Do greenhouse gas mitigation cost-effectiveness rankings based on the global warming potential favor sub-optimal allocation of resources?

The global warming potential GWP gas (H) relates radiative forcing of a single pulse emission of a 4 greenhouse gas, the absolute global warming potential AGWP gas (H), to the respective radiative 5 forcing of carbon dioxide over a defined time horizon H. Mitigation measures targeting short-lived 6 climate forcers (SLCFs) or reversible measures need to be applied permanently to be effective in the 7 long run, but cost effectiveness for a permanent application of a measure differs from a single 8 application. We propose a concept for an absolute global warming potential of permanent yearly 9 pulses AGWP’ gas (H), and several options for alternative indices to replace or complement the GWP: 10 For the GWP gas (H/H) and the GWP cgas (H/H) we keep the AGWP CO2 (H) in the denominator, which 11 allows the direct comparison with conventional estimates, while for the GWP’ gas (H) we define a new 12 metric replacing the denominator by the AGWP’ CO2 (H). Different cost-effectiveness indicators can be 13 defined respectively. We demonstrate the concept on the example of typical greenhouse gases 14 emitted or removed by the agricultural sector: methane, nitrous oxide and carbon dioxide, fossil and 15 stored as soil carbon. We show that, compared to GWP-based cost-effectiveness analysis, measures 16 targeting soil carbon are discouraged relative to measures targeting methane, nitrous oxide and 17 fossil carbon dioxide . 18


Introduction 22
In view of the Paris Agreement commitments to keep global temperature change below 1.5-2 23 degrees Celsius with limited time and financial resources available, the question of cost effectiveness 24 of potential mitigation measures is becoming increasingly important. Identification of the most cost-25 effective measures, however, is challenging because mitigation measures may target emissions of 26 different greenhouse gases with different life times in the atmosphere. Furthermore, some 27 mitigation options such as the storage of carbon in biomass or soils generally are reversible and 28 saturate so that their effect converges towards zero after some time. We define the cost-intensity of 29 mitigation measures as the yearly costs of a measure divided by the CO2 equivalents 1 of the yearly 30 mitigated emissions or the average yearly carbon removal expressed in CO2 in case of carbon 31 sequestration (in the following referred to as "conventional" methodology). In the literature this is 32 generally referred to as cost-effectiveness ratio, but we propose this term as it expresses the 33 concept better. Cost-efficiency can be defined as the reciprocal value of cost-intensity. 34 Recent literature raised concerns whether the conventional methodology is suitable to answer the 35 question on how to achieve desirable long-term climate impacts at the lowest costs. A series of 36 articles particularly address the issue of short-lived climate pollutants (SLCFs) which may have a large 37 impact in the short run, but will have disappeared from the atmosphere within a few years (Shine et  activity targeting such SLCFs today will hardly affect long-term temperature changes unless the 40 activity has a permanent character. Similarly, a mitigation activity targeting (soil) carbon 41 sequestration builds-up reversible carbon pools that reach an equilibrium after some time (providing 42 no further mitigation effect), and risking to be released again if not well managed. By contrast, long-43 lived greenhouse gases (LLGHGs) accumulate in the atmosphere, and the moment carrying out the 44 mitigation activity is less relevant for the long-term effect on temperature. 45 Studies have developed new metrics to overcome these issues, such as the Global Temperature 46 Change potential (GTP) or the GWP*, extending the analysis to the impact on global temperature 47 (see Shine  Here, we develop a concept for a systematic comparison of mitigation costs for mitigation measures, 53 which allows to take into account the different dynamic characteristics of affected climate 54 pollutants, building on radiative forcing and the global warming potential. 55 56 1 EUR, could be applied permanently over a period or just once in the initial year t0, and emission 72 reductions or removals of a single application correspond to 1 kg of CO2eq, using GWP100 73

Method: Concept for the integration of permanent yearly emission pulses in cost-
The formula for the GWP (Myhre, G., Shindell, D. et al, 2013) is: 74 H is the time horizon for which we take effects into account (for the example we use 100 years), 76 RFgas(t) is the functional form for the radiative forcing over time, describing the radiative forcing in 77 year t of an initial pulse in t0 , and AGWPgas is the absolute global warming potential of the gas, which 78 is the cumulative effect on radiative forcing over the time horizon. Let's further assume that 79 AGWPCO2(100) is exactly 1, which allows us to use GWP(100) and AGWP(100) as synonyms. If the 80 GWP(100) 28 for gasA and 265 for gasB, then measures A, B and D lead to a reduction of emissions of 81 (1/28) kg gasA, (1/265) kg gasB, and 1kg of CO2, while measure C removes 1kg of CO2 from the 82 atmosphere. Moreover, if we simplify the calculation assuming a constant value of RFgas(t) for the 83 lifetime ltgas (instantaneously disappearing after ltgas years), RFgas (t) can be described as follows: 84 , ( > ) = 0 85 Accordingly, the yearly values for RF per kg of the gases corresponds to 28 W m -2 kg -1 /12 yr = 2.33 86 W m -2 yr kg -1 for gasA (SLCF) and 265 W m -2 kg -1 / 100 yr =2.65 W m -2 yr kg -1 for gasB (LLGHG), 87 compared to 0.01 W m -2 yr kg -1 for CO2. 88 Finally, we define the mitigation cost intensity (CI) as the ratio of the measure's cost C (in EUR) and 89 the emission reduction E, which is the sum of the reduced emissions Q (in kg) of all gases multiplied 90 with their respective GWPs. The mitigation cost efficiency (CE) is the reciprocal value of the 91 mitigation cost intensity: 92

Single pulse application of mitigation measures with time weights (show-case examples) 119
An alternative would be to assign increasing weights to climate impacts further along the time 120 horizon, because we can expect the marginal costs per unit of radiative forcing to increase with the 121 absolute radiative forcing, and so the relevance of climate mitigation impacts to be higher in the 122 future than in the presence and the contribution to mitigation more valuable than today. Equation

123
(1) would be modified in the following way: 124 The simplest form would be a linear weighting function: 126 As an example we could assume W=30, which might be argued by many targets relating to 2050, a 139 net carbon removal time of S=20, select = 0.5 and =0.005 (which guarantees a weight of 1 after 140 100 years) or =0.017 (which guarantees a weight of 1 after 30 years), and book reversibility of 141 carbon removal correctly. Then mitigation cost intensity ratios 3 change from 1/1/1/1 for the 142 "conventional" method to 1.41/1/149/1 (weighting function type from equation 5a) or 1.52/1/180/1 143 (weighting function type 5b), for the SLCF, the LLGHG and the CO2 stored as soil carbon respectively. 144 145

Permanent application of mitigation measures for the time horizon H (show-case examples) 146
What changes if instead we apply the measures not just in the first year, but for the whole period of 147 100 years (see Figure 2)? Each of the four measures creates costs of 100 EUR if we apply an interest 148 rate of zero. The yearly impact of measure A increases for the first 12 years, then the disappearance 149 of the effect from former years cancels new effects from the measure in later years, keeping the 150 impact stable after 12 years. Measures B and D lead to a constant increase of the impact on radiative 151 forcing, but reaches the same level of yearly impact as measure A only after 100 years. Measure C 152 leads to increasing impacts via carbon removal for 20 years, and then keeps a constant impact at a 153 considerably lower level than the first two measures. If we compare figure  In order to achieve more accurate values, we have to relax the assumption of constant radiative 168 forcing and replace it by the respective functional forms usually applied in the literature. Moreover, 169 we need to abandon the assumption of the equality of the absolute global warming potential 170 (AGWP) and the global warming potential (GWP). If we consider methane and nitrous oxide as our 171 SLCF and LLGHG, respectively, and target measure C to soil carbon sequestration we can keep the 172 other assumptions. Remember that soil carbon sequestration is a process going on for a limited 173 period (IPCC assumes generally 20 years in the 2006 guidelines), converging towards a new soil 174 carbon equilibrium, and the process is reversible in the sense that if you return to the former farm 175 practice all the carbon sequestered will be lost again with a long term effect of almost zero. 176 The absolute global warming potential (AGWP) can be expressed as 5 : 177 180 4 This is calculated as the cost of the measure divided by the accumulated impact on radiative forcing, what we will define as ′ later in the text (shaded area in figure 2). Note that we do not relate to 2 ′ but AGWPCO2 (single pulse), which is equal to one in our example, and, therefore allows us to use the absolute values of AGWP and AGWP' equivalent to GWP and GWP'. We show the calculation on the example of gas A for H=100, with a life time of 12 years and an RF of 0.083 W m -2 yr -1 . For the first 12 years the yearly impact on radiative forcing is increasing because the impacts of the yearly pulses accumulate. So, the accumulated AGWP' for the first 12 years is: 1*0.083+2*0.083+…+12*0.083=6*0.083=6. For the remaining 88 years the yearly impact remains constant, which accumulates to: 88*12*0.083=88. The sum gives 94. The cost for the application of measure A is 100, and 100/94=1.06. 5  With the two weighting functions discussed above the formulas would change to: 187

200
We can show the effects on mitigation cost intensities for our four measures in the following table  201 for different values of and (all combinations are selected in a way that guarantees a weight of 1 202 after 100 years/30 years) and the two weighting functions (W assumed to be 30 years): 203 For the effect of a yearly pulse over the whole period H we have to modify the formulas 7a-7c. 216 Ignoring changes and interactions over time we get: 217   Carbon sequestration is treated like SLCFs if the period of sequestration is lower than the time 261 horizon H (S<H). We call this alternative Global warming potential for permanent pulses 262 GWP c (100/100). As can be seen from a time horizon of 20 years, but GWP' steadily decreases compared to GWP, going down to 7% for a 280 long time horizon of 500 years. 281

yearly pulse (AGWP') for different time horizons (20 years, 100 years and 500 years)
283   Table 4 shows the normalized mitigation cost intensities for the discussed gases, the three time 305 horizons, and the three types of global warming potentials. 306 horizons (20 years) the differences are smaller, but still methane being the cheapest followed by CO2 324 and N2O with similar values. There are no differences between fossil carbon and soil carbon 325 sequestration in the short term. The cost intensity ratios standardized by fossil CO2 therefore, favored by our methodology compared to both GWP and GWP*, due to its quick impact 388 and the fact that the impact of late pulses of N2O and CO2 are only counted for a few years. As 389 discussed in the previous section this bias for LLGHGs can be avoided by the use of GWP c (100/100). 390 The respective mitigation cost intensities are presented in columns 7-9 of table 5. 391 Comparing the farm practices and technologies considered in Eory (pers comm), conventionally 392 estimated (first column), covering slurry is the most cost efficient measure to reduce emissions while 393 nitrification inhibitors is the most costly mitigation measure. Considering reversibility (second 394 column) changes the ranking by increasing the mitigation cost intensities of cover crops and grass 395 leys considerably. If we weight long term impacts higher (column 3) competitiveness of nitrification 396 inhibitors, but also cover crops and grass leys due to their positive impacts on N2O emissions, 397 increases, while technologies targeting methane like 3NOP, biogas flaring and slurry cover become 398 more expensive. In the long term application for 100 years (column 4), mitigation technologies 399 become generally more expensive for SLCFs and LLGHGs, but in particular nitrification inhibitors 400 affecting N2O, a LLGHG. By contrast, measures like cover crops and grass leys affecting soil carbon 401 sequestration become more cost efficient than for a single pulse application (corrected values) 402 because only a permanent implementation of those farming practice guarantees the permanent 403 storage of carbon in soils. However, cost efficiency remains considerably lower than indicated in 404 conventional estimates because sequestration happens only for a limited time period while the 405 measure has to be applied permanently in order to avoid to lose the carbon stored before. If we use 406 the GWP c (100/100), nitrification inhibitors keep the higher cost efficiency of the conventional 407 estimates, and also cover crops and grass leys, due to the impacts on N2O, slightly improve 408 compared to GWP(100/100), while the other farm practices stay at the level of GWP(100/100). 409 Among the technologies considered in Perez et al. (2020), conventionally estimated, the increased 410 share of legumes in temporary grassland is the most cost efficient measure, followed by fallowing of 411 organic soils and nitrification inhibitors, while line seed and winter cover crops are by a factor of ten 412 less efficient to mitigate greenhouse gas emissions. Considering reversibility of carbon 413 sequestration, a single pulse application for one year would lead to a considerable downgrading of 414 the increased legume share on temporary grassland (by a factor of more than 10) and a very strong 415 decrease of cost efficiency for winter cover crops. Weighting the impact on radiative forcing turns 416 the impact of winter cover crops on GHG mitigation to a negative value (net emission increases due 417 to higher N2O emissions) and reduces competitiveness of line seed feeding. cost efficient measure to mitigate greenhouse gas emissions, followed by a higher share of grain 428 legumes and nitrification inhibitors, while feeding of unsaturated fats and buffer strips are high cost 429 measures. Considering reversibility of soil carbon sequestration, a single pulse has considerably 430 lower soil carbon gains for direct seeding and buffer strips, which leads to significant decreases of 431 mitigation cost efficiencies for those two measures. Weighting later impacts stronger improves cost 432 efficiency for nitrification inhibitors, grain legumes and buffer strips, while direct seeding will 433 massively lose competitiveness, and feed additives will become less cost attractive too. With the 434 GWP(100/100) mitigation cost intensities increase for all measures, but less for the feed measure. 435 Direct seeding remains considerably more expensive than grain legumes. GWP c (100/100) leads to 436 considerably lower mitigation cost intensities than GWP(100/100) except for feed additives, where 437 the values are identical. In particular, this is the case for nitrification inhibitors. 438 439  GWP(100) corrected for reversibility, GWP(100) weighted (α=0.05, β=0.017   Accumulation of impacts of yearly pulses on radiative forcing in the long run. The rst pulse starts in t0, the second in t1 etc.

Supplementary Files
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