Ensemble Correlation Research Articles

Distinct neural ensemble response statistics are associated with recognition and discrimination of natural sound textures

The perception of sound textures, a class of natural sounds defined by statistical sound structure such as fire, wind, and rain, has been proposed to arise through the integration of time-averaged summary statistics. Where and how the auditory system might encode these summary statistics to create internal representations of these stationary sounds, however, is unknown. Here, using natural textures and synthetic variants with reduced statistics, we show that summary statistics modulate the correlations between frequency organized neuron ensembles in the awake rabbit inferior colliculus (IC). These neural ensemble correlation statistics capture high-order sound structure and allow for accurate neural decoding in a single trial recognition task with evidence accumulation times approaching 1 s. In contrast, the average activity across the neural ensemble (neural spectrum) provides a fast (tens of milliseconds) and salient signal that contributes primarily to texture discrimination. Intriguingly, perceptual studies in human listeners reveal analogous trends: the sound spectrum is integrated quickly and serves as a salient discrimination cue while high-order sound statistics are integrated slowly and contribute substantially more toward recognition. The findings suggest statistical sound cues such as the sound spectrum and correlation structure are represented by distinct response statistics in auditory midbrain ensembles, and that these neural response statistics may have dissociable roles and time scales for the recognition and discrimination of natural sounds.

Influence of uniform momentum zones on frictional drag within the turbulent boundary layer* *Project supported by the National Natural Science Foundation of China (Grant Nos. 11732010, 11972251, 11872272, 11902218, and 11802195) and the National Key R&D Program of China (Grant No. 2018YFC0705300).

Based on a set of experimental databases of turbulent boundary layers obtained from particle image velocimetry in the streamwise-wall-normal plane at friction-velocity-based Reynolds number Reτ = 612, the influence of uniform momentum zones (UMZs) on the skin-friction drag is investigated. The skin-friction drag is measured by the single-pixel ensemble correlation method. The results show that the velocity fields with the number of UMZs larger than the mean value have a relatively low skin-friction drag, while the velocity fields with the number of UMZs less than the mean value have a relatively high skin-friction drag. By analyzing the statistical characteristics of UMZs, the dynamic correlation between the UMZs and skin-friction drag is explored. The velocity fields with a low number of UMZs present a sweep event. These sweep motions intensify the small-scale Reynolds shear stress in the near-wall region by modulation effects. The enhancement of small-scale Reynolds shear stress is the direct reason for the high skin-friction drag. Increasing the proportion of velocity fields with high UMZs amount may be a direction to reduce the skin-friction drag within the TBL.

Dynamical Structures of Cross-Domain Forecast Error Covariance of a Simulated Tropical Cyclone in a Convection-Permitting Coupled Atmosphere–Ocean Model

AbstractUnderstanding the dynamics of the flow-dependent forecast error covariance across the air–sea interface is beneficial toward revealing the potential influences of strongly coupled data assimilation on tropical cyclone (TC) initialization in coupled models, and the fundamental dynamics associated with TC air–sea interactions. A 200-member ensemble of convection-permitting forecasts from a coupled atmosphere–ocean regional model is used to investigate the forecast error covariance across the oceanic and atmospheric domains during the rapid intensification of Hurricane Florence (2018). Forecast uncertainties in both atmospheric and oceanic domains, from an Eulerian perspective, increase with forecast lead time, mainly from TC displacement errors. In a storm-relative framework, the ensemble forecast uncertainties in both domains are predominantly caused by differences in the simulated storm intensity and structure. The largest ensemble spread in the atmospheric pressure, temperature, and wind fields can be found within the TC inner-core region. Alternatively, the largest ensemble spread in the upper-ocean currents and temperature fields are located along the cold wake behind the storm. Cross-domain ensemble correlations between simulated atmospheric (oceanic) observations and oceanic (atmospheric) state variables in the storm-relative coordinates are highly anisotropic, variable dependent, and ultimately driven by the dynamics of TC air–sea interactions. Meaningful and dynamically consistent cross-domain ensemble correlations suggest that it is possible to use atmospheric and oceanic observations to simultaneously update state variables associated with the coupled ocean–atmosphere prediction of TCs using strongly coupled data assimilation. Sensitivity experiments demonstrate that at least 60–80 ensemble members are required to represent physically consistent cross-domain correlations and minimize sampling errors.

Monte Carlo ensemble correlation coefficient for association detection

Data characteristics are often summarized and represented by a set of variables. Identifying the relationship between these variables is crucial for prediction, hypothesis testing, and decision making. The relation between two variables is often quantified using a correlation factor. Once the correlation between a response and an independent variable is quantified, it can be used to make predictions regarding response variable for the observed factor. That is, if two variables are correlated, by observing one, we can make predictions about the other one. A more accurate prediction can be made where there is strong relationship between variables. Several correlation factors have been introduced. Among them, Pearson’s Correlation Coefficient has been commonly used, while Distance Correlation and Maximal Information Coefficient have been recently introduced to address the shortcomings of Pearson’s Correlation Coefficient. These correlation coefficients are developed to measure associations in different trends. For example, Pearson’s Correlation is used when dealing with linear trends while Spearman’s correlation is used when dealing with monotonic trends. However, in many applications, the underlying relationship is not obvious to determine the appropriate choice of the correlation coefficient. In this paper, we compare these factors through a series of simulations and we propose a single generic factor by aggregating these factors for general applications.

The Bio3D packages for structural bioinformatics.

Bio3D is a family of R packages for the analysis of biomolecular sequence, structure, and dynamics. Major functionality includes biomolecular database searching and retrieval, sequence and structure conservation analysis, ensemble normal mode analysis, protein structure and correlation network analysis, principal component, and related multivariate analysis methods. Here, we review recent package developments, including a new underlying segregation into separate packages for distinct analysis, and introduce a new method for structure analysis named ensemble difference distance matrix analysis (eDDM). The eDDM approach calculates and compares atomic distance matrices across large sets of homologous atomic structures to help identify the residue wise determinants underlying specific functional processes. An eDDM workflow is detailed along with an example application to a large protein family. As a new member of the Bio3D family, the Bio3D-eddm package supports both experimental and theoretical simulation-generated structures, is integrated with other methods for dissecting sequence-structure-function relationships, and can be used in a highly automated and reproducible manner. Bio3D is distributed as an integrated set of platform independent open source R packages available from: http://thegrantlab.org/bio3d/.

SINGLE-PIXEL ENSEMBLE CORRELATION ALGORITHM FOR BOUNDARY MEASUREMENT ON AXISYMMETRIC BOATTAIL SURFACE

Particle image velocimetry (PIV) measurement is an important technique in analyzing velocity fields. However, in traditional cross-correlation algorithm, the resolution of velocity fields is limited by the size of interrogation windows and the boundary layer was not captured well. In this study, single-pixel ensemble correlation algorithm was applied to analyze flow near the surface of an axisymmetric boattail model. The initial images data was obtained by experimental methods with the setup of PIV measurement. The results showed that the new algorithm was considerably improved resolution of flow fields near the surface and could be used to measure boundary-layer profile. Detailed characteristics of boundary-layer profile at different flow conditions were discussed. Interestingly, boundarylayer profile does not change much before the shoulder. However, the size of separation bubble on the boattail surface highly decreases with increasing Reynolds number. The study provides initial results of flow fields, which could be useful for further investigation of drag reduction by numerical and experimental techniques.

Evaluating Ensemble Kalman Filter Analyses of Severe Hailstorms on 8 May 2017 in Colorado: Effects of State Variable Updating and Multimoment Microphysics Schemes on State Variable Cross Covariances

Abstract Ensemble Kalman filter (EnKF) analyses of the storms associated with the 8 May 2017 Colorado severe hail event using either the Milbrandt and Yau (MY) or the NSSL double-moment bulk microphysics scheme in the forecast model are evaluated. With each scheme, two experiments are conducted in which the reflectivity (Z) observations update in addition to dynamic and thermodynamic variables: 1) only the hydrometeor mixing ratios or 2) all microphysical variables. With fewer microphysical variables directly constrained by the Z observations, only updating hydrometeor mixing ratios causes the forecast error covariance structure to become unreliable, and results in larger errors in the analysis. Experiments that update all microphysical variables produce analyses with the lowest Z root-mean-square innovations; however, comparing the estimated hail size against hydrometeor classification algorithm output suggests that further constraint from observations is needed to more accurately estimate surface hail size. Ensemble correlation analyses are performed to determine the impact of hail growth assumptions in the MY and NSSL schemes on the forecast error covariance between microphysical and thermodynamic variables. In the MY scheme, Z is negatively correlated with updraft intensity because the strong updrafts produce abundant small hail aloft. The NSSL scheme predicts the growth of large hail aloft; consequently, Z is positively correlated with storm updraft intensity and hail state variables. Hail production processes are also shown to alter the background error covariance for liquid and frozen hydrometeor species. Results in this study suggest that EnKF analyses are sensitive to the choice of MP scheme (e.g., the treatment of hail growth processes).

Single-pixel resolution velocity/convection velocity field of a supersonic jet measured by particle/schlieren image velocimetry

A single-pixel ensemble correlation method was applied to the schlieren and shadowgraph image velocimetry (SIV) and a velocimetry method that can obtain the convection velocity distribution of high spatial resolution without an expensive pulsed laser system being achieved for a laboratory-scale supersonic jet flow. A cold axisymmetric supersonic jet was employed, and the basic characteristics of the convection velocity fields are measured by SIV as well as those of the velocity fields by the particle image velocimetry (PIV) in the single-pixel resolution. The Mach number of a supersonic jet was 2.0, and the Reynolds number based on the diameter of the nozzle exit was 1.0 × 106. A pulsed light-emitting-diode light source was used for SIV as a less expensive light source. The single-pixel ensemble correlation method applied to PIV clearly visualizes the potential core and the shear layer development with the high spatial resolution. The axial velocity of SIV at the jet centerline is approximately 0.7–0.8 times of that of PIV which seems to relate to the convection velocity. The velocity calculated from the shadowgraph images agrees well with the convection velocity estimated from the Mach wave emission angle. The comparison between the scale of the visualized turbulent structure and the length scale of large eddies implied that the quantitative discussion of the SIV measurement requires careful consideration of the scale of the visualized turbulent structure on the SIV image.

Consistency index of daily activity pattern and its correlations with subjective ratings of QOL

Since sleep is under circadian and homeostatic regulation, the status of regulatory mechanisms can be known from daily activity patterns, including both sleep and wake states. Therefore, the relationship between their quantitative characterization and associated subjective QOL can be expected to provide practical knowledge for maintaining/improving QOL. An index quantifying the consistency of daily activity patterns over days, the activity consistency index (ACI), was developed, and its correlations with subjective QOL ratings based on the Pittsburgh sleep quality index (PSQI) and the Kessler Psychological Distress Scale (K6) were analyzed using actigraphy data obtained from university students and IT workers. The consistency of the parametrically transformed actigraphy data was quantified using a parameter set tuned to optimize an ensemble correlation between the consistency measure and QOL. Comparisons of ACI with a previously proposed index (SRI: sleep regularity index) were made according to their correlations with the participants’ subjective ratings of QOL. The comparison of ACI and SRI with respect to the various quantitative features of daily activity revealed that ACI tuned to PSQI was correlated only with mean sleep-onset time and mean sleep duration, while SRI was correlated with most of the quantitative features of sleep. In addition, the correlation profile showed gender dependency. For male and female subjects in their 20 s, the analysis indicated a significant correlation between PSQI and ACI, but not between PSQI and SRI. ACI was shown to work well as an index of daily activity patterns relevant to subjective sleep quality. This ability suggests that ACI could be a basis for predicting subjective sleep quality. Through evaluating daily activity patterns using ACI, an individual may be able to select an appropriate lifestyle for maintaining/improving QOL.

State of health prediction of medical lithium batteries based on multi-scale decomposition and deep learning

To guarantee rescue time and reduce medical accidents, a health degradation prediction model of medical lithium-ion batteries based on multi-scale deep neural network was proposed aiming at the problems of poor model adaptability and inaccurate prediction in current state of health prediction methods. The collected energy data of medical lithium-ion batteries were decomposed into main trend data and fluctuation data by ensemble empirical mode decomposition and correlation analysis. Then, deep Boltzmann machines and long short-term memory were used to model the main trend and fluctuation data, respectively. The predicting outcomes of deep Boltzmann machines and long short-term memory were effectively integrated to obtain the health predicted results of medical lithium-ion battery. The experimental results show that the method can effectively fit the health trend of medical lithium-ion batteries and obtain accurate state of health prediction results. The performance of the method is better than other typical prediction methods.

Inferring Surface Flow Velocities in Sediment-Laden Alaskan Rivers from Optical Image Sequences Acquired from a Helicopter

The remote, inaccessible location of many rivers in Alaska creates a compelling need for remote sensing approaches to streamflow monitoring. Motivated by this objective, we evaluated the potential to infer flow velocities from optical image sequences acquired from a helicopter deployed above two large, sediment-laden rivers. Rather than artificial seeding, we used an ensemble correlation particle image velocimetry (PIV) algorithm to track the movement of boil vortices that upwell suspended sediment and produce a visible contrast at the water surface. This study introduced a general, modular workflow for image preparation (stabilization and geo-referencing), preprocessing (filtering and contrast enhancement), analysis (PIV), and postprocessing (scaling PIV output and assessing accuracy via comparison to field measurements). Applying this method to images acquired with a digital mapping camera and an inexpensive video camera highlighted the importance of image enhancement and the need to resample the data to an appropriate, coarser pixel size and a lower frame rate. We also developed a Parameter Optimization for PIV (POP) framework to guide selection of the interrogation area (IA) and frame rate for a particular application. POP results indicated that the performance of the PIV algorithm was highly robust and that relatively large IAs (64–320 pixels) and modest frame rates (0.5–2 Hz) yielded strong agreement ( R 2 > 0.9 ) between remotely sensed velocities and field measurements. Similarly, analysis of the sensitivity of PIV accuracy to image sequence duration showed that dwell times as short as 16 s would be sufficient at a frame rate of 1 Hz and could be cut in half if the frame rate were doubled. The results of this investigation indicate that helicopter-based remote sensing of velocities in sediment-laden rivers could contribute to noncontact streamgaging programs and enable reach-scale mapping of flow fields.

An improved model‐based analogue forecasting for the prediction of the tropical Indo‐Pacific Sea surface temperature in a coupled climate model

AbstractAnalogue forecasting is a method with a long history in weather and climate prediction. Recently, model‐based analogue forecasting (MAF) was developed and applied in Indo‐Pacific sea surface temperature (SST) with the long‐term (>1,000 years) run of the coupled general circulation model as the prediction library dataset. Here, we use the MAF method for Indo‐Pacific SST prediction with a 1,600‐year uninitialized control run of ICMv2 as the library datasets to select the analogues. In the improved analogue strategy, subsurface thermal conditions are valid predictors besides the surface conditions. The anomaly of SST, subsurface temperature at 5‐ and 105‐m depth as the best‐performing predictors can better simulate the overall thermal conditions of the ocean. In addition, by increasing the length of the model library dataset, the number of selected analogue cases for the ensemble, using root‐mean‐square and pattern correlation combined analogue metric and subtracting the long‐term trend, the improved MAF can produce a skillful SST prediction in the tropical Indian Ocean, southwest and northwest Pacific Ocean across 1‐ to 9‐month lead times. The ACC of the improved MAF prediction in these regions significantly increases by more than 0.18 relatively to the SST‐initialized hindcast of ICMv2 with considerable savings in terms of computational resource.

Characterization of optical light curves of extreme variability quasars over a ∼16-yr baseline

ABSTRACT We study the optical light curves – primarily probing the variable emission from the accretion disc – of ∼900 extreme variability quasars (EVQs, with maximum flux variations more than 1 mag) over an observed-frame baseline of ∼16 yr using public data from the SDSS Stripe 82, PanSTARRS-1 and the Dark Energy Survey. We classify the multiyear long-term light curves of EVQs into three categories roughly in the order of decreasing smoothness: monotonic decreasing or increasing (3.7 per cent), single broad peak and dip (56.8 per cent), and more complex patterns (39.5 per cent). The rareness of monotonic cases suggests that the major mechanisms driving the extreme optical variability do not operate over time-scales much longer than a few years. Simulated light curves with a damped random walk model generally under-predict the first two categories with smoother long-term trends. Despite the different long-term behaviours of these EVQs, there is little dependence of the long-term trend on the physical properties of quasars, such as their luminosity, BH mass, and Eddington ratio. The large dynamic range of optical flux variability over multiyear time-scales of these EVQs allows us to explore the ensemble correlation between the short-term (≲6 months) variability and the seasonal-average flux across the decade-long baseline (the rms-mean flux relation). We find that unlike the results for X-ray variability studies, the linear short-term flux variations do not scale with the seasonal-average flux, indicating different mechanisms that drive the short-term flickering and long-term extreme variability of accretion disc emission. Finally, we present a sample of 16 EVQs, where the approximately bell-shaped large amplitude variation in the light curve can be reasonably well fit by a simple microlensing model.

Impact of Model Resolution on Tropical Cyclone Simulation Using the HighResMIP–PRIMAVERA Multimodel Ensemble

AbstractA multimodel, multiresolution set of simulations over the period 1950–2014 using a common forcing protocol from CMIP6 HighResMIP have been completed by six modeling groups. Analysis of tropical cyclone performance using two different tracking algorithms suggests that enhanced resolution toward 25 km typically leads to more frequent and stronger tropical cyclones, together with improvements in spatial distribution and storm structure. Both of these factors reduce typical GCM biases seen at lower resolution. Using single ensemble members of each model, there is little evidence of systematic improvement in interannual variability in either storm frequency or accumulated cyclone energy as compared with observations when resolution is increased. Changes in the relationships between large-scale drivers of climate variability and tropical cyclone variability in the Atlantic Ocean are also not robust to model resolution. However, using a larger ensemble of simulations (of up to 14 members) with one model at different resolutions does show evidence of increased skill at higher resolution. The ensemble mean correlation of Atlantic interannual tropical cyclone variability increases from ~0.5 to ~0.65 when resolution increases from 250 to 100 km. In the northwestern Pacific Ocean the skill keeps increasing with 50-km resolution to 0.7. These calculations also suggest that more than six members are required to adequately distinguish the impact of resolution within the forced signal from the weather noise.

LSTM guided ensemble correlation filter tracking with appearance model pool

Deep learning based visual trackers have the potential to provide good performance for object tracking. Most of them use hierarchical features learned from multiple layers of a deep network. However, issues related to deterministic aggregation of these features from various layers, difficulties in estimating variations in scale or rotation of the object being tracked, as well as challenges in effectively modeling the object’s appearance over long time periods leaves substantial scope to improve performance. In this paper, we propose a tracker that learns correlation filters over features from multiple layers of a VGG network. A correlation filter for an individual layer is used to predict the target location. We adaptively learn the contribution of an ensemble of correlation filters for the final location estimation using an LSTM. An adaptive approach is advantageous as different layers encode diverse feature representations and a uniform contribution would not fully exploit this contrastive information. To this end, we use an LSTM as it encodes the interactions for past appearances which is useful for tracking. Further, the scale and rotation parameters are estimated using respective correlation filters. Additionally, an appearance model pool is used that prevents the correlation filter from drifting. Experimental results achieved on five public datasets — Object Tracking Benchmark (OTB100), Visual Object Tracking (VOT) Benchmark 2016, VOT Benchmark 2017, Tracking Dataset and UAV123 Dataset, reveal that our approach outperforms state of the art approaches for object tracking.

A Multiresolution Ensemble Hybrid 4DEnVar for Global Numerical Prediction

Abstract A multiresolution ensemble (MR-ENS) method is developed to resolve a wider range of scales of the background error covariance (BEC) in the hybrid four-dimensional ensemble–variational (4DEnVar) while saving computational costs. MR-ENS is implemented in the NCEP Global Forecast System (GFS) gridpoint statistical interpolation (GSI) hybrid 4DEnVar. MR-ENS generates analysis increment by incorporating high-resolution static BEC and flow-dependent ensemble BECs from both high and low resolutions. MR-ENS is compared with three 4DEnVar update approaches: 1) the single-resolution (SR)-Low approach where the analysis increments are generated from the ensemble BEC and the static BEC at the same low resolution; 2) the dual-resolution (DR) approach where the analysis increment is generated using the high-resolution static BEC and low-resolution ensemble BEC; and 3) the SR-High approach, which is the same as 1) except that all covariances are at high-resolution. Experiments show that MR-ENS improves global and tropical cyclone track forecasts compared to SR-Low and DR. Inclusion of the high-resolution ensemble leads to increased background ensemble spread, better fitting of the background to observations, increased effective ranks, more accurate ensemble error correlation, and increased power of analysis increment at small scales. The majority of the improvement of MR-ENS relative to SR-Low is due to the partial use of high-resolution background ensemble. Compared to SR-High, MR-ENS decreases the overall cost by about 40% and shows comparable global and tropical cyclone track forecast performances. Diagnostics show that particularly in the tropics, MR-ENS improves the analysis increment over a wide range of scales and increases the effective rank of the ensemble BEC to the degree comparable to SR-High.

Drone-Based Optical Measurements of Heterogeneous Surface Velocity Fields around Fish Passages at Hydropower Dams

In Austria, more than a half of all electricity is produced with the help of hydropower plants. To reduce their ecological impact, dams are being equipped with fish passages that support connectivity of habitats of riverine fish species, contributing to hydropower sustainability. The efficiency of fish passages is being constantly monitored and improved. Since the likelihood of fish passages to be discovered by fish depends, inter alia, on flow conditions near their entrances, these conditions have to be monitored as well. In this study, we employ large-scale particle image velocimetry (LSPIV) in seeded flow conditions to analyse images of the area near a fish passage entrance, captured with the help of a ready-to-fly consumer drone. We apply LSPIV to short image sequences and test different LSPIV interrogation area sizes and correlation methods. The study demonstrates that LSPIV based on ensemble correlation yields velocities that are in good agreement with the reference values regarding both magnitude and flow direction. Therefore, this non-intrusive methodology has a potential to be used for flow monitoring near fish passages on a regular basis, enabling timely reaction to undesired changes in flow conditions when possible.

Observation of weakly damped modes using high resolution measurement of turbulence in a dipole confined plasma

When plasma is confined by a levitated superconducting current ring, the turbulent radial particle flux changes the direction depending upon the gradient of the particle number within tubes of equal magnetic flux [Garnier et al., Phys. Plasmas 24, 012506 (2017)]. When the density profile is highly peaked, the particle flux is outward. When the density profile is less peaked, turbulence drives an inward “particle pinch.” This change in the direction of particle flux coincides with a reversal of the mean toroidal propagation direction of turbulent fluctuations. Previously, only the mean wavenumber of the fluctuations was reported. The mean wavenumber was computed from the ensemble correlation between two probes. Here, the full frequency-wavenumber power spectrum of the saturated turbulence is calculated by applying Capon's “maximum likelihood method” to floating potential measurements from an array of probes. The power spectrum shows that the highest intensity modes are due to unstable entropy modes, and the less intense modes coincide with weakly damped convective cells, which rotate toroidally in the direction opposite to the unstable modes. Because the weakly damped modes make up a significant fraction of the fluctuating power, these measurements imply that saturated turbulence in a dipole-confined plasma involves the excitation of weakly damped rotating convective cells.

Coupling forecast calibration and data‐driven downscaling for generating reliable, high‐resolution, multivariate seasonal climate forecast ensembles at multiple sites

AbstractCalibration and downscaling of ensemble GCM forecasts is becoming increasingly important for hydrological and agricultural modelling in support of the management and protection of valuable natural resources. Moreover, skilful and reliable daily forecast sequences are required to drive decision support models that operate on a daily time step. While downscaling of daily GCM outputs has been developed extensively in climate impacts studies, much less attention has been paid to the downscaling of ensemble GCM forecasts, which has the confronting aspect of low and diminishing skill with increasing lead time. Evidence is building that simple bias‐correction methods that do not model correlation between forecasts and observations, nor attempt to correct spatial, temporal and inter‐variable correlations, produce downscaled forecasts that perform poorly in applications models. Thus downscaling GCM forecasts requires inclusion of a full calibration component to reduce bias, improve reliability, capture skill where it is available and remove negative skill. In this study, we propose a new methodology for coupling a full GCM forecast calibration with empirical methods to (a) instil correct temporal, spatial and inter‐variable correlations in ensembles and (b) perform a multivariate downscaling of ensembles to daily sequences at multiple sites. Through a case study application, the proposed methodology is shown to produce skilful monthly–seasonal forecasts of rainfall, temperature and solar radiation at regional spatial scales. It also produces realistic and coherent multivariate daily sequences at multiple sub‐grid locations. The new methodology can be applied to more effectively integrate climate forecasts into hydrological and crop models and to support proactive decision‐making in agriculture and natural resources management.

Existence of multiple scales in uncertainty of numerical weather prediction

Numerical weather prediction provides essential information of societal influence. Advances in the initial condition estimation have led to the improvement of the prediction skill. The process to produce the better initial condition (analysis) with the combination of short-range forecast and observation over the globe requires information about uncertainty of the forecast results to decide how much observation is reflected to the analysis and how far the observation information should be propagated. Forecast ensemble represents the error of the short-range forecast at the instance. The influence of observation propagating along with forecast ensemble correlation needs to be restricted by localized correlation function because of less reliability of sample correlation. So far, solitary radius of influence is usually used since there has not been an understanding about the realism of multiple scales in the forecast uncertainty. In this study, it is explicitly shown that multiple scales exist in short-range forecast error and any single-scale localization approach could not resolve this situation. A combination of Gaussian correlation functions of various scales is designed, which more weighs observation itself near the data point and makes ensemble perturbation, far from the observation position, more participate in decision of the analysis. Its outstanding performance supports the existence of multi-scale correlation in forecast uncertainty.