Optimal Interpolation Method Research Articles

Generalized Kalman Filter and Ensemble Optimal Interpolation, Their Comparison and Application to the Hybrid Coordinate Ocean Model

In this paper, we consider a recently developed data assimilation method, the Generalized Kalman Filter (GKF), which is a generalization of the widely-used Ensemble Optimal Interpolation (EnOI) method. Both methods are applied for modeling the Atlantic Ocean circulation using the known Hybrid Coordinate Ocean Model. The along-track altimetry data taken from the Archiving, Validating and Interpolating Satellite Oceanography Data (AVISO) were used for data assimilation and other data from independent archives of observations; particularly, the temperature and salinity data from the Pilot Research Array in the Tropical Atlantic were used for independent comparison. Several numerical experiments were performed with their results discussed and analyzed. It is shown that values of the ocean state variables obtained in the calculations using the GKF method are closer to the observations in terms of standard metrics in comparison with the calculations using the standard data assimilation method EnOI. Furthermore, the GKF method requires less computational effort compared to the EnOI method.

A multilevel dataset of microplastic abundance in the world\u2019s upper ocean and the Laurentian Great Lakes

A total of 8218 pelagic microplastic samples from the world’s oceans were synthesized to create a dataset composed of raw, calibrated, processed, and gridded data which are made available to the public. The raw microplastic abundance data were obtained by different research projects using surface net tows or continuous seawater intake. Fibrous microplastics were removed from the calibrated dataset. Microplastic abundance which fluctuates due to vertical mixing under different oceanic conditions was standardized. An optimum interpolation method was used to create the gridded data; in total, there were 24.4 trillion pieces (8.2 × 104 ~ 57.8 × 104 tons) of microplastics in the world’s upper oceans.

Optimal interpolation of global dissolved oxygen: 1965–2015

AbstractOxygen inventory of the global ocean has declined in recent decades potentially due to the warming‐induced reduction in solubility as well as the circulation and biogeochemical changes associated with ocean warming and increasing stratification. Earth System Models predict continued oxygen decline for this century with profound impacts on marine ecosystem and fisheries. Observational constraint on the rate of oxygen loss is crucial for assessing the ability of models to accurately simulate these changes. There are only a few observational assessments of the global oceanic oxygen inventory reporting a range of oxygen loss. This study develops a gridded data set of dissolved oxygen for the global oceans using optimal interpolation method. The resulting gridded product includes full‐depth map of dissolved oxygen as 5‐year moving average from 1965 to 2015 with uncertainty estimates. The uncertainty can come from unresolved small‐scale and high‐frequency variability and mapping errors. The multi‐decadal trend of global dissolved oxygen is in the range of −281 to −373 Tmol/decade. This estimate is more conservative than previous works. In this study, the grid points far from the observations are essentially set equal to zero anomaly from the climatology. Calculating global inventory with this approach produces a relatively conservative estimate; thus, the results from this study likely provide a useful lower bound estimate of the global oxygen loss.

Assessment of New High-resolution Regional Climatology in the East/Japan Sea

This study provides comprehensive assessment results for the most recent high-resolution regional climatology in the East/Japan Sea by comparing with the various existing climatologies. This new high-resolution climatology is generated based on the Optimal Interpolation (OI) method with individual profiles from the World Ocean Database and gridded World Ocean Atlas provided by the National Centers for Environmental Information (NCEI). It was generated from the recent previous study which had a primary focus to solve the abnormal horizontal gradient problem appearing in the other high-resolution climatology version of NCEI. This study showed that this new OI field simulates well the mesoscale features including closed-curve temperature spatial distribution associated with eddy formation. Quantitative spatial variability was compared to the other four different climatologies and significant variability at 160 km was presented through a wavelet spectrum analysis. In addition, the general improvement of the new OI field except for warm bias in the coastal area was confirmed from the comparison with serial observation data provided by the National Fisheries Research and Development Institute’s Korean Oceanic Data Center.

Optimal interpolation method to predict the bathymetry of Saldanha Bay

AbstractAccurate interpolation when compiling bathymetric maps is essential in any water depth study. In the case of Saldanha Bay, continuous dredging operations are constantly altering the ocean floor, which has a detrimental effect on sedimentation and coastal hydrodynamics. If the integrity of the coastline is to be secured, accurate bathymetry predictions would be invaluable in determining the effect of dredging operations on coastal erosion. Inverse distance weighting (IDW) and ordinary kriging (OK) are two well‐known and commonly used interpolation methods to produce surfaces through spatial autocorrelation for numerous applications, inter alia, to estimate bathymetry. This study aims to analyse and compare the efficiency of the IDW and OK interpolation methods to predict the bathymetry of Saldanha Bay. Three comparative interpolation tests, which vary according to the decrease in the quantity of sounding points, are conducted. SPSS statistical software was used to assess the performance of the interpolation methods. Firstly, 2D scatterplots were used to show the correlation between predicted and measured sounding values for each interpolation method. Secondly, analysis of variance was employed to investigate whether the difference between the IDW and OK interpolation methods was statistically significant, and to determine which method was best suited for determining the bathymetry of Saldanha Bay. Findings revealed a strong linear relationship between predicted and measured sounding values for both IDW and OK when 100% of the sounding points are used. Conversely, for medium and small quantities of sounding points, a weak correlation exists. Clear similarities exist in the way that IDW and OK estimate and generate the continuous surface of bathymetry. However, IDW consistently performed better than OK across all interpolation tests. The findings of this study will assist in selecting the most suitable interpolation method for future bathymetry surveys of Saldanha Bay.

Optimal Linear Interpolation of Planar Curves for NC Contour Machining

In NC machining of planar contours, the cutter path is frequently approximated by linear interpolation to a contour curve as target. In this situation, the interpolation error should be measured along the normal direction of the contour curve, and it is desired that only the fewest linear segments are needed with respect to the specified accuracy. However, how to determine the parameters of segment to match these requirements has not been completely solved. This paper presents a new linear interpolation approach for this problem. The approach is named as the optimal linear interpolation method and has three features which include: (1) the interpolation error along the normal direction of object curve satisfies the specified accuracy, and the number of the required segments is the fewest simultaneously; (2) the connection between any two adjacent segments on generated cutter path is natural and smooth, and the generation of extremely short segment is avoided as much as possible; (3) the algorithm is simple and with a high computation efficiency. The effectiveness of the proposed approach has been sufficiently confirmed by applying it to two interpolation examples of planar cam contours. At the same time, the reduction effect of interpolation data has also been verified through comparing the segment number required by the proposed method and Nishioka’s method, which is specially developed to precision machining of planar cam contour, relative to the same interpolation conditions.

Construction of the Mean Sea Surface Model Combined HY-2A With DTU18 MSS in the Antarctic Ocean

A new Mean Sea Surface (MSS) model called Shandong University of Science and Technology Antarctic Mean Sea Surface model (SDUST_ANT MSS) in the Antarctic Ocean is presented and validated in this paper. The SDUST_ANT MSS updates the DTU18 MSS with 6 years of Exact Repeat Mission (ERM) and Geodetic Mission (GM) data from HY-2A. Collinear adjustment was applied to all the ERM data to obtain the along-track mean sea surface height. Oceanic variability has been removed from the GM data. Crossover adjustment was applied to both the ERM and GM data. We constructed the HY-2A_MSS using HY-2A altimetry data based on optimal interpolation method. Several types of errors (such as white noise, residual effect of oceanic variability, and long wavelength bias) have been taken into account for the determination of MSS using optimal interpolation method. The SDUST_ANT MSS was constructed by mapping HY-2A_MSS onto the DTU18 MSS. The SDUST_ANT MSS was compared with DTU18 MSS and CNES_CLS15 MSS. At wavelengths below 150 km, differences between models are consistent with seafloor topographic gradient. At wavelengths above 150 km, differences are affected by the mesoscale activities and the altimetry errors in coastal areas. The errors of the three models, as indicated by their power spectral densities (PSDs), are of similar orders of magnitude. The absolute error is slightly smaller in SDUST_ANT than in CNES_CLS15 or DTU18.

Development of High-Resolution Regional Climatology in the East/Japan Sea With a Primary Focus on Meridional Temperature Gradient Correction

In this study, we developed a new high-resolution regional climatology (0.1° by 0.1° by 19 levels) in the East/Japan Sea. National Centers for Environmental Information and Korea Oceanic Data Center already released the regional climatology of East Asian seas including the East/Japan Sea with 0.1° by 0.1° resolution. It provides a reliable temperature and salinity structure compared to previous 1° or 0.25° climatologies. However, this study found an abnormal meridional temperature gradient problem when calculating geostrophic currents based on this new climatology. Geostrophic currents show a strong repetitive eastward flow along the 1° latitudinal band especially in the East/Japan Sea, which corresponds with abnormal meridional temperature gradients at the same areas. This problem could be related to the objective analysis procedure generating the high-resolution climatology. Here, we reproduced a high-resolution climatology without the abnormal meridional temperature gradient problem by using the optimal interpolation method. Results show that the meridional gradient problem can partly be attributed to both the use of the World Ocean Atlas background field on the 1° grid, and the spatial distribution of World Ocean database observation data; however, these are not the primary causes. We corrected the abnormal temperature gradient by increasing the meridional decorrelation length scale without losing the meso-scale feature in the East/Japan Sea, as shown by the wavelet analysis. Improvement of the new gridded field is also validated by using serial hydrographic data and the altimetry-derived surface current product.

Mean Dynamic Topography Modeling Based on Optimal Interpolation from Satellite Gravimetry and Altimetry Data

Mean dynamic topography (MDT) is crucial for research in oceanography and climatology. The optimal interpolation method (OIM) is applied to MDT modeling, where the error variance–covariance information of the observations is established. The global geopotential model (GGM) derived from GOCE (Gravity Field and Steady-State Ocean Circulation Explorer) gravity data and the mean sea surface model derived from satellite altimetry data are combined to construct MDT. Numerical experiments in the Kuroshio over Japan show that the use of recently released GOCE-derived GGM derives a better MDT compared to the previous models. The MDT solution computed based on the sixth-generation model illustrates a lower level of root mean square error (77.0 mm) compared with the ocean reanalysis data, which is 2.4 mm (5.4 mm) smaller than that derived from the fifth-generation (fourth-generation) model. This illustrates that the accumulation of GOCE data and updated data preprocessing methods can be beneficial for MDT recovery. Moreover, the results show that the OIM outperforms the Gaussian filtering approach, where the geostrophic velocity derived from the OIM method has a smaller misfit against the buoy data, by a magnitude of 10 mm/s (17 mm/s) when the zonal (meridional) component is validated. This is mainly due to the error information of input data being used in the optimal interpolation method, which may obtain more reasonable weights of observations than the Gaussian filtering method.

A Comparison of Precise Fertilization Prescription Rates to a Conventional Approach Based on the Open Source GIS Software

Fertilization is one of the most important components of precision agriculture, ensuring high and stable crop yields. The process of spatial interpolation of soil sample data is recognized as a reliable method of determining the prescription rates for precise fertilization. However, the application of a free open-source geographic information system (GIS) software was often overlooked in the process. In this study, a method of precise fertilization prescription map creation was developed using an open-source GIS software to enable a wider and cheaper availability of its application. The study area covered three independent locations in Osijek-Baranja County. A method was developed for the fertilization of sugar beet with phosphorous pentoxide, but its application is universal with regard to the crop type. An ordinary kriging was determined as an optimal interpolation method for spatial interpolation, with the mean RMSE of 1.8754 and R2of 0.6955. By comparing the precision fertilization prescription rates to a conventional approach, the differences of 4.1 kg ha-1 for Location 1, 15.8 kg ha-1 for Location 2, and 11.2 kg ha-1 for Location 3 were observed. These values indicate a general deficit in soil phosphorous pentoxide, and precise fertilization could ensure its optimal content in the future sowing seasons.

Mapping Altimetry in the Forthcoming SWOT Era by Back-and-Forth Nudging a One-Layer Quasigeostrophic Model

AbstractDuring the past 25 years, altimetric observations of the ocean surface from space have been mapped to provide two dimensional sea surface height (SSH) fields that are crucial for scientific research and operational applications. The SSH fields can be reconstructed from conventional altimetric data using temporal and spatial interpolation. For instance, the standard Developing Use of Altimetry for Climate Studies (DUACS) products are created with an optimal interpolation method that is effective for both low temporal and low spatial resolution. However, the upcoming next-generation SWOT mission will provide very high spatial resolution but with low temporal resolution. The present paper makes the case that this temporal–spatial discrepancy induces the need for new advanced mapping techniques involving information on the ocean dynamics. An algorithm is introduced, dubbed the BFN-QG, that uses a simple data assimilation method, the back-and-forth nudging (BNF), to interpolate altimetric data while respecting quasigeostrophic (QG) dynamics. The BFN-QG is tested in an observing system simulation experiments and compared to the DUACS products. The experiments consider as reference the high-resolution numerical model simulation NATL60 from which are produced realistic data: four conventional altimetric nadirs and SWOT data. In a combined nadirs and SWOT scenario, the BFN-QG substantially improves the mapping by reducing the root-mean-square errors and increasing the spectral effective resolution by 40 km. Also, the BFN-QG method can be adapted to combine large-scale corrections from nadir data and small-scale corrections from SWOT data so as to reduce the impact of SWOT correlated noises and still provide accurate SSH maps.

Seafloor Geodetic Pressure Measurements to Detect Shallow Slow Slip Events: Methods to Remove Contributions From Ocean Water

AbstractShallow slow slip events (SSEs) provide a mechanism for strain release in the shallow part of subduction zones, with fundamental implications for fault mechanics and tsunami hazards. Despite their importance, SSEs are challenging to monitor. They occur under the ocean far from land‐based GPS stations, and while seafloor pressure sensors can detect SSE vertical seafloor movements, the measured bottom pressure includes “ocean noise” signals from pressure variations within the water column. Seeking to improve techniques to remove ocean noise, a pilot study offshore Oregon collected seafloor pressure and near‐bottom current measurements at four sites from April to November 2017. Three methods were applied to reduce ocean noise: 1) subtract a reference pressure, 2) apply complex empirical orthogonal function analysis to pressure measurements, and 3) combine pressure and current measurements with optimal interpolation (OI). All three methods are established techniques from either geodesy or oceanography. Each method produced residual standard deviation, σ < 1 hPa. No SSE was detected during this study. For illustration purposes synthetic SSEs of 2 cm amplitude and 7‐days duration were added and detected, one at a time at different spots. Because currents are unaffected by a SSE, the combination of currents and pressures with the dynamical constraint of geostrophy in OI reduced the false interpretation of the synthetic SSEs as oceanic. OI produced the most reliable detection. Future seafloor geodesy field projects should consider adding current sensors and using OI methods to reduce ocean noise and to reveal tectonic signals.

How the variations of terrain factors affect the optimal interpolation methods for multiple types of climatic elements?

The spatial interpolation of meteorological data have important applications in ecological environment monitoring, such as soil erosion, ecological vulnerability evaluation. However, there are significant differences in the interpolation accuracy of climatic elements under different topographic and geomorphic conditions. Based on data of 810 meteorological stations across the country, five typical interpolation methods, namely ordinary Kriging method, inverse distance weight method, spline function method, natural neighborhood method and trend surface method, were utilized in this paper to analyze and compare the interpolation accuracy of five climate factors, namely temperature, precipitation, accumulated temperature(>10°),wind speed and sunshine hours, under different topographic and geomorphological conditions. The results showed that: (1) Ordinary kriging method of temperature had better applicability in plain, hill and medium-large undulating mountain areas for temperature while the inverse distance weight method and spline function method had higher interpolation accuracy in the platform area and the small undulating mountain area, respectively. (2) The optimal interpolation of the precipitation in plain, platform and medium-large undulating mountain areas was ordinary kriging method while the inverse distance weight method and spline function method had better applicability in small undulating mountain area. (3) For accumulated temperature (>10 °C), the spline function method had higher interpolation accuracy in plain and platform areas, while ordinary kriging method had better applicability in hilly, small and medium-large undulating mountain area al (4) The optimal spatial interpolation of wind speed in plain and hilly areas was the inverse distance weight method. The natural neighborhood method and the spline function method had the best applicability in plateau, medium-large undulating mountainous areas and small undulating mountain areas, respectively. (5) For sunshine hours, the optimal spatial interpolations in plain and hilly areas were natural neighborhood method and spline function method, respectively, while the ordinary kriging method and the inverse distance weighting method had better applicability in platform, large undulating mountainous areas and small undulating mountainous areas, respectively .

Generation of Vertical Fine Structure by the Internal Waves with the Regard for Turbulent Viscosity and Diffusion

Purpose. The study is aimed at evaluating effectiveness of the procedure of the observational data assimilation using the Kalman filter algorithm as compared to sequential analysis of the hydrophysical fields based on the optimal interpolation method, and at analyzing the mesoscale features of coastal circulation near the western Crimea coast and in the Sevastopol region. Methods and Results. Based on the hydrodynamic model adapted to the Black Sea coastal zone conditions including the open boundary and on the temperature and salinity data from the hydrological survey in 2007, the dynamic and energy characteristics of the Black Sea coastal circulation were calculated with high spatial resolution (horizontal grid is ~ 1.6 × 1.6 km and 30 vertical horizons). The hydrophysical fields were reconstructed using two algorithms of data assimilation: the sequential optimal interpolation and the modified Kalman filter. The kinetic energy changed mainly due to the wind action, vertical friction and the work of pressure forces; the potential energy – due to the potential energy advection and the horizontal turbulent diffusion. The following circulation features were reconstructed: the anticyclonic eddy with the radius about 15 km in the Kalamita Bay in the water upper layer, the anticyclonic eddy with the radius about 15 km between 32.2 and 32.6° E in the whole water layer, the intense current near Sevastopol and along the Crimea western coast directed to the north and northwest, and the submesoscale eddies of different signs of rotation in the upper layer. Conclusions. It is shown that having been taken into account, heterogeneity and non-isotropy of the error estimates of the temperature and salinity fields relative to the correlation function lead to qualitative and quantitative differences in the hydrodynamic fields (amplification of currents, change of the currents’ direction and eddy formations were better pronounced). At the same time, the mean square errors of the thermohaline fields’ estimates decreased. Formation of the anticyclonic eddy with the radius about 15 km in the Kalamita Bay could be related to the current shear instability. Submesoscale eddies with the diameters less than 5 km were formed when the current flowed around the coastline and the bottom topography inhomogeneities.

Assimilating In Situ and Remote Sensing Observations in a Highly Variable Estuary–Shelf Model

AbstractTo improve the forecasting performance in dynamically active coastal waters forced by winds, tides, and river discharges in a coupled estuary–shelf model off Hong Kong, a multivariable data assimilation (DA) system using the ensemble optimal interpolation method has been developed and implemented. The system assimilates the conductivity–temperature–depth (CTD) profilers, time series buoy measurement, and remote sensing sea surface temperature (SST) data into a high-resolution estuary–shelf ocean model around Hong Kong. We found that the time window selection associated with the local dynamics and the number of observation samples are two key factors in improving assimilation in the unique estuary–shelf system. DA with a varied assimilation time window that is based on the intratidal variation in the local dynamics can reduce the errors in the estimation of the innovation vector caused by the model–observation mismatch at the analysis time and improve simulation greatly in both the estuary and coastal regions. Statistically, the overall root-mean-square error (RMSE) between the DA forecasts and not-yet-assimilated observations for temperature and salinity has been reduced by 33.0% and 31.9% in the experiment period, respectively. By assimilating higher-resolution remote sensing SST data instead of lower-resolution satellite SST, the RMSE of SST is improved by ~18%. Besides, by assimilating real-time buoy mooring data, the model bias can be continuously corrected both around the buoy location and beyond. The assimilation of the combined buoy, CTD, and SST data can provide an overall improvement of the simulated three-dimensional solution. A dynamics-oriented assimilation scheme is essential for the improvement of model forecasting in the estuary–shelf system under multiple forcings.

Data Assimilation of AOD and Estimation of Surface Particulate Matters over the Arctic

In this study, more accurate information on the levels of aerosol optical depth (AOD) was calculated from the assimilation of the modeled AOD based on the optimal interpolation method. Additionally, more realistic levels of surface particulate matters over the Arctic were estimated using the assimilated AOD based on the linear relationship between the particulate matters and AODs. In comparison to the MODIS observation, the assimilated AOD was much improved compared with the modeled AOD (e.g., increase in correlation coefficients from −0.15–0.26 to 0.17–0.76 over the Arctic). The newly inferred monthly averages of PM10 and PM2.5 for April–September 2008 were 2.18–3.70 μg m−3 and 0.85–1.68 μg m−3 over the Arctic, respectively. These corresponded to an increase of 140–180%, compared with the modeled PMs. In comparison to in-situ observation, the inferred PMs showed better performances than those from the simulations, particularly at Hyytiala station. Therefore, combining the model simulation and data assimilation provided more accurate concentrations of AOD, PM10, and PM2.5 than those only calculated from the model simulations.

Effect of offset-frequency step size and interpolation methods on chemical exchange saturation transfer MRI computation in human brain.

Chemical exchange saturation transfer (CEST) MRI is a non-invasive molecular imaging technique with potential applications in pre-clinical and clinical studies. Applications of amide proton transfer-weighted (APT-w), glutamate-weighted (Glu-w) and creatine-weighted (Cr-w) CEST, among others, have been reported. In general, CEST data are acquired at multiple offset-frequencies. In reported studies, different offset-frequency step sizes and interpolation methods have been used during B0 inhomogeneity correction of data. The objective of the current study was to evaluate the effects of different step sizes and interpolation methods on CEST value computation. In the current study, simulation (Glu-w, Cr-w and APT-w) and experimental data from the brain were used. Experimental CEST data (Glu-w) were acquired from human volunteers at 7 T and brain tumor patients (APT-w) at 3 T. During B0 inhomogeneity correction, different interpolation methods (polynomial [degree-1, 2 and 3], cubic-Hermite, cubic-spline and smoothing-spline) were compared. CEST values were computed using asymmetry analysis. The effects of different step sizes and interpolation methods were evaluated using coefficient of variation (CV), normalized mean square error (nMSE) and coefficient of correlation parameters. Additionally, an optimum interpolation method for APT-w values was selected based upon fitting accuracy, T-test, receiver operating characteristic analysis, and its diagnostic performance in differentiating low-grade and high-grade tumors. CV and nMSE increase with an increase in step size irrespective of the interpolation method (except for cubic-Hermite and cubic-spline). The nMSE of Cr-w and Glu-w CEST values were least for polynomial (degree-2 and 3). The quality of Glu-w CEST maps became coarse with the increase in step size. There was a significant difference (P < .05) between low-grade and high-grade tumors using polynomial interpolation (degree-1, 2 and 3); however, linear interpolation outperforms other methods for APT-w data, providing the highest sensitivity and specificity. In conclusion, depending upon the saturation parameters and field strength, optimization of step size and interpolation should be carried out for different CEST metabolites/molecules. Glu-w, Cr-w and APT-w CEST data should be acquired with a step size of between 0.2 and 0.3 ppm. For B0 inhomogeneity correction, polynomial (degree-2) should be used for Glu-w and Cr-w CEST data at 7 T and linear interpolation should be used for APT-w data at 3 T for a limited frequency range.

Analiz dinamicheskikh i energeticheskikh kharakteristik tsirkulyatsii vod u beregov Zapadnogo Kryma na osnove assimilyatsii dannykh nablyudeniy v chislennoy modeli dinamiki Chernogo morya

Purpose. The study is aimed at evaluating effectiveness of the procedure of the observational data assimilation using the Kalman filter algorithm as compared to sequential analysis of the hydrophysical fields based on the optimal interpolation method, and at analyzing the mesoscale features of coastal circulation near the western Crimea coast and in the Sevastopol region. Methods and Results. Based on the hydrodynamic model adapted to the Black Sea coastal zone conditions including the open boundary and on the temperature and salinity data from the hydrological survey in 2007, the dynamic and energy characteristics of the Black Sea coastal circulation were calculated with high spatial resolution (horizontal grid is ~1.6×1.6 km and 30 vertical horizons). The hydrophysical fields were reconstructed using two algorithms of data assimilation: the sequential optimal interpolation and the modified Kalman filter. The kinetic energy changed mainly due to the wind action, vertical friction and the work of pressure forces; the potential energy – due to the potential energy advection and the horizontal turbulent diffusion. The following circulation features were reconstructed: the anticyclonic eddy with the radius about 15 km in the Kalamitsky Bay in the water upper layer, the anticyclonic eddy with the radius about 15 km between 32.2 and 32.6° E in the whole water layer, the intense current near Sevastopol and along the Crimea western coast directed to the north and northwest, and the submesoscale eddies of different signs of rotation in the upper layer. Conclusions. It is shown that having been taken into account, heterogeneity and non-isotropy of the error estimates of the temperature and salinity fields relative to the correlation function lead to qualitative and quantitative differences in the hydrodynamic fields (amplification of currents, change of the currents’ direction and eddy formations were better pronounced). At the same time, the mean square errors of the thermohaline fields’ estimates decreased. Formation of the anticyclonic eddy with the radius about 15 km in the Kalamitsky Bay could be related to the current shear instability. Submesoscale eddies with the diameters less than 5 km were formed when the current flowed around the coastline and the bottom topography inhomogeneities

Update China geodetic coordinate frame considering plate motion

China Geodetic Coordinate System 2000 (CGCS2000), as the formal national coordinate reference frame, has been used for 20 years. The coordinates of all Global Navigation Satellite System (GNSS) stations in China need referring to this system. To this end, the first step is to align the coordinates of all stations, usually included in a regional GNSS network, with a given International Terrestrial Reference Frame (ITRF), then these coordinates are corrected to the CGCS2000 in consideration of plate movement. For a better alignment result, regional control stations are needed and their coordinates were estimated from the combination of constraint-free normal equation systems provided by several International GNSS Service (IGS) analysis centers. The effect in using these refined coordinates, which determine a regional coordinate datum, on the alignment result should be evaluated by the coordinate corrections of the regional control stations to the regional coordinate datum, i.e. smaller corrections mean better alignments of the two associated frames. The test results show that the refined coordinates are more accurate than the ones calculated from the station's velocity, and are well aligned with the ITRF2005. Moreover, for obtaining the coordinates of GNSS stations in an updated CGCS2000 frame, a gridded linear velocity field based on the estimated velocities at 1025 CGCS2000 stations was generated for mainland China using the optimal interpolation method, the inverse distance weighting, which is selected from five interpolation methods. The overall precisions of the constructed velocity field at all stations in the East (E) and, North (N) directions are 0.78 mm/a and 0.95 mm/a, respectively. For evaluating the accuracy of the updated CGCS2000 frame, monthly solutions for the coordinates of some CGCS2000 CORS stations in the ITRF2014 during the period from 2000.0 to 2018 were obtained and the Root Mean Square (RMS) of the differences between the coordinates corrected to the CGCS2000 and the known coordinates at these stations are about 2–3 cm.

Improved Method for Distributed Parameter Model of Solenoid Valve Based on Kriging Basis Function Predictive Identification Program

In this paper, a method for the improvement of the calculation accuracy of the distributed parameter model (DPM) of electromagnetic devices is proposed based on the kriging basis function predictive identification program (PIP). Kriging is mainly an optimal interpolation method which uses spatial self-covariance, and takes a polynomial as the basis function. The accuracy of the kriging-based surrogate model can be improved by adjusting the related functions and hyperparameters. Based on the DPM of a solenoid valve, there exist certain errors in the estimation. They can be summarized as follows: Firstly, the estimation error of magnetic flux leakage (MFL) permeance is caused directly by the deviation of the magnetic flux tube due to the segmented magnetic field line. Secondly, the estimation error of soft magnetic resistance because of the nonlinearity of the permeability of soft magnetic material leads to the change of soft magnetic resistance alongside the magnetic flux. In this paper, an improved kriging error correction method is applied to modify the leak permeance and soft magnetic resistance calculation. The kriging basis function is adjusted to adapt to the data curve of the MFL permeance error data. The calculated MFL permeance data are compared with the error variation data to select the appropriate basis function. To improve the computational efficiency, the PIP is proposed to select the appropriate basis function. The modified MFL permeance data and soft magnetic resistance are substituted into the DPM for improving the computational accuracy and efficiency of the solenoid valve.