Quadratically increasing CO2 emission will increase CO2 concentration cubically and also the Earth’s temperature

This is to demonstrate that as CO2 emissions (inflow, gigatons/year) increase quadratically (2nd order), the CO2 concentration (or atmospheric CO2 in gigatons, gt) will increase cubically (3rd order). Therefore, it can be logically concluded that Earth’s temperature will increase non-linearly (much faster) as there is a relationship between atmospheric CO2 and temperature. I used the relationship between speed and distance as an analogy.
◼
  • If CO2 emission is constant, then CO2 concentration will increase linearly over time.
    • ◼
  • If CO2 emission increase linearly, then CO2 concentration will increase quadratically over time.
    • ◼
  • If CO2 emission increase quadratically, then CO2 concentration will increase cubically (3rd order).

    • Analogy : {speed (meter/second) vs. distance (meter)} and {CO2 emission (gt/year) vs. CO2 concentration (gt)}

    ​​​

    Speed and distance

    ◼
  • Case 1. Speed is constant
    • In[]:=
    sol=DSolve[{x'[t]9.8,x[0]0},x,{t,0,10}]
    Out[]=
    {{xFunction[{t},0.+9.8t]}}
    {Plot[{x'[t]/.sol},{t,0,10},FrameTrue,FrameLabel{"Time","Speed (m/s)"},PlotLegendsPlaced[{"Speed (m/s)"},Above],PlotRange{{0,10},{0,500}},GridLinesAutomatic,ImageSize300,PlotStyleRed],​​Plot[{x[t]/.sol},{t,0,10},FrameTrue,FrameLabel{"Time","Distance (m)"},PlotLegendsPlaced[{"Distance (m)"},Above],PlotRange{{0,10},{0,500}},GridLinesAutomatic,ImageSize300]}//Row
    Out[]=
    Speed (m/s)
    Distance (m)
    ◼
  • Case 2. Speed increases linearly
    • In[]:=
    sol2=DSolve[{x'[t]9.8*t,x[0]0},x,{t,0,10}]
    Out[]=
    {{xFunction[{t},4.9
    2
    t
    ]}}
    {Plot[{x'[t]/.sol2},{t,0,10},FrameTrue,FrameLabel{"Time","Speed (m/s)"},PlotLegendsPlaced[{"Speed (m/s)"},Above],PlotRange{{0,10},{0,500}},GridLinesAutomatic,ImageSize300,PlotStyleRed],​​Plot[{x[t]/.sol2},{t,0,10},FrameTrue,FrameLabel{"Time","Distance (m)"},PlotLegendsPlaced[{"Distance (m)"},Above],PlotRange{{0,10},{0,500}},GridLinesAutomatic,ImageSize300]}//Row
    Out[]=
    Speed (m/s)
    Distance (m)
    ◼
  • Case 3. Speed increases quadratically
    • In[]:=
    sol3=DSolve[{x'[t]1.98*t^2,x[0]0},x,{t,0,10}]
    Out[]=
    {{xFunction[{t},0.66
    3
    t
    ]}}
    In[]:=
    {Plot[{x'[t]/.sol3},{t,0,10},FrameTrue,FrameLabel{"Time","Speed (m/s)"},PlotLegendsPlaced[{"Speed (m/s)"},Above],PlotRange{{0,10},{0,500}},GridLinesAutomatic,ImageSize300,PlotStyleRed],​​Plot[{x[t]/.sol3},{t,0,10},FrameTrue,FrameLabel{"Time","Distance (m)"},PlotLegendsPlaced[{"Distance (m)"},Above],PlotRange{{0,10},{0,500}},GridLinesAutomatic,ImageSize300]}//Row
    Out[]=
    Speed (m/s)
    Distance (m)

    CO2 emission and concentration

    ◼
  • Case 1. CO2 emission (giga tons / year) is constant
    • In[]:=
    solC=DSolve[{concentration'[t]9.8,concentration[0]0},concentration,{t,0,10}]
    Out[]=
    {{concentrationFunction[{t},0.+9.8t]}}
    In[]:=
    (*Thevaluesusedforco2emissionandconcentrationareusedasademonstrationanddonotreflecttheactualvalues*)​​{Plot[{concentration'[t]/.solC},{t,0,10},FrameTrue,FrameLabel{"year","Emission (gt/year)"},PlotLegendsPlaced[{"Emission (gt/year)"},Above],PlotRange{{0,10},{0,500}},GridLinesAutomatic,ImageSize300,PlotStyleRed],​​Plot[{concentration[t]/.solC},{t,0,10},FrameTrue,FrameLabel{"year","Concentration (gt)"},PlotLegendsPlaced[{"Concentration (gt)"},Above],PlotRange{{0,10},{0,500}},GridLinesAutomatic,ImageSize300]}//Row
    Out[]=
    Emission (gt/year)
    Concentration (gt)
    ◼
  • Case 2. CO2 emission (giga tons / year) increases linearly
    • In[]:=
    sol2C=DSolve[{concentration'[t]9.8*t,concentration[0]0},concentration,{t,0,10}]
    Out[]=
    {{concentrationFunction[{t},4.9
    2
    t
    ]}}
    In[]:=
    {Plot[{concentration'[t]/.sol2C},{t,0,10},FrameTrue,FrameLabel{"year","Emission (gt/year)"},PlotLegendsPlaced[{"Emission (gt/year)"},Above],PlotRange{{0,10},{0,500}},GridLinesAutomatic,ImageSize300,PlotStyleRed],​​Plot[{concentration[t]/.sol2C},{t,0,10},FrameTrue,FrameLabel{"year","Concentration (gt)"},PlotLegendsPlaced[{"Concentration (gt)"},Above],PlotRange{{0,10},{0,500}},GridLinesAutomatic,ImageSize300]}//Row
    Out[]=
    Emission (gt/year)
    Concentration (gt)
    ◼
  • Case 3. CO2 emission (giga tons / year) increases quadratically. This reflects current economic development and has implications to Earth temperature
    • In[]:=
    sol3C=DSolve[{concentration'[t]1.98*t^2,concentration[0]0},concentration,{t,0,10}]
    Out[]=
    {{concentrationFunction[{t},0.66
    3
    t
    ]}}
    {Plot[{concentration'[t]/.sol3C},{t,0,10},FrameTrue,FrameLabel{"year","Emission (gt/year)"},PlotLegendsPlaced[{"Emission (gt/year) increases quadratically"},Above],PlotRange{{0,10},{0,500}},GridLinesAutomatic,ImageSize300,PlotStyleRed],​​​​Plot[{concentration[t]/.sol3C},{t,0,10},FrameTrue,FrameLabel{"year","Concentration (gt)"},PlotLegendsPlaced[{"Concentration (gt) increase cubically"},Above],PlotRange{{0,10},{0,500}},GridLinesAutomatic,ImageSize300]}//Row
    Out[]=
    Emission (gt/year) increases quadratically
    Concentration (gt) increase cubically

    CITE THIS NOTEBOOK

    Current CO2 emission will increase CO2 concentration cubically​
    by Sangdon Lee​
    Wolfram Community, STAFF PICKS, May 20 2023
    ​https://community.wolfram.com/groups/-/m/t/2922562