the
subfolder `/pics`

in the working directory. The following
example on the left shows a flux where HMR could not be fitted and the
3rd concentration is regarded as outlier by the robust linear estimate.
The second examples shows a flux that is well fitted by HMR which
increases the flux estimate twofold compared to the linear fit (see
numbers in the output above; `HMR.f0/linear.f0`

).

`selectfluxes`

functionIt is not apriori obvious which of the flux estimates should be
selected for an individual chamber measurement. In case of small fluxes
and large relativ measurement uncertainty linear estimates are the most
appropriate choice. However, if non-linear effects (like decreasing
diffusion gradient, lateral gas flow and chamber leakage) impact the
increase in concentration within the chamber, the non-inear estimate of
the HMR model is a better choice. The `selectfluxes`

function
offers some well defined decision algorithms that avoid the need for
manual decisions (like suggested in the original HMR package). The most
extensively tested decision ruleset is `kappa.max`

, which
optimises the balance between bias and uncertainty by taking the minimal
detectable flux of the current system (`f.detect`

see its
suggested calculation below) and the size of the flux into account (see Hüppi et
al. (2018) for details). `t.meas`

is the time of the
final concentration time point of the individual chamber measurement. To
apply the `kappa.max`

selection to your calculated fluxes use
the `selectfluxes`

function the following way:

```
selectfluxes(flux.results, select = "kappa.max", f.detect = 0.031, t.meas = 1)
#> ID linear.f0 linear.f0.se linear.f0.p linear.C0 linear.AIC linear.AICc
#> <char> <num> <num> <num> <num> <num> <num>
#> 1: ID6 0.0844683 0.03531910 0.13923269 0.3153645 -9.516839 Inf
#> 2: ID11 0.1139995 0.01920685 0.02723196 0.3525107 -14.609437 Inf
#> linear.RSE linear.r linear.diagnostics robust.linear.f0 robust.linear.f0.se
#> <num> <num> <char> <num> <num>
#> 1: 0.04919468 0.8607673 0.09719292 0.002805431
#> 2: 0.02602898 0.9727680 0.11399952 0.019206850
#> robust.linear.f0.p robust.linear.C0 robust.linear.weights
#> <num> <num> <char>
#> 1: 0.0006741157 0.3232908 1|1|0.033|1
#> 2: 0.0272319550 0.3525107 1|1|1|1
#> robust.linear.diagnostics HMR.f0 HMR.f0.se HMR.f0.p HMR.kappa HMR.phi
#> <char> <num> <num> <num> <num> <num>
#> 1: NA NA NA NA NA
#> 2: 0.2332107 0.01194175 0.03257022 1.628399 0.593832
#> HMR.AIC HMR.AICc HMR.RSE
#> <num> <num> <num>
#> 1: NA NA NA
#> 2: -33.15832 NA 0.002821234
#> HMR.diagnostics kappa.max
#> <char> <num>
#> 1: Missing value or an infinity produced when evaluating the model 2.724784
#> 2: 3.677404
#> flux flux.se flux.p method
#> <num> <num> <num> <char>
#> 1: 0.09719292 0.002805431 0.0006741157 robust linear
#> 2: 0.23321066 0.011941753 0.0325702174 HMR
flux.results[,c(1,26:30)]
#> ID kappa.max flux flux.se flux.p method
#> <char> <num> <num> <num> <num> <char>
#> 1: ID6 2.724784 0.09719292 0.002805431 0.0006741157 robust linear
#> 2: ID11 3.677404 0.23321066 0.011941753 0.0325702174 HMR
```

This appends the columns shown above with the selected and
recommanded `flux`

estimate and its `method`

used.

`f.detect`

The minimal detectable flux relevant for `kappa.max`

selection algorithm depends on the measurement precision of the GC
(`GC.sd`

), the chamber size (area `A`

and volume
`V`

) and the timing of the sampling scheme (`t`

i.e. at 0, 20, 40 and 60 minutes).

```
### estimate f.detect by simulation
C0 <- 325 #ambient concentration, here in [ppm]
GC.sd <- 5 #uncertainty of GC measurement, here in [ppm]
#create simulated concentrations corresponding to flux measurements with zero fluxes:
set.seed(42)
sim <- data.frame(t = seq(0, 1, length.out = 4), C = rnorm(4e3, mean = C0, sd = GC.sd),
id = rep(1:1e3, each = 4), A = 1, V = 0.535125) # specify your sampling scheme t (here in [h]) and chamber volume (V) and area (A)
#fit HMR model:
simflux <- gasfluxes(sim, .id = "id", .times = "t", methods = c("HMR", "linear"), plot = FALSE, verbose = F)
simflux[, f0 := HMR.f0]
simflux[is.na(f0), f0 := linear.f0] # use linear estimates where HMR could not be fitted
#dection limit as 97.5 % quantile (95 % confidence):
f.detect <- simflux[, quantile(f0, 0.975)]
f.detect # here in [ppm/h/m^2], use same unit as your flux estimates,
#> 97.5%
#> 28.16894
#e.g., convert to mass flux assuming chamber temperature of 15 degree celcius and standard air pressure
f.detect / 1000 * 28 * 273.15 / 22.4 / (273.15 + 15)
#> 97.5%
#> 0.03337822
```

Simulations are useful for understanding the behaviour of flux
calculation algorithms. The performance of a flux calculation scheme
depends on the precision of the GC (`GC.sd`

), height of the
chamber (`V/A`

), the sampling time scheme (especially the
chamber closure time, refered as `t.meas`

), the tightness of
the chambers, the reliability of the sampling vial handling etc. This is
why it makes sense to look at each specific measurement system and how
well it copes with non linear flux estimates (i.e. HMR).

With a simulation we can estimate the impact of the calculation scheme on the flux itself and hence its bias:

and the uncertainty associated with it:

Once having created a simulated flux dataset one can check, where the
fluxes are placed in the parameter space of the estimated
`kappa`

vs. flux `f0`

.

The code for the example simulation is available as a Gist and further details are described in Hüppi et al. (2018).