Digitization & computation notes for https://sealevel.info/BEST_vs_UAH_2020-06-14h.png

The graph is generated by:
https://woodfortrees.org/plot/best/from:1979/mean:12/plot/uah6/from:1979/mean:12/plot/best/from:1979/trend/plot/uah6/from:1979/trend

WfT does the linear regression and generates the linear trend line, but
does not report the slope. So I got the slopes from the graph.

First, I used mspaint to extend the two trend ines to intercept with the
1975 (left) and 2025 (right) borders, for ease of measuring the slopes.

Digitized the 1975 and 2025 intercepts for both trend lines, I found:
      x   y       x   y
BEST 94,481.5 -> 810,151   481.5-151 = 330.5 vertical pixels between 1975 & 2025 intercepts
UAH6 94,573   -> 810,341   573-341   = 232 vertical pixels between 1975 & 2025 intercepts

So, UAH shows (232/330.5) = 70.1966717% of the warming trend of BEST (rounds to 70.20%)

calibrating pixels / °C:
-0.4 °C is y = 615
 1.2 °C is y =  66
So scale is (616-66 pixels) / 1.6°C = 343.75 pixels per degree C

BEST shows (330.5 / 343.75) degrees / 5 decades = 0.19229 °C/decade
 = 0.192 °C/decade (rounded)

UAH6 shows (232 / 343.75) degrees / 5 decades = 0.13498 °C/decade
 = 0.134 °C/decade (rounded)

Since BEST's data implies sensitivity of 1.6°C/doubling, that means UAH6
implies sensitivity of 0.701966717 × 1.6 = 1.123°C/doubling.

ECS is usually estimated at 1.25× to 1.6× TCR. So:

If 1.6°C is the average of TCR & ECS (per BEST),
and ECS = 1.25×TCR, it means:
  1.6 = (tcr+ecs)/2, so
    tcr = 3.2-ecs
  ecs = 1.25×tcr
      = 1.25×(3.2-ecs)
      = 4 - (1.25×ecs), so
    2.25×ecs = 4
    ecs = 4/2.25 = 1.77777...
    tcr = 3.2 - (4/2.25) = 1.42222...

If 1.6°C is the average of TCR & ECS (per BEST),
and ECS = 1.6×TCR, it means:
  1.6 = (tcr+ecs)/2, so
    tcr = 3.2-ecs
  ecs = 1.6×tcr
      = 1.6×(3.2-ecs)
      = 5.12 - (1.6×ecs), so
    2.6×ecs = 5.12
    ecs = 5.12/2.6 = 1.96923
    tcr = 3.2 - (5.12/2.6) = 1.23077

If 1.23°C is the average of TCR & ECS (per UAH6),
and ECS = 1.25×TCR, it means:
  1.23 = (tcr+ecs)/2, so
    tcr = 2.46-ecs
  ecs = 1.25×tcr
      = 1.25×(2.46-ecs)
      = 3.075 - (1.25×ecs), so
    2.25×ecs = 3.075
    ecs = 3.075/2.25 = 1.36666...
    tcr = 2.46 - (3.075/2.25) = 1.09333...

If 1.23°C is the average of TCR & ECS (per UAH6),
and ECS = 1.6×TCR, it means:
  1.23 = (tcr+ecs)/2, so
    tcr = 2.46-ecs
  ecs = 1.6×tcr
      = 1.6×(2.46-ecs)
      = 3.936 - (1.6×ecs), so
    2.6×ecs = 3.936
    ecs = 3.936/2.6 = 1.51385
    tcr = 2.46 - (3.936/2.6) = 0.94615

Using BEST (1.6°C is avg of TCR & ECS):
TCR is 1.23077 to 1.42222
ECS is 1.77777 to 1.96923

Using UAH6 (1.23°C is avg of TCR & ECS):
TCR is 0.94615 to 1.09333
ECS is 1.36666 to 1.51385

Conclusion:
TCR is 0.95 to 1.42°C, and ECS is 1.37 to 1.97°C:

-DAB 6/16/2020