use theat_clim_month.nc 
use "/User/homes/lequere/archive/data/levitus/woa2001.nc" 
use "/User/homes/lequere/archive/tm3/roedenbeck/apostflux.nc" 

!
! input => temp = sea surface temperature in oC
! input => sal = sea surface salinity in psu
! input => theat = heat flux in W/m2
!
let c0=-59.6274
let c1=85.7661
let c2=24.3696
let c3=-0.051580
let c4=0.026329
let c5=-0.0037252            

set axis/modulo time

let ttt = (temp[k=1,d=2]+273.16) * 0.01
let sss = sal[k=1,d=2]
let heat = theat[d=1]

let k5= c0 + c1/ttt + c2*ln(ttt) + sss*(c3+c4*ttt+c5*ttt*ttt)
let a5 = 0.790   * ( exp(k5) / 22.4144)
let dn2dtt = 0.01 * a5 * ( (-1)*c1 / (ttt*ttt) + c2 / ttt + sss * ( c4 + 2*c5*ttt))
let n2_from_heat = 1000*heat[d=1]*dn2dtt/(1025*3993)*3.156e7

! units are mol/m2/yr

set variable/title="N2 flux due to Heat flux"/units="mol/m^2/yr" n2_from_heat   

shade n2_from_heat[l=1]
save/file=n2_from_heat.nc n2_from_heat

! 
! Reference: R. F. Weiss, The solubility of nitrogen, oxygen and argon in water and seawater.
! Deep-Sea Research, 17, pp 721-735.