Sahil Agarwal

The fluctuation statistics of the observed sea-ice extent during the satellite era are compared with model output from CMIP5 models using a multifractal time series method. The two robust features of the observations are that on annual to biannual time scales the ice extent exhibits white noise structure, and there is a decadal scale trend associated with the decay of the ice cover. It is shown that (i) there is a large inter-model variability in the time scales extracted from the models, (ii)… Show more

The fluctuation statistics of the observed sea-ice extent during the satellite era are compared with model output from CMIP5 models using a multifractal time series method. The two robust features of the observations are that on annual to biannual time scales the ice extent exhibits white noise structure, and there is a decadal scale trend associated with the decay of the ice cover. It is shown that (i) there is a large inter-model variability in the time scales extracted from the models, (ii) none of the models exhibits the decadal time scales found in the satellite observations, (iii) five of the 21 models examined exhibit the observed white noise structure, and (iv) the multi- model ensemble mean exhibits neither the observed white noise structure nor the observed decadal trend. It is proposed that the observed fluctuation statistics produced by this method serve as an appropriate test bed for modelling studies. Show less

We extend a data-based model-free multifractal method of exoplanet detection to probe exoplanetary atmospheres. Whereas the transmission spectrum is studied during the primary eclipse, we analyze the emission spectrum during the secondary eclipse, thereby probing the atmospheric limb. In addition to the spectral structure of exoplanet atmospheres, the approach provides information to study phenomena such as atmospheric flows, tidal-locking behavior, and the dayside-nightside redistribution of… Show more

We extend a data-based model-free multifractal method of exoplanet detection to probe exoplanetary atmospheres. Whereas the transmission spectrum is studied during the primary eclipse, we analyze the emission spectrum during the secondary eclipse, thereby probing the atmospheric limb. In addition to the spectral structure of exoplanet atmospheres, the approach provides information to study phenomena such as atmospheric flows, tidal-locking behavior, and the dayside-nightside redistribution of energy. The approach is demonstrated using Spitzer data for exoplanet HD189733b. The central advantage of the method is the lack of model assumptions in the detection and observational schemes. Show less

Understanding multi-decadal variability is an essential aspect of climate dynamics. For example, the recent phenomenon referred to as the "global warming hiatus" may reflect a coupling to an intrinsic, pre-industrial, multi-decadal variability process. Here, using a multi-fractal time series method, we demonstrate that forty-two data sets of seventy-nine proxies with global coverage exhibit the same pink (∼ 1/f) noise characteristics on multi-decadal time scales. To quantify the persistence of… Show more

Understanding multi-decadal variability is an essential aspect of climate dynamics. For example, the recent phenomenon referred to as the "global warming hiatus" may reflect a coupling to an intrinsic, pre-industrial, multi-decadal variability process. Here, using a multi-fractal time series method, we demonstrate that forty-two data sets of seventy-nine proxies with global coverage exhibit the same pink (∼ 1/f) noise characteristics on multi-decadal time scales. To quantify the persistence of this behavior, we examine high-resolution ice core and speleothem data to find pink noise in both pre- and post-industrial periods. We examine the spatial structure with Empirical Orthogonal Function (EOF) analysis of the monthly-averaged surface temperature from 1901 to 2012. The first mode clearly shows the distribution of ocean heat flux sinks located in the eastern Pacific and the Southern Ocean and has pink noise characteristics on a multi-decadal time-scale. We hypothesize that the combination of this pink noise multi-decadal spatial mode may resonate with externally-driven greenhouse gas forcing leading to substantial changes in the global temperature. Show less

In turbulent Rayleigh-B\'enard convection one seeks the relationship between the heat transport, captured by the Nusselt number, and the temperature drop across the convecting layer, captured by Rayleigh number. The maximal heat transport for a given Rayleigh number is the central experimental quantity and the key prediction of variational fluid mechanics in the form of an upper bound. Because the Lorenz equations act a simplified model of turbulent Rayleigh-B\'enard convection, it is natural… Show more

In turbulent Rayleigh-B\'enard convection one seeks the relationship between the heat transport, captured by the Nusselt number, and the temperature drop across the convecting layer, captured by Rayleigh number. The maximal heat transport for a given Rayleigh number is the central experimental quantity and the key prediction of variational fluid mechanics in the form of an upper bound. Because the Lorenz equations act a simplified model of turbulent Rayleigh-B\'enard convection, it is natural to ask for their upper bounds, which have not been viewed as having the same experimental counterpart. Here we describe a specially built circuit that is the experimental analogue of the Lorenz equations and compare its output to the recently determined stochastic upper bounds of the Lorenz equations (Agarwal & Wettlaufer 2016). In the chaotic regime, the upper bounds do not increase monotonically with noise amplitude, as described previously (Agarwal & Wettlaufer 2016). However, because the circuit is vastly more efficient than computational solutions, we can more easily examine this result in the context of the optimality of stochastic fixed points. Because of offsets that appear naturally in the circuit system, we are motivated to study unique bifurcation phenomena that arise as a result. Show less

In an effort to understand the dynamics of the Arctic sea-ice edge, we present a simple model of heat and mass transfer in the Fram Strait that reveals some fundamental mechanisms controlling sea-ice extent in the marginal seas and the depth and properties of the Arctic mixed layer. We identify and study key mechanisms relating to the sea-ice wedge described by Untersteiner, a boundary-layer structure near the ice edge, demonstrating how ice thickness and extent depend on ice-export rates… Show more

In an effort to understand the dynamics of the Arctic sea-ice edge, we present a simple model of heat and mass transfer in the Fram Strait that reveals some fundamental mechanisms controlling sea-ice extent in the marginal seas and the depth and properties of the Arctic mixed layer. We identify and study key mechanisms relating to the sea-ice wedge described by Untersteiner, a boundary-layer structure near the ice edge, demonstrating how ice thickness and extent depend on ice-export rates, atmospheric forcing and the properties of incoming warm and salty Atlantic water in the West Spitsbergen Current. Our time-dependent results demonstrate a seasonal asymmetry between the rates of ice advance and retreat and explain the significant variations in the Southerly extent of sea ice across the Fram Strait, with a long ice tongue corresponding with the East Greenland Current. Our simple model indicates that thinning of the Arctic sea-ice cover will lead to warming and freshening of the North Atlantic, which would give a de-stabilizing feedback to the Arctic ice cover, leading to a slowdown of the Atlantic Meridional Overturning Circulation. Show less

By arguing that the surface pressure field over the Arctic Ocean can be treated as an isotropic, stationary, homogeneous, Gaussian random field, Thorndike estimated a number of covariance functions from two years of data (1979 and 1980). Given the active interest in changes of general circulation quantities and indices in the polar regions during the recent few decades, the spatial correlations in sea ice velocity fields are of particular interest. It is thus natural to ask, ‘‘How persistent… Show more

By arguing that the surface pressure field over the Arctic Ocean can be treated as an isotropic, stationary, homogeneous, Gaussian random field, Thorndike estimated a number of covariance functions from two years of data (1979 and 1980). Given the active interest in changes of general circulation quantities and indices in the polar regions during the recent few decades, the spatial correlations in sea ice velocity fields are of particular interest. It is thus natural to ask, ‘‘How persistent are these correlations?’’ To this end, a multifractal stochastic treatment is developed to analyze observed Arctic sea ice velocity fields from satellites and buoys for the period 1978–2015. Since it was previously found that the Arctic equivalent ice extent (EIE) has a white noise structure on annual to biannual time scales, the connection between EIE and ice motion is assessed. The long- term stationarity of the spatial correlation structure of the velocity fields and the robustness of their white noise structure on multiple time scales is demonstrated; these factors (i) combine to explain the white noise characteristics of the EIE on annual to biannual time scales and (ii) explain why the fluctuations in the ice velocity are proportional to fluctuations in the geostrophic winds on time scales of days to months. Moreover, it is shown that the statistical structure of these two quantities is commensurate from days to years, which may be related to the increasing prevalence of free drift in the ice pack. Show less

Owing to technological advances, the number of exoplanets discovered has risen dramatically in the last few years. However, when trying to observe Earth analogs, it is often difficult to test the veracity of detection. We have developed a new approach to the analysis of exoplanetary spectral observations based on temporal multifractality, which identifies timescales that characterize planetary orbital motion around the host star and those that arise from stellar features such as spots… Show more

Owing to technological advances, the number of exoplanets discovered has risen dramatically in the last few years. However, when trying to observe Earth analogs, it is often difficult to test the veracity of detection. We have developed a new approach to the analysis of exoplanetary spectral observations based on temporal multifractality, which identifies timescales that characterize planetary orbital motion around the host star and those that arise from stellar features such as spots. Without fitting stellar models to spectral data, we show how the planetary signal can be robustly detected from noisy data using noise amplitude as a source of information. For observation of transiting planets, combining this method with simple geometry allows us to relate the timescales obtained to primary and secondary eclipse of the exoplanets. Making use of data obtained with ground-based and space-based observations we have tested our approach on HD 189733b. Moreover, we have investigated the use of this technique in measuring planetary orbital motion via Doppler shift detection. Finally, we have analyzed synthetic spectra obtained using the SOAP 2.0 tool, which simulates a stellar spectrum and the influence of the presence of a planet or a spot on that spectrum over one orbital period. We have demonstrated that, so long as the signal-to-noise-ratio >= 75, our approach reconstructs the planetary orbital period, as well as the rotation period of a spot on the stellar surface. Show less

We calculate the stochastic upper bounds for the Lorenz equations using an extension of the background method. In analogy with Rayleigh–Bénard convection the upper bounds are for heat transport versus Rayleigh number. As might be expected, the stochastic upper bounds are larger than the deterministic counterpart of Souza and Doering [2015], but their variation with noise amplitude exhibits interesting behavior. Below the transition to chaotic dynamics the upper bounds increase monotonically… Show more

We calculate the stochastic upper bounds for the Lorenz equations using an extension of the background method. In analogy with Rayleigh–Bénard convection the upper bounds are for heat transport versus Rayleigh number. As might be expected, the stochastic upper bounds are larger than the deterministic counterpart of Souza and Doering [2015], but their variation with noise amplitude exhibits interesting behavior. Below the transition to chaotic dynamics the upper bounds increase monotonically with noise amplitude. However, in the chaotic regime this monotonicity depends on the number of realizations in the ensemble; at a particular Rayleigh number the bound may increase or decrease with noise amplitude. The origin of this behavior is the coupling between the noise and unstable periodic orbits, the degree of which depends on the degree to which the ensemble represents the ergodic set. This is confirmed by examining the close returns plots of the full solutions to the stochastic equations and the numerical convergence of the noise correlations. The numerical convergence of both the ensemble and time averages of the noise correlations is sufficiently slow that it is the limiting aspect of the realization of these bounds. Finally, we note that the full solutions of the stochastic equations demonstrate that the effect of noise is equivalent to the effect of chaos. Show less

We examine the long-term correlations and multi-fractal properties of daily satellite retrievals of Arctic sea ice albedo and extent, for periods of approximately 23 years and 32 years, respectively. The approach harnesses a recent development called multi- fractal temporally weighted detrended fluctuation analysis, which exploits the intuition that points closer in time are more likely to be related than distant points. In both datasets, we extract multiple crossover times, as characterized by… Show more

We examine the long-term correlations and multi-fractal properties of daily satellite retrievals of Arctic sea ice albedo and extent, for periods of approximately 23 years and 32 years, respectively. The approach harnesses a recent development called multi- fractal temporally weighted detrended fluctuation analysis, which exploits the intuition that points closer in time are more likely to be related than distant points. In both datasets, we extract multiple crossover times, as characterized by generalized Hurst exponents, ranging from synoptic to decadal. The method goes beyond treatments that assume a single decay scale process, such as a first-order autoregression, which cannot be justifiably fitted to these observations. Importantly, the strength of the seasonal cycle ‘masks’ long-term correlations on time scales beyond seasonal. When removing the seasonal cycle from the original record, the ice extent data exhibit white noise behaviour from seasonal to bi-seasonal time scales, whereas the clear fingerprints of the short (weather) and long (approx. 7 and 9 year) time scales remain, the latter associated with the recent decay in the ice cover. Therefore, long-term persistence is re-entrant beyond the seasonal scale and it is not possible to distinguish whether a given ice extent minimum/maximum will be followed by a minimum/maximum that is larger or smaller in magnitude. Show less

A controlling factor in the seasonal and climatological evolution of the sea ice cover is its albedo a. Here we ana- lyze Arctic data from the Advanced Very High Resolution Radiometer (AVHRR) Polar Pathfinder and assess the sea- sonality and variability of broadband albedo from a 23 year daily record. We produce a histogram of daily albedo over ice covered regions in which the principal albedo transitions are seen; high albedo in late winter and spring, the onset of snowmelt and melt pond… Show more

A controlling factor in the seasonal and climatological evolution of the sea ice cover is its albedo a. Here we ana- lyze Arctic data from the Advanced Very High Resolution Radiometer (AVHRR) Polar Pathfinder and assess the sea- sonality and variability of broadband albedo from a 23 year daily record. We produce a histogram of daily albedo over ice covered regions in which the principal albedo transitions are seen; high albedo in late winter and spring, the onset of snowmelt and melt pond formation in the summer, and fall freezeup. The bimodal late summer distribution demonstrates the combination of the poleward progression of the onset of melt with the coexistence of perennial bare ice with melt ponds and open water, which then merge to a broad peak at a >= 0.5. We find the interannual variability to be dominated by the low end of the a distribution, highlighting the con- trolling influence of the ice thickness distribution and large‐ scale ice edge dynamics. The statistics obtained provide a simple framework for model studies of albedo parameteriza- tions and sensitivities. Show less