This document describes how to run a water and energy balance model that uses a more detailed approach for hydraulics and stomatal regulation. This document is meant to teach users to run the simulation model within R. All the details of the model design and formulation can be found at https://vegmod.ctfc.cat/software/medfate.
Most details of the soil plant water balance model inputs are already covered in vignette 1. Introduction to water balance simulation. Here only differences are mentioned.
The soil input for function is actually an object of class soil
that is created using a function with the same name:
Advanced soil plant energy and water balance modelling requires considering the temperature of soil. Hence, Temp
contains the temperature (in degrees) of soil layers:
## [1] NA NA
Soil layer temperatures are initialized to missing values, so that at the first time step they will be set to atmospheric temperature. While simple water balance modeling can be run using either Saxton’s or Van Genuchten’s equations as water retention curves, Van Genuchten’s model is forced for advanced modelling.
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:
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
:
## [1] "Name" "IFNcodes" "SpIndex"
## [4] "Group" "Order" "Family"
## [7] "GrowthForm" "Hmed" "Hmax"
## [10] "Z50" "Z95" "Zmax"
## [13] "a_ash" "a_bsh" "b_bsh"
## [16] "cr" "a_fbt" "b_fbt"
## [19] "c_fbt" "d_fbt" "a_cr"
## [22] "b_1cr" "b_2cr" "b_3cr"
## [25] "c_1cr" "c_2cr" "a_cw"
## [28] "b_cw" "PhenologyType" "LeafDuration"
## [31] "Sgdd" "SLA" "LeafDensity"
## [34] "r635" "pDead" "Al2As"
## [37] "WoodDensity" "LeafWidth" "minFMC"
## [40] "maxFMC" "LeafPI0" "LeafEPS"
## [43] "LeafAF" "StemPI0" "StemEPS"
## [46] "StemAF" "LigninPercent" "ParticleDensity"
## [49] "LeafLitterFuelType" "Flammability" "SAV"
## [52] "HeatContent" "gammaSWR" "alphaSWR"
## [55] "kPAR" "g" "Psi_Extract"
## [58] "Psi_Critic" "WUE" "pRootDisc"
## [61] "Gwmin" "Gwmax" "VCleaf_kmax"
## [64] "VCleaf_c" "VCleaf_d" "Kmax_stemxylem"
## [67] "VCstem_c" "VCstem_d" "Kmax_rootxylem"
## [70] "VCroot_c" "VCroot_d" "Narea"
## [73] "Vmax298" "Jmax298" "WoodC"
## [76] "RGRmax" "fHDmin" "fHDmax"
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 (https://vegmod.ctfc.cat/software/medfate).
Models included in medfate
were primarily designed to be ran on forest inventory plots (these are explained in detail in 1. Introduction to water balance simulation):
## $ID
## [1] "1"
##
## $patchsize
## [1] 10000
##
## $treeData
## Species N DBH Height Z50 Z95
## 1 54 168 37.55 800 750 3000
## 2 68 384 14.60 660 750 3000
##
## $shrubData
## Species Cover Height Z50 Z95
## 1 65 3.75 30 300 1500
##
## $herbCover
## [1] 10
##
## $herbHeight
## [1] 20
##
## attr(,"class")
## [1] "forest" "list"
Advanced water and energy balance modeling requires daily precipitation, radiation, wind speed, min/max temparatures and relative humitidy as inputs:
## MeanTemperature MinTemperature MaxTemperature Precipitation
## 2001-01-01 3.57668969 -0.5934215 6.287950 4.869109
## 2001-01-02 1.83695972 -2.3662458 4.569737 2.498292
## 2001-01-03 0.09462563 -3.8541036 2.661951 0.000000
## 2001-01-04 1.13866156 -1.8744860 3.097705 5.796973
## 2001-01-05 4.70578690 0.3288287 7.551532 1.884401
## 2001-01-06 4.57036721 0.5461322 7.186784 13.359801
## MeanRelativeHumidity MinRelativeHumidity MaxRelativeHumidity
## 2001-01-01 78.73709 65.15411 100.00000
## 2001-01-02 69.70800 57.43761 94.71780
## 2001-01-03 70.69610 58.77432 94.66823
## 2001-01-04 76.89156 66.84256 95.80950
## 2001-01-05 76.67424 62.97656 100.00000
## 2001-01-06 89.01940 74.25754 100.00000
## Radiation WindSpeed WindDirection PET
## 2001-01-01 12.89251 2.000000 172 1.3212770
## 2001-01-02 13.03079 7.662544 278 2.2185985
## 2001-01-03 16.90722 2.000000 141 1.8045176
## 2001-01-04 11.07275 2.000000 172 0.9200627
## 2001-01-05 13.45205 7.581347 321 2.2914449
## 2001-01-06 12.84841 6.570501 141 1.7255058
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.
Apart from data inputs, the behaviour of simulation models is controlled using a set of global parameters. The default parameterization is obtained using function defaultControl()
:
To use the complex soil water balance model we must change the values of transpirationMode
(to switch from “Granier” to “Sperry”) and soilFunctions
(to switch from Saxton’s retention curve, “SX”, to Van Genuchten’s retention curve, “VG”):
A last step is needed before running the simulation function, consisting in the compilation of parameters and the calculation of additional parameter values for each plant cohort. If one has a forest
object, the spwbInput
object can be generated in directly from it:
The spwbInput
object for advanced water and energy balance is similar to that of simple water balance simulations, but contains more elements. Information about the cohort species is found in element cohorts
(i.e. code, species and name):
## SP Name
## T1_54 54 Pinus halepensis
## T2_68 68 Quercus ilex
## S1_65 65 Quercus coccifera
Element canopy
contains state variables of the whole canopy, which include growth degree days and canopy temperature:
## $gdd
## [1] 0
##
## $Temp
## [1] NA
Canopy temperature is a state variable (as soil temperature) needed for energy balance. As you may already known, element above
contains the aboveground structure data that we already know:
## H CR LAI_live LAI_expanded LAI_dead Status
## T1_54 800 0.7150421 0.81670117 0.81670117 0 alive
## T2_68 660 0.6055642 0.79779523 0.79779523 0 alive
## S1_65 30 0.9738889 0.08913325 0.08913325 0 alive
Belowground parameters can be seen in below
, which in the case of advance water and energy balance include root distribution as well as maximum root and rhizosphere conductances by soil layer:
## $V
## 1 2
## T1_54 0.1933638 0.8066362
## T2_68 0.1933638 0.8066362
## S1_65 0.5554389 0.4445611
##
## $VGrhizo_kmax
## 1 2
## T1_54 3525625 5162814
## T2_68 17084691 25812448
## S1_65 1099645074 334060362
##
## $VCroot_kmax
## 1 2
## T1_54 0.4768082 1.082393
## T2_68 1.2828439 2.912158
## S1_65 4.1374255 3.081895
##
## $Wpool
## 1 2
## T1_54 1 1
## T2_68 1 1
## S1_65 1 1
##
## $RhizoPsi
## 1 2
## T1_54 0 0
## T2_68 0 0
## S1_65 0 0
The spwbInput
object also includes cohort parameter values for several kinds of traits. For example, plant anatomy parameters are described in paramsAnatomy
:
## Hmed Al2As SLA LeafWidth LeafDensity WoodDensity r635
## T1_54 970 1317.523 4.340 0.1 0.7 0.55253 1.964226
## T2_68 650 2512.563 5.870 3.0 0.7 0.90000 1.805872
## S1_65 70 2512.563 5.859 1.0 0.7 0.92000 2.289452
Parameters related to plant transpiration and photosynthesis can be seen in paramsTransp
:
## Gwmin Gwmax Vmax298 Jmax298 Kmax_stemxylem Kmax_rootxylem
## T1_54 0.00203 0.1900000 62.5 129.5000 0.1500000 0.893000
## T2_68 0.00450 0.2100000 66.2 130.0000 0.7735834 3.094334
## S1_65 0.01045 0.4518345 100.0 163.6253 0.2900000 1.160000
## VCleaf_kmax VCleaf_c VCleaf_d VCstem_kmax VCstem_c VCstem_d
## T1_54 6 12.712961 -3.526895 1.257285 12.712961 -5.290342
## T2_68 8 2.188265 -4.138168 4.299811 4.581685 -7.723800
## S1_65 8 2.511383 -6.122057 12.080826 2.511383 -9.183085
## VCroot_kmax VCroot_c VCroot_d Plant_kmax
## T1_54 1.559201 1.056898 -1.244767 0.6236803
## T2_68 4.195002 1.494098 -2.134283 1.6780008
## S1_65 7.219320 2.655734 -6.198418 2.8877280
Finally, parameters related to pressure-volume curves and water storage capacity of leaf and stem organs are in paramsWaterStorage
:
## LeafPI0 LeafEPS LeafAF Vleaf StemPI0 StemEPS StemAF Vsapwood
## T1_54 -2.11 12.18 0.162 0.1795440 -1.778525 10.43383 0.8 3.89345314
## T2_68 -2.39 19.26 0.170 0.1327463 -3.224000 46.25763 0.8 1.09165714
## S1_65 -2.37 17.23 0.240 0.1329955 -3.307200 50.36679 0.8 0.04807013
Finally, remember 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.
Before using the advanced water and energy balance model, is important to understand the parameters that influence the different sub-models. Package medfate
provides low-level functions corresponding to sub-models (light extinction, hydraulics, transpiration, photosynthesis…). In addition, there are several high-level plotting functions that allow examining several aspects of these processes.
Given a spwbInput
object, we can use function hydraulics_vulnerabilityCurvePlot()
to inspect vulnerability curves (i.e. how hydraulic conductance of a given segment changes with the water potential) for each plant cohort and each of the different segments of the soil-plant hydraulic network: rhizosphere, roots, stems and leaves:
The maximum values and shape of vulnerability curves for leaves and stems are regulated by parameters in paramsTransp
. Roots have vulnerability curve parameters in the same data frame, but maximum conductance values need to be specified for each soil layer and are given in below$VCroot_kmax
. Note that the last call to hydraulics_vulnerabilityCurvePlot()
includes a soil
object. This is because the van Genuchten parameters that define the shape of the vulnerability curve for the rhizosphere are stored in this object. Maximum conductance values in the rhizosphere are given in below$VGrhizo_kmax
.
The vulnerability curves conformng the hydraulic network are used in the model to build the supply function, which relates water flow (i.e. transpiration) with the drop of water potential along the whole hydraulic pathway. The supply function contains not only these two variables, but also the water potential of intermediate nodes in the the hydraulic network. Function hydraulics_supplyFunctionPlot()
can be used to inspect any of this variables:
Calls to hydraulics_supplyFunctionPlot()
always need both a spwbInput
object and a soil
object. The soil moisture state (i.e. its water potential) is the starting point for the calculation of the supply function, so different curves will be obtained for different values of soil moisture.
The soil water balance model determines stomatal conductance and transpiration separately for sunlit and shade leaves. Stomatal conductance is determined after building a photosynthesis function corresponding to the supply function and finding the value of stomatal conductance that maximizes carbon revenue while avoiding hydraulic damage (a profit-maximization approach). Given a meteorological and soil inputs and a chosen day and timestep, function transp_stomatalRegulationPlot()
allows displaying the supply and photosynthesis curves for sunlit and shade leaves, along with an indication of the values corresponding to the chosen stomatal aperture:
d = 100
transp_stomatalRegulationPlot(x, examplesoil, examplemeteo, day = d, timestep=12,
latitude = 41.82592, elevation = 100, type="E")
transp_stomatalRegulationPlot(x, examplesoil, examplemeteo, day = d, timestep=12,
latitude = 41.82592, elevation = 100, type="An")
transp_stomatalRegulationPlot(x, examplesoil, examplemeteo, day = d, timestep=12,
latitude = 41.82592, elevation = 100, type="Gw")
Soil water balance simulations will normally span periods of several months or years, but since the model operates at a daily and subdaily temporal scales, 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 the same day as before from the meteorological input data and perform soil water balance for that day only:
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])
The output of spwb_day()
is a list with several elements:
## [1] "cohorts" "WaterBalance" "EnergyBalance" "Soil"
## [5] "Stand" "Plants" "RhizoPsi" "SunlitLeaves"
## [9] "ShadeLeaves" "ExtractionInst" "PlantsInst" "SunlitLeavesInst"
## [13] "ShadeLeavesInst" "LightExtinction" "WindExtinction"
Element WaterBalance
contains the soil water balance flows of the day (precipitation, infiltration, transpiration, …)
## PET Rain Snow
## 5.0233468 0.0000000 0.0000000
## NetRain Snowmelt Runon
## 0.0000000 0.0000000 0.0000000
## Infiltration Runoff DeepDrainage
## 0.0000000 0.0000000 0.0000000
## SoilEvaporation PlantExtraction Transpiration
## 0.5000000 0.7756563 0.7756563
## HydraulicRedistribution
## 0.0000000
And Soil
contains water evaporated from each soil layer, water transpired from each soil layer and the final soil water potential:
## SoilEvaporation HydraulicInput HydraulicOutput PlantExtraction psi
## 1 4.999998e-01 0 0.2624687 0.2624687 -0.03487849
## 2 1.529512e-07 0 0.5131876 0.5131876 -0.03363650
Element EnergyBalance
contains subdaily variation in atmosphere, canopy and soil temperatures, as well as canopy and soil energy balance components.
## [1] "Temperature" "CanopyEnergyBalance" "SoilEnergyBalance"
Package medfate
provides a plot
function for objects of class spwb_day
that can be used to inspect the results of the simulation. We use this function to display subdaily dynamics in plant, soil and canopy variables. For example, we can use it to display temperature variations (only the temperature of the topmost soil layer is drawn):
Element Plants
contains output values by plant cohort. Several output variables can be inspected in this element.
## LAI Extraction Transpiration GrossPhotosynthesis NetPhotosynthesis
## T1_54 0.81670117 0.1868303 0.1868303 1.6346265 1.5243646
## T2_68 0.79779523 0.4888219 0.4888219 1.9042466 1.7669343
## S1_65 0.08913325 0.1000041 0.1000041 0.1965344 0.1766032
## RootPsi StemPsi StemPLC LeafPsiMin LeafPsiMax dEdP
## T1_54 -0.4854157 -0.7178573 1.179436e-12 -1.0477141 -0.04775427 0.3964411
## T2_68 -0.4201720 -0.6018091 1.743143e-06 -0.9855218 -0.04662024 1.1125368
## S1_65 -0.4244804 -0.5412868 2.205548e-04 -1.0131542 -0.04908003 1.9455107
## DDS StemRWC LeafRWC StemSympRWC LeafSympRWC WaterBalance
## T1_54 0.058877380 0.9953949 0.9763569 0.9769744 0.9717862 -9.269929e-18
## T2_68 0.018361026 0.9990103 0.9831359 0.9950587 0.9821478 2.818926e-18
## S1_65 0.002513824 0.9989809 0.9836487 0.9957865 0.9793928 -1.436568e-18
While Plants
contains one value per cohort and variable that summarizes the whole simulated day, information by disaggregated by time step can be accessed in PlantsInst
. Moreover, we can use function plot.spwb_day()
to draw plots of sub-daily variation per species of plant transpiration per ground area (L·m\(^{-2}\)), transpiration per leaf area (also in L·m\(^{-2}\)), plant net photosynthesis (in g C·m\(^{-2}\)), and plant water potential (in MPa):
The model distinguishes between sunlit and shade leaves for stomatal regulation. Static properties of sunlit and shade leaves, for each cohort, can be accessed via:
## LAI Vmax298 Jmax298 LeafPsiMin LeafPsiMax GW
## T1_54 0.39267054 48.58012 100.65801 -1.403274 -0.04775427 0.03167233
## T2_68 0.30498777 50.32556 98.82662 -1.668661 -0.04662024 0.06018376
## S1_65 0.02201173 70.01225 114.55776 -1.693565 -0.04908003 0.11515312
## LAI Vmax298 Jmax298 LeafPsiMin LeafPsiMax GW
## T1_54 0.42403063 41.02069 84.99488 -0.8449303 -0.04775427 -99998.98
## T2_68 0.49280746 45.36770 89.09065 -0.6176455 -0.04662024 -99998.96
## S1_65 0.06712152 70.01225 114.55776 -0.7807895 -0.04908003 -99998.88
Instantaneous values are also stored for sunlit and shade leaves. We can also use the plot
function for objects of class spwb_day
to draw instantaneous variations in temperature for sunlit and shade leaves:
Note that sunlit leaves of some species reach temperatures higher than the canopy. We can also plot variations in instantaneous gross and net photosynthesis rates:
Or variations in stomatal conductance:
Or variations in vapour pressure deficit:
Or variations in leaf water potential:
Users will often use function spwb()
to run the soil water balance model for several days. This function requires the spwbInput
object, the soil
object and the meteorological data frame. However, running spwb_day()
modified the input objects. In particular, the soil moisture at the end of the simulation was:
## [1] 0.9888590 0.9959673
And the temperature of soil layers:
## [1] 9.938291 8.032689
We can also see the current state of canopy variables:
## $gdd
## [1] 0
##
## $Temp
## [1] 6.40484
We simply use function resetInputs()
to reset state variables to their default values, so that the new simulation is not affected by the end state of the previous simulation:
## [1] 1 1
## [1] NA NA
## $gdd
## [1] 0
##
## $Temp
## [1] NA
Now we are ready to call function spwb()
. In this example, we only simulate 61 days to save computational time:
## Initial soil water content (mm): 195.696
## Initial snowpack content (mm): 0
## Performing daily simulations .......done.
## Final soil water content (mm): 140.327
## Final snowpack content (mm): 0
## Change in soil water content (mm): -55.369
## Soil water balance result (mm): -55.369
## Change in snowpack water content (mm): 0
## Snowpack water balance result (mm): 0
## Water balance components:
## Precipitation (mm) 36
## Rain (mm) 26 Snow (mm) 10
## Interception (mm) 6 Net rainfall (mm) 20
## Infiltration (mm) 30 Runoff (mm) 0 Deep drainage (mm) 19
## Soil evaporation (mm) 4 Transpiration (mm) 62
## Plant extraction from soil (mm) 62 Plant water balance (mm) -0 Hydraulic redistribution (mm) 0
Function spwb()
returns an object of class spwb. If we inspect its elements, we realize that the output is arranged differently than in spwb_day()
:
## [1] "latitude" "topography" "spwbInput" "soilInput"
## [5] "WaterBalance" "EnergyBalance" "Temperature" "Soil"
## [9] "Stand" "Plants" "SunlitLeaves" "ShadeLeaves"
## [13] "subdaily"
In particular, element spwbInput
contains a copy of the input parameters that were used to run the model:
## [1] "control" "canopy" "cohorts"
## [4] "above" "below" "paramsPhenology"
## [7] "paramsAnatomy" "paramsInterception" "paramsTranspiration"
## [10] "paramsWaterStorage" "internalPhenology" "internalWater"
As before, WaterBalance
contains water balance components, but in this case in form of a data frame with days in rows:
## PET Precipitation Rain Snow NetRain Snowmelt
## 2001-04-20 2.641801 2.1625135 0.0000000 2.162513 0.00000000 0.0000000
## 2001-04-21 1.875251 3.7992356 0.0000000 3.799236 0.00000000 0.0000000
## 2001-04-22 2.903129 4.1962782 0.0000000 4.196278 0.00000000 0.9135326
## 2001-04-23 3.633982 1.4698434 1.4698434 0.000000 0.59989217 9.2444948
## 2001-04-24 3.891957 0.1538991 0.1538991 0.000000 0.06281136 0.0000000
## 2001-04-25 4.171116 0.1317847 0.1317847 0.000000 0.05378573 0.0000000
## Infiltration Runoff DeepDrainage Evapotranspiration Interception
## 2001-04-20 0.00000000 0 0.0000000 0.3737607 0.00000000
## 2001-04-21 0.00000000 0 0.0000000 0.3669824 0.00000000
## 2001-04-22 0.91353255 0 0.1727894 0.4465237 0.00000000
## 2001-04-23 9.84438693 0 9.3978632 1.8692620 0.86995127
## 2001-04-24 0.06281136 0 0.0000000 1.0361939 0.09108774
## 2001-04-25 0.05378573 0 0.0000000 1.1362672 0.07799896
## SoilEvaporation PlantExtraction Transpiration
## 2001-04-20 0.0000000 0.3737607 0.3737607
## 2001-04-21 0.0000000 0.3669824 0.3669824
## 2001-04-22 0.0000000 0.4465237 0.4465237
## 2001-04-23 0.5000000 0.4993107 0.4993107
## 2001-04-24 0.1762646 0.7688415 0.7688415
## 2001-04-25 0.1163853 0.9418829 0.9418829
## HydraulicRedistribution
## 2001-04-20 0.0000000000
## 2001-04-21 0.0000000000
## 2001-04-22 0.0000000000
## 2001-04-23 0.0001523117
## 2001-04-24 0.0000000000
## 2001-04-25 0.0000000000
Elements Plants
is itself a list with several elements that contain daily output results by plant cohorts, for example leaf minimum (midday) water potentials are:
## T1_54 T2_68 S1_65
## 2001-04-20 -0.4633197 -0.4529739 -0.6292173
## 2001-04-21 -0.4393026 -0.4123564 -0.6758212
## 2001-04-22 -0.6063278 -0.6005490 -0.6459482
## 2001-04-23 -0.7481955 -0.6742358 -0.6629441
## 2001-04-24 -0.9720045 -0.8480627 -0.8473573
## 2001-04-25 -1.1920574 -0.9970816 -0.9796658
Package medfate
also provides a plot
function for objects of class spwb
. It can be used to show the meteorological input. Additionally, it can also be used to draw soil and plant variables. In the code below we draw water fluxes, soil water potentials, plant transpiration and plant (mid-day) water potential:
While the simulation model uses daily steps, users may 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:
## W.1 W.2 ML.1 ML.2 MLTot WTD SWE
## 2001-04-01 0.9825649 0.9892045 67.24495 125.88397 193.1289 1000 1.578978
## 2001-05-01 0.9302267 0.9422378 63.66302 119.90710 183.5701 1000 0.000000
## 2001-06-01 0.7758140 0.7818148 53.09529 99.49203 152.5873 1000 0.000000
## PlantExt.1 PlantExt.2 HydraulicInput.1 HydraulicInput.2 psi.1
## 2001-04-01 0.2235982 0.4384614 1.384652e-05 0 -0.03684843
## 2001-05-01 0.3345547 0.6663276 4.294104e-05 0 -0.04975510
## 2001-06-01 0.4069981 0.8460177 8.932938e-04 0 -0.11807384
## psi.2
## 2001-04-01 -0.03525367
## 2001-05-01 -0.04556479
## 2001-06-01 -0.10319953
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:
## T1_54 T2_68 S1_65
## 2001-04-01 0.05231551 0.01502576 0.001843056
## 2001-05-01 0.07348815 0.02353188 0.003550341
## 2001-06-01 0.11148084 0.03641770 0.005483257
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):
## Pinus halepensis Quercus coccifera Quercus ilex
## 2001-04-20 0.03558193 0.0010515180 0.007585715
## 2001-04-21 0.03724680 0.0016296887 0.007757482
## 2001-04-22 0.03925408 0.0010439526 0.010086334
## 2001-04-23 0.03958495 0.0007804469 0.009989884
## 2001-04-24 0.05477671 0.0015912479 0.015049521
## 2001-04-25 0.07233581 0.0025660608 0.021501624
Or we can combine the aggregation by species with a temporal aggregation (here monthly averages):
## Pinus halepensis Quercus coccifera Quercus ilex
## 2001-04-01 0.05231551 0.001843056 0.01502576
## 2001-05-01 0.07348815 0.003550341 0.02353188
## 2001-06-01 0.11148084 0.005483257 0.03641770