Climate Response Using a Three-Dimensional Operator Based on the Fluctuation–Dissipation Theorem

2007 ◽  
Vol 64 (7) ◽  
pp. 2558-2575 ◽  
Author(s):  
Andrey Gritsun ◽  
Grant Branstator
Keyword(s):  
Influence Function ◽  
General Circulation ◽  
Three Dimensional ◽  
Circulation Model ◽  
Tropical Indian Ocean ◽  
The Arctic ◽  
External Forcing ◽  
Fluctuation Dissipation ◽  
Fluctuation Dissipation Theorem ◽  
Reduced Space

Abstract The fluctuation–dissipation theorem (FDT) states that for systems with certain properties it is possible to generate a linear operator that gives the response of the system to weak external forcing simply by using covariances and lag-covariances of fluctuations of the undisturbed system. This paper points out that the theorem can be shown to hold for systems with properties very close to the properties of the earth’s atmosphere. As a test of the theorem’s applicability to the atmosphere, a three-dimensional operator for steady responses to external forcing is constructed for data from an atmospheric general circulation model (AGCM). The response of this operator is then compared to the response of the AGCM for various heating functions. In most cases, the FDT-based operator gives three-dimensional responses that are very similar in structure and amplitude to the corresponding GCM responses. The operator is also able to give accurate estimates for the inverse problem in which one derives the forcing that will produce a given response in the AGCM. In the few cases where the operator is not accurate, it appears that the fact that the operator was constructed in a reduced space is at least partly responsible. As an example of the potential utility of a response operator with the accuracy found here, the FDT-based operator is applied to a problem that is difficult to solve with an AGCM. It is used to generate an influence function that shows how well heating at each point on the globe excites the AGCM’s Northern Hemisphere annular mode (NAM). Most of the regions highlighted by this influence function, including the Arctic and tropical Indian Ocean, are verified by AGCM solutions as being effective locations for stimulating the NAM.

Climate Response of Linear and Quadratic Functionals Using the Fluctuation–Dissipation Theorem

2008 ◽  
Vol 65 (9) ◽  
pp. 2824-2841 ◽  
Author(s):  
Andrey Gritsun ◽  
Grant Branstator ◽  
Andrew Majda
Keyword(s):  
General Circulation ◽  
Atmospheric General Circulation Model ◽  
Circulation Model ◽  
Heat Fluxes ◽  
Heat Sources ◽  
State Variables ◽  
Fluctuation Dissipation ◽  
Fluctuation Dissipation Theorem ◽  
Low Pass ◽  
Momentum And Heat Fluxes

Abstract A generalization of the fluctuation–dissipation theorem (FDT) that allows generation of linear response operators that estimate the response of functionals of system state variables is tested for a system defined by an atmospheric general circulation model (AGCM). A sketch of the proof of this generalization is provided, followed by comparison of response estimates based on the theory and actual responses of the AGCM for various idealized anomalous equatorial heat sources. Tested response quantities include precipitation, variances of bandpass and low-pass streamfunction, and momentum and heat fluxes. The solutions from the FDT operators are very similar to the AGCM solutions in terms of structure while overestimating response amplitudes by about 20%. As an example of an application of such response operators, the FDT operator that estimates the response of bandpass upper-tropospheric streamfunction variance is used to find the most efficient means of disturbing the Atlantic storm tracks by tropical heating. The results of the study suggest that the generalized FDT is an attractive method for systematically studying response attributes of the climate system that are of interest to climate scientists and society.

scholarly journals The Response of a Simplified GCM to Axisymmetric Forcings: Applicability of the Fluctuation–Dissipation Theorem

2008 ◽  
Vol 65 (12) ◽  
pp. 3880-3898 ◽  
Author(s):  
Michael J. Ring ◽  
R. Alan Plumb
Keyword(s):  
General Circulation ◽  
Circulation Model ◽  
Quantitative Relationship ◽  
Model Atmosphere ◽  
Annular Mode ◽  
Annular Modes ◽  
Fluctuation Dissipation ◽  
Fluctuation Dissipation Theorem ◽  
Theoretical Predictions ◽  
The Tropics

Abstract Following on their previous work, in which they found the annular modes to be a preferred response of a simplified general circulation model atmosphere to a number of mechanical forcings, the authors now explore the quantitative relationship between forcing and response. In particular, the applicability of the fluctuation–dissipation theorem to this problem is investigated. First, the set of model trials is expanded by including runs in which the applied forcings are thermal rather than mechanical. For thermal forcings confined to the extratropics, “annular mode–like” responses, reminiscent of those found in earlier work, are found, but, as found in previous studies, the response is less like an annular mode when the forcing has significant amplitude in the tropics. Assuming small departures from the control climatology, and making a few further assumptions, the authors derive a theoretical relationship between forcing and response. This relationship is a statement of the fluctuation–dissipation theorem for this problem. The response of the model is found to be qualitatively consistent with the theoretical predictions. However, several aspects of the response diverge quantitatively from the theoretical expectation.

scholarly journals Practical Approximations to Seasonal Fluctuation–Dissipation Operators Given a Limited Sample

2016 ◽  
Vol 73 (6) ◽  
pp. 2529-2545 ◽  
Author(s):  
David Fuchs ◽  
Steven Sherwood
Keyword(s):  
General Circulation ◽  
Seasonal Fluctuation ◽  
Circulation Model ◽  
Small Sample ◽  
Prediction Errors ◽  
Limited Sample ◽  
State Response ◽  
Fluctuation Dissipation ◽  
Fluctuation Dissipation Theorem ◽  
Small Sample Sizes

Abstract This paper studies operators inspired by the fluctuation–dissipation theorem that consider the seasonality (nonstationarity) of the climate system under conditions of limited sample size relevant to application of the method to observational records. The approach is used to predict the steady-state response of an atmospheric general circulation model to localized temperature perturbations. A seasonal operator nominally requires a much larger data sample than a stationary operator; the authors study some strategies to overcome this. First, two methods for approximating the seasonality of the system are examined. Second, an alternative “transpose approach” to the standard dimension reduction is considered that is more efficient and accurate for small sample sizes and additionally enables the use of a kernel, which provides a convenient way to incorporate prior physical understanding into the operator. All operators show considerable skill in predicting seasonal responses for a variety of variables (temperature, winds, rainfall, and cloud cover) and better skill in predicting the annual-mean ones. A comparison of these predictions to ones done on the same system with temporally fixed boundary conditions shows unexpectedly that skill is, if anything, improved by the presence of a seasonal cycle. The authors suggest that the extra complexity due to a seasonal system is outweighed by the added information due to the seasonal forcing and the effect of seasonality in smoothing out prediction errors.

scholarly journals Estimating the Continental Response to Global Warming Using Pattern-Scaled Sea Surface Temperatures and Sea Ice

2016 ◽  
Vol 29 (24) ◽  
pp. 9125-9139 ◽  
Author(s):  
Adeline Bichet ◽  
Paul J. Kushner ◽  
Lawrence Mudryk
Keyword(s):  
Global Warming ◽  
Sea Ice ◽  
General Circulation ◽  
Circulation Model ◽  
Tropical Indian Ocean ◽  
Sea Surface ◽  
Climate Projections ◽  
Western Boundary ◽  
Sea Ice Concentration ◽  
Continental Climate

Abstract Better constraining the continental climate response to anthropogenic forcing is essential to improve climate projections. In this study, pattern scaling is used to extract, from observations, the patterned response of sea surface temperature (SST) and sea ice concentration (SICE) to anthropogenically dominated long-term global warming. The SST response pattern includes a warming of the tropical Indian Ocean, the high northern latitudes, and the western boundary currents. The SICE pattern shows seasonal variations of the main locations of sea ice loss. These SST–SICE response patterns are used to drive an ensemble of an atmospheric general circulation model, the National Center for Atmospheric Research (NCAR) Community Atmosphere Model, version 5 (CAM5), over the period 1980–2010 along with a standard AMIP ensemble using observed SST—SICE. The simulations enable attribution of a variety of observed trends of continental climate to global warming. On the one hand, the warming trends observed in all seasons across the entire Northern Hemisphere extratropics result from global warming, as does the snow loss observed over the northern midlatitudes and northwestern Eurasia. On the other hand, 1980–2010 precipitation trends observed in winter over North America and in summer over Africa result from the recent decreasing phase of the Pacific decadal oscillation and the recent increasing phase of the Atlantic multidecadal oscillation, respectively, which are not part of the global warming signal. The method holds promise for near-term decadal climate prediction but as currently framed cannot distinguish regional signals associated with oceanic internal variability from aerosol forcing and other sources of short-term forcing.

scholarly journals The Rossby radius in the Arctic Ocean

Ocean Science ◽  
2014 ◽  
Vol 10 (6) ◽  
pp. 967-975 ◽  
Author(s):  
A. J. G. Nurser ◽  
S. Bacon
Keyword(s):  
Arctic Ocean ◽  
General Circulation ◽  
Circulation Model ◽  
Ocean General Circulation Model ◽  
High Arctic ◽  
The Arctic ◽  
Hudson Bay ◽  
Ocean Eddies ◽  
Shelf Seas ◽  
The Impact

Abstract. The first (and second) baroclinic deformation (or Rossby) radii are presented north of ~60° N, focusing on deep basins and shelf seas in the high Arctic Ocean, the Nordic seas, Baffin Bay, Hudson Bay and the Canadian Arctic Archipelago, derived from climatological ocean data. In the high Arctic Ocean, the first Rossby radius increases from ~5 km in the Nansen Basin to ~15 km in the central Canadian Basin. In the shelf seas and elsewhere, values are low (1–7 km), reflecting weak density stratification, shallow water, or both. Seasonality strongly impacts the Rossby radius only in shallow seas, where winter homogenization of the water column can reduce it to below 1 km. Greater detail is seen in the output from an ice–ocean general circulation model, of higher resolution than the climatology. To assess the impact of secular variability, 10 years (2003–2012) of hydrographic stations along 150° W in the Beaufort Gyre are also analysed. The first-mode Rossby radius increases over this period by ~20%. Finally, we review the observed scales of Arctic Ocean eddies.

scholarly journals Operational ocean models in the Adriatic Sea: a skill assessment

Ocean Science ◽  
2008 ◽  
Vol 4 (1) ◽  
pp. 61-71 ◽  
Author(s):  
J. Chiggiato ◽  
P. Oddo
Keyword(s):  
General Circulation ◽  
Mean Squared Error ◽  
Three Dimensional ◽  
Circulation Model ◽  
Remote Sensing Data ◽  
Skill Assessment ◽  
Regional Models ◽  
Operational Systems ◽  
Forecasting System ◽  
The Mediterranean

Abstract. In the framework of the Mediterranean Forecasting System (MFS) project, the performance of regional numerical ocean forecasting systems is assessed by means of model-model and model-data comparison. Three different operational systems considered in this study are: the Adriatic REGional Model (AREG); the Adriatic Regional Ocean Modelling System (AdriaROMS) and the Mediterranean Forecasting System General Circulation Model (MFS-GCM). AREG and AdriaROMS are regional implementations (with some dedicated variations) of POM and ROMS, respectively, while MFS-GCM is an OPA based system. The assessment is done through standard scores. In situ and remote sensing data are used to evaluate the system performance. In particular, a set of CTD measurements collected in the whole western Adriatic during January 2006 and one year of satellite derived sea surface temperature measurements (SST) allow to asses a full three-dimensional picture of the operational forecasting systems quality during January 2006 and to draw some preliminary considerations on the temporal fluctuation of scores estimated on surface quantities between summer 2005 and summer 2006. The regional systems share a negative bias in simulated temperature and salinity. Nonetheless, they outperform the MFS-GCM in the shallowest locations. Results on amplitude and phase errors are improved in areas shallower than 50 m, while degraded in deeper locations, where major models deficiencies are related to vertical mixing overestimation. In a basin-wide overview, the two regional models show differences in the local displacement of errors. In addition, in locations where the regional models are mutually correlated, the aggregated mean squared error was found to be smaller, that is a useful outcome of having several operational systems in the same region.

scholarly journals Stratospheric temperatures and tracer transport in a nudged 4-year middle atmosphere GCM simulation

2005 ◽  
Vol 5 (1) ◽  
pp. 961-1006 ◽  
Author(s):  
M. K. van Aalst ◽  
J. Lelieveld ◽  
B. Steil ◽  
C. Brühl ◽  
P. Jöckel ◽  
...  
Keyword(s):  
Interannual Variability ◽  
General Circulation ◽  
Middle Atmosphere ◽  
Circulation Model ◽  
Detailed Comparison ◽  
The Arctic ◽  
Cold Bias ◽  
Tracer Transport ◽  
Quasi Biennial Oscillation ◽  
The Antarctic

Abstract. We have performed a 4-year simulation with the Middle Atmosphere General Circulation Model MAECHAM5/MESSy, while slightly nudging the model’s meteorology in the free troposphere (below 113 hPa) towards ECMWF analyses. We show that the nudging 5 technique, which leaves the middle atmosphere almost entirely free, enables comparisons with synoptic observations. The model successfully reproduces many specific features of the interannual variability, including details of the Antarctic vortex structure. In the Arctic, the model captures general features of the interannual variability, but falls short in reproducing the timing of sudden stratospheric warmings. A 10 detailed comparison of the nudged model simulations with ECMWF data shows that the model simulates realistic stratospheric temperature distributions and variabilities, including the temperature minima in the Antarctic vortex. Some small (a few K) model biases were also identified, including a summer cold bias at both poles, and a general cold bias in the lower stratosphere, most pronounced in midlatitudes. A comparison 15 of tracer distributions with HALOE observations shows that the model successfully reproduces specific aspects of the instantaneous circulation. The main tracer transport deficiencies occur in the polar lowermost stratosphere. These are related to the tropopause altitude as well as the tracer advection scheme and model resolution. The additional nudging of equatorial zonal winds, forcing the quasi-biennial oscillation, sig20 nificantly improves stratospheric temperatures and tracer distributions.

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