Orthogonal Function Approach Research Articles

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.

Optimal design of Luenberger reduced-order observer with low sensitivity for linear multivariable systems

For the linear multivariable systems, by combining both merits of orthogonal-function approach and evolutionary optimization, in this paper, a new method is presented for designing a Luenberger reduced-order observer to solve the low-sensitivity design issue for physical system parameter deviation and simultaneously to minimize a measurement of the quadratic performance for reducing state transient estimation error. Two given examples illustrate the effectiveness of the presented new low-sensitivity design approach on state estimation performance. From the given examples, it shows that the estimated state errors are not sensitive to system parameter deviation and have the asymptotical convergence property. Besides, the performances are apparently superior to those without considering low-sensitivity design means.

A Comparison of Multiple Approaches to Study the Modulation of Ocean Waves Due To Climate Variability

AbstractUsing multiple approaches, the modulation of climate variability on global ocean waves from 1981 to 2020 is investigated based on a wave hindcast model forced by ERA5 winds. These climate variabilities include El Niño–Southern Oscillation (ENSO), Antarctic Oscillation (AAO), Arctic Oscillation (AO), Pacific Decadal Oscillation (PDO), Atlantic Multidecadal Oscillation (AMO), and Indian Ocean Dipole. Linear regression and composite analysis results indicate that El Niño‐induced low‐pressure systems in December–February (DJF) generate energetic waves in the Pacific Ocean. Positive AAO events are associated with the southward movement of westerlies in the Southern Hemisphere and thus produce long‐period Southern Ocean swell that impacts the South Pacific Ocean. In the Northern Hemisphere, positive AO is associated with strengthening winds which generate larger waves around the Icelandic region. An empirical orthogonal function approach was further undertaken to study interannual variability of significant wave height (Hs) anomalies. In DJF, mode 1 marks the impacts of ENSO and PDO in the Pacific Ocean and AO in the North Atlantic Ocean. Mode 2 is controlled by AO, which is characterized by a dipole pattern in the North Atlantic Ocean. Mode 3 describes the AAO footprints in the Southern Ocean and the eastern Pacific Ocean. In June–August, the leading mode is influenced by AAO and AMO. Mode 2 indicates the importance of ENSO and PDO which exhibit opposite patterns in the Pacific Ocean sector of the Southern Ocean. Finally, a wavelet coherence analysis is conducted on the principal components and climate indexes, which shows their respective evolutions over the time–frequency domain.

Сравнительная оценка объемов данных, необходимых для вычисления значений геофизических параметров с помощью ортогональных функций и сеток на локальных участках земной поверхности

Two approaches to calculating geophysical parameters at arbitrarily specified points on local areas of the Earth`s surface are considered. They are based on orthogonal function and regular meshing methods. The problem of finding the relationship of the series terms number with the grid’s step is solved. It takes into account the spatial variability of the geophysical parameter, the required accuracy of its deducing at any point and the characteristics of the errors for the available measurement data. The solution of the problem is found based on the two-step generalized least squares method (the generalized instrumental variables estimator) and the one of canonical decomposition of a vector random function. It enabled rationalizing the choice one of those approaches as to the data volume amount needed to calculate the values of geophysical parameters at any specified point. An example of estimating the amount of the data required to calculate the values of the gravity anomaly at arbitrarily specified points on a local area is given. It takes into account the increased demands for accuracy and spatial resolution of geophysical parameters. The example shows that the use of orthogonal functions approach is more preferable in the view of the required data amount.

Spatio-temporal analysis of aerosol optical depth using rotated empirical orthogonal function over the Maritime Continent from 2001 to 2020

The deterioration in the annual air quality of the Maritime Continent (MC) is mainly caused by biomass burning haze (BBH) and the surrounding atmospheric conditions. This study aims to investigate the spatial and temporal variations of the aerosol optical depth (AOD) and its relationship with biomass burning and climate anomaly factors in the MC from 2001 to 2020. Using aerosol model reanalysis products from the Modern-Era Retrospective analysis for Research and Applications, version 2 (MERRA-2), values of the aerosol optical depth (AOD) over the MC were collected and processed to obtain a better understanding of the characteristics of the aerosol loading over the MC. Using the varimax rotated empirical orthogonal function (REOF) approach, we assess the spatio-temporal distributions of the AOD over the MC from 2001 to 2020. The REOF maximized the variances explained for the primary modes and has shown clearer relationship between the spatiotemporal patterns of identified modes. The first three REOF modes of the AOD accounted for a total variance of 73.7%. The first mode (REOF1) explaining 35.8% is the main mode that represent fire burning that concentrated over the 0° latitude. REOF1 represents the emission from burning activities which primarily occurred in the Kalimantan and Sumatra based on their correlation with the total hotspots, which reach 0.73, which a certain extent of correlation with the climate anomalies, including El Niño, positive DM, and their coincidence. The second (REOF2) also explaining 35.8% represents the AOD distribution influenced by the biomass burning emission transported from the Indochina in the area to the north of 5°N which has an opposite mode with the general mode in MC except for Java area. Meanwhile, PC3 AOD has reduced to 2.2% in the rotation process and represent the influence of monsoon movement on the AOD level. In short, the study highlights spatial and temporal AOD distribution and the phenomena of burning mass and climate indices in the long-term MERRA reanalysis dataset to allow more understanding of the causal links of AOD in MC to the climate features.

Space-time dynamics of soil moisture and groundwater in an agriculture-dominated critical zone observatory (CZO) in the Ganga basin, India

Space-time variability of soil moisture (SM) and ground water plays a fundamental role in shaping hydrology of terrestrial ecosystem, best represented as the Critical Zone (CZ), which extends from top of vegetation canopy to the bottom of groundwater table. In several parts of the world, a network of instrumented sites, known as Critical Zone Observatories (CZOs), have been set up to understand the hydrodynamics of soil–water system in particular reference to natural and anthropogenic forcings. Here, we employed the empirical orthogonal function (EOF), random combination, and temporal stability approach to understand the in-situ space–time dynamics of SM and depth to groundwater table (DTGT) over an agriculture-dominated CZO in the Ganga basin. Our results showed that both the components exhibit a constant temporal coefficient of variation, suggesting a consistent seasonal changing pattern. Around 91 % of the observed DTGT spatial variation are explained by first two spatial EOFs while the first five EOFs explain only 67 % of the total SM variability. On an annual basis, the spatial patterns of SM and DTGT are driven by topography and soil texture (% clay) while monsoon rainfall and post-monsoon crop cycle appear to be the leading factors for temporal variability of both components. Furthermore, we have demonstrated that randomly selected four sampling locations and three monitoring wells within the CZO could capture the mean spatial variability of SM (RMSE = 3 % vol/vol) and DTGT (RMSE = 0.7 mgbl) respectively. In addition, temporal stability analysis indicates that four representative sites and a single monitoring well can provide robust catchment mean with an absolute error of ±2 % vol/vol and 0.36 mgbl respectively. Overall, this study provides an insight to the hydrodynamics and controls of SM and groundwater in an agricultural landscape with significant implications for upscaling and efficient water resource management in such regions.

An effort saving method to establish global aerodynamic model using CFD

Purpose The typical approach of modeling the aerodynamics of an aircraft is to develop a complete database through testing or computational fluid dynamics (CFD). The database will be huge if it has a reasonable resolution and requires an unacceptable CFD effort during the conceptional design. Therefore, this paper aims to reduce the computing effort required via establishing a general aerodynamic model that needs minor parameters. Design/methodology/approach The model structure was a preconfigured polynomial model, and the parameters were estimated with a recursive method to further reduce the calculation effort. To uniformly disperse the sample points through each step, a unique recursive sampling method based on a Voronoi diagram was presented. In addition, a multivariate orthogonal function approach was used. Findings A case study of a flying wing aircraft demonstrated that generating a model with acceptable precision (0.01 absolute error or 5% relative error) costs only 1/54 of the cost of creating a database. A series of six degrees of freedom flight simulations shows that the model’s prediction was accurate. Originality/value This method proposed a new way to simplify the model and recursive sampling. It is a low-cost way of obtaining high-fidelity models during primary design, allowing for more precise flight dynamics analysis.

Variability of Chlorophyll-a and Secchi Disk Depth (1997–2019) in the Bohai Sea Based on Monthly Cloud-Free Satellite Data Reconstructions

Ocean colour data are crucial for monitoring and assessing marine ecosystems. In this study, the Data Interpolating Empirical Orthogonal Functions (DINEOF) approach was applied to the Ocean Colour Climate Change Initiative (OC-CCI), chlorophyll-a (Chl-a) and Secchi disk depth (Zsd) to completely reconstruct the missing pixels in the Bohai Sea during 1997–2019. The results of cross-validation demonstrate that the DINEOF reconstructed data have a good agreement with the satellite-measured data. Based on monthly cloud-free satellite data reconstructions, the Zsd series showed high negative correlation with log10 (Chl-a). The Zsd as a function of log10 (Chl-a) can be well fitted by the cubic polynomial in the offshore waters. The Chl-a in the entire Bohai Sea showed a significant decreasing trend (−0.013 mg/m3/year), while the Zsd exhibited a significant increasing trend (0.0065 m/year), and both had regional-seasonal variations. In addition, the ensemble empirical mode decomposition (EEMD) results reveal highly nonlinear trends of Chl-a and Zsd. The linear and nonlinear trends of Chl-a and Zsd suggest the deterioration of water quality in the Bohai Sea was not continued over the past two decades. This study presents the first simultaneous investigation of Chl-a and Zsd using the 23 years of cloud-free reconstructions in the Bohai Sea.

Two-Decade Variability of Sea Surface Temperature and Chlorophyll-a in the Northern South China Sea as Revealed by Reconstructed Cloud-Free Satellite Data

Monthly sea surface temperature (SST) and chlorophyll-a (Chl-a) concentration during 1997–2018 in the Northern South China Sea (NSCS) were gap-filled using the Data INterpolating Empirical Orthogonal Functions (DINEOFs) approach. Good accuracy of the reconstructed data was verified based on an independent cross-validation data set. Significant spatial heterogeneities and seasonal variations were observed in the cloud-free SST and Chl-a data. An apparent decreasing trend in SST was found along the coast of Guangdong, east of Hainan Island, and in the Taiwan Strait with an average decreasing rate amounting to 0.01 °C per year. Increase in SST was observed in Beibu Gulf and the deep offshore region in the NSCS at an average rate as high as 0.009 °C per year. An increasing trend in Chl-a was detected in the northern Beibu Gulf, near the mouth of the Pearl River estuary, and around Shantou with an average rate of 0.005 mg <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\cdot \text{m}^{-3}$ </tex-math></inline-formula> per year. EOF analysis of SST and Chl-a time series showed that the first three modes of both SST and Chl-a can explain most of their variances with accumulative contributions of 99.1% and 82.3%, respectively. The effects of surface net heat flux (NHF), Oceanic Niño Index (ONI), wind speed, and river flux on the first three modes of SST and Chl-a were quantitatively elucidated. Factors that affected the temporal and spatial variations of Chl-a and SST in the NSCS were qualitatively discussed, including El Niño-Southern Oscillation (ENSO), monsoon, upwelling, typhoon, internal waves, and Kuroshio intrusion.

Quantifying Seasonal‐to‐Interannual‐Scale Storm Impacts on Morphology Along a Cuspate Coast With a Hybrid Empirical Orthogonal Function Approach

AbstractThe direct impacts of storms on beaches have been well studied; less well understood are the controls of storms on their seasonal‐interannual evolution. We apply a novel empirical orthogonal function (EOF) analysis to a 5‐year data set of monthly subaerial beach topography at Kennedy Space Center, Florida, to extract dominant spatiotemporal topographic patterns. Our hybrid surface EOF (SEOF) approach applies 1‐D EOF techniques to a data set varying in two dimensions, thereby extracting topographic patterns in the longshore and cross‐shore simultaneously while preserving the analytical simplicity of 1‐D approaches. These topographic patterns are then linked to observations of storm impacts. Our approach comprehensively illustrates that storms influenced local topographic evolution over event‐to‐interannual‐timescales. The first mode of topographic variability captures an interannual‐scale change in behavior triggered by the impact of Hurricane Sandy (2012), whereby a cape feature began and sustained rapid aggradation following the event. This pattern is likely linked to storm‐response processes and pre‐existing morphodynamic feedbacks, illustrating that storm response can dictate poststorm recovery processes. This pattern overwhelmed a spatially uniform, seasonal topographic signal, which we attribute to seasonal variability in water level and storminess forcings. The third mode shows links to local framework geology and suggests that some storms can create and/or destroy subaerial berms at this site, where spatial variability of berm existence in discrete longshore compartments can remain stable until a future event. Our results illustrate mechanisms by which storms can create persistent topographic imprints that remain visible for months‐years following events, potentially influencing response to future storms.

Optimal parallel-distributed-compensation controller design for a class of time-varying Takagi–Sugeno fuzzy model–based time-delay systems by using the orthogonal function approach–assisted genetic algorithm

This study proposes a method of designing quadratic optimal fuzzy parallel-distributed-compensation controllers for a class of time-varying Takagi–Sugeno fuzzy model–based time-delay control systems used to solve the finite-horizon optimal control problem. The proposed method fuses the orthogonal function approach and the improved hybrid Taguchi-genetic algorithm. The Taguchi-genetic algorithm only requires algebraic computation to perform the algorithm used to solve time-varying Takagi–Sugeno fuzzy model–based time-delay feedback dynamic equations. The fuzzy parallel-distributed-compensation controller design problem is simplified by using the Taguchi-genetic algorithm to transform the static parameter optimization problem into an algebraic equation. The static optimization problem can then be solved easily by using the improved hybrid Taguchi-genetic algorithm to find the quadratic optimal parallel-distributed-compensation controllers of the time-varying Takagi–Sugeno fuzzy model–based time-delay control systems. The applicability of the proposed integrative method is demonstrated in a real-world design problem.

Two Contrasting African Easterly Wave Behaviors

AbstractThe dominant structural variability of African easterly waves (AEWs) is explored using an empirical orthogonal function (EOF) approach. The structure of AEWs is obtained by projecting the wind fields from reanalysis data and satellite-derived brightness temperature Tb onto the principal components associated with EOF patterns of filtered Tb (Tb EOF) and 700-hPa meridional wind (v700 EOF). The wave structure depicted by the Tb EOF has confined convection and circulation mostly south of the African easterly jet. It shares many characteristics with AEWs analyzed and discussed in the literature. In contrast, the v700 EOF exhibits less familiar characteristics and includes interactions with the equatorial and subtropical regions. The convective patterns are characterized by a “checkerboard” pattern of convection that has not been emphasized before. The most striking feature is the broad meridional extent, which depicts interactions with a mixed Rossby–gravity wave (MRG) in the equatorial region and interactions with the basic-state potential vorticity in the subtropics. The southern portion of the wave has a modified MRG structure, and this AEW–MRG hybrid cannot be separated using the EOF technique, indicating the prevalence of such structures. The subtropical interaction at mid- to lower levels establishes a vortex off the coast of Morocco that results in dry-air advection into the tropics in tandem with the northern vortex. At upper levels, a subtropical wave train is induced by the AEW-associated convective inflow and outflow. The contrasting AEW circulations are associated with differences in the precipitation rates and patterns over Africa. These results highlight the variability of AEW structures and their interactions with equatorial and subtropical waves.

Multivariate DINEOF Reconstruction for Creating Long-Term Cloud-Free Chlorophyll-a Data Records From SeaWiFS and MODIS: A Case Study in Bohai and Yellow Seas, China

A long-term reliable satellite chlorophyll- a (chl- a ) data record is essential in understanding the state of ocean biology and quantifying its changes. Creating a long-term data record requires a combination/merger of multiple satellite products into one data record, since the lifetime of any single ocean color sensor is finite. However, because of differences in sensor design, calibration, and retrieval models, apparent cross-mission biases are usually observed between different sensor products. To attain a coherent multisensor chl- a data record, the observed cross-mission biases should be accurately addressed in the data combination/merging schemes. In this study, a multivariable data interpolating empirical orthogonal functions (M-DINEOF) approach was used to create long-term chl- a records by applying the sea-viewing wide field-of-view sensor and moderate resolution imaging spectroradiometer products. Under the assumption that the single-sensor chl- a product is free from spurious temporal artifacts and can be reference time series representing the actual variability of chl- a , the discrepancies of trends derived from different chl- a series were quantitatively evaluated based on statistical t -test and Taylor diagram analyses. Compared with direct concatenation and linear regression methods, the M-DINEOF method more effectively reproduced the main trend patterns observed in reference data series during their overlapped periods. The results highlight the importance of a cross-mission bias correction when combining multisensor satellite data records and suggest that the M-DINEOF reconstruction provides a simple and effective path forward for creating reliable multisensor ocean color records suitable for long-term trend analysis.

Optimal design of reduced-order observers with specified eigenvalues and performance measurement of minimizing estimation errors using evolutionary optimization

A new method is proposed in this paper which designs a reduced-order observer of a non-observable-form-based dynamical system such that: (i) the eigenvalues are specified to satisfy desired convergence performance, (ii) a full-rank condition is satisfied, and (iii) a quadratic performance measurement of the deviation of the estimates from the actual states is minimized so as to reduce the large error occurring during the transient period of observation. The proposed approach combines the merits of both the orthogonal functions approach and evolutionary optimization. By solving a Sylvester equation, the proposed optimal design method can not only be used to design the reduced-order observer of a non-observable-form-based dynamical system, but also can avoid the shortcomings of approaches already existing in relevant literatures. Two examples are given to demonstrate the effectiveness and efficiency of the proposed new optimization method on the performance of state estimations. From the demonstrative examples, it can be seen that the estimated state errors asymptotically converge quickly to zero. In addition, the performance measurement values based on the proposed optimal design approach are apparently much lower than those based on the existing nonoptimal design method.

Optimal Observer Design of State Delay Systems

This paper proposes a new method to design the observer for state delay systems such that (i) state estimation errors converge to zero quickly and (ii), at the same time, a quadratic performance measurement of the deviation of estimates from the actual states is minimized for reducing large error during the transient period of observation. The proposed new approach fuses the merits of both the orthogonal functions approach and evolutionary optimization. One illustrative example is given to verify the effectiveness and efficiency of the proposed new optimization method on performance improvement of state estimations. From the illustrative example, in addition to the asymptotical convergence of the estimated state errors, the performance index for the proposed optimal design approach is clearly much lower than that of the nonoptimal design method.

Assessing the Potential Benefits of the Geostationary Vantage Point for Generating Daily Chlorophyll-a Maps in the Baltic Sea

Currently, observations from low-Earth orbit (LEO) ocean color sensors represent one of the most used tools to study surface optical and biogeochemical properties of the ocean. LEO observations are available at daily temporal resolution, and are often combined into weekly, monthly, seasonal, and annual averages in order to obtain sufficient spatial coverage. Indeed, daily satellite maps of the main oceanic variables (e.g., surface phytoplankton chlorophyll-a) generally have many data gaps, mainly due to clouds, which can be filled using either Optimal Interpolation or the Empirical Orthogonal Functions approach. Such interpolations, however, may introduce large uncertainties in the final product. Here, our goal is to quantify the potential benefits of having high-temporal resolution observations from a geostationary (GEO) ocean color sensor to reduce interpolation errors in the reconstructed hourly and daily chlorophyll-a products. To this aim, we used modeled chlorophyll-a fields from the Copernicus Marine Environment Monitoring Service’s (CMEMS) Baltic Monitoring and Forecasting Centre (BAL MFC) and satellite cloud observations from the Spinning Enhanced Visible and Infrared Imager (SEVIRI) sensor (on board the geostationary satellite METEOSAT). The sampling of a GEO was thus simulated by combining the hourly chlorophyll fields and clouds masks, then hourly and daily chlorophyll-a products were generated after interpolation from neighboring valid data using the Multi-Channel Singular Spectral Analysis (M-SSA). Two cases are discussed: (i) A reconstruction based on the typical sampling of a LEO and, (ii) a simulation of a GEO sampling with hourly observations. The results show that the root mean square and interpolation bias errors are significantly reduced using hourly observations.

Surface impacts of the Quasi Biennial Oscillation

Abstract. Teleconnections between the Quasi Biennial Oscillation (QBO) and the Northern Hemisphere zonally averaged zonal winds, mean sea level pressure (mslp) and tropical precipitation are explored. The standard approach that defines the QBO using the equatorial zonal winds at a single pressure level is compared with the empirical orthogonal function approach that characterizes the vertical profile of the equatorial winds. Results are interpreted in terms of three potential routes of influence, referred to as the tropical, subtropical and polar routes. A novel technique is introduced to separate responses via the polar route that are associated with the stratospheric polar vortex, from the other two routes. A previously reported mslp response in January, with a pattern that resembles the positive phase of the North Atlantic Oscillation under QBO westerly conditions, is confirmed and found to be primarily associated with a QBO modulation of the stratospheric polar vortex. This mid-winter response is relatively insensitive to the exact height of the maximum QBO westerlies and a maximum positive response occurs with westerlies over a relatively deep range between 10 and 70 hPa. Two additional mslp responses are reported, in early winter (December) and late winter (February/March). In contrast to the January response the early and late winter responses show maximum sensitivity to the QBO winds at ∼ 20 and ∼ 70 hPa respectively, but are relatively insensitive to the QBO winds in between (∼ 50 hPa). The late winter response is centred over the North Pacific and is associated with QBO influence from the lowermost stratosphere at tropical/subtropical latitudes in the Pacific sector. The early winter response consists of anomalies over both the North Pacific and Europe, but the mechanism for this response is unclear. Increased precipitation occurs over the tropical western Pacific under westerly QBO conditions, particularly during boreal summer, with maximum sensitivity to the QBO winds at 70 hPa. The band of precipitation across the Pacific associated with the Inter-tropical Convergence Zone (ITCZ) shifts southward under QBO westerly conditions. The empirical orthogonal function (EOF)-based analysis suggests that this ITCZ precipitation response may be particularly sensitive to the vertical wind shear in the vicinity of 70 hPa and hence the tropical tropopause temperatures.

Millennial-scale variability in south-east Australian hydroclimate between 30,000 and 10,000 years ago

Global climate variability during the late Quaternary is commonly investigated within the framework of the ‘bipolar seesaw’ pattern of asynchronous temperature variations in the northern and southern polar latitudes. The terrestrial hydrological response to this pattern in south-eastern Australia is not fully understood, as continuous, high-resolution, well-dated proxy records for the hydrological cycle in the region are sparse. Here we present a well-dated, highly resolved record of moisture balance spanning 30000–10000 calendar years before present (30–10 ka BP), based on x-ray fluorescence and organic carbon isotope (δ13COM) measurements of a sedimentary sequence from Lake Surprise in south-eastern Australia. The data provide a locally coherent record of the hydrological cycle. Elevated Si (reflecting windblown quartz and clays), and relatively high δ13COM, indicate an extended period of relative aridity between 28 and 18.5 ka BP, interrupted by millennial-scale episodes of decreased Si and δ13COM, suggesting increased moisture balance. This was followed by a rapid deglacial shift to low Si and δ13COM at 18.5 ka BP, indicative of wetter conditions. We find that these changes are coeval with other records from south-eastern Australia and New Zealand, and use a Monte Carlo Empirical Orthogonal Function approach to extract a common trend from three high-resolution records. Our analyses suggest that drivers of the regional hydrological cycle have varied on multi-millennial time scales, in response to major shifts in global atmosphere-ocean dynamics during the last glacial-interglacial transition. Southern Ocean processes were the dominant control on hydroclimate during glacial times, via a strong influence of cold sea surface temperatures on moisture uptake and delivery onshore. Following the last deglaciation (around 18 ka BP), the southward migration of cold Southern Ocean fronts likely resulted in the establishment of conditions more like those of the present day. Millennial-scale variability in records from the region is dominated by a persistent ca. 2300-year periodicity, consistent with other records across the Southern Hemisphere mid-latitudes; however, this pervasive periodicity is not obviously linked to the ‘bipolar seesaw’ and the mechanism remains equivocal.

Conditioned empirical orthogonal functions for interpolation of runoff time series along rivers: Application to reconstruction of missing monthly records

Reconstruction of missing runoff data is of important significance to solve contradictions between the common situation of gaps and the fundamental necessity of complete time series for reliable hydrological research. The conventional empirical orthogonal functions (EOF) approach has been documented to be useful for interpolating hydrological series based upon spatiotemporal decomposition of runoff variation patterns, without additional measurements (e.g., precipitation, land cover). This study develops a new EOF-based approach (abbreviated as CEOF) that conditions EOF expansion on the oscillations at outlet (or any other reference station) of a target basin and creates a set of residual series by removing the dependence on this reference series, in order to redefine the amplitude functions (components). This development allows a transparent hydrological interpretation of the dimensionless components and thereby strengthens their capacities to explain various runoff regimes in a basin. The two approaches are demonstrated on an application of discharge observations from the Ganjiang basin, China. Two alternatives for determining amplitude functions based on centred and standardised series, respectively, are tested. The convergence in the reconstruction of observations at different sites as a function of the number of components and its relation to the characteristics of the site are analysed. Results indicate that the CEOF approach offers an efficient way to restore runoff records with only one to four components; it shows more superiority in nested large basins than at headwater sites and often performs better than the EOF approach when using standardised series, especially in improving infilling accuracy for low flows. Comparisons against other interpolation methods (i.e., nearest neighbour, linear regression, inverse distance weighting) further confirm the advantage of the EOF-based approaches in avoiding spatial and temporal inconsistencies in estimated series.

Reconstructing Regional Ionospheric Electron Density: A Combined Spherical Slepian Function and Empirical Orthogonal Function Approach

The computerized ionospheric tomography is a method for imaging the Earth’s ionosphere using a sounding technique and computing the slant total electron content (STEC) values from data of the global positioning system (GPS). The most common approach for ionospheric tomography is the voxel-based model, in which (1) the ionosphere is divided into voxels, (2) the STEC is then measured along (many) satellite signal paths, and finally (3) an inversion procedure is applied to reconstruct the electron density distribution of the ionosphere. In this study, a computationally efficient approach is introduced, which improves the inversion procedure of step 3. Our proposed method combines the empirical orthogonal function and the spherical Slepian base functions to describe the vertical and horizontal distribution of electron density, respectively. Thus, it can be applied on regional and global case studies. Numerical application is demonstrated using the ground-based GPS data over South America. Our results are validated against ionospheric tomography obtained from the constellation observing system for meteorology, ionosphere, and climate (COSMIC) observations and the global ionosphere map estimated by international centers, as well as by comparison with STEC derived from independent GPS stations. Using the proposed approach, we find that while using 30 GPS measurements in South America, one can achieve comparable accuracy with those from COSMIC data within the reported accuracy (1 × 1011 el/cm3) of the product. Comparisons with real observations of two GPS stations indicate an absolute difference is less than 2 TECU (where 1 total electron content unit, TECU, is 1016 electrons/m2).