calculation RM 1 - 6   RM-1 const RM-2 exp RM-3 lin   RM-4 quadr RM-5 rad   RM-6 abs
constant annual reduction rate exponential increase of annual reduction rates is assumed linear increase of annual reduction rates is assumed quadratic formula for annual reduction rates radical formula for annual reduction rates constant absolute annual change
formula           correcting factor 0.5    
base data cumulative budget 2020 - 2100 in Mill. t cumulative budget 2020 - 2100 in Mill. t 159,335 cumulative budget 2020 - 2100 in Mill. t 159,335 cumulative budget 2020 - 2100 in Mill. t 159,335 cumulative budget 2020 - 2100 in Mill. t 159,335 cumulative budget 2020 - 2100 in Mill. t 159,335 cumulative budget 2020 - 2100 in Mill. t 159,335
input sheet 'gloal seek' scenario sum emissions 2020 - 2100 in Mill. t scenario sum emissions 2020 - 2100 in Mill. t 159,335   scenario sum emissions 2020 - 2100 in Mill. t 159,335 scenario sum emissions 2020 - 2100 in Mill. t 159,335 scenario sum emissions 2020 - 2100 in Mill. t 159,335 scenario sum emissions 2020 - 2100 in Mill. t 159,335 scenario sum emissions 2020 - 2100 in Mill. t 159,335
E_min in Mill. t E_min in Mill. t -237.0   E_min in Mill. t -237.0 E_min in Mill. t     -237.0 E_min in Mill. t       -237.0 E_min in Mill. t       -237.0 E_min in Mill. t     -237.0
goal seek scenario emissions in year 2100 in Mill. t scenario emissions in year 2100 in Mill. t -237.0   scenario emissions in year 2100 in Mill. t -237.0 scenario emissions in year 2100 in Mill. t -237.0 scenario emissions in year 2100 in Mill. t -237.0 scenario emissions in year 2100 in Mill. t -237.0 scenario emissions in year 2100 in Mill. t -237.0
sheet "goal seek"   RR_20; input value sheet "goal seek" -0.01% RR_20; input value sheet "goal seek" 2.40% RR_20; input value sheet "goal seek"   2.40% RR_20; input value sheet "goal seek" 2.40%          
free paramter -9.96% free paramter 142.98% free paramter -2.28% free paramter     -0.0035 free paramter     -0.0603 free paramter     -680.43
actual start year       2024
    year CO2 emissions
in Mill. t
absolute
change
vs. prev. year
in Mill. t
relative
change
vs. prev.
year
  CO2 emissions
in Mill. t
absolute
change
vs. prev. year
in Mill. t
relative
change
vs. prev.
year
  CO2 emissions
in Mill. t
absolute
change
vs. prev. year
in Mill. t
relative
change
vs. prev.
year
  CO2 emissions
in Mill. t
absolute
change
vs. prev. year
in Mill. t
relative
change
vs. prev.
year
  CO2 emissions
in Mill. t
absolute
change
vs. prev. year
in Mill. t
relative
change
vs. prev.
year
  CO2 emissions
in Mill. t
absolute
change
vs. prev. year
in Mill. t
relative
change
vs. prev.
year
 
    t formula
Et
Et - Et-1 RRt const actual RRt formula
Et
Et - Et-1 formula actual RRt formula
Et
Et - Et-1 formula actual RRt formula
Et
Et - Et-1 formula actual RRt formula
Et
Et - Et-1 formula actual RRt formula
Et
Et - Et-1 actual
Et - Et-1
RRt
1 base year 2019 11,850.59         11,850.59         11,850.59         11,850.59         11,850.59         11,850.59        
2   2020   12,022.43 171.84 -9.96% 1.45%     12,022.43 171.84 1.45%     12,022.43 171.84 1.45%     12,022.43 171.84 1.45%     12,022.43 171.84 1.45%     12,022.43 -680.43 171.84 1.45%  
3   2021 12,621.61 599.18 -9.96% 4.98%   12,621.61 599.18 4.98%   12,621.61 599.18 4.98%   12,621.61 599.18 4.98%   12,621.61 599.18 4.98%   12,621.61 -680.43 599.18 4.98%  
4   2022 12,526.83 -94.79 -9.96% -0.75%   12,526.83 -94.79 -0.75%   12,526.83 -94.79 -0.75%   12,526.83 -94.79 -0.75%   12,526.83 -94.79 -0.75%   12,526.83 -680.43 -94.79 -0.75%  
5   2023 13,259.64 732.81 -9.96% 5.85%   13,259.64 732.81 5.85%   13,259.64 732.81 5.85%   13,259.64 732.81 5.85%   13,259.64 732.81 5.85%   13,259.64 -680.43 732.81 5.85%  
6   2024 11,938.85 -1320.79 -9.96% -9.96%   13,258.31 -1.33 -0.01% -0.01%   13,577.87 318.23 2.40% 2.40%   13,577.87 318.23 2.40% 2.40%   13,577.87 318.23 2.40% 2.40%   12,579.21 -680.43 -680.43 -5.13%  
7   2025 10,749.62 -1189.23 -9.96% -9.96%   13,255.09 -3.22 -0.02% -0.02%   13,594.62 16.75 0.12% 0.12%   13,855.96 278.09 2.05% 2.05%   13,324.39 -253.48 -1.87% -1.87%   11,898.77 -680.43 -680.43 -5.41%  
8   2026 9,678.85 -1070.77 -9.96% -9.96%   13,247.27 -7.83 -0.06% -0.06%   13,301.89 -292.73 -2.15% -2.15%   13,993.48 137.52 0.99% 0.99%   12,659.43 -664.95 -4.99% -4.99%   11,218.34 -680.43 -680.43 -5.72%  
9   2027 8,714.75 -964.11 -9.96% -9.96%   13,228.26 -19.00 -0.14% -0.14%   12,712.63 -589.26 -4.43% -4.43%   13,886.18 -107.31 -0.77% -0.77%   11,755.42 -904.02 -7.14% -7.14%   10,537.91 -680.43 -680.43 -6.07%  
10   2028 7,846.67 -868.07 -9.96% -9.96%   13,182.15 -46.11 -0.35% -0.35%   11,860.06 -852.58 -6.71% -6.71%   13,437.66 -448.52 -3.23% -3.23%   10,710.46 -1044.96 -8.89% -8.89%   9,857.47 -680.43 -680.43 -6.46%  
11   2029 7,065.07 -781.61 -9.96% -9.96%   13,070.50 -111.65 -0.85% -0.85%   10,794.65 -1065.41 -8.98% -8.98%   12,578.08 -859.58 -6.40% -6.40%   9,596.50 -1113.96 -10.40% -10.40%   9,177.04 -680.43 -680.43 -6.90%  
12   2030 6,361.32 -703.75 -9.96% -9.96%   12,801.52 -268.99 -2.06% -2.06%   9,579.20 -1215.45 -11.26% -11.26%   11,286.63 -1291.44 -10.27% -10.27%   8,468.75 -1127.75 -11.75% -11.75%   8,496.61 -680.43 -680.43 -7.41%  
13   2031 5,727.67 -633.65 -9.96% -9.96%   12,161.38 -640.14 -5.00% -5.00%   8,282.52 -1296.68 -13.54% -13.54%   9,611.50 -1675.13 -14.84% -14.84%   7,369.12 -1099.63 -12.98% -12.98%   7,816.18 -680.43 -680.43 -8.01%  
14   2032 5,157.14 -570.53 -9.96% -9.96%   10,683.74 -1477.64 -12.15% -12.15%   6,972.80 -1309.72 -15.81% -15.81%   7,677.68 -1933.82 -20.12% -20.12%   6,328.19 -1040.93 -14.13% -14.13%   7,135.74 -680.43 -680.43 -8.71%  
15   2033 4,643.43 -513.70 -9.96% -9.96%   7,529.58 -3154.15 -29.52% -29.52%   5,711.44 -1261.36 -18.09% -18.09%   5,673.68 -2004.00 -26.10% -26.10%   5,366.76 -961.43 -15.19% -15.19%   6,455.31 -680.43 -680.43 -9.54%  
16   2034 4,180.90 -462.53 -9.96% -9.96%   2,128.22 -5401.37 -71.74% -71.74%   4,548.23 -1163.21 -20.37% -20.37%   3,813.44 -1860.24 -32.79% -32.79%   4,497.40 -869.36 -16.20% -16.20%   5,774.88 -680.43 -680.43 -10.54%  
17   2035 3,764.44 -416.46 -9.96% -9.96%   -237.00 -2365.22 -174.30%     3,518.38 -1029.85 -22.64% -22.64%   2,281.33 -1532.11 -40.18% -40.18%   3,725.94 -771.46 -17.15% -17.15%   5,094.44 -680.43 -680.43 -11.78%  
18   2036 3,389.47 -374.98 -9.96% -9.96%   -237.00 0.00 -423.53%     2,641.61 -876.76 -24.92% -24.92%   1,180.14 -1101.19 -48.27% -48.27%   3,052.91 -673.03 -18.06% -18.06%   4,414.01 -680.43 -680.43 -13.36%  
19   2037 3,051.84 -337.62 -9.96% -9.96%   -237.00 0.00 -500.00%     1,923.19 -718.42 -27.20% -27.20%   506.68 -673.46 -57.07% -57.07%   2,474.86 -578.05 -18.93% -18.93%   3,733.58 -680.43 -680.43 -15.42%  
20   2038 2,747.85 -303.99 -9.96% -9.96%   -237.00 0.00 -500.00%     1,356.37 -566.82 -29.47% -29.47%   169.40 -337.28 -66.57% -66.57%   1,985.54 -489.32 -19.77% -19.77%   3,053.14 -680.43 -680.43 -18.22%  
21   2039 2,474.14 -273.71 -9.96% -9.96%   -237.00 0.00 -500.00%     925.73 -430.64 -31.75% -31.75%   -167.88 -337.28 -76.77%     1,576.96 -408.58 -20.58% -20.58%   2,372.71 -680.43 -680.43 -22.29%  
22   2040 2,227.69 -246.45 -9.96% -9.96%   -237.00 0.00 -500.00%     610.74 -314.99 -34.03% -34.03%   -237.00 -69.12 -87.68%     1,240.17 -336.79 -21.36% -21.36%   1,692.28 -680.43 -680.43 -28.68%  
23   2041 2,005.79 -221.90 -9.96% -9.96%   -237.00 0.00 -500.00%     389.03 -221.72 -36.30% -36.30%   -237.00 0.00 -99.29%     965.95 -274.22 -22.11% -22.11%   1,011.85 -680.43 -680.43 -40.21%  
24   2042 1,805.99 -199.80 -9.96% -9.96%   -237.00 0.00 -500.00%     167.31 -221.72 -38.58% -56.99%   -237.00 0.00 -111.61%     745.29 -220.65 -22.84% -22.84%   331.41 -680.43 -680.43 -67.25%  
25   2043 1,626.10 -179.89 -9.96% -9.96%   -237.00 0.00 -500.00%     -54.41 -221.72 -40.86%     -237.00 0.00 -124.63%     569.74 -175.55 -23.55% -23.55%   -237.00 -680.43 -568.41  
26   2044 1,464.12 -161.98 -9.96% -9.96%   -237.00 0.00 -500.00%     -237.00 -182.59 -43.13%     -237.00 0.00 -138.35%     431.60 -138.14 -24.25% -24.25%   -237.00 -680.43 0.00  
27   2045 1,318.28 -145.84 -9.96% -9.96%   -237.00 0.00 -500.00%     -237.00 0.00 -45.41%     -237.00 0.00 -152.78%     324.04 -107.56 -24.92% -24.92%   -237.00 -680.43 0.00  
28   2046 1,186.97 -131.31 -9.96% -9.96%   -237.00 0.00 -500.00%     -237.00 0.00 -47.69%     -237.00 0.00 -167.91%     216.48 -107.56 -25.58% -33.19%   -237.00 -680.43 0.00  
29   2047 1,068.73 -118.23 -9.96% -9.96%   -237.00 0.00 -500.00%     -237.00 0.00 -49.96%     -237.00 0.00 -183.74%     108.92 -107.56 -26.22% -49.69%   -237.00 -680.43 0.00  
30   2048 962.28 -106.46 -9.96% -9.96%   -237.00 0.00 -500.00%     -237.00 0.00 -52.24%     -237.00 0.00 -200.28%     1.36 -107.56 -26.85% -98.76%   -237.00 -680.43 0.00  
31   2049 866.43 -95.85 -9.96% -9.96%   -237.00 0.00 -500.00%     -237.00 0.00 -54.52%     -237.00 0.00 -217.52%     -106.21 -107.56 -27.47%     -237.00 -680.43 0.00  
32   2050 780.12 -86.30 -9.96% -9.96%   -237.00 0.00 -500.00%     -237.00 0.00 -56.79%     -237.00 0.00 -235.47%     -213.77 -107.56 -28.07%     -237.00 -680.43 0.00  
33   2051 702.41 -77.71 -9.96% -9.96%   -237.00 0.00 -500.00%     -237.00 0.00 -59.07%     -237.00 0.00 -254.11%     -237.00 -23.23 -28.66%     -237.00 -680.43 0.00  
34   2052 632.45 -69.97 -9.96% -9.96%   -237.00 0.00 -500.00%     -237.00 0.00 -61.35%     -237.00 0.00 -273.47%     -237.00 0.00 -29.24%     -237.00 -680.43 0.00  
35   2053 569.45 -63.00 -9.96% -9.96%   -237.00 0.00 -500.00%     -237.00 0.00 -63.62%     -237.00 0.00 -293.52%     -237.00 0.00 -29.81%     -237.00 -680.43 0.00  
36   2054 512.73 -56.72 -9.96% -9.96%   -237.00 0.00 -500.00%     -237.00 0.00 -65.90%     -237.00 0.00 -314.29%     -237.00 0.00 -30.37%     -237.00 -680.43 0.00  
37   2055 456.00 -56.72 -9.96% -11.06%   -237.00 0.00 -500.00%     -237.00 0.00 -68.18%     -237.00 0.00 -335.75%     -237.00 0.00 -30.93%     -237.00 -680.43 0.00  
38   2056 399.28 -56.72 -9.96% -12.44%   -237.00 0.00 -500.00%     -237.00 0.00 -70.45%     -237.00 0.00 -357.92%     -237.00 0.00 -31.47%     -237.00 -680.43 0.00  
39   2057 342.56 -56.72 -9.96% -14.21%   -237.00 0.00 -500.00%     -237.00 0.00 -72.73%     -237.00 0.00 -380.79%     -237.00 0.00 -32.00%     -237.00 -680.43 0.00  
40   2058 285.84 -56.72 -9.96% -16.56%   -237.00 0.00 -500.00%     -237.00 0.00 -75.01%     -237.00 0.00 -404.36%     -237.00 0.00 -32.53%     -237.00 -680.43 0.00  
41   2059 229.11 -56.72 -9.96% -19.84%   -237.00 0.00 -500.00%     -237.00 0.00 -77.28%     -237.00 0.00 -428.64%     -237.00 0.00 -33.04%     -237.00 -680.43 0.00  
42   2060 172.39 -56.72 -9.96% -24.76%   -237.00 0.00 -500.00%     -237.00 0.00 -79.56%     -237.00 0.00 -453.63%     -237.00 0.00 -33.55%     -237.00 -680.43 0.00  
43   2061 115.67 -56.72 -9.96% -32.90%   -237.00 0.00 -500.00%     -237.00 0.00 -81.84%     -237.00 0.00 -479.31%     -237.00 0.00 -34.06%     -237.00 -680.43 0.00  
44   2062 58.94 -56.72 -9.96% -49.04%   -237.00 0.00 -500.00%     -237.00 0.00 -84.11%     -237.00 0.00 -505.70%     -237.00 0.00 -34.55%     -237.00 -680.43 0.00  
45   2063 2.22 -56.72 -9.96% -96.23%   -237.00 0.00 -500.00%     -237.00 0.00 -86.39%     -237.00 0.00 -532.80%     -237.00 0.00 -35.04%     -237.00 -680.43 0.00  
46   2064 -54.50 -56.72 -9.96%     -237.00 0.00 -500.00%     -237.00 0.00 -88.67%     -237.00 0.00 -560.60%     -237.00 0.00 -35.52%     -237.00 -680.43 0.00  
47   2065 -111.22 -56.72 -9.96%     -237.00 0.00 -500.00%     -237.00 0.00 -90.94%     -237.00 0.00 -589.10%     -237.00 0.00 -36.00%     -237.00 -680.43 0.00  
48   2066 -167.95 -56.72 -9.96%     -237.00 0.00 -500.00%     -237.00 0.00 -93.22%     -237.00 0.00 -618.30%     -237.00 0.00 -36.47%     -237.00 -680.43 0.00  
49   2067 -224.67 -56.72 -9.96%     -237.00 0.00 -500.00%     -237.00 0.00 -95.50%     -237.00 0.00 -648.21%     -237.00 0.00 -36.94%     -237.00 -680.43 0.00  
50   2068 -237.00 -12.33 -9.96%     -237.00 0.00 -500.00%     -237.00 0.00 -97.77%     -237.00 0.00 -678.82%     -237.00 0.00 -37.40%     -237.00 -680.43 0.00  
51   2069 -237.00 0.00 -9.96%     -237.00 0.00 -500.00%     -237.00 0.00 -100.05%     -237.00 0.00 -710.14%     -237.00 0.00 -37.85%     -237.00 -680.43 0.00  
52   2070 -237.00 0.00 -9.96%     -237.00 0.00 -500.00%     -237.00 0.00 -102.33%     -237.00 0.00 -742.16%     -237.00 0.00 -38.30%     -237.00 -680.43 0.00  
53   2071 -237.00 0.00 -9.96%     -237.00 0.00 -500.00%     -237.00 0.00 -104.60%     -237.00 0.00 -774.89%     -237.00 0.00 -38.75%     -237.00 -680.43 0.00  
54   2072 -237.00 0.00 -9.96%     -237.00 0.00 -500.00%     -237.00 0.00 -106.88%     -237.00 0.00 -808.31%     -237.00 0.00 -39.19%     -237.00 -680.43 0.00  
55   2073 -237.00 0.00 -9.96%     -237.00 0.00 -500.00%     -237.00 0.00 -109.15%     -237.00 0.00 -842.45%     -237.00 0.00 -39.62%     -237.00 -680.43 0.00  
56   2074 -237.00 0.00 -9.96%     -237.00 0.00 -500.00%     -237.00 0.00 -111.43%     -237.00 0.00 -877.28%     -237.00 0.00 -40.06%     -237.00 -680.43 0.00  
57   2075 -237.00 0.00 -9.96%     -237.00 0.00 -500.00%     -237.00 0.00 -113.71%     -237.00 0.00 -912.82%     -237.00 0.00 -40.48%     -237.00 -680.43 0.00  
58   2076 -237.00 0.00 -9.96%     -237.00 0.00 -500.00%     -237.00 0.00 -115.98%     -237.00 0.00 -949.06%     -237.00 0.00 -40.90%     -237.00 -680.43 0.00  
59   2077 -237.00 0.00 -9.96%     -237.00 0.00 -500.00%     -237.00 0.00 -118.26%     -237.00 0.00 -986.01%     -237.00 0.00 -41.32%     -237.00 -680.43 0.00  
60   2078 -237.00 0.00 -9.96%     -237.00 0.00 -500.00%     -237.00 0.00 -120.54%     -237.00 0.00 -1023.66%     -237.00 0.00 -41.74%     -237.00 -680.43 0.00  
61   2079 -237.00 0.00 -9.96%     -237.00 0.00 -500.00%     -237.00 0.00 -122.81%     -237.00 0.00 -1062.01%     -237.00 0.00 -42.15%     -237.00 -680.43 0.00  
62   2080 -237.00 0.00 -9.96%     -237.00 0.00 -500.00%     -237.00 0.00 -125.09%     -237.00 0.00 -1101.07%     -237.00 0.00 -42.55%     -237.00 -680.43 0.00  
63   2081 -237.00 0.00 -9.96%     -237.00 0.00 -500.00%     -237.00 0.00 -127.37%     -237.00 0.00 -1140.83%     -237.00 0.00 -42.96%     -237.00 -680.43 0.00  
64   2082 -237.00 0.00 -9.96%     -237.00 0.00 -500.00%     -237.00 0.00 -129.64%     -237.00 0.00 -1181.30%     -237.00 0.00 -43.36%     -237.00 -680.43 0.00  
65   2083 -237.00 0.00 -9.96%     -237.00 0.00 -500.00%     -237.00 0.00 -131.92%     -237.00 0.00 -1222.47%     -237.00 0.00 -43.75%     -237.00 -680.43 0.00  
66   2084 -237.00 0.00 -9.96%     -237.00 0.00 -500.00%     -237.00 0.00 -134.20%     -237.00 0.00 -1264.34%     -237.00 0.00 -44.15%     -237.00 -680.43 0.00  
67   2085 -237.00 0.00 -9.96%     -237.00 0.00 -500.00%     -237.00 0.00 -136.47%     -237.00 0.00 -1306.92%     -237.00 0.00 -44.54%     -237.00 -680.43 0.00  
68   2086 -237.00 0.00 -9.96%     -237.00 0.00 -500.00%     -237.00 0.00 -138.75%     -237.00 0.00 -1350.20%     -237.00 0.00 -44.92%     -237.00 -680.43 0.00  
69   2087 -237.00 0.00 -9.96%     -237.00 0.00 -500.00%     -237.00 0.00 -141.03%     -237.00 0.00 -1394.18%     -237.00 0.00 -45.31%     -237.00 -680.43 0.00  
70   2088 -237.00 0.00 -9.96%     -237.00 0.00 -500.00%     -237.00 0.00 -143.30%     -237.00 0.00 -1438.87%     -237.00 0.00 -45.69%     -237.00 -680.43 0.00  
71   2089 -237.00 0.00 -9.96%     -237.00 0.00 -500.00%     -237.00 0.00 -145.58%     -237.00 0.00 -1484.26%     -237.00 0.00 -46.06%     -237.00 -680.43 0.00  
72   2090 -237.00 0.00 -9.96%     -237.00 0.00 -500.00%     -237.00 0.00 -147.86%     -237.00 0.00 -1530.36%     -237.00 0.00 -46.44%     -237.00 -680.43 0.00  
73   2091 -237.00 0.00 -9.96%     -237.00 0.00 -500.00%     -237.00 0.00 -150.13%     -237.00 0.00 -1577.16%     -237.00 0.00 -46.81%     -237.00 -680.43 0.00  
74   2092 -237.00 0.00 -9.96%     -237.00 0.00 -500.00%     -237.00 0.00 -152.41%     -237.00 0.00 -1624.66%     -237.00 0.00 -47.18%     -237.00 -680.43 0.00  
75   2093 -237.00 0.00 -9.96%     -237.00 0.00 -500.00%     -237.00 0.00 -154.69%     -237.00 0.00 -1672.86%     -237.00 0.00 -47.54%     -237.00 -680.43 0.00  
76   2094 -237.00 0.00 -9.96%     -237.00 0.00 -500.00%     -237.00 0.00 -156.96%     -237.00 0.00 -1721.77%     -237.00 0.00 -47.91%     -237.00 -680.43 0.00  
77   2095 -237.00 0.00 -9.96%     -237.00 0.00 -500.00%     -237.00 0.00 -159.24%     -237.00 0.00 -1771.39%     -237.00 0.00 -48.27%     -237.00 -680.43 0.00  
78   2096 -237.00 0.00 -9.96%     -237.00 0.00 -500.00%     -237.00 0.00 -161.52%     -237.00 0.00 -1821.71%     -237.00 0.00 -48.62%     -237.00 -680.43 0.00  
79   2097 -237.00 0.00 -9.96%     -237.00 0.00 -500.00%     -237.00 0.00 -163.79%     -237.00 0.00 -1872.73%     -237.00 0.00 -48.98%     -237.00 -680.43 0.00  
80   2098 -237.00 0.00 -9.96%     -237.00 0.00 -500.00%     -237.00 0.00 -166.07%     -237.00 0.00 -1924.45%     -237.00 0.00 -49.33%     -237.00 -680.43 0.00  
81   2099 -237.00 0.00 -9.96%     -237.00 0.00 -500.00%     -237.00 0.00 -168.35%     -237.00 0.00 -1976.88%     -237.00 0.00 -49.68%     -237.00 -680.43 0.00  
82   2100 -237.00 0.00 -9.96%     -237.00 0.00 -500.00%     -237.00 0.00 -170.62%     -237.00 0.00 -2030.01%     -237.00 0.00 -50.03%     -237.00 -680.43 0.00  
sum 159,335         159,335         159,335         159,335         159,335         159,335        
-8,379  negative emissions in Mill. t -15,642  negative emissions in Mill. t -13,563  negative emissions in Mill. t -14,625  negative emissions in Mill. t   -12,170  negative emissions in Mill. t   -13,746  negative emissions in Mill. t  
Detailed mathematical description of the RM Scenario Types: Zenodo