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At least 55 records · Page 3

Quantifying the Resolution Sensitivity of the Kain–Fritsch Scheme Across the Gray Zone by Isolating Interactions: A TWP‐ICE Case Study

The resolution sensitivity of the Kain–Fritsch (KF) convection scheme and the role of interactions between the physics and dynamics within the gray zone (<10 km) were investigated using the Separate Physics and Dynamics Experiment (SPADE) framework. Two groups of experiments were conducted using the Weather Research and Forecasting (WRF) model via traditional (Tradition) runs and SPADE runs with resolutions of 1, 2, 4, and 8 km during the wet period of the Tropical Warm Pool–International Cloud Experiment (TWP‐ICE). Results show that the KF scheme simulates the weakened convective processes well as the resolution increases in both groups, and the changes in the convective variables with resolution in SPADE are smaller than in the Tradition group. This indicates the important effects of interactions between model components on convection parameterizations as the resolution changes. Additionally, the microphysics variables remain nearly unchanged with resolution in SPADE and weaken slightly in Tradition as the resolution decreases, suggesting the relatively weaker influences of model interactions for the resolved‐cloud parameterization. Therefore, the scale‐aware behavior of KF scheme is further strengthened in Tradition runs, primarily through inhibiting the strength of stratiform processes through physics–dynamics interactions and physical components.

54 ENVIRONMENTAL SCIENCES↗

Reducing Long‐Standing Surface Ozone Overestimation in Earth System Modeling by High‐Resolution Simulation and Dry Deposition Improvement

The overestimation of surface ozone concentration in low‐resolution global atmospheric chemistry and climate models has been a long‐standing issue. We first update the ozone dry deposition scheme in both high‐ (0.25°) and low‐resolution (1°) Community Earth System Model (CESM) version 1.3 runs, by adding the effects of leaf area index and correcting the sunlit and shaded fractions of stomatal resistances. With this update, 5‐year‐long summer simulations (2015–2019) using the low‐resolution CESM still exhibit substantial ozone overestimation (by 6.0–16.2 ppbv) over the U.S., Europe, eastern China, and ozone pollution hotspots. The ozone dry deposition scheme is further improved by adjusting the leaf cuticle conductance, reducing the mean ozone bias by 19%, and increasing the model resolution further reduces the ozone overestimation by 43%. We elucidate the mechanism by which model grid spacing influences simulated ozone, revealing distinctive pathways in urban versus rural areas. In rural areas, grid spacing mainly affects daytime ozone levels, where additional NO x emissions from nearby urban areas result in an ozone boost and overestimation in low‐resolution simulations. In contrast, over urban areas, daytime ozone overestimation follows a similar mechanism due to the influence of volatile organic compounds from surrounding rural areas. However, nighttime ozone overestimation is closely linked to weakened NO titration owing to the redistribution of urban NO x to rural areas. Additionally, stratosphere‐troposphere exchange may also contribute to reducing ozone bias in high‐resolution simulations, warranting further investigation. This optimized high‐resolution CESM may enhance understanding of ozone formation mechanisms, sources, and changes in a warming climate.

54 ENVIRONMENTAL SCIENCES↗

An accurate measurement of the spectral resolution of the JWST Near Infrared Spectrograph

The spectral resolution (R ≡ λ/Δλ) of spectroscopic data is crucial information for accurate kinematic measurements. In this letter we present a robust measurement of the spectral resolution of the JWST Near Infrared Spectrograph (NIRSpec) in fixed slit (FS) and integral field spectroscopy (IFS) modes. Due to the similarity of the utilized slit dimension in the FS mode to that of the shutters in the multi-object spectroscopy (MOS) mode, our resolution measurements in the FS mode can also be used for the MOS mode in principle. We modeled H and He lines of the planetary nebula SMP LMC 58 using a Gaussian line spread function (LSF) to estimate the wavelength-dependent resolution for multiple disperser and filter combinations. We corrected for the intrinsic width of the planetary nebula’s H and He lines due to its expansion velocity by measuring it from a higher-resolution X-shooter spectrum. We find that NIRSpec’s in-flight spectral resolutions exceed the pre-launch estimates provided in the JWST User Documentation by 11–53% in the FS mode and by 1–24% in the IFS mode across the covered wavelengths. We recover the expected trend that the resolution increases with the wavelength within a configuration. The robust and accurate LSFs presented in this letter will enable high-accuracy kinematic measurements using NIRSpec for applications in cosmology and galaxy evolution.

methods: data analysis↗

A High-Quality Workflow for Multi-Resolution Scientific Data Reduction and Visualization

Multi-resolution methods such as Adaptive Mesh Refinement (AMR) can enhance storage efficiency for HPC applications generating vast volumes of data. However, their applicability is limited and cannot be universally deployed across all applications. Furthermore, integrating lossy compression with multi-resolution techniques to further boost storage efficiency encounters significant barriers. To this end, we introduce an innovative workflow that facilitates high-quality multi-resolution data compression for both uniform and AMR simulations. Initially, to extend the usability of multi-resolution techniques, our workflow employs a compression-oriented Region of Interest (ROI) extraction method, transforming uniform data into a multi-resolution format. Subsequently, to bridge the gap between multi-resolution techniques and lossy compressors, we optimize three distinct compressors, ensuring their optimal performance on multi-resolution data. These optimizations can improve the compression ratio of SOTA approaches by up to 3.3× under the same data quality loss. Lastly, we incorporate an advanced uncertainty visualization method into our workflow to understand the potential impacts of lossy compression. Experimental evaluation demonstrates that our workflow achieves significant compression quality improvements.

Wang, Daoce↗

Estimating Fine-Resolution Shortwave Broadband Albedo of Croplands from Harmonized Landsat and Sentinel-2 Data

Altered surface albedo due to land-cover conversions and management is a significant driver of global climate change. Albedo can be directly measured at ground stations, and remote sensing data can be used to scale-up albedo values to regional and global levels. Some previous studies have retrieved fine-resolution (10–30 m) instantaneous albedo and coarse-resolution (500–1000 m) daily mean albedo from remote sensing data, but they all required the input of Moderate Resolution Imaging Spectroradiometer (MODIS) albedo information at 500-m resolution, and none have assembled both instantaneous and daily albedo based exclusively on fine-resolution satellite data. Here, to address this issue, we compiled 387 instantaneous and 346 daily albedo records using field net radiometer measurements from the bioenergy croplands at the W. K. Kellogg Biological Station in southwest Michigan. We then connected these albedo records with a suite of variables derived from harmonized Landsat and Sentinel-2 data through two machine learning algorithms (random forest regression and extreme gradient boosting) to retrieve clear-sky instantaneous and daily shortwave broadband albedo. The performance statistics indicate reasonable accuracy of model results [root-mean-square error (RMSE)] around or below 0.03 except for snow-covered surfaces), suggesting that the retrieval of both instantaneous and daily albedo based exclusively on fine-resolution satellite data is promising. To facilitate the use of fine-resolution albedo products at the global level, future efforts need to include more albedo records of diverse surface cover types, as well as to accurately model daily albedo for cloudy days to address the “clear-sky bias.”

Harmonized Landsat and Sentinel-2↗

High-Resolution Model Intercomparison Project phase 2 (HighResMIP2) towards CMIP7

Abstract. Robust projections and predictions of climate variability and change, particularly at regional scales, rely on the driving processes being represented with fidelity in model simulations. Consequently, the role of enhanced horizontal resolution in improved process representation in all components of the climate system continues to be of great interest. Recent simulations suggest the possibility of significant changes in both large-scale aspects of the ocean and atmospheric circulations and in the regional responses to climate change, as well as improvements in representations of small-scale processes and extremes, when resolution is enhanced. The first phase of the High-Resolution Model Intercomparison Project (HighResMIP1) was successful at producing a baseline multi-model assessment of global simulations with model grid spacings of 25–50 km in the atmosphere and 10–25 km in the ocean, a significant increase when compared to models with standard resolutions on the order of 1° that are typically used as part of the Coupled Model Intercomparison Project (CMIP) experiments. In addition to over 250 peer-reviewed manuscripts using the published HighResMIP1 datasets, the results were widely cited in the Intergovernmental Panel on Climate Change report and were the basis of a variety of derived datasets, including tracked cyclones (both tropical and extratropical), river discharge, storm surge, and impact studies. There were also suggestions from the few ocean eddy-rich coupled simulations that aspects of climate variability and change might be significantly influenced by improved process representation in such models. The compromises that HighResMIP1 made should now be revisited, given the recent major advances in modelling and computing resources. Aspects that will be reconsidered include experimental design and simulation length, complexity, and resolution. In addition, larger ensemble sizes and a wider range of future scenarios would enhance the applicability of HighResMIP. Therefore, we propose the High-Resolution Model Intercomparison Project phase 2 (HighResMIP2) to improve and extend the previous work, to address new science questions, and to further advance our understanding of the role of horizontal resolution (and hence process representation) in state-of-the-art climate simulations. With further increases in high-performance computing resources and modelling advances, along with the ability to take full advantage of these computational resources, an enhanced investigation of the drivers and consequences of variability and change in both large- and synoptic-scale weather and climate is now possible. With the arrival of global cloud-resolving models (currently run for relatively short timescales), there is also an opportunity to improve links between such models and more traditional CMIP models, with HighResMIP providing a bridge to link understanding between these domains. HighResMIP also aims to link to other CMIP projects and international efforts such as the World Climate Research Program lighthouse activities and various digital twin initiatives. It also has the potential to be used as training and validation data for the fast-evolving machine learning climate models.

54 ENVIRONMENTAL SCIENCES↗

Simulation of wind and solar energy generation over California with E3SM SCREAM regionally refined models at 3.25 km and 800 m resolutions

This study presents wind and solar power generation estimates derived from the US Department of Energy’s Simple Cloud-Resolving E3SM Atmosphere Model (SCREAM) Regionally Refined Models (RRM) over California at 3.25 km and 800 m horizontal resolutions, using the Python wrapper for the System Advisor Model (PySAM). The resulting wind and solar generation estimates are compared to monthly capacity factors reported to the Energy Information Administration (EIA), High-Resolution Rapid Refresh (HRRR, 3 km resolution) forecast model, and E3SM North American regionally refined model (NARRM, 25 km resolution). We systematically assess the impacts of generation modeling assumptions, meteorological models, and horizontal resolution. Results show that resolution plays a dominant role for wind energy: increasing from 25 to 3.25 km brings qualitative and quantitative improvements, most notably by resolving the phase error in the seasonal cycle found in coarser simulations. However, further refinement to 800 m offers minimal gains. SCREAM performs better than HRRR for solar power generation in single- and dual-axis tracking systems, likely due to more accurate surface radiation. The sensitivity of PySAM to system configuration, particularly for axis-tracking modeling in photovoltaics, is also highlighted. Overall, SCREAM-RRM shows strong potential for high-resolution energy assessments, with future progress depending on more in situ observations and clearer quantification of uncertainties in generation modeling.

Geosciences↗

Improving Chirped Fiber Bragg Grating Resolution for Position-Sensitive Sensors in Shock- and Detonation-Driven Experiments

Chirped fiber Bragg gratings (CFBGs) are robust diagnostic sensors that are widely used to track detonation-driven and shock wave propagation. CFBGs are inscribed with a linearly chirped periodic index of refraction changes that alter the Bragg wavelength along the length of the probe. The light return of each individual Bragg element is captured by a detector at a unique time to map the full reflected spectrum. The CFBG spectrum is measured with a dispersive Fourier transform of the reflected light that temporally stretches the spectrum to increase spatial resolution and make a one-to-one map of the wavelength on a time axis. Here, we propose an improvement of CFBG temporal resolution by incorporating two co-linear laser pulses with orthogonal polarization states and a 5 ns time offset. The two separate signals were split and tracked by two separate detectors. An oscilloscope captured good separation in the signals, and two separate spectrograms were generated and interleaved in the post-processing of the data. This novel technique doubled the CFBG temporal resolution and led to a doubled location resolution. As a proof-of-concept of this technique, the resolution improvement was compared between standard CFBG measurements and the two polarization states method on a position-sensitive CFBG sensor. CFBG resolution doubling will advance sensor capabilities and will have a direct impact on improving capture and analysis in dynamic, high-explosive experiments.

42 ENGINEERING↗

Improved Simulation of East Asian Summer Monsoon in the High-resolution CESM1 and Its Causes

Based on the high- and low-resolution Community Earth System Model, version 1 (CESM1), and corresponding simulations from phase 6 of the Coupled Model Intercomparison Project (CMIP6), we compare the interannual variability of the East Asian summer monsoon (EASM). The EASM interannual variability is characterized by the anomalous western North Pacific anticyclone (WNPAC) circulation and the dipole rainfall pattern with a negative southern lobe over the western North Pacific and a positive northern lobe along the Meiyu–Baiu region, which is better reproduced by the high-resolution models. Here, the reason for the improvement in the high-resolution models has been attributed to the better simulation of the warm temperature advection from the wind anomalies on the climatological temperature gradient. Positive sea surface temperature (SST) anomalies over the tropical Indian Ocean are the key to the improved wind anomalies featuring a WNPAC in the high-resolution models. The warm SST anomalies over the tropical Indian Ocean strengthen the WNPAC by triggering a Kelvin-wave response to the enhanced heat release induced by the increased precipitation. Based on the mixed-layer heat budget analysis, the warm SST anomalies over the western Indian Ocean in the high-resolution CESM1 are tied to the anomalous easterly wind along the equator, which reduces surface evaporation and upwelling. Therefore, the better simulations of air-sea feedback and the oceanic mesoscale eddy over the western Indian Ocean are the key for the improved simulation of the EASM interannual variations in the high-resolution CESM1.

54 ENVIRONMENTAL SCIENCES↗

A deep learning-based Bayesian framework for high-resolution calibration of building energy models

Calibrating building energy models (BEMs), i.e., closing discrepancy between modeling and field measurements, is of significance to support its applications in building sustainability and resilience analysis. However, as being widely used in practice, current Bayesian calibration is mostly performed in low-resolution (annual or monthly), instead of high-resolution (hourly or sub-hourly), which is crucial to support emerging BEM applications, such as building-renewable energy integration (demand response) and smart control. This is attributable to the gaps in current Bayesian calibration process, including (1) difficulty in supporting reliable high-resolution calibration with over-parameterization and multi-solution issues, (2) inadequacy of meta-model to capture temporal building dynamics in high-resolution, and (3) excessive computational burdens of covariance matrix calculation in Bayesian inference. Therefore, to close these gaps, this research proposes a novel deep learning-based Bayesian calibration framework, involving pre-calibration mechanism, Long Short-Term Memory as surrogate models, and simplified covariance matrix calculation, to calibrate BEMs in high temporal resolution (i.e., hourly) with enhanced accuracy and computational efficiency. Finally, the case study demonstrates its effectiveness to match modeling outcomes with measurements and realize CV-RMSE of < 30 % and NMBE of < 6 % in hourly resolution, as well as a significant reduction of calibration time (by > 99 %, from > 600 h to ~ 1.5 h).

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Evaluating Large‐Storm Dominance in High‐Resolution GCMs and Observations Across the Western Contiguous United States

Abstract Extreme precipitation events are projected to increase in frequency across much of the land‐surface as the global climate warms, but such projections have typically relied on coarse‐resolution (100–250 km) general circulation models (GCMs). The ensemble of HighResMIP GCMs presents an opportunity to evaluate how a more finely resolved atmosphere and land‐surface might enhance the fidelity of the simulated contribution of large‐magnitude storms to total precipitation, particularly across topographically complex terrain. Here, the simulation of large‐storm dominance, that is, the number of wettest days to reach half of the total annual precipitation, is quantified across the western United States (WUS) using four GCMs within the HighResMIP ensemble and their coarse resolution counterparts. Historical GCM simulations (1950–2014) are evaluated against a baseline generated from station‐observed daily precipitation (4,803 GHCN‐D stations) and from three gridded, observationally based precipitation data sets that are coarsened to match the resolution of the GCMs. All coarse‐resolution simulations produce less large‐storm dominance than in observations across the WUS. For two of the four GCMs, bias in the median large‐storm dominance is reduced in the HighResMIP simulation, decreasing by as much as 62% in the intermountain west region. However, the other GCMs show little change or even an increase (+28%) in bias of median large‐storm dominance across multiple sub‐regions. The spread in differences with resolution amongst GCMs suggests that, in addition to resolution, model structure and parameterization of precipitation generating processes also contribute to bias in simulated large‐storm dominance.

Environmental Sciences & Ecology↗

Future projections of storm surge in Hurricane Katrina and sensitivity to meteorological forcing resolution

In this study, we investigated whether and how the storm surge induced by Hurricane Katrina could change if it occurs in a future warmer climate, and the sensitivity of the changes to atmospheric forcing resolution. Climate model simulations of Hurricane Katrina at 27 km, 4.5 km, and 3 km resolutions were used to drive storm surge simulations in historical and future climates using the ADvanced CIRCulation (ADCIRC) model. We found that peak surge height increased significantly in the future with all forcing resolutions. However, the future projection is 22% greater in the 3 km forcing, typical of regional climate models, compared to the 27 km forcing, typical of state-of-the-art global climate models. Additionally, the spatial extent of the future change is highly sensitive to forcing resolution, extending most broadly under the 27 km forcing. Furthermore, we found that storm surge duration decreases in the future with all forcing resolutions due to increasing TC translation speed and decreasing ocean lifetime. However, the future change in the surge duration is sensitive to the forcing resolution, decreasing by 31% in the 27 km forcing and 6% in the 3 km forcing.

54 ENVIRONMENTAL SCIENCES↗

Deep-learning-based canopy height model generation from sub-meter resolution panchromatic satellite imagery

Canopy height models (CHMs) with sufficient resolution to distinguish individual trees are useful for a variety of applications. However, standard techniques to acquire such data, such as airborne lidar surveying, are often prohibitively expensive. Deep learning techniques for generating CHMs from high-resolution imagery are an attractive option to reduce costs. To date, success with these methods has been demonstrated using multichannel aerial photography and specialized satellite data products derived from multiple sensors, neither of which is commonly available at temporal resolutions finer than one year. Here we demonstrate a method to generate sub-meter resolution CHMs in three forests in California using a more abundant data source: sub-meter resolution, panchromatic satellite imagery from a single sensor. We show that phenology and species composition play important roles in model transferability; when trained using imagery from a single conifer forest in autumn, the model performs well on autumn imagery from a second conifer forest several hundred kilometers distant with no re-training. With modest additions to the training dataset, the same model generates minimally biased estimates of canopy height in both conifer and deciduous forests during multiple seasons. Because the model operates on satellite data with global coverage and a relatively short return interval, we propose its suitability to extrapolate tree-level canopy height data to remote regions and conduct high-temporal resolution monitoring of forest structure. We furthermore demonstrate the workflow’s applicability to fire modeling by conducting simulations in forests populated by trees measured using both this approach and airborne lidar surveying. We find minimal differences in fire behavior relative to a baseline case in which only statistical distributions of tree height and crown area are known. This result underscores the value of forest structural information derived from our workflow for improving the fidelity of wildland fire simulations, among other ecological applications.

54 ENVIRONMENTAL SCIENCES↗

Resolution requirements for numerical modeling of neutrino quantum kinetics

Neutrino quantum kinetics is a rapidly evolving field in computational astrophysics, with a primary focus on collective neutrino oscillations in core-collapse supernovae and postmerger phases of binary neutron star mergers. In recent years, there has been considerable debate concerning resolution dependence in numerical simulations. In this paper, we conduct a comprehensive resolution study in both angular- and spatial directions by using two independent schemes of quantum kinetic neutrino transport: finite volume and pseudospectral methods. We complement our discussion by linear stability analysis including inhomogeneous modes. Our result suggests that decreasing spatial resolutions underestimates the growth of flavor instability, and then leads to wrong asymptotic states of flavor conversions, which potentially has a critical impact on astrophysical consequences. We further delve into numerical results of low resolution simulations, that reveals the underlying mechanism responsible for numerical artifacts caused by insufficient resolutions. Finally, this study settles the debate on requirements of resolutions and serves as a guideline for numerical modeling of quantum kinetic neutrino transport.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Peering into cloud physics using ultra-fine resolution radar and lidar systems

Cloud microphysical processes, such as droplet activation, condensational growth, and collisional growth, play a central role in the evolution of clouds and precipitation. Accurate representations of these processes in numerical models are challenging partially due to incomplete understanding of them at the process-level arising from limited systematic observations. Most surface-based active remote sensors, including today’s operational cloud radars and lidars, have a resolution on the order of tens of meters. This resolution is insufficient to resolve cloud microphysical processes that manifest at finer (meter and sub-meter) scales. A new set of ultra-high-resolution ground-based radar and lidar systems have been developed to address this observational gap. The newly developed 94-GHz cloud radar has a range resolution down to 2.8 m, or a factor of 10 finer than typical radars, using a large bandwidth and quadratic phase coding techniques. The lidar has a range resolution down to 10 cm, or a factor of 100 finer than typical lidars, using a time-gated time-correlated single photon counting technique. Such high-resolution observations were previously only achievable through in situ aircraft measurements. Even then, aircraft measurements do not permit continuous long-term cloud observation as is possible with ground-based remote sensing instruments. In this study, the first-light cloud observations from the new radar and lidar systems are shown to reveal detailed cloud structures that conventional sensors could only perceive in a bulk sense, thus providing new avenues to investigate cloud microphysical processes and their impact on weather and climate.

54 ENVIRONMENTAL SCIENCES↗

Illuminating the Night: A Survey of Super-Resolution Methods for Nighttime Light Images

Nighttime Light (NTL) images provide critical insights into urbanization, disaster response, and energy consumption. The VIIRS Day/Night Band (DNB) sensor offers high-quality NTL imagery with daily revisit rates, but the available spatial resolution hinders fine-grained accurate analysis. Super-resolution techniques aim to increase the resolution of NTL images, enabling more detailed assessments of infrastructure, light pollution, economic activity, and power outages. However, existing state-of-the-art super-resolution methods designed for natural images struggle with the unique characteristics of NTL data. This work provides a comprehensive review of super-resolution methods across multiple image modalities, evaluates their effectiveness on VI-IRS DNB data, and proposes a multi-modal super-resolution approach tailored to NTL imagery. The proposed approach integrates VIIRS DNB data with road networks and land use information to improve reconstruction accuracy and spatial detail. Code is available for this project athttps://code.ornl.gov/viirs-sr/sr-demos.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Illuminating the Night: A Survey of Super-Resolution Methods for Nighttime Light Images

Nighttime Light (NTL) images provide critical insights into urbanization, disaster response, and energy consumption. The VIIRS Day/Night Band (DNB) sensor offers high-quality NTL imagery with daily revisit rates, but the available spatial resolution hinders fine-grained accurate analysis. Super-resolution techniques aim to increase the resolution of NTL images, enabling more detailed assessments of infrastructure, light pollution, economic activity, and power outages. However, existing state-of-the-art super-resolution methods designed for natural images struggle with the unique characteristics of NTL data. This work provides a comprehensive review of super-resolution methods across multiple image modalities, evaluates their effectiveness on VIIRS DNB data, and proposes a multi-modal super-resolution approach tailored to NTL imagery. The proposed approach integrates VIIRS DNB data with road networks and land use information to improve reconstruction accuracy and spatial detail. Code is available for this project at https://code.ornl.gov/viirs-sr/sr-demos.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Predicting High‐Resolution Spatial and Spectral Features in Mass Spectrometry Imaging with Machine Learning and Multimodal Data Fusion

Recent advancements in molecular Mass Spectrometry Imaging have sparked interest in integrating high spatial resolution methods with molecular mass-spectrometry-based chemical imaging. Fusion-based algorithms have proven effective in generating high spatial-resolution molecular mass spectra. However, a significant challenge stems from the differing physical mechanisms underlying image generation and data upsampling techniques, potentially leading to discrepancies in integrated information channels. Integrating physical constraints into data processing workflows is essential to tackle this issue. In this study, we propose an innovative approach that merges data from Fourier transform ion cyclotron resonance (FTICR), time-of-flight matrix-assisted laser desorption/ionization, and time-of-flight secondary ion mass spectrometry imaging techniques. By leveraging FT-ICR's unparalleled spectral resolution and ToF-SIMS's exceptional spatial resolution, we achieve submicron spatial resolution, enabling the observation of intact molecular species with remarkable spectral precision. Canonical correlation analysis is employed to incorporate physical constraints. Through sophisticated image processing and machine learning techniques, the results of this fusion hold significant promise for advancing our comprehension of complex systems and unveiling concealed molecular intricacies.

canonical correlation analysis↗