Advanced water and energy balance simulation

Miquel De Caceres

2020-05-17

About this vignette

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.

Preparing model inputs

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.

Soils

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.

Species data table

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).

Vegetation

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"

Meteorological forcing

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.

Simulation control

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”):

Water balance input object

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 spwbInputobject 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.

Static analysis of submodels

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.

Vulnerability curves

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.

Supply functions

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.

Stomatal regulation and photosynthesis

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:

Pressure volume curves

Water balance for a single day

Running the model

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:

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"

Water balance output

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

Soil and canopy energy balance

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):

Plant output

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):

Output for sunlit and shade leaves

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: