Tongchai Thailand by Jamal Munshi, PhD | May 18, 2021

*THIS POST IS A LIST OF LINKS TO POSTS ON THIS SITE THAT RELATE TO STATISTICS ERRORS IN CLIMATE SCIENCE. *

**STATISTICS POST#1: THE MATHEMATICAL INCONSISTENCY ISSUE BETWEEN ECS AND TCRE**.

*LINK: https://tambonthongchai.com/2020/08/26/a-mathematical-inconsistency/ *

THE EQUILIBRIUM CLIMATE SENSITIVITY ECS: The ECS measure of the impact of fossil fuel emissions on warming holds that atmospheric CO2 concentration at any given time is a linear function of cumulative emissions and that surface temperature is a logarithmic function of atmospheric CO2 concentration. These two relationships imply that surface temperature is a logarithmic function of cumulative emissions. That in turn implies that the amount of warming caused by a given level of cumulative emissions is the difference between the logarithms of the two cumulative emissions before and after.

TRANSIENT CLIMATE RESPONSE TO CUMULATIVE EMISSIONS TCR: The TCR measure of the impact of fossil fuel emissions on warming holds that the amount of warming is a linear function of cumulative emissions. This linearity is mathematically inconsistent with the ECS measure which implies that the amount of warming is proportional to the difference between the logarithms of the cumulative emissions before and after the period of warming under study.

IMPLICATIONS OF THIS MATHEMATICAL INCONSISTENCY: The mathematical inconsistency described above shows that the significant research effort in climate science to resolve the ECS and TCR measures of anthropogenic warming in terms of fossil fuel emissions with Earth System Models {ESM} is not possible because the two methods of computing the impact of emissions on temperature are not mathematically consistent and that makes it impossible for them to describe the same phenomenon in nature.

THE IMPOSSIBILITY OF EARTH SYSTEM MODELS {ESM} THAT EMPLOY THE TCRE. In a related post on ESM we argue that the ESM construction procedure of beginning with the TCR warming derived from cumulative emissions and then explaining the result from an arbitrarily expanded list of ECS climate drivers is a form of circular reasoning. In this post we find that a further and more serious flaw in this procedure is the mathematical impossibility of the ESM exercise of reconciling ECS and TCR: LINK: https://tambonthongchai.com/2020/08/25/earth-system-models-and-carbon-budgets/

**STATISTICS POST#2: THE MATHEMATICAL IMPOSSIBILITY OF THE TCRE**

**LINK: https://tambonthongchai.com/2018/05/06/tcre/ **

THE TCRE IS A CORRELATION BETWEEN THE CUMULATIVE VALUES OF TWO TIME SERIES DATA. IN A RELATED POST WE SHOW THAT THE THE TIME SERIES OF THE CUMULATIVE VALUES OF A TIME SERIES CONTAINS NEITHER TIME SCALE NOR DEGREES OF FREEDOM. THEREFORE A CORRELATION BETWEEN TWO SUCH TIME SERIES CONTAINS NO USEFUL INFORMATION ABOUT A RELATIONSHIP BETWEEN THE TWO TIME SERIES. IN THE CASE OF TH CORRELATION BETWEEN CUMULATIVE EMISSIONS AND CUMULATIVE WARMING, WE FIND THAT THE OBSERVED CORRELATION IS A CREATION OF A SIGN PATTERN IN THE DATA WHERE ANNUAL EMISSIONS ARE ALWAYS POSITIVE AND IN A TIME OF RISING TEMPERATURES, ANNUAL WARMING IS MOSTLY POSITIVE. THE CREATION OF THE TCRE CORRELATION FROM THIS TIME PATTERN IS CONFIRMED WITH A DEMNSTRATION THAT NOT JUST EMISSIONS BUT ANY TIME SERIES WITH POSITIVE VALUES WORKS JUST AS WELL, EVEN UFO SIGHTINGS.

*LINK: https://tambonthongchai.com/2018/12/03/tcruparody/ *

*STATISTICS POST#3: THE REMAINING CARBON BUDGET ANOMALY IN CLIMATE SCIENCE*

*LINK: https://tambonthongchai.com/2019/12/25/the-remaining-carbon-budget-anomaly-explained/ *

Carbon budgets are derived from the TCRE (Transient Climate Response to Cumulative Emissions) correlation between cumulative warming and cumulative emissions. The value of the TCRE is the regression coefficient of cumulative warming against cumulative emissions. In the previous item it is shown that the TCRE correlation derives not from the responsiveness of warming to emissions but from a sign pattern in which annual emissions are always positive and, during a warming trend, annual warming is mostly positive. Since emissions are always positive, *the TCRE regression coefficient in this proportionality is determined by the fraction of annual warming values that are positive*. Larger fractions of positive warming values yield higher values of the TCRE regression coefficient and it is the regression coefficient that determines the value of the carbon budget. *Because of the random nature of the annual warming values, it is highly unlikely that the fraction of annual warming values that are positive in the full span of the carbon budget period will be the same as the fraction of annual warming values that are positive in the two halves of the full span*. *Therefore we find that in general the TCRE regression coefficient for the full span of the carbon budget period, that for the first half of the carbon budget period, and that for the second half of the carbon budget period will be different.* ** It is this simple statistical issue that imposes the remaining carbon budget puzzle in climate science.** For the carbon budgets in the two halves of the carbon budget period to be the same, the positive fraction of the annual warming values would have to be the same in the two halves and in general they are not and that creates the Remaining Carbon Budget anomaly. Therefore, the climate science assumption that the Remaining Carbon Budget anomaly has an interpretation in terms of the climate science of additional forcings or feedbacks in climate models or of additional climate variables in Earth System Models is flawed. The only information here is that the fraction of annual warming values that are positive are random and will therefore differ in general in the two halves.

*STATISTICS POST#4: THE NULL HYPOTHESIS ISSUE IN CLIMATE SCIENCE *

*LINK: https://tambonthongchai.com/2021/04/05/the-null-hypothesis-issue/ *

**CLIMATE SCIENCE CONTAINS A BIAS FOR THE TRUTH OF THAT WHICH IS TO BE PROVEN AND THAT THEREFORE CLIMATE SCIENCE CANNOT BE CONSIDERED TO BE UNBIASED AND OBJECTIVE SCIENTIFIC INQUIRY.**

**SPECIFICALLY, IN OBJECTIVE UNBIASED SCIENTIFIC INQUIRY, THAT WHICH IS TO BE PROVEN MUST BE THE ALTERNATE HYPOTHESIS AND ITS NEGATION THEN BECOMES THE NULL HYPOTHESIS. THE UNBIASED DATA COLLECTION MUST THEN PROVIDE SIGNIFICANT EVIDENCE TO REJECT THE NULL IN ORDER TO ACCEPT THE TRUTH OF THAT WHICH IS TO BE PROVEN.**

**THE TRUTH OF THAT WHICH IS TO BE PROVEN WHEN TAKEN AS THE NULL HYPOTHESIS CONTAINS A BIAS AND IT VIOLATES THE SCIENTIFIC METHOD SUCH THAT THE RESEARCH FINDINGS OF THIS METHODOLOGY CANNOT BE TAKEN AS THE PRODUCT OF OBJECTIVE AND UNBIASED SCIENTIFIC INQUIRY.**

**THE ODD LOGIC IN CLIMATE SCIENCE DESCRIBED AS “THE LESS WE KNOW THE SCARIER IT GETS**” **DERIVES FROM THIS STATISTICAL ERROR. THE TRUTH OF THAT WHICH IS TO BE PROVEN STANDS AS TRUTH UNTIL PROVEN WRONG**. **THIS BIAS IS OFTEN ACKNOWLEDGED AND THEN DEFENDED WITH THE PRECAUTIONARY PRINCIPLE.**** **

*STATISTICS POST#5: THE PRECAUTIONARY PRINCIPLE IN CLIMATE SCIENCE. *

*LINK: https://tambonthongchai.com/2020/12/27/superstitious-humans/ *

THE ARGUMENT IS OFTEN SEEN IN CLIMATE SCIENCE CLAIMS THAT THE LESS THEY KNOW THE SCARIER IT GETS AS DESCRIBED IN THESE RELATED POSTS:

*THESE CLAIMS CONTAIN THE ASSUMPTION IN CLIMATE SCIENCE OF THE PRECAUTIONARY PRINCIPLE OFTEN SEEN IN ENVIRONMENTAL SCIENCE. IT HOLDS THAT THE CLAIMED HARM OF HUMAN ACTIVITIES IS THE NULL HYPOTHESIS AND IS ASSUMED TO BE TRUE UNTIL CONVINCING EVIDENCE AGAINST IT CAN BE PRESENTED. THIS STATISTICAL LOGIC IS THE EXACT OPPOSITE OF WHAT WE SEE IN THE REST OF SCIENCE AND IN STATISTICAL PRINCIPLES WHERE THAT WHICH IS TO BE PROVEN IS THE ALTERNATE HYPOTHESIS AND ITS NEGATION IS THE NULL HYPOTHESIS SUCH THAT TO ESTABLISH THE TRUTH OF THE ALTERNATE HYPOTHESIS SUFFICIENT EVIDENCE AGAINST THE NULL MUST BE PRESENTED SO THAT THE NULL HYPOTHESIS CAN BE REJECTED. THE ONLY WAY A CONCLUSION CAN BE DRAWN FROM A HYPOTHESIS TEST IS BY REJECTING THE NULL HYPOTHESIS. IN THE ABSENCE OF THAT REJECTION, THERE IS NO USEFUL INFORMATION CAN BE DRAWN FROM THE HYPOTHESIS TEST. “FAIL TO REJECT” DOES NOT CONTAIN USEFUL INFORMATION. IN FACT WHAT IT TELLS US IS THAT THERE IS NO USEFUL INFORMATION HERE.**THE USE OF THE PRECAUTIONARY PRINCIPLE IS A VIOLATION OF THE STATISTICS OF HYPOTHESIS TESTS. *

*STATISTICS POST#6: RESPONSIVENESS OF ATMOSPHERIC CO2 CONCENTRATION TO FOSSIL FUEL EMISSIONS #1 *

*LINK: https://tambonthongchai.com/2020/06/14/responsiveness-of-atmospheric-co2-to-fossil-fuel-emissions/ *

**A testable implication of the proposed causation sequence is that annual changes in atmospheric CO2 must be related to annual fossil fuel emissions at an annual time scale**. **This work is a test of this hypothesis.** **We find that ****detrended correlation analysis ****of annual emissions and annual changes in atmospheric CO2 does not support the anthropogenic global warming hypothesis that atmospheric CO2 concentration is responsive to fossil fuel emissions at an annual time scale. because. No evidence is found that changes in atmospheric CO2 are related to fossil fuel emissions at an annual time scale****.**

*STATISTICS POST#7: *

*THE UNCERTAINTY IN CARBON CYCLE FLOWS*

*LINK: https://tambonthongchai.com/2018/05/31/the-carbon-cycle-measurement-problem/ *

The problem with determining the cause of changes in atmospheric CO2 concentration at an annual time scale is that the relatively small flow of fossil fuel emissions go into and intermingle with natural carbon cycle flows that are an order of magnitude larger with large uncertainties in the flow rates. These flows cannot be measured but only inferred from circumstantial data. The issue here is ** uncertainty**.

*What we have here is a mixing problem that is overwhelmed with large uncertainties.***Relatively small** fossil fuel emissions of CO2 ** with known flow rates **go into the atmosphere and intermingle with

**relatively large**carbon cycle CO2 flows flowing in both directions. Their

**flow**. They can only be grossly

*rates are not known and cannot be measured***inferred**from circumstantial data.

** This complex system of the the mixing of these CO2 flows** is understood in climate science as the “

**” issue with the estimate that**

*Airborne Fraction*

*about half of the fossil fuel CO2 are removed by carbon cycle flows and the other half the fossil fuel CO2 stays in the atmosphere and causes atmospheric CO2 concentration to rise This assumed relationship is a foundational and critically important concept in the theory of anthropogenic global warming (AGW) and here we show that it is not well understood.*** The Airborne Fraction** ratio is

*estimated from the known flows of fossil fuel emissions and the known changes in atmospheric composition*without considertion of uncertainty in carbon cycle flows.

**The data that were used to construct the airborne fraction hypothesis are then used to validate that hypothesis.**

**.**

*This kind of hypothesis test is a form of circular reasoning, This is because THE DATA USED TO CONSTRUCT A HYPOTHESIS CANNOT BE USED TO TEST THAT HYPOTHESIS***That the mean value of the Airborne Fraction is about a half** means that about half of the CO2 in our fossil fuel emissions stays in the atmosphere and causes atmospheric CO2 to rise. However, the actual ** observed ratio is uncertan with a large variability**.

*The left frame of Figure 1 above*shows a large range of values for

*decadal mean Airborne Fraction*from zero% to 45% 1860 to 2017. This sample period includes ice core CO2 data from the Law Dome for years prior to 1958. When the sample period is restricted to the more precise

*with decadal mean*

**Mauna Loa**data from 1958, a much smaller range of values is seen in**the right frame of Figure 1****ans a mean of aroubd**

*airborne fraction of 45% to 65%***.**

*50%*These data appear to support the ** usual assumption in climate science that the Airborne Fraction is 50%** that serves as evidence that fossil fuel emissions cause atmospheric CO2 to rise.

**This relationship implies that atmospheric CO2 concentration is responsive to fossil fuel emissions at an annual time scale. The testable implication is a statistically significant detrended correlation at an annual time scale.**,

*Without this correlation***. The underlying issue here is of course the uncertainty in carbon cycle flows.**

*though an airborne fraction can be computed, it has no interpretation in terms of cause and effect in the phenomenon being studied***In the charts below** we present an analysis of the to determine whether the relatively small flow of fossil fuel CO2 emissions can be detected with statistical significance in the context of much larger and uncertain carbon cycle flows that can’t be directly measured but must be inferred. We use a range of assumed **carbon cycle flow uncertainties **with standard deviations from **1% of estimated flow to 6.5% of estimated flow. **We then carry out hypothesis tests to determine ** whether the carbon cycle flow with fossil fuel emissions is greater than the carbon cycle flow without fossil fuel emissions**, in other words,

*. T*

**whether the much smaller fossil fuel emissions can be detected in the context of the large flows and large uncertainties of carbon cycle flows****the p-value of the hypothesis test is less than 0.05 only when the uncertainty in carbon cycle flows is less than 2% of flowrate whereas the smallest uncertainty found in IPCC reports is in we see in the IPCC publications is for photosynthesis with a mean of 123 gigatonnes per year and standard deviation of 8 gigatonnes. Here the standard deviation is 6.5% of flowrate. We conclude from this analysis that the net effect of fossil fuel emissions relatively tiny fossil fuel emissions injected into large an uncertain carbon cycle flows cannot be detected and that therefore we have no information about the eeffect of fossil fuel emissions on atmospheric composition.**

*he p-values of these hypothesis tests are tabulated below and also shown graphically in the chart on the right. What we find is that**THE TEST MADE BY CLIMATE SCIENCE OF USING THE RATIO OF THE OBSERVED RISE IN ATMOSPHERIC CO2 TO THE FLOW OF CO2 IN FOSSIL FUEL EMISSIONS IN THEIR AIRBORNE FRACTION ARGUMENT IS A CREATION OF CIRCULAR REASONING AND CONFIRMATION BIAS. THE USUAL RESPONSE TO THIS ARGUMENT IS SOMETHING LIKE “**WHERE IS IT GOING THEN, WISE GUY?**” {Ken Caldeira}. MY ANSWER IS THAT WE DON’T KNOW BECAUSE WE CAN’T MEASURE THE MUCH LARGER CARBON CYCLE FLOWS WITH SUFFICIENT PRECISION TO EVEN DETECT THE PRESENCE OF FOSSIL FUEL EMISSIONS.*

*IT IS NOT NECESSARY FOR CRITICS OR DENIERS TO KNOW THE REAL ANSWER IN ORDER TO CHALLENGE THE ANSWER PROPOSED BY CLIMATE SCIENCE*** ON THE BASIS OF THE UNCERTAINTY THAT IS NOT IN DISPUTE**.

** STATISTICS POST#8: RESPONSIVENESS OF ATMOSPHERIC CO2 CONCENTRATION TO FOSSIL FUEL EMISSIONS #**2

** THE UNCERTAINTY IN CARBON CYCLE FLOWS** (CONTINUED):

ANOTHER WAY TO DEMONSTRATE THE ABSENCE OF INFORMATION ABOUT THE IMPACT OF FOSSIL FUEL EMISSIONS UNDER CONDITIONS OF LARGE UNCERTAINTIES IN CARBON CYCLE FLOWS IS A MONTE CARLO SIMULATION TO MIX FOSSIL FUEL EMISSIONS AND CARBON CYCLE FLOWS. THE RESULTS ARE SHOWN IN THE CHARTS BELOW.

*LINK: https://tambonthongchai.com/2020/06/10/a-monte-carlo-simulation-of-the-carbon-cycle/ *

*FINDINGS: THE COMPLEX MASS BALANCE OF UNCERTAIN FLOWS IS CARRIED OUT WITH MONTE CARLO SIMULATION WHERE 150 RANDOM VALUES ARE DRAWN FROM ALL POSSIBLE VALUES WITHIN THE STATED UNCERTAINTY OF CARBON CYCLE FLOWS.**THE IPCC PROVIDED AN UNCERTAINTY VALUE FOR THE FLOW OF CO2 REMOVED FROM THE ATMOSPHERE BY PHOTOSYNTHESIS AS A STANDARD DEVIATION OF σ=8 IN A FLOW WITH A MEAN VALUE OF μ=123. THE UNCERTAINTY IN THIS CASE CAN BE REPRESENTED AS σ=8/123 OR 6.5% OF THE MEAN . THE UNCERTAINTY FOR THE OTHER UNCERTAIN CARBON CYCLE FLOWS ARE NOT PROVIDED AND ARE THEREFORE ESTIMATED AS 6.5% OF THE MEAN.**IN THE MONTE CARLO SIMULATION, 150 POSSIBLE VALUES ARE DRAWN FROM WITHIN THIS UNCERTAINTY BAND FOR EACH UNCERTAIN CARBON CYCLE FLOW. LINES DRAWN THROUGH THESE 150 VALUES ARE DEPICTED IN THE CHARTS ABOVE FROM FIGURE 1 TO FIGURE 5. *

**WHAT WE FIND IN THE SIMULATION IS THAT WHEN FOSSIL FUEL EMISSIONS ARE INSERTED INTO THE CARBON CYCLE FLOWS, ****THE MEAN OF THE 150 RANDOM MONTE CARLO SIMULATION VALUES OF THE AIRBORNE FRACTION IS μ=4.77 WITH A STANDARD DEVIATION OF σ=12.7**** . THERE IS NO STATISTICALLY SIGNIFICANT CONTRIBUTION OF FOSSIL FUEL EMISSIONS TO ATMOSPHERIC COMPOSITION. ***FOSSIL FUEL EMISSIONS WE FIND THE MEAN OF THE AIRBORNE FRACTION IS CLOSE TO ZERO AS WE WOULD EXPECT WITH A COMPUTED MEAN OF μ= –1.7 BUT WITH A LARGE STANDARD DEVIATION OF σ=12.1 WITH THE IMPLICATION THAT THE COMPUTED MEAN HAS NO INTERPRETATION.*

**SUMMARY OF NET CO2 FLOWS TO THE ATMOSPHERE**

*CASE 1: NO FOSSIL FUEL EMISSIONS: MEAN=-1.7, STDEV=12.1, TSTAT=0.14*

*CASE 2: WITH FOSSIL FUEL EMISSIONS: MEAN=4.77, STDEV=12.7, TSTAT=0.375*

*CONCLUSION; THE TWO MEAN CONTRIBUTIONS OF THE CARBON CYCLE WITH AND WITHOUT FOSSIL FUEL EMISSIONS TO ATMOSPHERIC CO2 CONCENTRATION HAVE NO INTERPRETATION BECAUSE OF A COMPLETE ABSENCE OF STATISTICAL SIGNIFICANCE DUE TO LARGE UNCERTAINTIES.**WE CONCLUDE THAT WITHIN THE STATED UNCERTAINTIES OF CARBON CYCLE FLOWS, NO EVIDENCE IS FOUND IN THE DATA THAT FOSSIL FUEL EMISSIONS CAUSE CHANGES IN ATMOSPHERIC CO2 CONCENTRATION. THE UNCERTAINTIES IN CARBON CYCLE FLOWS ARE TOO LARGE TO DETECT THESE ASSUMED EFFECTS.**THE ASSUMED SENSITIVITY OF ATMOSPHERIC COMPOSITION TO FOSSIL FUEL EMISSIONS IS THE ESSENTIAL BASIS FOR THE THEORY OF ANTHROPOGENIC GLOBAL WARMING BY THE INDUSTRIAL ECONOMY AND THE CALL FOR COSTLY CLIMATE ACTION; BUT NO SUCH SENSITIVITY IS FOUND IN THE DATA. THIS RESULT IS SUPPORTED BY CORRELATION ANALYSIS PRESENTED IN A RELATED POST AT THIS SITE* [LINK TO CORRELATION ANALYSIS].

*STATISTICS POST#9: A HYPOTHESIS DERIVED FROM THE DATA CANNOT BE TESTED WITH THE SAME DATA*

*IN ITEM #5 AND ITEM#6 ABOVE WE FIND THAT THE AIRBORNE FRACTION OF 50% IS DERIVED FROM THE DATA. HOW IS THIS HYPOTHESIS TO BE TESTED? A HYPOTHESIS DERIVED FROM THE DATA CANNOT BE TESTED WITH THE SAME DATA. THAT KIND OF STATISTICS CONTANS A CIRCULAR REASONING FALLACY OFTEN DESCRIBED AS THE TEXAS SHARPSHOOTER FALLACY WHERE YOU SHOOT FIRST AND DRAW THE TARGET LATER. THEREFORE THE AIRBORNE FRACTION HYPOTHESIS DERIVED FROM THE DATA AS SHOWN ABOVE CANNOT BE TESTED. *

*STATISTICS POST#10: *SEA LEVEL RISE CORRELATED WITH FOSSIL FUEL EMISSIONS

** HERE WE PRESENT THE CLAIM BY CLIMATE SCIENCE THAT THEY HAVE FOUND EMPIRICAL EVIDENCE TO RELATE OBSERVED SEA LEVEL RISE TO GLOBAL WARMING BY WAY OF STTISTICS THAT SHOW A STRONG CORRELATION BETWEEN CUMULATIVE SEA LEVEL RISE AND CUMULATIVE EMISSIONS**.

*LINK: https://tambonthongchai.com/2021/02/04/a-tcre-of-sea-level-rise/ *

IN POST#2 ABOVE WE SHOWED THAT THE TCRE CORRELATION BETWEEN CUMULATIIVE ANNUAL EMISSIONS AND CUMULATIVE ANNUAL WARMING IS SPURIOUS AND IT DERIVES FROM A SIGN PATTERN IN WHICH ANNUAL FOSSIL FUEL EMISSIONS ARE ALWAYS POSITIVE AND IN A TIME OF WARMING, ANNUAL WARMING IS MOSTLY POSITIVE. THAT SAME SIGN PATTERN APPLIES TO SEA LEVEL RISE WHERE ANNUAL FOSSIL FUEL EMISSIONS ARE ALWAYS POSITIVE AND ANNUAL SEA LEVEL RISE DURING A TIME OF RISING SEAS, IS MOSTLY POSITIVE.

YET WHAT WE FIND IN THE RELATED POST LINKED ABOVE IS THAT CLIMATE SCIENCE HAS MISTKEN THIS SPURIOUS CORRELATION AS PROVIDING EMPIRICAL EVIDENCE THAT FOSSIL FUEL EMISSIONS DRIVE SEA LEVEL RISE.

*STATISTICS POST#11: EARTH SYSTEM MODELS AND THE TCRE *

*RELATED POST ON ESM: LINK: https://tambonthongchai.com/2020/08/25/earth-system-models-and-carbon-budgets/ *

WHAT WE FIND IN THE RELATED POST ON EARTH SYSTEM MODELS IS THAT THE STATISTICALLY FLAWED TCRE METRIC IS NOW AN IMPORTANT TOOL IN CLIMATE SCIENCE THAT HAS ALLOWED IT TO BYPASS ITS UNCERTAINTY DIFFICULTIES WITH EQUILIBRIUM CLIMATE SENSITIVITY. GIVEN THE TCRE, WE CAN BEGIN WITH EMISSIONS AND THE TCRE WARMING AND THEN LOOK THROUGH ALL POSSIBLE EXPLANATION FOR THE TCR WARMING IN A CONFIRMATION BIAS EXERCISE THAT CAN AND DOES CREATE CONTRADICTIONS.

** AS AN EXAMPLE OF THE PROBLEMS CREATED BY THE CIRCULAR REASONING EARTH SYSTEM MODEL METHODOLOGY WE PRESENT THE PAPER BELOW**.

Environmental Research Letters: Quantifying process-level uncertainty contributions to TCRE and Carbon Budgets for meeting Paris Agreement climate targets.

**Chris D Jone1 and Pierre Friedlingstein: 1 April 2020**: **Abstract: **To achieve the goals of the Paris Agreement requires deep and rapid reductions in anthropogenic CO2 emissions, but **uncertainty **surrounds the magnitude and depth of reductions. Earth system models provide a means to quantify the link from emissions to global climate change. Using the concept of **TCRE **– the transient climate response to cumulative carbon emissions – we can *estimate the remaining carbon budget to achieve 1.5 or 2 oC. But the uncertainty is large, and this hinders the usefulness of the concept*. Uncertainty in carbon budgets associated with a given global temperature rise is determined by the physical Earth system, and therefore Earth system modelling has a clear and high priority remit to address and reduce this

**uncertainty**. Here we explore multi-model carbon cycle simulations across three generations of Earth system models to quantitatively assess the sources of

**uncertainty**which propagate through to

**TCRE**. Our analysis brings new insights which will allow us to determine how we can better direct our research priorities in order to reduce this

**uncertainty**. We emphasize that uses of carbon budget estimates must bear in mind the

**uncertainty**stemming from the biogeophysical earth system, and we recommend specific areas where the carbon cycle research community needs to re-focus activity in order to try to reduce this

**uncertainty**. We conclude that we should revise focus from the climate feedback on the carbon cycle to place more emphasis on CO2 as the main driver of carbon sinks and their long-term behaviour. Our proposed framework will enable multiple constraints on components of the carbon cycle to propagate to constraints on remaining carbon budgets.

A CRITICAL ANALYSIS OF THIS PAPER IS PRESENTED IN A RELATED POST ON THIS SITE: *LINK: https://tambonthongchai.com/2020/04/09/climate-statistics/ *

*WHAT THE PAPER SAYS*

** (1) ABOUT THE TCRE**: A body of literature from 2009 found consistently that

*warming was much more closely related to the cumulative CO2 emissions*than the time profile or particular pathway. This

*relationship between warming and cumulative emissions is found in the IPCC’s Fifth Assessment Report (AR5)*as

*TCRE**: the Transient Climate Response to cumulative carbon Emissions*.

*The physical basis of TCRE*is described by Caldeira & Kasting (1993) who noted that

*saturation of the radiative effect of CO2 in the atmosphere could be balanced by saturation of uptake by ocean carbon leading to*insensitivity of the warming to the pathway of CO2 emissions. Literature since then has

*put this on a firm footing with numerous authors showing that trajectories of ocean heat and carbon uptake have similar effects on global temperature due to the diminishing radiative forcing from CO2 in the atmosphere and the diminishing efficiency of ocean heat uptake*.

*Terrestrial carbon uptake is equally important for the magnitude of TCRE*– in fact we will show here that

*land and ocean contribute equally to the magnitude of TCRE and that land dominates over the ocean in terms of model spread*.

**(2) ABOUT TCRE CARBON BUDGETS**: *The IPCC AR5* assessed a total *carbon budget of 790 PgC* to stay below 2C above pre-industrial, *of which about 630 PgC has been emitted* over the 1870-2018 period. However, *the* *uncertainty in the remaining carbon budget* to achieve 1.5C or 2C is very large – in fact possibly larger than the remaining budget itself*.* This large uncertainty hinders the potential usefulness of this simplifying concept to policy makers. All studies and reports which present estimates of *the remaining carbon budget* (e.g. The IPCC’s Fifth Assessment Report, its Special Report on Global Warming of 1.5oC, or the UNEP Gap Report) *have to make an assumption on how to deal with and present this uncertainty*. Some explicitly describe *the chosen assumptions (such as 50% or 66% probability of meeting targets) or tabulate multiple options, but all are hindered by the uncertainty*. The *AR5 Synthesis Report* quoted a value of *400 GtCO2 (110 GtC) remaining budget from 2011 for a 66% chance to keep warming below 1.5C*. It is now clear that this was an *underestimate* as this would mean a remaining budget of about 20 GtC from 2020. *Since AR5 there has been extensive literature on the application of the TCRE* concept and its limitations including the choice of temperature metric and baseline period and *issues of biases in Earth system models (ESMs)*. *Some studies accounted for climate model biases by relating warming from present day onwards to the remaining carbon budget* . Other studies have used the *historical record to constrain TCRE* and the remaining budget using simple models or attribution techniques. Both t*hese approaches find a substantial increase in the remaining carbon budget* for 1.5C compared to the IPCC AR5 SPM approach. Studies that have tried to additionally account for non-CO2 warming. show that *CO2-only TCRE budgets are a robust upper limit* but taking account of non-CO2 forcing results in lower allowable emissions. Some have proposed *techniques for combining emissions rates of short-lived climate pollutants with long-term CO2 cumulative emission budgets*. In light of these advances, the IPCC Special Report on Global Warming of 1.5C (SR15) quotes a value of *420 GtCO2 remaining carbon budget for a 66% chance to keep warming below 1.5C* – a value very similar to the AR5 value from 5 years earlier.

There is also a lot of focus on *how to achieve such carbon budgets* and the increasing realization of the *need for carbon dioxide removal* and research into the feasibility and implications of negative emissions technology.

**(3)** **ABOUT CARBON CAPTURE AND SEQUESTRATION: ** The discussion around carbon dioxide removal (*CDR*) requires more detailed assessment of the *magnitude and timing of any requirement for negative emissions technology and hence more precise estimates of remaining carbon budgets*. Glen Peters argues that large uncertainty in budget estimates may be used to justify further political inaction and Sutton (2018) argues for consideration of plausible *high impact outcomes in the tails of the likelihood distribution*. *The same argument applies to TCRE and carbon budgets: we need information on best estimates but also possible extremes however unlikely*. *The feasibility of achieving 1.5C without net negative emissions depends on the remaining budget being at the high end of current estimates*. Knowing the likelihood of the range as well as central estimate is required to inform the debate on requirements for negative emissions. We should break down individual the individual contributions to uncertainty in carbon budgets in terms of historical human induced warming to date, likely range of TCRE, potential additional warming after emissions reached zero, warming from non-CO2 forcing, and carbon emissions from Earth system feedbacks not yet in Earth System Models as in thawing permafrost. Our ability to model the climate-carbon cycle system is imperfect with uncertainties but it plays a dominant role in the remaining carbon budget issue.

The SR15 assumptions of no further warming after CO2 emissions cease is consistent with the multi-model mean. Similarly, CMIP6 and sophisticated ESMs begin to include additional Earth system feedbacks – *but the elephant in the room is that past generations of models have not seen a decreased spread in TCRE* remaining carbon budget and adding complexity doesn’t help. In terms of climate sensitivity, GCMs continue with the large range of 3°C (from about 1.5 to about 4.5 °C) since the Charney report of 1979. We need to figure out where the large uncertainty in the TCRE remaining carbon budget comes from so that we can control it with observational constraints.

**(4) WHAT’S NEW IN THIS PAPER**: Here we perform a new analysis of *three generations of Earth System Model results*, spanning over a decade, to examine whether or not existing simulations and analyses are well placed to answer the increasing requirements of policy makers on the* carbon cycle research* community. We present a *new analytical framework which allows us to quantify sources of uncertainty in carbon budgets to land or ocean response to CO2 or climate*. It is the carbon cycle response to CO2, rather than its response to climate, which dominates the uncertainty in TCRE and hence carbon budgets.

**CRITICAL EVALUATION OF THE PAPER **

**Climate science has misinterpreted the statistical anomalies of the TCRE as a climate science issue that needs to be resolved with climate models of greater complexity. Their struggle with the remaining carbon budget puzzle seen in the Jone-Friedlingstein paper demonstrates a failure of climate science to address statistical issues of the TCRE in terms of statistics. This failure has led them down a complex and confusing path of trying to find a climate science explanation of the remaining carbon budget anomaly. The Jone-Friedlingstein paper research paper serves as an example of this kind of climate research. The real solution to the remaining carbon budget puzzle is to understand the statistical flaws in the TCRE correlation and to stop using it. [LINK] [LINK] . **