---
title: "Basic water balance simulation"
author: "Miquel De Caceres"
date: "`r Sys.Date()`"
output: 
  rmarkdown::html_vignette:
    toc: TRUE
vignette: >
  %\VignetteIndexEntry{Basic water balance simulation}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignettePackage{medfate}
  \usepackage[utf8]{inputenc}
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
library(medfate)
```

## About this vignette

The present document describes how to run the soil plant water balance model described in De Cáceres et al. (2015) using package `medfate`. The  document indicates how to prepare the inputs, use the simulation functions and inspect the outputs. All the details of the model design and formulation can be found at https://vegmod.ctfc.cat/software/medfate. Because it introduces many basic features of package `medfate`, this document should be read before addressing advanced topics of water balance simulations or growth simulations.

## Preparing model inputs
Any forest water balance model needs information on **climate**, **vegetation** and **soils** of the forest stand to be simulated. Moreover, since the soil water balance in `medfate` differentiates between species,  **species-specific parameters** are also needed. In this subsection we explain the different steps (including optional pathways) to prepare all the data needed to run function `spwb()`.

### Soils

#### Required soil data
Simulation models in `medfate` require information on the physical attributes of soil, namely soil depth, texture, bulk density and rock fragment content. Soil information needs to be entered as a `data frame` with soil layers in rows and physical attributes in columns. The model accepts one to five soil layers with arbitrary widths. Soil physical attributes can be initialized to default values, for a given number of layers, using function `defaultSoilParams()`:

```{r}
spar = defaultSoilParams(2)
print(spar)
```
where `widths` are soil layer widths in mm; `clay` and `sand` are the percentage of clay and sand, in percent of dry weight, `om` stands for organic matter, `bd` is bulk density (in g·cm$^{-3}$) and `rfc` the percentage of rock fragments. Because soil properties vary strongly at fine spatial scales, ideally soil physical attributes should be measured on samples taken at the forest stand to be simulated. For those users lacking such data, soil properties modelled at larger scales are available via soilgrids.org (see function `soilgridsParams()`).

#### Soil input object

The soil input for function `spwb()` is actually a list of class `soil` that is created using a function with the same name:
```{r}
examplesoil = soil(spar)
class(examplesoil)
```

The list contains the following elements:
```{r}
names(examplesoil)
```
In addition to the physical soil description, this object contains soil parameters needed for soil water balance simulations. For example, `macro` specifies the macroporosity of each layer; `Gsoil` and `Ksoil` are parameters needed to model the process of water infiltration into the soil. The meaning of all elements in the soil object can be found in the help page for function `soil()`.

Importantly, the soil object is used to store the degree of moisture of each soil layer. In particular, element `W` contains the state variable that represents moisture content - the proportion of moisture **relative to field capacity** - which is normally initialized to 1 for each layer:
```{r}
examplesoil$W
```
It is important to remember that, unlike normal objects in R, any water balance simulation will modify the moisture values in the input soil object. That is, the state of the soil at the end of the simulated process (i.e. `W`) will be stored. Hence, one can use the same object to simulate water balance sequentially and the final state of one simulation is the initial state of the next.

#### Water retention curves

At any time, one can show the characteristics and status of the soil object using its `print` function:
```{r}
print(examplesoil, model = "SX")
```
The modelled moisture content of the soil depends on the **water retention curve** used to represent the relationship between soil volumetric water content ($\theta$; %) and soil water potential ($\Psi$; MPa). By default the Saxton (`model = "SX"`) equations are used to model the water retention curve, but the user may choose to follow Van Genuchten - Mualem equations, which will give slightly different values for the same texture:
```{r}
print(examplesoil, model="VG")
```
While Saxton equations use texture and organic matter as inputs, the Van Genuchten-Mualem equations need other parameters, which are estimated using pedotransfer functions and their names start with `VG_` (two alternative options are provided in function `soil` to estimate Van Genuchten parameters). The following code calls function `soil_retentionCurvePlot()` to illustrate the difference between the two water retention models in this soil:

```{r, fig = TRUE, fig.width= 5, fig.height=3, fig.align= 'center', echo=TRUE}
soil_retentionCurvePlot(examplesoil, model="both")
```

Low-level functions, such as `soil_psi2thetaSX()` and `soil_psi2thetaVG()` (and their counterparts `soil_theta2psiSX()` and `soil_theta2psiVG()`), can be used to calculate volumetric soil moisture from the water potential (and viceversa) using the two models. When simulating soil water balance, the user can choose among the two models (see `control` parameters below).

### Species-specific parameters

Simulation models in `medfate` require a data frame with species parameter values. The package provides a default data set of parameter values for 89 Mediterranean species (rows), resulting from bibliographic search, fit to empirical data or expert-based guesses:

```{r}
data("SpParamsMED")
```

These species commonly occur in the Spanish forest inventory of Catalonia, but may not be sufficient for other areas. A large number of parameters (columns) can be found in `SpParamsMED`:

```{r}
names(SpParamsMED)
```

Not all parameters are needed for all models. The user can find parameter definitions in the help page of this data set. However, to fully understand the role of parameters in the model, the user should read the details of model design and formulation (http://vegmod.ctfc.cat/software/medfate). 

### Vegetation

#### Forest plot data

Models included in `medfate` were primarily designed to be ran on **forest inventory plots**. In this kind of data, the  vegetation of a sampled area is described in terms of woody plants (trees and shrubs) along with their size and species identity. Forest plots in `medfate` are assumed to be in a format that follows closely the Spanish forest inventory. Each forest plot is represented in an object of class `forest`, a list that contains several elements. Among them, the most important items are two data frames, `treeData` (for trees) and `shrubData` for shrubs:
```{r}
data(exampleforestMED)
exampleforestMED
```
Trees are expected to be primarily described in terms of species, diameter (DBH) and height, whereas shrubs are described in terms of species, percent cover and mean height. 

#### Aboveground and belowground data
Because the forest plot format is rather specific, simulation functions in `medfate` allow starting in a more general way using two data frames, one with **aboveground** information (i.e. the leave area and size of plants) and the other with **belowground** information (i.e. root distribution). The aboveground data frame does not distinguish between trees and shrubs. It includes, for each plant cohort to be considered in rows, its *species identity*, *height* and *leaf area index* (LAI). While users can build their input data themselves, we use function `forest2aboveground()` on the object `exampleforestMED` to show how should the data look like:
```{r}
above = forest2aboveground(exampleforestMED, SpParamsMED)
above
```
Note that the call to `forest2aboveground()` included species parameters, because species-specific values are needed to calculate leaf area from tree diameters or shrub cover. Columns `N`, `DBH` and `Cover` are required for simulating growth, but not for soil water balance, which only requires columns `SP`, `H` (in cm), `CR` (i.e. the crown ratio), `LAI_live`, `LAI_expanded` and `LAI_dead`. Here plant cohorts are given unique codes that tell us whether they correspond to trees or shrubs, but the user can use other row identifiers as long as they are unique. In practice, the user only needs to worry to calculate the values for `LAI_live`. `LAI_live` and `LAI_expanded` can contain the same LAI values, and `LAI_dead` is normally zero. This is so because models update `LAI_expanded` and `LAI_dead` according to the leaf phenology of species.

Aboveground leaf area distribution (with or without distinguishing among cohorts) can be examined by calling function `vprofile_leafAreaDensity()`:

```{r, fig = TRUE, fig.width= 4, fig.height=3, fig.align= 'center', echo=TRUE}
vprofile_leafAreaDensity(above, byCohorts = F)
```
```{r, fig = TRUE, fig.width= 5, fig.height=3, fig.align= 'center', echo=TRUE}
vprofile_leafAreaDensity(above, byCohorts = T)
```

Regarding **belowground** information, a matrix describing for each plant cohort, the proportion of fine roots in each soil layer. As before, we use function `forest2belowground()` on the object `exampleforestMED` to show how should the data look like:
```{r}
below = forest2belowground(exampleforestMED, examplesoil, SpParamsMED)
below
```
Function `forest2belowground()` internally takes values of `Z50` and `Z95` and calls  function `root_ldrDistribution()` to estimate the distribution of fine roots according to the linear dose response model. For example the first row is:
```{r}
root_ldrDistribution(exampleforestMED$treeData$Z50[1], 
                     exampleforestMED$treeData$Z95[1],
                     examplesoil$dVec)
```
An analogous function `root_conicDistribution()` can be used to estimate fine root distribution according to a cone. The user is free to build any numeric matrix for root distribution, as long as values in rows sum always one (i.e. we have proportions). Otherwise, functions `root_conicDistribution()` and `root_ldrDistribution()` can be used to calculate root distribution under specific assumptions.

Users can visually inspect the distribution of fine roots of `forest` objects by calling function `vprofile_rootDistribution()`:

```{r, fig = TRUE, fig.width= 5, fig.height=3, fig.align= 'center', echo=TRUE}
vprofile_rootDistribution(exampleforestMED, SpParamsMED)
```


### Meteorological forcing

Soil water simulations require daily weather inputs. The weather variables that are required depend on the complexity of the soil water balance model we are using. In the simplest case, only mean temperature, precipitation and potential evapotranspiration is required, but the more complex simulation model also requires radiation, wind speed, min/max temparature and relative humitidy. Here we show an example of meteorological forcing data. 
```{r}
data(examplemeteo)
head(examplemeteo)
```
Simulation models in `medfate` have been designed to work along with data generated from package `meteoland`. The user is strongly recommended to resort to this package to obtain suitable weather input for soil water balance simulations.

### Simulation control

Apart from data inputs, the behaviour of simulation models can be controlled using a set of global parameters. The default parameterization is obtained using function `defaultControl()`:

```{r}
control = defaultControl()
control
```
Most of these parameters should normally be left to their default value. However, there are three that deserve explanation here: 

 1. Console output can be turned off by setting `verbose = FALSE`. 
 2. The soil water retention curves can be switched between Saxton's and Van Genuchten's using parameter `soilFunctions`. 
 3. The complexity of the soil water balance calculations will be very different if we set `transpirationMode = "Sperry"`. Most of the other options apply in the case of advanced soil water balance only. 
 
### Water balance input object

A last step is needed before calling simulation functions. It consists in the compilation of all aboveground and belowground parameters and the specification of additional parameter values for each plant cohort, such as their light extinction coefficient or their response to drought. This is done by calling function `spwbInput()` and taking species parameter values from species parameter data:
```{r}
x = spwbInput(above, below, examplesoil, SpParamsMED, control)
```
Different parameter variables will be drawn depending on the value of `transpirationMode`. For the simple water balance model (`transpirationMode = "Granier"`), relatively few parameters are needed. All the input information for forest data and species parameter values can be inspected by accessing the different elements of this object, whose names are.
```{r}
names(x)
```
As with the soil input object, the `spwbInput` object **will be modified** during simulations. In the case of soil water balance, these modifications are small, for example concerning `LAI_expanded`, but in the case of growth simulations the object is used to store the status of vegetation during and at the end of simulations. If one has a `forest` object, the `spwbInput` object can be generated in directly from it, avoiding the need to explicitly build aboveground and belowground data frames:

```{r}
x = forest2spwbInput(exampleforestMED, examplesoil, SpParamsMED, control)
```


Finally, note that one can play with plant-specific parameters for soil water balance (instead of using species-level values) by modifying manually the parameter values in this object.



## Executing the soil water balance model

### Water balance for a single day

Soil water balance simulations will normally span periods of several months or years, but since the model operates at a daily temporal scale, it is possible to perform soil water balance for one day only. This is done using function `spwb_day()`. In the following code we select day 100 from the meteorological input data and perform soil water balance for that day only:
```{r}
d = 100
sd1<-spwb_day(x, examplesoil, rownames(examplemeteo)[d],  
             examplemeteo$MinTemperature[d], examplemeteo$MaxTemperature[d], 
             examplemeteo$MinRelativeHumidity[d], examplemeteo$MaxRelativeHumidity[d], 
             examplemeteo$Radiation[d], examplemeteo$WindSpeed[d], 
             latitude = 41.82592, elevation = 100, 
             slope= 0, aspect = 0, prec = examplemeteo$Precipitation[d])
```
Function `spwb_day()` is most useful when working with the complex transpiration model. This is why so many meteorological variables are required. The output of `spwb_day()` is a list with five elements:
```{r}
names(sd1)
```

* **cohorts**: Table with the species code and species name of each cohort.
* **WaterBalance**: Contains the soil water balance flows (precipitation, infiltration, transpiration, ...)
* **Soil**: Contains output values by soil layer (i.e. water evaporated from each soil layer, water transpired from each soil layer and the final soil water potential).
* **Stand**: A list with stand LAI (expanded and dead leaves), canopy water retention capacity and the proportion of light (SWR or PAR) reaching the ground.
* **Plants**: Contains output values by plant cohort (i.e. LAI values, transpiration, water potential, drought stress index, ...).

```{r}
sd1
```

### Water balance for multiple days

Most often, users will use function `spwb()` to run the soil water balance model. This function requires the `spwbInput` object, the `soil` object and the meteorological data frame. However, function `spwb_day()` modified the state variables of the input objects. In particular, the values of soil moisture are now:
```{r}
examplesoil$W
```
We simply reset state variables to their default values so that new simulations are not affected by the end state of the previous simulation:
```{r}
resetInputs(x, examplesoil)
examplesoil$W
```
Now we are ready to call function `spwb()`:
```{r}
S = spwb(x, examplesoil, examplemeteo, latitude = 41.82592, elevation = 100)
```
Function `spwb()` returns an object of class with the same name, actually a list:
```{r}
class(S)
```
If we inspect its elements, we realize that the output is arranged differently than in `spwb_day()`:
```{r}
names(S)
```
In particular, element `spwbInput` contains a copy of the input parameters that were used to run the model:
```{r}
names(S$spwbInput)
```
As before, `WaterBalance` contains water balance components, but in this case in form of a data frame with days in rows:
```{r}
head(S$WaterBalance)
```
Element `Plants` is in turn a list with several dataframes with plant output variables, for example plant water potentials are in:
```{r}
head(S$Plants$PlantPsi)
```


## Inspecting model outputs
### Plots

Package `medfate` provides a simple `plot` function for objects of class `spwb`. It can be used to show meteorological inputs, snow dynamics, and different components of the water balance:
```{r, fig=TRUE, fig.align="center", fig.width=5, fig.height = 3.5}
plot(S, type = "PET_Precipitation")
plot(S, type = "Snow")
plot(S, type = "Export")
```

```{r, fig=TRUE, fig.align="center", fig.width=7, fig.height = 3.5}
plot(S, type = "Evapotranspiration")
```

Function `plot` is also allows displaying soil moisture dynamics by layer, which can be done in four different ways (the first two only imply a change in axis units):
```{r, fig=TRUE, fig.align="center", fig.width=7, fig.height = 4}
plot(S, type="SoilTheta")
plot(S, type="SoilRWC")
plot(S, type="SoilPsi")
plot(S, type="SoilVol")
```

Finally, the same function can also be used to draw the dynamics of plant variables by cohorts, such as transpiration, photosynthesis, water potential or drought stress:

```{r, fig=TRUE, fig.align="center", fig.width=7, fig.height = 4}
plot(S, type="PlantTranspiration")
plot(S, type="PlantPhotosynthesis")
plot(S, type="PlantPsi")
plot(S, type="PlantStress")
```

### General summaries
While the simulation model uses daily steps, users will normally be interested in outputs at larger time scales. The package provides a `summary` for objects of class `spwb`. This function can be used to summarize the model's output at different temporal steps (i.e. weekly, annual, ...). For example, to obtain the average soil moisture and water potentials by months one can use:

```{r}
summary(S, freq="months",FUN=mean, output="Soil")
```

Parameter `output` is used to indicate the element of the `spwb` object for which we desire summaries. Similarly, it is possible to calculate the average stress of plant cohorts by months:
```{r}
summary(S, freq="months",FUN=mean, output="PlantStress")
```
The `summary` function can be also used to aggregate the output by species. In this case, the values of plant cohorts belonging to the same species will be averaged using LAI values as weights. For example, we may average the daily drought stress across cohorts of the same species (here there is only one cohort by species, so this does not modify the output):
```{r}
head(summary(S, freq="day", output="PlantStress", bySpecies = TRUE))
```
Or we can combine the aggregation by species with a temporal aggregation (here monthly averages):
```{r}
summary(S, freq="month", FUN = mean, output="PlantStress", bySpecies = TRUE)
```

### Specific output functions
The package provides some functions to extract or transform specific outputs from soil plant water balance simulations. In particular, function `spwb_stress()` allows calculating several plant stress indices, such as the number of days with drought stress > 0.5 or the maximum drought stress:

```{r}
spwb_stress(S, index = "NDD", freq = "years", draw=FALSE)
spwb_stress(S, index = "MDS", freq = "years", draw=FALSE)
```
As the general summary function, `spwb_stress()` allows calculating stress indices at several temporal scales. For example the water stress index (integral of water potential values) can be calculated and drawn for every month:
```{r, fig=TRUE, fig.align="center", fig.width=7, fig.height = 4}
spwb_stress(S, index = "WSI", freq = "months", draw=TRUE)
```

Another specific summary function is `spwb_waterUseEfficiency()`. This is most useful with advanced water and energy balance modeling, but for simple water balance it calculates the ratio between photosynthesis and transpiration at the desired scale:

```{r}
spwb_waterUseEfficiency(S, type = "Stand An/E", freq = "months", draw=FALSE)
```