ESD Ideas: The stochastic climate model shows that underestimated Holocene trends and variability represent two sides of the same coin

Holocene sea surface temperature trends and variability are underestimated in models as compared to paleoclimate data. The idea is presented that the trends and variability are related which is elaborated in a conceptual framework of the stochastic climate model. The relation is a consequence of the fluctuation-dissipation theorem, connecting the linear response of a system to its statistical fluctuations. Consequently, the spectrum can be used to estimate the timescale-dependent climate sensitivity. The non-normality in the propagation operator introduces enhanced long-term variability related to non-equilibrium 5 and/or Earth system sensitivity. Climate and Earth system models are widely used to evaluate the impact of anthropogenic emissions on future climate. The validation of these models by simulating different climate scenarios is essential to understand the sensitivity of the climate system to external forcing. The models are clearly unrivalled in their ability to simulate a broad range of large-scale phenomena on seasonal to decadal time scales (Flato et al., 2013). However, the reliability of models to simulate climate variability on 10 multidecadal and longer time scales requires additional evaluation. Climate records derived from paleo-environmental proxyparameters facilitate the testing of models across these time scales. Interglacial periods provide the means for evaluating the performance of general circulation models in representing sea surface temperature (SST) anomalies and trends (e.g. Lohmann et al., 2013). One key finding is that the models do not capture the magnitude of the derived SSTs from marine proxy records in all climate simulations of the Holocene where the simu15 lated SST trends systematically underestimate the marine proxy-based temperature (Alkenone) trends. It is suggested that a part of such discrepancies can be caused either by too simplistic interpretation of the proxy data and/or by underestimated regional responses in climate models. Fig. 1a shows the scatter plot of simulated and reconstructed SST trends for the mid-tolate Holocene, based on results obtained within the Paleoclimate Modelling Intercomparison Project PMIP2/3 (Braconnot et al., 2007, 2012). Note that the orbital forcing has different signs at high and low latitudes (Berger, 1978). The slopes in Fig. 20 1a indicate that the response in the models is underestimated by an order of magnitude as compared to the SST reconstructions. 1 Earth Syst. Dynam. Discuss., https://doi.org/10.5194/esd-2018-43 Manuscript under review for journal Earth Syst. Dynam. Discussion started: 25 June 2018 c © Author(s) 2018. CC BY 4.0 License.

By using long-term multi-millenial climate model runs and paleoclimate data, a discrepancy is detected also with respect to variability (Fig. 1b)(see, Laepple and Huybers, 2014a,b).While most state-of-the-art climate models realistically simulate inter-annual variability (in this particular model the interannual variability is overeststimated), they underestimate variability on multidecadal to millennial time scales.This was revealed by a systematic comparison of climate model simulations, instrumental records and paleo-observations.In order to reconcile both :::: local sensitivity and variability, a model is presented which takes into account the mean as well as the variability, based on Hasselmann (1976).Imagine that the temperature of the ocean is governed by dT dt :::::::::::::::::::::: where the air-sea fluxes due to weather systems are represented by a white-noise process :::: Q net : with zero average < Q net >= 0 ::::::::::: ::::::::::::::::::::::: .
Recently, one focus of research was to identify feedback mechanisms in the Earth system enhancing the sensitivity (Stärz et al., 2016) or variability (Bakker et al., 2017).

Answer to Referee 1
Thanks for you detailed comments on the manuscript ESD Ideas: The stochastic climate model shows that underestimated Holocene trends and variability represent two sides of the same coin .In the following I give answers to all the issues raised.
Answer to the General comments: 1. Comment: "The results show that the observational SST trends are poorly defined, varying from -4K to +2K over the 6 kyr period.The modelled trends are considerably smaller, being confined mainly to the range -1K to +1K over the same period (Figure 1(a))." Answer: The analysis is a local one, i.e. the points at high latitudes have a general cooling trend whereas the low latitute points show a warming trend through the late Holocene.The general pattern of warming and cooling are consistent in the data and models (Figures 5a, 7a, 8a in Lohmann et al., 2013; see also Braconnot et al., 2012).In any of the analysis the local temperature trends based on proxy reconstructions and climate simulation are taken.
Action: In the revised manuscript, I will explicitly state that it is the local temperature trend as the response to latitudevarying orbital forcing.I wrote this in the ESD manuscript at line 20: " Note that the orbital forcing has different signs at high and low latitudes (Berger, 1978)." 2. Comment: "In view of the poor definition of the observational trends and the lack of knowledge regarding the partitioning of the observational variability, very strong caveats should be placed on any conclusions drawn from this observational/modelling comparison.In particular, since there is no global mean orbital forcing over the 6 kyr period studied, extreme care should be exercised in drawing any conclusions from the study as to the value of climate sensitivity to greenhouse gas increase." Answer: As written above, we are considering the local temperature trends based on proxy reconstructions and climate simulations.Indeed the global forcing is weak.The pattern of climate response to orbital forcing is a combination of the system's response to precession and obliquity.On the basis of the observed insolation-temperature relationship, different temperature response regimes across the Earth can be identified.Linear relationships dominate extratropical land areas whereas in midlatitude oceans, the seasonally varying mixed layer depth renders the temperature more sensitive to summer than to winter insolation (Laepple and Lohmann, 2009).
Action: In the revised manuscript, I will explicitly state that I am not analyzing the value of climate sensitivity to greenhouse gas increase.
Action: In the revised manuscript, I will explicitly mention the physics the non-normal dynamics, but will try to reduce the number of references in this direction.

4.
Comment: "There is also some concern about the mathematical notations.Equation ( 1) is originally presented with T as vector (if bold notation is indeed supposed to indicate a vector), with λ, a scalar.What would be the components of T? If they are different climatic components (ocean, and atmosphere), then we need different relaxation time scales.Let us suppose that the original interpretation of equation ( 1) assumes T as a scalar, and that T becomes a vector only at the point of introducing equation ( 7).Then, we can legitimately consider that the different components of T correspond to different components of the climate system, in which case we would expect some non-diagonal (linear, symmetric) coupling terms.There are no such terms in matrix A. So the reader needs to infer that the system was rotated in order to get rid of the coupling terms.What is in vector Q then?The second component of Q needs to be strictly positive, in order to excite the second component of T, and finally generate the extra variance produced by the factor N. This leaves a bit too much guess work to the reader." Answer: Sorry.The notation in (1) was meant to be for a scalar.Indeed, the vector is only introduced with (7).The vector Q is related to the variances of the individual components.In the ESD ideas mansucript, I have not specified it explicitely and normalized it to one.
Action: In the revised manuscript, I will explicitly mention Q to avoid guess work to the reader.Furthermore, it will be clearly stated that (1) is a scalar stochastic differential equation.
5. Comment: "Assuming these questions can be answered, there is, finally, some concern about the quality and performance of spectral estimators that would be needed to do the job of estimating A. Does the power spectrum contain enough information to constrain the non-diagonal elements of the transfer matrix?If it does, would it plausibly work given the palaeoclimate data available ?" Answer: In the paper, the spectra in Fig. 1c are calculated analytically.For real problems, the estimation of A can be done via the POP method (Hasselmann, 1988).Then the dynamical propagator has in general a non-normal structure.The POPs can be calculated from the paleoclimate time series, which would be a logical next step.For recent climates, there exists very nice examples in the framework of (linearized) stochastically forced dynamics (e.g., Whitaker and Sardeshmukh, 1998;Kwasniok, 2004).
Action: I will try to give a short outlook in this direction.