Ice albedo feedback

%auto #T is in degrees Celsius and A and B are from derived from atmospheric # conditions to be A = 218 Wm^2 and B = 1.90 W/m^2C # The value of C to be 10^7J/2.0 # I use some variables as I wanted to test the new symbolic support var('t Q gamma') ai = 0.35; af = 0.7 A = 218.0 B = 1.9 # effective heat capacity. C = 10^7/2.0 # solved for T at equilibrium T = function('T',t) # the co-albedo is a function of T ap(T) = ai + 0.5*(af-ai)*(1 + tanh(gamma*T)) # eq 2.36 bal_eq = C*diff(T,t) == -A - B*T + Q*ap # solve for steady state q_eq = solve(bal_eq.rhs() == 0,Q)[0].rhs() @interact def coalbedo(gamma_value=(0,1,.1)): # this is the ap and Q plot. #ga = graphics_array([qplot,aplot]) #show(qplot + aplot,figsize=5) plot(ap.substitute(gamma=gamma_value),(T,-50,50),legend_label='$a_p$').show() plot(q_eq.substitute(gamma=gamma_value),(T,-40,40),color="cyan",legend_label='$Q$').show() 

# plotting Q and ap for i [0.1,0.5,0.9]. Are the ap plots correct? [coalbedo(i) for i in srange(.1,1.,.2)] 

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