This vignette demonstrates the use of different model control option
setting (`options_90`

-argument of `runLWFB90()`

)
and parameters (`param_b90`

-argument).

Aside from the basic technical information of the simulation
(`startdate`

, `enddate`

, `fornetrad`

,
`prec_interval`

and `correct_prec`

), the model
control options control the annual course of leaf area index
(`lai_method`

), the phenology models to use
(`budburst_method`

, `leaffall_method`

), the input
and interpolations of annual stand properties
(`standprop_input`

, `standprop_interp`

,
`use_growthperiod`

) and which root density depth distribution
function to use (`root_method`

). The interplay of options and
parameters is shown briefly in the following paragraphs, by describing
how options and parameters are passed from the `options_b90`

and `param_b90`

arguments to the individual functions that
are called from within `run_LWFB90()`

.

For this purpose, we create basic lists of model control options and parameters, as well as soil and climate objects.

```
library(LWFBrook90R)
library(data.table)
<- set_optionsLWFB90()
options_b90 <- set_paramLWFB90() param_b90
```

The default parameter set (created with
`set_paramLWFB90()`

) represents a deciduous forest stand,
without leafs in winter and maximum leaf area index in summer. The
maximum leaf area index is defined by the parameter
`param_b90$maxlai`

, the minimum value in winter is internally
calculated as a fraction (`param_b90$winlaifrac`

) of
`param_b90$maxlai`

. The basic shape of the intra-annual leaf
area index dynamics can be selected by the option
`options_b90$lai_method`

. The default setting
`'b90'`

makes use of the parameters `budburstdoy`

,
`leaffalldoy`

, `emergedur`

and
`leaffalldur`

, that define the dates of budburst and
leaffall, and the durations of leaf unfolding and leaf shedding until
`maxlai`

, and respectively `winlaifrac`

in winter
are reached. Within `run_LWFB90()`

, the parameters are passed
to `make_seasLAI()`

that constructs the daily timeseries of
leaf area index development for a single year:

```
<- make_seasLAI(method = options_b90$lai_method,
LAI_b90 year = 2003,
maxlai = param_b90$maxlai,
winlaifrac = param_b90$winlaifrac,
budburst_doy = param_b90$budburstdoy,
leaffall_doy = param_b90$leaffalldoy,
emerge_dur = param_b90$emergedur,
leaffall_dur = param_b90$leaffalldur)
```

`make_seasLAI()`

also provides other shape functions that
require additional parameters. For example, the option
`lai_method = 'linear'`

uses value pairs of day-of-year and
leaf area index as fraction of `maxlai`

passed from
parameters `param_b90$lai_doy`

and
`param_b90$lai_frac`

. The doy/value-pairs are then used to
interpolate the intra-annual course of leaf area index to a daily time
series.

```
$lai_method <- "linear"
options_b90$lai_doy <- c(1,110,117,135,175,220,250,290,365)
param_b90$lai_frac <- c(0.1,0.1,0.5,0.7,1.2,1.2,1.0,0.1,0.1)
param_b90<- make_seasLAI(method = options_b90$lai_method,
LAI_linear year = 2003,
maxlai = param_b90$maxlai,
lai_doy = param_b90$lai_doy ,
lai_frac = param_b90$lai_frac)
```

A third shape-option for the intra-annual variation of leaf area
index is called ‘Coupmodel’ and uses the interpolation method as
implemented in the ‘Coupmodel’ (Jansson and
Karlberg 2004). With `lai_method ='Coupmodel`

, form
parameters for leaf unfolding and leaf fall (`shp_budburst`

,
`shp_leaffall`

), and the date when leaf area is at its
maximum (`shp_optdoy`

) are required, in addition to the
parameters required `by lai_method = 'b90'`

.

```
$lai_method <- "Coupmodel"
options_b90$shp_budburst <- 0.5
param_b90$shp_leaffall <- 5
param_b90$shp_optdoy <- 180
param_b90<- make_seasLAI(method = options_b90$lai_method,
LAI_coupmodel year = 2003,
maxlai = param_b90$maxlai,
budburst_doy = param_b90$budburstdoy,
leaffall_doy = param_b90$leaffalldoy,
shp_budburst = param_b90$shp_budburst,
shp_leaffall = param_b90$shp_leaffall,
shp_optdoy = param_b90$shp_optdoy)
```

A plot of all three methods shows the roles of the different parameters:

By passing a single value via `param_b90$maxlai`

we used
the same maximum leaf area index for each year of the simulation period.
In order to incorporate between-year variation of the leaf area index,
we can simply assign vectors of values for each year of the simulation
period to any of the parameters used by function
`make_seasLAI()`

. In the following example, we pass three
values for `maxlai`

and `shp_optdoy`

, to get
different seasonal courses of leaf area index for the three years of the
simulation period. Additionally, we add variation to the dates of
budburst, by assigning a vector of values to the parameter
`budburstdoy`

.

```
<- 2001:2003
years $maxlai <- c(4,6,5)
param_b90$shp_optdoy <- c(210,180,240)
param_b90$shp_budburst <- c(3,1,0.3)
param_b90$budburstdoy <- c(100,135,121)
param_b90<- make_seasLAI(method = options_b90$lai_method,
lai_variation year = years,
maxlai = param_b90$maxlai,
budburst_doy = param_b90$budburstdoy,
leaffall_doy = param_b90$leaffalldoy,
shp_budburst = param_b90$shp_budburst,
shp_leaffall = param_b90$shp_leaffall,
shp_optdoy = param_b90$shp_optdoy)
```

Beside the obvious between-year variation of maximum leaf area index,
we can also see the effect of the shape parameter for the leaf unfolding
phase `shp_budburst`

. Values greater 1 result in concave,
values below 1 in convex functions, while values of 1 give linear
progressions. The budburst day-of-year is varying as specified in the
parameters, but can also be estimated using temperature based phenology
models. By selecting other settings than the default
`options_b90$budburst_method = 'fixed'`

and
`options_b90$leaffall_method = 'fixed'`

, the
`vegperiod()`

function of the ‘vegperiod’-Package is called
from within `run_LWFB90`

. `budburstdoy`

and/or
`leaffalldoy`

are then calculated for each year from the
climate data using the desired methods. See `vegperiod`

for a
list of available models. The estimated values for
`budburstdoy`

and/or `leaffalldoy`

can be found in
the `param_b90`

list element of the results object after the
simulation.

`height`

, `sai`

,
`densef`

)Like the leaf area index parameters and budburst/leaffall-dates, it
is also possible to provide vectors of values for stand height
(`height`

), stem area index (`sai`

), and stand
density (`densef`

) to generate between-year variation of
stand characteristics. From the yearly values, daily values are
interpolated using the function `approx_standprop()`

. The
`approx.method`

- argument of the function defines how to
interpolate the yearly values passed by `y`

. Within
`run_LWFB90()`

, the option
`options_b90$standprop_interp`

is passed to the
`approx.method`

- argument of `approx_standprop`

.
The default interpolation method
`standprop_interp = 'constant'`

results in a yearly changing
step function, while `standprop_interp = 'linear'`

interpolates the values:

```
# constant 'interpolation'
$standprop_interp <- 'constant'
options_b90$height <- c(20.2,20.8,21.3)
param_b90<- 2002:2003
simyears <- approx_standprop(x_yrs=years,
height_c y = param_b90$height,
approx.method = options_b90$standprop_interp)
# linear interpolation
$standprop_interp <- 'linear'
options_b90$height_ini <- 19.1
param_b90<- approx_standprop(x_yrs=years,
height_l y = param_b90$height,
y_ini = param_b90$height_ini,
approx.method = options_b90$standprop_interp)
```

For linear interpolation, additional parameters
`height_ini`

, `sai_ini`

, `densef_ini`

have to be provided to `run_LWFB90()`

via the
`param_b90`

-argument. These parameters define the values at
the beginning of the simulation, to which the value of the first year is
interpolated to. By default, the yearly values are interpreted to be
valid at December 31st of the respective years, so that the interpolated
timeseries are linearly increasing or decreasing during the whole year.
In order to constrain the interpolation to the growth period only, the
option `options_b90$use_growthperiod`

was introduced, which
requires the arguments `startdoy`

and `enddoy`

,
when set to `TRUE`

. Then, values decrease or increase between
budburst and leaffall only, and remain constant during winter.

```
$use_growthperiod <- TRUE
options_b90<- approx_standprop(x_yrs = years,
height_l_gp y = param_b90$height,
y_ini = param_b90$height_ini,
use_growthperiod = options_b90$use_growthperiod,
startdoy = param_b90$budburstdoy,
enddoy = param_b90$leaffalldoy,
approx.method = options_b90$standprop_interp)
```

The following plot explains the differences between the interpolated timeseries of stand height using the different options and parameters:

Another option for incorporating between-year variation of plant
properties is to provide a data.frame with yearly values of
`height`

, `maxlai`

, `sai`

,
`densef`

and `age`

as list item
`standprop_table`

in `param_b90`

. To take effect,
the option `options_b90$standprop_input`

has to be set to
`'table'`

. In this case, the values passed via parameters
`height`

, `sai`

, `densef`

and
`age_ini`

are ignored. As `maxlai`

is also
provided via the table, the `maxlai`

value from parameters is
ignored as well, while the other parameters that affect intra-annual
leaf area development (e.g., `shp_budburst`

) are still
active.

For demonstration purposes we use the table
`slb1_standprop`

, that contains observed stand data of the
Solling Beech Experimental site from 1966 to 2014, along with estimated
leaf and stem area index derived using allometric functions. For
creating the daily timeseries of stand properties, we use
`run_LWFB90()`

, and make use of the option to not run the
model (`run = FALSE`

), but only return the model input.

```
#Extend simulation period
$startdate <- as.Date("1980-01-01")
options_b90$enddate <- as.Date("1999-12-31")
options_b90
<- cbind(slb1_soil, hydpar_wessolek_tab(texture = slb1_soil$texture))
soil
#set up options for table input
$standprop_input <- 'table'
options_b90$standprop_table <- slb1_standprop
param_b90
# Set up dynamic budburst and leaf fall
$budburst_method <- "Menzel"
options_b90$leaffall_method <- "vonWilpert"
options_b90$budburst_species <- "Fagus sylvatica"
param_b90
#run LWF-Brook90 without simulation
<- run_LWFB90(options_b90 = options_b90,
standprop_daily param_b90 = param_b90,
climate = slb1_meteo,
soil = soil,
output = output,
run = FALSE)$standprop_daily
```

The root depth density depth distribution can either be provided in
the column `rootden`

of the `soil`

- argument of
`run_LWFB90()`

, or can be derived from parameters using the
function `make_rootden()`

. In order to use root density as
specified in the soil data, the `root_method`

element of the
`options_b90`

-list has to be set to `'soilvar'`

.
Other method names are passed to `make_rootden()`

. Currently,
the function provides four methods to assign values of relative root
density to a vector of soil depths. The default method
`'betamodel'`

uses the model of Gale & Grigal (-Gale and Grigal (1987)), which is of the form
\(y = 1- \beta^d\), where \(y\) is the cumulative root fraction down to
soil depth \(d\) and \(\beta\) is the depth coefficient. Larger
values of \(\beta\) correspond to a
greater proportion of roots in deeper soil layers:

For larger values of \(\beta\), the
root density will reach zero only in very deep soil layers. In order to
set the root density to zero at any desired soil depth, the parameter
`maxrootdepth`

was defined. With this parameter, the root
density is set to zero in all soil layers that lie deeper than
`maxrootdepth`

. Within `run_LWFB90()`

, the
function is called in the following way:

```
$maxrootdepth <- -1.4
param_b90$root_method <- "betamodel"
options_b90<- make_rootden(soilnodes = c(max(slb1_soil$upper), slb1_soil$lower),
roots_beta maxrootdepth = param_b90$maxrootdepth,
beta = param_b90$betaroot,
method = options_b90$root_method)
```

A second option to define the root distribution for the soil layers
is to provide value pairs of soil depth and root density in a data.frame
and assign it to the `rootden_table`

-entry in
`param_b90`

. As an example, we set up a hypothetical root
density depth distribution:

```
$root_method <- 'table'
options_b90$rootden_table <- data.frame(
param_b90upper = c(0.03,0,-0.02, -0.15, -0.35, -0.5, -0.65,-0.9,-1.1,-1.3),
lower = c(0,-0.02, -0.15, -0.35, -0.5, -0.65,-0.9,-1.1,-1.3,-1.6),
rootden = c(10,15, 35, 15, 7.5, 4, 12, 2, 2, 0))
<- make_rootden(soilnodes = c(max(slb1_soil$upper), slb1_soil$lower),
roots_table method = options_b90$root_method,
rootdat = param_b90$rootden_table)
```

A third option generates a linear root density depth distribution,
with the maximum at the uppermost soil layer and a root density of 0 at
`maxrootdepth`

. If the parameter `relrootden`

is
provided, the first element of the vector is used as the maximum,
otherwise the interpolation is made between 0 and 1. The last option
returns a uniform root distribution, with the first vector-element of
`relrootden`

(if provided) as value for all layers down to
`maxrootdepth`

.

```
$root_method <- 'linear'
options_b90<- make_rootden(soilnodes = c(max(slb1_soil$upper), slb1_soil$lower),
roots_linear maxrootdepth = param_b90$maxrootdepth,
method = options_b90$root_method)
$root_method <- 'const'
options_b90<- make_rootden(soilnodes = c(max(slb1_soil$upper), slb1_soil$lower),
roots_constant maxrootdepth = param_b90$maxrootdepth,
method = options_b90$root_method)
```

Gale, M. R., and D. F. Grigal. 1987. “Vertical Root Distributions
of Northern Tree Species in Relation to Successional Status.”
*Canadian Journal of Forest Research* 17 (8): 829–34.

Jansson, P.-E., and L. Karlberg. 2004. “Coupled Heat and Mass
Transfer Model for Soil-Plant-Atmosphere Systems.” Stockholm:
Royal Institute of Technolgy, Dept of Civil; Environmental Engineering
Stockholm.