Intra annual density fluctuations (iadfs), also referred as false rings are defined as either latewood-like cells in earlywood or earlywood-like cells in latewood [@Fritts1976]. Although recent efforts are made to specify the position, extend as well as intensity of iadfs most studies use binary assignments to indicate presence or absence of iadfs [@Battipaglia2016]. While frequencies can easily be calculated as the proportion of rings showing an iadf in a specific year several studies suggest the consideration of variing variances, age trends as well as influence of ring size. This package implements all published approaches known by the package author, their usage is shortly explained in this vignette.

The data used in this vignette is included in the package. You can load the
data-sets called `example_rwl`

and `example_iadf`

by typing:

library("iadf") data("example_rwl") data("example_iadf")

`example_rwl`

is a data frame, similar to the class `rwl`

defined by the package
`dplR`

with series as columns and years as rows, rownames specifying the year.
The data shows the ring width with years not covered by the sample marked with
`NA`

.

knitr::kable(example_rwl[20:30, 10:16])

`example_iadf`

has the same dimensions as `example_rwl`

, just showing binary
assignements of iadfs instead of ring width.

knitr::kable(example_iadf[20:30, 10:16])

The proportion of rings showing an iadf can easily be calculated using base R:

rowMeans(example_iadf, na.rm = TRUE)

However, there's also a function in the package `iadf`

to calculate the false
ring proportion with data frame output consistent to the other package functions
and improved warning messages.

```
results_frp <- frp(example_iadf)
```

Please mention that this function is somehow slower
than using `rowMeans()`

, so consider using the base R code whenever computation
speed is critical.

As the variance of time series is dependend on sample size the variance can be
adjusted according to Osborn [[email protected]], using the function `afrp()`

:

```
results_afrp <- afrp(example_iadf)
```

As other tree ring parameters, also IADF occurence shows an age trend. Novak [[email protected]] suggested a detrending procedure to reduce this bias.

First the iadf frequency per cambial age needs to be calculated:

```
frq <- novak_freq(example_iadf)
```

Then we try to model the influence of age on iadf frequency using a Weibull function as suggested by Novak [[email protected]], limiting the data pairs used to cambial ages representing at least 15 years:

mdl <- novak_weibull(frq, 15)

If you encounter an error its likely due to insufficient starting values
for the curve fitting function (which can be found using
`novak_weibull_find_start()`

and will be discussed for
`campelo_chapman_find_start()`

in the next section).

Next we hand the model and the original data to the function `novak_index()`

to
calculate the iadf proportion with age trend removed:

```
results_novak <- novak_index(example_iadf, mdl)
```

Campelo [[email protected]] states that beneath ring age also ring width influences iadf formation and introduced another standardization approach.

The workflow implemented in `iadf`

is almost the same as for the approach above.
Fist we calculate frequencies per ring width class using both data sets:

```
frq <- campelo_freq(example_iadf, example_rwl)
```

Then we fit a chapman function to our frequencies:

```
mdl <- campelo_chapman(frq)
```

In case the function throws an error it's likely due to insufficient starting
values. These can be found interactively with `campelo_chapman_find_start()`

and
then used in `campelo_chapman()`

:

st <- campelo_chapman_find_start(frq) mdl <- campelo_chapman(frq, start = st)

Next the index is calculated using both data sets and the model:

```
results_campelo <- campelo_index(example_iadf, example_rwl, mdl)
```

plot(NULL, xlim = range(as.numeric(rownames(example_iadf))), ylim = c(-0.5, 2.5), xlab = '', ylab = '') lines(results_frp, col = 'blue') lines(results_afrp, col = 'green') lines(results_novak, col = 'purple') lines(results_campelo[ , c(1,3)], col = 'red') legend('topright', col = c('blue', 'green', 'purple', 'red'), legend = c('frp', 'afrp', 'Novak', 'Campelo'), bty = 'n', lty = 1)

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