THIS POST IS A CRITICAL REVIEW OF A RESEARCH PAPER ON THE SEA LEVEL RISE HORROR OF CIMATE CHANGE PUBLISHED BY THE NEILS BOHR INSTITUTE OF THE UNIVERSITY OF COPENHAGEN

“Physics of Ice, Climate and Earth, Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark”: LINK: https://os.copernicus.org/articles/17/181/2021/

SUMMARY: THE SOURCE PAPER REVIEWED HERE USES THE CORRELATION BETWEEN CUMULATIVE EMISSIONS AND CUMULATIVE SEA LEVEL RISE AS DESCRIBED BY PETER CLARK IN A RELATED POST: https://tambonthongchai.com/2018/09/14/cumulativeslr/ AND ALSO CITES THE PETER CLARK PAPER. It contains the same statistical errors found in the paper by Peter Clark. The theoretical argument for the spuriousness of correlations between cumulative values is that the multiplicity in the use of the data for constructing cumulative values removes the available degrees of freedom in the data. The time series of cumulative values of another time series contains neither time scale nor degrees of freedom. Correlations computed with such time series data cannot provide a causation interpretation because these correlations contain no information except perhaps for the existence of a fortuitous and spurious sign pattern.

It is of course not feasible that sea level should respond to emissions at an annual time scale but a time scale must be specified from theory so that a testable implication and its empirical test can be carried out. In a related post, time scales of 30 to 50 years were tried but no correlation between emissions and sea level rise was found [LINK] .

Based on the statistical issues described above and in the related post on the Peter Clark paper, we find that the evidence presented for attribution of sea level rise to fossil fuel emissions is flawed and therefore not credible.

PART-1: WHAT THE RESEARCH PAPER SAYS

The transient sensitivity of sea level rise 09 Jul 2020

CITATION: Grinsted, A. and Christensen, J. H.: The transient sensitivity of sea level rise, Ocean Sci., 17, 181–186, https://doi.org/10.5194/os-17-181-2021, 2021.
Abstract: Recent assessments from the Intergovernmental Panel on Climate Change (IPCC) imply that global mean sea level is unlikely to rise more than about 1.1 m within this century but will increase further beyond 2100. Even within the most intensive future anthropogenic greenhouse gas emission scenarios, higher levels are assessed to be unlikely. However, some studies conclude that considerably greater sea level rise could be realized, and a number of experts assign a substantially higher likelihood of such a future. To understand this discrepancy, it would be useful to have scenario-independent metrics that can be compared between different approaches. The concept of a transient climate sensitivity has proven to be useful to compare the global mean temperature response of climate models to specific radiative forcing scenarios. Here, we introduce a similar metric for sea level response. By analyzing the mean rate of change in sea level (not sea level itself), we identify a nearly linear relationship with global mean surface temperature (and therefore accumulated carbon dioxide emissions) both in model projections and in observations on a century scale. This motivates us to define the “transient sea level sensitivity” as the increase in the sea level rate associated with a given warming in units of meters per century per kelvin. We find that future projections estimated on climate model responses fall below extrapolation based on recent observational records. This comparison suggests that the likely upper level of sea level projections in recent IPCC reports would be too low. 1 Introduction
Our planet is warming as anthropogenic emissions are increasing the atmospheric concentration of carbon dioxide. This warming causes sea levels to rise as oceans expand and ice on land melts. A perturbation in greenhouse gas concentrations changes the balance of energy fluxes between the atmosphere and the ocean surface, and the balance of mass fluxes to and from glaciers and ice sheets. However, the oceans and ice sheets are vast, and it takes centuries to heat the oceans and millennia for ice sheets to respond and retreat to a new equilibrium (Clark et al., 2018; Li et al., 2013; DeConto and Pollard, 2016; Oppenheimer et al., 2019). In this sense the ice sheets and oceans have a large inertia: an increase in forcing results in a long-term commitment to sea level rise. Simulations by Clark et al. (2018) indicate an equilibrium sea level sensitivity of ∼ 2 m per 100 GtC emitted CO2. The equilibrium sensitivity can be compared to paleodata (e.g., Foster and Rohling, 2013). Initially the response to a perturbation in forcing is a flux imbalance, i.e., a change in the rate of sea level rise. Hence, sea level rise by 2100 does not immediately reflect the temperature in 2100; instead the entire pathway since the forcing change was introduced is important. We therefore expect 21st century sea level rise to better correlate with the century-averaged temperature than temperature itself by 2100. Following this, we therefore propose to linearize the relationship between average rate of sea level rise and temperature increase representing the entire preceding century. The slope of this relationship then expresses how sensitive sea level is to century-timescale warming, and we will refer to it as the transient sea level sensitivity (TSLS). The intercept – where the sea level rate of change is zero – we interpret as a balance temperature. The relationship between the temperature and the rate of sea level rise has previously been noted (e.g., Warrick and Oerlemans, 1990) and has been used to motivate semi-empirical models of sea level rise (Rahmstorf, 2007; Grinsted et al., 2010; Church et al., 2013; Kopp et al., 2016; Mengel et al., 2016). A key assumption behind such semi-empirical model projections is that the sensitivity implied by historical records is stationary and hence can be extrapolated into the future. However, there may be processes that can cause future sensitivity to be different from the past (Church et al., 2013). These changes can broadly be categorized as being due to a non-linear response to forcing, or due to a non-stationary response where the response depends on the state of the system. For example, the sensitivity of small glaciers to warming will depend on how much glacier mass there is left to be lost, and we therefore expect this to have a non-stationary response. Nature is complex and will be both non-linear and non-stationary, and this places limits on extrapolation. Regardless, the sea level response can always be characterized using the TSLS metric, and we can compare and contrast different estimates. 2 Reflections on the method: Sea level projections in the IPCC Fifth Assessment Report (AR5; Church et al., 2013) and the Special Report on the Ocean and Cryosphere in a Changing Climate (SROCC; Oppenheimer et al., 2019) are unfortunately not accompanied by hindcasts using the same model framework used for projections. It is therefore impossible to verify that these models can reproduce historical sea level rise. We can, however, compare the TSLS of model projections to the TSLS implied by historical records, and this can serve as a reality check. We have to keep in mind that TSLS can potentially change over time, and that a comparison between different periods cannot be as conclusive. We therefore recommend that future sea level based on modeling are not only used for projections but also include results based on model hindcasts. Ice sheets and ocean heat content has multi-century response times, and this can lead to model drift if the model is not perfectly initialized. To inform about the future, it is therefore a necessity but not sufficient that a model can reproduce the total sea level rise over the 20th century. It is critical that sea level models also have sensitivities that are compatible with observations. We therefore propose that the historical TSLS should be used as an emergent constraint of sea level models.

https://os.copernicus.org/articles/17/181/2021/os-17-181-2021-f01
Figure 1Illustrative example demonstrating how changing relative sea level contributions can arise in a world where all contributors respond linearly to temperature. (a) Temperature forcing. (b) The rate of sea level rise (S˙) is modeled as the sum of two contributors: ice melt (M˙) and steric expansion (E˙); both contributions are modeled as linear in T. (c) The sea level curve obtained by integrating S˙. (d) The relative contributions from ice melt and steric expansion (e.g., E˙/S˙). Frederikse et al. (2020) find multi-decadal variability in the relative contributions of the major sea level contributors over the 20th century. In recent years the contribution from ice melt has increased relative to that from thermal expansion. We also expect the individual major sea level contributors to have different sensitivities to warming. One might be misled to conclude that TSLS must be changing substantially already. Here, we demonstrate that even in a completely linear world we would expect to have the budget to be changing over time (see Fig. 1). For illustrative purposes we construct a simple linear model where global sea level rise (S˙) only has two contributors: ice mass loss (M˙) and thermal expansion (E˙). We write S˙=M˙+E˙.(1). These two contributions each respond linearly to warming. M˙=aMT+bME˙=aET+bE(2)(3) We insert and get a linear model for the sea level rate: S˙=(aM+aE)T+bM+bE.(4)
The proportion of sea level rise due to ice melt becomes M˙S˙=aMT+bM(aM+aE)T+bM+bE.(5). This is not generally constant in T (see Fig. 1), demonstrating that a changing proportion of ice melt does not necessarily imply a changing sensitivity to warming. Church et al. (2013) note that it is very likely that ice-sheet dynamical changes have contributed only a small part of the historical sea level rise, implying that semi-empiric models are unlikely to be able predict a large future contribution. The fact that ice dynamical changes have only been a minor contributor historically, while we expect it to play an increasingly important role in the future, does not imply that TSLS cannot be close to stationary. 3 Data: Here we restrict our analysis to published estimates of the global mean sea level (GMSL) rate. We use three estimates of the historical rate: (1) the tide gauge record (TG) for the period 1900–1990 (Dangendorf et al., 2017); (2) the satellite-altimetry record (Sat; Ablain et al., 2019) from 1993–2017; (3) a reconstruction for the 1850–1900 preindustrial period (PI; Kopp et al., 2016). The corresponding temporally averaged temperature anomalies and uncertainties are calculated from the HADCRUT4 observationally based ensemble of global mean surface temperature (GMST) reconstructions (Morice et al., 2012). We follow IPCC AR5 and use a 1986–2005 baseline for temperature anomalies to avoid introducing additional uncertainties from re-baselining the IPCC assessed projections. The historical estimates are compared to the projected sea level rate and temperature from 2000–2100 from two recent IPCC reports for a range of scenarios: the AR5 (Church et al., 2013) and the SROCC (Oppenheimer et al., 2019). Finally, we show the results of an expert elicitation (Bamber et al., 2019) which pertain to scenarios with a 2 and a 5 ∘C warming by 2100 relative to the preindustrial era. These estimates are shown in Fig. 2. https://os.copernicus.org/articles/17/181/2021/os-17-181-2021-f02
Figure 2The rate of sea level rise versus long-term average temperature as seen in observations (black), model projections (red/blue), and expectations in an expert elicitation (orange). Each point represents an average over a time period (PI: 1850–1900; TG: 1900–1990; SAT: 1993–2017; AR5/SROCC/experts: 2000–2100). Sea level projections as assessed in AR5 and SROCC systematically fall below what would be expected from extrapolating observations to warmer conditions, as well as below the expert elicitation. Error bars show estimated likely ranges (17 %–83 %). Likely ranges for SROCC and AR5 are shown as slanted error bars.

4 Methods: The relationship between temperature and GMSL rate is estimated for each group of points using linear regression. The three observational estimates of both temperature and sea level rate (Fig. 2, black) are uncertain. We take the uncertainties to be independent as the three estimates are sourced from separate studies using different data sources and different methods and are well separated in time. We assume independent Gaussian errors which we propagate to our estimates of the line parameters listed in Table 1 using Monte Carlo sampling. Uncertainties in the projections assessed in AR5 and SROCC are specified as a central estimate and a likely range for both temperature and sea level (Church et al., 2013; Oppenheimer et al., 2019; Mastrandea et al., 2010). The IPCC sources do not provide information on the uncertainty covariance between projections of temperature and sea level. However, we observe that the upper and lower likely limits of temperature paired with the corresponding limit of sea level falls very close to the curve between central estimates (see Fig. 2). This indicates that there may well be a very high degree of covariance. For simplicity, we therefore assume full covariance between uncertainties in projected temperature and projected sea level and depict this using the slanted error bars displayed in Fig. 2. This assumption allows us to derive the upper and lower limit of the likely TSLS range by fitting a line to the corresponding limit of sea level projections. Similarly, we assume covariance between the elicitation-derived uncertainties of the two warming scenarios.

Table 1Transient sea level sensitivity and balance temperatures estimated from different sources. Intervals are likely ranges (17 %–83 %). Symbols indicate that the difference from the observational estimate is significant at * p<0.05 and ** p<0.1 using a two-tailed test assuming normality. Table 1 reports several estimates of TSLS, and we want to understand if each is substantially different to the corresponding observational estimate considering the uncertainties. We therefore test if the absolute difference is larger than zero considering uncertainties in both estimates, using a standard two-tailed hypothesis test assuming normality. NWe show the total cumulated anthropogenic CO2 emissions associated with a given temperature as a secondary horizontal axis in Fig. 2 (IPCC, 2013; Meinshausen et al., 2011). We established this relationship using both historical data and the mid-range temperature projections for the RCP scenarios and thus do not account for uncertainties in, for example, the climate sensitivity. The cumulated emission and temperatures were averaged over the same time intervals. 5 Results: The estimates of the temporal average rate of sea level rise against the corresponding temporal average of GMST from a variety of sources are shown in Fig. 2. The AR5 and SROCC projected rates of sea level rise over the 21st century from different scenarios show a close correspondence with projected temperatures (Fig. 2, red and blue). The Pearson correlations are above 0.98 with p<0.001 in a two-tailed test for both AR5 (N=15) and SROCC (N=9), where N is 3 times the number of scenarios as we include the lower, mid, and upper likely estimates from the reports. We fit straight lines to these projections, and the slope gives a TSLS of 0.27+0.03−0.01 m per century per kelvin for AR5, and 0.39+0.04−0.03 m per century per kelvin for the models assessed in SROCC (Table 1). The historical rates of sea level rise in three different periods (PI, TG, and Sat) also show a close relationship to warming (Fig. 2, black) with a correlation coefficient of 0.998 (N=3; p<0.05). From this we estimate a TSLS of 0.40±0.05 m per century per kelvin. Finally, we represent the results of expert elicitation of 21st century sea level rise under two different warming scenarios (Bamber et al., 2019), which yield a sensitivity of 0.42+0.31−0.09 m per century per kelvin. The balance temperatures corresponding to all TSLS estimates are listed in Table 1.

6 Discussion: We find that both model projections and observations show a nearly linear relationship between century-averaged temperature change and the average rate of sea level rise (Fig. 2). A linearization captures the bulk of the sea level response on these timescales. This shows that the concept is sound and that TSLS is a suitable new metric for assessing the graveness of global mean sea level changes.

The relationship deduced from model projections differs systematically from extrapolation of the observational relationship (Table 1 and Fig. 2). Sea level projections assessed in AR5 have a substantially smaller TSLS than exhibited by historical observations, whereas SROCC is more comparable (Table 1). The greater SROCC sensitivity is driven by the warmest scenario and the higher TSLS is accompanied by a warmer balance temperature that is far from the observationally based estimate (Table 1). Future TSLS may well be different from the past due to non-linearities or non-stationarities in the relationship (Church et al., 2013). Thus, the discrepancy highlighted by Fig. 2 does not necessarily demonstrate a bias in model projections, but it at least highlights the need for a yet-to-be-prepared detailed explanation. Ideally, we would test the models using hindcasts to verify their ability to reproduce the past. Unfortunately, such hindcasts are unavailable for sea level projection models assessed in both AR5 and SROCC. This is critical as Slangen et al. (2017) identified substantial biases in hindcasts of Greenland surface mass balance, glacier mass loss, and deep ocean heating. Adjusting for these systematic biases increases the modeled sea level rise over the 20th century by ∼ 50 %. The discrepancy between historical and projected sensitivities is puzzling considering the lack of possibilities for a validation of the model projections. In order for non-linearities to explain the discrepancy between the past and future relationship between warming and the rate of sea level rise, it is evident from Fig. 2 that these would have to be sub-linear. This is incompatible with our current understanding. Major non-linearities are not expected this century according to the process knowledge encoded in the model projections assessed in both AR5 and SROCC, with SROCC presenting some signs of a super-linear response (Fig. 2). Antarctica, in particular, may have a super-linear response (Oppenheimer et al., 2019; DeConto and Pollard, 2016; Edwards et al., 2019; Bamber et al., 2019). Further, expert elicitation results overlap with the relationship found for the historical period but have a higher sensitivity (Table 1), which may be due to an anticipated super-linear response not captured by AR5 and SROCC assessment of model results. Antarctic rapid ice dynamics was considered as scenario independent in the IPCC AR5 (Church et al., 2013), in stark contrast to later results (Oppenheimer et al., 2019; DeConto and Pollard, 2016; Edwards et al., 2019). We therefore propose that AR5 has a TSLS likely upper bound, which is biased low.

7 Conclusions: We define a new transient sea level sensitivity (TSLS) metric, which relates the rate of global mean sea level rise to global century-long mean surface temperature change. We find that this metric can account for most of sea level response to temperature increases on this timescale. The TSLS metric is useful as it allows for model sensitivity comparisons, even if the models have not been run for the same set of scenarios, e.g., different radiative forcing. By framing the transient sensitivity in terms of temperature we separate the sea level sensitivity from climate sensitivity to a large extent. This allows for easier comparison between sea level models that are forced by different Earth system models. We propose that TSLS estimated from hindcast simulations can serve as a valuable emergent constraint of sea level models, although this is currently hampered by the lack of information needed to construct these. We compare the model projections over the 21st century assessed by the IPCC with historical records from 1850–2017. We find that the model projections assessed in both AR5 and SROCC fall substantially below an extrapolation of historical records (Fig. 2). This is reflected in the estimates of TSLS and balance temperature, which do not match the historical estimates (Table 1). Future sensitivity may be different from the past as the relationship between warming and sea level rate may be non-linear or non-stationary. We reason that a non-linearity cannot explain the mismatch as the required curvature would be inconsistent with process knowledge encoded by model projections assessed in SROCC and expert expectations (Oppenheimer et al., 2019; Bamber et al., 2019). Based on our analyses we cannot fully reject that the sensitivity between the historical period (1850–2017) and the projection period (2000–2100) differs. The major sea level contributors have characteristic response times of several centuries (Clark et al., 2018; Li et al., 2013; DeConto and Pollard, 2016; Oppenheimer et al., 2019; Church et al., 2013), which suggests that the sensitivity is unlikely to change substantially between these periods. The outcome of an expert elicitation is more consistent with an extrapolation of the historical relationship than AR5 and SROCC (Fig. 2 and Table 1). Further, Slangen et al. (2017) identified substantial biases in process model hindcasts, which draws into question whether the AR5- and SROCC-assessed models would be able to reproduce the time evolution of historical sea level rise. This is supported by our interpretation of the TSLS discrepancy between past and future. Our analysis implies that the model states used for the assessment in SROCC are too close to balance for present-day conditions and at the same time underestimate TSLS. Taken together this suggests that the projected global sea level rise by the end of this century in various IPCC reports is at best conservative and consequently underestimates the upper bound of what is referred to as the likely sea level rise by the end of this century.

PART-2: CRITICAL COMMENTARY

(1): In a related post on the Transient Climate Response to Cumulative Emissions (TCRE): LINK: https://tambonthongchai.com/2018/05/06/tcre/ we present the climate science proposition that the causal relationship between fossil fuel emissions and global warming is best understood in terms of the observed near perfect correlation between cumulative annual fossil fuel emissions and cumulative annual warming. In that post we show that this observed correlation is spurious. First, a time series of the cumulative v alues of another time series contains neither time scale nor degrees of freedom. Second, we show that the observed correlation is a creation of the patterns in the data such that emissions are always positive and during a time of global warming, annual warming is mostly positive. This pattern is demonstated with random numbers for emissions and for annual warming with and without this sign pattern where the sign pattern is seen to create the faux correlation that disappears when the sign pattern is random.

A further demonstration of this anomaly is PRESENTED in another related post: LINK: https://tambonthongchai.com/2018/12/03/tcruparody/ where we show that not just emissions but any variable with positive values works just as well as fossil fuel emissions, even UFO sightings. We conclude from these demonstrations that correlation between the time series of the cumulative values of time series data do not provide evidence of a causal relationship.

Yet another issue with the TCRE metric: is that in the foundational science of anthropogenic global warming, the impact of fossil fuel emissions is that they cause atmospheric CO2 concentration (ACC) to rise – and that causes the global mean surface temperature (GMST) to rise by way of the greenhouse effect of atmospheric CO2 concentration in which GMST is a logarithmic function of ACC. Since ACC is a linear function of cumulative emissions, the greenhouse effect equation requires that GMST must b e a logarithmic function of cumulative emissions. Therefore the linear relationship between cumulative emissions and GMST proposed in the TCRE contans a mathematical inconsistency with the foundational theory of AGW as described in a related post: LINK: https://tambonthongchai.com/2020/08/26/a-mathematical-inconsistency/

(2): This property of the cumulaive values of time series data that follow certain sign patterns can be invoked regardless of what the variables are. In yet another related post we show how this faux correlation was used in a study of sea level rise by Professor Peter Clark of Oregon State University published in Nature Climate Change: LINK: https://tambonthongchai.com/2018/09/14/cumulativeslr/ . In the case of sea level rise the sign pattern is even stronger than it is in the TCRE because in this case we find that both sea level rise and emissions are always positive and so a strong faux correlation is created between the corresponding cumulative values as shown in the two videos from that document reproduced below.

IN THIS FIRST VIDEO, THE RANDOM SEA LEVEL RISE VALUES ARE CONSTRAINED TO POSITIVE VALUES. THE EMMISSIONS VALUES ARE ALWAYS POSITIVE BY DEFINITION. HERE WE SEE THE STRONG CORRELATION BETWEEN CUMULATIVE EMISSIONS AND CUMULATIVE SEA LEVEL RISE REPORTED IN THE PAPER.

DOWN HERE IN THE SECOND VIDEO, RANDOM SEA LEVEL RISE VALUES ARE NOT SIGN CONSTRAINED AND WE FIND THAT THE STRONG CORRELATION SEEN IN THE CONSTRAINED CASE ABOVE IS NOT FOUND IN THE UNCONSTRAINED VIDEO BELOW.

AS IN THE TCRE CASE WITH EMISSIONS AND TEMPERATURE WE FIND THAT THE STRONG CORRELATION REPORTED IN THE SEA LEVEL RISE STUDY IS A CREATION OF A FORTUITOUS SIGN PATTERN AND NOT A RESPONSIVENESS OF SEA LEVEL RISE TO EMISSIONS.

It should also be noted that it is not feasible that sea level can respond to emissions at an annual time scale as a much longer time scale of decades is needed for the causation sequence from emissions to warming to ice melt and ocean heat content. This test can only be carried out after a time scale is determined. That time scale and a testable implication must be derived from theory so that its empirical test can be carried out. In a related post, time scales of 30 to 50 years were tried but no correlation between emissions and sea level rise was found [LINK] .

CONCLUSION: THE SOURCE PAPER REVIEWED HERE USES THE CORRELATION BETWEEN CUMULATIVE EMISSIONS AND CUMULATIVE SEA LEVEL RISE AS DESCRIBED BY PETER CLARK IN A RELATED POST: https://tambonthongchai.com/2018/09/14/cumulativeslr/ AND ALSO CITES THE PETER CLARK PAPER. It contains the same statistical errors found in the paper by Peter Clark. The theoretical argument for the spuriousness of correlations between cumulative values is that the multiplicity in the use of the data for constructing cumulative values removes the available degrees of freedom in the data. The time series of cumulative values of another time series contains neither time scale nor degrees of freedom. Correlations computed with such time series data cannot provide a causation interpretation because these correlations contain no information except perhaps for the existence of a fortuitous and spurious sign pattern.

Sea level does not respond to emissions at an annual time scale. To carry out an empirical test of causation, a time scale must be specified from theory so that a testable implication and its empirical test can be carried out. In a related post, time scales of 30 to 50 years were tried but no correlation between emissions and sea level rise was found [LINK] .

Based on the statistical issues described above and in the related post on the Peter Clark paper, we find that the evidence presented for attribution of sea level rise to fossil fuel emissioons is flawed and therefore not credible.

IN RELATED POSTS ON THIS SITE WE SHOW THAT THE DATA DO NOT SHOW THAT SEA LEVEL RISE IS RELATED TO FOSSIL FUEL EMISSIONS.

RELATED POST#1: A STUDY OF THE JEVREJEVA RECONSTRUCTION OF GLOBAL MEAN SEA LEVEL

LINK: https://tambonthongchai.com/2018/12/05/attenuate-slr/

RELATED POST#2: A STUDY OF THE CSIRO RECONSTRUCTION OF GLOBAL MEAN SEA LEVEL

LINK: https://tambonthongchai.com/2019/02/20/csiroslr/