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# Reassessing the RCPs

by Kevin Murphy

A response to: “Is RCP8.5 an impossible scenario?”. This post demonstrates that RCP8.5 is so highly improbable that it should be dismissed from consideration, and thereby draws into question the validity of RCP8.5-based assertions such as those made in the Fourth National Climate Assessment from the U.S. Global Change Research Program.

Analyses of future climate change since the IPCC’s 5^{th} Assessment Report (AR5) have been based on representative concentration pathways (RCPs) that detail how a range of future climate forcings might evolve.

Several years ago, a set of RCPs were requested by the climate modeling research community to span the range of net forcing from 2.6 W/m^{2} to 8.5 W/m^{2} (in year 2100 relative to 1750) so that physics within the models could be fully exercised. Four of them were developed and designated as RCP2.6, RCP4.5, RCP6.0 and RCP8.5. They have been used in ongoing research and as the basis for impact analyses and future climate projections.

AR5 does not provide probability assignments for any of the RCPs, and yet many impact assessments utilize RCP8.5 to declare consequences of inaction. For example, while RCP4.5 and RCP8.5 are utilized for the Fourth National Climate Assessment (NCA4), the majority of its assertions are based in RCP8.5. The NCA4 states, “RCP8.5 implies a future with continued high emissions growth, whereas the other RCPs represent different pathways of mitigating emissions.” (Executive Summary, p.7). The reader is left with the impression that, although “high” is not defined, it is the present state of things and RCP8.5 delineates how it will grow higher. Further, the statement portrays the other RCPs as mitigation scenarios that are not being acted upon. Therefore, RCP8.5 has been portrayed as the “business as usual” scenario, and impact assessments continue to spread this falsehood.

This article employs some quantitative analysis and the original RCP documentation to demonstrate how the use of RCP8.5 is misleadingly wrong and a lower, narrower range of future CO_{2} atmospheric concentrations can be identified.

**A Long-Range Forecast Based in the Evidence**

The “C” in RCP is for concentration (and not emissions), to emphasize that greenhouse gas (GHG) concentrations are the primary product of the RCPs and inputs to climate models. The Earth’s radiative balance responds to the net result of GHG sources, sinks, and sub-processes as expressed in atmospheric concentration levels. CO_{2} is by far the dominant GHG contributor and therefore the subject of this analysis.

Long, rigorous ongoing CO_{2} measurement data sets are available from the South Pole since 1957 and from Mauna Loa since 1958. The values are reported with very small measurement uncertainties, and they reveal a consistent positive trend over the past 60 years with a slightly concave-upward shape. While their annual CO_{2} values were similar in the late-1950s (at 315 ppm), Mauna Loa data have been increasing slightly more than South Pole data and both now exceed 400 ppm (Fig. 2). Other measurement stations subsequently added to global CO_{2} monitoring comprise a marine surface data set with values between the South Pole and Mauna Loa series. South Pole and Mauna Loa data are employed for this analysis since they are the longest time series and they bracket other data.

**Figure 2.** History and forecasts of CO_{2} concentration. RCP8.5 is defined by 936 ppm in 2100.

Increasing CO_{2} is a long-term substitution process as it transitions to a larger fractional share of atmospheric concentration. If well underway, such a process can be studied utilizing a logistic function as described by J.C. Fisher & R.H. Pry in their landmark forecasting paper, *A Simple Substitution Model of Technological Change*. The methodology provides a top-down appraisal of an ongoing transition assuming continuity in evolution of its contributing elements into the future. The method has been successfully employed in thousands of long-range forecasting applications across many fields of study. Its form is shown in Figure 1.

**Figure 1.** Fisher-Pry formulation of a logistic substitution model.

If sufficient historical data is available, the differential equation in Figure 1 can be readily solved through minimization of a rigorously constructed Chi-Square function. A solution reveals the ceiling value, process mid-point and rate constant; and it thereby has predictive power. The early portion of the S-curve is approximately exponential, followed by a transition towards the inflection point at which growth rate peaks, thereafter declining as the cumulative curve approaches its long-term ceiling.

For the case of CO_{2}, the cumulative S-curve rests upon the pre-industrial starting level of 270-280 ppm. The rate of change in CO_{2} concentration is presently still increasing (Fig. 3), so the inflection point has not been reached; and second-difference calculations show no acceleration, indicating we are beyond the early exponential phase. The current substitution level should therefore lie between 15% and 50%, and this is found to be the case for the solutions shown in Figures 2 & 3.

**Figure 3.** Rate of change in CO_{2} concentration. RCP8.5 abruptly deviates from the historical trend.

The logistic CO_{2} forecasts project South Pole reaching 587 ppm and Mauna Loa reaching 654 ppm in the year 2100 (Fig. 2). The 90% confidence limits are calculated from variance of observations relative to the logistic fit and as a function of substitution level reached (Mauna Loa 24%, South Pole 33%). The result is well-constrained limits, and the slight divergence between data series continues into the future. RCP4.5 and RCP6.0 are similar to the South Pole forecast until mid-century, when RCP4.5 plateaus under mitigation assumptions and RCP6.0 increases towards the Mauna Loa forecast. RCP6.0 eventually reaches a ceiling below the Mauna Loa logistic ceiling. Results are detailed in Table 1 along with the values defining the RCPs.

**Table 1.** Atmospheric CO_{2} concentration projections.

Figure 3 displays the rate of change in CO_{2} concentration for the historical record, the logistic forecasts, and what is required to attain the defined RCP concentrations. The 60 year histories have a consistent upward trend, although with year-to-year variability. The highest transients above the trend are attributable to strong El Niño years (most recently 1998, 2016), which impair global vegetative response forming the seasonal CO_{2} cycle so that the annual value is temporarily elevated. The logistic rates-of-change are projected to attain their maximums (50% substitution) around 2037-2051 for South Pole and 2060-2080 for Mauna Loa. RCP4.5 and RCP6.0 rates bracket the South Pole forecast until mid-century, with transitions thereafter.

But what is glaringly apparent is the excessive rate-of-change required to attain RCP8.5’s 936 ppm in the year 2100. The rate would have to immediately depart from the historical pattern towards more than double any other forecast or RCP. In fact, since the RCPs were developed several years ago, it should have already transitioned to a very high trend to support an RCP8.5 expectation. This has clearly not occurred, and ongoing measurements show it is not happening. Other mathematical formulations were attempted for 936 ppm, but no logically consistent one was found. Even if it were assumed we remain in the early exponential phase of a substitution process the numbers do not support such a high expectation. RCP8.5 is a mathematically flawed projection for the future and clearly not the “business as usual” case. Rather, something similar to RCP6.0 should be assigned that designation, although with some modifications as to how it will evolve.

**Revisiting the Origins of RCP8.5**

The RCPs were presented in detail in a set of papers published in Climatic Change in 2011, and are worth reviewing. Recall that there was a desire to perform climate modeling over a wide range of forcing values – to fully exercise them from 2.6 W/m^{2} to 8.5 W/m^{2}. This is understandable from an exploratory research standpoint, but says nothing about the likelihood of specific future outcomes. But, the papers do shed some light upon that.

RCP8.5 is described by the van Vuuren et al. *The representative concentration pathways: an overview* as a very high emissions scenario required to attain the desired forcing level. “RCP8.5 is a highly energy-intensive scenario as a result of high population growth and a lower rate of technology development.” Figures published in the paper identify where each RCP’s assumptions lie within the literature available at the time they were developed. Those taken for RCP8.5 lie at limits of 90^{th} or 98^{th} percentile bands (1% to 5% probability). The population projection is at the high limit of United Nations scenarios. Its primary energy consumption projection lies at the 99^{th} percentile through most of this century. Energy intensity of the economy (energy/GDP) aligns with the 99^{th} percentile from the literature. Improvement in RCP8.5’s carbon factor (CO_{2}/energy) is minimal and at the 95^{th} percentile, reflecting heavy reliance on fossil fuels. Coal comprises nearly 50% of RCP8.5’s energy mix, something which has not been seen since early in the last century. RCP8.5 has consequently been called a “return to coal” scenario (*Why do climate change scenarios return to coal?*, ). This is inconsistent with natural long-term sequential evolutions of energy technologies that project a declining share of the energy mix for coal.

It should come as no surprise then that a concatenation of very low probability assumptions yields a highly unlikely CO_{2} concentration at end-century. This result is given by van Vuuren et al. and shown in Figure 4. The RCP8.5 curve exits the literature envelope. The logistic forecasting exercise above confirms the most likely CO_{2} level that van Vuuren reported several years ago in the vicinity of 600 ppm in 2100 (Fig. 4). Their graph also serves as guidance for what might constitute a “worst case” CO_{2} scenario, which could be assessed to be in the range of 700-750 ppm.

**Figure 4.** Graph from van Vuuren et al. 2011 (Fig.9, p.23), the RCP CO_{2} concentrations. Gray areas indicate 90^{th} and 98^{th} percentile bands (dark/light gray) of referenced literature. RCP4.5/6.0 is centered; RCP8.5 exceeds the upper limit.

So, since it was documented years ago that RCP8.5’s CO_{2} concentration has a vanishingly small probability of actually occurring, then why has it been promulgated for impact assessments and to inform climate policy? And why have researchers who realize that a true “business as usual” future lies closer to RCP6.0 found that when they go to the climate model library the RCP6.0 model runs do not exist? Have they been purposefully directed to RCP8.5, or is anything less than RCP8.5 unable to force a hypothesized impact?

**Conclusions**

The 60-year records of rigorous CO_{2} concentration measurements provide valuable forecasting information that is highly amenable to logistic growth modeling. It is clear that a substitution process is well underway that can be quantified to provide constraints upon expectations of future concentrations. The consistent concave-upward CO_{2} trend, rising rate-of-change, and well-bounded variance about the logistic solution provide confidence in the resulting forecasts and rejection of significantly inconsistent projections such as RCP8.5.

CO_{2} concentrations in 2100 will likely fall in the 565-680 ppm range and well short of 936 ppm indicated by RCP8.5. In preparation for the next IPCC assessment report, RCP8.5 has been redefined at even higher CO_{2} concentrations [link]. Modifications to inconsistent assumptions in minor-GHGs cause CO_{2} in the new RCP8.5 to exceed 1000 ppm in 2100 through even more coal consumption to retain 8.5 W/m^{2} forcing. RCP8.5 requires a CO_{2} rate of change inconsistent with the observed record that will be worsened by higher concentrations.

The RCP reference literature documents how RCP8.5 was based on low probabilities and questionable assumptions. It is not “business as usual” or even a worst case scenario. Consequently, the findings of any impact assessment based in RCP8.5 should be critically reviewed, as they reflect a highly unlikely, if not impossible, outcome.

The NCA4 (Executive Summary, p.22) states “The observed increase in global carbon emissions over the past 15-20 years has been consistent with higher scenarios (e.g., RCP8.5) (very high confidence).” This statement suggests either dismissal of observational evidence or that carbon budget model calculations from emissions to concentration are unable to replicate the historical CO_{2} measurement record. As evident in Figure 3, the recent record does not support an RCP8.5 pathway, and the statement is false.

Unfortunately the compulsion towards exaggeration can be stronger than duty to facts, and without them it will be impossible to make progress towards preparing for the future. The RCP6.0 pathway is the scenario coming closest to the forecast presented above and therefore a more realistic expectation of the future, and mitigation actions could evolve it towards RCP4.5.

**Acknowledgements.** The author thanks his colleague, Theodore Modis (growth-dynamics.com), for conducting the logistic forecast calculations. For those interested, the methodology is well-documented in his book *Natural Laws in the Service of the Decision Maker *(2013).

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