Unconstrained Ensemble Research Articles

The Impact of “Hot Models” on a CMIP6 Ensemble Used by Climate Service Providers in Canada: Do Global Constraints Lead to Appreciable Differences in Regional Projections?

Abstract Canadian climate service providers offer projections from the Coupled Model Intercomparison Project (CMIP6) to help inform climate change mitigation and adaptation decisions. CMIP6 includes several “hot” climate models whose sensitivity to greenhouse gas forcings exceeds the likely range inferred from multiple lines of evidence. Global warming estimates assessed in the Sixth Assessment Report (AR6) of the Intergovernmental Panel on Climate Change (IPCC) were reduced by applying observational constraints on the historical rate of warming to the CMIP6 ensemble. This study assesses whether globally constrained CMIP6 projections for Canada are appreciably different from unconstrained projections. Two constraints are considered: one that removes models whose transient climate response lies outside the AR6 assessed range (TCRlikely), and the other that weights models to match the assessed distribution of equilibrium climate sensitivity (ECSall). Both constraints lead to appreciably cooler and drier projections than the unconstrained ensemble, with the strongest reductions seen in the upper end of the ensemble range, high-emissions scenario, end-of-century time period, and northern regions of Canada. In this case, constrained projections of annual mean temperature are 2°–3°C cooler than the unconstrained projections, whereas projections of annual total precipitation are typically 20%–40% drier. Appreciable differences are also detected in the ensemble median of temperature extreme indices. Based on these results, it is recommended that a constrained ensemble be considered for regional projections to avoid the “hot model” problem. Alternatively, projections can be communicated conditional on a specified level of global warming, with global constraints then used to inform the timing of the warming level exceedance.

Interpretable physiological forecasting in the ICU using constrained data assimilation and electronic health record data

Objective:Prediction of physiological mechanics are important in medical practice because interventions are guided by predicted impacts of interventions. But prediction is difficult in medicine because medicine is complex and difficult to understand from data alone, and the data are sparse relative to the complexity of the generating processes. Computational methods can increase prediction accuracy, but prediction with clinical data is difficult because the data are sparse, noisy and nonstationary. This paper focuses on predicting physiological processes given sparse, non-stationary, electronic health record data in the intensive care unit using data assimilation (DA), a broad collection of methods that pair mechanistic models with inference methods. Methods:A methodological pipeline embedding a glucose–insulin model into a new DA framework, the constrained ensemble Kalman filter (CEnKF) to forecast blood glucose was developed. The data include tube-fed patients whose nutrition, blood glucose, administered insulins and medications were extracted by hand due to their complexity and to ensure accuracy. The model was estimated using an individual’s data as if they arrived in real-time, and the estimated model was run forward producing a forecast. Both constrained and unconstrained ensemble Kalman filters were estimated to compare the impact of constraints. Constraint boundaries, model parameter sets estimated, and data used to estimate the models were varied to investigate their influence on forecasting accuracy. Forecasting accuracy was evaluated according to mean squared error between the model-forecasted glucose and the measurements and by comparing distributions of measured glucose and forecast ensemble means. Results:The novel CEnKF produced substantial gains in robustness and accuracy while minimizing the data requirements compared to the unconstrained ensemble Kalman filters. Administered insulin and tube-nutrition were important for accurate forecasting, but including glucose in IV medication delivery did not increase forecast accuracy. Model flexibility, controlled by constraint boundaries and estimated parameters, did influence forecasting accuracy. Conclusion:Accurate and robust physiological forecasting with sparse clinical data is possible with DA. Introducing constrained inference, particularly on unmeasured states and parameters, reduced forecast error and data requirements. The results are not particularly sensitive to model flexibility such as constraint boundaries, but over or under constraining increased forecasting errors.

Modified Thirring model beyond the excluded-volume approximation

Long-range interacting systems may exhibit ensemble inequivalence and can possibly attain equilibrium states under completely open conditions, for which energy, volume and number of particles simultaneously fluctuate. Here we consider a modified version of the Thirring model for self-gravitating systems with attractive and repulsive long-range interactions in which particles are treated as hard spheres in dimension d = 1, 2, 3. Equilibrium states of the model are studied under completely open conditions, in the unconstrained ensemble, by means of both Monte Carlo simulations and analytical methods and are compared with the corresponding states at fixed number of particles, in the isothermal-isobaric ensemble. Our theoretical description is performed for an arbitrary local equation of state, which allows us to examine the system beyond the excluded-volume approximation. The simulations confirm the theoretical prediction of the possible occurrence of first-order phase transitions in the unconstrained ensemble. This work contributes to the understanding of long-range interacting systems exchanging heat, work and matter with the environment.

Logarithmic corrections to the entropy function of black holes in the open ensemble

An ‘open’ or (μ,P,T)-ensemble describes equilibrium systems whose control parameters are chemical potential μ, pressure P and temperature T. Such an unconstrained ensemble is seldom used for applications to standard thermodynamic systems due to the fact that the corresponding free energy identically vanishes as a result of the Euler relation. However, an open ensemble is perfectly regular for the case of black holes, as the entropy is a quasi-homogeneous function of extensive thermodynamic variables with scaling dictated by the Smarr formula. Following a brief discussion on thermodynamics in the open ensemble, we compute the general form of logarithmic corrections to the entropy of a typical system, due to fluctuations in energy, thermodynamic volume and a generic charge N. This is then used to obtain the exact analytic form of the logarithmically corrected black hole entropy for charged and rotating black holes in anti-de Sitter spacetimes.

Monte Carlo simulations in the unconstrained ensemble.

The unconstrained ensemble describes completely open systems whose control parameters are the chemical potential, pressure, and temperature. For macroscopic systems with short-range interactions, thermodynamics prevents the simultaneous use of these intensive variables as control parameters, because they are not independent and cannot account for the system size. When the range of the interactions is comparable with the size of the system, however, these variables are not truly intensive and may become independent, so equilibrium states defined by the values of these parameters may exist. Here, we derive a Monte Carlo algorithm for the unconstrained ensemble and show that simulations can be performed using the chemical potential, pressure, and temperature as control parameters. We illustrate the algorithm by applying it to physical systems where either the system has long-range interactions or is confined by external conditions. The method opens up an avenue for the simulation of completely open systems exchanging heat, work, and matter with the environment.

Atmospheric dynamic constraints on Tibetan Plateau freshwater under Paris climate targets

Rivers originating in the Tibetan Plateau provide freshwater to downstream populations, yet runoff projections from warming are unclear due to precipitation uncertainties. Here, we use a historical atmospheric circulation–precipitation relationship to constrain future modelled wet-season precipitation over the Tibetan Plateau. Our constraint reduces precipitation increases to half of those from the unconstrained ensemble and reduces spread by around a factor of three. This constrained precipitation is used with estimated glacier melt contributions to constrain future runoff for seven rivers. We estimate runoff increases of 1.0–7.2% at the end of the twenty-first century for global mean warming of 1.5–4 °C above pre-industrial levels. Because population projections diverge across basins, this runoff increase will reduce the population fraction living under water scarcity conditions in the Yangtze and Yellow basins but not in the Indus and Ganges basins, necessitating improved water security through climate change adaptation policies in these regions at higher risk. Tibetan Plateau runoff projections are uncertain due to precipitation change uncertainty in climate models. Historical precipitation–circulation relationships constrain future wet-season precipitation and runoff change, suggesting worsening water scarcity for the Indus and Ganges river basins.

Solid–electrolyte-interphase design in constrained ensemble for solid-state batteries

All-solid-state battery is fundamentally different from liquid electrolyte batteries. To design interface stabilities, the solid system must be described by the constrained thermodynamic ensemble rather than the conventional unconstrained ensemble.

Phase transitions in the unconstrained ensemble

The unconstrained ensemble describes completely open systems in which energy, volume and number of particles fluctuate. Here we show that not only equilibrium states can exist in this ensemble, but also that completely open systems can undergo first-order phase transitions. This is shown by studying a modified version of the Thirring model with attractive and repulsive interactions and with particles of finite size. The model exhibits first-order phase transitions in the unconstrained ensemble, at variance with the analogous model with point-like particles. While unconstrained and grand canonical ensembles are equivalent for this model, we found inequivalence between the unconstrained and isothermal–isobaric ensembles. By comparing the thermodynamic phase diagram in the unconstrained case with that obtained in the isothermal–isobaric ensemble, we show that phase transitions under completely open conditions for this model are different from those in which the number of particles is fixed, highlighting the inequivalence of ensembles.

Concavity, Response Functions and Replica Energy.

In nonadditive systems, like small systems or like long-range interacting systems even in the thermodynamic limit, ensemble inequivalence can be related to the occurrence of negative response functions, this in turn being connected with anomalous concavity properties of the thermodynamic potentials associated with the various ensembles. We show how the type and number of negative response functions depend on which of the quantities E, V and N (energy, volume and number of particles) are constrained in the ensemble. In particular, we consider the unconstrained ensemble in which E, V and N fluctuate, which is physically meaningful only for nonadditive systems. In fact, its partition function is associated with the replica energy, a thermodynamic function that identically vanishes when additivity holds, but that contains relevant information in nonadditive systems.

Nongrowing season methane emissions-a significant component of annual emissions across northern ecosystems.

Wetlands are the single largest natural source of atmospheric methane (CH4 ), a greenhouse gas, and occur extensively in the northern hemisphere. Large discrepancies remain between "bottom-up" and "top-down" estimates of northern CH4 emissions. To explore whether these discrepancies are due to poor representation of nongrowing season CH4 emissions, we synthesized nongrowing season and annual CH4 flux measurements from temperate, boreal, and tundra wetlands and uplands. Median nongrowing season wetland emissions ranged from 0.9g/m2 in bogs to 5.2g/m2 in marshes and were dependent on moisture, vegetation, and permafrost. Annual wetland emissions ranged from 0.9gm-2 year-1 in tundra bogs to 78gm-2 year-1 in temperate marshes. Uplands varied from CH4 sinks to CH4 sources with a median annual flux of 0.0±0.2gm-2 year-1 . The measured fraction of annual CH4 emissions during the nongrowing season (observed: 13% to 47%) was significantly larger than that was predicted by two process-based model ensembles, especially between 40° and 60°N (modeled: 4% to 17%). Constraining the model ensembles with the measured nongrowing fraction increased total nongrowing season and annual CH4 emissions. Using this constraint, the modeled nongrowing season wetland CH4 flux from >40° north was 6.1±1.5Tg/year, three times greater than the nongrowing season emissions of the unconstrained model ensemble. The annual wetland CH4 flux was 37±7Tg/year from the data-constrained model ensemble, 25% larger than the unconstrained ensemble. Considering nongrowing season processes is critical for accurately estimating CH4 emissions from high-latitude ecosystems, and necessary for constraining the role of wetland emissions in a warming climate.

Long-range interacting systems in the unconstrained ensemble.

Completely open systems can exchange heat, work, and matter with the environment. While energy, volume, and number of particles fluctuate under completely open conditions, the equilibrium states of the system, if they exist, can be specified using the temperature, pressure, and chemical potential as control parameters. The unconstrained ensemble is the statistical ensemble describing completely open systems and the replica energy is the appropriate free energy for these control parameters from which the thermodynamics must be derived. It turns out that macroscopic systems with short-range interactions cannot attain equilibrium configurations in the unconstrained ensemble, since temperature, pressure, and chemical potential cannot be taken as a set of independent variables in this case. In contrast, we show that systems with long-range interactions can reach states of thermodynamic equilibrium in the unconstrained ensemble. To illustrate this fact, we consider a modification of the Thirring model and compare the unconstrained ensemble with the canonical and grand-canonical ones: The more the ensemble is constrained by fixing the volume or number of particles, the larger the space of parameters defining the equilibrium configurations.

Seasonal-to-decadal predictions with the ensemble Kalman filter and the Norwegian Earth System Model: a twin experiment

Here, we firstly demonstrate the potential of an advanced flow dependent data assimilation method for performing seasonal-to-decadal prediction and secondly, reassess the use of sea surface temperature (SST) for initialisation of these forecasts. We use the Norwegian Climate Prediction Model (NorCPM), which is based on the Norwegian Earth System Model (NorESM) and uses the deterministic ensemble Kalman filter to assimilate observations. NorESM is a fully coupled system based on the Community Earth System Model version 1, which includes an ocean, an atmosphere, a sea ice and a land model. A numerically efficient coarse resolution version of NorESM is used. We employ a twin experiment methodology to provide an upper estimate of predictability in our model framework (i.e. without considering model bias) of NorCPM that assimilates synthetic monthly SST data (EnKF-SST). The accuracy of EnKF-SST is compared to an unconstrained ensemble run (FREE) and ensemble predictions made with near perfect (i.e. microscopic SST perturbation) initial conditions (PERFECT). We perform 10 cycles, each consisting of a 10-yr assimilation phase, followed by a 10-yr prediction. The results indicate that EnKF-SST improves sea level, ice concentration, 2 m atmospheric temperature, precipitation and 3-D hydrography compared to FREE. Improvements for the hydrography are largest near the surface and are retained for longer periods at depth. Benefits in salinity are retained for longer periods compared to temperature. Near-surface improvements are largest in the tropics, while improvements at intermediate depths are found in regions of large-scale currents, regions of deep convection, and at the Mediterranean Sea outflow. However, the benefits are often small compared to PERFECT, in particular, at depth suggesting that more observations should be assimilated in addition to SST. The EnKF-SST system is also tested for standard ocean circulation indices and demonstrates decadal predictability for Atlantic overturning and sub-polar gyre circulations, and heat content in the Nordic Seas. The system beats persistence forecast and shows skill for heat content in the Nordic Seas that is close to PERFECT.

Sensitivity of tropical carbon to climate change constrained by carbon dioxide variability

The release of carbon from tropical forests may exacerbate future climate change, but the magnitude of the effect in climate models remains uncertain. Coupled climate-carbon-cycle models generally agree that carbon storage on land will increase as a result of the simultaneous enhancement of plant photosynthesis and water use efficiency under higher atmospheric CO(2) concentrations, but will decrease owing to higher soil and plant respiration rates associated with warming temperatures. At present, the balance between these effects varies markedly among coupled climate-carbon-cycle models, leading to a range of 330 gigatonnes in the projected change in the amount of carbon stored on tropical land by 2100. Explanations for this large uncertainty include differences in the predicted change in rainfall in Amazonia and variations in the responses of alternative vegetation models to warming. Here we identify an emergent linear relationship, across an ensemble of models, between the sensitivity of tropical land carbon storage to warming and the sensitivity of the annual growth rate of atmospheric CO(2) to tropical temperature anomalies. Combined with contemporary observations of atmospheric CO(2) concentration and tropical temperature, this relationship provides a tight constraint on the sensitivity of tropical land carbon to climate change. We estimate that over tropical land from latitude 30° north to 30° south, warming alone will release 53 ± 17 gigatonnes of carbon per kelvin. Compared with the unconstrained ensemble of climate-carbon-cycle projections, this indicates a much lower risk of Amazon forest dieback under CO(2)-induced climate change if CO(2) fertilization effects are as large as suggested by current models. Our study, however, also implies greater certainty that carbon will be lost from tropical land if warming arises from reductions in aerosols or increases in other greenhouse gases.

On the choice of importance distributions for unconstrained and constrained state estimation using particle filter

Recursive state estimation of constrained nonlinear dynamical system has attracted the attention of many researchers in recent years. For nonlinear/non-Gaussian state estimation problems, particle filters have been widely used (Arulampalam et al. [1]). As pointed out by Daum [2], particle filters require a proposal distribution and the choice of proposal distribution is the key design issue. In this paper, a novel approach for generating the proposal distribution based on a constrained Extended Kalman filter (C-EKF), Constrained Unscented Kalman filter (C-UKF) and constrained Ensemble Kalman filter (C-EnkF) has been proposed. The efficacy of the proposed state estimation algorithms using a particle filter is illustrated via a successful implementation on a simulated gas-phase reactor, involving constraints on estimated state variables and another example problem, which involves constraints on the process noise (Rao et al. [10]). We also propose a state estimation scheme for estimating state variables in an autonomous hybrid system using particle filter with Unscented Kalman filter as a proposal and unconstrained Ensemble Kalman filter (EnKF) as a proposal. The efficacy of the proposed state estimation scheme for an autonomous hybrid system is demonstrated by conducting simulation studies on a three-tank hybrid system. The simulation studies underline the crucial role played by the choice of proposal distribution in formulation of particle filters.

A Particle Filter for Inverse Lagrangian Prediction Problems

Abstract The authors present a numerical method for the inverse Lagrangian prediction problem, which addresses retrospective estimation of drifter trajectories through a turbulent flow, given their final positions and some knowledge of the flow field. Of particular interest is probabilistic estimation of the origin (or launch site) of drifters for practical applications in search and rescue operations, drifting sensor array design, and biochemical source location. A typical solution involves a Monte Carlo simulation of an ensemble of Lagrangian trajectories backward in time using the known final locations, a set of velocity estimates, and a stochastic model for the unresolved flow components. Because of the exponential dispersion of the trajectories, however, the distribution of the drifter locations tends to be too diffuse to be able to reliably locate the launch site. A particle filter that constrains the drifter ensemble according to the empirical dispersion characteristics of the flow field is examined. Using the filtering method, launch-site prediction cases with and without a dispersion constraint are compared in idealized as well as realistic scenarios. It is shown that the ensemble with the dispersion constraint can locate the launch site more specifically and accurately than the unconstrained ensemble.

Statistical characteristics of irreversible predictability time in regional ocean models

Abstract. Probabilistic aspects of regional ocean model predictability is analyzed using the probability density function (PDF) of the irreversible predictability time (IPT) (called τ-PDF) computed from an unconstrained ensemble of stochastic perturbations in initial conditions, winds, and open boundary conditions. Two-attractors (a chaotic attractor and a small-amplitude stable limit cycle) are found in the wind-driven circulation. Relationship between attractor's residence time and IPT determines the τ-PDF for the short (up to several weeks) and intermediate (up to two months) predictions. The τ-PDF is usually non-Gaussian but not multi-modal for red-noise perturbations in initial conditions and perturbations in the wind and open boundary conditions. Bifurcation of τ-PDF occurs as the tolerance level varies. Generally, extremely successful predictions (corresponding to the τ-PDF's tail toward large IPT domain) are not outliers and share the same statistics as a whole ensemble of predictions.