Noisy Data Research Articles

MFF‐DenseNet: Densely Connected Convolutional Network With Multi‐Scale Feature Fusion for Magnetotelluric Noise Suppression

AbstractMagnetotelluric (MT) is a geophysical technique for detecting subsurface electrical structures. However, MT data collected in areas with frequent human activity often encounter various types of electromagnetic (EM) noise, which can mask or distort the signals we aim to analyze. Over the past decades, data processing methods based on deep learning has become the focus of multiple disciplines. Training neural networks to identify and handle noise has been proven effective in reducing the impact of noise. Therefore, ensuring the neural network accurately learns the noise and signal characteristics during the training is crucial. Against this background, we propose a multi‐scale feature fusion technique based on the densely connected network and apply it to processing MT data. First, we construct a data set resembling the noise in field data and use it to train the network. Leveraging dense connections, we extract feature maps of EM noise from noisy data and utilize Spatial Pyramid Pooling to integrate feature maps of various scales, enabling the network to capture features of the noise precisely. At the same time, we reduce the computation of feature fusion by introducing the Channel‐wise Squeezed Layer to compress the channels of the feature maps. Ultimately, we apply the trained model to the field noisy data. The results of synthetic and field data demonstrate that our method suppresses low‐amplitude and continuous high‐amplitude noise while preserving low‐frequency valuable signal. Apparent resistivity‐phase curves and polarization direction shows a noticeable improvement in the mid and low‐frequency bands with our method.

Quantitative evaluation of internal cluster validation indices using binary data sets

AbstractAimsDifferent clustering methods often classify the same data set differently. Selecting the “best” clustering solution from alternatives is possible with cluster validation indices. Because of the large variety of cluster validation indices (CVIs), choosing the most suitable index concerning the data set and clustering algorithms is challenging. We aim to assess different internal clustering validation indices.MethodsArtificial binary data sets with equal‐ and unequal‐sized well‐separated a priori clusters were simulated and three levels of noise were then added. Twenty replications of each of the six types of data sets (two group sizes × three levels of noise) were created and analyzed by three clustering algorithms with Jaccard dissimilarity. Twenty‐seven clustering validation indices are evaluated including both geometric and non‐geometric indices.ResultsAlthough, in theory, all CVIs could differentiate between good and wrong classifications, only a few perform as expected with noisy data. Tau and silhouette widths proved to be the best geometric CVIs both for equal and unequal cluster sizes. Among non‐geometric indices, crispness and OptimClass performed best.ConclusionWe recommend using these best‐performing CVIs. We suggest plotting the CVI value against the number of clusters because the lack of a sharp peak means that the position of the maximum is uncertain.

A Systematic Review of Real-Time Deep Learning Methods for Image-Based Cancer Diagnostics.

Deep Learning (DL) drives academics to create models for cancer diagnosis using medical image processing because of its innate ability to recognize difficult-to-detect patterns in complex, noisy, and massive data. The use of deep learning algorithms for real-time cancer diagnosis is explored in depth in this work. Real-time medical diagnosis determines the illness or condition that accounts for a patient's symptoms and outward physical manifestations within a predetermined time frame. With a waiting period of anywhere between 5 days and 30 days, there are currently several ways, including screening tests, biopsies, and other prospective methods, that can assist in discovering a problem, particularly cancer. This article conducts a thorough literature review to understand how DL affects the length of this waiting period. In addition, the accuracy and turnaround time of different imaging modalities is evaluated with DL-based cancer diagnosis. Convolutional neural networks are critical for real-time cancer diagnosis, with models achieving up to 99.3% accuracy. The effectiveness and cost of the infrastructure required for real-time image-based medical diagnostics are evaluated. According to the report, generalization problems, data variability, and explainable DL are some of the most significant barriers to using DL in clinical trials. Making DL applicable for cancer diagnosis will be made possible by explainable DL.

A Postlaunch Update on the Effects of Instrumental Measurement Errors on SWOT Estimates of Sea Surface Height, Velocity, and Vorticity

Abstract The Ka-band radar interferometer (KaRIn) on the Surface Water and Ocean Topography (SWOT) satellite that was launched in December 2022 is providing the first two-dimensional altimetric views of sea surface height (SSH). Measurements are made across two parallel swaths of 50-km width separated by a 20-km gap. In the data product that will be used for most oceanographic applications, SSH estimates with a footprint diameter of about 3 km are provided on a 2 km × 2 km grid. Early analyses of in-flight KaRIn data conclude that the instrumental noise for this footprint diameter has a standard deviation less than σ3km = 0.40 cm for conditions of 2-m significant wave height. This is a factor of 2.3 better than the prelaunch expectation based on the science requirement specification. The SSH fields measured by KaRIn allow the first satellite estimates of essentially instantaneous surface current velocity and vorticity computed geostrophically from SSH. The effects of instrumental noise on smoothed estimates of velocity and vorticity based on early postlaunch assessments are quantified here as functions of the half-power filter cutoff wavelength of the smoothing. Signal-to-noise ratios for smoothed estimates of velocity and vorticity are determined from simulated noisy KaRIn data derived from a high-resolution numerical model of the California Current System. The wavelength resolution capabilities for σ3km = 0.40 cm are found to be about 17 and 35 km for velocity and vorticity, respectively, which correspond to feature diameters of about 8.5 and 17.5 km, and are better than the prelaunch expectations by about 45% and 35%.

PROSE: Predicting Multiple Operators and Symbolic Expressions using multimodal transformers

Approximating nonlinear differential equations using a neural network provides a robust and efficient tool for various scientific computing tasks, including real-time predictions, inverse problems, optimal controls, and surrogate modeling. Previous works have focused on embedding dynamical systems into networks through two approaches: learning a single operator (i.e., the mapping from input parameterised functions to solutions) or learning the governing system of equations (i.e., the constitutive model relative to the state variables). Both of these approaches yield different representations for the same underlying data or function. Observing that families of differential equations often share key characteristics, we seek one network representation across a wide range of equations. Our multimodality approach, called Predicting Multiple Operators and Symbolic Expressions (PROSE), is capable of constructing multi-operators and governing equations simultaneously through a novel fusion structure. In particular, PROSE solves differential equations, predicts future states, and generates the underlying equations of motion by incorporating symbolic “words” through a language model. Experiments with 25600 distinct equations show that PROSE benefits from its multimodal nature, resulting in robust generalization (e.g. noisy observations, equation misspecification, and data imbalance) supported by comparison and ablation studies. PROSE provides a new operator learning framework that incorporates multimodal input/output and language models for solving forward and inverse problems related to differential equations.

Exploring the Potential of Neutrosophic Topological Spaces in Computer Science

Neutrosophic topological spaces (NTS) offer a novel framework for uncertainty modeling by incorporating degrees of truth, indeterminacy, and falsity. This paper investigates the potential applications of NTS in computer science. We provide background on neutrosophic sets and their extension to topological spaces. We then explore how NTS could be used for uncertainty modeling in data analysis (e.g., handling noisy data in sensor networks), pattern recognition (e.g., improving image classification with imprecise features), and information retrieval (e.g., enhancing search results by considering relevance uncertainty). We discuss the challenges associated with applying NTS and highlight promising areas for future research, such as developing efficient algorithms for NTS operations. Overall, this paper aims to stimulate further exploration of how neutrosophic topological spaces can contribute to advancements in various computer science domains.

Tackling Noisy Labels With Network Parameter Additive Decomposition.

Given data with noisy labels, over-parameterized deep networks suffer overfitting mislabeled data, resulting in poor generalization. The memorization effect of deep networks shows that although the networks have the ability to memorize all noisy data, they would first memorize clean training data, and then gradually memorize mislabeled training data. A simple and effective method that exploits the memorization effect to combat noisy labels is early stopping. However, early stopping cannot distinguish the memorization of clean data and mislabeled data, resulting in the network still inevitably overfitting mislabeled data in the early training stage. In this paper, to decouple the memorization of clean data and mislabeled data, and further reduce the side effect of mislabeled data, we perform additive decomposition on network parameters. Namely, all parameters are additively decomposed into two groups, i.e., parameters w are decomposed as w=σ+γ. Afterward, the parameters σ are considered to memorize clean data, while the parameters γ are considered to memorize mislabeled data. Benefiting from the memorization effect, the updates of the parameters σ are encouraged to fully memorize clean data in early training, and then discouraged with the increase of training epochs to reduce interference of mislabeled data. The updates of the parameters γ are the opposite. In testing, only the parameters σ are employed to enhance generalization. Extensive experiments on both simulated and real-world benchmarks confirm the superior performance of our method.

Integrating imprecise data in generative models using interval-valued Variational Autoencoders

Variational Autoencoders (VAEs) enable the integration of diverse data sources into a unified latent representation, facilitating the fusion of information from various inputs and the creation of disentangled representations that separate different factors of variation in the data. Traditional VAEs, however, are limited by assuming a single prior distribution for latent variables, which restricts their ability to handle epistemic uncertainty from imprecise measurements and incomplete data. This paper introduces the Interval-Valued Variational Autoencoder (iVAE), which employs a family of prior distributions and incorporates specialized neurons and redefined objective functions for handling interval-valued data. This architecture maintains computational efficiency while extending the model’s applicability to scenarios with pronounced epistemic uncertainty. The iVAE’s efficacy is demonstrated in managing two types of data: intrinsically interval-valued and noisy data preprocessed into interval formats. The first category is exemplified by a graphical analysis of questionnaires, while the second involves case studies focused on estimating the remaining useful life of aviation engines, where the iVAE outperforms traditional methods, thereby providing more accurate diagnostics and robust predictions.

L1-Tree: A novel algorithm for constructing 3D tree models and estimating branch architectural traits using terrestrial laser scanning data

Branch architecture provides crucial information for the understanding of plant trait variability and the adaptive strategies employed by trees in response to their environment. High-fidelity terrestrial laser scanning (TLS) data provide an accurate, efficient, and non-destructive means for constructing three-dimensional (3D) tree models and estimating architectural traits. However, the complex canopy structure of trees in natural forests and the presence of occlusion in TLS data pose significant challenges to achieving this goal. In this study, we present a novel algorithm, L1-Tree, for the construction of 3D tree models and the estimation of architectural traits from TLS data. This algorithm is grounded in the L1-Median algorithm and integrates a tree skeleton optimization procedure that considers the structural characteristics of tree branches. By comparing modeling results and manually derived branch traits for 24 trees of 24 species, we found that the L1-Tree algorithm achieved precision, recall, and F-score values of 0.94 for branch identification, coefficient of determination, root-mean-squared error, and normalized root-mean-squared error of 0.998, 0.068 m, and 0.3 % for branch length estimation, and a respective value of 0.958, 0.257 cm and 0.9 % for branch radius estimation. Additionally, the branch identification accuracy and accuracy in branch architectural trait estimation remained satisfactory across branch orders. Compared to established 3D tree model construction algorithms (e.g., TreeQSM), our L1-Tree algorithm demonstrated a superior capability in handling noisy environments and data gaps, making it a robust tool for TLS data-based tree architecture studies. Leaf-wood separation emerged as a crucial step influencing the performance of the L1-Tree algorithm. We observed significant drop in branch identification accuracy when using an automatic leaf-wood separation algorithm as input, highlighting the urgent need to develop effective leaf-wood separation algorithms to generate high-quality wood point clouds for tree architecture studies.

Artificial intelligence-driven real-world battery diagnostics

Addressing real-world challenges in battery diagnostics, particularly under incomplete or inconsistent boundary conditions, has proven difficult with traditional methodologies such as first-principles and atomistic calculations. Despite advances in data assimilation techniques, the overwhelming volume and diversity of data, coupled with the lack of universally accepted models, underscore the limitations of these traditional approaches. Recently, deep learning has emerged as a highly effective tool in overcoming persistent issues in battery diagnostics by adeptly managing expansive design spaces and discerning intricate, multidimensional correlations. This approach resolves challenges previously deemed insurmountable, especially with lost, irregular, or noisy data through the design of specialized network architectures that adhere to physical invariants. However, gaps remain between academic advancements and their practical applications, including challenges in explainability and the computational costs associated with AI-driven solutions. Emerging technologies such as explainable artificial intelligence (XAI), AI for IT operations (AIOps), lifelong machine learning to mitigate catastrophic forgetting, and cloud-based digital twins open new opportunities for intelligent battery life-cycle assessment. In this perspective, we outline these challenges and opportunities, emphasizing the potential of innovative technologies to transform battery diagnostics, as demonstrated by our recent practice and the progress made in the field. This includes promising achievements in both academic and industry field demonstrations in modeling and forecasting the dynamics of multiphysics and multiscale battery systems. These systems feature inhomogeneous cascades of scales, informed by our physical, electrochemical, observational, empirical, and/or mathematical understanding of the battery system. Through data assimilation efforts, meticulous craftsmanship, and elaborate implementations—and by considering the wealth and spatio-temporal heterogeneity of available data—such AI-based intelligent learning philosophies have great potential to achieve better accuracy, faster training, and improved generalization.

Physics-Informed Masked Autoencoder for active sparse imaging

Imaging technology based on detecting individual photons has seen tremendous progress in recent years, with broad applications in autonomous driving, biomedical imaging, astronomical observation, and more. Comparing with conventional methods, however, it takes much longer time and relies on sparse and noisy photon-counting data to form an image. Here we introduce Physics-Informed Masked Autoencoder (PI-MAE) as a fast and efficient approach for data acquisition and image reconstruction through hardware implementation of the MAE (Masked Autoencoder). We examine its performance on a single-photon LiDAR system when trained on digitally masked MNIST data. Our results show that, with 1.8×10-6\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1.8\ imes 10^{-6}$$\\end{document} or less detected photons per pulse and down to 9 detected photons per pixel, it achieves high-quality image reconstruction on unseen object classes with 90% physical masking. Our results highlight PI-MAE as a viable hardware accelerator for significantly improving the performance of single-photon imaging systems in photon-starving applications.

Inverse analysis of soil hydraulic parameters of layered soil profiles using physics‐informed neural networks with unsaturated water flow models

AbstractInformation about the spatial distribution of soil hydraulic parameters is necessary for the accurate prediction of soil water flow and the coupled movement of chemicals and heat at the field scale using a process‐based model. Physics‐informed neural networks (PINNs), which can provide physical constraints in deep learning to obtain a mesh‐free solution, can be used to inversely estimate soil hydraulic parameters from less and noisy training data. Previous studies using PINNs have successfully estimated soil hydraulic parameters for homogeneous soil but estimating such parameters of layered soil profiles where the interface depth and the parameters are unknown still has some difficulties. The objective of this study was to develop PINNs to inversely estimate the distribution of soil hydraulic parameters, such as saturated hydraulic conductivity and α and n of the Mualem–van Genuchten model directly within layered soil profiles by predicting changes in the pressure head from training data based on simulation results at given depths during infiltration. The impact of factors affecting PINNs performance, such as the weights assigned to each component of the loss function, time range used in error computations, and number of samples used to assess the physical constraint, was investigated. By assigning a larger weight to the physical constraint and excluding the earlier stage of infiltration in the loss function, the changes in the pressure head and the three soil hydraulic parameter distributions within the layered soil were successfully estimated. The developed PINNs can be further applied to more complex soils and can be improved.

A comparison of machine learning methods for recovering noisy and missing 4D flow MRI data.

Experimental blood flow measurement techniques are invaluable for a better understanding of cardiovascular disease formation, progression, and treatment. One of the emerging methods is time-resolved three-dimensional phase-contrast magnetic resonance imaging (4D flow MRI), which enables noninvasive time-dependent velocity measurements within large vessels. However, several limitations hinder the usability of 4D flow MRI and other experimental methods for quantitative hemodynamics analysis. These mainly include measurement noise, corrupt or missing data, low spatiotemporal resolution, and other artifacts. Traditional filtering is routinely applied for denoising experimental blood flow data without any detailed discussion on why it is preferred over other methods. In this study, filtering is compared to different singular value decomposition (SVD)-based machine learning and autoencoder-type deep learning methods for denoising and filling in missing data (imputation). An artificially corrupted and voxelized computational fluid dynamics (CFD) simulation as well as in vitro 4D flow MRI data are used to test the methods. SVD-based algorithms achieve excellent results for the idealized case but severely struggle when applied to in vitro data. The autoencoders are shown to be versatile and applicable to all investigated cases. For denoising, the in vitro 4D flow MRI data, the denoising autoencoder (DAE), and the Noise2Noise (N2N) autoencoder produced better reconstructions than filtering both qualitatively and quantitatively. Deep learning methods such as N2N can result in noise-free velocity fields even though they did not use clean data during training. This work presents one of the first comprehensive assessments and comparisons of various classical and modern machine-learning methods for enhancing corrupt cardiovascular flow data in diseased arteries for both synthetic and experimental test cases.

Content-Aware Few-Shot Meta-Learning for Cold-Start Recommendation on Portable Sensing Devices.

The cold-start problem in sequence recommendations presents a critical and challenging issue for portable sensing devices. Existing content-aware approaches often struggle to effectively distinguish the relative importance of content features and typically lack generalizability when processing new data. To address these limitations, we propose a content-aware few-shot meta-learning (CFSM) model to enhance the accuracy of cold-start sequence recommendations. Our model incorporates a double-tower network (DT-Net) that learns user and item representations through a meta-encoder and a mutual attention encoder, effectively mitigating the impact of noisy data on auxiliary information. By framing the cold-start problem as few-shot meta-learning, we employ a model-agnostic meta-optimization strategy to train the model across a variety of tasks during the meta-learning phase. Extensive experiments conducted on three real-world datasets-ShortVideos, MovieLens, and Book-Crossing-demonstrate the superiority of our model in cold-start recommendation scenarios. Compared to MetaCs-DNN, the second-best approach, CFSM, achieves improvements of 1.55%, 1.34%, and 2.42% under the AUC metric on the three datasets, respectively.

Smoothing of the Noisy Lithium-ion Battery Surface Temperature Data Based on Savitzky–Golay (SG) Filter

As the charging current and surrounding temperatures rise concurrently in an electric vehicle's (EV) battery pack, the battery temperature increases abruptly beyond safe limits. The battery is susceptible to triggering thermal runaway at higher temperatures, leading to battery damage and even an explosion. The control system depends on these measurement data from the sensors to prevent dangerous situations and maximize the performance and cycle life of batteries. However, traditional noisy temperature measurement sensors in a real application, such as thermistors and thermocouples, are extensively used. In this paper, the experimental setup, the heat pipe-based battery thermal management system (BTMS) was designed and experimented with high input power. The battery was sandwiched with heat pipes, and heated at 30, 40, 50, and 60 W. The Savitzky-Golay filter technique is applied to the noisy temperature data of the surface temperature of the lithium-ion batteries (LIBs) used to estimate the condition of the battery. According to this study, the start-up time parameter in battery thermal management can be controlled by the Savitzky-Golay filter. This will attenuate random temperature fluctuations of battery temperature noise and avoid the cooling system from being falsely triggered. The results are measured by the signal-to-noise (SNR) to demonstrate the ability of the Savitzky-Golay filter to eliminate noise

Denoising of imaginary time response functions with Hankel projections

Imaginary-time response functions of finite-temperature quantum systems are often obtained with methods that exhibit stochastic or systematic errors. Reducing these errors comes at a large computational cost—in quantum Monte Carlo simulations, the reduction of noise by a factor of two incurs a simulation cost of a factor of four. In this paper, we relate certain imaginary-time response functions to an inner product on the space of linear operators on Fock space. We then show that data with noise typically does not respect the positive definiteness of its associated Gramian. The Gramian has the structure of a Hankel matrix. As a method for denoising noisy data, we introduce an alternating projection algorithm that finds the closest positive definite Hankel matrix consistent with noisy data. We test our methodology at the example of fermion Green's functions for continuous-time quantum Monte Carlo data and show remarkable improvements of the error, reducing noise by a factor of up to 20 in practical examples. We argue that Hankel projections should be used whenever finite-temperature imaginary-time data of response functions with errors is analyzed, be it in the context of quantum Monte Carlo, quantum computing, or in approximate semianalytic methodologies. Published by the American Physical Society 2024

Data-Driven Control-Oriented Modeling for Response of Fluidic Thrust Vectoring

Response to control input is of significance to the application of real-time active flow control (AFC). In this paper, a novel data-driven framework is used to discover the underlying physics of the dynamic response process of fluidic thrust vectoring (FTV), a typical application of AFC. In the proposed framework, sparse identification of a nonlinear dynamics (SINDy) algorithm is used to identify the governing equations of the flow control responses of sets of noisy measurement data. The clustering algorithm is then used to seek the generalized coefficients of basis functions for different sets of data, which improve the robustness of the model to noisy measurement data. First, a simulated mechanical system is used to validate the effect of the framework. To simplify the modeling, control performance and characteristics are investigated in a detailed manner. Then a dimensionless parameter ΔCp based on the pressure coefficient is found to exhibit a linear relationship with the vector angle under different working conditions. This parameter is introduced in the proposed framework to model the dynamic process of response to control input. The obtained governing equations can describe the dynamic process accurately based on the validation of testing data. The form of the governing equation is rewritten and analyzed based on the control theory, revealing the physics of this process, which is significant to practical AFC implementation.

Robust seismic data denoising via self-supervised deep learning

Seismic data denoising is a critical component of seismic data processing, yet effectively removing erratic noise, characterized by its non-Gaussian distribution and high amplitude, remains a substantial challenge for conventional methods and deep-learning (DL) algorithms. Supervised learning frameworks typically outperform others, but they require pairs of noisy data sets alongside corresponding clean ground truth, which is impractical for real-world seismic data sets. In contrast, unsupervised learning (UL) methods, which do not rely on ground truth during training, often fall short in performance when compared with their supervised or traditional denoising counterparts. Moreover, current unsupervised DL methods fail to address the specific challenges posed by erratic seismic noise adequately. This paper introduces a novel zero-shot unsupervised DL framework designed specifically to mitigate random and erratic noise, with a particular emphasis on blended noise. Drawing inspiration from Noise2Noise (N2N) and data augmentation principles, we develop a robust self-supervised denoising network called robust Noiser2Noiser. Our approach eliminates the need for paired noisy and clean data sets as required by supervised methods or paired noisy data sets as in N2N. Instead, our framework relies solely on the original noisy seismic data set. Our methodology generates two independent recorrupted data sets from the original noisy data set, using one as the input and the other as the training target. Subsequently, we use a DL-based denoiser, denoising convolutional neural network, for training purposes. To address various types of random and erratic noise, the original noisy data set is recorrupted with the same noise type. Detailed explanations for generating training input and target data for blended data are provided. We apply our network to synthetic and real marine data examples, demonstrating significantly improved noise attenuation performance compared with traditional denoising methods and state-of-the-art UL Codes are available on https://github.com/Ji-seismic/N2N_deblending .

SelfMixed: Self-supervised mixed noise attenuation for distributed acoustic sensing data

Distributed acoustic sensing (DAS) is an emerging data acquisition technique known for its high sensing density, cost effectiveness, and environmental friendliness, making it a technology with significant future application potential in many fields. However, DAS signals are often contaminated by various types of noise, such as high-frequency, high-amplitude erratic, and horizontal noise, making their processing challenging. Therefore, it is crucial to leverage the physical characteristics of these diverse types of noise in DAS data and effectively attenuate them. In this work, we develop SelfMixed, a novel self-supervised learning method for mixed noise suppression of DAS data. We fully exploit the physical characteristics of different types of noise in DAS data and introduce a physical characteristic-based training strategy. Specifically, we use the [Formula: see text] norm to characterize random noise, the [Formula: see text] norm for erratic noise, and horizontal smoothness and vertical nonsmoothness for horizontal noise. In addition, we use a blind-spot-based training strategy for DAS denoising, relying solely on observed noisy data. To more effectively attenuate horizontal noise, we also introduce a Fourier transform-based parameterization method. By combining self-supervised deep priors with the physical characteristics of mixed DAS noise, our method effectively attenuates complex mixed noise in field DAS data. Extensive experiments on synthetic and field data from various geographic scenarios validate the superiority of SelfMixed over seven state-of-the-art DAS denoising approaches.

Particle filter data assimilation for ubiquitous unstable trajectories of two-dimensional three-state cellular automata

Estimating the states of error-growing (sensitive to initial state) cellular automata (CA) based on noisy imperfect data is challenging due to the discreteness of the dynamical system. This paper proposes particle filter (PF)–based data assimilation (DA) for three-state error-growing CA and demonstrates that the PF-based DA can predict the present and future state even with noisy and sparse observations. The error-growing CA used in the present study comprised a competitive system of land, grass, and sheep. To the best of the authors’ knowledge, this is the first application of DA to such CA. The performance of DA for different observation sets was evaluated in terms of observational error, density, and frequency, and a series of sensitivity tests of the internal parameters in the DA was conducted. The inflation and localization parameters were tuned according to the sensitivity tests.