Description

# fossil fuel unit is million metric tons 1e12 gram C
# unit PgC is 1e15 gram C # 1ppm CO2 is 2.13 PgC/GtC
gamma_pd =pd.read_csv(‘global.1751_2014.csv’,index_col= [‘Year’])
# Spline interpolation
gamma = UnivariateSpline(gamma_pd.index, gamma_pd[‘Total carbon emissions from foss gamma.set_smoothing_factor(0.5)
In [1]:
method to solve ODE questions
def dmove(Point,t,sets):
k12,k21,gamma = sets gamma_t =gamma(t+1986)*1e-3 n1,n2 = Point
return np.array([ -k12*n1+k21*n2+gamma_t, k12*n1-k21*n2]) def move(Point,t,sets):
k12,k21,gamma,sita,n02 = sets gamma_t =gamma(t+1986)*1e-3 n1,n2 = Point
return np.array([ -k12*n1+k21*(n02+sita*(n2-n02))+gamma_t, k12*n1-k21*(n02+sita
# from 1986 to 2007 t = np.arange(0,20,1)
In [2]:
plot Q1
P1 = odeint(dmove,(740,900),t,args = ([105/740,102/900,gamma],))[:,0]/2.13
# plot
fig =plt.figure(figsize=(7,4),dpi =100) plt.plot(t+1986,P1) plt.title(‘The atmonsphere CO2 concentration trend predicted by the two box without plt.ylabel(‘CO2 concentration (ppm)’) plt.xlabel(‘Year’) plt.show()
In [3]:

plot Q2
buff =0.95
P2 = odeint(move,(740+79,900-79),t,args = ([105/(740+79),102/(900-79),gamma,buff,82
# plot
fig =plt.figure(figsize=(7,4),dpi =100) plt.plot(t+1986,P2) plt.title(‘The atmonsphere CO2 concentration trend predicted by the two box without plt.ylabel(‘CO2 concentration (ppm)’) plt.xlabel(‘Year’) plt.show()
set buffer effect as 0.95 In [4]:

plot Q3
obs =pd.read_csv(‘co2_annmean_mlo.csv’, nrows= 20)
# plot
fig =plt.figure(figsize=(8,4),dpi =100) plt.scatter(obs.year, obs.Mean, label =’observations’) plt.plot(t+1986,P1, label =’without buffer effect’) plt.plot(t+1986,P2, label =’with buffer effect(beffer =0.95)’) plt.title(‘The atmonsphere CO2 concentration trend’) plt.ylabel(‘CO2 concentration (ppm)’) plt.xlabel(‘Year’) plt.legend() plt.show()
In [5]:

Q4
cannot find σ dataset( emission rate to the atmonsphere by changes in land use)
def sevenBox(Point,t,sets):
k12,k21,k23,k24,k32,k34,k43,k45,k51,k67,k71, n02,f,sigma,sita,gamma = sets gamma_t =gamma(t+1751)*1e-3 n1,n2,n3,n4,n5,n6,n7 = Point return np.array([ -k12*n1+k21*(n02+sita*(n2-n02))+gamma_t-f+sigma+k51*n5+k71*n7 k12*n1-k21*(n02+sita*(n2-n02))-k23*n2+k32*n3-k24*n2, k23*n2-k32*n3-k34*n3+k43*n4, k34*n3-k43*n4+k24*n2-k45*n4, k45*n4-k51*n5, f-k67*n6-2*sigma, k67*n6-k71*n7+sigma
]) t2 =np.arange(0,260,1)
In [6]:

P3 = odeint(sevenBox,
(615,842,9744,26280,90000000,731,1238), t2, args = ([60/615, 60/842, 9/842, 43/842, 52/9744, 162/9744, 205/26280, 0
842,62, 0.7,0.38, gamma,],) )[:,0]/2.13
P4 = odeint(sevenBox,
(615,842,9744,26280,90000000,731,1238), t2, args = ([60/615, 60/842, 9/842, 43/842, 52/9744, 162/9744, 205/26280, 0
842,62, 0.8,0.5, gamma,],) )[:,0]/2.13
fig =plt.figure(figsize=(8,4),dpi =100) plt.plot(t2+1751,P3, label =’with buffer effect(buffer =0.38′) plt.plot(t2+1751,P4, label =’with buffer effect(beffer =0.50)’) plt.title(‘The atmonsphere CO2 concentration trend’) plt.ylabel(‘CO2 concentration (ppm)’) plt.xlabel(‘Year’) plt.legend() plt.show()
In [7]: In [8]: