Introduction

About this vignette

This document describes how to run the water balance model on a forest plot at Font-Blanche (France), using the R function spwb() included in package medfate. The document indicates how to prepare the model inputs, use the model simulation function, evaluate the predictions against available observations and inspect the outputs.

About the Font-Blanche research forest

The Font-Blanche research forest, located in southeastern France (43º14′27″ N 5°40′45″ E, 420 m elevation), is composed of a top strata of Pinus halepensis (Aleppo pine) reaching about 12 m, a lower strata of Quercus ilex (holm oak), reaching about 6 m, and an understorey strata dominated by Quercus coccifera but including other species such as Phillyrea latifolia. It is spatially heterogeneous: not all trees in each strata are contiguous, so trees from the lower stratas are partially exposed to direct light. The forest grows on rocky and shallow soils that have a low retention capacity and are of Jurassic limestone origin. The climate is Mediterranean, with a water stress period in summer, cold or mild winters and most precipitation occurring between September and May. The experimental site, which is dedicated to study forest carbon and water cycles, has an enclosed area of 80×80 m (Simioni et al. 2013) but our specific plot is a quadrat of dimensions 25x25 m.

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. Since FontBlanche is one of the sites used for evaluating the model, and much of the data can be found in Moreno et al. (2021). We can use a data list fb with all the necessary inputs:

fb <- medfatereports::load_list("FONBLA")
fb <- readRDS("fb_data.rds")
names(fb)
##  [1] "treeData"       "shrubData"      "customParams"   "measuredData"  
##  [5] "meteoData"      "miscData"       "soilData"       "terrainData"   
##  [9] "remarks"        "sp_params"      "forest_object1"

Soil

We require information on the physical attributes of soil in Font-Blanche, 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. 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()). In our case soil physical attributes are already defined in the data bundled for FontBlanche:

spar <- fb$soilData
print(spar)
##   widths clay sand om   bd rfc
## 1    300   39   26  6 1.45  50
## 2    700   39   26  3 1.45  65
## 3   1000   39   26  1 1.45  90
## 4   2500   39   26  1 1.45  95

The soil input for function spwb() is actually an object of class soil that is created using a function with the same name:

fb_soil <- soil(spar)

The print() function for objects soil provides a lot of information on soil physical properties and water capacity:

print(fb_soil)
## Soil depth (mm): 4500 
## 
## Layer  1  [ 0  to  300 mm ] 
##     clay (%): 39 silt (%): 29 sand (%): 26 organic matter (%): 6 [ Clay loam ]
##     Rock fragment content (%): 50 Macroporosity (%): 7 
##     Theta WP (%): 25 Theta FC (%): 39 Theta SAT (%): 54 Theta current (%) 39 
##     Vol. WP (mm): 37 Vol. FC (mm): 58 Vol. SAT (mm): 81 Vol. current (mm): 58 
##     Temperature (Celsius): NA 
## 
## Layer  2  [ 300  to  1000 mm ] 
##     clay (%): 39 silt (%): 32 sand (%): 26 organic matter (%): 3 [ Clay loam ]
##     Rock fragment content (%): 65 Macroporosity (%): 7 
##     Theta WP (%): 24 Theta FC (%): 38 Theta SAT (%): 49 Theta current (%) 38 
##     Vol. WP (mm): 59 Vol. FC (mm): 93 Vol. SAT (mm): 121 Vol. current (mm): 93 
##     Temperature (Celsius): NA 
## 
## Layer  3  [ 1000  to  2000 mm ] 
##     clay (%): 39 silt (%): 34 sand (%): 26 organic matter (%): 1 [ Clay loam ]
##     Rock fragment content (%): 90 Macroporosity (%): 7 
##     Theta WP (%): 24 Theta FC (%): 37 Theta SAT (%): 47 Theta current (%) 37 
##     Vol. WP (mm): 24 Vol. FC (mm): 37 Vol. SAT (mm): 47 Vol. current (mm): 37 
##     Temperature (Celsius): NA 
## 
## Layer  4  [ 2000  to  4500 mm ] 
##     clay (%): 39 silt (%): 34 sand (%): 26 organic matter (%): 1 [ Clay loam ]
##     Rock fragment content (%): 95 Macroporosity (%): 7 
##     Theta WP (%): 24 Theta FC (%): 37 Theta SAT (%): 47 Theta current (%) 37 
##     Vol. WP (mm): 29 Vol. FC (mm): 47 Vol. SAT (mm): 58 Vol. current (mm): 47 
##     Temperature (Celsius): NA 
## 
## Total soil saturated capacity (mm): 306 
## Total soil water holding capacity (mm): 235 
## Total soil extractable water (mm): 106 
## Total soil current Volume (mm): 235 
## 
## Snow pack water equivalent (mm): 0 
## Soil water table depth (mm): 4500

The soil object is also used to store the moisture degree of each soil layer. In particular, W contains the state variable that represents moisture content - the proportion of moisture relative to field capacity - which is by default initialized to 1 for each layer:

fb_soil$W
## [1] 1 1 1 1

Species parameters

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

data("SpParamsMED")

However, sometimes one may wish to override species defaults with custom values. In the case of FontBlanche there is a table of preferred parameters:

fb$customParams
##               Species VCleaf_P12 VCleaf_P50 VCleaf_P88 VCleaf_slope VCstem_P12
## 1 Phillyrea latifolia         NA         NA         NA           NA  -1.971750
## 2    Pinus halepensis         NA         NA         NA           NA  -3.707158
## 3        Quercus ilex         NA         NA         NA           NA  -4.739642
##   VCstem_P50 VCstem_P88 VCstem_slope VCroot_P12 VCroot_P50 VCroot_P88
## 1      -6.50 -11.028250           11         NA         NA         NA
## 2      -4.79  -5.872842           46         -1  -1.741565  -2.301482
## 3      -6.40  -8.060358           30         NA         NA         NA
##   VCroot_slope VCleaf_kmax LeafEPS LeafPI0 LeafAF StemEPS StemPI0 StemAF Gswmin
## 1           NA        3.00   12.38   -2.13    0.5   12.38   -2.13    0.4  0.002
## 2           NA        4.00    5.31   -1.50    0.6    5.00   -1.65    0.4  0.001
## 3           NA        2.63   15.00   -2.50    0.4   15.00   -2.50    0.4  0.002
##   Gswmax    Gs_P50 Gs_slope    Al2As
## 1 0.2200 -2.207094 89.41176       NA
## 2 0.2175 -1.871216 97.43590  631.000
## 3 0.2200 -2.114188 44.70588 1540.671

We can use function modifySpParams() to replace the values of parameters for the desired traits, leaving the rest unaltered:

SpParamsFB <- modifySpParams(SpParamsMED, fb$customParams)
SpParamsFB
##                    Name IFNcodes SpIndex        AcceptedName
## 143 Phillyrea latifolia        8     142 Phillyrea latifolia
## 149    Pinus halepensis       24     148    Pinus halepensis
## 169        Quercus ilex   45/245     168        Quercus ilex
##                 Species     Genus   Family    Order      Group GrowthForm
## 143 Phillyrea latifolia Phillyrea Oleaceae Lamiales Angiosperm       Tree
## 149    Pinus halepensis     Pinus Pinaceae  Pinales Gymnosperm       Tree
## 169        Quercus ilex   Quercus Fagaceae  Fagales Angiosperm Tree/Shrub
##         LifeForm LeafShape LeafSize      PhenologyType DispersalType Hmed Hmax
## 143 Phanerophyte     Broad   Medium oneflush-evergreen            NA  150  900
## 149 Phanerophyte    Needle    Small oneflush-evergreen            NA  850 1900
## 169 Phanerophyte     Broad   Medium oneflush-evergreen            NA  500 1300
##     Z50  Z95 fHDmin fHDmax    a_ash    b_ash    a_bsh     b_bsh    a_btsh
## 143  NA 2353     45    109       NA       NA       NA        NA        NA
## 149  NA 7500     80    160       NA       NA       NA        NA        NA
## 169  NA 5020     40    100 1.857486 1.885548 0.523883 0.7337293 0.7327147
##       b_btsh cr BTsh      a_fbt    b_fbt       c_fbt    a_cr  b_1cr    b_2cr
## 143       NA NA   NA         NA       NA          NA      NA     NA       NA
## 149       NA NA   NA 0.07607828 1.462411 -0.02280106      NA     NA       NA
## 169 0.737577 NA   NA 0.07848713 1.497670 -0.00309341 1.98539 -0.552 -0.01386
##            b_3cr    c_1cr    c_2cr      a_cw   b_cw      a_bt      b_bt
## 143           NA       NA       NA        NA     NA        NA        NA
## 149           NA       NA       NA 0.6415296 0.7310 0.5535741 1.1848613
## 169 -0.000110736 -0.00685 -0.20101 0.5681897 0.7974 0.5622245 0.9626839
##     LeafDuration t0gdd  Sgdd Tbgdd  Ssen Phsen Tbsen xsen ysen      SLA
## 143     2.556345    NA    NA    NA    NA    NA    NA   NA   NA 6.881886
## 149     2.536875    NA    NA    NA    NA    NA    NA   NA   NA 5.140523
## 169     2.183837  54.5 240.7  4.34 10178  12.5  28.5    2    2 6.340000
##     LeafDensity WoodDensity FineRootDensity conduit2sapwood     r635    pDead
## 143   0.5327417   0.7050000              NA              NA 1.917579 0.119768
## 149   0.2982842   0.6077016              NA       0.9236406 1.964226 0.000500
## 169   0.4893392   0.9008264              NA       0.6238125 1.805872 0.000260
##        Al2As Ar2Al LeafWidth      SRL RLD    maxFMC   minFMC LeafPI0 LeafEPS
## 143 1698.950    NA 1.2000000       NA  NA 108.24724 56.53442   -2.13   12.38
## 149  631.000    NA 0.1384772 3172.572  NA 126.03063 86.22550   -1.50    5.31
## 169 1540.671    NA 1.7674359 4398.812  NA  93.15304 57.44192   -2.50   15.00
##     LeafAF StemPI0 StemEPS StemAF  SAV HeatContent LigninPercent LeafAngle
## 143    0.5   -2.13   12.38    0.4 9630       21400            NA        NA
## 149    0.6   -1.65    5.00    0.4 6050       22150      24.52473        NA
## 169    0.4   -2.50   15.00    0.4 4050       19300      28.97492        NA
##     LeafAngleSD ClumpingIndex gammaSWR alphaSWR kPAR  g   Tmax_LAI   Tmax_LAIsq
## 143          NA            NA       NA       NA   NA NA         NA           NA
## 149          NA            NA       NA       NA   NA NA 0.13847869 -0.006200539
## 169          NA            NA       NA       NA   NA NA 0.09146279 -0.004095349
##     Psi_Extract Exp_Extract      WUE   WUE_par     WUE_co2    WUE_vpd Gswmin
## 143  -1.8969940          NA       NA        NA          NA         NA  0.002
## 149  -0.8507809     1.47061 8.523012 0.6843513 0.002517798 -0.3035192  0.001
## 169  -1.6598896     1.06530 8.447722 0.2523021 0.002721234 -0.5791330  0.002
##     Gswmax Gs_Toptim Gs_Tsens    Gs_P50 Gs_slope VCleaf_kmax VCleaf_P12
## 143 0.2200        NA       NA -2.207094 89.41176        3.00         NA
## 149 0.2175        NA       NA -1.871216 97.43590        4.00      -0.65
## 169 0.2200        NA       NA -2.114188 44.70588        2.63         NA
##     VCleaf_P50 VCleaf_P88 VCleaf_slope Kmax_stemxylem VCstem_P12 VCstem_P50
## 143         NA         NA           NA      0.4083769  -1.971750      -6.50
## 149  -1.195000         NA     115.1515      0.1500000  -3.707158      -4.79
## 169  -2.663333         NA           NA      0.4000000  -4.739642      -6.40
##     VCstem_P88 VCstem_slope Kmax_rootxylem VCroot_P12 VCroot_P50 VCroot_P88
## 143 -11.028250           11             NA -3.1224807  -5.300000  -7.477519
## 149  -5.872842           46             NA -1.0000000  -1.741565  -2.301482
## 169  -8.060358           30             NA -0.2572776  -1.836667  -4.728482
##     VCroot_slope  Vmax298  Jmax298    Nleaf Nsapwood Nfineroot     WoodC
## 143     17.45105 65.23250 146.2701 16.09170  2.78000        NA        NA
## 149    102.98981 72.19617 124.1687 11.91507  1.26556  9.187476 0.4979943
## 169     22.56335 68.51600 118.7863 14.11983  5.66150 12.166747 0.4740096
##        RERleaf RERsapwood RERfineroot CCleaf CCsapwood CCfineroot RGRleafmax
## 143         NA         NA          NA 1.6300        NA         NA         NA
## 149 0.01210607         NA          NA 1.5905      1.47        1.3         NA
## 169 0.01757808         NA          NA 1.4300        NA         NA         NA
##     RGRsapwoodmax RGRcambiummax RGRfinerootmax SRsapwood SRfineroot   RSSG
## 143            NA  0.0009891472             NA        NA         NA     NA
## 149            NA  0.0034108138             NA        NA         NA 0.3725
## 169            NA  0.0015540115             NA        NA         NA 0.9500
##     MortalityBaselineRate SurvivalModelStep SurvivalB0 SurvivalB1
## 143           0.001622378                NA         NA         NA
## 149           0.005000000                10   7.311515 -0.6532989
## 169           0.001000000                10   7.484348 -0.5420550
##     SeedProductionHeight SeedMass SeedLongevity DispersalDistance
## 143                   NA       NA            NA                NA
## 149                   NA       NA            NA                NA
## 169                   NA       NA            NA                NA
##     DispersalShape   ProbRecr MinTempRecr MinMoistureRecr MinFPARRecr
## 143             NA 0.04459023   -2.570181      0.05070956   0.4943654
## 149             NA 0.02473379    1.083300      0.10154153   4.5625766
## 169             NA 0.03005748   -3.744526      0.09657161   0.1307250
##     RecrTreeDBH RecrTreeHeight RecrShrubHeight RecrTreeDensity RecrShrubCover
## 143          NA       52.54367              NA              NA             NA
## 149          NA       56.93647              NA              NA             NA
## 169          NA       47.23629              NA              NA             NA
##     RecrZ50 RecrZ95 RespFire RespDist RespClip IngrowthTreeDensity
## 143      NA      NA      0.9     0.95     0.96            235.1347
## 149      NA      NA       NA       NA       NA            246.2793
## 169      NA      NA      0.9     0.95     0.96            352.2668
##     IngrowthTreeDBH
## 143              NA
## 149              NA
## 169              NA

Note that the function returns a subset of rows for the species mentioned in customParams. Not all parameters are needed for the soil water balance model. 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://emf-creaf.github.io/medfate).

Vegetation

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:

fb_forest <- emptyforest()
fb_forest
## $treeData
## [1] Species DBH     Height  N       Z50     Z95    
## <0 rows> (or 0-length row.names)
## 
## $shrubData
## [1] Species Height  Cover   Z50     Z95    
## <0 rows> (or 0-length row.names)
## 
## $herbCover
## [1] NA
## 
## $herbHeight
## [1] NA
## 
## $seedBank
## [1] Species Percent
## <0 rows> (or 0-length row.names)
## 
## attr(,"class")
## [1] "forest" "list"

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. In our case, we will for simplicity avoid shrubs and concentrate on the main three tree species in the Font-Blanche forest plot: Phillyrea latifolia (code 142), Pinus halepensis (Alepo pine, code 148), and Quercus ilex (holm oak; code 168). In order to run the model, one has to prepare a data table like this one, already prepared for Font-Blanche:

fb$treeData
##               Species       DBH    Height    N Z50  Z95       LAI
## 1 Phillyrea latifolia  2.587859  323.0000 1248 390 1470 0.2581029
## 2    Pinus halepensis 26.759914 1195.7667  256 300 1200 1.0035486
## 3        Quercus ilex  6.220031  495.5532 3104 500 2287 1.4383485

Trees have been grouped by species, so DBH and height values are means (in cm), and N indicates the number of trees in each category. Package medfate allows separating trees by size, but for simplicity we do not distinguish here between tree sizes within each species. Columns Z50 and Z95 indicate the depths (in mm) corresponding to cumulative 50% and 95% of fine roots, respectively.

In order to use this data, we need to replace the part corresponding to trees into the forest object that we created before:

fb_forest$treeData <- fb$treeData
fb_forest
## $treeData
##               Species       DBH    Height    N Z50  Z95       LAI
## 1 Phillyrea latifolia  2.587859  323.0000 1248 390 1470 0.2581029
## 2    Pinus halepensis 26.759914 1195.7667  256 300 1200 1.0035486
## 3        Quercus ilex  6.220031  495.5532 3104 500 2287 1.4383485
## 
## $shrubData
## [1] Species Height  Cover   Z50     Z95    
## <0 rows> (or 0-length row.names)
## 
## $herbCover
## [1] NA
## 
## $herbHeight
## [1] NA
## 
## $seedBank
## [1] Species Percent
## <0 rows> (or 0-length row.names)
## 
## attr(,"class")
## [1] "forest" "list"

Because the forest plot format is rather specific, medfate also allows starting in an alternative 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, leaf area index (LAI) and crown ratio. While users can build their input data themselves, we use function forest2aboveground() on the object fb_forest to show how should the data look like:

fb_above <- forest2aboveground(fb_forest, SpParamsFB)
fb_above
##         SP    N       DBH Cover         H        CR  LAI_live LAI_expanded
## T1_142 142 1248  2.587859    NA  323.0000 0.5510653 0.2581029    0.2581029
## T2_148 148  256 26.759914    NA 1195.7667 0.6126601 1.0035486    1.0035486
## T3_168 168 3104  6.220031    NA  495.5532 0.5531152 1.4383485    1.4383485
##        LAI_dead
## T1_142        0
## T2_148        0
## T3_168        0

Note that the call to forest2aboveground() included species parameters, because species-specific parameter values are needed to calculate leaf area from tree diameters or shrub cover using allometric relationships. 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. 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.

We see that at Font-Blanche holm oaks (code 68) represent most of the total leaf area. On the other hand, pines are taller than oaks. medfate assumes that leaf distribution follows a truncated normal curve between the crown base height and the total height. This can be easily inspected using function vprofile_leafAreaDensity():

vprofile_leafAreaDensity(fb_forest, SpParamsFB, byCohorts = T, bySpecies = T)

Regarding belowground information, the usuer should supply 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 fb_forest to show how should the data look like:

fb_below <- forest2belowground(fb_forest, fb_soil, SpParamsFB)
fb_below
##                1         2          3          4
## T1_142 0.3602157 0.5332967 0.08477533 0.02171222
## T2_148 0.5016024 0.4291685 0.05479894 0.01443019
## T3_168 0.2752236 0.5286425 0.14537757 0.05075634

In our case, these proportions were implicitly specified in parameters Z50 and Z95. In fact, these values describe a continuous distribution of fine roots along depth, which can be displayed using function vprofile_rootDistribution():

vprofile_rootDistribution(fb_forest, SpParamsFB, bySpecies = T)

Note that in Font-Blanche we set that the root system of Aleppo pines (Pinus halepensis) would be more superficial than that of the other two species. Moreover, holm oak trees are the ones who extend their roots down to deepest soil layers.

Meteorology

Water balance simulations of function spwb() 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 evapo-transpiration (PET) is required, but the more complex simulation model also requires radiation, wind speed, min/max temparature and relative humitidy. Here we already have a data frame with the daily meteorology measured at Font-Blanche for year 2014:

fb_meteo <- fb$meteoData
head(fb_meteo)
##        dates MeanTemperature MinTemperature MaxTemperature MeanRelativeHumidity
## 1 2014-01-01        7.661856       5.988889       8.960000             87.78224
## 2 2014-01-02        9.525431       7.958333      11.550000             96.40669
## 3 2014-01-03        9.482417       8.176111      11.762220             93.05705
## 4 2014-01-04       10.016813       6.313000      11.010000             96.31667
## 5 2014-01-05        6.619919       4.766000       9.060555             57.77938
## 6 2014-01-06        8.923008       6.793889      12.329440             64.40477
##   MinRelativeHumidity MaxRelativeHumidity WindSpeed Precipitation Radiation
## 1            80.37265            98.48404  2.317495      0.000000 1.5050178
## 2            84.22588           100.00000  2.407691      0.000000 2.6173102
## 3            79.93501           100.00000  1.950114      0.000000 3.9089762
## 4            90.14023           100.00000  3.596797      2.590674 0.4753025
## 5            48.92043            65.71329  7.310334      0.000000 8.6224570
## 6            51.31975            74.46718  2.301697      0.000000 6.7835715

Simulation models in medfate have been designed to work along with data generated from package meteoland (De Cáceres et al. 2018), which specifies conventions for variable names and units. The user is strongly recommended to resort to this package to obtain suitable weather input for soil water balance simulations (see http://emf-creaf.github.io/meteoland).

Simulation control

Apart from data inputs, the behavior of simulation models can be controlled using a set of global parameters. The default global parameter values are obtained using function defaultControl():

fb_control <- defaultControl()
fb_control$transpirationMode <- "Sperry"
fb_control$subdailyResults <- TRUE
fb_control$cavitationRefillStem <- "rate"
fb_control$cavitationRefillLeaves <- "total"
fb_control$fracRootResistance <- 0.4

Where the following changes are set to control parameters:

  1. Transpiration is set transpirationMode = "Sperry", which implies a greater complexity of plant hydraulics and energy balance calculations.
  2. Soil water retention curves are calculated using Van Genuchten’s equations.
  3. Subdaily results generated by the model are kept.
  4. Coarse root resistance is assumed to be 40% of total plant resistance

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. If one has a forest object, the spwbInput object can be generated in directly from it, avoiding the need to explicitly build fb_above and fb_below data frames:

fb_x <- forest2spwbInput(fb_forest, fb_soil, SpParamsFB, fb_control)

Different species parameter variables will be drawn from SpParamsMED depending on the value of transpirationMode. For the simple water balance model, relatively few parameters are needed. All the input information for forest data and species parameter values can be inspected by printing the input object.

Finally, note that one can play with plant-specific parameters for soil water balance (instead of using species-level values) by using function modifyCohortParams().

Running the model

Function spwb() requires two main objects as input:

  • A spwbInput object with forest and soil parameters (fb_x in our case).
  • A data frame with daily meteorology for the study period (fb_meteo in our case).

Now we are ready to call function spwb():

fb_SWB <- spwb(fb_x, fb_meteo, elevation = 420, latitude = 43.24083)
## Package 'meteoland' [ver. 2.2.1]
## Initial plant water content (mm): 31.8864
## Initial soil water content (mm): 213.886
## Initial snowpack content (mm): 0
## Performing daily simulations
## 
##  [Year 2014]:....................................
## 
## Final plant water content (mm): 19.7795
## Final soil water content (mm): 209.81
## Final snowpack content (mm): 0
## Change in plant water content (mm): -12.1068
## Plant water balance result (mm): 1.03427e-15
## Change in soil water content (mm): -4.07556
## Soil water balance result (mm): 128.999
## Change in snowpack water content (mm): 0
## Snowpack water balance result (mm): 0
## Water balance components:
##   Precipitation (mm) 1066
##   Rain (mm) 1066 Snow (mm) 0
##   Interception (mm) 141 Net rainfall (mm) 925
##   Infiltration (mm) 447 Runoff (mm) 478 Deep drainage (mm) 9
##   Soil evaporation (mm) 9  Herbaceous transpiration (mm) 0 Woody plant transpiration (mm) 300
##   Plant extraction from soil (mm) 300  Plant water balance (mm) 0 Hydraulic redistribution (mm) 50

Console output provides the water balance totals for the period considered, which may span several years. The output of function spwb() is an object of class with the same name, actually a list:

class(fb_SWB)
## [1] "spwb" "list"

If we inspect its elements, we realize that there are several components:

names(fb_SWB)
##  [1] "latitude"      "topography"    "weather"       "spwbInput"    
##  [5] "spwbOutput"    "WaterBalance"  "EnergyBalance" "Temperature"  
##  [9] "Soil"          "Stand"         "Plants"        "SunlitLeaves" 
## [13] "ShadeLeaves"   "subdaily"

For example, WaterBalance contains water balance components in form of a data frame with days in rows:

head(fb_SWB$WaterBalance)
##                  PET Precipitation     Rain Snow   NetRain Snowmelt
## 2014-01-01 0.6209989      0.000000 0.000000    0 0.0000000        0
## 2014-01-02 0.5671238      0.000000 0.000000    0 0.0000000        0
## 2014-01-03 0.5418115      0.000000 0.000000    0 0.0000000        0
## 2014-01-04 0.6072565      2.590674 2.590674    0 0.7213133        0
## 2014-01-05 2.0447148      0.000000 0.000000    0 0.0000000        0
## 2014-01-06 0.9330456      0.000000 0.000000    0 0.0000000        0
##            Infiltration Runoff DeepDrainage Evapotranspiration Interception
## 2014-01-01    0.0000000      0  0.004043731          0.2355285      0.00000
## 2014-01-02    0.0000000      0  0.004045897          0.1959278      0.00000
## 2014-01-03    0.0000000      0  0.004048036          0.1400658      0.00000
## 2014-01-04    0.7213133      0  0.004050273          1.9680840      1.86936
## 2014-01-05    0.0000000      0  0.004035678          1.3082763      0.00000
## 2014-01-06    0.0000000      0  0.004010134          0.8389883      0.00000
##            SoilEvaporation HerbTranspiration PlantExtraction Transpiration
## 2014-01-01      0.21454034                 0    2.098815e-02   0.020988148
## 2014-01-02      0.19592778                 0   -8.402567e-19   0.000000000
## 2014-01-03      0.13158239                 0    8.483367e-03   0.008483367
## 2014-01-04      0.09872381                 0    6.938894e-18   0.000000000
## 2014-01-05      0.11716244                 0    1.191114e+00   1.191113898
## 2014-01-06      0.06883559                 0    7.701527e-01   0.770152695
##            HydraulicRedistribution
## 2014-01-01             0.000000000
## 2014-01-02             0.006148750
## 2014-01-03             0.009327612
## 2014-01-04             0.016023155
## 2014-01-05             0.002212903
## 2014-01-06             0.006349963

Comparing results with observations

Before examining the results of the model, it is important to compare its predictions against observed data, if available. The following observations are available from the experimental forest plot for year 2014:

  • Stand total evapotranspiration estimated using an Eddy-covariance flux tower.
  • Soil moisture content of the first 0-30 cm layer.
  • Cohort transpiration estimates derived from sapflow measurements for Q. ilex and P. halepensis.
  • Pre-dawn and midday leaf water potentials for Q. ilex and P. halepensis.

We first load the measured data into the workspace and filter for the dates used in the simulation:

fb_observed <- fb$measuredData
fb_observed <- fb_observed[fb_observed$dates %in% fb_meteo$dates,]
row.names(fb_observed) <- fb_observed$dates
head(fb_observed)
##                 dates       SWC SWC.err       ETR E_T2_148 E_T2_148_err
## 2014-01-01 2014-01-01 0.5813407      NA 0.2259528       NA           NA
## 2014-01-02 2014-01-02 0.6507478      NA 0.2337668       NA           NA
## 2014-01-03 2014-01-03 0.6224243      NA 0.5229000       NA           NA
## 2014-01-04 2014-01-04        NA      NA 0.1117191       NA           NA
## 2014-01-05 2014-01-05 0.6285134      NA 0.8132403       NA           NA
## 2014-01-06 2014-01-06 0.6035415      NA 0.6012234       NA           NA
##            E_T3_168 E_T3_168_err PD_T2_148 PD_T2_148_err PD_T3_168
## 2014-01-01       NA           NA        NA            NA        NA
## 2014-01-02       NA           NA        NA            NA        NA
## 2014-01-03       NA           NA        NA            NA        NA
## 2014-01-04       NA           NA        NA            NA        NA
## 2014-01-05       NA           NA        NA            NA        NA
## 2014-01-06       NA           NA        NA            NA        NA
##            PD_T3_168_err MD_T2_148 MD_T2_148_err MD_T3_168 MD_T3_168_err
## 2014-01-01            NA        NA            NA        NA            NA
## 2014-01-02            NA        NA            NA        NA            NA
## 2014-01-03            NA        NA            NA        NA            NA
## 2014-01-04            NA        NA            NA        NA            NA
## 2014-01-05            NA        NA            NA        NA            NA
## 2014-01-06            NA        NA            NA        NA            NA

Stand evapotranspiration

Package medfate contains several functions to assist the evaluation of model results. We can first compare the observed vs modelled total evapotranspiration. We can plot the two time series:

evaluation_plot(fb_SWB, fb_observed, type = "ETR", plotType="dynamics")+
  theme(legend.position = c(0.8,0.85))

It is easy to see that in rainy days the predicted evapotranspiration is much higher than that of the observed data. We repeat the comparison but excluding the intercepted water from modeled results:

evaluation_plot(fb_SWB, fb_observed, type = "SE+TR", plotType="dynamics")+
  theme(legend.position = c(0.8,0.85))

The relationship can be shown in a scatter plot:

evaluation_plot(fb_SWB, fb_observed, type = "SE+TR", plotType="scatter")

Where we see a reasonably good relationship, but the model tends to underestimate total evapotranspiration during seasons with low evaporative demand. Function evaluation_stats() allows us to generate evaluation statistics:

evaluation_stats(fb_SWB, fb_observed, type = "SE+TR")
##           n        Bias    Bias.rel         MAE     MAE.rel           r 
## 365.0000000  -0.4858695 -36.4663375   0.8137626  61.0759530   0.5636700 
##         NSE     NSE.abs 
##  -1.5106731  -0.6343325

Soil moisture

We can compare observed vs modelled soil moisture content in a similar way as we did for total evapotranspiration:

evaluation_plot(fb_SWB, fb_observed, type = "SWC", plotType="dynamics")

Clearly, the absolute values of the modeled and measured SMC do not match, which can indicate that either the soil moisture sensors are not calibrated or that we are using an inappropriate soil texture in the model. To avoid this issue, we can use relative extractable water, where in the case of observed data the function divides the observed values by the 95% quantile:

evaluation_plot(fb_SWB, fb_observed, type = "REW", plotType="dynamics")

As before, we can generate a scatter plot:

evaluation_plot(fb_SWB, fb_observed, type = "REW", plotType="scatter")

or examine evaluation statistics:

evaluation_stats(fb_SWB, fb_observed, type = "REW")
##            n         Bias     Bias.rel          MAE      MAE.rel            r 
## 364.00000000   0.01975867   2.81734292   0.08552408  12.19467790   0.91752414 
##          NSE      NSE.abs 
##   0.75550133   0.59019069

Plant transpiration

The following plots display the observed and predicted transpiration dynamics for Pinus halepensis and Quercus ilex:

g1<-evaluation_plot(fb_SWB, fb_observed, 
                            cohort = "T2_148",
                            type="E", plotType = "dynamics")+
  theme(legend.position = c(0.85,0.83))
g2<-evaluation_plot(fb_SWB, fb_observed, 
                            cohort = "T3_168",
                            type="E", plotType = "dynamics")+
  theme(legend.position = c(0.85,0.83))
plot_grid(g1, g2, ncol=1)

In general, the agreement is quite good, but the model seems to overestimate the transpiration of P. halepensis in early summer and after the first drought period. The transpiration of Q. ilex seems also overestimated in spring and autumn. We can also inspect the evaluation statistics for both species using:

evaluation_stats(fb_SWB, fb_observed, cohort = "T2_148", type="E")
##            n         Bias     Bias.rel          MAE      MAE.rel            r 
## 300.00000000   0.07791512  37.88325613   0.27619960 134.29152897   0.57659331 
##          NSE      NSE.abs 
##  -9.64213859  -1.79113909
evaluation_stats(fb_SWB, fb_observed, cohort = "T3_168", type="E")
##            n         Bias     Bias.rel          MAE      MAE.rel            r 
## 309.00000000   0.05170847  17.86385401   0.29006885 100.21081805   0.57392818 
##          NSE      NSE.abs 
##  -3.60360469  -0.97617808

Leaf water potentials

Finally, we can compare observed with predicted water potentials. In this case measurements are available for three dates, but they include the standard deviation of several measurements.

g1<-evaluation_plot(fb_SWB, fb_observed, 
                            cohort = "T2_148",
                            type="WP", plotType = "dynamics")+
  theme(legend.position = c(0.85,0.23))
g2<-evaluation_plot(fb_SWB, fb_observed, 
                            cohort = "T3_168",
                            type="WP", plotType = "dynamics")+
  theme(legend.position = c(0.85,0.23))
plot_grid(g1, g2, ncol=1)

The model seems to underestimate water potentials (i.e. it predicts more negative values than those observed) during the drought season.

Drawing plots

Package medfate provides a simple plot function for objects of class spwb. Here we will use this function to display the seasonal variation predicted by the model, as well as the variation at higher temporal resolution within four different selected 3-day periods that we define here:

d1 = seq(as.Date("2014-03-01"), as.Date("2014-03-03"), by="day")
d2 = seq(as.Date("2014-06-01"), as.Date("2014-06-03"), by="day")
d3 = seq(as.Date("2014-08-01"), as.Date("2014-08-03"), by="day")
d4 = seq(as.Date("2014-10-01"), as.Date("2014-10-03"), by="day")

Meteorological input and input/output water flows

Function plot() can be used to show the meteorological input:

plot(fb_SWB, type = "PET_Precipitation")

It is apparent the climatic drought period between april and august 2014. This should have an impact on soil moisture and plant stress.

If we are interested in forest hydrology, we can plot the amount of water that the model predicts to leave the forest via surface runoff or drainage to lower water compartments.

plot(fb_SWB, type = "Export")

As expected, water exported from the forest plot was only relevant for the autumn and winter periods. Note also that the model predicts some runoff during convective storms during autumn, whereas winter events occur when the soil is already full, so that most exported water is assumed to be lost via deep drainage. One can also display the evapotranspiration flows, which we do in the following plot that also combines the two previous:

g1<-plot(fb_SWB)+scale_x_date(date_breaks = "1 month", date_labels = "%m")+theme(legend.position = "none")
g2<-plot(fb_SWB, "Evapotranspiration")+scale_x_date(date_breaks = "1 month", date_labels = "%m")+theme(legend.position = c(0.13,0.73))
g3<-plot(fb_SWB, "Export")+scale_x_date(date_breaks = "1 month", date_labels = "%m")+theme(legend.position = c(0.35,0.60))
plot_grid(g1,g2, g3, ncol=1, rel_heights = c(0.4,1,0.6))

Soil moisture dynamics and hydraulic redistribution

It is also useful to plot the dynamics of soil state variables by layer, such as the percentage of moisture in relation to field capacity:

plot(fb_SWB, type="SoilTheta")

Note that the model predicts soil drought to occur earlier in the season for the first three layers (0-200 cm) whereas the bottom layer dries out much more slowly. At this point is important to mention that the water balance model incorporates. We can also display the dynamics of the corresponding soil layer water potentials:

plot(fb_SWB, type="SoilPsi")

or draw a composite plot including absolute soil water volume:

g1<-plot(fb_SWB)+scale_x_date(date_breaks = "1 month", date_labels = "%m")+theme(legend.position = "none")
g2<-plot(fb_SWB, "SoilVol")+scale_x_date(date_breaks = "1 month", date_labels = "%m")+theme(legend.position = c(0.08,0.65))
g3<-plot(fb_SWB, "SoilPsi")+scale_x_date(date_breaks = "1 month", date_labels = "%m")+theme(legend.position = c(0.08,0.5))
plot_grid(g1, g2,  g3, rel_heights = c(0.4,0.8,0.8), ncol=1)

Root water uptake and hydraulic redistribution

The following composite plot shows the daily root water uptake (or release) from different soil layers, and the daily amount of water entering soil layers due to hydraulic redistribution:

g1<-plot(fb_SWB, "SoilPsi")+scale_x_date(date_breaks = "1 month", date_labels = "%m")+theme(legend.position = "none")+ylab("Soil wp (MPa)")
g2<-plot(fb_SWB, "PlantExtraction")+scale_x_date(date_breaks = "1 month", date_labels = "%m")+theme(legend.position = c(0.08,0.68))
g3<-plot(fb_SWB, "HydraulicRedistribution")+scale_x_date(date_breaks = "1 month", date_labels = "%m")+theme(legend.position = c(0.08,0.5))
plot_grid(g1, g2,  g3, rel_heights = c(0.4,0.8,0.8), ncol=1)

If we create a composite plot including subdaily water uptake/release patterns, we can further understand the redistribution flows created by the model during different periods:

g0<-plot(fb_SWB, "PlantExtraction")+scale_x_date(date_breaks = "1 month", date_labels = "%m")+theme(legend.position = c(0.08,0.68))
g1<-plot(fb_SWB, "PlantExtraction", subdaily = T, dates = d1)+scale_x_datetime(date_breaks = "1 day",  date_labels = "%m/%d")+theme(legend.position = "none")+ylim(c(-0.05,0.13))
g2<-plot(fb_SWB, "PlantExtraction", subdaily = T, dates = d2)+scale_x_datetime(date_breaks = "1 day",  date_labels = "%m/%d")+theme(legend.position = "none")+ylab("")+ylim(c(-0.05,0.13))
g3<-plot(fb_SWB, "PlantExtraction", subdaily = T, dates = d3)+scale_x_datetime(date_breaks = "1 day",  date_labels = "%m/%d")+theme(legend.position = "none")+ylab("")+ylim(c(-0.05,0.13))
g4<-plot(fb_SWB, "PlantExtraction", subdaily = T, dates = d4)+scale_x_datetime(date_breaks = "1 day",  date_labels = "%m/%d")+theme(legend.position = "none")+ylab("")+ylim(c(-0.05,0.13))
plot_grid(g0,plot_grid(g1, g2, g3, g4, ncol=4),ncol=1)

Plant transpiration

We can use function plot() to display the seasonal dynamics of cohort-level variables, such as plant transpiration per leaf area:

par(mar=c(5,5,1,1))
plot(fb_SWB, type="TranspirationPerLeaf", bySpecies = T)

Where we can observe that some species transpire more than others due to their vertical position within the canopy.

g1<-plot(fb_SWB)+scale_x_date(date_breaks = "1 month", date_labels = "%m")+theme(legend.position = "none")
g2<-plot(fb_SWB, "TranspirationPerLeaf", bySpecies = T)+scale_x_date(date_breaks = "1 month", date_labels = "%m")+theme(legend.position = c(0.1,0.75))
g21<-plot(fb_SWB, "LeafTranspiration", subdaily = T, dates = d1)+scale_x_datetime(date_breaks = "1 day",  date_labels = "%m/%d")+theme(legend.position = "none")+ylim(c(0,0.32))
g22<-plot(fb_SWB, "LeafTranspiration", subdaily = T, dates = d2)+scale_x_datetime(date_breaks = "1 day",  date_labels = "%m/%d")+theme(legend.position = "none")+ylab("")+ylim(c(0,0.32))
g23<-plot(fb_SWB, "LeafTranspiration", subdaily = T, dates = d3)+scale_x_datetime(date_breaks = "1 day",  date_labels = "%m/%d")+theme(legend.position = "none")+ylab("")+ylim(c(0,0.32))
g24<-plot(fb_SWB, "LeafTranspiration", subdaily = T, dates = d4)+scale_x_datetime(date_breaks = "1 day",  date_labels = "%m/%d")+theme(legend.position = "none")+ylab("")+ylim(c(0,0.32))
plot_grid(g1, g2,  
          plot_grid(g21,g22,g23,g24, ncol=4), 
          ncol=1, rel_heights = c(0.4,0.8,0.8))

Plant stress

In the model, reduction of (whole-plant) plant transpiration is what used to define drought stress, which depends on the species identity:

plot(fb_SWB, type="PlantStress", bySpecies = T)

To examine the impact of drought on plants, one can inspect the whole-plant conductance (from which the stress index is derived) or the stem percent loss of conductance derived from embolism, as we do in the following composite plot:

g1<-plot(fb_SWB)+scale_x_date(date_breaks = "1 month", date_labels = "%m")+theme(legend.position = "none")
g2<-plot(fb_SWB, "SoilPlantConductance", bySpecies = T)+scale_x_date(date_breaks = "1 month", date_labels = "%m")+
  ylab(expression(paste("Soil-plant conductance ",(mmol%.%m^{-2}%.%s^{-1}))))+
  theme(legend.position = "none")
g3<-plot(fb_SWB, "StemPLC", bySpecies = T)+scale_x_date(date_breaks = "1 month", date_labels = "%m")+theme(legend.position = c(0.2,0.75))
plot_grid(g1, g2,g3,                          
          ncol=1, rel_heights = c(0.4,0.8,0.8))

Leaf water potentials

g1<-plot(fb_SWB)+scale_x_date(date_breaks = "1 month", date_labels = "%m")+theme(legend.position = "none")
g2<-plot(fb_SWB, "LeafPsiRange", bySpecies = T)+scale_x_date(date_breaks = "1 month", date_labels = "%m")+theme(legend.position = c(0.1,0.25)) + ylab("Leaf water potential (MPa)")
g21<-plot(fb_SWB, "LeafPsi", subdaily = T, dates = d1)+scale_x_datetime(date_breaks = "1 day",  date_labels = "%m/%d")+theme(legend.position = "none")+ylim(c(-7,0))
g22<-plot(fb_SWB, "LeafPsi", subdaily = T, dates = d2)+scale_x_datetime(date_breaks = "1 day",  date_labels = "%m/%d")+theme(legend.position = "none")+ylab("")+ylim(c(-7,0))
g23<-plot(fb_SWB, "LeafPsi", subdaily = T, dates = d3)+scale_x_datetime(date_breaks = "1 day",  date_labels = "%m/%d")+theme(legend.position = "none")+ylab("")+ylim(c(-7,0))
g24<-plot(fb_SWB, "LeafPsi", subdaily = T, dates = d4)+scale_x_datetime(date_breaks = "1 day",  date_labels = "%m/%d")+theme(legend.position = "none")+ylab("")+ylim(c(-7,0))
plot_grid(g1, g2,                          
          plot_grid(g21,g22,g23,g24, ncol=4), 
          ncol=1, rel_heights = c(0.4,0.8,0.8))

Stomatal conductance

g1<-plot(fb_SWB)+scale_x_date(date_breaks = "1 month", date_labels = "%m")+theme(legend.position = "none")
g2<-plot(fb_SWB, "GSWMax_SL", bySpecies = T)+scale_x_date(date_breaks = "1 month", date_labels = "%m")+theme(legend.position = c(0.5,0.74))+ylab("Sunlit leaf stomatal conductance")+ylim(c(0,0.3))
g21<-plot(fb_SWB, "LeafStomatalConductance", subdaily = T, dates = d1)+scale_x_datetime(date_breaks = "1 day",  date_labels = "%m/%d")+theme(legend.position = "none")+ylim(c(0,0.2))
g22<-plot(fb_SWB, "LeafStomatalConductance", subdaily = T, dates = d2)+scale_x_datetime(date_breaks = "1 day",  date_labels = "%m/%d")+theme(legend.position = "none")+ylab("")+ylim(c(0,0.2))
g23<-plot(fb_SWB, "LeafStomatalConductance", subdaily = T, dates = d3)+scale_x_datetime(date_breaks = "1 day",  date_labels = "%m/%d")+theme(legend.position = "none")+ylab("")+ylim(c(0,0.2))
g24<-plot(fb_SWB, "LeafStomatalConductance", subdaily = T, dates = d4)+scale_x_datetime(date_breaks = "1 day",  date_labels = "%m/%d")+theme(legend.position = "none")+ylab("")+ylim(c(0,0.2))
plot_grid(g1, g2,
          plot_grid(g21,g22,g23,g24, ncol=4),
          ncol=1, rel_heights = c(0.4,0.8,0.8))

Generating output summaries

While the water balance model operates at daily and sub-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, monthly or annual). For example, to obtain the average soil moisture and water potentials by months one can use:

summary(fb_SWB, freq="months",FUN=sum, output="WaterBalance")
##                  PET Precipitation      Rain Snow     NetRain Snowmelt
## 2014-01-01  27.03414     205.04814 205.04814    0 182.5767907        0
## 2014-02-01  37.11592     181.09641 181.09641    0 155.2573002        0
## 2014-03-01  80.49737      44.61248  44.61248    0  39.8917051        0
## 2014-04-01 109.24874      15.00000  15.00000    0   7.2713589        0
## 2014-05-01 147.99639      21.60000  21.60000    0  16.3281633        0
## 2014-06-01 167.27898      33.60000  33.60000    0  25.8839490        0
## 2014-07-01 183.99299       0.60000   0.60000    0   0.1428946        0
## 2014-08-01 159.66330      60.40000  60.40000    0  52.8025568        0
## 2014-09-01 103.42793     137.60000 137.60000    0 125.8957242        0
## 2014-10-01  63.53896      50.60000  50.60000    0  41.9066889        0
## 2014-11-01  30.12083     222.60000 222.60000    0 198.0975096        0
## 2014-12-01  26.01617      93.00000  93.00000    0  78.7534201        0
##            Infiltration     Runoff DeepDrainage Evapotranspiration Interception
## 2014-01-01  105.6926965  76.884094 1.489993e-01          37.842937   22.4713498
## 2014-02-01   82.5533425  72.703958 2.157036e+00          50.431550   25.8391081
## 2014-03-01   30.8785403   9.013165 5.210121e+00          72.738964    4.7207713
## 2014-04-01    7.2713589   0.000000 1.352726e+00          91.055003    7.7286411
## 2014-05-01   16.3281633   0.000000 6.342456e-02          64.532566    5.2718367
## 2014-06-01   25.8839490   0.000000 6.932312e-07          39.430349    7.7160510
## 2014-07-01    0.1428946   0.000000 1.219688e-07           8.926743    0.4571054
## 2014-08-01   18.0726432  34.729914 8.281271e-08          12.124911    7.5974432
## 2014-09-01   41.9593682  83.936356 2.327626e-07          16.557205   11.7042748
## 2014-10-01   15.4607993  26.445890 9.145557e-07          13.203868    8.6933111
## 2014-11-01   54.1792430 143.918267 2.270922e-06          26.920300   24.5024904
## 2014-12-01   48.4837019  30.269718 4.338650e-06          16.160213   14.2465799
##            SoilEvaporation HerbTranspiration PlantExtraction Transpiration
## 2014-01-01      1.79496105                 0       13.576626     13.576626
## 2014-02-01      2.16884684                 0       22.423595     22.423595
## 2014-03-01      1.64202559                 0       66.376168     66.376168
## 2014-04-01      0.22242883                 0       83.103933     83.103933
## 2014-05-01      0.03567143                 0       59.225058     59.225058
## 2014-06-01      0.01424565                 0       31.700052     31.700052
## 2014-07-01      0.00000000                 0        8.469637      8.469637
## 2014-08-01      0.04548686                 0        4.481981      4.481981
## 2014-09-01      0.09045928                 0        4.762471      4.762471
## 2014-10-01      0.68995549                 0        3.820601      3.820601
## 2014-11-01      1.11267067                 0        1.305139      1.305139
## 2014-12-01      0.85803677                 0        1.055597      1.055597
##            HydraulicRedistribution
## 2014-01-01               0.6722996
## 2014-02-01               0.2313978
## 2014-03-01               1.0975995
## 2014-04-01               5.6907891
## 2014-05-01              14.4989429
## 2014-06-01              11.2760214
## 2014-07-01               0.2218172
## 2014-08-01               4.8755086
## 2014-09-01               4.3544596
## 2014-10-01               3.9836520
## 2014-11-01               2.1810951
## 2014-12-01               0.7433501

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 the three tree species by months:

summary(fb_SWB, freq="months",FUN=mean, output="PlantStress", bySpecies = TRUE)
##            Phillyrea latifolia Pinus halepensis Quercus ilex
## 2014-01-01        0.0004433573     3.278079e-05 8.205441e-06
## 2014-02-01        0.0010020336     6.922987e-05 2.002251e-05
## 2014-03-01        0.0041604112     1.016083e-03 2.357837e-04
## 2014-04-01        0.0154083646     8.558489e-03 3.084838e-03
## 2014-05-01        0.2318173799     3.595759e-01 1.615418e-01
## 2014-06-01        0.4844323573     9.176857e-01 5.598546e-01
## 2014-07-01        0.7389237506     1.000000e+00 8.646694e-01
## 2014-08-01        0.6116679612     1.000000e+00 1.000000e+00
## 2014-09-01        0.4429184720     1.000000e+00 1.000000e+00
## 2014-10-01        0.3700286698     1.000000e+00 1.000000e+00
## 2014-11-01        0.3400187283     1.000000e+00 1.000000e+00
## 2014-12-01        0.3119629065     1.000000e+00 1.000000e+00

In this case, the summary function aggregates the output by species using LAI values as weights.

Bibliography

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