Biome model

Equations in Desktop
variable: D = graph(month)
variable: month = fmod(time(1),12)
variable: bare = 1-sum([f])
variable: total_transp1 = sum([transp1])
variable: total_transp2 = sum([transp2])

Equations in VEGETATION TYPE
variable: Aa = ap*phi_d*phi_t 
   Units must be mol(CO2) per month
variable: temp = graph(month)
variable: a = 0.08
   "Ratio of leaf respiration to photosynthetic capacity" 
   (but also (p.653)    described as merely "an empirical parameter")
variable: sigma = (1-alpha/td)^0.5 
   "sigma is a dimensionless factor that depends only on the 
   fractional daylength (td) and the ratio of leaf respiration to 
   photosynthetic capacity (alpha)"
variable: Ap = fpar*sigma*phi*im 
   "Ap  =  monthly potential photosynthesis"
   Units must be mol(CO2) per month
variable: FPAR = 0.5
   Value???   "fraction of incoming PAR absorbed by the green vegetation"
variable: Im = graph(month)
   Value?????   "total monthly incident PAR"
   Units nust be mol(photons) per month
variable: td = 0.5
   "fractional daylength"
variable: phi = (if temp<13 then 0.07 else(if temp>38 then 0.04 else 0.04+0.03*(temp-13)/(38-13)))
   "quantum efficiency of gross photosynthesis at prescribed ambient CO2"
   "mol(CO2)/mol(photons)"
  "C3 plants at 13C  =  0.07, at 38C  =  0.04"
   "C4 plants  =  0.054, at any temp"
   "Field values c. 50% lower"
variable: PHI D = e/d 
   "drought scalar, ratio of actual to equilibrium evapotranspiration
    for the month as calculated by the water flux model"
variable: PHI T = (if temp<5 then 0 else(if temp>35 then 0 else(if temp<20 then(temp-5)/(20-5)else(if temp>30 then(temp-30)/(35-30)else 1))))
   "monthly temperature scalar, is set to unity across a range of 
   temperatures from T2 to T3.   Below T2 the scalar decreases linearly
   to a value of zero at a temperature T1, and above T3 the scalar decreases
   to zero at a temperature T4"
variable: alpha = z*w1/(z*w1+(1-z)*w2)
variable: f = element([1,0,0,0],index(1))
variable: E = min(s,d)
   Instantaneous evapotranspiration rate, mm/hour.   In the paper,
   this is "integrated analytically over the 24 hour period".  In the
   present model, it is NOT.  Need to think about this:  can we do
   numerically, by integrating over the fractiosn of a "typical day"
   for each month? (i.e. time unit  =  1 month, time step  =  0.05 'day')
variable: transp1 = alpha*f*e 
variable: beta = (1-z)*w2/(z*w1+(1-z)*w2)
variable: transp2 = beta*f*e 
variable: Z = element([0.33,0.33,0.9,0.9],index(1))
variable: Wr = z*w1+(1-z)*w2 
variable: C = 1
   mm/hour   "maximum possible rate of evapotranspiration by plant species"
   Value is given in paper.
variable: S = c*wr 
   "supply function" for plant species.  mm/hour
variable: Pnet = aa-0.4*ap 

Equations in WATER
compartment: Water = 100
   mm
flow: rain = 40
   mm/month
flow: transpiration = transp+transp2 
flow: evaporation = 20*bare 
variable: W1 = water*thetamax1*d1/(d1+d2)
variable: W2 = water*thetamax2*d2/(d1+d2)
variable: d1 = 500
   mm:  depth of upper layer
variable: d2 = 1500
   mm:  depth of lower layer
variable: thetamax2 = 200
variable: thetamax1 = 300