Orthogonal Functions Research Articles

An EOF-Based Global Plasmaspheric Electron Content Model and Its Potential Role in Vertical-Slant TEC Conversion

Topside total electron content (TEC) data measured by COSMIC/FORMAT-3 during 2008 and 2016 were used to analyze and model the global plasmaspheric electron content (PEC) above 800 km with the help of the empirical orthogonal function (EOF) analysis method, and the potential role of the proposed PEC model in helping Global Navigation Satellite System (GNSS) users derive accurate slant TEC (STEC) from existing high-precision vertical TEC (VTEC) products was validated. A uniform gridded PEC dataset was first obtained using the spherical harmonic regression method, and then, it was decomposed into EOF basis modes. The first four major EOF modes contributed more than 99% of the total variance. They captured the pronounced latitudinal gradient, longitudinal differences, hemispherical differences, diurnal and seasonal variations, and the solar activity dependency of global PEC. A second-layer EOF decomposition was conducted for the spatial pattern and amplitude coefficients of the first-layer EOF modes, and an empirical PEC model was constructed by fitting the second-layer basis functions related to latitude, longitude, local time, season, and solar flux. The PEC model was designed to be driven by whether solar proxy or parameters derived from the Klobuchar model meet the real-time requirements. The validation of the results demonstrated that the proposed PEC model could accurately simulate the major spatiotemporal patterns of global PEC, with a root-mean-square (RMS) error of 1.53 and 2.24 TECU, improvements of 40.70% and 51.74% compared with NeQuick2 model in 2009 and 2014, respectively. Finally, the proposed PEC model was applied to conduct a vertical-slant TEC conversion experiment with high-precision Global Ionospheric Maps (GIMs) and dual-frequency carrier phase observables of more than 400 globally distributed GNSS sites. The results of the differential STEC (dSTEC) analysis demonstrated the effectiveness of the proposed PEC model in aiding precise vertical-slant TEC conversion. It improved by 18.52% in dSTEC RMS on a global scale and performed better in 90.20% of the testing days compared with the commonly used single-layer mapping function.

Functionalization of Siloxanes with Arynes Generated from o-Triazenylarylboronic Acids.

Herein, we report the functionalization of polyhedral oligosilsesquioxanes (POSS) and related siloxanes with arynes. Using o-triazenylarylboronic acids as aryne precursors and silica gel as the activator, the transformation of siloxane bearing various arynophilic moieties on the side chains was achieved with high yields without touching the siloxane core. This method was applied to the conjugation of POSS and pharmaceutical cores using an aryne derived from the synthetic intermediate of cabozantinib. Furthermore, orthogonal dual functionalization of POSS was realized by combining the aryne reaction with Huisgen cyclization.

Skew Symplectic and Orthogonal Schur Functions

Using the vertex operator representations for symplectic and orthogonal Schur functions, we define two families of symmetric functions and show thatthey are the skew symplectic and skew orthogonal Schur polynomials defined implicitly by Koike and Terada and satisfy the general branching rules. Furthermore, we derive the Jacobi-Trudi identities and Gelfand-Tsetlin patterns for these symmetric functions. Additionally, the vertex operator method yields their Cauchy-type identities. This demonstrates that vertex operator representations serve not only as a tool for studying symmetric functions but also offers unified realizations for skew Schur functions of types A, C, and D.

Assessment of Rainfall and Temperature Trends in the Yellow River Basin, China from 2023 to 2100

China’s Yellow River Basin (YRB) is sensitive to climate change due to its delicate ecosystem and complex geography. Water scarcity, soil erosion, and desertification are major challenges. To mitigate the YRB’s ecological difficulties, climate change must be predicted. Based on the analysis of the evolution features of hydro-meteorological elements, the CMIP6 climate model dataset with Delta downscaling and the Empirical Orthogonal Function (EOF) is utilized to quantitatively explore the future variations in precipitation and temperature in the YRB. The following results are drawn: The spatial resolution of the CMIP6 climate model is less than 0.5° × 0.5° (i.e., about 55 km × 55 km), which is improved to 1 km × 1 km by the downscaling of Delta and has outstanding applicability to precipitation and temperature in the YRB. The most accurate models for monthly mean temperature are CESM2-WACCM, NorESM2-LM, and ACCESS-CM2, and for precipitation are ACCESS-ESM1-5, CESM2-WACCM, and IPSL-CM6A-LR. Between 2023 and 2100, annual precipitation increases by 6.89, 5.31, 7.02, and 10.18 mm/10a under the ssp126, ssp245, ssp370, and ssp585 climate scenarios, respectively, with considerable variability in precipitation in the YRB. The annual temperature shows a significant upward trend, and the change rates under the different climate scenarios are, respectively, 0.1 °C/10a, 0.3 °C/10a, 0.5 °C/10a, and 0.7 °C/10a. The increase is positively correlated with emission intensity. Based on the EOF analysis, temperature and precipitation mainly exhibit a consistent regional trend from 2023 to 2100, with the primary modal EOF1 of precipitation for each scenario exhibiting a clear spatial distribution in the southeast–northwest.

Investigation of the Historical Trends and Variability of Rainfall Patterns during the March–May Season in Rwanda

This study explores the spatiotemporal variability and determinants of rainfall patterns during the March to May (MAM) season in Rwanda, incorporating an analysis of teleconnections with oceanic–atmospheric indices over the period 1983–2021. Utilizing the Climate Hazards Group Infrared Precipitation with Stations (CHIRPS) dataset, the study employs a set of statistical tools including standardized anomalies, empirical orthogonal functions (EOF), Pearson correlation, the Mann–Kendall (MK) trend test, and Sen’s slope estimator to dissect the intricacies of rainfall variability, trends, and their association with large-scale climatic drivers. The findings reveal a distinct southwest to northwest rainfall gradient across Rwanda, with the MK test signaling a decline in annual precipitation, particularly in the southwest. The analysis for the MAM season reveals a general downtrend in rainfall, attributed in part to teleconnections with the Indian Ocean Sea surface temperatures (SSTs). Notably, the leading EOF mode for MAM rainfall demonstrates a unimodal pattern, explaining a significant 51.19% of total variance, and underscoring the pivotal role of atmospheric dynamics and moisture conveyance in shaping seasonal rainfall. The spatial correlation analysis suggests a modest linkage between MAM rainfall and the Indian Ocean Dipole, indicating that negative (positive) phases are likely to result in anomalously wet (dry) conditions in Rwanda. This comprehensive assessment highlights the intricate interplay between local rainfall patterns and global climatic phenomena, offering valuable insights into the meteorological underpinnings of rainfall variability during Rwanda’s critical MAM season.

Satellite-Based Estimation of Near-Surface NO2 Concentration in Cloudy and Rainy Areas

Satellite-based remote sensing enables the quantification of tropospheric NO2 concentrations, offering insights into their environmental and health impacts. However, remote sensing measurements are often impeded by extensive cloud cover and precipitation. The scarcity of valid NO2 observations in such meteorological conditions increases data gaps and thus hinders accurate characterization and variability of concentration across geographical regions. This study utilizes the Empirical Orthogonal Function interpolation in conjunction with the Extreme Gradient Boosting (XGBoost) algorithm and dense urban atmospheric observed station data to reconstruct continuous daily tropospheric NO2 column concentration data in cloudy and rainy areas and thereby improve the accuracy of NO2 concentration mapping in meteorologically obscured regions. Using Chengdu City as a case study, multiple datasets from satellite observations (TROPOspheric Monitoring Instrument, TROPOMI), near-surface NO2 measurements, meteorology, and ancillary data are leveraged to train models. The results showed that the integration of reconstructed satellite observations with provincial and municipal control surface measurements enables the XGBoost model to achieve heightened predictive accuracy (R2 = 0.87) and precision (RMSE = 5.36 μg/m3). Spatially, this approach effectively mitigates the problem of missing values in estimation results due to absent satellite data while simultaneously ensuring increased consistency with ground monitoring station data, yielding images with more continuous and refined details. These results underscore the potential for reconstructing satellite remote sensing information and combining it with dense ground observations to greatly improve NO2 mapping in cloudy and rainy areas.

A reduced order model formulation for left atrium flow: an atrial fibrillation case

A data-driven reduced order model (ROM) based on a proper orthogonal decomposition-radial basis function (POD-RBF) approach is adopted in this paper for the analysis of blood flow dynamics in a patient-specific case of atrial fibrillation (AF). The full order model (FOM) is represented by incompressible Navier–Stokes equations, discretized with a finite volume (FV) approach. Both the Newtonian and the Casson’s constitutive laws are employed. The aim is to build a computational tool able to efficiently and accurately reconstruct the patterns of relevant hemodynamics indices related to the stasis of the blood in a physical parametrization framework including the cardiac output in the Newtonian case and also the plasma viscosity and the hematocrit in the non-Newtonian one. Many FOM-ROM comparisons are shown to analyze the performance of our approach as regards errors and computational speed-up.

Gyro-kinetic simulations of trapped electron collision effects on low-frequency drift-wave instabilities in tokamak plasmas

Low-frequency drift-wave instabilities play a crucial role in the radial transport of present-day tokamaks, and trapped electron collisions can significantly influence these instabilities. In this paper, the effects of trapped electron collisions on these instabilities are investigated based on linear gyro-kinetic simulations. The basic numerical techniques including dispersion relation integral method and orthogonal basis function expansion are presented in detail with necessary benchmark work. The results demonstrate that in medium gradients, the increase of trapped electron proportions promotes the growth rate and radial heat transport largely for quasi-linear trapped electron modes (TEMs) and ion temperature gradient (ITG) modes. Moreover, trapped electron collisions have strong stabilizing effects, especially for TEMs driven by electron temperature gradients. Two distinctive branches, namely Mode #1 and #2, are investigated in steep gradients. Both behave in a varied instability nature during different ranges of the normalized wave vector k^θ . Mode #1 mainly induces radial heat transport during k^θ<0.5 and is significantly suppressed by the collisions. Mode #2 mainly induces radial heat transport during 0.4<k^θ<0.8 , and is largely enhanced by the collisions. When the collisionality is large enough, Mode #2 has stronger transport capacity than the other. Mode #2 at the medium wave vector, known as dissipative TEM, may provide the mechanism of the edge coherent mode observed in EAST H-mode plasmas, wherein collisionality plays an important role in the mode excitation.

Reconstructing the sound speed profile of South China Sea using remote sensing data and long short-term memory neural networks

IntroductionSound waves are refracted along the direction of their propagation owing to spatial and temporal fluctuations in the speed of sound in seawater. Errors are compounded when sound speed profiles (SSPs) with low precision are used to detect and locate distant underwater targets because an accurate SSP is critical for the identification of underwater objects based on acoustic data. Only sparse historical spatiotemporal data on the SSP of the South China Sea are available owing to political issues, its complex atmospheric system, and the unique topography of its seabed, because of which frequent oceanic movements at the mesoscale affect the accuracy of inversion of its SSP.MethodIn this study, we propose a method for the inversion of the SSP of the South China Sea based on a long short-term memory model. We use continuous-time data on the SSP of the South China Sea as well as satellite observations of the height and temperature of the sea surface to make use of the long-term and short-term memory-related capacities of the proposed model.ResultIt can achieve highly accurate results while using a small number of samples by virtue of the unique structure of its memory. Compared with the single empirical orthogonal function regression method, the inversion accuracy of this model is improved by 24.5%, and it performed exceptionally well in regions with frequent mesoscale movements.DiscussionThis enables it to effectively address the challenges posed by the sparse sample distribution and the frequent mesoscale movements of the South China Sea.

Proper orthogonal descriptors for multi-element chemical systems

We introduce the proper orthogonal descriptors for efficient and accurate interatomic potentials of multi-element chemical systems. The potential energy surface of a multi-element system is represented as a many-body expansion of parametrized potentials which are functions of atom positions, atom types, and parameters. The proper orthogonal decomposition is employed to decompose the parametrized potentials as a linear combination of orthogonal basis functions. The orthogonal basis functions are used to construct proper orthogonal descriptors based on the elements of atoms, thus leading to multi-element descriptors. We compose the multi-element proper orthogonal descriptors to develop linear and quadratic interatomic potentials. We devise an algorithm to efficiently compute the total energy and forces of the interatomic potentials constructed from the proper orthogonal descriptors. The potentials are demonstrated for indium phosphide and titanium dioxide in comparison with the spectral neighbor analysis potential (SNAP) and atomic cluster expansion (ACE) potentials.

Attribution analysis and forecast of salinity intrusion in the Modaomen estuary of the Pearl River Delta

Attribution analysis and forecast of salinity intrusion in the Modaomen estuary of the Pearl River Delta

Leveraging Transfer Learning and U-Nets Method for Improved Gap Filling in Himawari Sea Surface Temperature Data Adjacent to Taiwan

Satellite sea surface temperature (SST) images are valuable for various oceanic applications, including climate monitoring, ocean modeling, and marine ecology. However, cloud cover often obscures SST signals, creating gaps in the data that reduce resolution and hinder spatiotemporal analysis, particularly in the waters near Taiwan. Thus, gap-filling methods are crucial for reconstructing missing SST values to provide continuous and consistent data. This study introduces a gap-filling approach using the Double U-Net, a deep neural network model, pretrained on a diverse dataset of Level-4 SST images. These gap-free products are generated by blending satellite observations with numerical models and in situ measurements. The Double U-Net model excels in capturing SST dynamics and detailed spatial patterns, offering sharper representations of ocean current-induced SST patterns than the interpolated outputs of Data Interpolating Empirical Orthogonal Functions (DINEOFs). Comparative analysis with buoy observations shows the Double U-Net model’s enhanced accuracy, with better correlation results and lower error values across most study areas. By analyzing SST at five key locations near Taiwan, the research highlights the Double U-Net’s potential for high-resolution SST reconstruction, thus enhancing our understanding of ocean temperature dynamics. Based on this method, we can combine more high-resolution satellite data in the future to improve the data-filling model and apply it to marine geographic information science.

Estimation of groundwater storage variations in African river basins: Response to global climate change using GRACE and GRACE-FO among past two decades

Groundwater Storage (GWS) is an important component of the water cycle and a vital resource for supplying water to millions of people as well as sustaining domestic and economic activities, especially in arid and semi-arid regions such as Africa. This study aims to estimate and analyze the recent groundwater changes (ΔGW) for 11 major African basins in light of climate changes and global warming utilizing the data from the Gravity Recovery and Climate Experiment (GRACE) and GRACE Follow-On (GRACE-FO) from January 2003 to December 2021. We proposed a new gap-filling technique to calculate the missing months between GRACE and GRACE-FO missions for the continuous estimation of groundwater changes. Then, we establish a new framework to analyze and investigated the climate parameters that could affect groundwater changes using Empirical Orthogonal Function (EOF) technique. Our analysis reveals that the new gap-filling technique is significantly consistent with the TWS time-series based on the trend line analysis. The lowest GPCC drought index value occurs in the lower Nile basin by approximately −0.93, while the highest occurs in the middle of Africa in Congo basin by approximately −0.02. The precipitation rate is mostly concentrated in mid-Africa while North and South Africa shows a weak rate. Meanwhile, according to the analysis of dependent climate parameters, climate change has had a negative impact on groundwater. However, the long-term effect on the groundwater does not clearly appear because most of Africa is located within semi-arid and arid regions. The effect of rain on groundwater was evident through EOF analysis, which shows GWS EOF Mode-2 (36.28%) and precipitation EOF Mode-1 (78.34%) were found to be in significant agreement in spatio-temporal domains.

Asymmetric responses of summer soil moisture anomalies to the large-scale teleconnections on the Loess Plateau between 2000 and 2020

Soil moisture is a key regulator of hydrological cycle and is closely related to vegetation growth and climate changes, which is mainly replenished by summer precipitation on the Loess Plateau. However, the response of soil moisture content (SMC) anomalies during summer on the Loess Plateau to large-scale teleconnection remains unclear. Here, using the empirical orthogonal function (EOF) method, this study extracted a homogenized area with significant variability of normalized difference vegetation index (NDVI) (p<0.01), which was called sensitive areas for vegetation restoration (SAVR) of the Loess Plateau. Based on 1 km daily soil moisture dataset named SMCI1.0 at top 1 m, we demonstrated that there was an interannual fluctuation of summer SMC from 2000 to 2020 over the SAVR of the Loess Plateau. Spatially, SMC during summer in the SAVR of the Loess Plateau exhibited an enhanced regional difference characterized by ‘dry to drier and wet to wetter’. Importantly, abnormal SMC during summer in the SAVR of the Loess Plateau can been attributed to distinct circulation pattern and anomalous water vapor transport, which showed asymmetrical distributions between positive and negative anomalous years of summer SMC. Due to the activities of western Pacific subtropical high (WPSH) and low-pressure system around the Lake Baikal (an anomalous anticyclone prevailed over the western north Pacific), the positive (negative) anomalous years of summer SMC witnessed net water vapor influx (outflux) anomalies to the Loess Plateau compared to the climatology, corresponding to anomalous upward (sinking) motions, further leading to more (less) SMC in summer over the SAVR of the Loess Plateau, respectively. The conclusions of this study have implications for excavating early warning information of SMC anomalies and natural restoration sustainable management on the Loess Plateau.

Investigating a novel feature of multi-phase rotated empirical orthogonal function to capture spatiotemporal temperature variations

Investigating a novel feature of multi-phase rotated empirical orthogonal function to capture spatiotemporal temperature variations

Spectral solutions for fractional Klein–Gordon models of distributed order

The Klein–Gordon equation is a fundamental theoretical physics concept, governing the behavior of relativistic quantum particles with spin-zero. Its numerical solution is crucial in fields like quantum field theory, particle physics, and cosmology. The study explores numerical methodologies for solving this equation, highlighting their significance and challenges. This study uses the collocation method to approximate fractional Klein–Gordon models of distributed order based on Shifted Jacobi orthogonal polynomials and Shifted fractional order Jacobi orthogonal functions. While, the distributed term (integral term) was treat using Legendre–Gauss–Lobatto quadrature. It assesses residuals through finite expansion and yields accurate numerical results. The method is more factual and fair when initial and boundary conditions are enforced. Numerical simulations are presented to demonstrate the method’s accuracy, particularly in fractional Klein–Gordon models of distributed order. Furthermore, we offer a few numerical test scenarios to show that the method is able to maintain the non-smooth solution of the underlying issue.

Trend and interannual variability of summer marine heatwaves in the tropical Indian ocean: Patterns, mixed layer heat budget, and seasonal prediction

Marine heatwaves (MHWs) are extreme sea surface temperature (SST) events in all ocean basins, with far-reaching impacts on marine ecosystems and socio-economy. The leading patterns, trend, and interannual variability of summer MHWs in the tropical Indian Ocean (TIO) are investigated in this study. The first empirical orthogonal function (EOF) mode of frequency of MHWs exhibits a monopole pattern over the entire basin. This mode is highly associated with the concurrent Indian Ocean Basin warming, indicating a remarkable trend over the past four decades. The linear trend in MHW properties largely relates to increased summer Indian Ocean mean SST. The second EOF mode exhibits a zonal dipole with the MHW numbers increasing in the west and decreasing in the east. On the interannual timescale, the first two EOF modes are remotely affected by antecedent and concurrent El Niño events, respectively. The ocean mixed layer budget is utilized for examining the formation of different summer MHW patterns. During the preceding spring, the surface heat flux is important for the development of MHWs, while the ocean advections play a secondary role in the South Indian Ocean for the MHW monopole. Once the SST anomaly rises in summer, the ocean advections play a dominant role in maintaining the SST. Last, we assess the prediction skill of summer TIO MHWs by performing a bilinear seasonal statistical prediction model. Our results suggest the frequency of summer MHWs in the TIO could be predicted one season in advance. This study has great implications for understanding and predicting ocean extreme events in the TIO.

A 3-D minimum-enstrophy vortex in stratified quasi-geostrophic flows

Applying a variational analysis, a minimum-enstrophy vortex in three-dimensional (3-D) fluids with continuous stratification is found, under the quasi-geostrophic hypothesis. The buoyancy frequency is held constant. This vortex is an ideal limiting state in a flow with an enstrophy decay while energy and generalized angular momentum remain fixed. The variational method used to obtain two-dimensional (2-D) minimum-enstrophy vortices is applied here to 3-D integral quantities. The solution from the first-order variation is expanded on a basis of orthogonal spherical Bessel functions. By computing second-order variations, the solution is found to be a true minimum in enstrophy. This solution is weakly unstable when inserted in a numerical code of the quasi-geostrophic equations. After a stage of linear instability, nonlinear wave interaction leads to the reorganization of this vortex into a tripolar vortex. Further work will relate our solution with maximal entropy 3-D vortices.

Analysis of sea level variability and its contributions in the Bohai, Yellow Sea, and East China Sea

Understanding the sea level variability of the Bohai, Yellow Sea, and East China Sea (BYECS) is crucial for the socio-cultural and natural ecosystems of the coastal regions. In this study, based on satellite altimetry data, selected time range from 1993 to 2020, using the cyclostationary empirical orthogonal function (CSEOF) analysis method distinguishes the primary sea level variability modes. The analysis encompasses the seasonal signal, trend, and El Niño-Southern Oscillation (ENSO) associated mode of sea level anomaly. The amplitude of the annual cycle demonstrates a non-stationary signal, fluctuating between -15% and 15% from the average. Monsoons, atmospheric forcing, ocean circulation, wind-driven Ekman transport, and the Kuroshio emerge as the primary factors influencing BYECS variability on seasonal scales. The satellite altimetry sea level exhibits an average trend within the range of 3-4 mm/year, while the steric sea level trend is generally smaller, falling within the range of 0-2 mm/year. Throughout the entire period, the contribution of steric sea level to the mean sea level trend consistently remains below 25%. Furthermore, BYECS sea level variations have a sensitive response to strong El Niño years, with a clear regionalization of the response, which is related to the intricate atmospheric circulation and local wind pressures, as well as the influence of ocean circulation. In conclusion, we gained a more comprehensive understanding of sea level variability in the BYECS, especially the annual cycle of sea level amplitude and the response of ENSO. However, more studies still need to be done to differentiate the various factors in sea level variations.

Analysis on characteristics of extreme precipitation indices and atmospheric circulation in Northern Shanxi

This article utilizes daily precipitation data from 28 national meteorological stations in northern Shanxi Province spanning from 1972 to 2020, and the US NCEP/NCAR monthly average reanalysis and ERA5 monthly average reanalysis data. The study employs techniques such as empirical orthogonal function (EOF) decomposition, Mann-Kendall mutation and other methods to investigate the spatiotemporal distribution of extreme precipitation index in northern Shanxi and their correlation with atmospheric circulation. The research results show that: the absolute index, relative index, intensity index and sustained dry period index (CDD) in the continuous index appear from southwest to northeast. The spatial distribution characteristics of the central region decrease, while the continuous wet period (CWD) decreases from the central to the east and west. The three indices Rx1day, Rx5day, and CWD mutated in 1978, 1975, and 1983 respectively, and other extreme precipitation indices all appeared in a sudden change from a low-value period to a high-value period occurred around 2010. In the high-value years of the summer extreme precipitation index, there is a significant negative anomaly in the height field in the mid-high latitude regions of Eurasia. Northern Shanxi is controlled by a broad low-pressure trough in the Lake Baikal area. Water vapor transported via the east, west, and south routes converges in the northern Shanxi region and encounters cold air from the north. There is a strong upward motion anomaly at 500 hPa in the troposphere, and the dynamic conditions of upper-level divergence and lower-level convergence lead to more summer extreme precipitation in the northern Shanxi region. Conversely, in the low-value years of the summer extreme precipitation index, northern Shanxi is affected by a strong high-pressure ridge north of Lake Baikal. There is a downward motion anomaly at 500 hPa, and the northern Shanxi region lacks water vapor. The cold and warm air cannot converge, and both the water vapor conditions and dynamic conditions are poor, which is not conducive to the production of extreme precipitation in northern Shanxi.