Application of linear dynamical mode decomposition to ensembles of climate simulations

2021 ◽  
Author(s):  
Maria Buyanova ◽  
Sergey Kravtsov ◽  
Andrey Gavrilov ◽  
Dmitry Mukhin ◽  
Evgeny Loskutov ◽  
...  
Keyword(s):  
Time Series ◽  
Climate Variability ◽  
20Th Century ◽  
Time Scales ◽  
Principal Components ◽  
Internal Variability ◽  
Forced Response ◽  
Climate System ◽  
External Forcing ◽  
Function Decomposition

<p>An analysis of the climate system is usually complicated by its very high dimensionality and its nonlinearity which impedes spatial and time scale separation. An even more difficult problem is to obtain separate estimates of the climate system’s response to external forcing (e.g. anthropogenic emissions of greenhouse gases and aerosols) and the contribution of the climate system’s internal variability into recent climate trends. Identification of spatiotemporal climatic patterns representing forced signals and internal variability in global climate models (GCMs) would make it possible to characterize these patterns in the observed data and to analyze dynamical relationships between these two types of climate variability.</p><p>In contrast with real climate observations, many GCMs are able to provide ensembles of many climate realizations under the same external forcing, with relatively independent initial conditions (e.g. LENS [1], MPI-GE [2], CMIP ensembles of 20th century climate). In this report, a recently developed method of empirical spatio-temporal data decomposition into linear dynamical modes (LDMs) [3] based on Bayesian approach, is modified to address the problem of self-consistent separation of the climate system internal variability modes and the forced response signals in such ensembles. The LDM method provides the time series of principal components and corresponding spatial patterns; in application to an ensemble of realizations, it determines both time series of the internal variability modes of current realization and the time series of forced response (defined as signal shared by all realizations). The advantage of LDMs is the ability to take into account the time scales of the system evolution better than some other linear techniques, e.g. traditional empirical orthogonal function decomposition. Furthermore, the modified ensemble LDM (E-LDM) method is designed to determine the optimal number of principal components and to distinguish their time scales for both internal variability modes and forced response signals.</p><p>The technique and results of applying LDM method to different GCM ensemble realizations will be presented and discussed. This research was supported by the Russian Science Foundation (Grant No. 18-12-00231).</p><p>[1] Kay, J. E., Deser, C., Phillips, A., Mai, A., Hannay, C., Strand, G., Arblaster, J., Bates, S., Danabasoglu, G., Edwards, J., Holland, M. Kushner, P., Lamarque, J.-F., Lawrence, D., Lindsay, K., Middleton, A., Munoz, E., Neale, R., Oleson, K., Polvani, L., and M. Vertenstein (2015), The Community Earth System Model (CESM) Large Ensemble Project: A Community Resource for Studying Climate Change in the Presence of Internal Climate Variability, Bulletin of the American Meteorological Society, doi: 10.1175/BAMS-D-13-00255.1, 96, 1333-1349 </p><p>[2] Maher, N., Milinski, S., Suarez-Gutierrez, L., Botzet, M., Dobrynin, M., Kornblueh, L., Kröger, J., Takano, Y., Ghosh, R., Hedemann, C., Li, C., Li, H., Manzini, E., Notz, N., Putrasahan, D., Boysen, L., Claussen, M., Ilyina, T., Olonscheck, D., Raddatz, T., Stevens, B. and Marotzke, J. (2019). The Max Planck Institute Grand Ensemble: Enabling the Exploration of Climate System Variability. Journal of Advances in Modeling Earth Systems, 11, 1-21. https://doi.org/10.1029/2019MS001639</p><p>[3] Gavrilov, A., Kravtsov, S., Mukhin, D. (2020). Analysis of 20th century surface air temperature using linear dynamical modes. Chaos: An Interdisciplinary Journal of Nonlinear Science, 30(12), 123110. https://doi.org/10.1063/5.0028246</p>

scholarly journals Understanding drivers of glacier-length variability over the last millennium

2021 ◽  
Vol 15 (3) ◽  
pp. 1645-1662
Author(s):  
Alan Huston ◽  
Nicholas Siler ◽  
Gerard H. Roe ◽  
Erin Pettit ◽  
Nathan J. Steiger
Keyword(s):  
Climate Variability ◽  
Climate Model ◽  
Volcanic Eruptions ◽  
Internal Variability ◽  
Forced Response ◽  
Last Millennium ◽  
External Forcing ◽  
Climate History ◽  
Temperature And Precipitation ◽  
Glacier Length

Abstract. Changes in glacier length reflect the integrated response to local fluctuations in temperature and precipitation resulting from both external forcing (e.g., volcanic eruptions or anthropogenic CO2) and internal climate variability. In order to interpret the climate history reflected in the glacier moraine record, the influence of both sources of climate variability must therefore be considered. Here we study the last millennium of glacier-length variability across the globe using a simple dynamic glacier model, which we force with temperature and precipitation time series from a 13-member ensemble of simulations from a global climate model. The ensemble allows us to quantify the contributions to glacier-length variability from external forcing (given by the ensemble mean) and internal variability (given by the ensemble spread). Within this framework, we find that internal variability is the predominant source of length fluctuations for glaciers with a shorter response time (less than a few decades). However, for glaciers with longer response timescales (more than a few decades) external forcing has a greater influence than internal variability. We further find that external forcing also dominates when the response of glaciers from widely separated regions is averaged. Single-forcing simulations indicate that, for this climate model, most of the forced response over the last millennium, pre-anthropogenic warming, has been driven by global-scale temperature change associated with volcanic aerosols.

scholarly journals Understanding Drivers of Glacier Length Variability Over the Last Millennium

2020 ◽  
Author(s):  
Alan Huston ◽  
Nicholas Siler ◽  
Gerard H. Roe ◽  
Erin Pettit ◽  
Nathan J. Steiger
Keyword(s):  
Climate Variability ◽  
Volcanic Eruptions ◽  
Internal Variability ◽  
Forced Response ◽  
Last Millennium ◽  
External Forcing ◽  
Climate History ◽  
Temperature And Precipitation ◽  
Glacier Length ◽  
Length Changes

Abstract. Changes in glacier length reflect the integrated response to local fluctuations in temperature and precipitation resulting from both external forcing (e.g., volcanic eruptions or anthropogenic CO2) and internal climate variability. In order to interpret the climate history reflected in the glacier moraine record, therefore, the influence of both sources of climate variability must be considered. Here we study the last millennium of glacier length variability across the globe using a simple dynamic glacier model, which we force with temperature and precipitation time series from a 13-member ensemble of simulations from a global climate model. The ensemble allows us to quantify the contributions to glacier length variability from external forcing (given by the ensemble mean) and internal variability (given by the ensemble spread). Within this framework, we find that internal variability drives most length changes in mountain glaciers that have a response timescale of less than a few decades. However, for glaciers with longer response timescales (more than a few decades) external forcing has a greater influence than internal variability. We further find that external forcing also dominates when the response of glaciers from widely separated regions is averaged. Single-forcing simulations indicate that most of the forced response over the last millennium, pre-anthropogenic warming, has been driven by global-scale temperature change associated with volcanic aerosols.

scholarly journals The early Spörer Minimum – a period of extraordinary climate and socio-economic changes in Western and Central Europe

2016 ◽  
Author(s):  
Chantal Camenisch ◽  
Kathrin M. Keller ◽  
Melanie Salvisberg ◽  
Benjamin Amann ◽  
Martin Bauch ◽  
...  
Keyword(s):  
Climate Variability ◽  
Central Europe ◽  
Climate Model ◽  
Internal Variability ◽  
Climatic Conditions ◽  
Food Prices ◽  
External Forcing ◽  
Adaptation Measures ◽  
Model Simulations ◽  
15Th Century

Abstract. Throughout the last millennium, mankind was affected by prolonged deviations from the climate mean state. While periods like the Maunder Minimum in the 17th century have been assessed in greater detail, earlier cold periods such as the 15th century received much less attention due to the sparse information available. Based on new evidence from different sources ranging from proxy archives to model simulations, it is now possible to provide an end-to-end assessment about the climate state during an exceptionally cold period in the 15th century, the role of internal, unforced climate variability and external forcing in shaping these extreme climatic conditions, and the impacts on and responses of the medieval society in Central Europe. Climate reconstructions from a multitude of natural and human archives indicate that, during winter, the period of the early Spörer Minimum (1431–1440 CE) was the coldest decade in Central Europe in the 15th century. The particularly cold winters and normal but wet summers resulted in a strong seasonal cycle that challenged food production and led to increasing food prices, a subsistence crisis, and a famine in parts of Europe. As a consequence, authorities implemented adaptation measures, such as the installation of grain storage capacities, in order to be prepared for future events. The 15th century is characterised by a grand solar minimum and enhanced volcanic activity, which both imply a reduction of seasonality. Climate model simulations show that periods with cold winters and strong seasonality are associated with internal climate variability rather than external forcing. Accordingly, it is hypothesised that the reconstructed extreme climatic conditions during this decade occurred by chance and in relation to the partly chaotic, internal variability within the climate system.

scholarly journals On the Milankovitch sensitivity of the Quaternary deep-sea record

2013 ◽  
Vol 9 (2) ◽  
pp. 1237-1257
Author(s):  
W. H. Berger
Keyword(s):  
Climate Change ◽  
Global Warming ◽  
Climate Variability ◽  
Deep Sea ◽  
Climate System ◽  
Ice Age ◽  
External Forcing ◽  
Orbital Forcing ◽  
Early Pliocene ◽  
System A

Abstract. The response of the climate system to external forcing has become an item of prime interest in the context of global warming, especially with respect to the rate of melting land-based ice masses. The deep-sea record of ice-age climate change has been useful in assessing the sensitivity of the climate system to such forcing, notably to orbital forcing, which is well-known for the last several million years. When comparing response and forcing, one finds that sensitivity varies greatly through time, apparently in dependence on the state of the system. The changing stability of ice masses presumably is the underlying cause for the changing state of the system. A buildup of vulnerable ice masses within the latest Tertiary, when going into the ice ages, is conjectured to cause a stepwise increase of climate variability since the early Pliocene.

scholarly journals On the Milankovitch sensitivity of the Quaternary deep-sea record

2013 ◽  
Vol 9 (4) ◽  
pp. 2003-2011 ◽  
Author(s):  
W. H. Berger
Keyword(s):  
Climate Change ◽  
Global Warming ◽  
Climate Variability ◽  
Deep Sea ◽  
Climate System ◽  
Ice Age ◽  
External Forcing ◽  
Orbital Forcing ◽  
System A ◽  
Yield Information

Abstract. The response of the climate system to external forcing (that is, global warming) has become an item of prime interest, especially with respect to the rate of melting of land-based ice masses. The deep-sea record of ice-age climate change has been useful in assessing the sensitivity of the climate system to a different type of forcing; that is, to orbital forcing, which is well known for the last several million years. The expectation is that the response to one type of forcing will yield information about the likely response to other types of forcing. When comparing response and orbital forcing, one finds that sensitivity to this type of forcing varies greatly through time, evidently in dependence on the state of the system and the associated readiness of the system for change. The changing stability of ice masses is here presumed to be the chief underlying cause for the changing state of the system. A buildup of vulnerable ice masses within the latest Tertiary, when going into the ice ages, is thus here conjectured to cause a stepwise increase of climate variability since the early Pliocene.

Separating Internal Variability from the Externally Forced Climate Response

2015 ◽  
Vol 28 (20) ◽  
pp. 8184-8202 ◽  
Author(s):  
Leela M. Frankcombe ◽  
Matthew H. England ◽  
Michael E. Mann ◽  
Byron A. Steinman
Keyword(s):  
Time Series ◽  
Climate Variability ◽  
Low Frequency ◽  
Internal Variability ◽  
Atlantic Multidecadal Oscillation ◽  
Ensemble Member ◽  
Internal Climate Variability ◽  
Climate Simulations ◽  
Scaling Methods ◽  
Synthetic Time Series

Abstract Separating low-frequency internal variability of the climate system from the forced signal is essential to better understand anthropogenic climate change as well as internal climate variability. Here both synthetic time series and the historical simulations from phase 5 of CMIP (CMIP5) are used to examine several methods of performing this separation. Linear detrending, as is commonly used in studies of low-frequency climate variability, is found to introduce large biases in both amplitude and phase of the estimated internal variability. Using estimates of the forced signal obtained from ensembles of climate simulations can reduce these biases, particularly when the forced signal is scaled to match the historical time series of each ensemble member. These so-called scaling methods also provide estimates of model sensitivities to different types of external forcing. Applying the methods to observations of the Atlantic multidecadal oscillation leads to different estimates of the phase of this mode of variability in recent decades.

scholarly journals What could we learn about climate sensitivity from variability in the surface temperature record?

2020 ◽  
Author(s):  
James Douglas Annan ◽  
Julia Catherine Hargreaves ◽  
Thorsten Mauritsen ◽  
Bjorn Stevens
Keyword(s):  
Time Series ◽  
Climate Sensitivity ◽  
Internal Variability ◽  
Forced Response ◽  
Balance Model ◽  
Temperature Record ◽  
Full Time ◽  
Case Scenario ◽  
True Parameter ◽  
Equilibrium Climate Sensitivity

Abstract. We examine what can be learnt about climate sensitivity from variability in the surface air temperature record over the instrumental period, from around 1880 to the present. While many previous studies have used the trend in the time series to constrain equilibrium climate sensitivity, it has also been argued that temporal variability may also be a powerful constraint. We explore this question in the context of a simple widely used energy balance model of the climate system. We consider two recently-proposed summary measures of variability and also show how the full information content can be optimally used in this idealised scenario. We find that the constraint provided by variability is inherently skewed and its power is inversely related to the sensitivity itself, discriminating most strongly between low sensitivity values and weakening substantially for higher values. It is only when the sensitivity is very low that the variability can provide a tight constraint. Our investigations take the form of perfect model experiments, in which we make the optimistic assumption that the model is structurally perfect and all uncertainties (including the true parameter values and nature of internal variability noise) are correctly characterised. Therefore the results might be interpreted as a best case scenario for what we can learn from variability, rather than a realistic estimate of this. In these experiments, we find that for a moderate sensitivity of 2.5 °C, a 150 year time series of pure internal variability will typically support an estimate with a 5–95 % range of around 5 °C (e.g. 1.9–6.8 °C). Total variability including that due to the forced response, as observed in the detrended observational record, can provide a stronger constraint with an equivalent 5–95 % posterior range of around 4 °C (e.g. 1.7–5.6 °C) even when uncertainty in aerosol forcing is considered. Using a statistical summary of variability based on autocorrelation and the magnitude of residuals after detrending proves somewhat less powerful as a constraint than the full time series in both situations. Our results support the analysis of variability as a potentially useful tool in helping to constrain equilibrium climate sensitivity, but suggest caution in the interpretation of precise results.

scholarly journals Long-range memory in millennium-long ESM and AOGCM experiments

2014 ◽  
Vol 5 (1) ◽  
pp. 363-401 ◽  
Author(s):  
L. Østvand ◽  
T. Nilsen ◽  
K. Rypdal ◽  
D. Divine ◽  
M. Rypdal
Keyword(s):  
Long Range ◽  
Time Scales ◽  
General Circulation ◽  
Climate Model ◽  
Climate System ◽  
Fluctuation Analysis ◽  
Scaling Exponent ◽  
External Forcing ◽  
Internal Dynamics ◽  
Temperature Records

Abstract. Northern Hemisphere (NH) temperature records from a reconstruction and a number of millennium-long climate model experiments are investigated for long-range memory (LRM). The models are two Earth system models and two atmospheric-ocean general circulation models. The periodogram, detrended fluctuation analysis and wavelet variance analysis are applied to examine scaling properties and to estimate a scaling exponent of the temperature records. A simple linear model for the climate response to external forcing is also applied to the reconstruction and the forced climate model runs, and then compared to unforced control runs to extract the LRM generated by internal dynamics of the climate system. With one exception the climate models show strong persistent scaling with power spectral densities of the form S(f) ~ f−β with 0.8 < β < 1 on time scales from years to several centuries. This is somewhat stronger persistence than found in the reconstruction (β ≈ 0.7). The exception is the HadCM3 model, which exhibits β ≈ 0.6. We find no indication that LRM found in these model runs are induced by external forcing, which suggests that LRM on sub-decadal to century time scales in NH mean temperatures is a property of the internal dynamics of the climate system. Temperature records for a local site, Reykjanes Ridge, are also studied, showing that strong persistence is found also for local ocean temperature.

scholarly journals The Atlantic Multidecadal Oscillation Inferred from the Forced Climate Response in Coupled General Circulation Models

2009 ◽  
Vol 22 (7) ◽  
pp. 1610-1625 ◽  
Author(s):  
Jeff R. Knight
Keyword(s):  
North Atlantic ◽  
General Circulation ◽  
Internal Variability ◽  
Atlantic Multidecadal Oscillation ◽  
Forced Response ◽  
Climate System ◽  
Climate Response ◽  
The North ◽  
Ensemble Mean ◽  
The North Atlantic

Abstract Instrumental sea surface temperature records in the North Atlantic Ocean are characterized by large multidecadal variability known as the Atlantic multidecadal oscillation (AMO). The lack of strong oscillatory forcing of the climate system at multidecadal time scales and the results of long unforced climate simulations have led to the widespread, although not ubiquitous, view that the AMO is an internal mode of climate variability. Here, a more objective examination of this hypothesis is performed using simulations with natural and anthropogenic forcings from the Coupled Model Intercomparison Project phase 3 (CMIP3) database. Ensemble means derived from these data allow an estimate of the response of models to forcings, as averaging leads to cancellation of the internal variability between ensemble members. In general, the means of individual model ensembles appear to be inconsistent with observed temperatures, although small ensemble sizes result in uncertainty in this conclusion. Combining the ensembles from different models creates a multimodel ensemble of sufficient size to allow for a good estimate of the forced response. This shows that the variability in observed North Atlantic temperatures possess a clearly distinct signature to the climate response expected from forcings. The reliability of this finding is confirmed by sampling those models with low decadal internal variability and by comparing simulated and observed trends. In contrast to the inconsistency with the ensemble mean, the observations are consistent with the spread of responses in the ensemble members, suggesting they can be accounted for by the combined effects of forcings and internal variability. In the most recent period, the results suggest that the North Atlantic is warming faster than expected, and that the AMO entered a positive phase in the 1990s. The differences found between observed and ensemble mean temperatures could arise through errors in the observational data, errors in the models’ response to forcings or in the forcings themselves, or as a result of genuine internal variability. Each of these possibilities is discussed, and it is concluded that internal variability within the natural climate system is the most likely origin of the differences. Finally, the estimate of internal variability obtained using the model-derived ensemble mean is proposed as a new way of defining the AMO, which has important advantages over previous definitions.

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