# This script contains 4 functions used to model ET0 and water balance:
# 1. 'snowmod' estimates snowfall and snowpack and net moisture input as
a function of temperature, precip, and existing
#
snowpack. It also outputs a vector of albedo values, generally 0.2
if there is no snow, or 0.8 if there is snow.
# 2. 'monthlyETO' for calculating monthly reference evapotranspiration
# 3. 'dailyET0' for calculating daily reference evapotranspiration
# 4. 'aetmod' estimates actual et, deficit, soil moisture and runoff as a
function of moisture input, existing
#
soil moisture, and soil water capacity.
#
# Author: Alan Swanson 2012
#########################################################################
######
snowmod <function(tmean,ppt,radiation=NULL,snowpack_prev=NULL,albedo=0.23,albedo_s
now=0.8){
# This function computes monthly estimated snowfall and snowmelt.
Output includes end-of-month snowpack,
# water "input" (snowmelt plus rain), and albedo.
# Arguments:
# tmean - vector of mean monthly temperatures
# radiation - vector of shortwave solar radiation in MJ/m^2/day.
# snowpack_prev - vector of snowpack at the beginning of the
month. If NULL this is
#
taken to be zero.
# albedo - a single value for albedo in the absence of snow cover.
# albedo_snow - single value of albedo given snow cover
#
# Value: dataframe with three columns for end-of-month snowpack,
H2O input (rain plus snowmelt),
# and albedo.
N <- length(tmean)
if(is.null(snowpack_prev)) snowpack_prev <- rep(0,N)
snowpack <- rep(NA,N)
input <- rep(NA,N)
# this is for radiation in MJ/m^2/day
mf <- function(t,t0,t1) pmin(pmax((t-t0)/(t1-t0),0),1)
linrmelt <- function(temp,radiation,b0,b1,b2)
pmax((b0+temp*b1+radiation*b2),0)
parvec <- c(-4.604,6.329,-398.4,81.75,25.05)
mfsnow <- mf(tmean,parvec[1],parvec[2])
mfmelt <- linrmelt(tmean,radiation,parvec[3],parvec[4],parvec[5])
# calculate values
snow <- (1-mfsnow)*ppt
rain <- mfsnow*ppt
melt <- pmin(mfmelt,snow+snowpack_prev)
snowpack <- snowpack_prev+snow-melt
input <-rain+melt
# make vector of albedo values
albedo <- rep(albedo,N)
albedo[snowpack>0 | (snowpack_prev>0)] <- albedo_snow
return(data.frame(snowpack=snowpack,input=input,albedo=albedo))
}
monthlyET0 <function(radiation,tmax,tmin,wind,lat,elev,dpt,tmean_prev,albedo=0.23,mon
th){
# This function runs Reference ET estimates for monthly timesteps
using methods based on
# the Penman-Montieth equation as presented in Allen et al (1998). It
incorporates a
# modification which adjusts stomatal conductance downwards at
temperatures below 5 C.
#
# Arguments:
# radiation: vector of monthly average shortwave radiation in
MJ/m^2/day
# tmax, tmin: vectors of monthly average maximum and minimum
temperatures in C,
# wind: vector of monthly average wind speed in m/s at 10m above
ground,
# tmean_prev: vector of mean temp for the previous month,
# lat: vector of latitude in degrees
# elev: vector of elevation in meters,
# dpt: vector of dewpoint temperature in C.
# tmean_prev: vector of mean temp of previous month in C
# albedo: vector or scalar of albedo values,
# month: scalar 1-12.
#
# Value:
# Returns a vector of ET0 values.
t0<-unclass(Sys.time())
daysinmonth=c(31,28,31,30,31,30,31,31,30,31,30,31)
d2=c(31,59,90,120,151,181,212,243,273,304,334,365)
d1=c(1,32,60,91,121,152,182,213,244,274,305,335)
DoY <- (d1[month]+d2[month])/2 # use middle day of month to
represent monthly average.
n_days <- daysinmonth[month]
# calculate soil heat flux (total for the month) using change in
temperature from previous month
tmean <- (tmax+tmin)/2
G <- 0.14*(tmean-tmean_prev) # fixed from previous version
# convert to wind height at 2m
hw=10 # height of wind measurements
wind <- wind*(4.87/log(67*hw-5.42))
# convert to wind height at 2m
# stomatal conductance adjustment for low temperatures
sr=100 # stomatal resistance sec/m
ks_min=.01 # minimum value for temps below T1
Tl=-10
# minimum temp (sc goes to ks_min below this temp)
T0=5
# optimal temp
Th=100
# maximum temp (sc goes to zero above this)
thresh=5
# temperature threshold below which to apply Jarvis
equation (ks=1 above this temp)
b4 <- (Th-T0)/(Th-Tl)
b3 <- 1/((T0-Tl)*(Th-T0)^b4)
ks <- pmax(pmin(b3*(tmean-Tl)*(Th-tmean)^b4,1),ks_min)
ks[is.na(ks)] <- ks_min
ks[tmean>=thresh] <- 1
# convert to stomatal resistance.
sr <- sr/ks
# ra is aerodynamic resistance, rs is bulk surface resistance
ra <- 208/wind #(log((2-2/3*0.12)/(0.123*0.12))*log((22/3*0.12)/(0.1*0.123*0.12)))/(0.41^2*wind) # equal to 208/wind for
hh=hw=2.
#ra <- 208/wind
rs <- sr/(0.5*24*0.12) # value of 70 when sr=100
# Saturation vapor pressure ,
es <0.6108*exp(tmin*17.27/(tmin+237.3))/2+0.6108*exp(tmax*17.27/(tmax+237.3))
/2
ea <- 0.6108*exp((dpt)*17.27/((dpt)+237.3))
vpd <- es - ea
vpd[vpd<0] <- 0
# added because this can be negative if dewpoint
temperature is greater than mean temp (implying vapor pressure greater
than saturation).
# delta - Slope of the saturation vapor pressure vs. air
temperature curve at the average hourly air temperature
delta <- (4098 * es)/(tmean + 237.3)^2
P <- 101.3*((293-0.0065*elev)/293)^5.26
# Barometric pressure in
kPa
lambda <- 2.501-2.361e-3*tmean # latent heat of vaporization
cp <- 1.013*10^-3 # specific heat of air
gamma <- cp*P/(0.622*lambda) # Psychrometer constant (kPa C-1)
pa <- P/(1.01*(tmean+273)*0.287) # mean air density at constant
pressure
# Calculate potential max solar radiation or clear sky radiation
GSC=0.082
# MJ m -2 min-1 (solar constant)
phi <- pi*lat/180
dr <- 1+0.033*cos(2*pi/365*DoY)
delt <- 0.409*sin(2*pi/365*DoY-1.39)
omegas <- acos(-tan(phi)*tan(delt))
Ra <- 24*60/pi*GSC*dr*(omegas*sin(phi)*sin(delt)
+cos(phi)*cos(delt)*sin(omegas))
# Daily extraterrestrial radiation
Rso <- Ra*(0.75+2e-5*elev)
#For a cloudless day, Rs is roughly
75% of extraterrestrial radiation (Ra)
# radfraction is a measure of relative shortwave radiation, or of
# possible radiation (cloudy vs. clear-sky)
radfraction <- radiation/Rso
radfraction[radfraction>1] <- 1
# longwave and net radiation
longw <- 4.903e-9*n_days*((tmax+273.15)^4+(tmin+273.15)^4)/2*(.34.14*sqrt(ea))*(1.35*radfraction-.35)
netrad <- radiation*n_days*(1-albedo)-longw
# ET0
et0 <- .408*((delta*(netradG))+(pa*cp*vpd/ra*3600*24*n_days))/(delta+gamma*(1+rs/ra))
return(et0)
}
dailyET0 <function(radiation,tmax,tmin,wind,lat,elev,albedo=0.23,dpt,doy){
# This is a ET0 function designed for daily inputs.
# Arguments:
# radiation: vector of monthly average shortwave radiation in
MJ/m^2/day
# tmax, tmin: vectors of monthly average maximum and minimum
temperatures in C,
# wind: vector of monthly average wind speed in m/s,
# tmean_prev: vector of mean temp for the previous month,
# lat: vector of latitude in degrees
# elev: vector of elevation in meters,
# albedo: scaler or vector of albedo values,
# doy: scalar day of year 1-365,
#
# Value:
# Returns a vector of ET0 values.
tmean <- (tmin+tmax)/2
n_days <- 1
G <- 0 # assume soil heat flux to be zero
# wind adjustment to 2m from 10m output
hw=10 # height at which wind is measured
wind <- wind*(4.87/log(67*hw-5.42))
# stomatal conductance adjustment for low temperatures
sr=100 # stomatal resistance sec/m
ks_min=.01 # minimum value for temps below T1
Tl=-10
# minimum temp (sc goes to ks_min below this temp)
T0=5
# optimal temp
Th=100
# maximum temp (sc goes to zero above this)
thresh=5
# temperature threshold below which to apply Jarvis
equation (ks=1 above this temp)
b4=(Th-T0)/(Th-Tl) # from Jarvis 1978
b3=1/((T0-Tl)*(Th-T0)^b4)
ks=pmax(pmin(b3*(tmean-Tl)*(Th-tmean)^b4,1),ks_min)
ks[is.na(ks)] <- ks_min
ks[tmean>=thresh] <- 1
# convert to stomatal resistance.
sr <- sr/ks
# ra is aerodynamic resistance, rs is bulk surface resistance
ra <- 208/wind #
rs <- sr/(0.5*24*0.12) # value of 70 when sr=100
# Saturation vapor pressure ,
es <0.6108*exp(tmin*17.27/(tmin+237.3))/2+0.6108*exp(tmax*17.27/(tmax+237.3))
/2 # saturation vapor pressure
ea <- 0.6108*exp((dpt)*17.27/((dpt)+237.3))
# actual vapor pressure
vpd <- es - ea
vpd[vpd<0] <- 0
# delta - Slope of the saturation vapor pressure vs. air
temperature curve
delta <- (4098 * es)/(tmean + 237.3)^2
P <- 101.3*((293-0.0065*elev)/293)^5.26 # Barometric pressure in
kPa
lambda <- 2.501-2.361e-3*tmean # latent heat of vaporization
cp <- 1.013*10^-3 # specific heat of air
gamma <- cp*P/(0.622*lambda) # Psychrometer constant (kPa C-1)
pa <- P/(1.01*(tmean+273)*0.287) # mean air density at constant
pressure
# Calculate potential max solar radiation or clear sky radiation.
GSC = 0.082
# MJ m -2 min-1 (solar constant)
phi <- pi*lat/180
dr <- 1+0.033*cos(2*pi/365*doy)
delt <- 0.409*sin(2*pi/365*doy-1.39)
omegas <- acos(-tan(phi)*tan(delt))
Ra <- 24*60/pi*GSC*dr*(omegas*sin(phi)*sin(delt)
+cos(phi)*cos(delt)*sin(omegas)) # daily extraterrestrial radiation
Rso <- Ra*(0.75+2e-5*elev)
#For a cloudless day, Rs is roughly
75% of extraterrestrial radiation (Ra)
# radfraction is a measure of relative shortwave radiation, or of
# possible radiation (cloudy vs. clear-sky), needs to be less than
1
radfraction <- radiation/Rso
radfraction[radfraction>1] <- 1
# longwave radiation
longw <- 4.903e-9*n_days*((tmax+273.15)^4+(tmin+273.15)^4)/2*(.34.14*sqrt(ea))*(1.35*radfraction-.35)
# net radiation
netrad <- radiation*n_days*(1-albedo)-longw
# ET from long-form P-M eqn.
et0 <- .408*((delta*(netradG))+(pa*cp*vpd/ra*3600*24*n_days))/(delta+gamma*(1+rs/ra))
return(et0)
}
aetmod <- function(et0,input,awc,soil_prev=NULL){
# This function computes AET given ET0, H2O input, soil water capacity,
and beginning-of-month soil moisture
# Arguments:
# et0: vector of monthly reference evapotranspiration in mm
# input: vector of monthly water input to soil in mm
# awc: vector of soil water capacity in mm
# soil_prev: vector of soil water content for the previous month (mm).
If left NULL this is assigned to be zero.
#
# Value:
# returns a data frame with columns for AET, deficit, end-of-month soil
moisture, and runoff.
N <- length(et0)
runoff <- def <- aet <- soil <- rep(NA,N) #
if(is.null(soil_prev)) soil_prev <- rep(0,N)
deltasoil <- input-et0 # positive=excess H2O, negative=H2O deficit
# Case when there is a moisture surplus:
Case <- deltasoil>=0
if(sum(Case)>0){
aet[Case] <- et0[Case]
def[Case] <- 0
soil[Case] <- pmin(soil_prev[Case]+deltasoil[Case],awc[Case])
#
increment soil moisture, but not above water holding capacity
runoff[Case] <- pmax(soil_prev[Case]+deltasoil[Case]-awc[Case],0) #
when awc is exceeded, send the rest to runoff
}
# Case where there is a moisture deficit: soil moisture is reduced
Case <- deltasoil<0
if(sum(Case)>0){
soildrawdown <- soil_prev[Case]*(1-exp(-(et0-input)[Case]/awc[Case]))
# this is the net change in soil moisture (neg)
aet[Case] <- pmin(input[Case] + soildrawdown,et0[Case])
def[Case] <- et0[Case] - aet[Case]
soil[Case] <- soil_prev[Case]-soildrawdown
runoff[Case] <- 0
}
return(data.frame(aet=aet,def=def,soil=soil,runoff=runoff))
}