Stochastic Ensemble Research Articles

Downslope Windstorms of San Diego County. Part II: Physics Ensemble Analyses and Gust Forecasting

Abstract The “Santa Ana” winds of Southern California represent a high-impact weather event because their dry, fast winds can significantly elevate the wildfire threat. This high-resolution numerical study of six events of moderate or greater strength employs physics parameterization and stochastic perturbation ensembles to determine the optimal model configuration for predicting winds in San Diego County, with verification performed against observations from the San Diego Gas and Electric (SDG&E) mesonet. Results demonstrate model physics can have a material effect on the strength, location, and timing of the winds, with the land surface model playing an outsized role via its specification of surface roughness lengths. Even when bias in the network-averaged sustained wind forecasts is minimized, systematic biases remain in that many stations are consistently over- or underforecasted. The argument is made that this is an “unavoidable” error that represents localized anemometer exposure issues revealed through the station gust factor. A very simple gust parameterization is proposed for the mesonet based on the discovery that the network-averaged gust factor is independent of weather conditions and results in unbiased forecasts of gusts at individual stations and the mesonet as a whole. Combined with atmospheric humidity and fuel moisture information, gust forecasts can help in the assessment of wildfire risks.

Unsupervised machine learning account of magnetic transitions in the Hubbard model.

We employ several unsupervised machine learning techniques, including autoencoders, random trees embedding, and t-distributed stochastic neighboring ensemble (t-SNE), to reduce the dimensionality of, and therefore classify, raw (auxiliary) spin configurations generated, through Monte Carlo simulations of small clusters, for the Ising and Fermi-Hubbard models at finite temperatures. Results from a convolutional autoencoder for the three-dimensional Ising model can be shown to produce the magnetization and the susceptibility as a function of temperature with a high degree of accuracy. Quantum fluctuations distort this picture and prevent us from making such connections between the output of the autoencoder and physical observables for the Hubbard model. However, we are able to define an indicator based on the output of the t-SNE algorithm that shows a near perfect agreement with the antiferromagnetic structure factor of the model in two and three spatial dimensions in the weak-coupling regime. t-SNE also predicts a transition to the canted antiferromagnetic phase for the three-dimensional model when a strong magnetic field is present. We show that these techniques cannot be expected to work away from half filling when the "sign problem" in quantum Monte Carlo simulations is present.

Efficient River Management using Stochastic MPC and Ensemble Forecast of Uncertain In-flows

Abstract Efficient river management is essential in improving water resource utilisation. However, river flows and water-levels are affected by unregulated in- and out-flows. Therefore, it is important to consider the forecasts of these unregulated flows and the uncertainties in the forecasts. The paper describes control and modelling tools from the literature that suit the river management problem. Specifically, a scenario-based Stochastic Model Predictive Control (MPC) strategy, that makes use of ensemble forecast of unregulated flows, is proposed, where the ensemble forecast contains multiple flow scenarios to characterise future flows and their uncertainties, and are obtained from catchment hydrological models.

SPSA‐based data‐driven control strategy for load frequency control of power systems

To meet the demands of the modern power system for satisfactory operation and control, here, a novel data-driven control strategy is proposed to solve the load frequency control (LFC) problems of power systems, with complete convergence analysis. This data-based LFC approach is designed based on the simultaneous perturbation stochastic approximation (SPSA) method and neural network ensemble. The data-based controller is constructed using a function approximator, which is fixed as a neural network. Being the control parameters, the connection weights of the neural network controller are updated at each iteration step. In order to improve the overall control accuracy and get more stable control performance, the idea of neural network ensemble is introduced for the data-based controller structure design. The proposed data-based controller takes past and current system information as input and generates a control signal that can affect future system performance as output, and during the whole process, it is not necessary to build mathematical model for the controlled plant. A one-area LFC problem with system parametric uncertainties as well as a typical two-area LFC problem have been introduced for simulation tests, and the feasibility and effectiveness of this newly proposed data-based LFC strategy is well revealed through simulation results.

Particle–wave dichotomy in quantum Monte Carlo: unlocking the quantum correlations

Here, a dichotomy of particles and waves is employed in a quantum Monte Carlo calculation of interacting electrons. Through the creation and propagation of concurrent stochastic ensembles of walkers in physical space and in Hilbert space, one can correctly predict the ground state and the real-time evolution of a single electron interacting with a larger quantum system. It is shown that such walker ensembles can be constructed straightforwardly through a stochastic sampling (windowing) applied to the mean-field approximation. Our calculations reveal that the ground state and the real-time evolution of the probability distributions and the decoherence due to the Coulomb interaction in the presence of strong ultrashort laser pulses can be accounted for correctly by calculating the density matrix of the electron, without referencing the quantum many-body state of the whole system.

Visual Analysis of Stochastic Trajectory Ensembles in Organic Solar Cell Design

We present a visualization system for analyzing stochastic particle trajectory ensembles, resulting from Kinetic Monte-Carlo simulations on charge transport in organic solar cells. The system supports the analysis of such trajectories in relation to complex material morphologies. It supports the inspection of individual trajectories or the entire ensemble on different levels of abstraction. Characteristic measures quantify the efficiency of the charge transport. Hence, our system led to better understanding of ensemble trajectories by: (i) Capturing individual trajectory behavior and providing an ensemble overview; (ii) Enabling exploration through linked interaction between 3D representations and plots of characteristics measures; (iii) Discovering potential traps in the material morphology; (iv) Studying preferential paths. The visualization system became a central part of the research process. As such, it continuously develops further along with the development of new hypothesis and questions from the application. Findings derived from the first visualizations, e.g., new efficiency measures, became new features of the system. Most of these features arose from discussions combining the data-perspective view from visualization with the physical background knowledge of the underlying processes. While our system has been built for a specific application, the concepts translate to data sets for other stochastic particle simulations.

Integral bubble and jet models with pressure forces

Modifications of integral bubble and jet models including the pressure force are proposed. Exact solutions are found for the modified model of a stationary convective jet from a point source of buoyancy and momentum. The exact solutions are compared against analytical solutions of the integral models for a stationary jet that are based on the approximation of the vertical boundary layer. It is found that the modified integral models of convective jets retain the power-law dependences on the altitude for the vertical velocity and buoyancy obtained in classical models. For a buoyant jet in a neutrally stratified atmosphere, the inclusion of the pressure force increases the amplitude of buoyancy and decreases the amplitude of vertical velocity. The total amplitude change is about 10%. It is shown that in this model there is a dynamic invariant expressing the law of a uniform distribution of the potential and kinetic energy along the jet axis. For a spontaneous jet rising in an unstably stratified atmosphere, the inclusion of the pressure force retains the amplitude of buoyancy and increases the amplitude of vertical velocity by about 15%. It is shown that in the model of a spontaneous jet there is a dynamic invariant expressing the law of a uniform distribution of the available potential and kinetic energy along the jet axis. The results are of interest for the problems of anthropogenic pollution diffusion in the air and water environments and the formulation of models for statistical and stochastic ensembles of thermals in a mass-flux parameterization of turbulent moments.

A non-stationary stochastic ensemble generator for radar rainfall fields based on the short-space Fourier transform

Abstract. In this paper we present a non-stationary stochastic generator for radar rainfall fields based on the short-space Fourier transform (SSFT). The statistical properties of rainfall fields often exhibit significant spatial heterogeneity due to variability in the involved physical processes and influence of orographic forcing. The traditional approach to simulate stochastic rainfall fields based on the Fourier filtering of white noise is only able to reproduce the global power spectrum and spatial autocorrelation of the precipitation fields. Conceptually similar to wavelet analysis, the SSFT is a simple and effective extension of the Fourier transform developed for space–frequency localisation, which allows for using windows to better capture the local statistical structure of rainfall. The SSFT is used to generate stochastic noise and precipitation fields that replicate the local spatial correlation structure, i.e. anisotropy and correlation range, of the observed radar rainfall fields. The potential of the stochastic generator is demonstrated using four precipitation cases observed by the fourth generation of Swiss weather radars that display significant non-stationarity due to the coexistence of stratiform and convective precipitation, differential rotation of the weather system and locally varying anisotropy. The generator is verified in its ability to reproduce both the global and the local Fourier power spectra of the precipitation field. The SSFT-based stochastic generator can be applied and extended to improve the probabilistic nowcasting of precipitation, design storm simulation, stochastic numerical weather prediction (NWP) downscaling, and also for other geophysical applications involving the simulation of complex non-stationary fields.

Quantification of the Uncertainties in Soil and Vegetation Parameterizations for Regional Climate Simulations in Europe

Abstract The deterministic description of the subgrid-scale land–atmosphere interaction in regional climate model (RCM) simulations is changed by using stochastic soil and vegetation parameterizations. For this, the land–atmosphere interaction parameterized in a land surface model (LSM) is perturbed stochastically by adding a random value to the input parameters using a random number generator. In this way, a stochastic ensemble is created that represents the impact of the uncertainties in these subgrid-scale processes on the resolved scale circulation. In a first step, stochastic stand-alone simulations with the VEG3D LSM are performed to identify sensitive model parameters. Afterward, VEG3D is coupled to the Consortium for Small-Scale Modeling–Climate Limited-Area Modeling (COSMO-CLM) RCM and stochastically perturbed simulations driven by ERA-Interim (2001–10) are performed for the Coordinated Downscaling Experiment–European Domain (EURO-CORDEX) at a horizontal resolution of 0.22°. The simulation results reveal that the impact of stochastically varied soil and vegetation parameterizations on the simulated climate conditions differs regionally. In central Europe the impact on the mean temperature and precipitation characteristics is very weak. In southern Europe and North Africa, however, the resolved scale circulation is very sensitive to the local soil water conditions. Furthermore, it is demonstrated that the use of stochastic soil and vegetation parameterizations considerably improves the variability of monthly rainfall sums all over Europe by improving the representation of the land–atmosphere interaction in the stochastic ensemble on a daily basis. In particular, inland rainfall during summer is simulated much better.

A Kriging and Stochastic Collocation ensemble for uncertainty quantification in engineering applications

We propose a new surrogate modeling approach by combining two non-intrusive techniques: Kriging and Stochastic Collocation. The proposed method relies on building a sufficiently accurate Stochastic Collocation model which acts as a basis to construct a Kriging model on the residuals, to combine the accuracy and efficiency of Stochastic Collocation methods in describing stochastic quantities with the flexibility and modeling power of Kriging-based approaches. We investigate and compare performance of the proposed approach with state-of-art techniques over benchmark problems and practical engineering examples on various experimental designs.

A Performance Comparison between Multiphysics and Stochastic Approaches within a North American RAP Ensemble

Abstract A stochastic parameter perturbation (SPP) scheme consisting of spatially and temporally varying perturbations of uncertain parameters in the Grell–Freitas convective scheme and the Mellor–Yamada–Nakanishi–Niino planetary boundary scheme was developed within the Rapid Refresh ensemble system based on the Weather Research and Forecasting Model. Alone the stochastic parameter perturbations generate insufficient spread to be an alternative to the operational configuration that utilizes combinations of multiple parameterization schemes. However, when combined with other stochastic parameterization schemes, such as the stochastic kinetic energy backscatter (SKEB) scheme or the stochastic perturbation of physics tendencies (SPPT) scheme, the stochastic ensemble system has comparable forecast performance. An additional analysis quantifies the added value of combining SPP and SPPT over an ensemble that uses SPPT only, which is generally beneficial, especially for surface variables. The ensemble combining all three stochastic methods consistently produces the best spread–skill ratio and generally outperforms the multiphysics ensemble. The results of this study indicate that using a single-physics suite ensemble together with stochastic methods is an attractive alternative to multiphysics ensembles and should be considered in the design of future high-resolution regional and global ensembles.

A novel stochastic method for reconstructing daily precipitation times-series using tree-ring data from the western Canadian Boreal Forest

Abstract Tree ring data provide proxy records of historical hydroclimatic conditions that are widely used for reconstructing precipitation time series. Most previous applications are limited to annual time scales, though information about daily precipitation would enable a range of additional analyses of environmental processes to be investigated and modelled. We used statistical downscaling to simulate stochastic daily precipitation ensembles using dendrochronological data from the western Canadian boreal forest. The simulated precipitation series were generally consistent with observed precipitation data, though reconstructions were poorly constrained during short periods of forest pest outbreaks. The proposed multiple temporal scale precipitation reconstruction can generate annual daily maxima and persistent monthly wet and dry episodes, so that the observed and simulated ensembles have similar precipitation characteristics (i.e. magnitude, peak, and duration)—an improvement on previous modelling studies. We discuss how ecological disturbances may limit reconstructions by inducing non-linear responses in tree growth, and conclude with suggestions of possible applications and further development of downscaling methods for dendrochronological data.

Motion compensation using origin ensembles in awake small animal positron emission tomography

In emission tomographic imaging, the stochastic origin ensembles algorithm provides unique information regarding the detected counts given the measured data. Precision in both voxel and region-wise parameters may be determined for a single data set based on the posterior distribution of the count density allowing uncertainty estimates to be allocated to quantitative measures. Uncertainty estimates are of particular importance in awake animal neurological and behavioral studies for which head motion, unique for each acquired data set, perturbs the measured data. Motion compensation can be conducted when rigid head pose is measured during the scan. However, errors in pose measurements used for compensation can degrade the data and hence quantitative outcomes. In this investigation motion compensation and detector resolution models were incorporated into the basic origin ensembles algorithm and an efficient approach to computation was developed. The approach was validated against maximum liklihood—expectation maximisation and tested using simulated data. The resultant algorithm was then used to analyse quantitative uncertainty in regional activity estimates arising from changes in pose measurement precision. Finally, the posterior covariance acquired from a single data set was used to describe correlations between regions of interest providing information about pose measurement precision that may be useful in system analysis and design. The investigation demonstrates the use of origin ensembles as a powerful framework for evaluating statistical uncertainty of voxel and regional estimates. While in this investigation rigid motion was considered in the context of awake animal PET, the extension to arbitrary motion may provide clinical utility where respiratory or cardiac motion perturb the measured data.

Stratified drought analysis using a stochastic ensemble of simulated and in-situ soil moisture observations

Abstract This study proposes a multi-wavelet Bayesian ensemble of two Land Surface Models (LSMs) using in-situ observations for accurate estimation of soil moisture for Contiguous United States (CONUS). In the absence of a continuous, accurate in-situ soil moisture dataset at high spatial resolution, an ensemble of Noah and Mosaic LSMs is derived by performing a Bayesian Model Averaging (BMA) of several wavelet-based multi-resolution regression models (WR) of the simulated soil moisture from the LSMs and in-situ volumetric soil moisture dataset obtained from the U.S. Climate Reference Network (USCRN) field stations. This provides a proxy to the in-situ soil moisture dataset at 1/8th degree spatial resolution called Hybrid Soil Moisture (HSM) for three soil layers (1–10 cm, 10–40 cm and 40–100 cm) for the CONUS. The derived HSM is used further to study the layer-wise response of soil moisture to drought, highlighting the necessity of the ensemble approach and soil profile perspective for drought analysis. A correlation analysis between HSM, the long-term (PDSI, PHDI, SPI-9, SPI-12 and SPI-24) and the short-term (Palmer Z index, SPI-1 and SPI-6) drought indices is carried out for the nine climate regions of the U.S. indicating a higher sensitivity of soil moisture to drought conditions for the Southern U.S. Furthermore, a layer-wise soil moisture percentile approach is proposed and applied for drought reconstruction in CONUS with a focus on the Southern U.S. for the year 2011.

A 60‐year reconstructed high‐resolution local meteorological data set in Central Sahel (1950–2009): evaluation, analysis and application to land surface modelling

ABSTRACTThe Sahel has experienced strong climate variability in the past decades. Understanding its implications for natural and cultivated ecosystems is pivotal in a context of high population growth and mainly agriculture‐based livelihoods. However, efforts to model processes at the land–atmosphere interface are hindered, particularly when the multi‐decadal timescale is targeted, as climatic data are scarce, largely incomplete and often unreliable.This study presents the generation of a long‐term, high‐temporal resolution, multivariate local climatic data set for Niamey, Central Sahel. The continuous series spans the period 1950–2009 at a 30‐min timescale and includes ground station‐based meteorological variables (precipitation, air temperature, relative and specific humidity, air pressure, wind speed, downwelling long‐ and short‐wave radiation) as well as process‐modelled surface fluxes (upwelling long‐ and short‐wave radiation, latent, sensible and soil heat fluxes and surface temperature). A combination of complementary techniques (linear/spline regressions, a multivariate analogue method, artificial neural networks and recursive gap filling) was used to reconstruct missing meteorological data. The complete surface energy budget was then obtained for two dominant land cover types, fallow bush and millet, by applying the meteorological forcing data set to a finely field‐calibrated land surface model. Uncertainty in reconstructed data was expressed by means of a stochastic ensemble of plausible historical time series.Climatological statistics were computed at sub‐daily to decadal timescales and compared with local, regional and global data sets such as CRU and ERA‐Interim. The reconstructed precipitation statistics, ∼1 °C increase in mean annual temperature from 1950 to 2009, and mean diurnal and annual cycles for all variables were in good agreement with previous studies. The new data set, denoted NAD (Niamey Airport‐derived set) and publicly available, can be used to investigate the water and energy cycles in Central Sahel, while the methodology can be applied to reconstruct series at other stations.

Predictability and Dynamics of Tropical Cyclone Rapid Intensification Deduced from High-Resolution Stochastic Ensembles

AbstractRapid intensification (RI) of tropical cyclones (TCs) remains one of the most challenging issues in TC prediction. This study investigates the predictability of RI, the uncertainty in predicting RI timing, and the dynamical processes associated with RI. To address the question of environmental versus internal control of RI, five high-resolution ensembles of Hurricane Earl (2010) were generated with scale-dependent stochastic perturbations from synoptic to convective scales. Although most members undergo RI and intensify into major hurricanes, the timing of RI is highly uncertain. While environmental conditions including SST control the maximum TC intensity and the likelihood of RI during the TC lifetime, both environmental and internal factors contribute to uncertainty in RI timing. Complex interactions among environmental vertical wind shear, the mean vortex, and internal convective processes govern the TC intensification process and lead to diverse pathways to maturity. Although the likelihood of Earl undergoing RI seems to be predictable, the exact timing of RI has a stochastic component and low predictability.Despite RI timing uncertainty, two dominant modes of RI emerged. One group of members undergoes RI early in the storm life cycle; the other one later. In the early RI cases, a rapidly contracting radius of maximum wind accompanies the development of the eyewall during RI. The late RI cases have a well-developed eyewall prior to RI, while an upper-level warm core forms during the RI process. These differences indicate that RI is associated with distinct physical processes during particular stages of the TC life cycle.

Retooling Poverty Targeting Using Out-of-Sample Validation and Machine Learning

Proxy means test (PMT) poverty targeting tools have become common tools for beneficiary targeting and poverty assessment where full means tests are costly. Currently popular estimation procedures for generating these tools prioritize minimization of in-sample prediction errors; however, the objective in generating such tools is out-of-sample prediction. We present evidence that prioritizing minimal out-of-sample error, identified through cross-validation and stochastic ensemble methods, in PMT tool development can substantially improve the out-of-sample performance of these targeting tools. We take the United States Agency for International Development (USAID) poverty assessment tool and base data for demonstration of these methods; however, the methods applied in this paper should be considered for PMT and other poverty-targeting tool development more broadly.

Synchronizing stochastic circadian oscillators in single cells of Neurospora crassa.

The synchronization of stochastic coupled oscillators is a central problem in physics and an emerging problem in biology, particularly in the context of circadian rhythms. Most measurements on the biological clock are made at the macroscopic level of millions of cells. Here measurements are made on the oscillators in single cells of the model fungal system, Neurospora crassa, with droplet microfluidics and the use of a fluorescent recorder hooked up to a promoter on a clock controlled gene-2 (ccg-2). The oscillators of individual cells are stochastic with a period near 21 hours (h), and using a stochastic clock network ensemble fitted by Markov Chain Monte Carlo implemented on general-purpose graphical processing units (or GPGPUs) we estimated that >94% of the variation in ccg-2 expression was stochastic (as opposed to experimental error). To overcome this stochasticity at the macroscopic level, cells must synchronize their oscillators. Using a classic measure of similarity in cell trajectories within droplets, the intraclass correlation (ICC), the synchronization surface ICC is measured on >25,000 cells as a function of the number of neighboring cells within a droplet and of time. The synchronization surface provides evidence that cells communicate, and synchronization varies with genotype.

Localization and spectral isolation of special nuclear material using stochastic image reconstruction

Abstract In this work we present a technique for isolating the gamma-ray and neutron energy spectra from multiple radioactive sources localized in an image. Image reconstruction algorithms for radiation scatter cameras typically focus on improving image quality. However, with scatter cameras being developed for non-proliferation applications, there is a need for not only source localization but also source identification. This work outlines a modified stochastic origin ensembles algorithm that provides localized spectra for all pixels in the image. We demonstrated the technique by performing three experiments with a dual-particle imager that measured various gamma-ray and neutron sources simultaneously. We showed that we could isolate the peaks from 22 Na and 137 Cs and that the energy resolution is maintained in the isolated spectra. To evaluate the spectral isolation of neutrons, a 252 Cf source and a PuBe source were measured simultaneously and the reconstruction showed that the isolated PuBe spectrum had a higher average energy and a greater fraction of neutrons at higher energies than the 252 Cf. Finally, spectrum isolation was used for an experiment with weapons grade plutonium, 252 Cf, and AmBe. The resulting neutron and gamma-ray spectra showed the expected characteristics that could then be used to identify the sources.

Assessing the relative importance of parameter and forcing uncertainty and their interactions in conceptual hydrological model simulations

Abstract Predictions of river flow dynamics provide vital information for many aspects of water management including water resource planning, climate adaptation, and flood and drought assessments. Many of the subjective choices that modellers make including model and criteria selection can have a significant impact on the magnitude and distribution of the output uncertainty. Hydrological modellers are tasked with understanding and minimising the uncertainty surrounding streamflow predictions before communicating the overall uncertainty to decision makers. Parameter uncertainty in conceptual rainfall-runoff models has been widely investigated, and model structural uncertainty and forcing data have been receiving increasing attention. This study aimed to assess uncertainties in streamflow predictions due to forcing data and the identification of behavioural parameter sets in 31 Irish catchments. By combining stochastic rainfall ensembles and multiple parameter sets for three conceptual rainfall-runoff models, an analysis of variance model was used to decompose the total uncertainty in streamflow simulations into contributions from (i) forcing data, (ii) identification of model parameters and (iii) interactions between the two. The analysis illustrates that, for our subjective choices, hydrological model selection had a greater contribution to overall uncertainty, while performance criteria selection influenced the relative intra-annual uncertainties in streamflow predictions. Uncertainties in streamflow predictions due to the method of determining parameters were relatively lower for wetter catchments, and more evenly distributed throughout the year when the Nash-Sutcliffe Efficiency of logarithmic values of flow (lnNSE) was the evaluation criterion.