Optimal Interpolation Technique Research Articles

Mesan, an operational mesoscale analysis system

A system for mesoscale analyses of selected variables has been developed. The analysed parametersare of general interest in operational weather forecasting, but normally not availablefrom NWP systems, or available, but with a significantly lower quality than achieved by themesoscale analysis system. A supplementary objective is to produce initial information to beused for now-casting techniques. Examples of parameters are precipitation, temperature, humidity, visibility, wind and clouds. The basis of the analysis system is the optimal interpolationtechnique (OI). The use of observations from automatic stations, radars and satellites havebeen investigated. The investigation indicates that a dense network of ordinary precipitationgauge measurements can produce more accurate analyses than more elaborate systems likeradar that suffers from anomalous echoes and other errors.

An assessment of spatial and temporal variation of sulfur dioxide levels over Istanbul, Turkey

Sulfur dioxide concentration levels are investigated in Istanbul to assess air pollution during the heating seasons in which the concentration of air pollutants reach high levels due to the consumption of low-quality fossil fuels. Results reveal that in the 1985–91 period there is an increasing trend in the concentrations of air pollutants. One reason for this increase is found to be the switching to use of low-quality fossil fuels instead of cleaner ones; the consumption ratio of coal/fuel-oil increased drastically in the 1980s from the ratio of 0.62 during 1980 to 3.09 by 1990. Linear regression analysis also indicated the similar variability of sulfur dioxide and particulate matter curves with a correlation coefficient R 2=0.87. An optimum interpolation technique, kriging, is used to obtain the spatial distribution of sulfur dioxide over the area. Results indicated that the maximum concentration regions over the European side, exceeding 300 μg/m 3 monthly averages, are found to be the Fatih–Gaziosmanpaşa–Bayrampaşa, Beyoğlu–Şişli, and Eminönü areas. On the Asian side, the Göztepe–Kadıköy area received a major threat from sulfur dioxide pollution. Results also indicated that there was a considerable decrease in air pollution levels over Istanbul in the 1995–96 season compared with the previous two seasons. This can be explained by (1) the increase in ventilation, (2) switching to natural gas as a home and business heating fuel, and (3) treatment of coal before its entrance to the city. The variability in weather conditions is explained by the adoption of a ventilation index, which is the product of wind speed and inversion height.

Spatial modeling and prediction of snow‐water equivalent using ground‐based, airborne, and satellite snow data

In this research we modify existing spatial interpolation methodologies so that we can use ground‐based and remotely sensed (airborne and satellite) snow data to characterize the spatial distribution of snow‐water equivalent (SWE) and obtain optimal gridded SWE predictions in the upper Mississippi River basin. We developed and tested the models using ground‐based, airborne, and satellite snow data collected over North and South Dakota, Minnesota, Wisconsin, Iowa, Illinois, and Michigan between March 3 and 6, 1996. Using these data and the spatial models, we obtained optimal gridded predictions of SWE and the associated root mean square prediction errors over a 5 min by 5 min grid covering Minnesota and parts of Wisconsin, North and South Dakota, Iowa, Michigan, and Canada. Because we use an optimal interpolation technique and incorporate satellite areal extent of snow cover data, the predictions are expected to be more accurate than those that would be obtained from interpolation procedures currently used by the National Weather Service. Maps of the gridded snow water equivalent predictions and of the associated error estimates provide a means to investigate the spatial distributions of the predictions and of the associated error estimates. Our research enables hydrologists and others not only to examine these spatial distributions but also to generate optimal gridded predictions of snow‐water equivalent that will aid flood forecasting and water resource management efforts.

Soil‐moisture nudging experiments with a single‐column version of the ECMWF model

AbstractThe soil‐moisture nudging technique suggests using model forecast errors in near‐surface air temperature and relative humidity to re‐initialize (update) soil moisture in atmospheric models. This study investigates the application of soil‐moisture nudging using a single‐column version of the European Centre for Medium‐Range Weather Forecasts (ECMWF) model. the model was applied at 16 sites selected to sample a range of climates and land covers across the globe, with atmospheric forcing taken from the ECMWF operational analysis for 15 June 1994 and 15 December 1994. When observation errors are set to zero, the Optimal Interpolation technique for deriving estimates of nudging coefficients shows computational instability because strong correlation between near‐surface temperature and near‐surface relative humidity forecast errors makes the coefficient matrix of the linear equations ill‐posed. Therefore, Principal Component Analysis (PCA) is used as a pre‐processor to identify the independent and dependent components of temperature and relative humidity errors. With PCA, the soilmoisture nudging coefficients appropriate to the dominant principal component become stable and effective for correcting soil moisture within days. Such coefficients, when derived for the northern hemisphere summer over the 16 sites, are sufficiently consistent to propose using their all‐site, daily‐average values in a globally applicable soil‐moisture analysis scheme. Tests of this method at the First ISLSCP (International Satellite Land Surface Climatology Program) Field Experiment (FIFE) site confirm that soil‐moisture nudging can provide good estimates of near‐surface weather variables and surface fluxes in a numerical weather prediction (NWP) model which gives poor simulation of precipitation (thereby poor soil moisture). However, the PCA method is unable to give an accurate determination of the location of the soil moisture within soil layers that are accessible to the atmosphere. Further, these tests show that, if the NWP model has good simulation of precipitation but poor simulation of surface radiation, soil‐moisture nudging could wrongly vary the soil moisture so as to provide good estimates of the surface sensible‐heat flux, but poor estimates of surface latent‐heat flux. an approach to distinguish error sources from surface radiation and soil moisture is necessary for further improvement.

A Comparative Study of Interpolation Methods for Mapping Soil Properties

AbstractThe choice of an optimal interpolation technique for estimating soil properties at unsampled locations is an important issue in site‐specific management. The objective of this study was to evaluate inverse distance (InvD) weighting, ordinary kriging (KO), and lognormal ordinary kriging (KOlog) to determine the optimal interpolation method for mapping soil properties. Relationships between statistical properties of the data and performance of the methods were analyzed using soil test P and K data from 30 agricultural fields. For InvD weighting, we used powers of 1, 2, 3, and 4. The numbers of the closest neighboring points ranged from 5 to 30 for the three methods. The results suggest that KOlog can improve estimation precision compared with KO for lognormally distributed data. The criteria helpful in deciding whether KOlog is applicable for the given data set were the Kolmogorov‐Smirnov goodness‐of‐fit statistic, coefficient of variation, skewness, kurtosis, and the size of the data set. Careful choice of the exponent value for InvD weighting and of the number of the closest neighbors for both InvD weighting and kriging (KO or KOlog) significantly improved the estimation accuracy (P≤ 0.05). However, no a priori decision could be made about the optimal exponent and the number of the closest neighbors based on the statistical properties of the data. For the majority of the data sets, kriging with the optimal number of the neighboring points, a carefully selected variogram model, and appropriate log‐transformation of the data performed better than InvD weighting. Correlation coefficients between experimental data and estimated results of kriging were higher than those of InvD for 57 out of a total of 60 data sets, kriging mean absolute errors were lower for 44 data sets, and kriging mean errors were lower than those of InvD weighting for 31 data sets.

A prototype upper-atmospheric data assimilation scheme based on optimal interpolation: 1. Theory

Introduced almost 40 years ago, the method of optimal interpolation (OI) has been successfully used in various forms for data analysis in meteorology and oceanography. At the same time upper-atmospheric applications of OI and other techniques based on optimal estimation have remained relatively limited. The theory of OI and related methods is reviewed. Properties of optimal estimation relevant to typical problems of data analysis in the upper atmosphere are highlighted. As a specific example, a simple one-dimensional scheme of OI in time is considered. The scheme is devised to address an important problem of the upper-atmospheric data analysis: extraction of periodic (tidal) components from observations covering a fraction of a day. Possible generalizations of the scheme are also briefly discussed. © 1999 Elsevier Science Ltd. All rights reserved.

Robust Tracking of a Lightweight Manipulator System

A robust control design for high performance joint trajectory tracking of a flexible lightweight manipulator system is proposed. The design is based on a combined controller-observer scheme involving the sliding manifold approach and the optimal interpolation technique. This controller provides the designer with an enhanced joint tracking performance when the system is subject to parametric variations due to structural disturbances caused by link flexibility and load uncertainties. The parametric variations are handled by sliding control and the estimation of the nonlinearly excited elastic dynamics by an optimal interpolator of the structure's dynamic responses. The design procedure is progressive, i.e., we start with a basic controller and then modify it in order to improve the performance. Closed loop simulations with the various designed controllers are used to validate the analytical results and to help choosing the most suitable one.

Reduced space optimal analysis for historical data sets: 136 years of Atlantic sea surface temperatures

A computationally efficient method for analyzing meteorological and oceanographic historical data sets has been developed. The method combines data reduction and least squares optimal estimation. The data reduction involves computing empirical orthogonal functions (EOFs) of the data based on their recent, high‐quality portion and using a leading EOF subset as a basis for the analyzed solution and for fitting a first‐order linear model of time transitions. We then formulate optimal estimation problems in terms of the EOF projection of the analyzed field to obtain reduced space analogues of the optimal smoother, the Kalman filter, and optimal interpolation techniques. All reduced space algorithms are far cheaper computationally than their full grid prototypes, while their solutions are not necessarily inferior since the sparsity and error in available data often make estimation of small‐scale features meaningless. Where covariance patterns can be estimated from the available data, the analysis methods fill gaps, correct sampling errors, and produce spatially and temporally coherent analyzed data sets. As with classical least squares estimation, the reduced space versions also provide theoretical error estimates for analyzed values. The methods are demonstrated on Atlantic monthly sea surface temperature (SST) anomalies for 1856–1991 from the United Kingdom Meteorological Office historical sea surface temperature data set (version MOHSST5). Choice of a reduced space dimension of 30 is shown to be adequate. The analyses are tested by withholding a significant part of the data and prove to be robust and in agreement with their own error estimates; they are also consistent with a partially independent optimal interpolation (OI) analysis by Reynolds and Smith [1994] produced in the National Centers for Environmental Prediction (NCEP)(known as the NCEP OI analysis). A simple statistical model is used to depict the month‐to‐month SST evolution in the optimal smoother algorithm. Results are somewhat superior to both the Kalman filter, which relies less on the model, and the optimal interpolation, which does not use it at all. The method generalizes a few recent works on using a reduced space for data set analyses. Difficulties of methods which simply fit EOF patterns to observed data are pointed out, and the more complete analysis procedures developed here are suggested as a remedy.

Assimilation of wave spectra from pitch‐and‐roll buoys in a North Sea wave model

A technique for the assimilation of spectral wave observations in wave models is presented and tested. The method uses the concept of spectral partitioning to project the entire wave spectrum onto a few essential mean parameters. Model and observed partition parameters are assimilated using an optimal interpolation (OI) technique. After data reduction, obtained by the partitioning, the cost of the assimilation is negligible compared to the cost of the model run itself. Therefore the optimal interpolation of partitions (OI‐P) method is a very attractive assimilation technique for operational wave forecasting. The paper focuses on the assimilation of pitch‐and‐roll buoy spectra in a North Sea version of the WAM wave model. Treatment of the (non‐fully two‐dimensional) buoy spectra is discussed. Appropriate choices for the OI weight functions are made. The problem of correlating wave partitions in different spectra is addressed, which is essential for obtaining a robust and efficient system. In order to assess the influence of spectral wave observations on the analysis of the sea state, the method is compared to a second scheme, optimal interpolation of integral parameters (OI‐I), which can only be used to assimilate observations of significant wave height and mean wave period. First, tests with synthetic data are described, which illustrate advantages of the partitioning method over the OI‐I scheme. Also, the inherent limitations of OI are shown in both methods. Experiments with buoy observations for actual North Sea conditions show the benefits of the system, especially when several wave systems are present at the same time.

Edge‐enhanced image zooming

A new adaptive algorithm for image interpolation with percep- tual edge enhancement is proposed. Here, perceptual means that edges are enhanced and interpolated in a visually pleasing way. Each pixel neighborhood is classified into one of three categories (constant, ori- ented, or irregular). In each case, an optimal interpolation technique finds the missing pixels without generating unpleasant artifacts such as aliasing or ringing effects. Furthermore, a quadratic Volterra filter is em- ployed to extract perceptually important details from the original image, which are then used to improve the overall sharpness and contrast. Both qualitative and quantitative simulation results clearly show the superiority of our method over standard low-pass interpolation algorithms such as bilinear, diamond-filter, or B-spline interpolation. © 1996 Society of Photo-Optical Instrumentation Engineers. Subject terms: image interpolation; zooming; quadratic Volterra filters; detail en- hancement; image enhancement; edge enhancement.

Improvements in the GFDL Hurricane Prediction System

Abstract The hurricane model initialization scheme developed at GFDL was modified to improve the representation of the environmental fields in the initial condition. The filter domain defining the extent of the tropical cyclone in the global analysis is determined from the distribution of the low-level disturbance winds. The shape of the domain is generally not circular in order to minimize the removal of important nonhurricane features near the storm region. An optimum interpolation technique is used to determine the environmental fields within the filter domain. Outside of the domain, the environmental fields are identical to the original global analysis. The generation process of the realistic and model-compatible vortex has also undergone some minor modifications so that reasonable vortices are produced for various data conditions. The upgraded hurricane prediction system was tested for a number of cases and compared against the previous version and yielded an overall improvement in the forecasts of s...

Kriging and mapping of copper, lead, and mercury contents in surface soil in Shenzhen area

Two-dimensional ordinary block kriging as an optimal interpolation technique was applied to produce regular grids of predicted estimates of copper, lead, and mercury contents in surface soil in the Shenzhen area for mapping purposes. The kriging analysis was based on theoretical variograms calculated from measured data of eighty three top soil samples. The appropriateness of the whole procedure of kriging analysis was evaluated by both cross-validation and kriging standard deviation mapping. The similarity in area variation between the distribution of soil parent material and the mapped results of copper and lead is demonstrated. The possible influence of agricultural contamination on the spatial distribution pattern of mercurcy is also discussed.

On the pointing robustness issue of a class of new generation spacecraft

A control design procedure for dealing with the robust slewing and pointing manoeuvres of a class of new generation spacecraft is proposed. The technique is based on the application of the optimal interpolation technique to the sliding control approach. This is used subsequently for insuring high pointing and tracking performance of the system in the presence of induced structural disturbances and modeling uncertainties. Numerical simulations are carried out, and suggestions for further studies are outlined.

Variational Wave Data Assimilation in a Third-Generation Wave Model

Abstract The adjoint of the wave model WAM, which runs operationally performing global wave forecast at the European Centre for Medium-Range Weather Forecasts, has been constructed. In this model, the nonlinear interactions are described by the discrete interaction approximation of Hasselmann et al., and the wind input and the dissipation are consistent with the theory of Janssen. The drag coefficient depends not only on the wind speed, but also on the wave-induced stress, reflecting in this way the dependence of winds on waves. The adjoint scheme constitutes a new (the first variational) method to assimilate arbitrary wave data into the WAM. Up to now, this had been done using an optimal interpolation technique (sequential method), and only for wave heights. The new assimilation scheme has been tested with a one-gridpoint version of the WAM. Assimilating only wave data-significant wave height and mean wave direction—is sufficient to reconstruct all wind fields, significant wave height, and two-dimensiona...

Improved Global Sea Surface Temperature Analyses Using Optimum Interpolation

The new NOAA operational global sea surface temperature (SST) analysis is described. The analyses use 7 days of in situ (ship and buoy) and satellite SST. These analyses are produced weekly and daily using optimum interpolation (OI) on a 1° grid. The OI technique requires the specification of data and analysis error statistics. These statistics are derived and show that the SST rms data errors from ships are almost twice as large as the data errors from buoys or satellites. In addition, the average e-folding spatial error scales have been found to be 850 km in the zonal direction and 615 km in the meridional direction. The analysis also includes a preliminary step that corrects any satellite biases relative to the in situ data using Poisson's equation. The importance of this correction is demonstrated using recent data following the 1991 eruptions of Mt. Pinatubo. The OI analysis has been computed using the in situ and bias-corrected satellite data for the period 1985 to present.

Robust optimization of multivariable feedback systems with time-varying nonlinear uncertainties

Abstract A design criterion is developed to achieve the input-output decoupling of multivariable feedback systems and the robust stabilization of systems with time-varying nonlinear uncertainties. Moreover, an effective design algorithm is derived to achieve the robust optimization of multivariable feedback systems subjected to time-varying nonlnear uncertainties. The theory of minimum H∞ -norm and the optimal interpolation technique are employed to solve this robust optimization problem. Since the requirements of internal stability are satisfied, this design algorithm performs appropriately, even if the plant is unstable and/or non-minimum phase. From the result of the robust optimization, we can predict the maximum sector bounds of nonlinear uncertainties that can be tolerated in the multivariable feedback system.

An Evaluation of the WOCE Volunteer Observing Ship–XBT Network in the Atlantic

Abstract A volunteer observing ship (VOS)-expendable bathythermograph (XBT) network has been proposed for the Atlantic Ocean to satisfy World Ocean Circulation Experiment (WOCE) objectives in the upper water column. These objectives include measuring changes in upper-layer temperature. An evaluation of the proposed WOCE XBT network to resolve variability in sea surface temperature (SST), temperature distribution at 150 m (T150), and average temperature of the upper 400 m (T400L) between 25°S and 35°N is performed. A sampling design study based on an optimum interpolation (OI) of the historical XBT dataset is used to construct uncertainty distributions for various XBT networks. The OI technique requires statistical representations of the variability (in the form of structure functions) of the three variables that are derived from the historical database. The structure functions and various sampling grids are used to construct uncertainty maps. Two seasons are used in the analysis of SST. In both seasons, u...

Mapping the mean sea surface elevation field from satellite altimetry data using optimal interpolation

Abstract Optimal interpolation technique is applied to satellite altimetry data in order to recover a sea surface elevation signal from the data, which includes a large satellite radial orbit error, also to make a map of temporal mean sea surface dynamic topography (SSDT, the mean surface height relative to the geoid). The method is applied to Seasat data for a study area southeast of Japan, for which a fairly precise gravimetric geoid is available. Estimated mean elevation field relative to the best available geoid qualitatively shows existence of the Kuroshio in a limited local area close to Honshu, Japan. But for the whole of the area studied, the elevation field is much more rugged than expected mean SSDT and appears to include a relatively large geoid error; namely, the mapped mean sea surface elevation field cannot describe the mean SSDT field. Instead, correction of the provided geoid is evaluated by this altimetrically estimated elevation field together with the mean SSDT estimated from hydrograph...

Accuracy assessment of optimum interpolation in multichannel precipitation analysis

The accuracy of an optimum interpolation technique in filling missing values in multichannel (or multisite) hydrologic series containing time-coincident data gaps is examined. The applied methodology is based on the maximum entropy method (MEM) of spectral estimation or multivariate autoregressive modeling and heavily depends upon the properties of multichannel prediction error filter (PEF). Six precipitation time series spatially located within a hydrologic basin are used and time-coincident artificial gaps are created in all six series. The performance of the technique is assessed by comparing the filled-in series to the observed and by employing spectral analysis. The results reveal the usefulness of the method in multichannel hydrologic analysis.

Robust optimization of feedback systems with time-varying non-linear uncertainties

A design criterion is developed to achieve the robust stabilization of a feedback system with time-varying non-linear uncertainties. Moreover, an effective design algorithm is derived to achieve the robust optimization of a feedback system subjected to time-varying non-linear uncertainties. The theory of minimum H ∞-norm and the optimal interpolation technique are employed to solve this robust optimization problem. Since the requirements of internal stability are satisfied, this design algorithm performs appropriately, even if the plant is unstable and/or is non-minimum phase. From the result of the robust optimization, we can predict the maximum sector bound of non-linear uncertainties that can be tolerated in the feedback system.