Improving the Representation of Historical Climate Precipitation Indices Using Optimal Interpolation Methods

Six kinds of interpolation methods, including projection-shape function method, three-dimensional linear interpolation method, optimal interpolation method, constant volume transformation method and so on, were adoped in the study of interpolation accuracy. From the point of view about the characterization of matching condition of two different grids and interpolation function, the infuencing factor on the interpolation accuracy was studied. The results revealed that different interpolation methods had different interpolation accuracy. The projection-shape function interpolation method had the best effect and the more complex interpolation function had lower accuracy. In many cases, the matching condition of two grids had much greater impact on the interpolation accuracy than the method itself. The error of interpolation method is inevitable, but the error caused by the grid quality could be reduced through efforts.

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Optimal interpolation methods for farmland soil organic matter in various landforms of a complex topography

Ecological Indicators ◽

10.1016/j.ecolind.2019.105926 ◽

2020 ◽

Vol 110 ◽

pp. 105926 ◽

Cited By ~ 1

Author(s):

Jun Long ◽

Yaling Liu ◽

Shihe Xing ◽

Liming Zhang ◽

Mingkai Qu ◽

...

Keyword(s):

Organic Matter ◽

Soil Organic Matter ◽

Optimal Interpolation ◽

Complex Topography ◽

Interpolation Methods ◽

Farmland Soil

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A Surrogate Ensemble Study of Sea Level Reconstructions

Journal of Climate ◽

10.1175/2010jcli3014.1 ◽

2010 ◽

Vol 23 (16) ◽

pp. 4306-4326 ◽

Cited By ~ 46

Author(s):

Bo Christiansen ◽

T. Schmith ◽

P. Thejll

Keyword(s):

Sea Level ◽

Covariance Structure ◽

Optimal Interpolation ◽

Tide Gauges ◽

Sea Levels ◽

Calibration Period ◽

Interpolation Methods ◽

Reconstruction Methods ◽

Homogeneous Pattern ◽

Global Mean

Abstract This study investigates the possibility of reconstructing past global mean sea levels. Reconstruction methods rely on historical measurements from tide gauges combined with knowledge about the spatial covariance structure of the sea level field obtained from a shorter period with spatially well-resolved satellite measurements. A surrogate ensemble method is applied based on sea levels from a 500-yr climate model simulation. Tide gauges are simulated by selecting time series from grid points along continental coastlines and on ocean islands. Reconstructions of global mean sea levels can then be compared to the known target, and the ensemble method allows an estimation of the statistical properties originating from the stochastic nature of the reconstructions. Different reconstruction methods previously used in the literature are studied, including projection and optimal interpolation methods based on EOF analysis of the calibration period. This study also includes methods where these EOFs are augmented with a homogeneous pattern, with the purpose of better capturing a possible geographically homogeneous trend. These covariance-based methods are compared to a simple weighted mean method. It is concluded that the projection and optimal interpolation methods are very sensitive to the length of the calibration period. For realistic lengths of 10 and 20 yr, very large biases and spread in the reconstructed 1900–49 trends are found. Including a homogeneous pattern in the basis drastically improves the reconstructions of the trend and reduces the sensitivity to the length of the calibration period. The projection and optimal interpolation methods are now comparable to the weighted mean with biases less than 10% in the trend. However, the spread is still considerable. The amplitude of the year-to-year variability is in general strongly overestimated by all reconstruction methods. With regards to year-to-year variability, several methods outperform the simple mean. Finally, for the projection method, reconstruction errors are decomposed into contributions from the sparse coverage of tide gauges and the incomplete knowledge of the covariance structure of the sea level field. The study finds that the contributions of the different sources depend on the diagnostics of the reconstruction. It is noted that sea level is constrained by the approximate conservation of the total mass of the ocean. This poses challenges for the sea level reconstructions that are not present for other fields such as temperature.

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Technology for restoring functional dependencies to determine reliability parameters

BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS ◽

10.31489/2021m1/78-86 ◽

2021 ◽

Vol 101 (1) ◽

pp. 78-86

Author(s):

V.P. Kvasnikov ◽

◽

S.V. Yehorov ◽

T.Yu. Shkvarnytska ◽

◽

...

Keyword(s):

Interpolation Polynomial ◽

Electronic Equipment ◽

Optimal Interpolation ◽

Electronic Systems ◽

Functional Dependencies ◽

Interpolation Methods ◽

Reliability Parameters ◽

Discrete Sample ◽

Failure Statistics ◽

Qualitative Characteristics

The problem of determining the properties of the object by analyzing the numerical and qualitative characteristics of a discrete sample is considered. A method has been developed to determine the probability of trouble-free operation of electronic systems for the case if the interpolation fields are different between several interpolation nodes. A method has been developed to determine the probability of trouble-free operation if the interpolation polynomial is the same for the entire interpolation domain. It is shown that local interpolation methods give more accurate results, in contrast to global interpolation methods. It is shown that in the case of global interpolation it is possible to determine the value of the function outside the given values by extrapolation methods, which makes it possible to predict the probability of failure. It is shown that the use of approximation methods to determine the probability of trouble-free operation reduces the error of the second kind. A method for analyzing the qualitative characteristics of functional dependences has been developed, which allows us to choose the optimal interpolation polynomial. With sufficient statistics, using the criteria of consent, it is possible to build mathematical models for the analysis of failure statistics of electronic equipment. Provided that the volume of statistics is not large, such statistics may not be sufficient and the application of consent criteria will lead to unsatisfactory results. Another approach is to use an approximation method that is applied to statistical material that was collected during testing or controlled operation. In this regard, it is extremely important to develop a method for determining the reliability of electronic systems in case of insufficiency of the collected statistics of failures of electronic equipment.

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Fuzzy Interpolation and Other Interpolation Methods Used in Robot Calibrations

Journal of Robotics ◽

10.1155/2012/376293 ◽

2012 ◽

Vol 2012 ◽

pp. 1-9 ◽

Cited By ~ 3

Author(s):

Ying Bai ◽

Nailong Guo ◽

Gerald Agbegha

Keyword(s):

Industrial Robot ◽

Industrial Applications ◽

Industrial Robots ◽

Optimal Interpolation ◽

Manufacturing Processes ◽

Interpolation Algorithm ◽

Fuzzy Interpolation ◽

Interpolation Methods ◽

Testing And Measurement ◽

Manufacturing Applications

A novel interpolation algorithm, fuzzy interpolation, is presented and compared with other popular interpolation methods widely implemented in industrial robots calibrations and manufacturing applications. Different interpolation algorithms have been developed, reported, and implemented in many industrial robot calibrations and manufacturing processes in recent years. Most of them are based on looking for the optimal interpolation trajectories based on some known values on given points around a workspace. However, it is rare to build an optimal interpolation results based on some random noises, and this is one of the most popular topics in industrial testing and measurement applications. The fuzzy interpolation algorithm (FIA) reported in this paper provides a convenient and simple way to solve this problem and offers more accurate interpolation results based on given position or orientation errors that are randomly distributed in real time. This method can be implemented in many industrial applications, such as manipulators measurements and calibrations, industrial automations, and semiconductor manufacturing processes.

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