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