Large Ensemble Size Research Articles

Impacts of Initial Condition Perturbation Blending in 10- and 40-Member Convection-Allowing Ensemble Forecasts

Abstract A series of convection-allowing 36-h ensemble forecasts during the 2018 spring season are used to better understand the impacts of ensemble configuration and blending different sources of initial condition (IC) perturbation. Ten- and forty-member ensemble configurations are initialized with the multiscale IC perturbations generated as a product of convective-scale data assimilation (MULTI) and initialized with the MULTI IC perturbations blended with IC perturbations downscaled from coarser-resolution ensembles (BLEND). The forecast performance of both precipitation and nonprecipitation variables is consistently improved by the larger ensemble size. The benefit of the larger ensemble is largely, but not entirely, due to compensating for underdispersion in the fixed-physics ensemble configuration. A consistent improvement in precipitation forecast skill results from blending in the 10-member ensemble configuration, corresponding to a reduction in the ensemble calibration error (i.e., reliability component of Brier score). In the 40-member ensemble configuration, the advantage of blending is limited to the ∼18–22-h lead times at all precipitation thresholds and the ∼35–36-h lead times at the lowest threshold, both corresponding to an improved resolution component of the Brier score. The advantage of blending in the 40-member ensemble during the diurnal convection maximum of ∼18–22-h lead times is primarily due to cases with relatively weak synoptic-scale forcing, while advantages at later lead times beyond ∼30-h lead time are most prominent on cases with relatively strong synoptic-scale forcing. The impacts of blending and ensemble configuration on forecasts of nonprecipitation variables are generally consistent with the impacts on the precipitation forecasts.

Convergence of ensemble forecast distributions in weak and strong forcing convective weather regimes

AbstractThe constraint of computational power and the huge number of degrees of freedom of the atmosphere means a sampling uncertainty exists in probabilistic ensemble forecasts. In our previous study, the uncertainty could be quantified, creating a convergence measure which converges proportional to in the limit of large ensemble size . This power law can then be extrapolated to determine how sampling uncertainty would decrease with larger ensemble sizes and hence find the necessary ensemble size. It is unknown, however, how the sampling uncertainty depends on different weather regimes. This study extends the previous idealised ensemble developed, by including weak and strong forcing convective weather regimes, to look at how sampling uncertainty convergence differs in each. Two ‐member ensembles were run, with weak and strong forcing respectively. Comparisons with a kilometre‐scale weather prediction model ensured realistic weak and strong forcing regimes by comparing the rain, convective available potential energy (CAPE), convective adjustment timescale, and distribution shapes throughout the diurnal cycle. Differences in distribution shape between the regimes led to differences in the convergence measure. Large differences in spread between weak and strong forcing runs throughout the hr period led to large differences in sampling uncertainty of the mean and standard deviation, which could be quantified according to well‐known equations. The timing of these differences was case‐dependent. For extreme statistics such as the quantile and for cases where there was precipitation, the moisture variables for the weak forcing case had the largest sampling uncertainty and required the most members for convergence proportional to . This was due to the tails of the weak forcing moisture variables containing the least amount of density. Different ensemble sizes will hence be required depending on whether one is in the weak or strong forcing convective weather regime.

Extreme precipitation and temperature indices under future climate change in central Asia based on CORDEX-CORE

The present study analyzes the projected changes of extreme climate indices over Central Asia using regional climate model (RCM) simulations from the Coordinated Regional Climate Downscaling Experiment (CORDEX) - Coordinated Output for Regional Evaluations (CORE). The extreme indices are based on precipitation and temperature and are inspected for present (1981–2005) and future periods - near- (2031–2055) and far-future (2071–2095) - to assess the long-term climate change under the representative concentration pathway RCP8.5. Projected changes are analyzed for three different model ensembles. These ensembles are based on CORDEX-Central Asia (ENS_CAS, four ensemble members) and CORDEX-East Asia (ENS_EAS, six ensemble members), and a combination of both (ENS, ten ensemble members) for our study area centered over high mountain Asia, called Central East Asia (CEAS). For precipitation indices, an increase of consecutive dry days (CDD) in ENS_EAS and a slight to moderate decrease in northern parts in ENS_CAS during near-future is observed. Consecutive wet days (CWD), very heavy precipitation events (R20mm), maximum one-day precipitation (RX1day), and very wet days (R95p) are projected to increase in most areas. All indices show a further intensification towards the end of the century over large parts of the domain, e.g., + 7.8% / +5.6 days for CDD, + 96.6% / +0.26 days for R20mm, and + 19.7% for RX1day as median of ENS over CEAS. For temperature indices, the ensembles project a strong increase over the high mountain regions and southern parts for consecutive summer days (CSU, + 108.5% / +38.3 days), heat wave duration index (HWDI, + 1379.1% / +91.37 days), and the percentage of very hot days (TX90p, + 391.1% / +34.54 days). Accordingly, the number of consecutive frost days (CFD, -43.7% / -25.2 days) and the percentage of very cold days (TX10p, -83.4% / -8.13 days) are projected to decrease. The first-time usage of CORDEX-CORE and the larger ensemble size by considering simulations from overlapping domains increase the robustness of the findings from earlier studies. However, some discrepancies in the projected changes prevail among the different RCMs being part of the two CORDEX-domains and in specific landscapes like complex mountainous or lake areas. These uncertainties may be tackled by further model development with improved land-surface processes and potentially higher spatial resolution.

Deep learning-based ensemble forecast and predictability analysis of the Kuroshio intrusion into the South China Sea

Abstract The Kuroshio intrusion (KI) into the South China Sea (SCS) significantly affects the environment, ecology, and climate change of the SCS. However, due to the nonlinearity of KI, its numerical prediction often requires large ensemble size to measure prediction uncertainty. The huge computational costs of large numbers of members and high-resolution numerical models pose significant challenges for KI prediction. We, therefore, construct a Kuroshio ensemble deep learning prediction system (KurNet) through taking different values of parameters to predict KI paths because the deep learning models have high prediction skills and low computational cost. The KurNet containing 64 ensemble members can not only output ensemble mean forecast result of the Kuroshio path, but also estimate probability density functions for the path types. The KurNet illustrates a high predictive ability for the KI with the mean classification accuracy of 71.9% and root mean square error of 0.913 on the testing set, which is superior to the single control prediction by ∼1.0–2.9%, although the control prediction model is selected as one of the ensemble members with the best predictive ability on the validation set. Furthermore, the predictability analysis of 10 KI events indicates that when the lead time is 3 days, the most important areas are in the east of Luzon Island due to the upstream Kuroshio transport. As the lead time increases, the most important area is in the Luzon Strait due to the eddy activity. Observing system simulation experiments reveal that the KI forecast skill can be enhanced by ∼12–18%, when uncertainties of the input data in these important regions are removed.

Assessment of the Pan-Arctic Accelerated Rate of Sea Ice Decline in CMIP6 Historical Simulations

Abstract Arctic sea ice loss in response to a warming climate is assessed in 42 models participating in phase 6 of the Coupled Model Intercomparison Project (CMIP6). Sea ice observations show a significant acceleration in the rate of decline commencing near the turn of the twenty-first century. It is our assertion that state-of-the-art climate models should qualitatively reflect this accelerated trend within the limitations of internal variability and observational uncertainty. Our analysis shows that individual CMIP6 simulations of sea ice depict a wide range of model spread on biases and anomaly trends both across models and among their ensemble members. While the CMIP6 multimodel mean captures the observed sea ice area (SIA) decline relatively well, an individual model’s ability to represent the acceleration in sea ice decline remains a challenge. Seventeen (40%) out of 42 CMIP6 models and 37 (13%) out of the total 286 ensemble members reasonably capture the observed trends and acceleration in SIA decline. In addition, a larger ensemble size appears to increase the odds for a model to include at least one ensemble member skillfully representing the accelerated SIA trends. Simulations of sea ice volume (SIV) show much larger spread and uncertainty than SIA; however, due to limited availability of sea ice thickness data, these are not as well constrained by observations. Finally, we find that models with more ocean heat transport simulate larger sea ice declines, which suggests an emergent constraint in CMIP6 ensembles. This relationship points to the need for better understanding and modeling of ice–ocean interactions, especially with respect to frazil ice growth.

The Local Unscented Transform Kalman Filter for the Weather Research and Forecasting Model

In this study, the local unscented transform Kalman filter (LUTKF) proposed in the previous study estimates the state of the Weather Research and Forecasting (WRF) model through local analysis. Real observations are assimilated to investigate the analysis performance of the WRF-LUTKF system. The WRF model as a regional numerical weather prediction (NWP) model is widely used to explain the atmospheric state for mesoscale meteorological fields, such as operational forecasting and atmospheric research applications. For the LUTKF based on the sigma-point Kalman filter (SPKF), the state of the nonlinear system is estimated by propagating ensemble members through the unscented transformation (UT) without making any linearization assumptions for nonlinear models. The main objective of this study is to examine the feasibility of mesoscale data assimilations for the LUTKF algorithm using the WRF model and real observations. Similar to the local ensemble transform Kalman filter (LETKF), by suppressing the impact of distant observations on model state variables through localization schemes, the LUTKF can eliminate spurious long-distance correlations in the background covariance, which are induced by the sampling error due to the finite ensemble size; therefore, the LUTKF used in the WRF-LUTKF system can efficiently execute the data assimilation with a small ensemble size. Data assimilation test results demonstrate that the LUTKF can provide reliable analysis performance in estimating the WRF model state with real observations. Experiments with various ensemble size show that the LETKF can provide better estimation results with a larger ensemble size, while the LUTKF can achieve accurate and reliable assimilation results even with a smaller ensemble size.

A Comparative Study on the Set-size Effects in Polygon and Words in Visual Search Task

Collection size has a very important effect on visual working memory. In this paper, we use an interview and repeated measure design to empirically investigate the relationship between larger ensemble sizes (more than four distractors) and reaction times for participant responses. We set up a scene for daily observation of polygons and words. Participants were required to identify a correctly written Chinese character and the target item, and the pentagon in the hexagon (distractor). The study found that there was no significant difference in the impact trend of large and small groups on people, and there was a high degree of consistency. At the same time, this experiment also found that the effect of ensemble size may be different for males and females. And the reaction time has a great relationship with the location of the target and the reading habits of the subjects. This requires further exploration.

Convergence of forecast distributions in a 100,000‐member idealised convective‐scale ensemble

AbstractMany operational weather services use ensembles of forecasts to generate probabilistic predictions. Computational costs generally limit the size of the ensemble to fewer than 100 members, although the large number of degrees of freedom in the forecast model would suggest that a vastly larger ensemble would be required to represent the forecast probability distribution accurately. In this study, we use a computationally efficient idealised model that replicates key properties of the dynamics and statistics of cumulus convection to identify how the sampling uncertainty of statistical quantities converges with ensemble size. Convergence is quantified by computing the width of the 95% confidence interval of the sampling distribution of random variables, using bootstrapping on the ensemble distributions at individual time and grid points. Using ensemble sizes of up to 100,000 members, it was found that for all computed distribution properties, including mean, variance, skew, kurtosis, and several quantiles, the sampling uncertainty scaled as for sufficiently large ensemble size . This behaviour is expected from the Central Limit Theorem, which further predicts that the magnitude of the uncertainty depends on the distribution shape, with a large uncertainty for statistics that depend on rare events. This prediction was also confirmed, with the additional observation that such statistics also required larger ensemble sizes before entering the asymptotic regime. By considering two methods for evaluating asymptotic behaviour in small ensembles, we show that the large‐ theory can be applied usefully for some forecast quantities even for the ensemble sizes in operational use today.

Emergent microrobotic oscillators via asymmetry-induced order

Spontaneous oscillations on the order of several hertz are the drivers of many crucial processes in nature. From bacterial swimming to mammal gaits, converting static energy inputs into slowly oscillating power is key to the autonomy of organisms across scales. However, the fabrication of slow micrometre-scale oscillators remains a major roadblock towards fully-autonomous microrobots. Here, we study a low-frequency oscillator that emerges from a collective of active microparticles at the air-liquid interface of a hydrogen peroxide drop. Their interactions transduce ambient chemical energy into periodic mechanical motion and on-board electrical currents. Surprisingly, these oscillations persist at larger ensemble sizes only when a particle with modified reactivity is added to intentionally break permutation symmetry. We explain such emergent order through the discovery of a thermodynamic mechanism for asymmetry-induced order. The on-board power harvested from the stabilised oscillations enables the use of electronic components, which we demonstrate by cyclically and synchronously driving a microrobotic arm. This work highlights a new strategy for achieving low-frequency oscillations at the microscale, paving the way for future microrobotic autonomy.

Scalable uncertainty quantification for deep operator networks using randomized priors

We present a simple and effective approach for posterior uncertainty quantification in deep operator networks (DeepONets); an emerging paradigm for supervised learning in function spaces. We adopt a frequentist approach based on randomized prior ensembles, and put forth an efficient vectorized implementation for fast parallel inference on accelerated hardware. Through a collection of representative examples in computational mechanics and climate modeling, we show that the merits of the proposed approach are fourfold. (1) It can provide more robust and accurate predictions when compared against deterministic DeepONets. (2) It shows great capability in providing reliable uncertainty estimates on scarce data sets with multi-scale function pairs. (3) It can effectively detect out-of-distribution and adversarial examples. (4) It can seamlessly quantify uncertainty due to model bias, as well as noise corruption in the data. Finally, we provide an optimized JAX library called UQDeepONet that can accommodate large model architectures, large ensemble sizes, as well as large data sets with excellent parallel performance on accelerated hardware, thereby enabling uncertainty quantification for DeepONets in realistic large-scale applications. All code and data accompanying this manuscript will be made available at https://github.com/PredictiveIntelligenceLab/UQDeepONet.

Distributions and convergence of forecast variables in a 1,000‐member convection‐permitting ensemble

AbstractThe errors in numerical weather forecasts resulting from limited ensemble size are explored using 1,000‐member forecasts of convective weather over Germany at 3‐km resolution. A large number of forecast variables at different lead times were examined, and their distributions could be classified into three categories: quasi‐normal (e.g., tropospheric temperature), highly skewed (e.g. precipitation), and mixtures (e.g., humidity). Dependence on ensemble size was examined in comparison to the asymptotic convergence law that the sampling error decreases proportional to N−1/2 for large enough ensemble size N, independent of the underlying distribution shape. The asymptotic convergence behavior was observed for the ensemble mean of all forecast variables, even for ensemble sizes less than 10. For the ensemble standard deviation, sizes of up to 100 were required for the convergence law to apply. In contrast, there was no clear sign of convergence for the 95th percentile even with 1,000 members. Methods such as neighborhood statistics or prediction of area‐averaged quantities were found to improve accuracy, but only for variables with random small‐scale variability, such as convective precipitation.

21st Century alpine climate change

A comprehensive assessment of twenty-first century climate change in the European Alps is presented. The analysis is based on the EURO-CORDEX regional climate model ensemble available at two grid spacings (12.5 and 50 km) and for three different greenhouse gas emission scenarios (RCPs 2.6, 4.5 and 8.5). The core simulation ensemble has been subject to a dedicated evaluation exercise carried out in the frame of the CH2018 Climate Scenarios for Switzerland. Results reveal that the entire Alpine region will face a warmer climate in the course of the twenty-first century for all emission scenarios considered. Strongest warming is projected for the summer season, for regions south of the main Alpine ridge and for the high-end RCP 8.5 scenario. Depending on the season, medium to high elevations might experience an amplified warming. Model uncertainty can be considerable, but the major warming patterns are consistent across the ensemble. For precipitation, a seasonal shift of precipitation amounts from summer to winter over most parts of the domain is projected. However, model uncertainty is high and individual simulations can show change signals of opposite sign. Daily precipitation intensity is projected to increase in all seasons and all sub-domains, while the wet-day frequency will decrease in the summer season. The projected temperature change in summer is negatively correlated with the precipitation change, i.e. simulations and/or regions with a strong seasonal mean warming typically show a stronger precipitation decrease. By contrast, a positive correlation between temperature change and precipitation change is found for winter. Among other indicators, snow cover will be strongly affected by the projected climatic changes and will be subject to a widespread decrease except for very high elevation settings. In general and for all indicators, the magnitude of the change signals increases with the assumed greenhouse gas forcing, i.e., is smallest for RCP 2.6 and largest for RCP 8.5 with RCP 4.5 being located in between. These results largely agree with previous works based on older generations of RCM ensembles but, due to the comparatively large ensemble size and the high spatial resolution, allow for a more decent assessment of inherent projection uncertainties and of spatial details of future Alpine climate change.

Seasonal-to-decadal prediction of El Ni\xf1o\u2013Southern Oscillation and Pacific Decadal Oscillation

The growing demand for skillful near-term climate prediction encourages an improved prediction of low-frequency sea surface temperature (SST) variabilities such as the El Niño-Southern Oscillation (ENSO) and Pacific Decadal Oscillation (PDO). This study assesses their seasonal-to-decadal prediction skills using large ensembles of the Coupled Model Intercomparison Project phases 5 and 6 retrospective decadal predictions. A multi-model ensemble reforecast successfully predicts ENSO over a year in advance. While its seasonal prediction skill in the following spring and summer is achieved by multi-model ensemble averaging of relatively smaller ensemble members, the multi-year prediction of winter ENSO needs a larger ensemble size. The PDO is significantly predicted at a lead time of five-to-nine years but such a long-lead prediction is sourced from external radiative forcing instead of initialization, as evidenced from uninitialized historical simulations. The effect of model initialization lasts only two years. These results confirm that both the model initialization and the proper estimate of near-term radiative forcing are required to improve the seasonal-to-decadal prediction in the Pacific Basin.

Stochastic simplex approximation gradient for reservoir production optimization: Algorithm testing and parameter analysis

Production optimization is an effective technique to maximize the oil recovery or the net present value in reservoir development. Recently, the stochastic simplex approximation gradient (StoSAG) optimization algorithm draws significant attention in the optimization algorithm family. It shows high searching quality in large-scale engineering problems. However, its optimization performance and features are not fully understood. This study evaluated and analyzed the influence of some key parameters related to the optimization process of StoSAG including the ensemble size to estimate the approximation gradient, the step size, the cut number, the perturbation size, and the initial position by using 47 mathematical benchmark functions. Statistical analysis was employed to diminish the randomness of the algorithm. The quality of the optimization results, the convergence, and the computational time consuming were analyzed and compared. The parameter selection strategy was presented. The results showed that a larger ensemble size was not always favorable to obtain better optimization results. The increase of the search step size was favorable to escape from the local optimum. A large step size needed to match a large cut number. The increase of cut number was beneficial to increase the local searchability, but also made the algorithm more easily fall into the local optimum. The random initial position was beneficial to find the global optimal point. Moreover, the effectiveness of the parameter selection strategy was tested by a classical reservoir production optimization example. The final net present value (NPV) for water flooding reservoir production optimization substantially increased, which indicated the excellent performance of StoSAG by adjusting the key parameters.

Parallel Implementation of the Deterministic Ensemble Kalman Filter for Reservoir History Matching

In this paper, the deterministic ensemble Kalman filter is implemented with a parallel technique of the message passing interface based on our in-house black oil simulator. The implementation is separated into two cases: (1) the ensemble size is greater than the processor number and (2) the ensemble size is smaller than or equal to the processor number. Numerical experiments for estimations of three-phase relative permeabilities represented by power-law models with both known endpoints and unknown endpoints are presented. It is shown that with known endpoints, good estimations can be obtained. With unknown endpoints, good estimations can still be obtained using more observations and a larger ensemble size. Computational time is reported to show that the run time is greatly reduced with more CPU cores. The MPI speedup is over 70% for a small ensemble size and 77% for a large ensemble size with up to 640 CPU cores.

A New Scheme of Adaptive Covariance Inflation for Ensemble Filtering Data Assimilation

Due to the model and sampling errors of the finite ensemble, the background ensemble spread becomes small and the error covariance is underestimated during filtering for data assimilation. Because of the constraint of computational resources, it is difficult to use a large ensemble size to reduce sampling errors in high-dimensional real atmospheric and ocean models. Here, based on Bayesian theory, we explore a new spatially and temporally varying adaptive covariance inflation algorithm. To increase the statistical presentation of a finite background ensemble, the prior probability of inflation obeys the inverse chi-square distribution, and the likelihood function obeys the t distribution, which are used to obtain prior or posterior covariance inflation schemes. Different ensemble sizes are used to compare the assimilation quality with other inflation schemes within both the perfect and biased model frameworks. With two simple coupled models, we examined the performance of the new scheme. The results show that the new inflation scheme performed better than existing schemes in some cases, with more stability and fewer assimilation errors, especially when a small ensemble size was used in the biased model. Due to better computing performance and relaxed demand for computational resources, the new scheme has more potential applications in more comprehensive models for prediction initialization and reanalysis. In a word, the new inflation scheme performs well for a small ensemble size, and it may be more suitable for large-scale models.

A novel sampling-free algorithm for subsurface data assimilation using Gaussian process-derived sensitivities

Accurate characterization of hydraulic parameters is vital for modeling subsurface flow and transport. In the past decade, ensemble-based methods have been widely applied in estimating unknown parameters from state measurements. However, these methods require sufficiently large ensemble sizes to guarantee the accuracy of the ensemble averaged parameter sensitivities, leading to heavy computational burdens especially in large-scale problems. Although different surrogates have been introduced to alleviate the computational burden, the sensitivity information therein is still calculated by sampling the surrogate. Therefore, the sampling error is still inevitable. In this study, we propose an adaptive Gaussian process (GP) based iterative smoother (GPIS) algorithm in which the parameter sensitivity indices are analytically derived from the GP surrogate. During the iterations, the GP surrogate is adaptively refined by taking the updated parameter realizations as new base points. Both numerical and experimental cases are conducted to test the effectiveness of GPIS. We also compare its performance in estimating the heterogeneous hydraulic conductivity field with that of its prototype iterative ensemble smoother (IES) and our previously developed GP based iterative ensemble smoother (GPIES). Results show that, using the GP-derived sensitivity indices, GPIS shows advantages over GPIES in terms of both estimation accuracy and computational efficiency. Although subsurface flow and transport problems are considered in this work, the proposed method can be equally applied in other hydrological problems.

Mode delocalization in disordered photonic Chern insulator

In disordered two dimensional Chern insulators, a single bulk extended mode is predicted to exist per band, up to a critical disorder strength; all the other bulk modes are localized. This behavior contrasts strongly with topologically trivial two-dimensional phases, whose modes all become localized in the presence of disorder. Using a tight-binding model of a realistic photonic Chern insulator, we show that delocalized bulk eigenstates can be observed in an experimentally realistic setting. This requires the selective use of resonator losses to suppress topological edge states, and acquiring sufficiently large ensemble sizes using variable resonator detunings.

Efficient Dimensionality Reduction Methods in Reservoir History Matching

Production forecasting is the basis for decision making in the oil and gas industry, and can be quite challenging, especially in terms of complex geological modeling of the subsurface. To help solve this problem, assisted history matching built on ensemble-based analysis such as the ensemble smoother and ensemble Kalman filter is useful in estimating models that preserve geological realism and have predictive capabilities. These methods tend, however, to be computationally demanding, as they require a large ensemble size for stable convergence. In this paper, we propose a novel method of uncertainty quantification and reservoir model calibration with much-reduced computation time. This approach is based on a sequential combination of nonlinear dimensionality reduction techniques: t-distributed stochastic neighbor embedding or the Gaussian process latent variable model and clustering K-means, along with the data assimilation method ensemble smoother with multiple data assimilation. The cluster analysis with t-distributed stochastic neighbor embedding and Gaussian process latent variable model is used to reduce the number of initial geostatistical realizations and select a set of optimal reservoir models that have similar production performance to the reference model. We then apply ensemble smoother with multiple data assimilation for providing reliable assimilation results. Experimental results based on the Brugge field case data verify the efficiency of the proposed approach.

Error suppression in adiabatic quantum computing with qubit ensembles

Incorporating protection against quantum errors into adiabatic quantum computing (AQC) is an important task due to the inevitable presence of decoherence. Here, we investigate an error-protected encoding of the AQC Hamiltonian, where qubit ensembles are used in place of qubits. Our Hamiltonian only involves total spin operators of the ensembles, offering a simpler route towards error-corrected quantum computing. Our scheme is particularly suited to neutral atomic gases where it is possible to realize large ensemble sizes and produce ensemble-ensemble entanglement. We identify a critical ensemble size Nc where the nature of the first excited state becomes a single particle perturbation of the ground state, and the gap energy is predictable by mean-field theory. For ensemble sizes larger than Nc, the ground state becomes protected due to the presence of logically equivalent states and the AQC performance improves with N, as long as the decoherence rate is sufficiently low.