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In this work, we present a new diagnostic tool for El Niño Southern Oscillation (ENSO) simulations in Earth System Models (ESMs) based on the analysis of upper ocean heat content data. It allows us to identify the seasonally dependent structure of temperature anomalies in the equatorial Pacific Ocean in the form of a dominant spatio-temporal pattern. We demonstrate the results of applying a tool to analysis of real data as well as climate simulations in two versions of the Institute of Numerical Mathematics ESM. We find that the latest version of the model, with improved parameterizations of clouds, large-scale condensation, and aerosols, provides significantly better reproduction of ENSO-related structure of anomalies, as well as the phase locking of ENSO to the annual cycle. We recommend to use the tool for diagnostic analysis of ESMs regarding simulation of climate phenomena with strong seasonality. [ABSTRACT FROM AUTHOR]

Advanced numerical climate models are known to exhibit biases in simulating some features of El Niño–Southern Oscillation (ENSO), which is a key mode of interannual climate variability. In this study we analyze how two fundamental features of observed ENSO – asymmetry between hot and cold states and phase-locking to the annual cycle – are reflected in two different versions of the INMCM Earth system model (state-of-the-art Earth system model participating in the Coupled Model Intercomparison Project). We identify the above ENSO features using the conventional empirical orthogonal functions (EOF) analysis, which is applied to both observed and simulated upper ocean heat content (OHC) data in the tropical Pacific. We obtain that the observed tropical Pacific OHC variability is described well by two leading EOF-modes, which roughly reflect the fundamental recharge-discharge mechanism of ENSO. These modes exhibit strong seasonal cycles associated with ENSO phase locking while the revealed nonlinear dependencies between amplitudes of these cycles reflect ENSO asymmetry.We also assess and compare the predictability of observed and simulated ENSO based on linear inverse modelling. We find that the improved INMCM6 model has significant benefits in simulating described features of observed ENSO as compared with the previous INMCM5 model. The improvements of the INMCM6 model providing such benefits are discussed. We argue that proper cloud parameterization scheme is crucial for accurate simulation of ENSO dynamics with numerical climate models. [ABSTRACT FROM AUTHOR]

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.

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.

Unstable periodic orbits (UPOs) are a valuable tool for studying chaotic dynamical systems, as they allow one to distill their dynamical structure. We consider here the Lorenz 1963 model with the classic parameters' value. We investigate how a chaotic trajectory can be approximated using a complete set of UPOs up to symbolic dynamics' period 14. At each instant, we rank the UPOs according to their proximity to the position of the orbit in the phase space. We study this process from two different perspectives. First, we find that longer period UPOs overwhelmingly provide the best local approximation to the trajectory. Second, we construct a finite-state Markov chain by studying the scattering of the orbit between the neighborhood of the various UPOs. Each UPO and its neighborhood are taken as a possible state of the system. Through the analysis of the subdominant eigenvectors of the corresponding stochastic matrix, we provide a different interpretation of the mixing processes occurring in the system by taking advantage of the concept of quasi-invariant sets. [ABSTRACT FROM AUTHOR]