Experiments with ice albedo feedback in The Azimuth Project

[[!redirects Experiments with ice albedo feedback]]
# Contents
* sl
{:toc}

## Idea

To make a simple model of how [[albedo]] impacts global temperature
The first [[Sage]] [draft is here for discussion](http://demo.sagenb.org/home/pub/238/). Where i plotted $a_p$ and Q for several values of $\gamma$.

Are the plots for $a_p$ **looking correct? Do I need to calculate T_e before
I calculate Q?**

## Details
### Draft Code

<pre>
#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 = 0.3; af = 0.7
A = 218.0
B = 1.9
# effective heat capacity. transform C in K to C?
C = 10^7/2.0

# should this be solved for Te?
T = function('T',t)

# the co-albedo is a function of T
#ap = function('ap',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

# or should we use t_e from eq. 2.9 instead in 2.37 ?
q_eq = solve(bal_eq.rhs() == 0,Q)[0].rhs()

@interact
def coalbedo(gamma_value=(0,1,.1)):
    # this is the Q plot and ap plot. 
    #ga = graphics_array([qplot,aplot])
    #show(qplot + aplot,figsize=5)
    plot(q_eq.substitute(gamma=gamma_value),(T,0,40),color="cyan",legend_label='$Q$').show()
    plot(ap.substitute(gamma=gamma_value),(T,-4,4),legend_label='$a_p$').show()

</pre>

## References

category:experiments