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functions.R
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functions.R
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allocate_numerical_libs_stuff <- function () {
xp <<- vector("numeric", kmax)
yp <<- matrix(nrow = N, ncol = kmax)
yscal <<- vector("numeric", N)
y <<- vector("numeric", N)
dydx <<- vector("numeric", N)
ystart <<- vector("numeric", N)
ak2 <<- vector("numeric", N)
ak3 <<- vector("numeric", N)
ak4 <<- vector("numeric", N)
ak5 <<- vector("numeric", N)
ak6 <<- vector("numeric", N)
ytemp <<- vector("numeric", N)
yerr <<- vector("numeric", N)
}
initialise_roots <- function () {
# Set up all the rooting arrays for use with the hydraulics assumptions
thickness <<- vector("numeric", n_layers)
# root mass is g biomass, i.e. ~twice the C content
root_mass <<- vector("numeric", n_layers)
root_length <<- vector("numeric", n_layers)
layer_depth <<- vector("numeric", n_layers)
thick <- 0.1
layer_depth[1] <<- thick
thickness[1] <<- thick
for (i in 2:n_layers) {
thick <- thick + layer_thickness
layer_depth[i] <<- thick
thickness[i] <<- layer_thickness
# made up initalisation, following SPA, get replaced second timestep
root_mass[i] <<- 0.1
root_length[i] <<- 0.1
rooted_layers <<- n_layers
}
}
write_output_subdaily_header <- function() {
# Write 30 min fluxes headers to an output CSV file. This is very basic
# for now...
#create data frame with 0 rows and 3 columns
df <- data.frame(matrix(ncol = 9, nrow = 0))
#provide column names
colnames(df) <- c('year', 'doy', 'hod', 'an_canopy', 'rd_canopy', 'gsc_canopy', 'apar_canopy', 'trans_canopy', 'tleaf')
return (df)
}
write_output_header <- function() {
df <- data.frame(matrix(ncol = 107, nrow = 0))
#provide column names
colnames(df) <- c(
'year', 'doy', 'wtfac_root', 'wtfac_topsoil', 'pawater_root', 'pawater_topsoil',
'shoot', 'lai', 'branch', 'stem', 'root', 'croot',
'shootn', 'branchn', 'stemn', 'rootn', 'crootn',
'shootp', 'branchp', 'stemp', 'rootp', 'crootp',
'cstore', 'nstore', 'pstore',
'soilc', 'soiln', 'soilp', 'inorgn',
'inorgp', 'inorgavlp', 'inorglabp', 'inorgsorbp', 'inorgssorbp', 'inorgoccp', 'inorgparp',
'litterc', 'littercag', 'littercbg', 'litternag', 'litternbg',
'litterpag', 'litterpbg',
'activesoil', 'slowsoil', 'passivesoil',
'activesoiln', 'slowsoiln', 'passivesoiln', 'activesoilp', 'slowsoilp', 'passivesoilp',
'et', 'transpiration', 'soil_evap', 'canopy_evap', 'runoff',
'gs_mol_m2_sec', 'ga_mol_m2_sec',
'deadleaves', 'deadbranch', 'deadstems', 'deadroots', 'deadcroots',
'deadleafn', 'deadbranchn', 'deadstemn', 'deadrootn', 'deadcrootn',
'deadleafp', 'deadbranchp', 'deadstemp', 'deadrootp', 'deadcrootp',
'nep', 'gpp', 'npp', 'hetero_resp', 'auto_resp', 'apar',
'cpleaf', 'cpbranch', 'cpstem', 'cproot', 'cpcroot',
'npleaf', 'npbranch', 'npstemimm', 'npstemmob', 'nproot', 'npcroot',
'ppleaf', 'ppbranch', 'ppstemimm', 'ppstemmob', 'pproot', 'ppcroot',
'nuptake', 'ngross', 'nmineralisation', 'nloss',
'puptake', 'pgross', 'pmineralisation', 'ploss',
'leafretransn', 'leafretransp'
)
return (df)
}
setup_hydraulics_arrays <- function () {
potA <<- vector("numeric", n_layers)
potB <<- vector("numeric", n_layers)
cond1 <<- vector("numeric", n_layers)
cond2 <<- vector("numeric", n_layers)
cond3 <<- vector("numeric", n_layers)
porosity <<- vector("numeric", n_layers)
field_capacity <<- vector("numeric", n_layers)
soil_conduct <<- vector("numeric", n_layers)
swp <<- vector("numeric", n_layers)
soilR <<- vector("numeric", n_layers)
fraction_uptake <<- vector("numeric", n_layers)
ppt_gain <<- vector("numeric", n_layers)
water_loss <<- vector("numeric", n_layers)
water_gain <<- vector("numeric", n_layers)
water_frac <<- vector("numeric", n_layers)
wetting_bot <<- vector("numeric", wetting)
wetting_top <<- vector("numeric", wetting)
est_evap <<- vector("numeric", n_layers)
}
fill_up_solar_arrays <- function() {
hour_idx <<- 1
ntimesteps <- total_num_days * 48
cz_store <<- vector("numeric", ntimesteps)
ele_store <<- vector("numeric", ntimesteps)
df_store <<- vector("numeric", ntimesteps)
for (nyr in 1:num_years) {
year <- ma$year[hour_idx]
if (is_leap_year(year)) {
num_days <- 366
} else {
num_days <- 365
}
for (doy in 1:num_days) {
for (hod in 1:num_hlf_hrs) {
# calculate solar geometry
hod <- hod / 2
gamma <- day_angle(doy)
rdec <- calculate_solar_declination(doy, gamma)
et <- calculate_eqn_of_time(gamma)
t0 <- calculate_solar_noon(et, longitude)
h <- calculate_hour_angle(hod, t0)
rlat <- DEG2RAD(latitude)
# A13 - De Pury & Farquhar
sin_beta <- sin(rlat) * sin(rdec) + cos(rlat) * cos(rdec) * cos(h)
cos_zenith <<- sin_beta # The same thing, going to use throughout
if (cos_zenith > 1.0)
cos_zenith <<- 1.0
else if (cos_zenith < 0.0)
cos_zenith <<- 0.0
zenith_angle <- RAD2DEG(acos(cos_zenith))
elevation <<- 90.0 - zenith_angle
sw_rad <- ma$par[hour_idx] * PAR_2_SW
#get diffuse frac
# sine of the elev of the sun above the horizon is the same as cos_zen
So <- calc_extra_terrestrial_rad(doy, cos_zenith)
# atmospheric transmisivity
tau <- estimate_clearness(sw_rad, So)
cos_zen_sq <- cos_zenith * cos_zenith
# For zenith angles > 80 degrees, diffuse_frac = 1.0
if (cos_zenith > 0.17) {
# Spitters formula
R <- 0.847 - 1.61 * cos_zenith + 1.04 * cos_zen_sq
K <- (1.47 - R) / 1.66
if (tau <= 0.22) {
diffuse_frac <<- 1.0
} else if (tau > 0.22 && tau <= 0.35) {
diffuse_frac <<- 1.0 - 6.4 * (tau - 0.22) * (tau - 0.22)
} else if (tau > 0.35 && tau <= K) {
diffuse_frac <<- 1.47 - 1.66 * tau
} else {
diffuse_frac <<- R
}
} else {
diffuse_frac <<- 1.0
}
# doubt we need this, should check
if (diffuse_frac <= 0.0) {
diffuse_frac <<- 0.0
} else if (diffuse_frac >= 1.0) {
diffuse_frac <<- 1.0
}
direct_frac <<- 1.0 - diffuse_frac
cz_store[hour_idx] <<- cos_zenith
ele_store[hour_idx] <<- elevation
df_store[hour_idx] <<- diffuse_frac
hour_idx <<- hour_idx + 1
}
}
}
}
calc_carbon_allocation_fracs <- function (npitfac) {
# Carbon allocation fractions to move photosynthate through the plant.
#
# Parameters:
# -----------
# npitfac : float
# the smallest value of leaf N:C as a fraction of 'Ncmaxfyoung' (max 1.0) &
# leaf P:C as a fraction of "Pcmaxfyoung" (max 1.0)
#
# Returns:
# --------
# alleaf : float
# allocation fraction for shoot
# alroot : float
# allocation fraction for fine roots
# albranch : float
# allocation fraction for branches
# alstem : float
# allocation fraction for stem
#
# References:
# -----------
# Corbeels, M. et al (2005) Ecological Modelling, 187, 449-474.
# McMurtrie, R. E. et al (2000) Plant and Soil, 224, 135-152.
# this is obviously arbitary
min_stem_alloc <- 0.01
if (alloc_model == FIXED){
alleaf <<- (c_alloc_fmax + npitfac *
(c_alloc_fmax - c_alloc_fmin))
alroot <<- (c_alloc_rmax + npitfac *
(c_alloc_rmax - c_alloc_rmin))
albranch <<- (c_alloc_bmax + npitfac *
(c_alloc_bmax - c_alloc_bmin))
# allocate remainder to stem
alstem <<- 1.0 - alleaf - alroot - albranch
alcroot <<- c_alloc_cmax * alstem
alstem <<- alstem - alcroot
} else if (alloc_model == GRASSES) {
# First figure out root allocation given available water & nutrients hyperbola shape to allocation
alroot <<- (c_alloc_rmax * c_alloc_rmin /
(c_alloc_rmin + (c_alloc_rmax - c_alloc_rmin) * prev_sma))
alleaf <<- 1.0 - alroot
# Now adjust root & leaf allocation to maintain balance, accounting
# for stress e.g. Sitch et al. 2003, GCB.
#
# leaf-to-root ratio under non-stressed conditons
# lr_max = 0.8
#
# Calculate adjustment on lr_max, based on current "stress"
# calculated from running mean of N and water stress
# stress = lr_max * prev_sma
#
# calculate new allocation fractions based on imbalance in *biomass*
# mis_match = shoot / (root * stress)
#
#
# if (mis_match > 1.0) {
# reduce leaf allocation fraction
# adj = alleaf / mis_match
# alleaf = MAX(c_alloc_fmin, MIN(c_alloc_fmax, adj))
# alroot = 1.0 - alleaf
# } else {
# reduce root allocation
# adj = alroot * mis_match
# alroot = MAX(c_alloc_rmin, MIN(c_alloc_rmax, adj))
# alleaf = 1.0 - alroot
# }
alstem <<- 0.0
albranch <<- 0.0
alcroot <<- 0.0
} else if (alloc_model == ALLOMETRIC) {
# Calculate tree height: allometric reln using the power function
# (Causton, 1985)
canht <<- heighto * (stem ^ htpower)
# LAI to stem sapwood cross-sectional area (As m-2 m-2)
# (dimensionless)
# Assume it varies between LS0 and LS1 as a linear function of tree
# height (m)
arg1 <- sapwood * TONNES_AS_KG * M2_AS_HA
arg2 <- canht * density * cfracts
sap_cross_sec_area <- arg1 / arg2
leaf2sap <- lai / sap_cross_sec_area
# Allocation to leaves dependant on height. Modification of pipe
# theory, leaf-to-sapwood ratio is not constant above a certain
# height, due to hydraulic constraints (Magnani et al 2000 Deckmyn
# et al. 2006).
if (canht < height0) {
leaf2sa_target <- leafsap0
} else if (float_eq(canht, height1)) {
leaf2sa_target <- leafsap1
} else if (canht > height1) {
leaf2sa_target <- leafsap1
} else {
arg1 <- leafsap0
arg2 <- leafsap1 - leafsap0
arg3 <- canht - height0
arg4 <- height1 - height0
leaf2sa_target <- arg1 + (arg2 * arg3 / arg4)
}
alleaf <<- alloc_goal_seek(leaf2sap, leaf2sa_target, c_alloc_fmax, targ_sens)
# Allocation to branch dependent on relationship between the stem
# and branch
target_branch <- branch0 * (stem ^ branch1)
albranch <<- alloc_goal_seek(branch, target_branch, c_alloc_bmax, targ_sens)
coarse_root_target <- croot0 * (stem ^ croot1)
alcroot <<- alloc_goal_seek(croot, coarse_root_target, c_alloc_cmax, targ_sens)
# figure out root allocation given available water & nutrients
# hyperbola shape to allocation, this is adjusted below as we aim
# to maintain a functional balance
alroot <<- (c_alloc_rmax * c_alloc_rmin /
(c_alloc_rmin + (c_alloc_rmax - c_alloc_rmin) * prev_sma))
alstem <<- 1.0 - alroot - albranch - alleaf - alcroot
# minimum allocation to leaves - without it tree would die, as this
# is done annually.
if (deciduous_model) {
if (alleaf < 0.05) {
min_leaf_alloc <- 0.05
if (alstem > min_leaf_alloc)
alstem <<- alstem - min_leaf_alloc
else
alroot <<- alroot - min_leaf_alloc
alleaf <<- min_leaf_alloc
}
}
} else {
stop(paste("Unknown C allocation model:", alloc_model))
}
# fprintf(stderr, "alleaf %f, alstem %f, alroot %f, canht %f\n",
# alleaf, albranch + alstem, alroot, canht)
#
# Total allocation should be one, if not print warning
total_alloc <- alroot + alleaf + albranch + alstem + alcroot
if (total_alloc > 1.0 + EPSILON) {
stop(paste("Allocation fracs > 1:", total_alloc))
}
}
allocate_stored_cnp <- function() {
# Allocate stored C,N and P. This is either down as the model is initialised
# for the first time or at the end of each year.
# ========================
# Carbon - fixed fractions
# ========================
c_to_alloc_shoot <<- alleaf * cstore
c_to_alloc_root <<- alroot * cstore
c_to_alloc_croot <<- alcroot * cstore
c_to_alloc_branch <<- albranch * cstore
c_to_alloc_stem <<- alstem * cstore
# =========================================================
# Nitrogen - Fixed ratios N allocation to woody components.
# =========================================================
# N flux into new ring (immobile component structrual components)
n_to_alloc_stemimm <<- cstore * alstem * ncwimm
# N flux into new ring (mobile component can be retrans for new woody tissue)
n_to_alloc_stemmob <<- cstore * alstem * (ncwnew - ncwimm)
n_to_alloc_branch <<- cstore * albranch * ncbnew
n_to_alloc_croot <<- cstore * alcroot * nccnew
# Calculate remaining N left to allocate to leaves and roots
ntot <- max(0.0, (nstore - n_to_alloc_stemimm - n_to_alloc_stemmob - n_to_alloc_branch))
# allocate remaining N to flexible-ratio pools
n_to_alloc_shoot <<- (ntot * alleaf / (alleaf + alroot * ncrfac))
n_to_alloc_root <<- ntot - n_to_alloc_shoot
# leaf_NC = n_to_alloc_shoot / c_to_alloc_shoot
# if leaf_NC > 0.04:
# n_to_alloc_shoot = c_to_alloc_shoot * 0.14
#
# n_to_alloc_root = ntot - n_to_alloc_shoot
#
#
# root_NC = n_to_alloc_root / c_to_alloc_root
# ncmaxr = 0.04 * ncrfac
# if root_NC > ncmaxr:
# extrar = (n_to_alloc_root -
# (c_to_alloc_root * ncmaxr))
#
# inorgn += extrar
# n_to_alloc_root -= extrar
#
#
# =========================================================
# Phosphorus - Fixed ratios P allocation to woody components.
# =========================================================
#
# P flux into new ring (immobile component structrual components)
p_to_alloc_stemimm <<- cstore * alstem * pcwimm
# P flux into new ring (mobile component can be retrans for new woody tissue
p_to_alloc_stemmob <<- cstore * alstem * (pcwnew - pcwimm)
p_to_alloc_branch <<- cstore * albranch * pcbnew
p_to_alloc_croot <<- cstore * alcroot * pccnew
# Calculate remaining P left to allocate to leaves and roots
ptot <- max(0.0, (pstore - p_to_alloc_stemimm - p_to_alloc_stemmob - p_to_alloc_branch))
# allocate remaining P to flexible-ratio pools
p_to_alloc_shoot <<- (ptot * alleaf / (alleaf + alroot * pcrfac))
p_to_alloc_root <<- ptot - p_to_alloc_shoot
}
SMA_ADD <- function (value) {
sma_obj$lv <<- sma_obj$lv + 1
if (sma_obj$lv <= sma_obj$period) {
sma_obj$values[sma_obj$lv] <<- value
sma_obj$sum <<- sma_obj$sum + value
sma_obj$sma <<- sma_obj$sum / sma_obj$lv
} else {
if (sma_obj$lv %% sma_obj$period == 0) {
idx <- sma_obj$period
} else {
idx <- sma_obj$lv %% sma_obj$period
}
sma_obj$sum <<- sma_obj$sum - sma_obj$values[idx]
sma_obj$sum <<- sma_obj$sum + value
sma_obj$sma <<- sma_obj$sum / sma_obj$period
sma_obj$values[idx] <<- value
}
}
correct_rate_constants <- function(output) {
# adjust rate constants for the number of days in years
if (output) {
rateuptake <<- rateuptake * NDAYS_IN_YR
prateuptake <<- prateuptake * NDAYS_IN_YR
rateloss <<- rateloss * NDAYS_IN_YR
prateloss <<- prateloss * NDAYS_IN_YR
retransmob <<- retransmob * NDAYS_IN_YR
pfdecay <<- pfdecay * NDAYS_IN_YR
fdecaydry <<- fdecaydry * NDAYS_IN_YR
crdecay <<- crdecay * NDAYS_IN_YR
prdecay <<- prdecay * NDAYS_IN_YR
rdecaydry <<- rdecaydry * NDAYS_IN_YR
bdecay <<- bdecay * NDAYS_IN_YR
wdecay <<- wdecay * NDAYS_IN_YR
sapturnover <<- sapturnover * NDAYS_IN_YR
kdec1 <<- kdec1 * NDAYS_IN_YR
kdec2 <<- kdec2 * NDAYS_IN_YR
kdec3 <<- kdec3 * NDAYS_IN_YR
kdec4 <<- kdec4 * NDAYS_IN_YR
kdec5 <<- kdec5 * NDAYS_IN_YR
kdec6 <<- kdec6 * NDAYS_IN_YR
kdec7 <<- kdec7 * NDAYS_IN_YR
nuptakez <<- nuptakez * NDAYS_IN_YR
puptakez <<- puptakez * NDAYS_IN_YR
nmax <<- nmax * NDAYS_IN_YR
pmax <<- pmax * NDAYS_IN_YR
p_atm_deposition <<- p_atm_deposition * NDAYS_IN_YR
p_rate_par_weather <<- p_rate_par_weather * NDAYS_IN_YR
max_p_biochemical <<- max_p_biochemical * NDAYS_IN_YR
rate_sorb_ssorb <<- rate_sorb_ssorb * NDAYS_IN_YR
rate_ssorb_occ <<- rate_ssorb_occ * NDAYS_IN_YR
} else {
rateuptake <<- rateuptake / NDAYS_IN_YR
prateuptake <<- prateuptake / NDAYS_IN_YR
rateloss <<- rateloss / NDAYS_IN_YR
prateloss <<- prateloss / NDAYS_IN_YR
retransmob <<- retransmob / NDAYS_IN_YR
pfdecay <<- pfdecay / NDAYS_IN_YR
fdecaydry <<- fdecaydry / NDAYS_IN_YR
crdecay <<- crdecay / NDAYS_IN_YR
prdecay <<- prdecay / NDAYS_IN_YR
rdecaydry <<- rdecaydry / NDAYS_IN_YR
bdecay <<- bdecay / NDAYS_IN_YR
wdecay <<- wdecay / NDAYS_IN_YR
sapturnover <<- sapturnover / NDAYS_IN_YR
kdec1 <<- kdec1 / NDAYS_IN_YR
kdec2 <<- kdec2 / NDAYS_IN_YR
kdec3 <<- kdec3 / NDAYS_IN_YR
kdec4 <<- kdec4 / NDAYS_IN_YR
kdec5 <<- kdec5 / NDAYS_IN_YR
kdec6 <<- kdec6 / NDAYS_IN_YR
kdec7 <<- kdec7 / NDAYS_IN_YR
nuptakez <<- nuptakez / NDAYS_IN_YR
puptakez <<- puptakez / NDAYS_IN_YR
nmax <<- nmax / NDAYS_IN_YR
pmax <<- pmax / NDAYS_IN_YR
p_atm_deposition <<- p_atm_deposition / NDAYS_IN_YR
p_rate_par_weather <<- p_rate_par_weather / NDAYS_IN_YR
max_p_biochemical <<- max_p_biochemical / NDAYS_IN_YR
rate_sorb_ssorb <<- rate_sorb_ssorb / NDAYS_IN_YR
rate_ssorb_occ <<- rate_ssorb_occ / NDAYS_IN_YR
}
}
day_end_calculations <- function(days_in_year, init) {
# Calculate derived values from state variables.
# Parameters:
# -----------
# day : integer
# day of simulation
#
# INIT : logical
# logical defining whether it is the first day of the simulation
# update N:C and P:C of plant pool
if (float_eq(shoot, 0.0)) {
shootnc <<- 0.0
shootpc <<- 0.0
} else {
shootnc <<- shootn / shoot
shootpc <<- shootp / shoot
}
# Explicitly set the shoot N:C
if (ncycle == FALSE)
shootnc <<- prescribed_leaf_NC
if (pcycle == FALSE)
shootpc <<- prescribed_leaf_PC
if (float_eq(root, 0.0)) {
rootnc <<- 0.0
rootpc <<- 0.0
} else {
rootnc <<- max(0.0, rootn / root)
rootpc <<- max(0.0, rootp / root)
}
# total plant, soil & litter nitrogen
soiln <<- inorgn + activesoiln + slowsoiln + passivesoiln
litternag <<- structsurfn + metabsurfn
litternbg <<- structsoiln + metabsoiln
littern <<- litternag + litternbg
plantn <<- shootn + rootn + crootn + branchn + stemn
totaln <<- plantn + littern + soiln
# total plant, soil & litter phosphorus
inorgp <<- inorglabp + inorgsorbp + inorgssorbp + inorgoccp + inorgparp
soilp <<- inorgp + activesoilp + slowsoilp + passivesoilp
litterpag <<- structsurfp + metabsurfp
litterpbg <<- structsoilp + metabsoilp
litterp <<- litterpag + litterpbg
plantp <<- shootp + rootp + crootp + branchp + stemp
totalp <<- plantp + litterp + soilp # + inorgssorbp + inorgoccp + inorgparp
# total plant, soil, litter and system carbon
soilc <<- activesoil + slowsoil + passivesoil
littercag <<- structsurf + metabsurf
littercbg <<- structsoil + metabsoil
litterc <<- littercag + littercbg
plantc <<- root + croot + shoot + stem + branch
totalc <<- soilc + litterc + plantc
# optional constant passive pool
if (passiveconst) {
passivesoil <<- passivesoilz
passivesoiln <<- passivesoilnz
passivesoilp <<- passivesoilpz
}
if (init == FALSE)
# Required so max leaf & root N:C can depend on Age
age <<- age + 1.0 / days_in_year
}
get_soil_fracs <- function(soil_type) {
# Based on Table 2 in Cosby et al 1984, page 2.
# Fractions of silt, sand and clay (in that order)
fsoil <- rep(0, 3)
if (soil_type == "sand") {
fsoil[1] <- 0.05
fsoil[2] <- 0.92
fsoil[3] <- 0.03
} else if (soil_type == "loamy_sand") {
fsoil[1] <- 0.12
fsoil[2] <- 0.82
fsoil[3] <- 0.06
} else if (soil_type == "sandy_loam") {
fsoil[1] <- 0.32
fsoil[2] <- 0.58
fsoil[3] <- 0.1
} else if (soil_type == "loam") {
fsoil[1] <- 0.39
fsoil[2] <- 0.43
fsoil[3] <- 0.18
} else if (soil_type == "silty_loam") {
fsoil[1] <- 0.7
fsoil[2] <- 0.17
fsoil[3] <- 0.13
} else if (soil_type == "sandy_clay_loam") {
fsoil[1] <- 0.15
fsoil[2] <- 0.58
fsoil[3] <- 0.27
} else if (soil_type == "clay_loam") {
fsoil[1] <- 0.34
fsoil[2] <- 0.32
fsoil[3] <- 0.34
} else if (soil_type == "silty_clay_loam") {
fsoil[1] <- 0.56
fsoil[2] <- 0.1
fsoil[3] <- 0.34
} else if (soil_type == "sandy_clay") {
fsoil[1] <- 0.06
fsoil[2] <- 0.52
fsoil[3] <- 0.42
} else if (soil_type == "silty_clay") {
fsoil[1] <- 0.47
fsoil[2] <- 0.06
fsoil[3] <- 0.47
} else if (soil_type == "clay") {
fsoil[1] <- 0.2
fsoil[2] <- 0.22
fsoil[3] <- 0.58
} else {
stop(paste("Could not understand soil type:" + soil_type))
}
return (fsoil)
}
get_soil_params <- function(soil_type) {
# For a given soil type, get the parameters for the soil
# moisture availability based on Landsberg and Waring, with updated
# parameters from Landsberg and Sands (2011), pg 190, Table 7.1
#
# Table also has values from Saxton for soil texture, perhaps makes more
# sense to use those than Cosby? Investigate?
#
# Reference
# ---------
# Landsberg and Sands (2011) Physiological ecology of forest production.
# Landsberg and Waring (1997) Forest Ecology & Management, 95, 209-228.
# Clapp & Hornberger (1978) Water Resources Research, 14, 601–604.
if (soil_type == "clay") {
c_theta <- 0.4
n_theta <- 3.0
} else if (soil_type == "clay_loam") {
c_theta <- 0.5
n_theta <- 5.0
} else if (soil_type == "loam") {
c_theta <- 0.55
n_theta <- 6.0
} else if (soil_type == "loamy_sand") {
c_theta <- 0.65
n_theta <- 8.0
} else if (soil_type == "sand") {
c_theta <- 0.7
n_theta <- 9.0
} else if (soil_type == "sandy_clay") {
c_theta <- 0.45
n_theta <- 4.0
} else if (soil_type == "sandy_clay_loam") {
c_theta <- 0.525
n_theta <- 5.5
} else if (soil_type == "sandy_loam") {
c_theta <- 0.6
n_theta <- 7.0
} else if (soil_type == "silt") {
c_theta <- 0.625
n_theta <- 7.5
} else if (soil_type == "silty_clay") {
c_theta <- 0.425
n_theta <- 3.5
} else if (soil_type == "silty_clay_loam") {
c_theta <- 0.475
n_theta <- 4.5
} else if (soil_type == "silty_loam") {
c_theta <- 0.575
n_theta <- 6.5
} else {
stop(paste("There are no parameters for your soil type:", soil_type))
}
return (c(c_theta, n_theta))
}
calc_soil_params <- function(fsoil) {
# Cosby parameters for use within the Clapp Hornberger soil hydraulics
# scheme are calculated based on the texture components of the soil.
#
# NB: Cosby et al were ambiguous in their paper as to what log base to
# use. The correct implementation is base 10, as below.
#
# Parameters:
# ----------
# fsoil : list
# fraction of silt, sand, and clay (in that order
#
# Returns:
# --------
# theta_fc : float
# volumetric soil water concentration at field capacity
# theta_wp : float
# volumetric soil water concentration at the wilting point
#
# soil suction of 3.364m and 152.9m, or equivalent of -0.033 & -1.5 MPa
pressure_head_wilt <- -152.9
pressure_head_crit <- -3.364
# *Note* subtle unit change to be consistent with fractions as opposed
# to percentages of sand, silt, clay, e.g. I've changed the slope in
# the "b" Clapp paramter from 0.157 to 15.7
#
# Also Cosby is unclear about which log base were used. 'Generally' now
# assumed that logarithms to the base 10
# Clapp Hornberger exponent [-]
b <- 3.1 + 15.7 * fsoil[CLAY] - 0.3 * fsoil[SAND]
# soil matric potential at saturation, taking inverse of log (base10)
# units = m
psi_sat <- CM_2_M * -(10.0 ^ (1.54 - 0.95 * fsoil[SAND] + 0.63 * fsoil[SILT]))
psi_sat_mpa <- psi_sat * METER_OF_HEAD_TO_MPA
# volumetric soil moisture concentrations at the saturation point
theta_sp <- 0.505 - 0.037 * fsoil[CLAY] - 0.142 * fsoil[SAND]
# volumetric soil moisture concentrations at the wilting point
# assumed to equal suction of -1.5 MPa or a depth of water of 152.9 m
theta_wp <- theta_sp * ((psi_sat / pressure_head_wilt) ^ (1.0 / b))
# volumetric soil moisture concentrations at field capacity assumed to
# equal a suction of -0.0033 MPa or a depth of water of 3.364 m
theta_fc <- theta_sp * ((psi_sat / pressure_head_crit) ^ (1.0 / b))
return (c(theta_fc, theta_wp, theta_sp, b, psi_sat_mpa))
}
zbrent <- function(func, x1, x2, tol, root_biomass,
surf_biomass, rooted_layers, top_lyr_thickness, root_reach) {
#Using Brent’s method, find the root of a function func known to lie
#between x1 and x2. The root, returned as zbrent, will be refined
#until its accuracy is tol.
#Numerical Recipies in C, chapter 9.3
a <- x1
b <- x2
fa <- func(a, root_biomass, surf_biomass, rooted_layers, top_lyr_thickness, root_reach)
fb <- func(b, root_biomass, surf_biomass, rooted_layers, top_lyr_thickness, root_reach)
ITMAX <- 100 # Maximum allowed number of iterations.
EPS <- 3.0e-8 # Machine floating-point precision.
if (fb * fa > 0.0) {
stop("ERROR: Root must be bracketed in ZBRENT")
}
fc <- fb
for (iter in 1:ITMAX) {
if (fb * fc > 0.0) {
c <- a
fc <- fa
d <- b - a
e <- b - a
}
if (abs(fc) < abs(fb)) {
a <- b
b <- c
c <- a
fa <- fb
fb <- fc
fc <- fa
}
tol1 <- 2.0 * EPS * abs(b) + 0.5 * tol
xm <- 0.5 * (c-b)
if (abs(xm) <= tol1 || fb == 0.0)
return (b)
if (abs(e) >= tol1 && abs(fa) > abs(fb)) {
s <- fb / fa
if (a == c) {
p <- 2.0 * xm * s
q <- 1.0 - s
} else {
q <- fa / fc
r <- fb / fc
p <- s * (2.0 * xm * q * (q - r) - (b - a) * (r - 1.0))
q <- (q - 1.0) * (r - 1.0) * (s - 1.0)
}
if (p > 0.0) q <- -q
p <- abs(p)
min1 <- 3.0 * xm * q - abs(tol1 * q)
min2 <- abs(e*q)
if (2.0 * p < min(min1, min2)) {
e <- d
d <- p / q
} else {
d <- xm
e <- d
}
} else {
d <- xm
e <- d
}
a <- b
fa <- fb
if (abs(d) > tol1) {
b <- b + d
} else {
b <- b + (if (xm > 0.0) abs(tol1) else -abs(tol1))
}
fb <- func(b, root_biomass, surf_biomass, rooted_layers,
top_lyr_thickness, root_reach)
}
stop("Maximum number of iterations exceeded in ZBRENT")
}
saxton_field_capacity <- function(xval, potA, potB, dummy1, dummy2, dummy3) {
# field capacity calculations for saxton eqns
air_entry_swp <- 10.0 # (kPa)
MPa_2_kPa <- 1000.0
# calculate the soil water potential (MPa)
swp <- -0.001 * potA * (xval ^ potB)
return (MPa_2_kPa * swp + air_entry_swp)
}
calc_saxton_stuff <- function(fsoil) {
# Calculate the key parameters of the Saxton equations:
# cond1, 2, 3 and potA, B
#
# NB: Currently I'm assuming a single texture for the entire root zone,
# we could set it by layer obviously and we probably should...
#
# Reference:
# ---------
# * Saxton, K. E., Rawls, W. J., Romberger, J. S. & Papendick, R. I.
# (1986) Estimating generalized soil-water characteristics from texture.
# Soil Science Society of America Journal, 90, 1031-1036.
mult1 <- 100.0
mult2 <- 2.778E-6
mult3 <- 1000.0
A <- -4.396
B <- -0.0715
CC <- -4.880E-4
D <- -4.285E-5
E <- -3.140
F <- -2.22E-3
G <- -3.484E-5
H <- 0.332
J <- -7.251E-4
K <- 0.1276
P <- 12.012
Q <- -7.551E-2
R <- -3.895
T <- 3.671e-2
U <- -0.1103
V <- 8.7546E-4
x1 <- 0.1
x2 <- 0.7
tol <- 0.0001
dummy <- 0.0
sand <- fsoil[SAND] * 100.0
clay <- fsoil[CLAY] * 100.0
# As we aren't currently changing texture by layer, the loop is redundant,
# but it is probably best to leave it under the assumption we change
# this later
for (i in 1:n_layers) {
potA[i] <<- exp(A + B * clay + CC * sand * sand + D * sand * sand * clay) * 100.0
potB[i] <<- E + F * clay * clay + G * sand * sand * clay
cond1[i] <<- mult2
cond2[i] <<- P + Q * sand
cond3[i] <<- R + T * sand + U * clay + V * clay * clay
porosity[i] <<- H + J * sand + K * log10(clay)
# field capacity is water content at which SWP = -10 kPa
field_capacity[i] <<- zbrent(saxton_field_capacity, x1, x2, tol,
potA[i], potB[i],
dummy, dummy, dummy)
}
}
calc_soil_conductivity <- function(water_frac, cond1, cond2, cond3) {
# Soil hydraulic conductivity (m s-1 ) per soil layer based on
# Saxton et al. (1986) equations. Used in the soil drainage integrator
# Avoid floating-underflow error
if (water_frac < 0.05) {
scond <- 1E-30
} else {
scond <- cond1 * exp(cond2 + cond3 / water_frac)
}
return (scond)
}
calc_soil_root_resistance <- function() {
# head of pressure (MPa/m)
head <- 0.009807
root_xsec_area <- pi * root_radius * root_radius
# Store each layers resistance, used in LWP calculatons
rsum <- 0.0
for (i in 1:rooted_layers) {
# converts from ms-1 to m2 s-1 MPa-1
Lsoil <- soil_conduct[i] / heads
if (Lsoil < 1e-35) {
# prevent floating point error
soilR[i] <<- 1e35
} else {
rs <- sqrt(1.0 / (root_length[i] * M_PI))
arg1 <- log(rs / root_radius)
arg2 <- 2.0 * pi * root_length[i] * thickness[i] * Lsoil
# soil resistance, convert from MPa s m2 m-3 to MPa s m2 mmol-1
soilR1 <- (arg1 / arg2) * 1E-6 * 18. * 0.001
# Need to combine resistances in parallel, but we only want the
# soil term as the root component is part of the plant resistance
rsum <- rsum + 1.0 / soilR1
# second component of below ground resistance related to root
# hydraulics
soilR2 <- root_resist / (root_mass[i] * thickness[i])
# soilR[i] <- soilR1 + soilR2 # MPa s m2 mmol-1
soilR[i] <<- soilR1 + soilR2 # MPa s m2 mmol-1
}
}
total_soil_resist <<- 1.0 / rsum
}
calc_soil_water_potential <- function() {
# Calculate the SWP (MPa) in each soil layer based on algorithms from
# Saxton et al. (1986). We are not updating the water fraction in each
# layer
for (i in 1:rooted_layers) {
if (water_frac[i] > 0.0) {
swp[i] <- -0.001 * potA[i] * (water_frac[i] ^ potB[i])
} else {
swp[i] <- -9999.0
}
}
}
calc_water_uptake_per_layer <- function() {
# Determine which layer water is extracted from. This is achieved by
# roughly estimating the maximum rate of water supply from each rooted
# soil layer, using SWP and hydraulic resistance of each layer. Actual
# water from each layer is determined using the estimated value as a
# weighted factor.
total_est_evap <- 0.0
weighted_swp <<- 0.0
# Estimate max transpiration from gradient-gravity / soil resistance
for (i in 1:rooted_layers) {
est_evap[i] <<- max(0.0, (swp[i] - min_lwp) / soilR[i])
total_est_evap <- total_est_evap + est_evap[i]
}
if (total_est_evap > 0.0) {
# fraction of water taken from layer
for (i in 1:rooted_layers) {
weighted_swp <<- weighted_swp + swp[i] * est_evap[i]
fraction_uptake[i] <<- est_evap[i] / total_est_evap
}
weighted_swp <<- weighted_swp / total_est_evap
} else {
# No water was evaporated
for (i in 1:rooted_layers) {
fraction_uptake[i] <<- 1.0 / rooted_layers
}
}
if (fraction_uptake[1] > 1 || fraction_uptake[1] < 0) {
stop("Problem with the uptake fraction")
}
}
initialise_soils_sub_daily <- function() {
# Initialise soil water state & parameters
# - We have two options: (i) simple two-layer bucket, or
# - multi-layer soil model.
#
# Currently, I'm just using the same soil type for all layers in the
# multi-layer model, once it all works we can add something to allow
# texture to be changes by layer/depth.