Wednesday, October 26, 2016

The Ocean in Climate Econometrics

Third excerpt (previous excerpts):

Most studies of global climate change using econometric methods have ignored the role of the ocean. Though these studies sometimes produce plausible estimates of the climate sensitivity, they universally produce implausible estimates of the rate of adjustment of surface temperature to long-run equilibrium. For example, Kaufmann and Stern (2002) find that the rate of adjustment of temperature to changes in radiative forcing is around 50% per annum even though they estimate an average global climate sensitivity of 2.03K. Similarly, Kaufmann et al. (2006) estimate a climate sensitivity of 1.8K, while the adjustment coefficient implies that more than 50% of the disequilibrium between forcing and temperature is eliminated each year. Furthermore, the autoregressive coefficient in the carbon dioxide equation of 0.832 implies an unreasonably high rate of removal of CO2 from the atmosphere. The methane rate of removal is also very high.

Simple AR(1) I(1) autoregressive models of this type assume that temperature adjusts in an exponential fashion towards the long run equilibrium. The estimate of that adjustment rate tends to go towards that of the fastest adjusting process in the system, if, as is the case, that is the most obvious in the data. Schlesinger et al. (no date) illustrate these points with a very simple first order autoregressive model of global temperature and radiative forcing. They show that such a model approximates a model with a simple mixed layer ocean. Parameter estimates can be used to infer the depth of such an ocean. The models that they estimate have inferred ocean depths of 38.7-185.7 meters. Clearly, an improved time series model needs to simulate a deeper ocean component.
Stern (2006) used a state space model inspired by multicointegration. The estimated climate sensitivity for the preferred model is 4.4K, which is much higher than previous time series estimates and temperature responds much slower to increased forcing. However, this model only used data on the top 300m of the ocean and the estimated increase in heat content in the pre-observational period seems too large.

Pretis (2015) estimates an I(1) VAR for surface temperature and the heat content of the top 700m of the ocean for observed data for 1955-2011. The climate sensitivity is 1.67K for the preferred model but 2.16K for a model, which excludes the level of volcanic forcing from the radiative forcing aggregate, entering only as first differences. With two cointegrating vectors it is not possible to “read off” the rate of adjustment of surface temperature to increased forcing and Pretis does not simulate impulse or transient response functions.


Kaufmann, R. K., Kauppi, H., Stock, J. H., 2006. Emissions, concentrations, and temperature: a time series analysis. Climatic Change 77(3-4), 249-278.

Kaufmann, R. K., Stern, D. I., 2002. Cointegration analysis of hemispheric temperature relations. Journal of Geophysical Research 107(D2), Article No. 4012.

Pretis, F., 2015. Econometric models of climate systems: The equivalence of two-component energy balance models and cointegrated VARs. Oxford Department of Economics Discussion Paper 750.

Schlesinger, M. E., Andronova, N. G., Kolstad, C. D., Kelly, D. L., no date. On the use of autoregression models to estimate climate sensitivity. mimeo, Climate Research Group, Department of Atmospheric Sciences, University of Illinois at Urbana-Champaign, IL.

Stern, D. I., 2006. An atmosphere-ocean multicointegration model of global climate change. Computational Statistics and Data Analysis 51(2), 1330-1346.  

Monday, October 24, 2016

Recent Estimates of the Climate Sensitivity

Another excerpt from our literature review:

Estimates of the climate sensitivity have been the focus of ongoing debate with widely differing estimates (Armour, 2016) and notable differences between observation and model based sensitivity estimates. The consensus in the IPCC 5th Assessment Report (Bindoff et al., 2013) is that the equilibrium climate sensitivity (ECS) falls in the range of 1.5-4.5 K with more than 66% probability. The transient climate response (TCR) falls in the range 1-2.5 K with more than 66% probability. Armour (2016) notes that the range of ECS supported by recent observations is 1-4 K with a best estimate of around 2 K and the TCR is estimated at 0.9-2.0 K. This suggests that climate model based estimates are too sensitive.

Richardson et al. (2016) note that sea surface temperature measurements measure water rather than air temperature, which has warmed faster. Additionally, the most poorly measured regions on Earth, such as the Arctic, have also warmed the most. Richardson et al. (2016) process the CMIP5 model output in the same way as the HADCRUT4 temperature series is constructed – using seawater temperatures and under-sampling some regions. They infer an observation-based best estimate for TCR of 1.66 K, with a 5–95% range of 1.0–3.3 K, consistent with the climate models considered in the IPCC 5th Assessment Report.

Marvel et al. (2016) argue that the efficacy of other forcings is typically less than that of greenhouse gases so that total radiative forcing is less than standard calculations estimate. When single-forcing experiment results are reported to estimate these efficacies, and TCR and ECS are estimated from observed twentieth-century warming, both TCR and ECS estimates are revised upward to 1.7K and to 2.6-3.0 K, depending on the feedbacks included. Armour (2016) highlights the joint (multiplicative) importance of the Richardson et al. (2016) and the Marvel et al. (2016) studies, which together should raise observational ECS by 60%, which reconciles the discrepancy between observation and model based estimates.


Armour, K. C., 2016. Projection and prediction: Climate sensitivity on the rise. Nature Climate Change 6, 896–897.

Bindoff, N. L., Stott, P. A., K. AchutaRao, M., Allen, M. R., Gillett, N., Gutzler, D., Hansingo, K., Hegerl, G., Hu, Y., Jain, S., Mokhov, I. I., Overland, J., Perlwitz, J., Sebbari, R., Zhang, X., 2013: Detection and attribution of climate change: from global to regional. In: Climate Change 2013: The Physical Science Basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change [Stocker, T.F., D. Qin, G.-K. Plattner, M. Tignor, S.K. Allen, J. Boschung, A. Nauels, Y. Xia, V. Bex and P.M. Midgley (eds.)]. Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA.

Marvel, K., Schmidt, G. A., Miller, R. L., Nazarenko, L., 2016. Implications for climate sensitivity from the response to individual forcings. Nature Climate Change 6(4), 386-389.

Richardson, M., Cowtan, K., Hawkins, E., Stolpe, M. B., 2016. Reconciled climate response estimates from climate models and the energy budget of Earth, Nature Climate Change 6, 931-935.

Saturday, October 22, 2016

The Role of the Oceans in Global Climate Change

From the draft of the literature review of a paper I am writing with Zsuzsanna Csereklyei and Stephan Bruns. Stephan will be presenting some preliminary results next week at the conference on climate econometrics in Aarhus:

Historical record high global temperatures occured in 2015 and are expected in 2016. Nevertheless, the period between 1998 and 2014, when surface temperatures increased much slower than in the previous quarter century has been the subject of intense scrutiny. As the search for the missing pieces of the puzzle began, a number of potential culprits surfaced.

Among the suggested candidates were an increase in anthropogenic sulfur emissions (Kaufmann et al., 2011), declining solar irradiance (Tollefson, 2014, Trenberth 2015; Kaufmann et al., 2011), and an increase in volcanic aerosols (Andersson et al., 2016) over the examined period, which also coincided with a negative phase of the Pacific Decadal Oscillation (PDO). Similarly, Fyfe et al. (2016) mention anthropogenic sulfate aerosols as contributing factors to the earlier hiatus period from the 1950s to the 1970s. Smith et al. 2016 recently suggested that anthropogenic aerosol emissions might be a driver of the negative PDO. This is however in contrast with the findings of Kosaka and Xie (2013) who attribute with high probability the hiatus to internal variability, instead of forcing.

Karl et al. (2015) argued that the apparent hiatus was due to mis-measurement of surface temperature data. They correct the temperature data for several biases finding the result warming trends between 1950-1999 and 2000-2014 to be “virtually indistinguishable”. However, their approach was critiqued, by among others Fyfe et al. (2016,) who argue that the starting and ending dates of the observation period matter significantly, as the 1950-1970 period also included a big hiatus.

The majority of recent studies agree, however, that exchange of heat between the atmosphere and the oceans is a key player in explaining the surface warning slowdown. Nonetheless, the mechanisms by which oceans absorb and then again release heat were not well understood until recently, when this process was found closely linked to the decadal oscillation of the oceans. Decadal ocean variability, in particular the Pacific Decadal Oscillation (PDO), but also the variability of the Atlantic and Indian Oceans, seem to play a key part in explaining atmosphere – ocean interactions (Kosaka and Xie, 2013; Meehl et al. 2011). According to Meehl et al. (2011), hiatuses might be relatively common climate occurrences, where enhanced heat uptake by the ocean is linked to La Nina-like conditions. By contrast, the positive phase of the PDO favors El Nino conditions and injects heat into the atmosphere (Tollefson, 2014). Stronger trade winds during La Nina episodes drive warm surface water westwards across the Pacific, then down into the lower layers of the ocean. Simultaneously cold water upwells in the eastern Pacific (Trenberth and Fasullo, 2012). It is possible that extreme La Nina events, such as that in 1998, may tip the ocean into a cool phase of the PDO.

While the heat uptake and content of the world ocean is a key factor in the Earth’s energy balance, observations of ocean heat content are sparse. Currently, systematic annual observations for the upper 700m only reach back to 1955, while for the upper 2000 meters only to 2005. Pentadal ocean heat estimates for the upper 2000 meters (Levitus et al. 2012) are available since the mid 1950s. Due to the lack of systematic observations, the pentadal estimates (Levitus et al. 2000) used composites of all available historical temperature observations for respective 5-year periods. Therefore, the farther we go back in time, the larger the uncertainty surrounding ocean heat uptake and the larger potential biases might be.

Estimates for 1955-2010 (Levitus et al., 2012) show a rate of heat uptake of 0.39 Wm-2 for the upper 2000 meters of the world ocean but the uptake has varied over time. Half of the heat accumulated since 1865 accumulated after 1997 (Gleckler et al., 2016) Balmaseda et al. (2013) estimate that heat uptake in the 2000s was 0.84 Wm-2 for the entire ocean with 0.21 Wm-2 of that being stored below 700m, but in the 1990s uptake was negative (-0.18 Wm-2) though other sources find a lower but positive rate of uptake in that period. The vast majority of warming is concentrated in the top 2000m of the ocean (Purkey and Johnson, 2010). Johnson et al. (2016) estimate net ocean heat uptake in the top 1800m of the ocean of 0.71Wm-2 from 2005 to 2015, and 0.07Wm-2 below 1800m. However, during the recent hiatus period, the upper layers of the ocean did not show enough warming to account for the imbalance in the energy system (Balsameda et al. 2013). This “missing energy” was actually stored in the deep oceans (Trenberth and Fasullo, 2012). Estimates of deep ocean heat fluxes are very limited. Kouketsu et al. (2011) calculate world ocean temperature changes for the 1990s and 2000s for waters below 3000m, estimating heat changes below 3000 meters to be around 0.05 Wm-2. Purkey and Johnson (2010) estimate the heat uptake below 4000m to be 0.027 Wm-2.

Andersson, S. M., Martinsson, B. G., Vernier, J. P., Friberg, J., Brenninkmeijer, C. A. M., Hermann, M., van Velthoven, P. F. J., Zahn, A., 2015. Significant radiative impact of volcanic aerosol in the lowermost stratosphere. Nature Communications 6, 7692.

Balmaseda, M. A., Trenberth, K. E., E. Källén, E., 2013. Distinctive climate signals in reanalysis of global ocean heat content. Geophysical Research Letters 40, 1754–1759.

Fyfe J. C., Meehl, G. A., England, M. H., Mann, M. E., Santer, B. D., Flato, G. M., Hawkins, E., Gillett, N. P., Xie, S. P., Kosaka, Y., Swart, N. C., 2016. Making sense of the early-2000s warming slowdown. Nature Climate Change 6, 224-228.

Gleckler, P. J., Durack, P. J., Stouffer, R. J., Johnson, G. C., Forest, C. E., 2016. Industrial-era global ocean heat uptake doubles in recent decades. Nature Climate Change 6, 394-398.

Johnson, G. C., Lyman, J. M., Loeb, N. G., 2016. Improving estimates of Earth's energy imbalance. Nature Climate Change 6(7), 639-640.

Karl, T. R., Arguez, A., Huang, B., Lawrimore, J. H., McMahon, J. R., Menne, M. J., Peterson, T. C., Vose, R. S., Zhang, H.-M., 2015. Possible artifacts of data biases in the recent global surface warming hiatus. Science 348 (6242), 1469-1472.

Kaufmann, R. K., Kauppi, H., Mann, M. L., Stock, J. H., 2011. Reconciling anthropogenic climate change with observed temperature 1998–2008. Proceedings of the National Academy of Sciences 108(29), 11790-11793.

Kosaka, Y., Xie, S.-P., 2013. Recent global-warming hiatus tied to equatorial Pacific surface cooling. Nature 501, 403–408.

Kouketsu, S., et al. , 2011. Deep ocean heat content changes estimated from observation and reanalysis product and their influence on sea level change. Journal of Geophysical Research 116, C03012.

Levitus, S., Antonov, J. L., Boyer, T. P., Stephens, C., 2000. Warming of the world ocean. Science 287, 2225-2229.

Levitus, S., Antonov, J. I., Boyer, T. P., Baranova, O. K., Garcia, H. E., Locarnini, R. A., Mishonov, A. V., Reagan, J.R., Seidov, D., Yarosh, E.S., Zweng, M.M., 2012. World ocean heat content and thermosteric sea level change (0–2000 m), 1955–2010. Geophysical Research Letters 39, L10603.

Meehl, G. A., Arblaster, J. M., Fasullo, J. T., Hu, A., Trenberth, K. E., 2011. Model-based evidence of deep-ocean heat uptake during surface-temperature hiatus periods. Nature Climate Change 1, 360–364.

Purkey, S. G., Johnson, G. J., 2010. Warming of global abyssal and deep southern ocean waters between the 1990s and 2000s: contributions to global heat and sea level rise budgets. Journal of Climate 23, 6336-6351.

Smith, D. M., et al., 2016. Role of volcanic and anthropogenic aerosols in the recent global surface warming slowdown. Nature Climate Change 6, 936-940.

Tollefson, J., 2014. Climate change: The case of the missing heat. Nature 505, 276-278.

Trenberth, K. E., 2015. Has there been a hiatus? Science 349, 691-692.

Trenberth, K. E., Fasullo, J. T., 2012. Tracking Earth’s energy: from El Nino to global warming. Surveys in Geophysics, 33(3-4), 413–426.