Grid Distance Research Articles

Interpolation Artefacts in Mutual Information-Based Image Registration

Image registration requires the transformation of one image to another so as to spatially align the two images. This involves interpolation to estimate gray values of one of the images at positions other than the grid points. When registering two images that have equal grid distances in one or more dimensions, the grid points can be aligned in those dimensions for certain geometric transformations. Consequently, the number of times interpolation is required to compute the registration measure of two images is dependent on the image transformation. When an entropy-based registration measure, such as mutual information, is plotted as a function of the transformation, it will show sudden changes in value for grid-aligning transformations. Such patterns of local extrema impede the registration optimization process. More importantly, they rule out subvoxel accuracy. In this paper, two frequently applied interpolation methods in mutual information-based image registration are analyzed, viz. linear interpolation and partial volume interpolation. It is shown how the registration function depends on the interpolation method and how a slight resampling of one of the images may drastically improve the smoothness of this function.

Strongly stratified easterly flows across Spitsbergen

Strongly stratified easterly flow across the Svalbard archipelago is investigated by means of anumerical model with a grid distance of 10 km. Idealized simulations of flow over idealized andreal orography with Brunt–Väisälä frequency fixed at N=0.019 s-1 and with a uniform backgroundvelocity varying between 8.7 and 26 ms-1 are performed. With a maximum height of the orography at 916 m, the non-dimensional mountain height ĥ=Nh/U varies between 0.67and 2.0. The Rossby number Ro=U/fL is of order unity. Robust features of these simulationsare an upstream velocity minimum south of Hinlopenstretet and a downstream wake to thenorth of Isfjorden. Over the downslopes, upstream of the wake, the velocities are high in thesimulations at the lower end of ĥ due to vigorous gravity wave activity. As ĥ is increasedtowards 2.0, the gravity wave activity in this area is greatly reduced, and the associated velocitymaximum disappears. Downstream jets are radiating from the three resolved fjords Isfjorden, van Mijenfjorden and Hornsund, and the two former jets merge into one further downstream. The absolute velocity maximas are found in the south, where the velocities are enhanced relativeto the upstream undisturbed velocity by factors of 1.7 to 2.2. The highest velocities are recognizedto be associated with the gravity wave activity. However, velocities are generally high in thesouth due to the left–right asymmetry induced by planetary rotation. The simulation of a realcase largely confirms these findings. In this case wind speeds reaching between 35 and 40 ms-1 are simulated near the southern tip of Spitsbergen. An investigation of the zonal wind speedsat Spitsbergen is also presented and reveals that from 1990 to 1997, 13 situations with upstreamwind speed of the same strength as in the case study have occurred.

Regional stretched grid generation and its application to the NCAR RegCM

A method for the generation and application of a regional variable resolution stretched grid system is developed. In the modeling domain, a stretched grid buffer zone surrounds the central uniform grid region. To be comparable with current nesting methods, two integers are specifically considered in the design of the grid system. The first integer is the total stretching rate, which is the ratio of the maximum grid distance to the minimum grid distance, and the other integer is the ratio of the width of the buffer zone to the maximum grid distance. The grid distance is uniformly reduced from the outer lateral boundary of the model domain to the edge of the central uniform grid region. The final purpose of this grid is to facilitate the two‐way interaction between global and regional models. However, the primary objective of this paper is to present the theoretical framework of the stretched grid system and its implementation within the NCAR regional climate model (RegCM). We provide an example of the performance of the stretched grid model configuration by applying it to an adiabatic version of the RegCM and completing a 3‐day simulation over a domain encompassing the continental United States. The stretched grid version of the model produces results comparable to a control run with uniform resolution. The computational cost of running the stretched grid system is about 40% lower than that of the uniform grid system because of the smaller number of grid points in the lateral buffer area. These preliminary numerical tests with the RegCM illustrate the robustness of our new regional stretched grid method.

Precision Farming Protocols: Part 1. Grid Distance and Soil Nutrient Impact on the Reproducibility of Spatial Variability Measurements

To determine temporal changes in soil nutrient status, reproducible results must be obtained at each time step. The objective of this paper was to determine the impact of grid distance on the reproducibility of spatial variability measurements. Soil samples from the 0 to 15 cm depth were collected from a 30 by 30 m grid in May 1995 in a 65 ha notill corn (Zea mays L.) field. Each bulk sample contained 15 individual cores, collected at sample points located every 11.4 cm along a transect that transversed 3 corn rows (57 cm). At each sampling point latitude, longitude, elevation, landscape position, and soil series were determined. The 30 m grid was used to develop 4 and 9 independent data sets having a 60 and 90 m, grids, respectively. Semivariograms, nugget to sill ratios, and mean squared errors were calculated for each data set. At 60 m: (i) the total N, total C, and pH semivariograms, of different start points, were similar, while semivariograms for Olsen P, K, and Zn were different; (ii) the spatial dependence ratings, based on the nugget to sill ratio, for total N, total C, and pH semivariograms were consistent and suggested moderate spatial dependence; (iii) the spatial dependence rating for Olsen P, K, and Zn for the 4 semivariograms were not consistent and ranged from weak to moderate spatial dependence. At 90 m all soil nutrients had different semivariograms for each start point, while the spatial dependence rating for each total N, total C, and pH start point were consistent and showed moderate spatial dependence. The total C, P, K, Zn, and pH MSE values at 60 m, were 30, 30, 41, 28, and 72% lower than the variance, respectively. This study showed that semivariogram, semivariance, MSE, and nugget to sill ratios reproducibility were dependent on soil nutrient and grid distance.

Smooth quasi‐homogeneous gridding of the sphere

AbstractWe describe a variational technique for generating smooth quasi‐homogeneous numerical grids covering the sphere. This work extends our earlier studies of non‐standard global grids by relaxing the requirement of conformality to admit a greater degree of homogeneity. The motivation for this extension is to increase the minimum grid distance and thus to enable a larger time step to be used within an Eulerian grid‐point model. The grids described here are specified by balancing terms in a variational principle that penalizes departures of grid‐point density from smoothness and homogeneity. Grids generated by the new procedure are tested in both the cubic and octagonal configurations we have described in our earlier studies. The time‐step restriction is successfully alleviated without significant loss of solution accuracy.

Suppression of moiré patterns in scanned halftone images by double scans with grid movements

Moiré patterns often appear in images obtained from scanning printings on magazines or newspapers. The patterns do not exist in the original printings but come from alias sampling of the screened halftone pictures. A new method of scanning is proposed to suppress the moiré patterns. First, the Fourier analyses of both screening and scanning are presented, from which the new moiré suppression scanning method is derived. The method employs a double-scan process. In the second scan, the scan position is shifted by half of the sampling grid distance of the first scan in either or both of the horizontal and vertical directions. Then by averaging the images of the two scans, most of the moiré fringes can be removed. Some experimental results are shown to demonstrate the feasibility of the proposed approach.

Microscale heterogeneity of acidity related stress-parameters in the soil solution of a forested cambic podzol

Acid related stress in soils might be caused by high concentrations of H + and Al 3+ in soil solution. Sampling of soil solution so far integrates over a relatively large soil volume, in the range of dm 3 . In order to study the microscale hcterogeneity of acidity related stress-parameters the soil profile of a podzolic cambisol was covered by a 10x6 matrix of micro suction cups with a grid distance of 2 cm. The soil solution collected at 10 sampling events was analyzed for free cations and anions by capillary electrophoresis and for total metal content by a micro injection technique on ICP-OES. pH and UV absorption were also measured. There was a general trend of increasing pH and decreasing UV absorption with increasing soil depth, however without a clear correlation of concentration isolines to soil horizon borders. The latter was also true for total Al (Al tot ) and Al 3+ , with the exception of the soil horizon border A be /B h ,which was very well reflected by Al + and also by the fraction of bound Al. In the A be horizon less than 30%, in deeper mineral soil less than 50% of Al tot were present as free Al 3+ . This fact is critical when calculating Ca/Al ratios as a stress parameter, because total metal content measured by ICP clearly overestimates the risk of root damage, even in deeper horizons of acid forest soils, where organic complexation of Al is of minor importance. The heterogeneity of soil solution chemistry and toxicity parameters on the cm-scale was found to be significant, for example with gradients of more than 0,5 pH-units within 2 cm. Because plant roots also experience soil on a microscale, high resolution investigations of soil solution chemistry offer a new approach for looking at the chemical environment relevant for root growth and plant nutrition.

The exact region of stability for MacCormack scheme

Let the two dimensional scalar advection equation be given by $$\frac{{\partial u}}{{\partial t}} = \hat a\frac{{\partial u}}{{\partial x}} + \hat b\frac{{\partial u}}{{\partial y}}.$$ We prove that the stability region of the MacCormack scheme for this equation isexactly given by $$\left( {\hat a\frac{{\Delta _t }}{{\Delta _x }}} \right)^{2/3} + \left( {\hat b\frac{{\Delta _t }}{{\Delta _x }}} \right)^{2/3} \leqslant 1$$ where Δt, Δx and Δy are the grid distances. It is interesting to note that the stability region is identical to the one for Lax-Wendroff scheme proved by Turkel.

The exact stability region of the MacCormack scheme for the scalar advection equation

This note announces that the stability region of the MacCormack scheme for the scalar advection equation u t = au x + bu y is exactly given by a Δt Δx 2 3 + b Δt Δy 2 3 ≥ 1 where Δ t , Δ x and Δ y are the grid distances. This improves upon the result obtained by Wendroff [1] and corrects a mistake in it.

ScanSAR processing using standard high precision SAR algorithms

Processing ScanSAR or burst-mode SAR data by standard high precision algorithms (e.g., range/Doppler, wavenumber domain, or chirp scaling) is shown to be an interesting alternative to the normally used SPECAN (or deramp) algorithm. Long burst trains with zeroes inserted into the interburst intervals can be processed coherently. This kind of processing preserves the phase information of the data-an important aspect for ScanSAR interferometry. Due to the interference of the burst images the impulse response shows a periodic modulation that can be eliminated by a subsequent low-pass filtering of the detected image. This strategy allows an easy and safe adaptation of existing SAR processors to ScanSAR data if throughput is not an issue. The images are automatically consistent with regular SAR mode images both with respect to geometry and radiometry. The amount and diversity of the software for a multimode SAR processor are reduced. The impulse response and transfer functions of a burst-mode end-to-end system are derived. Special attention is drawn to the achievable image quality, the radiometric accuracy, and the effective number of looks. The scalloping effect known from burst-mode systems can be controlled by the spectral weighting of the processor transfer function. It is shown that the fact that the burst cycle period is in general not an integer multiple of the sampling grid distance does not complicate the algorithm. An image example using X-SAR data for simulation of a burst system is presented.

The Use of Nested Models for Air Pollution Studies: An Application of the EURAD Model to a SANA Episode

A multiple-nesting version of the European Acid Deposition Model (EURAD) has been developed in order to increase the horizontal resolution in a region of enhanced pollution, namely the former German Democratic Republic. This new technique allows the ability to simulate large-scale features together with the development of smaller-scale structures in the nested regions. This multiple-nesting approach was applied to a case that occurred in October 1990, the so-called SANA 1 episode. SANA is a German acronym that stands for “scientific program for the assessment of the air pollution situation in the former German Democratic Republic.” The SANA program was established to observe the rapid change in composition of air pollutants and their concentration levels over the eastern part of Germany due to political and economical changes. Thus, within the SANA program there is a unique chance to observe and control the effect of air quality strategies. Two nested areas are embedded in a coarse domain that covers the main parts of Europe. The second nested domain is nested within the first nested domain. For EURAD, the nesting is two-way for the meteorological part and one-way for the chemistry transport module (CTM). This means that the meteorological variables that coincide with the boundaries in the nested domain are interpolated by a monotone flux-corrected transport method from the next coarser domain and provide a feedback from the nested domain to the next coarser domain. For the CTM the inflow boundary conditions are dynamically determined by interpolation from coarse-grid results. The outflow conditions are specified by continuous advection at the boundary in order to eliminate numerical reflections. The results of the simulations indicate a strong dependence of the horizontal distribution of both meteorological quantities and atmospheric constituents on increased spatial resolution. They exhibit a much more realistic structure, especially for the simulations in the nested domain with highest resolution (8.89-km horizontal grid distance). Comparisons for the predicted SO2 concentrations with observations from selected stations clearly demonstrate that the simulations agree best with observations in the nested domain of highest horizontal resolution.

Using GPS Results in True 3‐D Coordinate System

GPS computations are performed in the geocentric coordinate system and transformed to geographic (latitude/longitude) or state plane coordinates for extended use in data‐base applications or engineering projects. State plane coordinates are very useful, but for some applications the difference between grid and ground distance becomes particularly bothersome. State department of transportation (DOT) offices are confronted with the grid/ground distance dilemma on highway projects, for which center‐line stationing must be ground based and state plane coordinates are used for project control. A questionnaire was sent to all 50 state DOTs asking for input as to how the problem is currently being addressed and asking for suggestions for solutions. Responses received from 46 of the 50 state DOTs are summarized in an appendix. The proposal included in this paper is to use the geocentric coordinate system as the basis for all three‐dimensional control computations, including conventional terrestrial measurements. To eliminate the distance distortion problem, results can be outputted in a local coordinate system. Equations for transforming between geographic, geocentric, and local coordinate systems are included in an appendix.

Beyond gender: the basis of sexual attraction in bisexual men and women.

The construct of sexual orientation has typically considered the gender of the sexual partner as defining whether the individual is homosexual, bisexual, or heterosexual, and the Kinsey scale conceptualises bisexuality as a point midway between homosexuality and heterosexuality. We propose an alternative model which places homosexuality and heterosexuality at one end of a continuum as gender-linked choices of sexual partner, and bisexuality at the other as nongender-specific. As a test of this model, we administered repertory grids to nine bisexual men and women to investigate the characteristics of sexual attraction in individuals for whom gender of partner was not a critical variable. Results supported the hypothesis that gender is not a critical variable in sexual attraction in bisexual individuals. Personality or physical dimensions not related to gender and interaction style were the salient characteristics on which preferred sexual partners were chosen, and there was minimal grid distance between preferred male and preferred female partners. These data support the argument that, for some bisexual individuals, sexual attraction is not gender-linked.

An analytical exericise to elucidate quasi-geostrophic frontogenesis

Frontogenesis is frequently described by theQ-vector (Hoskins et al., 1978), a term being composed of several derivatives of basic meteorological parameters and their products. Its distribution and especially the ∇ H ·Q-fields are highly important to estimate frontogenesis and cross frontal circulation. Although theQ-vector (Hoskins et al., 1978) allows an easier assessment of the vertical wind forcing than the original omega equation of the quasi-geostrophic theory, it is still difficul to imagine the three-dimensional (3-d) spatial distribution ofQ and ∇ H ·Q even for standard atmospheric fields. Thus there is a need to shed more light in theQ and ∇ H ·Q-fields for special synoptic situations. This is done here by constructing analytical 3-d geostrophically balanced wind-and temperature fields, for which theQ-forcing (Qformed with the geostrophic wind) can easily be computed and presented. Three examples (see Sections 3 to 5) are discussed yielding typical and realistic (compared to known pattern) 3-d forcing distributions ofQ and ∇ H ·Q. Within the simple analytical scheme used here their origin can casily be understood. These fields of a 2000×2000 km2 horizontal domain ranging up to 250 hPa are: A modified Bergeron deformation field containing a cold front (case I a) and a warm front (case I b); an upper tropospheric jet including a jet-parallel transition zone between warm and cold air (case II); and a circular low pressure circulation pattern with two fronts (case III). The paper presents these 3-d fields with the advantage that the analytical method is not affected by any kind of limited numerical resolution. It also shows how these fields degenerate with decreasing resolution if the analytical data are used in descrete form. This simulates working with discrete numerical data and demonstrates how narrow frontal zones of structure elements ofQ and ∇ H ·Q considerably smooth out with increasing grid distances.

Significant Impact Area and Vulnerable Zone Screening Analysis

Significant impact area, and vulnerable zone, both circular and delimited by prescribed ground-level concentration values, appear in several environmental regulations. The radius of the circle is often estimated by atmospheric dispersion models in an iterative approach using various grid distances which are applied until the maximum distance is found where the concentration no longer exceeds the prescribed value. In this paper, formulas are presented to estimate the radius directly. As required by Prevention of Significant Deterioration (PSD) regulations, a major new source (or modification of an existing major source) must analyze existing air quality in the vicinity of the new source, and demonstrate that emissions from the new source and other nearby sources will not violate National Ambient air Quality Standards (NAAQS) or PSD incremental limits. Detailed modeling is used to demonstrate compliance of the new source and other nearby sources with NAAQS and PSD incremental limits. Nearby sources are taken to mean any sources which would have an impact on the significant impact area (SIA) of the new source. The SIA is the circular area beyond which the impact of the new source alone is less than significance levels established by the Environmental Protection Agency (EPA). The formulas presentedmore » would be useful as conservative screening tools for short-term (e.g., 1-3 h) impact area assessments.« less

A fine mesh analysis scheme designed for mountainous terrain

A fine mesh analysis scheme (grid distance approximately 47 km) has been developed which takes care of mountain ridges of different height, to be able to study cyclogenesis induced by the Alps from the standpoint of observational quantitative vorticity dynamics.

Analysis of mesometeorological temperature fields

An objective procedure of a three-dimensional temperature analysis in a topography following (zeta) coordinate system is presented. Temperature data from various conventional sources (ground stations, RAWIN, synoptic analysis) are interpolated into the grid points of the zeta system (the horizontal grid distance is 1 km, vertical resolution is 11 levels up to 2500 m) by a topography variability considering horizontal interpolation. As the correlations between the synop and also the upper air data from pairs of stations on different sides of a mountain barrier show a rapid decrease (Lanzinger and Steinacker, 1989), the Euclidic distances between the points with measurements and the grid points are corrected according to the variability of the gird points are corrected according to the variability of the topography between the two points. If the topography between the two points is flat, or if there is only a valley, the Euclidean distance is used as an interpolation distance. In case of a ridge between the two poinst the interpolation distance is increased according to the topography height variation and the stability of the air mass. In the vertical interpolations a synthetic temperature profile is used made of the data from Rawin, the measurements from meteorological tower and the measurements from some meteorological stations located at high altitude.

Condensation and Cloud Parameterization Studies with a Mesoscale Numerical Weather Prediction Model

Abstract This paper presents the implementation of a parameterization scheme for convective and stratiform condensation (with cloud water as a prognostic variable) into a fine mesh numerical weather prediction model. The results from a 36 h integration of the model, with grid distance 50 km, indicate that the new condensation scheme contributes to an improved forecast compared to that obtained by the original model. Furthermore, from a qualitative comparison with satellite pictures, it is found that the prediction of condensation-cloud parameters is quite realistic.

Description and performance of an hourly nowcasting and very short‐range forecasting system

AbstractSince the disaster in The Netherlands caused by a mesoscale gale on 12 May 1983, an hourly nowcasting and very short‐range forecasting system has been developed using all available hourly surface observations of pressure and wind over the North Sea and the surrounding countries.Hourly analyses and prognoses are produced using hourly interpolated background fields and lateral boundaries from the fine mesh United Kingdom prognoses, which are received from Bracknell twice a day based on 00 and 12 GMT up to 36 hours in advance at 3‐hour intervals.The computational area consists of a grid of 35 × 35 points with a grid distance of 50 km covering the North Sea and surroundings. The update and forecast model is a two‐parameter model based on filtered equations with the geopotential height fields at 500 and 1000 mb as input and output. It is called VIMOLA (vertically integrated model on limited area). A new method is used for the analysis at 1000 mb. The observations of pressure and wind are directly assimilated onto the computational grid, and in this way wind measurements are converted into pressure gradients. All 10‐minute‐mean winds are taken into account. The analysis system is called APW (assimilation of pressure and wind).Every hour analyses and prognoses are produced up to nine hours in advance. The prognoses are merged with the fine mesh U.K. prognoses, i.e. the final prognoses are a linear combination of VIMOLA prognoses and U.K. prognoses. For one hour in advance no merging takes place and after nine hours the final prognoses are identical to the U.K. prognoses.For The Netherlands and surrounding regions winds computed from the forecasts have been verified against the observations. Winds from the U.K. prognoses have been verified in the same way. The U.K. prognoses show a very good quality and a small error growth during the first 24 hours. However, the hourly incorporation of the observations gives an improvement, especially for the first hours of the forecast period.Because no upper air observations are needed, a very short data cut‐off time can be applied (20–45 minutes after the time of observation). In practice, the system is suitable for operational gale warnings and tidal surge forecasts. Due to the hourly character, the system is able to detect temporal variations in the surface wind field such as the diurnal cycle over land and air mass variability. Practical examples are given in this paper, including some results obtained for the storm of 15–16 October 1987, which hit the south‐eastern part of England.

Inclusion of ice cover in a storm surge model for the Beaufort Sea

Storm surges in the Beaufort Sea present a severe problem for navigation as well as for offshore oil drilling activities. Influence of ice cover on storm surges in the Beaufort Sea is examined making use of a numerical model as well as a set of observations. The automated shallow-water model of Henry has been modified to incorporate ice cover and is adapted to the Beaufort Sea. The leading edge of the permanent ice is calculated from the loci of identifiable points. Generalized similarity theory is employed to compute wind stresses. Simulations are made using model-predicted ice concentrations and observed ice concentrations. Ice motion is relatively small in units of model grid distance (approximately 18 km) during surges. Spherical effects are important and should be included in future adaptations of the model. Comparison of the computed surges with observed surges for eight different events showed reasonable agreement.