A Inbuilt parameter estimation

A.1 Introduction

Package medfate has been designed to allow simulations requiring a minimum set of vegetation functional parameters. This entails that several other parameters have to be estimated automatically (via inbuilt procedures) before starting simulations. Inbuilt parameter estimation is done in functions spwbInput() and growthInput(), with the user controlling the process through the species parameter table input (e.g., SpParamsMED) and the object control (see default control values in defaultControl()).

A.2 Strict, scaled and imputable parameters

Different kinds of vegetation functional parameters can be distinguished according to whether inbuilt parameter estimation is possible and how it is conducted:

Strictly-required parameters are those for which there are no inbuilt estimation procedures implemented in the initialization functions. Hence, either values in the species parameter table input are non-missing or suitable values need to be specified before running simulation models. Since medfate ver. 2.3, only plant/leaf classification parameters and plant size parameters are strict. The remaining ones can be estimated from other parameters. This facilitates having a functional species parameter table, because only a set of parameters have to be strictly filled, from either soft trait databases or forest inventory data.
Scaled parameters are functional parameters that cannot be defined at the species level, because they need to be estimated taking into account the size and structure of the plant cohort. These are not normally defined at the level of species parameter table. Specific control parameters are used to determine how scaling is performed.
Imputable parameters parameters are those for which the initialization routines can provide default values or estimations derived from relationships with other parameters. Parameter imputation is conducted if control parameter fillMissingSpParams = TRUE. Sometimes, default parameter values are also specified in the control object.

The following tables describe how the different functional parameters are dealt with, grouped by function. Links are given to the chapter subsections where scaling and/or imputation procedures are described.

Plant/leaf classification

Symbol	R	Description	Strict	Scaled	Imputable
\(GF\)	`GrowthForm`	Growth form, defined depending on the treatment in forest inventory plots (Tree, Shrub or Tree/Shrub)	Yes	No	No
\(LF\)	`LifeForm`	Raunkiaer life form	Yes	No	No
\(L_{shape}\)	`LeafShape`	Leaf type (Linear, Needle, Broad, Scale, Spines or Succulent)	Yes	No	No
\(L_{size}\)	`LeafSize`	Leaf size (Small, Medium, Large)	Yes	No	No
\(L_{pheno}\)	`PhenologyType`	Leaf phenology type	Yes	No	No

Plant size

Symbol	R	Description	Strict	Scaled	Imputable
\(H_{max}\)	`Hmed`	Maximum plant height	Yes	No	No
\(H_{med}\)	`Hmed`	Median plant height	Yes	No	No
\(Z_{50}\)	`Z50`	Depth above which 50% of the fine root mass is located	No	No	A.3.1
\(Z_{95}\)	`Z95`	Depth above which 95% of the fine root mass is located	Yes	No	No
\(Z_{100}\)	`Z100`	Depth above which 100% of the fine root mass is located	No	No	A.3.1

Allometric coefficients

Symbol	R	Description	Strict	Scaled	Imputable
\(a_{ash}\), \(b_{ash}\)	`a_ash`, `b_ash`	Coefficients relating the square of shrub height with shrub area	No	No	A.3.2
\(a_{bsh}\), \(b_{bsh}\)	`a_bsh`, `b_bsh`	Coefficients relating crown volume with dry weight of shrub individuals	No	No	A.3.2
\(cr\)	`cr`	Ratio between crown length and total height for shrubs	No	No	A.3.2
\(a_{fbt}\), \(b_{fbt}\), \(c_{fbt}\)	`a_fbt`, `b_fbt`, `c_fbt`	Coefficients to calculate foliar biomass of an individual tree	No	No	A.3.3
\(a_{cr}\), \(b_{1cr}\), \(b_{2cr}\), \(b_{3cr}\), \(c_{1cr}\), \(c_{2cr}\)	`a_cr`, `b_1cr`, `b_2cr`, `b_3cr`, `c_1cr`, `c_2cr`	Coefficients to calculate crown ratio of trees	No	No	A.3.3
\(a_{cw}\), \(b_{cw}\)	`a_cw`, `b_cw`	Regression coefficients used to calculate the crown width of trees	No	No	A.3.3
\(f_{HD,min}\)	`fHDmin`	Minimum height-to-diameter ratio	No	No	A.3.3
\(f_{HD,max}\)	`fHDmax`	Maximum height-to-diameter ratio	No	No	A.3.3

Leaf phenology

Symbol	R	Description	Strict	Scaled	Imputable
\(LD\)	`LeafDuration`	Average duration of leaves	No	No	A.3.9
\(t_{0,eco}\)	`t0gdd`	Degree days corresponding to leaf budburst	No	No	A.3.9
\(S^*_{eco}\)	`Sgdd`	Degree days corresponding to leaf budburst	No	No	A.3.9
\(T_{eco}\)	`Tbgdd`	Base temperature for the calculation of degree days to leaf budburst	No	No	A.3.9
\(S^*_{sen}\)	`Ssen`	Degree days corresponding to leaf senescence	No	No	A.3.9
\(Ph_{sen}\)	`Phsen`	Photoperiod corresponding to start counting senescence degree-days	No	No	A.3.9
\(T_{sen}\)	`Tbsen`	Base temperature for the calculation of degree days to leaf senescence	No	No	A.3.9
\(x_{sen}\)	`xsen`	Discrete values, to allow for any absent/proportional/more than proportional effects of temperature on senescence	No	No	A.3.9
\(y_{sen}\)	`ysen`	Discrete values, to allow for any absent/proportional/more than proportional effects of photoperiod on senescence	No	No	A.3.9

Plant anatomy

Symbol	R	Description	Strict	Scaled	Imputable
\(1/H_{v}\)	`Al2As`	Ratio of leaf area to sapwood area	No	No	A.3.7
\(RLR\)	`Ar2Al`	Fine root area to leaf area ratio	No	No	A.3.8
\(LW\)	`LeafWidth`	Leaf width	No	No	A.3.4
\(SLA\)	`SLA`	Specific leaf area	No	No	A.3.4
\(\rho_{leaf}\)	`LeafDensity`	Leaf tissue density	No	No	A.3.5
\(\rho_{wood}\)	`WoodDensity`	Wood tissue density	No	No	A.3.5
\(\rho_{fineroot}\)	`FineRootDensity`	Fine root tissue density	No	No	A.3.5
\(f_{conduits}\)	`conduit2sapwood`	Proportion of sapwood corresponding to xylem conduits	No	No	A.3.7
\(SRL\)	`SRL`	Specific fine root length	No	No	A.3.6
\(RLD\)	`RLD`	Fine root length density	No	No	A.3.6
\(r_{6.35}\)	`r635`	Ratio between the weight of leaves plus branches and the weight of leaves alone for branches of 6.35 mm	No	No	A.3.4

Radiation balance and water interception

Symbol	R	Description	Strict	Scaled	Imputable
\(k_{b}\)	`kDIR`	Direct light extinction coefficient	No	No	A.3.11
\(k_{PAR}\)	`kPAR`	PAR extinction coefficient	No	No	A.3.11
\(\alpha_{SWR}\)	`alphaSWR`	Short-wave radiation leaf absorbance coefficient	No	No	A.3.11
\(\gamma_{SWR}\)	`gammaSWR`	Short-wave radiation leaf reflectance (albedo)	No	No	A.3.11
\(s_{water}\)	`g`	Crown water storage capacity	No	No	A.3.11

Hydraulics, transpiration, photosynthesis

Symbol	R	Description	Strict	Scaled	Imputable
\(T_{max, LAI}\)	`Tmax_LAI`	Empirical coefficient relating LAI with the ratio of maximum transpiration over potential evapotranspiration	No	No	A.3.10
\(T_{max, sqLAI}\)	`Tmax_LAIsq`	Empirical coefficient relating squared LAI with the ratio of maximum transpiration over potential evapotranspiration	No	No	A.3.10
\(WUE_{\max}\)	`WUE`	Water use efficiency at VPD = 1kPa and without light or CO2 limitations	No	No	A.3.10
\(WUE_{PAR}\)	`WUE_par`	Coefficient describing the progressive decay of WUE with lower light levels	No	No	A.3.10
\(WUE_{CO2}\)	`WUE_co2`	Coefficient for WUE dependency on atmospheric CO2 concentration	No	No	A.3.10
\(WUE_{VPD}\)	`WUE_vpd`	Coefficient for WUE dependency on vapor pressure deficit	No	No	A.3.10
\(\Psi_{extract}\)	`Psi_Extract`	The water potential at which plant transpiration is 50% of its maximum	No	No	A.3.10
\(\Psi_{critic}\)	`Psi_Critic`	The water potential corresponding to 50% of stem xylem cavitation	No	No	A.3.16
\(g_{swmin}\)	`Gwmin`	Minimum stomatal conductance to water vapour	No	No	A.3.12
\(g_{swmax}\)	`Gwmax`	Maximum stomatal conductance to water vapour	No	No	A.3.12
\(J_{max, 298}\)	`Jmax298`	Maximum rate of electron transport at 298K	No	No	A.3.17
\(V_{max, 298}\)	`Vmax298`	Rubisco’s maximum carboxylation rate at 298K	No	No	A.3.17
\(K_{stem,max,ref}\)	`Kmax_stemxylem`	Maximum stem sapwood reference conductivity per leaf area unit	No	No	A.3.14
\(K_{root,max,ref}\)	`Kmax_rootxylem`	Maximum root sapwood reference conductivity per leaf area unit	No	No	A.3.14
\(k_{leaf, \max}\)	`VCleaf_kmax`	Maximum leaf hydraulic conductance	No	A.4.2	A.3.15
\(k_{stem, \max}\)	`VCstem_kmax`	Maximum stem hydraulic conductance	No	A.4.1	No
\(k_{root, \max,s}\)	`VCroot_kmax`	Maximum root hydraulic conductance for each soil layer	No	A.4.3	No
\(k_{rhizo,\max, s}\)	`VGrhizo_kmax`	Maximum hydraulic conductance of the rhizosphere for each soil layer	No	A.4.4	No
\(c_{leaf}\), \(d_{leaf}\)	`VCleaf_c`, `VCleaf_d`	Parameters of the vulnerability curve for leaves	No	No	A.3.16
\(c_{stem}\), \(d_{stem}\)	`VCstem_c`, `VCstem_d`	Parameters of the vulnerability curve for stem xylem	No	No	A.3.16
\(c_{root}\), \(d_{root}\)	`VCroot_c`, `VCroot_d`	Parameters of the vulnerability curve for root xylem	No	No	A.3.16

Plant water storage

Symbol	R	Description	Strict	Scaled	Imputable
\(\epsilon_{leaf}\)	`LeafEPS`	Modulus of elasticity of leaves	No	No	A.3.13
\(\epsilon_{stem}\)	`StemEPS`	Modulus of elasticity of symplastic xylem tissue	No	No	A.3.13
\(\pi_{0,leaf}\)	`LeafPI0`	Osmotic potential at full turgor of leaves	No	No	A.3.13
\(\pi_{0,stem}\)	`StemPI0`	Osmotic potential at full turgor of symplastic xylem tissue	No	No	A.3.13
\(f_{apo,leaf}\)	`LeafAF`	Apoplastic fraction in leaf tissues	No	No	A.3.13
\(f_{apo,stem}\)	`StemAF`	Apoplastic fraction in stem tissues	No	No	A.3.13
\(V_{leaf}\)	`Vleaf`	Leaf water capacity per leaf area unit	No	A.4.5	No
\(V_{sapwood}\)	`Vsapwood`	Sapwood water capacity per leaf area unit	No	A.4.5	No

Growth and mortality

Symbol	R	Description	Strict	Scaled	Imputable
\(N_{leaf}\)	`Nleaf`	Leaf nitrogen concentration per dry mass	No	No	A.3.18
\(N_{sapwood}\)	`Nsapwood`	Sapwood nitrogen concentration per dry mass	No	No	A.3.18
\(N_{fineroot}\)	`Nfineroot`	Fine root nitrogen concentration per dry mass	No	No	A.3.18
\(MR_{leaf}\)	`RERleaf`	Leaf respiration rate at 20 ºC	No	No	A.3.18
\(MR_{sapwood}\)	`RERsapwood`	Living sapwood (parenchymatic tissue) respiration rate at 20 ºC	No	No	A.3.18
\(MR_{fineroot}\)	`RERfineroot`	Fine root respiration rate at 20 ºC	No	No	A.3.18
\(RGR_{leaf, max}\)	`RGRleafmax`	Maximum leaf area daily growth rate, relative to sapwood area	No	No	A.3.19
\(RGR_{cambium, max}\)	`RGRsapwoodmax`	Maximum tree daily sapwood growth rate relative to cambium perimeter length	No	No	A.3.19
\(RGR_{sapwood, max}\)	`RGRsapwoodmax`	Maximum shrub daily sapwood growth rate relative to sapwood area	No	No	A.3.19
\(RGR_{fineroot, max}\)	`RGRfinerootmax`	Maximum daily fine root relative growth rate	No	No	A.3.19
\(SR_{sapwood}\)	`SRsapwood`	Daily sapwood senescence rate	No	No	A.3.20
\(SR_{fineroot}\)	`SRfineroot`	Daily fine root senescence rate	No	No	A.3.20
\(RSSG\)	`RSSG`	Minimum relative starch for sapwood growth	No	No	A.3.21
\(C_{wood}\)	`WoodC`	Wood carbon content per dry weight	No	No	A.3.22
\(P_{mort,base}\)	`MortalityBaselineRate`	Default deterministic proportion or probability specifying the baseline reduction of cohort’s density occurring in a year	No	No	A.3.23

Recruitment

Symbol	R	Description	Strict	Scaled	Imputable
\(H_{seed}\)	`SeedProductionHeight`	Minimum height for seed production	No	No	A.3.24
\(TCM_{recr}\)	`MinTempRecr`	Minimum average temperature (Celsius) of the coldest month for successful recruitment	No	No	A.3.24
\(MI_{recr}\)	`MinMoistureRecr`	Minimum value of the moisture index for successful recruitment	No	No	A.3.24
\(FPAR_{recr}\)	`MinFPARRecr`	Minimum percentage of PAR at the ground level for successful recruitment	No	No	A.3.24
\(DBH_{recr}\)	`RecrTreeDBH`	Recruitment DBH for trees	No	No	A.3.24
\(H_{tree, recr}\)	`RecrTreeHeight`	Recruitment height for trees	No	No	A.3.24
\(N_{tree, recr}\)	`RecrTreeDensity`	Recruitment density for trees	No	No	A.3.24
\(Cover_{shrub, recr}\)	`RecrShrubCover`	Recruitment cover for shrubs	No	No	A.3.24
\(H_{shrub, recr}\)	`RecrShrubHeight`	Recruitment height for shrubs	No	No	A.3.24
\(Z50_{recr}\)	`RecrZ50`	Soil depth corresponding to 50% of fine roots for recruitment	No	No	A.3.24
\(Z95_{recr}\)	`RecrZ95`	Soil depth corresponding to 95% of fine roots for recruitment	No	No	A.3.24

Flammability

Symbol	R	Description	Strict	Scaled	Imputable
\(\rho_{p}\)	`PD`	Density of fuel particles	No	No	A.3.25
\(\sigma\)	`SAV`	Surface-area-to-volume ratio of the small fuel (1h) fraction (leaves and branches < 6.35mm)	No	No	A.3.25
\(h\)	`HeatContent`	High fuel heat content.	No	No	A.3.25
\(LI\)	`PercentLignin`	Percentage of lignin in leaves	No	No	A.3.25

A.3 Imputation of missing values

The following figure summarizes the percentage of missing values in SpParamsMED for different model parameters and the other model parameters used for the imputation of missing values:

Representation of imputation relationships between model parameters. The percentage of missing parameter values increases from left to right. Left-most parameters are strict.

Figure A.1: Representation of imputation relationships between model parameters. The percentage of missing parameter values increases from left to right. Left-most parameters are strict.

A.3.1 Rooting depth

Parameter \(Z_{95}\) is a strict parameter, but \(Z_{50}\) and \(Z_{100}\) can be imputed when missing, using the following formulae: \[\begin{eqnarray} Z_{50} &=& \exp(\log(Z_{95})/1.4) \\ Z_{100} &=& \exp(\log(Z_{95})/0.95) \end{eqnarray}\]

Note that \(Z_{100}\) will be imputed only if truncateRootDistribution = TRUE in the control parameters.

A.3.2 Shrub allometric coefficients

Missing shrub allometric coefficients are filled using information from Raunkiaer’s life form and maximum plant height (\(H_{max}\)).

Life form	\(H_{max}\)	\(a_{ash}\)	\(b_{ash}\)	\(a_{bsh}\)	\(b_{bsh}\)	\(cr\)
Chamaephyte	[any]	24.5888	1.1662	0.7963	0.3762	0.8076
Phanerophyte	< 300 cm	1.0083	1.8700	0.7900	0.6942	0.6630
Phanerophyte	> 300 cm	5.8458	1.4944	0.3596	0.7138	0.7190
(Hemi)cryptophyte	[any]	24.5888	1.1662	0.7963	0.3762	0.9500

Allometric coefficients were taken from De Cáceres et al. (2019).

A.3.3 Tree allometric coefficients

Missing tree allometric coefficients are replaced with values depending on whether the plant species is a gymnosperm or an angiosperm:

Parameter	Gymnosperm	Angiosperm
\(a_{fbt}\)	0.1300	0.0527
\(b_{fbt}\)	1.2285	1.5782
\(c_{fbt}\)	-0.0147	-0.0066
\(a_{cw}\)	0.747	0.839
\(b_{cw}\)	0.672	0.735
\(a_{cr}\)	1.995	1.506
\(b_{1cr}\)	-0.649	-0.706
\(b_{2cr}\)	-0.020	-0.078
\(b_{3cr}\)	-0.00012	0.00018
\(c_{1cr}\)	-0.004	-0.007
\(c_{2cr}\)	-0.159	0.000
\(fHD_{min}\)	80	40
\(fHD_{max}\)	120	140

A.3.4 Leaf width, specific leaf area and fine foliar ratio

Leaf width (\(LW\)), specific leaf area (\(SLA\)) and the ratio between the weight of leaves plus branches and the weight of leaves alone for branches of 6.35 mm (\(r_{6.35}\)) are key anatomical parameters. When missing from species parameter table, default estimates for these parameters are obtained from combinations of leaf shape and leaf size:

Leaf shape	Leaf size	\(SLA\)	\(LW\)	\(r_{6.35}\)
Broad	Large	16.039	6.898	2.278
Broad	Medium	11.499	3.054	2.359
Broad	Small	9.540	0.644	3.026
Linear	Large	5.522	0.639	3.261
Linear	Medium	4.144	0.639	3.261
Linear	Small	13.189	0.639	3.261
Needle	[any]	9.024	0.379	1.716
Spines	[any]	9.024	0.379	1.716
Scale	[any]	4.544	0.101	1.483

These estimates have been obtained by averaging species-level values across combinations of the categorical variables.

A.3.5 Tissue density

Default values for the dry weight density of leaves and wood (in \(g \cdot cm^{-3}\)) are determined from taxonomic family using an internal data set (medfate:::trait_family_means):

Table A.1: Default leaf density and wood density values by taxonomic family.
	LeafDensity	WoodDensity
Acanthaceae	0.2310902	0.5981987
Achariaceae	0.3622472	0.5929146
Achatocarpaceae	NA	0.8700000
Acoraceae	0.1000000	0.2150687
Actinidiaceae	0.3853788	0.3661986
Aextoxicaceae	NA	0.5665464
Aizoaceae	0.0824125	0.1309780
Akaniaceae	NA	0.5643064
Alismataceae	0.1770311	0.1003792
Altingiaceae	0.6833971	0.5793130
Alzateaceae	NA	0.6618027
Amaranthaceae	0.1992600	0.4491914
Amaryllidaceae	0.1274997	0.1243875
Anacardiaceae	0.4272640	0.5525121
Anemiaceae	0.4485000	NA
Anisophylleaceae	NA	0.5925310
Annonaceae	0.3647908	0.5327526
Aphloiaceae	0.4627060	0.6196231
Apiaceae	0.3266250	0.2683729
Apocynaceae	0.2992119	0.5413259
Aquifoliaceae	0.3669026	0.5761555
Araceae	0.1784983	0.0884992
Araliaceae	0.2815114	0.4109454
Araucariaceae	0.3673951	0.4604497
Arecaceae	0.4233905	0.5766195
Aristolochiaceae	0.2681434	0.2450201
Asparagaceae	0.1876144	0.2853077
Asphodelaceae	0.5572184	0.4161553
Aspleniaceae	0.3415951	0.3000000
Asteraceae	0.2327573	0.4010659
Asteropeiaceae	NA	0.8147979
Atherospermataceae	0.2400872	0.4954002
Athyriaceae	0.1300500	NA
Austrobaileyaceae	0.2620992	0.3633400
Balanopaceae	NA	0.7292784
Balsaminaceae	0.3896645	0.1610732
Basellaceae	NA	0.2000000
Begoniaceae	0.1626789	0.0505647
Berberidaceae	0.3969251	0.6689267
Berberidopsidaceae	NA	0.3300000
Betulaceae	0.4943342	0.5715354
Bignoniaceae	0.3551775	0.5682189
Bixaceae	0.3630204	0.3281375
Blechnaceae	0.3147993	0.3706000
Bonnetiaceae	0.2797829	0.7998694
Boraginaceae	0.3017691	0.4622858
Brassicaceae	0.2447160	0.2042822
Bromeliaceae	0.1775524	0.2232105
Brunelliaceae	NA	0.3786244
Bruniaceae	NA	0.5639571
Burseraceae	0.4207978	0.5195267
Butomaceae	NA	0.1008326
Buxaceae	0.2706294	0.6034565
Cactaceae	0.1531726	0.5706428
Calophyllaceae	0.3939765	0.6102283
Calycanthaceae	0.3654239	0.6294628
Calyceraceae	0.1689366	0.1639900
Campanulaceae	0.2293807	0.2235703
Canellaceae	NA	0.6665330
Cannabaceae	0.3131495	0.5273109
Capparaceae	0.3795366	0.6065482
Caprifoliaceae	0.2945652	0.3662727
Cardiopteridaceae	NA	0.5116202
Caricaceae	0.2520206	0.1638124
Caryocaraceae	0.4728080	0.6595063
Caryophyllaceae	0.1994095	0.2119747
Casuarinaceae	0.7304083	0.7175374
Celastraceae	0.3968452	0.6277886
Centroplacaceae	NA	0.6543534
Cephalotaxaceae	NA	0.5314087
Ceratophyllaceae	NA	0.1568096
Cercidiphyllaceae	0.2896931	0.4496726
Chloranthaceae	0.1869660	0.3447274
Chrysobalanaceae	0.4003510	0.7635310
Cibotiaceae	NA	0.2600000
Cistaceae	0.3033082	0.2496262
Cleomaceae	NA	0.5494493
Clethraceae	0.5035936	0.4745893
Clusiaceae	0.3425793	0.6321076
Colchicaceae	NA	0.1358900
Columelliaceae	NA	0.3947403
Combretaceae	0.3519810	0.6205452
Commelinaceae	0.1758634	0.1066381
Connaraceae	0.4140614	0.5334766
Convolvulaceae	0.2589092	0.3981555
Coriariaceae	NA	0.5421684
Cornaceae	0.3363286	0.5679732
Corynocarpaceae	0.2498751	0.5719471
Crassulaceae	NA	0.1339248
Crypteroniaceae	NA	0.5566678
Ctenolophonaceae	NA	0.7795964
Cucurbitaceae	0.2517204	0.2499163
Cunoniaceae	0.4004446	0.5626879
Cupressaceae	0.3387614	0.4965447
Curtisiaceae	NA	0.7502920
Cyatheaceae	0.1297339	0.4198563
Cycadaceae	0.6579167	NA
Cyperaceae	0.3803538	0.2653759
Cyrillaceae	NA	0.6033612
Cystopteridaceae	0.2532393	NA
Daphniphyllaceae	NA	0.4929575
Davalliaceae	0.2300000	NA
Degeneriaceae	NA	0.3386660
Dennstaedtiaceae	0.4023875	0.3000000
Diapensiaceae	NA	0.2792700
Dichapetalaceae	0.3396426	0.6078527
Dicksoniaceae	0.4697549	NA
Didiereaceae	NA	0.3823914
Dilleniaceae	0.3435600	0.5703766
Dioscoreaceae	0.1793296	0.4758931
Dipentodontaceae	0.2965124	0.4853172
Dipterocarpaceae	0.4602906	0.6000863
Distichiaceae	NA	0.4800000
Droseraceae	0.1342673	0.1674038
Dryopteridaceae	0.3183348	0.4330000
Ebenaceae	0.4251667	0.6971571
Elaeagnaceae	0.3121046	0.5360191
Elaeocarpaceae	0.4168437	0.5367562
Elatinaceae	NA	0.1954300
Ephedraceae	NA	0.7800000
Equisetaceae	0.2590369	0.2006271
Ericaceae	0.4140529	0.5982991
Erythroxylaceae	0.3288289	0.7017518
Escalloniaceae	0.2192402	0.5417501
Eucommiaceae	NA	0.7620000
Euphorbiaceae	0.3282755	0.4623727
Euphroniaceae	NA	0.6200000
Eupomatiaceae	0.2445709	0.4786317
Eupteleaceae	NA	0.5085121
Fabaceae	0.3818876	0.6420488
Fagaceae	0.4563950	0.7549043
Flagellariaceae	NA	0.4166889
Fouquieriaceae	0.2453718	NA
Francoaceae	0.2942168	0.6216474
Frankeniaceae	NA	0.5000000
Garryaceae	0.3937368	0.6919549
Gelsemiaceae	NA	0.6350000
Gentianaceae	0.2770247	0.6378318
Geraniaceae	0.3375530	0.2003237
Gesneriaceae	0.1013848	0.4571409
Ginkgoaceae	0.2224367	0.4690176
Gleicheniaceae	0.4916560	NA
Gnetaceae	0.3000000	0.5698692
Goodeniaceae	0.2051090	0.5170666
Goupiaceae	0.4660717	0.7237935
Griseliniaceae	NA	0.5872083
Grossulariaceae	0.3485915	0.6321564
Gyrostemonaceae	NA	0.3484853
Haloragaceae	0.1312446	0.1387809
Hamamelidaceae	0.4927203	0.6208086
Hernandiaceae	0.4152598	0.3072347
Himantandraceae	NA	0.4679312
Humiriaceae	0.4891605	0.7677334
Hydrangeaceae	0.1690825	0.5080759
Hydrocharitaceae	0.4004979	0.0913568
Hymenophyllaceae	0.4053143	NA
Hypericaceae	0.2904221	0.5335419
Hypoxidaceae	0.1299171	NA
Icacinaceae	0.5382570	0.4687041
Iridaceae	0.2861913	0.2656611
Irvingiaceae	NA	0.8676422
Iteaceae	NA	0.6500000
Ixonanthaceae	0.3649649	0.6609945
Juglandaceae	0.4807922	0.5092280
Juncaceae	0.2039020	0.2480501
Juncaginaceae	NA	0.1314000
Kirkiaceae	NA	0.5053267
Lacistemataceae	0.2326940	0.5051846
Lamiaceae	0.2808167	0.4078139
Lauraceae	0.4219117	0.5251415
Lecythidaceae	0.4252525	0.6308205
Lentibulariaceae	NA	0.1148845
Lepidobotryaceae	NA	0.4958449
Liliaceae	0.1000000	0.1127077
Linaceae	0.3285808	0.5785248
Linderniaceae	0.0590000	0.1403948
Loasaceae	0.2700000	NA
Loganiaceae	0.4011219	0.6172494
Loranthaceae	0.4175607	0.5281071
Lycopodiaceae	0.4802434	NA
Lygodiaceae	0.5066007	NA
Lythraceae	0.4022554	0.5753905
Magnoliaceae	0.3194220	0.4746065
Malpighiaceae	0.2996019	0.5912761
Malvaceae	0.3125575	0.4674502
Marcgraviaceae	0.1698113	0.4362610
Marsileaceae	0.2430000	NA
Melanthiaceae	0.1811793	0.1469991
Melastomataceae	0.3062381	0.5548110
Meliaceae	0.3601542	0.5485740
Menispermaceae	0.3685390	0.4782935
Menyanthaceae	0.1224487	0.1654287
Metteniusaceae	0.3927588	0.5487151
Molluginaceae	0.1400000	NA
Monimiaceae	0.2820634	0.4857449
Montiaceae	0.0859106	0.1353818
Moraceae	0.3368104	0.5197178
Moringaceae	NA	0.2611627
Muntingiaceae	0.3376553	0.3805000
Myodocarpaceae	NA	0.5470802
Myricaceae	0.3885906	0.5725421
Myristicaceae	0.3847458	0.4853322
Myrtaceae	0.4463350	0.6944200
Nartheciaceae	NA	0.1358900
Nelumbonaceae	NA	0.1144600
Nephrolepidaceae	0.1720000	NA
Nitrariaceae	NA	0.2547468
Nothofagaceae	0.4440280	0.5887117
Nyctaginaceae	0.2332418	0.4634826
Nymphaeaceae	NA	0.1694307
Nyssaceae	0.4925194	0.4861665
Ochnaceae	0.4521852	0.7445164
Olacaceae	0.4041490	0.7159514
Oleaceae	0.4202768	0.6907926
Onagraceae	0.2956682	0.2408648
Onocleaceae	0.2663707	NA
Ophioglossaceae	0.2025797	NA
Opiliaceae	0.3161129	0.7071164
Orchidaceae	0.1958100	0.3617788
Orobanchaceae	0.2464242	0.2582964
Osmundaceae	0.2614744	NA
Oxalidaceae	0.2731828	0.4819666
Paeoniaceae	0.2851982	0.4237290
Pandaceae	0.4000000	0.5886261
Pandanaceae	NA	0.3616584
Papaveraceae	0.3995381	0.2186988
Paracryphiaceae	0.4686036	0.5111858
Passifloraceae	0.2256141	0.4809513
Paulowniaceae	NA	0.2558340
Penaeaceae	NA	0.7374920
Pennantiaceae	NA	0.4890300
Pentaphylacaceae	0.3613636	0.5529800
Penthoraceae	0.1942110	NA
Peraceae	0.3914384	0.6847804
Peridiscaceae	NA	0.7022541
Petiveriaceae	0.2459257	0.4886309
Phrymaceae	0.1098008	0.5026328
Phyllanthaceae	0.2964189	0.6083502
Phytolaccaceae	0.2966153	0.2135265
Picramniaceae	0.4300212	0.5489201
Picrodendraceae	0.8566338	0.7469544
Pinaceae	0.3252366	0.5494595
Piperaceae	0.2317202	0.3022284
Pittosporaceae	0.3454131	0.6380359
Plantaginaceae	0.2457856	0.2496493
Platanaceae	0.5125387	0.5075861
Plumbaginaceae	0.2039055	0.4009266
Poaceae	0.4286284	0.2930797
Podocarpaceae	0.5279975	0.5011060
Polemoniaceae	0.2438751	0.2767809
Polygalaceae	0.2522276	0.6025810
Polygonaceae	0.3043490	0.5030070
Polypodiaceae	0.3286179	NA
Pontederiaceae	0.1500000	0.0980497
Portulacaceae	0.3800000	0.1613700
Potamogetonaceae	0.1636516	0.1566868
Primulaceae	0.2727519	0.5559870
Proteaceae	0.4782523	0.6170314
Pteridaceae	0.1928298	NA
Putranjivaceae	0.3928464	0.6848579
Ranunculaceae	0.2701728	0.2075756
Resedaceae	0.1507363	0.2849534
Rhabdodendraceae	0.2511215	0.7389675
Rhamnaceae	0.4207970	0.6291283
Rhizophoraceae	0.3513338	0.7155434
Ripogonaceae	NA	0.4793500
Rosaceae	0.4167064	0.6149021
Rousseaceae	NA	0.5923332
Rubiaceae	0.2961776	0.5373021
Ruppiaceae	NA	0.1669700
Rutaceae	0.3364140	0.6351832
Sabiaceae	0.2269258	0.4553299
Salicaceae	0.3629298	0.5460071
Salvadoraceae	NA	0.5927267
Santalaceae	0.3134227	0.6689317
Sapindaceae	0.4134253	0.6517107
Sapotaceae	0.4234042	0.6755645
Sarcolaenaceae	NA	0.8715990
Sarraceniaceae	NA	0.2006700
Saxifragaceae	0.1191451	0.1879898
Schisandraceae	NA	0.5612605
Schoepfiaceae	0.3474414	0.7147271
Sciadopityaceae	NA	0.6320000
Scrophulariaceae	0.4126767	0.6475876
Selaginellaceae	0.2176000	0.2933500
Simaroubaceae	0.3002075	0.4061432
Siparunaceae	0.2188592	0.4890548
Sladeniaceae	NA	0.5700000
Smilacaceae	0.2017709	0.6206841
Solanaceae	0.2302326	0.4316266
Stachyuraceae	NA	0.5600000
Staphyleaceae	0.2801318	0.3786974
Stemonuraceae	0.3123012	0.5432797
Stilbaceae	0.4577089	0.6769478
Strasburgeriaceae	0.4306632	NA
Styracaceae	0.3603805	0.4391644
Surianaceae	0.2843963	0.8299023
Symplocaceae	0.4066931	0.5120362
Talinaceae	0.2671358	0.1482700
Tamaricaceae	NA	0.6197357
Tapisciaceae	NA	0.3971646
Taxaceae	0.4541759	0.5899917
Tetramelaceae	NA	0.3020393
Tetrameristaceae	NA	0.6155117
Theaceae	0.4120753	0.5769310
Thymelaeaceae	0.3084940	0.4975963
Tofieldiaceae	NA	0.2301024
Torricelliaceae	0.3561337	NA
Trigoniaceae	NA	0.6959254
Trochodendraceae	NA	0.3874550
Tropaeolaceae	NA	0.1696033
Typhaceae	0.1890320	0.1599894
Ulmaceae	0.4582164	0.6155479
Urticaceae	0.3056832	0.3202581
Velloziaceae	0.3115000	NA
Verbenaceae	0.3328344	0.4765360
Viburnaceae	0.4007504	0.4996133
Violaceae	0.3067478	0.5262725
Vitaceae	0.2071073	0.3553502
Vochysiaceae	0.3618973	0.5366080
Welwitschiaceae	NA	0.4640000
Winteraceae	0.3587840	0.4861082
Zamiaceae	0.4044942	0.3661833
Zingiberaceae	NA	0.1540300
Zosteraceae	NA	0.1003700
Zygophyllaceae	0.4236423	0.8986018

If the family is not any of those in the table, default values are \(\rho_{leaf} = 0.7\) and \(\rho_{wood} = 0.652\). The default value for fine root density is always \(\rho_{fineroot} = 0.165\).

A.3.6 Specific root length and root length density

Default values for specific fine root length and fine root length density are \(3870\, cm \cdot g^{-1}\) and \(10\, cm \cdot cm^{-3}\), respectively. [JUSTIFICATION MISSING]

A.3.7 Huber value and ratio of conduits to sapwood

Missing values for Al2As, the inverse of the Huber value (\(1/Hv\)) are determined from taxonomic family using an internal data set (medfate:::trait_family_means):

Table A.2: Default leaf area to sapwood area (m2/m2) / Huber value (cm2/m2) and fraction of sapwood corresponding to conduits by taxonomic family.
	Al2As	Hv	conduit2sapwood
Acanthaceae	1803.6645	5.5442683	0.6300000
Achariaceae	8300.0000	1.2048193	NA
Actinidiaceae	11543.4188	0.8662945	NA
Aextoxicaceae	66666.6667	0.1500000	NA
Altingiaceae	6472.3731	1.5450284	0.8015000
Amaranthaceae	973.0677	10.2767778	NA
Amborellaceae	4257.6596	2.3487082	NA
Anacardiaceae	21764.4502	0.4594649	0.7105300
Annonaceae	9203.3824	1.0865570	0.5603750
Apiaceae	1389.4314	7.1971890	NA
Apocynaceae	20941.4964	0.4775208	0.7112500
Aquifoliaceae	7414.6991	1.3486724	0.6528500
Araliaceae	5044.9277	1.9821890	0.7785000
Araucariaceae	3860.5770	2.5902864	0.9375000
Arecaceae	9560.5163	1.0459686	NA
Asteraceae	2465.6724	4.0556888	0.7098857
Atherospermataceae	5080.5040	1.9683086	0.7560000
Austrobaileyaceae	15384.6154	0.6500000	NA
Berberidaceae	3461.9656	2.8885325	NA
Betulaceae	6262.0017	1.5969335	0.8305000
Bignoniaceae	15502.7818	0.6450455	0.6325556
Bixaceae	1758.3128	5.6872701	0.7070000
Boraginaceae	9807.0622	1.0196734	0.6300000
Burseraceae	16869.9644	0.5927695	0.8204286
Buxaceae	NA	NA	0.8330000
Cactaceae	2339.3221	4.2747427	0.3574375
Calophyllaceae	186.1379	53.7236013	0.7335000
Calycanthaceae	3400.6803	2.9405881	0.6535500
Cannabaceae	8831.3429	1.1323306	0.7497500
Capparaceae	31194.7329	0.3205669	0.7005000
Caprifoliaceae	6676.0300	1.4978962	NA
Caryocaraceae	4219.6483	2.3698657	NA
Casuarinaceae	3539.4588	2.8252907	NA
Celastraceae	10374.6170	0.9638910	NA
Chloranthaceae	4545.4550	2.1999998	NA
Chrysobalanaceae	NA	NA	0.5876000
Cistaceae	2033.6941	4.9171604	NA
Clusiaceae	7794.8918	1.2828914	0.5005000
Combretaceae	30131.5424	0.3318781	0.6378214
Coriariaceae	7330.3881	1.3641843	NA
Cornaceae	7974.5466	1.2539898	0.6740000
Cunoniaceae	6686.8312	1.4954767	0.7110000
Cupressaceae	2257.7750	4.4291393	0.9204471
Daphniphyllaceae	5054.9451	1.9782609	NA
Dilleniaceae	5414.7340	1.8468128	0.5432500
Dipterocarpaceae	NA	NA	0.7043750
Ebenaceae	10188.3995	0.9815084	0.6300000
Elaeagnaceae	5807.3021	1.7219700	0.5641000
Elaeocarpaceae	7243.7219	1.3805058	0.6970000
Ericaceae	4049.6552	2.4693460	0.7423400
Erythroxylaceae	13269.8867	0.7535859	NA
Escalloniaceae	NA	NA	0.5755000
Euphorbiaceae	7787.9196	1.2840400	0.6699375
Eupomatiaceae	12399.6999	0.8064711	0.6010000
Eupteleaceae	10863.6388	0.9205019	NA
Fabaceae	8713.9029	1.1475914	0.6085936
Fagaceae	2483.9302	4.0258780	0.6263370
Garryaceae	3188.9011	3.1358765	NA
Gnetaceae	9742.2564	1.0264563	NA
Goodeniaceae	1871.0000	5.3447354	NA
Goupiaceae	NA	NA	0.6360000
Grossulariaceae	7145.4018	1.3995014	NA
Hamamelidaceae	5312.9552	1.8821917	NA
Hernandiaceae	7544.0224	1.3255528	0.6350000
Humiriaceae	NA	NA	0.7292500
Hydrangeaceae	8830.6060	1.1324251	NA
Hypericaceae	8535.3570	1.1715972	NA
Iteaceae	3507.1429	2.8513238	NA
Juglandaceae	15184.2700	0.6585763	0.7167500
Lamiaceae	6395.0891	1.5636999	0.6936538
Lardizabalaceae	23364.4860	0.4280000	NA
Lauraceae	8287.4007	1.2066510	0.6915000
Lecythidaceae	7479.9092	1.3369146	0.5955000
Linaceae	6600.0000	1.5151515	0.7125000
Loranthaceae	1132.0417	8.8335972	NA
Lythraceae	7059.8168	1.4164673	0.6600000
Magnoliaceae	10365.0443	0.9647812	0.8189375
Malpighiaceae	12032.1276	0.8311082	NA
Malvaceae	5655.4751	1.7681980	0.5270412
Melastomataceae	8340.9425	1.1989053	NA
Meliaceae	14895.4904	0.6713441	0.6461538
Metteniusaceae	NA	NA	0.6300000
Monimiaceae	2343.6667	4.2668184	NA
Moraceae	10486.8078	0.9535790	0.5184000
Myricaceae	5600.0000	1.7857143	NA
Myristicaceae	6784.6014	1.4739259	0.6990000
Myrtaceae	5265.0764	1.8993077	0.6906786
Nothofagaceae	1890.9966	5.2882169	NA
Nyctaginaceae	50930.0144	0.1963479	NA
Nyssaceae	6432.1927	1.5546798	0.8282500
Ochnaceae	25322.6647	0.3949031	0.6960000
Olacaceae	NA	NA	0.7601000
Oleaceae	6559.7773	1.5244420	0.7426167
Opiliaceae	6800.0000	1.4705882	NA
Paeoniaceae	15250.3590	0.6557223	NA
Pandaceae	8941.1121	1.1184291	NA
Paracryphiaceae	2838.0000	3.5236082	NA
Passifloraceae	NA	NA	0.3455000
Pentaphylacaceae	6994.3829	1.4297187	NA
Peraceae	NA	NA	0.6800000
Petiveriaceae	88497.7876	0.1129972	NA
Phrymaceae	1943.8530	5.1444219	0.5515000
Phyllanthaceae	7361.9917	1.3583281	0.6230000
Picramniaceae	NA	NA	0.6370000
Picrodendraceae	5700.9416	1.7540962	0.5635000
Pinaceae	2764.5688	3.6172006	0.9258273
Piperaceae	18974.0741	0.5270349	NA
Pittosporaceae	6546.2106	1.5276013	NA
Plantaginaceae	1022.7190	9.7778569	NA
Platanaceae	NA	NA	0.6000000
Podocarpaceae	3336.3567	2.9972814	0.9086667
Polygalaceae	10338.1895	0.9672874	NA
Polygonaceae	NA	NA	0.8932000
Primulaceae	5791.5681	1.7266481	0.5600000
Proteaceae	3157.2469	3.1673164	0.5774167
Ranunculaceae	NA	NA	0.8130000
Rhamnaceae	4744.9248	2.1075149	0.8077222
Rhizophoraceae	4539.2194	2.2030219	0.7810000
Rosaceae	8157.7904	1.2258221	0.7084800
Rubiaceae	9822.6685	1.0180533	0.6739571
Rutaceae	7314.1224	1.3672180	0.7235000
Sabiaceae	11140.9740	0.8975876	NA
Salicaceae	9721.0844	1.0286918	0.7525000
Santalaceae	3405.9897	2.9360042	0.6450000
Sapindaceae	5504.7720	1.8166057	0.7548077
Sapotaceae	9552.9633	1.0467956	0.5657500
Schisandraceae	5468.5275	1.8286458	NA
Scrophulariaceae	1893.1314	5.2822535	NA
Simaroubaceae	6378.8105	1.5676904	0.5160000
Smilacaceae	10275.7248	0.9731674	NA
Solanaceae	15730.1525	0.6357217	0.7681667
Stachyuraceae	5647.6744	1.7706403	NA
Staphyleaceae	5796.1430	1.7252852	NA
Stemonuraceae	9030.1376	1.1074028	0.4470000
Styracaceae	5310.8433	1.8829402	NA
Symplocaceae	5320.6654	1.8794642	NA
Tamaricaceae	3386.6942	2.9527319	NA
Taxaceae	NA	NA	0.8600000
Theaceae	7777.0065	1.2858418	NA
Thymelaeaceae	2208.8388	4.5272656	0.8361500
Trochodendraceae	14951.4572	0.6688311	NA
Ulmaceae	35822.2922	0.2791558	0.7650000
Urticaceae	20290.3995	0.4928439	0.6850000
Verbenaceae	NA	NA	0.7923500
Viburnaceae	6796.7308	1.4712956	NA
Violaceae	1050.2101	9.5219044	0.4460000
Vitaceae	10890.6791	0.9182164	0.5700000
Vochysiaceae	2455.8417	4.0719236	0.6060000
Winteraceae	2662.0146	3.7565533	NA
Zygophyllaceae	NA	NA	0.7712000

If there is no information derived from taxonomic family for Al2As, a default value is given depending on leaf shape and leaf size:

Leaf shape	Leaf size	`Al2As`
Broad	Large	4768.7
Broad	Medium	2446.1
Broad	Small	2284.9
Linear	Large	2156.0
Linear	Medium	2156.0
Linear	Small	2156.0
Needle	[any]	2751.7
Scale	[any]	1696.6

Missing values for \(f_{conduits}\), the fraction of sapwood corresponding to conduits are derived from taxonomic family (see table above). If information from taxonomic family is missing, default values are \(f_{conduits} = 0.7\) (i.e. 30% of parenchyma) for angiosperms, and \(f_{conduits} = 0.925\) (i.e. 7.5% of parenchyma) for gymnosperms (Plavcová & Jansen 2015).

A.3.8 Fine root to leaf area ratio

When missing, the fine root area to leaf area ratio is given a default value of \(RLR = 1\; m^2\cdot m^{-2}\).

A.3.9 Leaf phenology

When missing, leaf duration is assigned a value of 1 year for winter-deciduous species and 2.41 years for the remaining leaf phenology types.

Default values for leaf phenological parameters are the same regardless of the leaf phenology type:

Phenology type	`t0gdd`	`Sgdd`	`Ssen`	`Phsen`	`Tbsen`	`xsen`	`ysen`
One-flush evergreen	50	200	8268	12.5	28.5	2	2
Winter deciduous	50	200	8268	12.5	28.5	2	2
Winter semi-deciduous	50	200	8268	12.5	28.5	2	2
Drought deciduous	50	200	8268	12.5	28.5	2	2

Leaf senescence values were derived for deciduous broad-leaved forests by Delpierre et al. (2009).

A.3.10 Basic transpiration and water-use efficiency

When the basic soil water balance model is used, \(T_{max,LAI}\) and \(T_{max,sqLAI}\) are species-specific parameters that regulate the maximum transpiration of plant cohorts (see 6.1.1). When these parameters are missing from SpParams table, they are given default values \(T_{max,LAI} = 0.134\) and \(T_{max,sqLAI} = -0.006\), according to Granier et al. (1999).

When maximum water use efficiency (\(WUE_{\max}\)) is missing, it is given a value of \(WUE_{\max} = 7.55\). By default, the coefficient describing the decay of water use efficiency with lower light levels is given a default value of \(WUE_{PAR} = 0.2812\), and the coefficient regulating the relationship between gross photosynthesis and CO2 concentration is given a default \(WUE_{CO2} = 0.0028\).

When missing, the water potential corresponding to 50% of transpiration (\(\Psi_{extract}\)) is estimated by calculating the water potential corresponding to the loss leaf turgor (\(\Psi_{tlp}\)), using equation (10.4) from Bartlett et al. (2012). The parameters of the leaf pressure-volume curve needed for applying equation (10.4) may be themselves estimated (see A.3.13). Note that \(\Psi_{tlp}\) has been found to be highly correlated to \(\Psi_{gs50}\), the water potential corresponding to 50% of stomatal conductance (Bartlett et al. 2016).

A.3.11 Radiation balance and water interception

Default value for direct light extinction is \(k_b = 0.8\). Default values for diffuse radiation extinction, absorbance, reflectance and water interception parameters depend on the leaf shape:

Leaf shape	\(k_{PAR}\)	\(\alpha_{SWR}\)	\(\gamma_{SWR}\)	\(s_{water}\)
Broad	0.55	0.70	0.18	0.5
Linear	0.45	0.70	0.15	0.8
Needle/Scale	0.50	0.70	0.14	1.0

where \(k_{PAR}\) is the diffuse PAR extinction coefficient, \(\alpha_{SWR}\) is the short-wave radiation leaf absorbance coefficient, \(\gamma_{SWR}\) is the short-wave radiation leaf reflectance (albedo) and \(s_{water}\) is the crown water storage capacity per LAI unit.

A.3.12 Stomatal conductance

Default values for minimum and maximum conductance to water vapour (\(g_{swmin}\) and \(g_{swmax}\); in \(mol\, H_2O \cdot s^{-1} \cdot m^{-2}\)) were defined depending on taxonomic family, from Duursma et al. (2018) and Hoshika et al. (2018), and stored in an internal data set (medfate:::trait_family_means):

Table A.3: Default minimum and maximum conductance to water vapour by taxonomic family.
	Gswmin	Gswmax
Acanthaceae	NA	0.2500000
Altingiaceae	0.0031009	0.5000000
Amaranthaceae	0.0113781	0.0750000
Amaryllidaceae	0.0093743	NA
Anacardiaceae	0.0043356	0.2017136
Annonaceae	0.0046000	NA
Apiaceae	0.0051617	NA
Apocynaceae	0.0030300	NA
Aquifoliaceae	0.0017827	0.2600000
Araceae	0.0042445	NA
Araliaceae	0.0005668	NA
Araucariaceae	0.0018786	NA
Arecaceae	0.0009988	NA
Aristolochiaceae	0.0035896	NA
Asparagaceae	0.0010977	NA
Asphodelaceae	0.0055481	NA
Aspleniaceae	0.0045607	NA
Asteraceae	0.0107116	0.1976901
Balsaminaceae	0.0126573	NA
Berberidaceae	0.0016500	NA
Betulaceae	0.0031703	0.3536968
Bignoniaceae	0.0026880	NA
Bixaceae	0.0027600	NA
Boraginaceae	0.0060135	0.2900000
Brassicaceae	0.0113630	NA
Burseraceae	0.0027100	NA
Cactaceae	0.0014808	NA
Calophyllaceae	NA	0.1350000
Campanulaceae	0.0059265	NA
Cannabaceae	NA	0.3300000
Caryocaraceae	0.0050839	NA
Caryophyllaceae	0.0018519	NA
Cephalotaxaceae	0.0022700	NA
Cercidiphyllaceae	NA	0.4000000
Chrysobalanaceae	NA	0.1740000
Cistaceae	0.0201725	NA
Clethraceae	NA	0.2500000
Combretaceae	0.0079950	NA
Convolvulaceae	0.0043347	NA
Cornaceae	NA	0.3000000
Crassulaceae	0.0015807	NA
Cucurbitaceae	0.0053377	NA
Cupressaceae	0.0062570	0.0840000
Cyperaceae	0.0134175	NA
Dennstaedtiaceae	0.0099857	NA
Dilleniaceae	0.0056080	NA
Dipterocarpaceae	NA	0.3533333
Dryopteridaceae	0.0023310	NA
Ebenaceae	0.0046400	NA
Elaeagnaceae	NA	0.1700000
Ephedraceae	0.0023268	NA
Equisetaceae	0.0045238	NA
Ericaceae	0.0037819	0.1723333
Euphorbiaceae	0.0028670	0.2632500
Fabaceae	0.0067574	0.3103490
Fagaceae	0.0051596	0.2830277
Geraniaceae	0.0043050	NA
Ginkgoaceae	0.0045718	NA
Hamamelidaceae	NA	0.2600000
Iridaceae	0.0054978	NA
Juglandaceae	0.0039951	0.4900000
Krameriaceae	NA	0.1600000
Lamiaceae	0.0055927	0.7300000
Lardizabalaceae	0.0045189	NA
Lauraceae	0.0030484	0.2152608
Magnoliaceae	0.0043399	0.2850000
Malpighiaceae	0.0042100	NA
Malvaceae	0.0060961	0.5376667
Meliaceae	NA	0.1600000
Moraceae	0.0063409	0.3835000
Myristicaceae	NA	0.0880000
Myrtaceae	0.0060944	0.2352857
Nephrolepidaceae	0.0006570	NA
Oleaceae	0.0045387	0.1807354
Onagraceae	0.0169506	NA
Oxalidaceae	0.0071964	NA
Paeoniaceae	0.0082000	NA
Papaveraceae	0.0078173	NA
Pentaphylacaceae	NA	0.1200000
Phyllanthaceae	0.0077900	NA
Pinaceae	0.0027864	0.1703783
Plantaginaceae	0.0061946	NA
Platanaceae	0.0058727	0.2540248
Poaceae	0.0113947	0.5044242
Podocarpaceae	0.0073176	NA
Polygalaceae	NA	0.0870000
Polygonaceae	0.0163056	NA
Polypodiaceae	0.0015299	NA
Proteaceae	0.0062236	NA
Ranunculaceae	0.0107253	NA
Rhamnaceae	0.0055679	0.1683289
Rosaceae	0.0048340	0.3292679
Rubiaceae	0.0055505	NA
Rutaceae	0.0090200	NA
Salicaceae	0.0086194	0.2828571
Santalaceae	0.0057571	NA
Sapindaceae	0.0034823	0.2265433
Sapotaceae	0.0029100	0.1870000
Sciadopityaceae	0.0066554	NA
Simaroubaceae	NA	0.6320000
Solanaceae	0.0035967	0.6000000
Taxaceae	0.0037033	NA
Theaceae	0.0051754	0.4600000
Ulmaceae	NA	0.4133333
Urticaceae	0.0018700	0.6075000
Verbenaceae	0.0120000	NA
Viburnaceae	0.0039044	NA
Vitaceae	0.0053247	NA
Vochysiaceae	0.0039300	NA
Zingiberaceae	0.0018748	NA
Zygophyllaceae	NA	0.1580769

If there is no information derived from taxonomic family, \(g_{swmin} = 0.0049\) and \(g_{swmax} = 0.200\).

A.3.13 Pressure-volume curves

Parameters of the pressure-volume curve (i.e. \(\pi_{0,stem}\) and \(\epsilon_{stem}\)) for leaf and stem symplastic tissue are required for each species.

When parameters for stem tissue are missing, medfate estimates them from wood density following Christoffersen et al. (2016): \[\begin{equation} \pi_{0,stem} = 0.52 - 4.16 \cdot \rho_{wood} \end{equation}\]

\[\begin{equation} \epsilon_{stem} = \sqrt{1.02 \cdot e^{8.5\cdot \rho_{wood}}-2.89} \end{equation}\] while the apoplastic fraction of stem is assumed \(f_{apo,stem} = f_{conduits}\) (see A.3.7).

Default values for leaf pressure-volume parameters, i.e. \(\pi_{0,leaf}\), \(\epsilon_{leaf}\) and \(f_{apo,leaf}\), are determined from taxonomic family using an internal data set (medfate:::trait_family_means):

Table A.4: Default leaf pressure-volume parameters by taxonomic family.
	LeafPI0	LeafEPS	LeafAF
Acanthaceae	-3.3950000	23.230000	0.1270000
Amaranthaceae	-1.4810943	5.641365	0.6930000
Anacardiaceae	-2.0183556	12.760000	NA
Anemiaceae	-1.3700000	20.040000	0.2550000
Annonaceae	-2.5250000	34.215000	NA
Apiaceae	-1.1040000	23.410000	0.8380000
Apocynaceae	-1.4950000	17.955000	0.7930000
Aquifoliaceae	-2.3000000	20.700000	0.4000000
Araliaceae	-1.4535028	11.387712	0.5620000
Arecaceae	-3.4000000	73.400000	0.2000000
Asparagaceae	-1.7922006	22.810356	NA
Asphodelaceae	-1.3794753	7.425622	NA
Aspleniaceae	-1.2400000	35.300000	NA
Asteraceae	-1.3018058	6.022339	0.4066000
Atherospermataceae	-1.3400000	8.380000	NA
Berberidaceae	-1.7100000	NA	NA
Betulaceae	-1.3583989	4.458000	NA
Bignoniaceae	-1.9900000	17.610000	0.1770000
Boraginaceae	-1.5210000	11.797333	NA
Brassicaceae	-1.4200000	NA	NA
Burseraceae	-1.4350000	14.980000	NA
Cactaceae	NA	8.700000	NA
Campanulaceae	-0.8345534	3.195661	NA
Cannabaceae	-1.5666667	10.910000	0.5330000
Capparaceae	-2.8400000	14.750000	0.1723333
Caprifoliaceae	-0.7300000	NA	NA
Caryocaraceae	-1.7100000	11.340000	NA
Casuarinaceae	-0.6515152	1.066667	NA
Celastraceae	-2.6000000	19.060000	NA
Cistaceae	-1.3850000	NA	NA
Combretaceae	-2.0521277	6.830000	NA
Connaraceae	-2.2500000	18.010000	NA
Convolvulaceae	-1.3200000	NA	NA
Cucurbitaceae	-0.9800000	NA	NA
Cupressaceae	-1.6250000	9.585000	0.2720000
Cyperaceae	-0.6022136	3.661024	NA
Davalliaceae	-1.3100000	23.870000	0.7120000
Dilleniaceae	-1.2547562	7.402922	NA
Dipterocarpaceae	-1.1314286	23.630000	0.4634286
Dryopteridaceae	-1.4250000	48.950000	NA
Ebenaceae	-2.1100000	14.650000	NA
Ericaceae	-1.5615000	16.293750	0.5805000
Erythroxylaceae	-1.9166667	16.993333	NA
Euphorbiaceae	-1.6166667	15.023333	0.4745000
Fabaceae	-1.7299989	13.783893	0.3460667
Fagaceae	-1.5501782	16.818546	0.2331579
Geraniaceae	-0.9251760	6.538282	NA
Ginkgoaceae	-1.3400000	21.150000	0.7490000
Goodeniaceae	-1.7350000	15.306667	NA
Grossulariaceae	-1.8450000	NA	NA
Hypericaceae	-1.8700000	NA	NA
Irvingiaceae	-1.6900000	38.380000	0.4760000
Lamiaceae	-1.2190435	5.047793	0.2200000
Lauraceae	-2.0260251	18.827830	0.3700000
Lecythidaceae	-1.2800257	NA	NA
Limnanthaceae	-0.5600000	NA	NA
Linderniaceae	-0.6600000	6.680000	0.3080000
Loranthaceae	NA	10.884849	NA
Lythraceae	-1.5350000	6.055000	NA
Magnoliaceae	-1.4300000	9.140000	0.1560000
Malpighiaceae	-1.5400000	9.450000	NA
Malvaceae	-1.7157143	24.540000	0.8050000
Marsileaceae	-1.5600000	21.780000	0.5090000
Melastomataceae	-1.7540000	12.306667	NA
Meliaceae	-1.8600000	14.170000	NA
Montiaceae	-0.6900000	NA	NA
Moraceae	-1.5576579	27.041455	0.8097500
Myrtaceae	-1.8860350	14.846841	0.3532500
Nephrolepidaceae	-1.0000000	17.750000	0.7650000
Nothofagaceae	-1.4800000	8.380000	NA
Nyctaginaceae	-1.2800000	NA	NA
Oleaceae	-2.0368246	11.051000	0.4185000
Onagraceae	-1.2050000	NA	NA
Orchidaceae	-0.5300000	14.766667	0.2366667
Orobanchaceae	-1.3950000	NA	NA
Osmundaceae	-1.3700000	20.660000	0.2630000
Paeoniaceae	-1.8600000	NA	NA
Papaveraceae	-1.3133333	NA	NA
Pentaphylacaceae	-1.5500000	9.270000	NA
Phyllanthaceae	-1.2633333	13.966667	0.3036667
Phytolaccaceae	-1.2900000	19.430000	0.4790000
Pinaceae	-1.3275862	11.525319	0.3361875
Pittosporaceae	-1.5308960	8.754086	0.5660000
Plantaginaceae	-1.6170000	13.100000	NA
Platanaceae	-1.5959642	8.810000	0.3600000
Plumbaginaceae	-1.2100000	16.990000	0.6350000
Poaceae	-1.3714286	7.882000	0.4535000
Polemoniaceae	-1.0650000	NA	NA
Polygalaceae	-1.5900000	26.760000	0.4140000
Polygonaceae	-1.3950000	5.030000	NA
Polypodiaceae	-1.2028571	32.741429	0.2606667
Primulaceae	-1.7000000	15.320000	NA
Proteaceae	-1.7312364	12.889072	NA
Ranunculaceae	-2.0000000	NA	NA
Rhamnaceae	-1.8983333	6.230000	0.0770000
Rhizophoraceae	-2.3200000	9.650000	NA
Rosaceae	-1.9815228	11.747759	0.5180000
Rubiaceae	-1.6398227	12.128359	0.4500000
Rutaceae	-1.7261925	8.367725	NA
Salicaceae	-1.5900000	12.995000	0.7800000
Santalaceae	-2.9700000	18.860000	NA
Sapindaceae	-1.3065207	9.571238	0.1000000
Sapotaceae	-1.7850000	17.835000	0.3830000
Scrophulariaceae	-1.7711111	10.272941	NA
Simmondsiaceae	-2.4200000	NA	NA
Solanaceae	-1.0487500	8.056667	0.6290000
Stylidiaceae	-1.4679810	9.001625	NA
Styracaceae	-2.2800000	24.565000	NA
Symplocaceae	-1.4850000	NA	NA
Taxaceae	-2.6000000	NA	NA
Tetrameristaceae	-2.9700000	NA	NA
Theaceae	-1.6100000	7.710000	0.2320000
Thymelaeaceae	-1.7900000	4.870000	NA
Urticaceae	-1.0402500	9.126500	NA
Velloziaceae	-0.6700000	9.030000	0.7565000
Verbenaceae	-1.3550000	4.850000	0.2270000
Viburnaceae	-1.3066667	12.790000	NA
Violaceae	-1.3350000	17.840000	0.3720000
Vitaceae	-1.1211600	10.992800	0.5816667
Vochysiaceae	-2.1350000	19.995000	NA
Winteraceae	-1.4800000	11.620000	NA
Zamiaceae	-2.2500000	14.380000	NA
Zygophyllaceae	-2.7800000	NA	NA

If family-level values are missing, following Bartlett et al. (2012) average values for Mediterranean climate leaves are taken as defaults, i.e. \(\pi_{0,leaf} = -2\) MPa, \(\epsilon_{leaf} = 17\), whereas a 29% leaf apoplastic fraction is assumed (i.e. \(f_{apo,leaf} = 0.29\)).

A.3.14 Stem and root maximum hydraulic conductivity

Tissue-level maximum conductivity parameters (i.e. \(K_{stem,max,ref}\) and \(K_{root,max,ref}\)) are not direct parameters to simulation functions. Instead, theay are scaled to estimate stem- and root-level hydraulic conductances (i.e. \(k_{stem, \max}\) and \(k_{root, \max}\)) using plant size (see A.4.1 and A.4.3 for details). \(K_{stem,max,ref}\) and \(K_{root,max,ref}\) are supplied via species parameter table and missing values can therefore occur.

Default values for \(K_{stem,max,ref}\) are determined from taxonomic family using an internal data set (medfate:::trait_family_means):

Table A.5: Default maximum stem hydraulic conductivity by taxonomic family.
	Kmax_stemxylem
Acanthaceae	3.6524786
Actinidiaceae	1.4453860
Aextoxicaceae	0.3800000
Altingiaceae	1.3055515
Alzateaceae	3.2168629
Amaranthaceae	0.1564636
Amborellaceae	0.5400000
Anacardiaceae	3.5289937
Annonaceae	4.3383977
Apiaceae	0.5150000
Apocynaceae	1.9545389
Aquifoliaceae	0.7222116
Araliaceae	1.6541078
Araucariaceae	0.7378000
Arecaceae	4.0884057
Aristolochiaceae	45.0000000
Asparagaceae	0.0034500
Asteraceae	2.4028983
Atherospermataceae	0.5500000
Austrobaileyaceae	2.3000000
Berberidaceae	0.2374195
Betulaceae	2.6700672
Bignoniaceae	1.9256324
Bixaceae	7.7500000
Boraginaceae	4.9482106
Brunelliaceae	1.0977628
Bruniaceae	0.3807548
Burseraceae	4.1829227
Cactaceae	1.6672222
Calophyllaceae	2.3932233
Calycanthaceae	0.4100000
Cannabaceae	4.2072251
Capparaceae	0.4952286
Caprifoliaceae	0.6668459
Cardiopteridaceae	4.9325604
Caryocaraceae	4.6951819
Casuarinaceae	2.1286706
Celastraceae	0.7511413
Chloranthaceae	1.8640142
Chrysobalanaceae	4.9895558
Cistaceae	0.3749778
Cleomaceae	0.3400000
Clethraceae	1.2896672
Clusiaceae	3.4487818
Combretaceae	4.4459416
Convolvulaceae	18.6000000
Coriariaceae	1.2443808
Cornaceae	3.1635287
Cucurbitaceae	90.0000000
Cunoniaceae	1.5276355
Cupressaceae	1.0432269
Daphniphyllaceae	0.5423333
Dennstaedtiaceae	21.9800000
Dilleniaceae	3.2473415
Dipentodontaceae	1.5398815
Ebenaceae	2.8967426
Elaeagnaceae	0.7000356
Elaeocarpaceae	1.4975290
Ericaceae	0.6528026
Erythroxylaceae	0.5317000
Escalloniaceae	3.0711737
Euphorbiaceae	3.4644373
Eupomatiaceae	1.1226467
Eupteleaceae	2.5516777
Fabaceae	3.9666512
Fagaceae	1.6691619
Fouquieriaceae	1.6400000
Garryaceae	1.9333333
Gnetaceae	1.2180000
Grossulariaceae	1.0199413
Hamamelidaceae	0.8420000
Hernandiaceae	4.4493753
Hydrangeaceae	0.6830196
Hypericaceae	3.3370649
Iteaceae	0.4100000
Juglandaceae	4.2447014
Lacistemataceae	0.4971272
Lamiaceae	3.4936965
Lauraceae	2.9792406
Lecythidaceae	4.5380334
Linaceae	0.8200000
Loranthaceae	0.6557303
Lythraceae	5.8900000
Magnoliaceae	1.9684958
Malpighiaceae	4.1150025
Malvaceae	4.1826217
Melastomataceae	2.2636030
Meliaceae	4.3079641
Metteniusaceae	2.4401784
Monimiaceae	1.8698825
Moraceae	3.7853604
Myricaceae	1.5818539
Myristicaceae	2.4842755
Myrothamnaceae	0.8700000
Myrtaceae	3.7443863
Nothofagaceae	0.8797083
Nyctaginaceae	5.4121757
Nyssaceae	0.9098000
Ochnaceae	1.3450000
Olacaceae	1.3017070
Oleaceae	1.4557139
Onagraceae	1.0800000
Paeoniaceae	3.6490971
Pandaceae	1.1963139
Passifloraceae	40.0000000
Pentaphylacaceae	0.6913458
Petiveriaceae	1.9488000
Phyllanthaceae	4.1181929
Picramniaceae	0.7344822
Picrodendraceae	3.9400000
Pinaceae	0.8567006
Piperaceae	2.4729541
Pittosporaceae	1.5175000
Poaceae	11.5500000
Podocarpaceae	0.5902734
Polygalaceae	0.4600559
Polygonaceae	1.1684655
Primulaceae	1.4083963
Proteaceae	1.9307135
Putranjivaceae	0.6000000
Rhamnaceae	3.0375638
Rhizophoraceae	1.7477273
Rosaceae	2.6829816
Rubiaceae	1.8643524
Rutaceae	1.6446345
Sabiaceae	2.3621512
Salicaceae	2.4189368
Santalaceae	2.0009728
Sapindaceae	2.1806033
Sapotaceae	1.0012081
Schisandraceae	0.0324678
Scrophulariaceae	0.2606843
Simaroubaceae	2.6728105
Siparunaceae	2.6577110
Smilacaceae	0.2402817
Solanaceae	2.2060863
Stachyuraceae	0.4675000
Staphyleaceae	2.1602223
Styracaceae	2.3740813
Symplocaceae	1.5349361
Tamaricaceae	4.0980498
Taxaceae	0.3200000
Theaceae	1.4441817
Thymelaeaceae	0.7514288
Trochodendraceae	1.4753706
Ulmaceae	3.3599365
Urticaceae	7.0823153
Viburnaceae	1.7692087
Violaceae	1.9123525
Vitaceae	29.8785362
Vochysiaceae	1.6303209
Winteraceae	0.5969203
Zygophyllaceae	0.6888000

If family-level values are missing, suitable \(K_{stem,max,ref}\) values are decided according to combinations of taxon group (either Angiosperm or Gymnosperm), growth form (either tree or shrub) and leaf phenology (Maherali et al. 2004):

Group	Growth form	Leaf phenology	\(K_{stem,max,ref}\)
Angiosperm	Tree	Winter-(semi)deciduous	1.58
Angiosperm	Shrub	Winter-(semi)deciduous	1.55
Angiosperm	Tree/Shrub	Evergreen	2.43
Gymnosperm	Tree	any	0.48
Gymnosperm	Shrub	any	0.24

Following Oliveras et al. (2003), missing values for \(K_{root,max,ref}\) are assumed to be four-times the values given or estimated for \(K_{stem,max,ref}\).

A.3.15 Leaf maximum hydraulic conductance

Leaf maximum hydraulic conductance (\(k_{l, max}\), in \(mmol \cdot m^{-2} \cdot s^{-1} \cdot MPa^{-1}\)) is an input parameter that should be provided for each species. When missing, leaf maximum hydraulic conductance can be estimated from maximum stomatal conductance (\(g_{swmax}\)), following Franks (2006) (original coefficients were modified for better fit): \[\begin{equation} k_{l, max} = (g_{swmax}/0.015)^{1/1.3} \end{equation}\] Note that values for \(g_{swmax}\) may also be imputed (see A.3.12).

A.3.16 Xylem vulnerability

Default values for \(\Psi_{50,stem}\) are determined from taxonomic family using an internal data set (medfate:::trait_family_means):

Table A.6: Default stem P50 values by taxonomic family.
	VCstem_P50
Acanthaceae	-5.7450000
Achariaceae	-3.1500000
Actinidiaceae	-0.9833333
Altingiaceae	-2.7349020
Amaranthaceae	-3.0284442
Amborellaceae	-3.0000000
Anacardiaceae	-2.6108245
Annonaceae	-3.1516340
Apiaceae	-5.7000000
Apocynaceae	-2.2883044
Aquifoliaceae	-4.2944620
Araliaceae	-2.0065789
Araucariaceae	-2.7808696
Arecaceae	-1.8100000
Asparagaceae	-2.1080000
Asteraceae	-3.3353531
Atherospermataceae	-3.3118889
Austrobaileyaceae	-0.4990000
Berberidaceae	-4.5000000
Betulaceae	-2.0812191
Bignoniaceae	-1.5351814
Bixaceae	-1.4403556
Boraginaceae	-2.3958000
Bruniaceae	-3.0448784
Burseraceae	-1.5985357
Buxaceae	-8.0000000
Cactaceae	-2.0000000
Calophyllaceae	-1.7505034
Calycanthaceae	-1.9780000
Canellaceae	-1.7880000
Cannabaceae	-2.0810432
Capparaceae	-2.4200000
Caprifoliaceae	-5.5124953
Caryocaraceae	-1.7105556
Casuarinaceae	-4.0269167
Celastraceae	-3.0952354
Chloranthaceae	-2.1332500
Chrysobalanaceae	-2.0405480
Cistaceae	-6.4054545
Cleomaceae	-2.1841785
Clusiaceae	-1.6479464
Combretaceae	-2.1545455
Convolvulaceae	-1.6000000
Cornaceae	-3.8960714
Cupressaceae	-7.5420160
Daphniphyllaceae	-3.5120000
Dennstaedtiaceae	-1.9900000
Dilleniaceae	-1.4800000
Dipterocarpaceae	-0.5350000
Ebenaceae	-1.7272655
Elaeocarpaceae	-3.8346654
Ericaceae	-3.8438828
Euphorbiaceae	-2.0076038
Eupomatiaceae	-0.3966667
Fabaceae	-2.6469364
Fagaceae	-3.0260244
Fouquieriaceae	-1.3700000
Garryaceae	-6.3733333
Gentianaceae	-4.4100000
Ginkgoaceae	-4.0500417
Gnetaceae	-2.9972500
Goupiaceae	-2.2000000
Grossulariaceae	-3.5675000
Hamamelidaceae	-4.1350000
Himantandraceae	-1.3000000
Humiriaceae	-1.5800000
Hypericaceae	-0.8300000
Iteaceae	-2.5400000
Juglandaceae	-2.0424445
Lamiaceae	-3.8246828
Lauraceae	-2.7898156
Lecythidaceae	-2.1875400
Lepidobotryaceae	-0.4305852
Linaceae	-0.9994750
Lythraceae	-2.2322222
Magnoliaceae	-3.1453153
Malpighiaceae	-1.3000000
Malvaceae	-1.8380572
Melastomataceae	-2.6319500
Meliaceae	-2.0456193
Menispermaceae	-0.6400000
Moraceae	-1.3813461
Myricaceae	-2.0449781
Myristicaceae	-1.0496037
Myrtaceae	-2.4979370
Nothofagaceae	-3.3889375
Nyctaginaceae	-3.5750000
Nyssaceae	-2.5571429
Ochnaceae	-1.7112500
Olacaceae	-1.8803921
Oleaceae	-4.5607396
Onagraceae	-1.6233333
Opiliaceae	-4.1600000
Paeoniaceae	-1.1192104
Pandaceae	-2.5987836
Pentaphylacaceae	-3.4092707
Peraceae	-4.8388621
Petiveriaceae	-2.9250000
Phyllanthaceae	-2.2386319
Picrodendraceae	-6.3162500
Pinaceae	-3.8695287
Pittosporaceae	-3.8100000
Platanaceae	-1.7696667
Poaceae	-3.1886703
Podocarpaceae	-3.7224333
Polygalaceae	-2.1578781
Polygonaceae	-1.8667274
Primulaceae	-2.6500853
Proteaceae	-2.5764625
Putranjivaceae	-2.6825000
Ranunculaceae	-1.6100000
Rhamnaceae	-5.9801923
Rhizophoraceae	-5.5375000
Rosaceae	-4.9511072
Rubiaceae	-2.8300494
Rutaceae	-2.1479958
Sabiaceae	-1.3983333
Salicaceae	-1.9355948
Santalaceae	-3.0086667
Sapindaceae	-3.0038375
Sapotaceae	-2.2002755
Schisandraceae	-2.8510000
Sciadopityaceae	-2.4300000
Scrophulariaceae	-3.5360000
Simaroubaceae	-1.3643359
Siparunaceae	-0.8175236
Solanaceae	-2.0322012
Stachyuraceae	-4.3100000
Staphyleaceae	-2.0050000
Stemonuraceae	-0.1800000
Styracaceae	-3.0006250
Symplocaceae	-2.3671429
Tamaricaceae	-1.1285522
Taxaceae	-6.9935714
Theaceae	-4.3414687
Thymelaeaceae	-4.8714335
Trimeniaceae	-0.9038000
Trochodendraceae	-1.8850000
Ulmaceae	-1.7778604
Urticaceae	-1.2959081
Verbenaceae	-2.6000000
Viburnaceae	-3.6032533
Violaceae	-2.5168906
Vitaceae	-0.9343333
Vochysiaceae	-1.7912470
Winteraceae	-3.4368274
Zygophyllaceae	-3.3448285

If family-level values is missing, a suitable estimate of \(\Psi_{50,stem}\) the water potential corresponding to 50% of conductance loss, can be obtained from Maherali et al. (2004) according to combinations of taxon group (either Angiosperm or Gymnosperm), growth form (either tree or shrub) and leaf phenology:

Group	Growth form	Leaf phenology	\(\Psi_{50,stem}\)
Angiosperm	Tree/Shrub	Winter-(semi)deciduous	-2.34
Angiosperm	Tree	Evergreen	-1.51
Angiosperm	Shrub	Evergreen	-5.09
Gymnosperm	Tree	any	-4.17
Gymnosperm	Shrub	any	-8.95

\(\Psi_{50,stem}\) estimates are taken for parameter \(\Psi_{critic}\), in the case of the basic water balance model.

Vulnerability curves in the advanced model need to be specified for leaves, stem and root segments via the two parameters of the Weibull function (see 10.2). When any of the parameters of the stem vulnerability curve is missing, a regression equation using data from Choat et al. (2012) can be used to estimate \(\Psi_{88,stem}\) from \(\Psi_{50,stem}\): \[\begin{equation} \Psi_{88,stem} = -1.4264 + 1.2593 \cdot \Psi_{50,stem} \end{equation}\]

Finally, estimates for \(c_{stem}\) and \(d_{stem}\) are obtained from \(\Psi_{50,stem}\) and \(\Psi_{88,stem}\) via function hydraulics_psi2Weibull().

Vulnerability curves for root xylem are less common than for stem xylem. If these values are missing, \(\Psi_{50,stem}\) is first estimated according to its definition and the stem vulnerability curve parameters, \(c_{stem}\) and \(d_{stem}\). Then, a relationship from Bartlett et al. (2016) is used to estimate \(\Psi_{50, root}\) from \(\Psi_{50,stem}\): \[\begin{equation} \Psi_{50, root} = 0.4892 + 0.742 \cdot \Psi_{50,stem} \end{equation}\] Finally, \(\Psi_{88,stem}\) and the Weibull vulnerability parameters are obtained as explained for stems.

Vulnerability curves for leaf xylem are also less common than for stem xylem. If these values are missing, the water potential at turgor los point \(\Psi_{tlp}\) is first estimated from \(\pi_{leaf}\) and \(\epsilon_{leaf}\) according to eq. (10.4). Then, a relationship calibrated with data from Bartlett et al. (2016) is used to estimate \(\Psi_{50, leaf}\) from \(\Psi_{tlp}\): \[\begin{equation} \Psi_{50, leaf} = 0.2486 + 0.9944 \cdot \Psi_{tlp} \end{equation}\] Finally, \(\Psi_{88,leaf}\) and the Weibull vulnerability parameters are obtained as explained for stems.

A.3.17 Photosynthesis rates

Rubisco’s maximum carboxylation rate at 25ºC (\(V_{max, 298}\), in \(\mu mol CO_2 \cdot s^{-1} \cdot m^{-2}\)) is a required input parameter for each species (Vmax298). When missing, the work by Walker et al. (2014) suggests that suitable estimates can be derived from \(SLA\) and \(N_{area}\), the latter being the nitrogen concentration per leaf area: \[\begin{equation} V_{max, 298} = e^{1.993 + 2.555\cdot \log(N_{area}) - 0.372 \cdot \log(SLA) + 0.422 \cdot \log(N_{area})\cdot \log(SLA) } \end{equation}\]

In turn, imputation for \(SLA\) is explained in A.3.4, whereas values for \(N_{area}\) are determined from \(N_{leaf}\) and \(SLA\), being \(N_{leaf}\) estimated as indicated in A.3.18. Would \(N_{leaf}\) and \(SLA\) values be both unavailable, a default value of 100 \(\mu mol CO_2 \cdot s^{-1} \cdot m^{-2}\) is used for \(V_{max, 298}\) imputation.

When the maximum rate of electron transport at the same temperature (\(J_{max, 298}\)) is not provided by the user, it can be estimated from \(V_{max, 298}\) using (Walker et al. 2014):

\[\begin{equation} J_{max, 298} = e^{1.197 + 0.847\cdot \log(V_{max,298})} \end{equation}\]

A.3.18 Maintenance respiration rates

When missing at the species parameter table, maintenance respiration rates for leaves, sapwood and fine roots (\(RER_{leaf}\), \(RER_{sapwood}\) and \(RER_{fineroot}\); all in \(g\,gluc\cdot g\,dry^{-1}\cdot day^{-1}\)) are estimated from corresponding tissue nitrogen concentrations (\(N_{leaf}\), \(N_{sapwood}\) and \(N_{fineroot}\); all in \(mg\,N \cdot g\,dry^{-1}\)) following the equations given by Reich et al. (2008) (after appropriate unit conversion): \[\begin{eqnarray} RER_{leaf} &=& e^{0.691+ 1.639 \cdot \log(N_{leaf}))} \\ RER_{sapwood} &=& e^{1.024 + 1.344 \cdot \log(N_{sapwood}))} \\ RER_{fineroot} &=& e^{0.980 + 1.352 \cdot \log(N_{fineroot}))} \end{eqnarray}\] where in the previous equations nitrogen concentrations are in \(mmol\,N\cdot g\,dry^{-1}\) and respiration rates in \(nmol\,CO2\cdot g\,dry^{-1}\cdot s^{-1}\).

In turn, when tissue nitrogen concentrations are missing they are estimated from taxonomic family using an internal data set (medfate:::trait_family_means):

Table A.7: Default nitrogen concentration per dry mass in different tissues by taxonomic family.
	Nleaf	Nsapwood	Nfineroot
Acanthaceae	28.166211	NA	7.805074
Achariaceae	22.638233	NA	NA
Acoraceae	18.000000	NA	NA
Actinidiaceae	22.057101	NA	24.905621
Aextoxicaceae	9.652280	NA	NA
Aizoaceae	14.800000	NA	NA
Alismataceae	24.279413	NA	35.985750
Alstroemeriaceae	18.484000	NA	NA
Altingiaceae	15.704509	NA	10.723118
Alzateaceae	9.802997	NA	NA
Amaranthaceae	25.143267	NA	10.971150
Amaryllidaceae	27.807973	NA	11.188333
Anacardiaceae	17.851435	NA	16.859303
Anemiaceae	21.440000	NA	NA
Annonaceae	23.182512	NA	20.282433
Apiaceae	25.885090	NA	10.599666
Apocynaceae	21.091263	NA	13.757041
Aquifoliaceae	15.239218	NA	10.155075
Araceae	19.587660	NA	NA
Araliaceae	17.527488	NA	16.451735
Araucariaceae	18.412875	NA	13.000000
Arecaceae	17.618260	NA	12.267625
Aristolochiaceae	31.050092	NA	NA
Asparagaceae	24.878019	NA	12.888227
Asphodelaceae	10.880839	NA	NA
Aspleniaceae	25.425769	NA	11.177640
Asteliaceae	7.205741	NA	8.305000
Asteraceae	21.823946	NA	12.814810
Atherospermataceae	14.776944	NA	23.200000
Athyriaceae	27.001204	NA	NA
Aulacomniaceae	8.000000	NA	NA
Balsaminaceae	35.893386	NA	17.328412
Begoniaceae	27.734506	NA	NA
Berberidaceae	20.459188	NA	20.252051
Betulaceae	24.816045	12.5340000	12.843458
Bignoniaceae	25.194014	12.9641116	19.420246
Bixaceae	20.220367	NA	NA
Blechnaceae	11.907284	NA	9.353304
Bonnetiaceae	10.472527	NA	NA
Boraginaceae	25.911014	NA	17.421666
Brassicaceae	39.093972	NA	18.495733
Bromeliaceae	8.659121	NA	NA
Brunelliaceae	16.166560	NA	NA
Bruniaceae	7.785422	NA	NA
Bryaceae	16.050000	NA	NA
Burseraceae	18.524135	NA	12.769375
Butomaceae	42.600000	NA	NA
Buxaceae	19.346119	NA	NA
Cabombaceae	19.500000	NA	NA
Cactaceae	16.597289	NA	NA
Calomniaceae	6.280000	NA	NA
Calophyllaceae	13.474516	NA	NA
Calycanthaceae	21.297115	NA	19.029600
Calyceraceae	38.773333	NA	NA
Campanulaceae	27.418234	NA	11.512892
Cannabaceae	28.800070	NA	22.210000
Cannaceae	39.700000	NA	NA
Capparaceae	29.938498	9.4563746	2.700000
Caprifoliaceae	19.082170	NA	12.978113
Cardiopteridaceae	18.941928	NA	NA
Caricaceae	35.461166	NA	NA
Caryocaraceae	16.562719	NA	NA
Caryophyllaceae	24.271292	NA	14.382715
Casuarinaceae	13.180973	2.6269500	8.650000
Celastraceae	17.572451	NA	13.093011
Centroplacaceae	15.828213	NA	NA
Cephalotaxaceae	19.725000	NA	NA
Ceratophyllaceae	42.089727	NA	NA
Chenopodiaceae	23.782500	NA	NA
Chloranthaceae	17.831761	NA	17.726398
Chrysobalanaceae	16.262886	NA	4.475000
Cibotiaceae	16.645813	NA	15.741024
Cistaceae	18.266485	NA	9.487500
Cleomaceae	40.580000	NA	NA
Clethraceae	12.799670	NA	NA
Clusiaceae	15.529731	NA	19.935000
Colchicaceae	22.970964	NA	NA
Combretaceae	18.111460	3.0457448	9.776883
Commelinaceae	22.345377	NA	NA
Connaraceae	14.849045	NA	5.600000
Convolvulaceae	27.797009	NA	14.153389
Coriariaceae	22.456652	NA	21.410911
Cornaceae	18.969030	NA	11.817210
Corynocarpaceae	30.000000	NA	34.200000
Costaceae	20.054024	NA	NA
Crassulaceae	23.198458	NA	9.510000
Crypteroniaceae	11.190000	NA	NA
Cucurbitaceae	33.257775	NA	8.940000
Cunoniaceae	11.323882	NA	10.338400
Cupressaceae	11.538057	5.2000000	11.590274
Curtisiaceae	14.749804	NA	NA
Cyatheaceae	20.111096	NA	8.858000
Cycadaceae	21.413044	NA	NA
Cyclanthaceae	19.600000	NA	NA
Cyperaceae	21.157128	NA	8.268713
Cyrillaceae	11.665016	NA	3.400000
Cystopteridaceae	22.764184	NA	14.145786
Daltoniaceae	11.000000	NA	NA
Daphniphyllaceae	17.926319	NA	12.754570
Davalliaceae	17.400000	NA	NA
Dennstaedtiaceae	22.688744	NA	8.835127
Diapensiaceae	14.462500	NA	NA
Dichapetalaceae	17.233456	NA	NA
Dicksoniaceae	14.013965	NA	10.440000
Dicranaceae	7.960000	NA	NA
Didiereaceae	13.591252	NA	NA
Dilleniaceae	12.952704	NA	4.090000
Dioscoreaceae	24.081768	NA	14.355430
Dipterocarpaceae	16.161134	NA	9.566667
Droseraceae	12.829382	NA	NA
Dryopteridaceae	17.978481	NA	13.321727
Ebenaceae	16.313200	NA	12.524699
Elaeagnaceae	32.443308	NA	26.765000
Elaeocarpaceae	16.354645	NA	13.201362
Ephedraceae	14.236421	NA	NA
Equisetaceae	16.615733	NA	14.176764
Ericaceae	13.248438	2.7515333	7.731757
Eriocaulaceae	21.240414	NA	NA
Erythroxylaceae	20.958075	NA	NA
Escalloniaceae	17.094207	NA	NA
Euphorbiaceae	24.531702	4.2254769	8.574675
Eupteleaceae	18.391141	NA	25.864178
Fabaceae	27.898679	7.7178975	22.096443
Fagaceae	20.111341	8.6278077	13.589169
Fissidentaceae	15.100000	NA	NA
Flagellariaceae	23.897812	NA	NA
Fouquieriaceae	13.559698	NA	NA
Francoaceae	22.163814	NA	NA
Garryaceae	13.347972	NA	NA
Gentianaceae	22.502968	NA	12.173321
Geraniaceae	22.351384	NA	10.006003
Gesneriaceae	17.533740	NA	NA
Ginkgoaceae	19.560000	NA	23.900000
Gleicheniaceae	10.506400	NA	6.764580
Gnetaceae	24.092325	NA	NA
Goodeniaceae	14.129719	NA	NA
Goupiaceae	17.454183	NA	NA
Griseliniaceae	9.986674	NA	24.090000
Grossulariaceae	21.799287	NA	12.475793
Gunneraceae	22.700000	NA	NA
Gyrostemonaceae	16.700000	NA	NA
Haemodoraceae	35.460000	NA	NA
Halophytaceae	12.770000	NA	NA
Haloragaceae	25.885840	NA	NA
Hamamelidaceae	12.666023	NA	11.637352
Heliconiaceae	23.189264	NA	NA
Hemidictyaceae	24.343333	NA	NA
Hernandiaceae	24.545125	NA	NA
Hookeriaceae	12.100000	NA	NA
Humiriaceae	14.008948	NA	NA
Hydrangeaceae	25.124177	NA	19.980929
Hydrocharitaceae	31.374421	NA	NA
Hylocomiaceae	8.000000	NA	NA
Hymenophyllaceae	13.110392	NA	NA
Hypericaceae	18.361228	NA	6.099405
Hypoxidaceae	19.166667	NA	NA
Icacinaceae	27.470051	NA	NA
Iridaceae	17.324563	NA	9.253111
Irvingiaceae	22.784536	NA	NA
Iteaceae	12.508392	NA	13.550000
Ixonanthaceae	26.177587	NA	NA
Juglandaceae	20.953465	NA	13.096168
Juncaceae	19.522722	NA	10.673303
Juncaginaceae	27.575346	NA	12.951379
Krameriaceae	18.612081	NA	NA
Lacistemataceae	21.780647	NA	NA
Lamiaceae	22.174066	7.2386408	13.960086
Lardizabalaceae	15.968174	NA	12.200000
Lauraceae	19.753224	8.4500000	19.210708
Lecythidaceae	21.720373	NA	11.537591
Lejeuneaceae	5.000000	NA	NA
Lentibulariaceae	17.947779	NA	NA
Lepidobotryaceae	16.533388	NA	NA
Leucobryaceae	5.960000	NA	NA
Liliaceae	29.116429	NA	14.910000
Linaceae	21.176845	NA	11.011668
Linderniaceae	16.149854	NA	NA
Lindsaeaceae	26.776000	NA	NA
Loasaceae	13.160000	NA	NA
Loganiaceae	18.843579	NA	NA
Loranthaceae	14.686177	NA	NA
Lycopodiaceae	9.652829	NA	9.419025
Lygodiaceae	35.050000	NA	NA
Lythraceae	17.847630	NA	32.660000
Magnoliaceae	21.168715	NA	20.654571
Malpighiaceae	20.506269	2.9006066	16.219026
Malvaceae	22.686123	7.2466977	12.671967
Marantaceae	22.255620	NA	NA
Marattiaceae	21.721250	NA	NA
Marcgraviaceae	12.700000	NA	NA
Marsileaceae	22.673258	NA	NA
Mazaceae	25.876667	NA	NA
Melanthiaceae	28.932731	NA	14.394140
Melastomataceae	18.870678	NA	10.898612
Meliaceae	24.415018	2.8494354	17.237693
Menispermaceae	18.991467	NA	NA
Menyanthaceae	32.391410	NA	7.084952
Metteniusaceae	19.154989	NA	NA
Molluginaceae	25.043091	NA	NA
Monimiaceae	21.329016	NA	26.640000
Montiaceae	26.080338	NA	16.260000
Moraceae	21.017327	NA	14.947530
Musaceae	34.141383	NA	NA
Myodocarpaceae	9.800000	NA	NA
Myricaceae	19.513672	NA	13.107552
Myristicaceae	21.136054	NA	9.580000
Myrtaceae	13.191641	3.1737143	11.290578
Nartheciaceae	24.515476	NA	NA
Nelumbonaceae	28.178153	NA	NA
Nephrolepidaceae	13.429499	NA	NA
Nitrariaceae	30.763968	NA	21.340000
Nothofagaceae	15.554369	NA	5.519130
Nyctaginaceae	36.758133	NA	11.849257
Nymphaeaceae	30.012332	NA	NA
Nyssaceae	15.836730	NA	13.265458
Ochnaceae	14.616129	NA	NA
Olacaceae	23.036636	2.3319000	NA
Oleaceae	20.532569	2.7800000	16.055835
Oleandraceae	16.600000	NA	NA
Onagraceae	23.405205	NA	10.422963
Onocleaceae	27.300918	NA	16.146795
Ophioglossaceae	31.483647	NA	NA
Opiliaceae	43.195099	NA	NA
Orchidaceae	18.565815	NA	17.729445
Orobanchaceae	27.315181	NA	11.884684
Orthotrichaceae	6.080000	NA	NA
Osmundaceae	21.342325	NA	9.349762
Oxalidaceae	31.194124	NA	12.635202
Paeoniaceae	16.838447	NA	NA
Pandaceae	33.892686	NA	NA
Pandanaceae	17.218513	NA	NA
Papaveraceae	31.710639	NA	22.828408
Paracryphiaceae	12.264861	NA	12.456667
Passifloraceae	30.682488	NA	10.000000
Paulowniaceae	15.174200	NA	NA
Pedaliaceae	22.632669	NA	NA
Penaeaceae	16.218192	NA	NA
Pentaphylacaceae	12.276999	NA	8.146194
Penthoraceae	40.820000	NA	NA
Peraceae	17.551803	NA	NA
Peridiscaceae	13.556156	NA	NA
Petiveriaceae	31.717332	NA	NA
Phrymaceae	17.067174	NA	NA
Phyllanthaceae	21.347428	NA	20.991696
Phytolaccaceae	42.140000	NA	NA
Picramniaceae	24.391070	NA	NA
Picrodendraceae	12.383333	NA	NA
Pinaceae	12.355719	0.8944936	11.007179
Piperaceae	29.049710	NA	NA
Pittosporaceae	13.075790	NA	13.192372
Plagiogyriaceae	23.332250	NA	NA
Plantaginaceae	20.631812	NA	11.331125
Platanaceae	18.665457	NA	8.198385
Plumbaginaceae	23.700133	NA	11.922716
Poaceae	19.354168	NA	9.590219
Podocarpaceae	10.639253	NA	12.365011
Polemoniaceae	19.897455	NA	10.585835
Polygalaceae	21.094736	NA	NA
Polygonaceae	29.772689	NA	11.173626
Polypodiaceae	11.339605	NA	NA
Polytrichaceae	11.378150	NA	NA
Pontederiaceae	35.011303	NA	14.020000
Porellaceae	17.337819	NA	NA
Portulacaceae	19.565181	NA	16.055783
Potamogetonaceae	36.619753	NA	14.518003
Pottiaceae	15.300000	NA	NA
Primulaceae	16.464569	NA	13.089968
Proteaceae	7.442857	1.7538857	11.481181
Pteridaceae	16.236413	NA	13.013953
Putranjivaceae	22.976760	NA	6.620000
Quillajaceae	10.311738	NA	NA
Ranunculaceae	24.937137	NA	12.389131
Resedaceae	33.916667	NA	9.690000
Restionaceae	6.869995	NA	NA
Rhamnaceae	22.311828	NA	15.865578
Rhizophoraceae	15.997339	NA	7.744000
Rosaceae	21.084318	NA	12.680397
Rubiaceae	22.615146	NA	13.947067
Rutaceae	23.750962	10.4788732	20.646972
Sabiaceae	15.073190	NA	5.533330
Salicaceae	23.553194	2.2070997	12.626054
Salvadoraceae	23.694941	NA	NA
Salviniaceae	33.065307	NA	NA
Santalaceae	16.360744	2.7344667	NA
Sapindaceae	21.744774	3.5530800	11.056128
Sapotaceae	19.064746	7.2818569	12.318919
Sarcobataceae	16.895034	NA	NA
Sarraceniaceae	10.419962	NA	NA
Saxifragaceae	17.937672	NA	13.101412
Schisandraceae	15.616078	NA	NA
Schlegeliaceae	8.200000	NA	NA
Schoepfiaceae	29.187926	NA	13.852399
Scrophulariaceae	17.952230	NA	13.644772
Sematophyllaceae	6.900000	NA	NA
Simaroubaceae	22.291023	NA	13.306877
Simmondsiaceae	16.968936	NA	NA
Siparunaceae	27.449222	NA	NA
Smilacaceae	16.569126	NA	15.064851
Solanaceae	31.486107	NA	34.759615
Sphagnaceae	8.866667	NA	NA
Staphyleaceae	19.246516	NA	NA
Stemonuraceae	20.151472	NA	NA
Strasburgeriaceae	7.566667	NA	NA
Stylidiaceae	12.808803	NA	NA
Styracaceae	14.958015	NA	18.722697
Symplocaceae	14.550237	NA	NA
Tamaricaceae	19.243046	NA	12.982222
Tapisciaceae	21.837653	NA	NA
Taxaceae	18.827718	NA	15.300000
Tectariaceae	23.730000	NA	NA
Theaceae	12.223663	NA	9.768648
Thelypteridaceae	23.934450	NA	NA
Thymelaeaceae	23.936648	NA	10.000000
Tofieldiaceae	15.554056	NA	NA
Trigoniaceae	25.447789	NA	NA
Trochodendraceae	17.990183	NA	NA
Typhaceae	19.787479	NA	22.550000
Ulmaceae	23.450220	NA	15.576070
Urticaceae	25.705412	NA	10.887530
Velloziaceae	18.554232	NA	NA
Verbenaceae	22.650000	NA	4.246698
Viburnaceae	20.766177	NA	14.542169
Violaceae	25.161527	NA	20.492986
Vitaceae	24.573439	NA	24.246752
Vochysiaceae	14.927290	NA	NA
Welwitschiaceae	17.790000	NA	NA
Winteraceae	11.199250	NA	12.683333
Zamiaceae	16.322513	NA	NA
Zingiberaceae	20.883188	NA	14.278156
Zygophyllaceae	22.224580	NA	16.544981

When family values are also missing, default tissue-averaged nitrogen concentrations are given: \(N_{leaf} = 20.088\), \(N_{sapwood} = 3.9791\) and \(N_{fineroot} = 12.207\).

Default control values (\(MR_{leaf} = 0.00260274\)), sapwood (\(MR_{sapwood} = 6.849315e-05\)) and fine roots (\(MR_{fineroot} 0.002054795\)) were used in previous model versions, derived from Ogle & Pacala (2009), but these are no longer used because of easier parameterization using tissue nitrogen concentration.

A.3.19 Relative growth rates

When missing at the species parameter table, maximum relative growth rates for leaves, sapwood and fine roots are taken from control parameters. Default values are provided in 15.5.3.

A.3.20 Senescence rates

When missing at the species parameter table, senescence rates for sapwood and fine roots are taken from control parameters. The default daily senescence rate for fine roots is \(0.001897231\, day^{-1}\) which corresponds to a 50% annual turnover rate (Gill & Jackson 2000).

A.3.21 Relative starch for sapwood growth

When missing at the species parameter table, the minimum relative starch for sapwood growth is taken from control parameters. Default value is provided in 15.5.3.

A.3.22 Wood carbon

Default values for \(C_{wood}\) are determined from taxonomic family using an internal data set (medfate:::trait_family_means):

Table A.8: Default wood carbon content by taxonomic family.
	WoodC
Acanthaceae	0.4108250
Altingiaceae	0.4435000
Amaranthaceae	0.4199317
Amaryllidaceae	0.4508400
Anacardiaceae	0.4580588
Annonaceae	0.4683333
Apiaceae	0.4382558
Apocynaceae	0.4928286
Aquifoliaceae	0.4400000
Araliaceae	0.4517143
Arecaceae	0.4556000
Asparagaceae	0.4631000
Asteraceae	0.4291509
Betulaceae	0.4750059
Bignoniaceae	0.4692962
Boraginaceae	0.4536333
Brassicaceae	0.4244838
Burseraceae	0.4703312
Calophyllaceae	0.4729500
Campanulaceae	0.4489120
Cannabaceae	0.4706000
Caprifoliaceae	0.4458123
Caryophyllaceae	0.3988381
Casuarinaceae	0.4200000
Celastraceae	0.4900000
Chrysobalanaceae	0.4886000
Cistaceae	0.4698925
Clethraceae	0.4400000
Combretaceae	0.4738116
Convolvulaceae	0.4200000
Corynocarpaceae	0.4520000
Cupressaceae	0.5167800
Cyperaceae	0.4618583
Dipterocarpaceae	0.4748308
Ebenaceae	0.4828000
Elaeocarpaceae	0.4350000
Ericaceae	0.4893318
Euphorbiaceae	0.4667487
Fabaceae	0.4526129
Fagaceae	0.4752026
Gentianaceae	0.4637950
Geraniaceae	0.4381400
Hypericaceae	0.4547167
Juglandaceae	0.4890615
Juncaceae	0.4170530
Juncaginaceae	0.4056355
Lamiaceae	0.4711357
Lauraceae	0.4724000
Lecythidaceae	0.4635571
Lentibulariaceae	0.4450200
Loganiaceae	0.4943000
Lythraceae	0.4219000
Magnoliaceae	0.4500000
Malpighiaceae	0.4765989
Malvaceae	0.4698024
Melastomataceae	0.4679833
Meliaceae	0.4726584
Moraceae	0.4667333
Muntingiaceae	0.4200000
Myristicaceae	0.4891714
Myrtaceae	0.4161398
Nothofagaceae	0.5225000
Ochnaceae	0.4840000
Oleaceae	0.4817818
Orobanchaceae	0.4437020
Pentaphylacaceae	0.5000000
Phyllanthaceae	0.4795857
Pinaceae	0.5027283
Pittosporaceae	0.4630000
Plantaginaceae	0.4229996
Platanaceae	0.4864667
Plumbaginaceae	0.4459770
Poaceae	0.4001785
Podocarpaceae	0.4700000
Polygalaceae	0.4819000
Polygonaceae	0.4461900
Primulaceae	0.4150869
Quillajaceae	0.4900000
Ranunculaceae	0.4398919
Rhamnaceae	0.4794000
Rhizophoraceae	0.4389000
Rosaceae	0.4367044
Rubiaceae	0.4675777
Rutaceae	0.4808400
Salicaceae	0.4787914
Sapindaceae	0.4778069
Sapotaceae	0.4579000
Schisandraceae	0.4550000
Scrophulariaceae	0.4400000
Simaroubaceae	0.4649167
Solanaceae	0.4325000
Staphyleaceae	0.4490000
Styracaceae	0.4750000
Theaceae	0.4760500
Ulmaceae	0.4853286
Urticaceae	0.4569500
Violaceae	0.4576550
Vochysiaceae	0.4750429

If family-level values are missing, default value of \(C_{wood} = 0.5\,g\,C\cdot g\,dry^{-1}\) is used.

A.3.23 Mortality baseline rate

When missing at the species parameter table, the mortality baseline rate is taken from control parameters. Default value is provided in 15.5.3.

A.3.24 Recruitment

Imputation of missing values for recruitment is specified via control parameters. Default values are provided in 19.4.3.

A.3.25 Flammability

Default values for the surface-area-to-volume ratio (\(\sigma\)), fuel heat content (\(h\)) and lignin percent (\(LI\)) are defined from leaf size and leaf shape as follows:

Leaf shape	Leaf size	\(\sigma\)	\(h\)	\(LI\)
Broad	Large	5740	19740	15.50
Broad	Medium	4039	19825	20.21
Broad	Small	4386	20062	22.32
Linear/Needle	Large	3620	18250	24.52
Linear/Needle	Medium	4758	21182	24.52
Linear/Needle	Small	6697	21888	18.55
Spines	[any]	6750	20433	14.55
Scale	[any]	1120	20504	14.55

Default value for the density of fuel particles (\(\rho_p\)) is 400 \(kg\cdot m^{-3}\).

A.4 Scaling size-related parameters

A.4.1 Stem xylem maximum conductance

Estimation of maximum stem conductance (\(k_{s,max}\), in \(mmol \cdot m^{-2} \cdot s^{-1} \cdot MPa^{-1}\)) is done by function hydraulics_maximumStemHydraulicConductance() and follows the work by Savage et al. (2010), Olson et al. (2014) and Christoffersen et al. (2016). Calculations are based on tree height and two species-specific parameters: maximum sapwood reference conductivity (\(K_{s,max,ref}\)) and the ratio of leaf area to sapwood area (\(A_{l}/A_{s}\); Al2As in SpParamsMED), i.e. the inverse of the Huber value \(H_v\).

The reference value for maximum sapwood conductivity \(K_{s,max,ref}\) is assumed to have been measured on a terminal branch of a plant of known height \(H_{ref}\). If our target plant is very different in height, the conduits of terminal branches will have different radius and hence conductivity. We correct the reference conductivity to the target plant height using the following empirical relationship, developed by Olson et al. (2014) between tree height and diameter of conduits for angiosperms and the equation described by Christoffersen et al. (2016): \[\begin{eqnarray} 2 \cdot r_{int,H}&=& 10^{1.257+(0.24\cdot log_{10}(H))} \\ 2 \cdot r_{int,ref}&=&10^{1.257+(0.24\cdot log_{10}(H_{ref}))}\\ K_{s,max,cor}&=&K_{s,max,ref}\cdot (r_{int,H}/r_{int,ref})^{2} \end{eqnarray}\] Where \(r_{int,H}\) is the radius of conduits for a terminal branch of a tree of height \(H\) and \(r_{int,ref}\) is the corresponding radius for a tree of height \(H_{ref}\) (\(H\) and \(H_{ref}\) are measured in m). The form of the empirical relationship by Olson et al. (2014) is:

Let’s consider an example for a Quercus ilex target tree of 4m height and where species-specific conductivity \(K_{s,max,ref} = 0.77\) is the apical value for trees of \(H_{ref} = 6.6\) m (in , values of \(H_{ref}\) are taken from median height values; see parameter Hmed in SpParamsMED). The corrected conductivity for a tree of height 4 m will be a bit lower than that of the reference height:

xylem_kmax = 0.77
H = 400 # in cm
Href = 660 # in cm
f = hydraulics_referenceConductivityHeightFactor(Href, H);
f

## [1] 0.7863352

xylem_kmax_cor = xylem_kmax * f
xylem_kmax_cor

## [1] 0.6054781

Once the reference conductivity is corrected, the maximum stem conductance without accounting for conduit taper is: \[\begin{equation} k_{s,max, notaper}=\frac{1000}{0.018} \frac{K_{s,max,cor}\cdot A_{s}}{H\cdot A_{l}} \end{equation}\] where \(H\) is the tree height (here in m), \(A_{s}\) is the sapwood area, \(A_{l}\) is the leaf area and 1000/0.018 is a factor used to go from kg to mmol. The ratio \(A_{l}/A_{s} = 1/H_v\) is a fixed species parameter in soil water balance calculations (see parameter Al2As), but becomes variable when simulating plant growth. Let’s assume that Quercus ilex the leaf to sapwood area ratio is \(A_{l}/A_{s} = 2512\). The maximum (leaf-specific) stem conductance without taper (\(k_{s, max, notaper}\)) for the tree of 4 m height is then:

Al2As = 2512 

kstemmax = hydraulics_maximumStemHydraulicConductance(xylem_kmax, 
                  Href, Al2As, H, taper = FALSE)
kstemmax

## [1] 3.347698

In order to consider taper of xylem conduits we calculate the whole-tree conductance per unit leaf area (\(k_{s, max, taper}\)) as described in Christoffersen et al. (2016): \[\begin{equation} k_{s, max, taper}=\frac{1000}{0.018} \cdot \frac{K_{s,max,pet}\cdot A_{s}}{H\cdot A_{l}}\cdot \chi_{tap:notap,ag}(H) \end{equation}\] where \(K_{s,max,pet}\) is the conductivity at the petiole level and \(\chi_{tap:notap,ag}(H)\) is the taper factor accounting for the decrease in the xylem conduits diameter with the height, from the petiole to base of the trunk, which mitigates the negative effects of height on the hydraulic safety. The conductivity at the petiole level is obtained from \(K_{s,max,ref}\) using again: \[\begin{equation} K_{s,max,pet} = K_{s,max,ref}\cdot (r_{int, pet}/r_{int,ref})^{2} \end{equation}\] where \(r_{int, pet}\) is the radius of the petiole in the model of Savage et al. (2010). Christoffersen et al. (2016) use \(r_{int, pet} = 10\) \(\mu m\) but we define it as the radius of apical conduits in a tree of 1 m height:

hydraulics_terminalConduitRadius(100.0)

## [1] 9.035871

\(\chi_{tap:notap,ag}(H)\) is calculated as described in the Appendix 1 section of Christoffersen et al. (2016) (see also Savage et al. (2010)). The following figure shows the value of \(\chi_{tap:notap,ag}\) for different heights:

Note that, since \(\chi_{tap:notap,ag}(1) = 3.82\) (indicated using grey dashed lines in the last figure), the equation of maximum conductance with taper would give a higher conductance than the equation without taper for a tree of 1 m height, which is supposed to have a conductance equal to conductivity. To solve this issue we define the taper factor as \(\chi_{tap:notap,ag}(H)/\chi_{tap:notap,ag}(1)\): \[\begin{equation} k_{s, max, taper}=\frac{1000}{0.018} \cdot \frac{K_{s,max,pet}\cdot A_{s}}{H\cdot A_{l}}\cdot \frac{\chi_{tap:notap,ag}(H)}{\chi_{tap:notap,ag}(1)} \end{equation}\] The maximum stem conductance with taper (\(k_{s, max, taper}\)) of a Q. ilex tree of 4 m height, calculated with this second equation, is:

kstemmax_tap = hydraulics_maximumStemHydraulicConductance(xylem_kmax, 
                      Href, Al2As, H, taper = TRUE)
kstemmax_tap

## [1] 4.764396

The next two plots show the variation of \(k_{s,max}\) for Q. ilex depending on the tree height and with/without considering taper of conduits. The plot on the right (both axes in log) show the slope of the dependency of conductance with height in both cases:

A.4.2 Leaf maximum hydraulic conductance

A.4.3 Root xylem maximum hydraulic conductance

To obtain maximum root xylem conductance (\(k_{r, max}\), in \(mmol \cdot m^{-2} \cdot s^{-1} \cdot MPa^{-1}\)), one option taken by Christoffersen et al. (2016) is to assume that minimum stem resistance (inverse of maximum conductance) represents a fixed proportion of the minimum total tree (stem+root) resistance. A value 0.625 (i.e. 62.5%) suggested by these authors leads to maximum total tree conductance for our Q. ilex tree being:

ktot = kstemmax*0.625
ktot

## [1] 2.092311

and the maximum root xylem conductance would be therefore:

krootmax = 1/((1/ktot)-(1/kstemmax))
krootmax

## [1] 5.579497

Now, we need to divide total maximum conductance of the root system xylem among soil layers we need weights inversely proportional to the length of transport distances (Sperry et al. 2017). Vertical transport lengths can be calculated from soil depths and radial spread can be calculated assuming cylinders with volume proportional to the proportions of fine root biomass. Let’s assume a soil with three layers:

s <- soil(defaultSoilParams(3))
d <- s$widths
d

## [1]  300  700 1000

The proportion of fine roots in each layer, assuming a linear dose response model, will be:

Z50 <- 200
Z95 <- 1500
v1 <- root_ldrDistribution(Z50,Z95, NA, d)
v1

##           [,1]      [,2]       [,3]
## [1,] 0.6661036 0.2784153 0.05548106

Having this information, the calculation of root length (i.e. the sum of vertical and radial lengths) to each layer (\(L_j\)) is done using function root_coarseRootLengths():

rfc <- c(20,50,70)
Vol <- root_coarseRootSoilVolumeFromConductance(1.0, 2500,krootmax,
                                               v1, d, rfc)
l <- root_coarseRootLengthsFromVolume(Vol, v1, d, rfc)
l

## [1] 4503.445 3250.363 3085.055

where lengths are in mm. The proportion of total root xylem conductance corresponding to each layer (\(w_j\)) is given by root_xylemConductanceProportions():

w1 <- hydraulics_rootxylemConductanceProportions(v1, l)
w1

## [1] 0.09131268 0.15767645 0.75101087

Xylem conductance proportions can be quite different than the fine root biomass proportions. This is because radial lengths are largest for the first top layers and vertical lengths are largest for the bottom layers. The maximum root xylem conductances of each layer will be the product of maximum total conductance of root xylem and weights:

w1*krootmax

## [1] 0.5094788 0.8797553 4.1902629

The maximum root xylem conductances of each layer would be:

krootmaxvec = w1*krootmax
krootmaxvec

## [1] 0.5094788 0.8797553 4.1902629

and the fraction of total xylem resistance due to stem would be:

(1/kstemmax)/((1/kstemmax)+(1/krootmax))

## [1] 0.625

In contrast with the approach of Christoffersen et al. (2016), in this approach the root maximum conductance depends root length and distribution, and is not a fixed fraction of stem maximum conductance. Assuming constant root length, then the proportion of total resistance due to the stem will increase with tree height (Magnani et al. 2000):

where the horizontal gray line indicates the value of 62.5%. Of course rooting depth also increases with tree age, but young trees have higher root-to-shoot ratios than older ones. Hence, a root maximum conductance that is not fixed but increases with age seems a priori more realistic. Moreover, Christoffersen et al. (2016) justify the value of 62.5% from a study which quantified total aboveground and belowground resistance in tropical trees (Fisher et al. 2006) under near-saturated (wet season) conditions, but values of belowground resistance reported in this study for wet conditions and trees of 30 m height are around 13%, which equals to 87% fraction of aboveground resistance. On the other hand, while rooting depths are limited by soil depth, lateral root length increases with age and, hence, the model could be made more realistic if this is taken into account and the curve above would probably saturate at lower percentages.

A.4.4 Rhizosphere maximum hydraulic conductance

Maximum rhizosphere conductance (\(k_{rh, max}\), in \(mmol \cdot m^{-2} \cdot s^{-1} \cdot MPa^{-1}\)) is difficult to measure directly, as it depends on the rhizosphere (i.e. fine root) surface in each soil layer, and will probably always be a parameter to be calibrated. Instead of trying to estimate rhizosphere surface from root architecture (Sperry et al. 1998), we follow Sperry et al. (2016) and determine the maximum rhizosphere conductance in each layer from an inputed ‘average percentage rhizosphere resistance’. The percentage of continuum resistance corresponding to the rhizosphere is calculated from the vulnerability curves of stem, root and rhizosphere at the same water potential. The average resistance is found by evaluating the percentage for water potential values between 0 and \(\Psi_{crit}\). The following figure illustrates how the supply function, for different soil water potentials, is affected by increasing values of the average percentage of rhizosphere resistance:

Sperry et al. (2016) found average percentages of rhizosphere resistance around 67%, but these exceptionally-high values were probably a consequence of using an unsegmented supply function (i.e. single vulnerability curve for roots, stem and leaves). If we specify a 15% of average resistance in the rhizosphere (see parameter averageFracRhizosphereResistance in function defaultControl()), the maximum rhizosphere conductance values for the three layers are found calling:

krmax = rep(0,3) 
krmax[1]= hydraulics_findRhizosphereMaximumConductance(15, 
                     s$VG_n[1],s$VG_alpha[1],
                     krootmax, rootc,rootd, 
                     kstemmax, stemc, stemd,
                     kleafmax, leafc, leafd, 0)
krmax[2] = hydraulics_findRhizosphereMaximumConductance(15, 
                      s$VG_n[2],s$VG_alpha[2],
                      krootmax, rootc,rootd, 
                      kstemmax, stemc, stemd,
                      kleafmax, leafc, leafd, 0)
krmax[3] = hydraulics_findRhizosphereMaximumConductance(15, 
                      s$VG_n[3],s$VG_alpha[3],
                      krootmax, rootc,rootd, 
                      kstemmax, stemc, stemd,
                      kleafmax, leafc, leafd, 0)
krmax

## [1] 85636744 85636744 85636744

The values are the same because the texture of the three layers is the same in this case. If we take into account root distribution, actual maximum rhizosphere conductance values are:

krmax*v1

##          [,1]     [,2]    [,3]
## [1,] 57042945 23842581 4751218

A.4.5 Plant water storage capacity

The water storage capacity of sapwood tissue per leaf area unit (\(V_{sapwood}\); in \(l \cdot m^{-2}\)) can be estimated as the product of stem height (\(H\) in m) and Huber value (\(H_v\); ratio of sapwood area to leaf area in \(m^2 \cdot m^{-2}\)) times a factor to account for the non-cylindrical shape (http://www.fao.org/forestry/17109/en/): \[\begin{equation} V_{sapwood} = 10^3 \cdot 0.48 \cdot H \cdot H_v \cdot \Theta_{sapwood} \end{equation}\] \(\Theta_{sapwood}\) is sapwood porosity (\(cm^3\) of water per \(cm^3\) of sapwood tissue), which can be estimated from wood density (\(\rho_{wood}\); in \(g \cdot cm^{-3}\)): \[\begin{equation} \Theta_{sapwood} = 1 - (\rho_{wood} / 1.54) \end{equation}\] where the density of wood substance can be assumed to be fixed and equal to 1.54 \(g \cdot cm^{-3}\) (Dunlap 1914). For example, wood densities ranging from 0.443 to 1.000 \(g \cdot cm^{-3}\) result in sapwood porosity values between 0.35 and 0.71.

Water storage capacity of leaf tissue per leaf area unit (\(V_{leaf}\); in \(l \cdot m^{-2}\)) can be estimated as the product of specific leaf area (SLA; in \(m^2 \cdot kg^{-1}\)) and leaf density (\(\rho_{leaf}\); in \(g \cdot cm^{-3}\)): \[\begin{equation} V_{leaf} = \frac{1}{SLA \cdot \rho_{leaf}} \cdot \Theta_{leaf} \end{equation}\] \(\Theta_{leaf}\) is leaf porosity (\(cm^3\) of water per \(cm^3\) of leaf tissue), which can be estimated from leaf density: \[\begin{equation} \Theta_{leaf} = 1 - (\rho_{leaf} / 1.54) \end{equation}\] where the density of wood substance can be assumed to be fixed and equal to 1.54 \(g \cdot cm^{-3}\) (Dunlap 1914).

For example, let’s calculate the stem and leaf water capacity for a Q. ilex tree of 15 m height:

ld = 0.7
SLA = 5.870 
moisture_leafWaterCapacity(SLA, ld)

## [1] 0.1327463

A.4.6 Horizontal root overlap

A.4.6.1 Basic water balance

A given plant cohort \(i\) will have its roots in layer \(s\) partitioned among different water pools. We thus need to define \(fr_{i,s,j}\), the (horizontal) proportion of fine roots of cohort \(i\) in layer \(s\) of the water pool \(j\), with the restriction that: \[\begin{equation} \sum_{j}{fr_{i,s,j}} = 1 \,\, \forall i,s \end{equation}\] It is important to realize that proper estimation of \(fr_{i,s,j}\) is challenging when we do not have explicit plant coordinates, root lateral widths, etc. For this reason, an intuitive approach is followed here based on the following two premises:

The amount of overlap between roots of different plants should monotonically increase along with the LAI of the stand (i.e. \(LAI^{live}_{stand}\)).
The amount of overlap between roots of different plants at a given soil depth should increase/decrease with the vertical proportion of roots at that depth.

The specific formulation we chose for \(fr_{i,s,j}\) is: \[\begin{equation} fr_{i,s,j} = f_{pool,j} \cdot (1 - \exp(- f_{overlap} \cdot LAI^{live}_{stand})) \cdot \left( \frac{\sqrt{FRP_{i,s} \cdot FRP_{j,s}}}{\max_{s}(FRP_{i,s})} \right) \end{equation}\] for all \(j \neq i\), where \(f_{overlap}\) is an overlap factor (a control parameter called poolOverlapFactor). For \(j=i\) then we simply have: \[\begin{equation} fr_{i,s,i} = 1 - \sum_{j}{fr_{i,s,j}} \end{equation}\] Note that if \(f_{overlap} = 0\) then \(fr_{i,s,j} = 1\) if \(j=i\) and zero otherwise (i.e. plants exploit their corresponding water pools only. For very large values of \(LAI^{live}_{stand}\) and/or \(f_{overlap}\) we have that \((1 - \exp(- f_{overlap} \cdot LAI^{live}_{stand})) = 0\) and \(fr_{i,s,j} = f_{pool,j}\) (neglecting vertical differences), so that plants exploit the each water pool in the same proportion as the fraction of stand occupied by the pool (i.e. overlap is maximum).

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