Initial Ensemble Research Articles

The Shannon entropy as a measure of diffusion in multidimensional dynamical systems

In the present work, we introduce two new estimators of chaotic diffusion based on the Shannon entropy. Using theoretical, heuristic and numerical arguments, we show that the entropy, S, provides a measure of the diffusion extent of a given small initial ensemble of orbits, while an indicator related with the time derivative of the entropy, $$S'$$ , estimates the diffusion rate. We show that in the limiting case of near ergodicity, after an appropriate normalization, $$S'$$ coincides with the standard homogeneous diffusion coefficient. The very first application of this formulation to a 4D symplectic map and to the Arnold Hamiltonian reveals very successful and encouraging results.

Parameterizations for ensemble Kalman inversion

The use of ensemble methods to solve inverse problems is attractive because it is a derivative-free methodology which is also well-adapted to parallelization. In its basic iterative form the method produces an ensemble of solutions which lie in the linear span of the initial ensemble. Choice of the parameterization of the unknown field is thus a key component of the success of the method. We demonstrate how both geometric ideas and hierarchical ideas can be used to design effective parameterizations for a number of applied inverse problems arising in electrical impedance tomography, groundwater flow and source inversion. In particular we show how geometric ideas, including the level set method, can be used to reconstruct piecewise continuous fields, and we show how hierarchical methods can be used to learn key parameters in continuous fields, such as length-scales, resulting in improved reconstructions. Geometric and hierarchical ideas are combined in the level set method to find piecewise constant reconstructions with interfaces of unknown topology.

Stochastic nonlinear inversion of seismic data for the estimation of petroelastic properties using the ensemble smoother and data reparameterization

We have developed a new stochastic nonlinear inversion method for seismic reservoir characterization studies to jointly estimate elastic and petrophysical properties and to quantify their uncertainty. Our method aims to estimate multiple reservoir realizations of the entire set of reservoir properties, including seismic velocities, density, porosity, mineralogy, and saturation, by iteratively updating the initial ensemble of models based on the mismatch between their seismic response and the measured seismic data. The initial models are generated using geostatistical methods and the geophysical forward operators include rock-physics relations and a seismic forward model. The optimization is achieved using an iterative ensemble-based algorithm, namely, the ensemble smoother with multiple data assimilation, in which each iteration is based on a Bayesian updating step. The advantages of the proposed method are that it can be applied to nonlinear inverse problems and it can provide an ensemble of solutions from which we can quantify the uncertainty of the model properties of interest. To reduce the computational cost of the inversion, we perform the optimization in a lower dimensional data space reparameterized by singular value decomposition. The proposed methodology is validated on a synthetic case in which the set of petroelastic properties is recovered with satisfactory accuracy. Then, we applied the inversion method to a real seismic data set from the Norne field in the Norwegian Sea.

Avoiding population exposure to heat-related extremes: demographic change vs climate change

Heat waves are among the most dangerous climate-related hazards, and they are projected to increase in frequency and intensity over the coming century. Exposure to heat waves is a function of the spatial distribution of physical events and the corresponding population distribution, and future exposure will be impacted by changes in both distributions. Here, we project future exposure using ensembles of climate projections that account for the urban heat island effect, for two alternative emission scenarios (RCP4.5/RCP8.5) and two alternative population and urbanization (SSP3/SSP5) outcomes. We characterize exposure at the global, regional, and grid-cell level; estimate the exposure that would be avoided by mitigating future levels of climate change (to RCP4.5); and quantify the dependence of exposure on population outcomes. We find that climate change is a stronger determinant of exposure than demographic change in these scenarios, with a global reduction in exposure of over 50% under a lower emissions pathway, while a slower population growth pathway leads to roughly 30% less exposure. Exposure reduction varies at the regional level, but in almost all cases, the RCP remains more influential than the SSP. Uncertainty in outcomes is dominated by inter-annual variability in heat extremes (relative to variability across initial condition ensemble members). For some regions, this variability is large enough that a reduction in annual exposure is not guaranteed in each individual year by following the lower forcing pathway. Finally, we find that explicitly considering the urban heat island effect and separate urban and rural heat extremes and populations can substantially influence results, generally increasing projected exposure.

High-dimensional geostatistical history matching

Hydrocarbon reservoir modelling and characterisation is a challenging subject within the oil and gas industry due to the lack of well data and the natural heterogeneities of the Earth’s subsurface. Integrating historical production data into the geo-modelling workflow, commonly designated by history matching, allows better reservoir characterisation and the possibility of predicting the reservoir behaviour. We present herein a geostatistical-based multi-objective history matching methodology. It starts with the generation of an initial ensemble of the subsurface petrophysical property of interest through stochastic sequential simulation. Each model is then ranked according the match between its dynamic response, after fluid flow simulation, and the observed available historical production data. This enables building regionalised Pareto fronts and the definition of a large ensemble of optimal subsurface Earth models that fit all the observed production data without compromising the exploration of the uncertainty space. The proposed geostatistical multi-objective history matching technique is successfully implemented in a benchmark synthetic reservoir dataset, the PUNQ-S3, where 12 objectives are targeted.

Emergent dynamics of the Kuramoto ensemble under the effect of inertia

We study the emergent collective behaviors for an ensemble of identical Kuramoto oscillators under the effect of inertia. In the absence of inertial effects, it is well known that the generic initial Kuramoto ensemble relaxes to the phase-locked states asymptotically (emergence of complete synchronization) in a large coupling regime. Similarly, even for the presence of inertial effects, similar collective behaviors are observed numerically for generic initial configurations in a large coupling strength regime. However, this phenomenon has not been verified analytically in full generality yet, although there are several partial results in some restricted set of initial configurations. In this paper, we present several improved complete synchronization estimates for the Kuramoto ensemble with inertia in two frameworks for a finite system. Our improved frameworks describe the emergence of phase-locked states and its structure. Additionally, we show that as the number of oscillators tends to infinity, the Kuramoto ensemble with infinite size can be approximated by the corresponding kinetic mean-field model uniformly in time. Moreover, we also establish the global existence of measure-valued solutions for the Kuramoto equation and its large-time asymptotics.

Impact of the Mesoscale Dynamics on Ocean Deep Convection: The 2012–2013 Case Study in the Northwestern Mediterranean Sea

AbstractWinter 2012–2013 was a particularly intense and well‐observed Dense Water Formation (DWF) event in the Northwestern Mediterranean Sea. In this study, we investigate the impact of the mesoscale dynamics on DWF. We perform two perturbed initial state simulation ensembles from summer 2012 to 2013, respectively, mesoscale‐permitting and mesoscale‐resolving, with the AGRIF refinement tool in the Mediterranean configuration NEMOMED12. The mean impact of the mesoscale on DWF occurs mainly through the high‐resolution physics and not the high‐resolution bathymetry. This impact is shown to be modest: the mesoscale does not modify the chronology of the deep convective winter nor the volume of dense waters formed. It however impacts the location of the mixed patch by reducing its extent to the west of the North Balearic Front and by increasing it along the Northern Current, in better agreement with observations. The maximum mixed patch volume is significantly reduced from 5.7 ± 0.2 to 4.2 ± 0.6 × 1013 m3. Finally, the spring restratification volume is more realistic and enhanced from 1.4 ± 0.2 to 1.8 ± 0.2 × 1013 m3 by the mesoscale. We also address the mesoscale impact on the ocean intrinsic variability by performing perturbed initial state ensemble simulations. The mesoscale enhances the intrinsic variability of the deep convection geography, with most of the mixed patch area impacted by intrinsic variability. The DWF volume has a low intrinsic variability but it is increased by 2–3 times with the mesoscale. We relate it to a dramatic increase of the Gulf of Lions eddy kinetic energy from 5.0 ± 0.6 to 17.3 ± 1.5 cm2/s2, in remarkable agreement with observations.

Intercomparison of model response and internal variability across climate model ensembles

Characterization of climate uncertainty at regional scales over near-term planning horizons (0–30 years) is crucial for climate adaptation. Climate internal variability (CIV) dominates climate uncertainty over decadal prediction horizons at stakeholders’ scales (regional to local). In the literature, CIV has been characterized indirectly using projections of climate change from multi-model ensembles (MME) instead of directly using projections from multiple initial condition ensembles (MICE), primarily because adequate number of initial condition (IC) runs were not available for any climate model. Nevertheless, the recent availability of significant number of IC runs from one climate model allows for the first time to characterize CIV directly from climate model projections and perform a sensitivity analysis to study the dominance of CIV compared to model response variability (MRV). Here, we measure relative agreement (a dimensionless number with values ranging between 0 and 1, inclusive; a high value indicates less variability and vice versa) among MME and MICE and find that CIV is lower than MRV for all projection time horizons and spatial resolutions for precipitation and temperature. However, CIV exhibits greater dominance over MRV for seasonal and annual mean precipitation at higher latitudes where signals of climate change are expected to emerge sooner. Furthermore, precipitation exhibits large uncertainties and a rapid decline in relative agreement from global to continental, regional, or local scales for MICE compared to MME. The fractional contribution of uncertainty due to CIV is invariant for precipitation and decreases for temperature as lead time progresses towards the end of the century.

Characterization of Various Channel Fields Using an Initial Ensemble Selection Schemeand Covariance Localization

Ensemble Kalman filter (EnKF) uses recursive updates for data assimilation and provides dependable uncertainty quantification. However, it requires high computing cost. On the contrary, ensemble smoother (ES) assimilates all available data simultaneously. It is simple and fast, but prone to showing two key limitations: overshooting and filter divergence. Since channel fields have non-Gaussian distributions, it is challenging to characterize them with conventional ensemble based history matching methods. In many cases, a large number of models should be employed to characterize channel fields, even if it is quite inefficient. This paper presents two novel schemes for characterizing various channel reservoirs. One is a new ensemble ranking method named initial ensemble selection scheme (IESS), which selects ensemble members based on relative errors of well oil production rates (WOPR). The other is covariance localization in ES, which uses drainage area as a localization function. The proposed method integrates these two schemes. IESS sorts initial models for ES and these selected are also utilized to calculate a localization function of ES for fast and reliable channel characterization. For comparison, four different channel fields are analyzed. A standard EnKF even using 400 models shows too large uncertainties and updated permeability fields lose channel continuity. However, the proposed method, ES with covariance localization assisted by IESS, characterizes channel fields reliably by utilizing good 50 models selected. It provides suitable uncertainty ranges with correct channel trends. In addition, the simulation time of the proposed method is only about 19% of the time required for the standard EnKF.

Determination of 0–0-Transition Frequencies from Diffuse Vibronic Spectra

The equality of the probabilities of direct and inverse vibronic transitions between the initial and final elementary quantum Franck–Condon states in the adiabatic approximation is taken as the equality of the probabilities of one electronic transition in which only the initial and final elementary vibrational ensembles exchange places. The transition frequencies will have mirror symmetry with respect to the 0–0-transition frequency ν0. Accounting for this and selecting hot molecules in the anti-Stokes regions with the initial state in thermal equilibrium leads to a restoration of the known relation for the transition cross sections σ(ν) in the form [σ(ν)/ν] exp (±hν/2kT) = 𝜑[(ν – ν0)2], where ″+″ denotes emission; ″–″, absorption. Examples of using the relation to determine ν0 from absorption, fluorescence, and phosphorescence spectra are given and compared with ν0 obtained by jet-cooling.

An “Observational Large Ensemble” to Compare Observed and Modeled Temperature Trend Uncertainty due to Internal Variability

Abstract Estimates of the climate response to anthropogenic forcing contain irreducible uncertainty due to the presence of internal variability. Accurate quantification of this uncertainty is critical for both contextualizing historical trends and determining the spread of climate projections. The contribution of internal variability to uncertainty in trends can be estimated in models as the spread across an initial condition ensemble. However, internal variability simulated by a model may be inconsistent with observations due to model biases. Here, statistical resampling methods are applied to observations in order to quantify uncertainty in historical 50-yr (1966–2015) winter near-surface air temperature trends over North America related to incomplete sampling of internal variability. This estimate is compared with the simulated trend uncertainty in the NCAR CESM1 Large Ensemble (LENS). The comparison suggests that uncertainty in trends due to internal variability is largely overestimated in LENS, which has an average amplification of variability of 32% across North America. The amplification of variability is greatest in the western United States and Alaska. The observationally derived estimate of trend uncertainty is combined with the forced signal from LENS to produce an “Observational Large Ensemble” (OLENS). The members of OLENS indicate the range of observationally constrained, spatially consistent temperature trends that could have been observed over the past 50 years if a different sequence of internal variability had unfolded. The smaller trend uncertainty in OLENS suggests that is easier to detect the historical climate change signal in observations than in any given member of LENS.

Improved Consistency of Climate Projections over Europe after Accounting for Atmospheric Circulation Variability

Abstract The influence of atmospheric circulation on winter temperature and precipitation trends over Europe in the period 2006–50 is investigated in a 21-member initial condition ensemble from a fully coupled global climate model and in a multimodel framework consisting of 40 different models. Five versions of a dynamical adjustment method based on empirical orthogonal function analysis of sea level pressure are introduced, and their performance in removing the effect of atmospheric circulation on temperature and precipitation is tested. The differences in atmospheric circulation as simulated by different models in their control runs and under the historical and representative concentration pathway 8.5 (RCP8.5) forcing scenarios are investigated. Dynamical adjustment is applied to the multimodel ensemble to demonstrate that a substantial fraction of the uncertainty in projected European temperature and precipitation trends is explained by atmospheric circulation variability. A statistically significant response of sea level pressure to anthropogenic forcing is identified in the multimodel ensemble under the RCP8.5 scenario. This forced response in atmospheric circulation is associated with a dynamical contribution to the long-term multimodel mean temperature and precipitation trends. The results highlight the importance of accounting for the impact of atmospheric circulation variability on trends in regional climate projections.

Arctic sea ice response to the eruptions of Agung, El Chichón, and Pinatubo

AbstractUsing a large initial condition ensemble of climate model simulations, we examine the impact of volcanic activity on Arctic sea ice cover from 1960 to 2005, a period that includes three very large tropical eruptions. Ensemble averaging across simulations with natural (volcanic and solar) forcings alone reduces noise due to internal variability to show a decade of increased Arctic sea extent (of up to half a million square kilometers) following each of the Mount Agung (1963), Mount El Chichón (1982), and Mount Pinatubo (1991) eruptions. A similar impact is seen when averaging over a large ensemble of simulations with natural and all‐known anthropogenic forcings. We show that the volcanic response in sea ice cover is sensitive to preeruption temperature, with warmer conditions before an eruption being associated with a larger than average response. Finally, a detection and attribution analysis using second‐generation Canadian Earth System Model (CanESM2) did not identify a significant response in the observations, while finding no evidence of inconsistency between observations and CanESM2 since regression coefficients were consistent with unity. A similar detection and attribution analysis using the somewhat stronger volcanic response from the simulations in the average of the CMIP5 models did identify a detectable natural forcing response in four observational sea ice extent data sets.

Investigation of stickiness influence in the anomalous transport and diffusion for a non-dissipative Fermi–Ulam model

We study the dynamics of an ensemble of non interacting particles constrained by two infinitely heavy walls, where one of them is moving periodically in time, while the other is fixed. The system presents mixed dynamics, where the accessible region for the particle to diffuse chaotically is bordered by an invariant spanning curve. Statistical analysis for the root mean square velocity, considering high and low velocity ensembles, leads the dynamics to the same steady state plateau for long times. A transport investigation of the dynamics via escape basins reveals that depending of the initial velocity ensemble, the decay rates of the survival probability present different shapes and bumps, in a mix of exponential, power law and stretched exponential decays. After an analysis of step-size averages, we found that the stable manifolds play the role of a preferential path for faster escape, being responsible for the bumps and different shapes of the survival probability.

Adiabatically deformed ensemble: Engineering nonthermal states of matter

We propose a route towards engineering non-thermal states of matter, which show largely unexplored physics. The main idea relies on the adiabatic passage of a thermal ensemble under slow variations of the system Hamiltonian. If the temperature of the initial thermal ensemble is either zero or infinite the ensemble after the passage is a simple thermal one with the same vanishing or infinite temperature. However, for any finite non-zero temperature intriguing non-thermal ensembles can be achieved. We exemplify this in: (a) a single oscillator (b) a dimerized interacting one dimensional chain of spinless fermions, (c) a BCS-type superconductor and (d) the topological Kitaev chain. We solve these models with a combination of methods; either exactly, numerically using the density matrix renormalization group (DMRG) or within an approximate functional renormalization group (FRG) scheme. The designed states show strongly non-thermal behavior in each of the considered models. For example, for the chain of spinless fermions we exemplify how long ranged non-thermal power-law correlations can be stabilized and for the Kitaev chain we elucidate how the non-thermal ensemble can largely alter the transition temperature separating topological and trivial phases.

Future summer mega-heatwave and record-breaking temperatures in a warmer France climate

This study focuses on future very hot summers associated with severe heatwaves and record-breaking temperatures in France. Daily temperature observations and a pair of historical and scenario (greenhouse gas radiative concentration pathway 8.5) simulations with the high-resolution (∼12.5 km) ALADIN regional climate model provide a robust framework to examine the spatial distribution of these extreme events and their 21st century evolution.Five regions are identified with an extreme event spatial clustering algorithm applied to observed temperatures. They are used to diagnose the 21st century heatwave spatial patterns. In the 2070s, we find a simulated mega-heatwave as severe as the 2003 observed heatwave relative to its contemporaneous climate. A 20-member initial condition ensemble is used to assess the sensitivity of this future heatwave to the internal variability in the regional climate model and to pre-existing land surface conditions. Even in a much warmer and drier climate in France, late spring dry land conditions may lead to a significant amplification of summer extreme temperatures and heatwave intensity through limitations in evapotranspiration. By 2100, the increase in summer temperature maxima exhibits a range from 6 °C to almost 13 °C in the five regions in France, relative to historical maxima. These projections are comparable with the estimates given by a large number of global climate models.

Seasonal differences in the response of Arctic cyclones to climate change in CESM1

The dramatic warming of the Arctic over the last three decades has reduced both the thickness and extent of sea ice, opening opportunities for business in diverse sectors and increasing human exposure to meteorological hazards in the Arctic. It has been suggested that these changes in environmental conditions have led to an increase in extreme cyclones in the region, therefore increasing this hazard. In this study, we investigate the response of Arctic synoptic scale cyclones to climate change in a large initial value ensemble of future climate projections with the CESM1-CAM5 climate model (CESM-LE). We find that the response of Arctic cyclones in these simulations varies with season, with significant reductions in cyclone dynamic intensity across the Arctic basin in winter, but with contrasting increases in summer intensity within the region known as the Arctic Ocean cyclone maximum. There is also a significant reduction in winter cyclogenesis events within the Greenland–Iceland–Norwegian sea region. We conclude that these differences in the response of cyclone intensity and cyclogenesis, with season, appear to be closely linked to changes in surface temperature gradients in the high latitudes, with Arctic poleward temperature gradients increasing in summer, but decreasing in winter.

Regeneration of Initial Ensembles With Facies Analysis for Efficient History Matching

Reservoir characterization is needed for estimating reservoir properties and forecasting production rates in a reliable manner. However, it is challenging to figure out reservoir properties of interest due to limited information. Therefore, well-designed reservoir models, which reflect characteristics of a true field, should be selected and fine-tuned. We propose a novel scheme of generating initial reservoir models by using static data and production history data available. We select representative reservoir models by projecting reservoir models onto a two-dimensional (2D) plane using principal component analysis (PCA) and calculating errors of production rates against observed data. These selected models, which will have similar geological properties with the reference, are used to regenerate models by perturbing along the boundary of the different facies. These regenerated models have all the different facies distributions but share principal characteristics based on the selected models. We compare cases using 400 ensemble members, 100 models with unbiased uniform sampling, and 100 regenerated models by the proposed method. We analyze two synthetic reservoirs with different permeability distributions: one is a typical heterogeneous reservoir and the other is a channel reservoir with a bimodal permeability distribution. Compared to the cases using all the 400 models with ensemble Kalman filter (EnKF), the simulation time is dramatically reduced to 4.7%, while the prediction quality on oil and water productions is improved. Even in the more complex reservoir case, the proposed method shows great improvements with reduced uncertainties against the other cases.

Collection/aggregation algorithms in Lagrangian cloud microphysical models: rigorous evaluation in box model simulations

Abstract. Recently, several Lagrangian microphysical models have been developed which use a large number of (computational) particles to represent a cloud. In particular, the collision process leading to coalescence of cloud droplets or aggregation of ice crystals is implemented differently in various models. Three existing implementations are reviewed and extended, and their performance is evaluated by a comparison with well-established analytical and bin model solutions. In this first step of rigorous evaluation, box model simulations, with collection/aggregation being the only process considered, have been performed for the three well-known kernels of Golovin, Long and Hall. Besides numerical parameters, like the time step and the number of simulation particles (SIPs) used, the details of how the initial SIP ensemble is created from a prescribed analytically defined size distribution is crucial for the performance of the algorithms. Using a constant weight technique, as done in previous studies, greatly underestimates the quality of the algorithms. Using better initialisation techniques considerably reduces the number of required SIPs to obtain realistic results. From the box model results, recommendations for the collection/aggregation implementation in higher dimensional model setups are derived. Suitable algorithms are equally relevant to treating the warm rain process and aggregation in cirrus.

The role of natural variability in projections of climate change impacts on U.S. ozone pollution

AbstractClimate change can impact air quality by altering the atmospheric conditions that determine pollutant concentrations. Over large regions of the U.S., projected changes in climate are expected to favor formation of ground‐level ozone and aggravate associated health effects. However, modeling studies exploring air quality‐climate interactions have often overlooked the role of natural variability, a major source of uncertainty in projections. Here we use the largest ensemble simulation of climate‐induced changes in air quality generated to date to assess its influence on estimates of climate change impacts on U.S. ozone. We find that natural variability can significantly alter the robustness of projections of the future climate's effect on ozone pollution. In this study, a 15 year simulation length minimum is required to identify a distinct anthropogenic‐forced signal. Therefore, we suggest that studies assessing air quality impacts use multidecadal simulations or initial condition ensembles. With natural variability, impacts attributable to climate may be difficult to discern before midcentury or under stabilization scenarios.