Summary:

Climate Sensitivity (CS) in this case is the change in average earth surface temperature  (ΔT) over the time it takes for atmospheric CO2 to double from 400 ppm to 800 ppm (Δt).  Climate Sensitivity is also defined as the additional radiative forcing required to maintain equilibrium between solar heat absorbed in and heat radiated out to space after atmospheric CO2 doubles from 400 ppm to 800 ppm, in units of watts/m².  There are also other concepts of CS, each of which is a measure of projected global warming, but the CS defined here is most commonly used.

Herein statistical treatment of real data is used to compute  ΔT/Δt.  The ΔT/Δt is then multiplied by the number of years between 2016 (400 ppm CO2) and the year in which 800 ppm CO2 is attained.  This treatment requires projection (extrapolation) beyond the limit of data available (2020).   In statistics this often very risky.  To estimate confidence, four runs for CO2 content were made and compared: intervals 1980-2020, 1990-2020, 2000-2020, and 2010-2020.  The 1980-2020 interval has the most data, the 2010-2020 interval has the least data but represents the latest trend.  For CO2 ppm a quadratic curve fit was used, and the year 800 ppm is reached was determined by trial and error.  For temperature change per year a linear curve fit (from 1980 to 2020) was used and projection was made using the resulting slope.  R² for the slope was 0.604 for linear fit (due wide scatter in data, see Figure1), 0.602 for quadratic fit.  See graphs of data.

The ModTran program is used to compute radiative forcing, for the extreme case of no clouds and no rain for the condition defined as “1976 Standard Atmosphere”.

Procedure:

1. 1. Compute  ΔT/Δt Estimate annual average earth surface ΔT as described above, From linear regression of satellite global temperature data, determine the slope of the linear curve fit.
      Result: Slope = 0.0145 C/yr
   2. Compute Years to Achieve 800 ppm CO2.
      a. From four quadratic equations for ppmCO2 vs. year, for annual intervals 1980, 1990, 2000 and 2010 to 2020. From NOAA data of CO2 at Mauna Loa, HI observatory, calculate annual ppm of CO2 in air, from 1979 to 2020 as average of monthly data (which itself is average of daily readings).
      b. The year1980 is taken as base year because satellite global temperature data         became available in 1978.
      c. Atmospheric CO2 was 401 ppm in 2016
      d.  For each base year (period base yr to 2020) obtain quadratic equation and compute, by trial  and error, compute year when CO2 level reaches 800 ppm.  (MyCurveFit.com was used to do this):
      Results: x = year, y = annual average ppm CO2, R² of each >0.999

      Base Yr	Final Yr = 2020		Used 12 mo avge ppm CO2
      2010	y = 105268.1 – 106.5321*x + 0.02704167*x^2
      2000	y = 69793.63 – 71.27313*x + 0.01828053*x^2
      1990	y = 76149.17 – 77.60133*x + 0.01985576*x^2
      1980	y = 64038.83 – 65.52178*x + 0.01684362*x^2

   3. Calculate Climate Sensitivity by multiplying 0.0145 ΔT/Δt by the average (over 4 intervals) number of years Δt to reach 800 ppm.  Result:
      

      Base Yr	800 ppm Yr	Yrs 400 to 800 ppm	Climate Sensitivity, ºC
      1980	2114	98	1.4
      1990	2108	92	1.3
      2000	2111	95	1.4
      2010	2100	84	1.2

   4. Compute radiative forcing for CS with ModTran
      a. Set ModTran base conditions as 400 ppm, Water Vapor Scale at 1.00, Locality 1976 U.S. Standard Atmosphere, No Clouds/No Rain, average earth surface temperature = 288.2K (15C).  Record radiation to space in watts/m².
      Result: CS = 2.98 watts/m²
      b. Adjust the ModTran Temperature Offset to closely match the 267.8 watts/m² radiation for initial 400 ppm case.  This estimates the global surface temperature resulting from doubling to 800 ppm CO2.
      Result: CS = 0.7C
      c. Repeat above step for the following conditions: 800 ppm CO2 as the only change; then change Water Vapor Scale to 1.067, 1.100, and 1.135, corresponding to surface temperature changes of 1C, 1.5C and 2C, respectively to account for humidity increase due to surface temperature increase.
      Results: For Water Vapor Scales 0C, 1C, 1.5 and 2C; radiative forcing is 2.98, 3.90, 4.40, and  4.80 watts/m².

Discussion:
The radiative CS computed using ModTran is approximately 3 watts/m², which is in agreement with that found by several reputable scientists.  The temperature CS of 0.7C from ModTran disagrees with the statistical treatment of historical data that yields approximately 1.2C.  When estimating the CS with ModTran and adjusting for water vapor increase, the CS increases by only 0.07C.