Areal interpolation of rainfall with a double Fourier series

Thorpe, W.R.; Rose, C. W.; Simpson, R.W.

doi:10.1016/0022-1694(79)90012-x

Cited by 10 publications

(5 citation statements)

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“…The deformed surface of each side of the measurement plane was measured with a laser scanning profilometer along the cross-section with a measurement spacing of 100 μm in the thickness direction and 200 μm in the width direction, so that there were roughly 190,000 data points for each surface. Both sides of the cut surface are averaged on a common grid, and the average surface is fit with a smooth bivariate Fourier series [17]. A level of smoothing is determined by choosing fitting parameters during data reduction.…”

Section: Methodsmentioning

confidence: 99%

Assessment of Weld Residual Stress Measurement Precision: Mock-Up Design and Results for the Contour Method

Olson

Hill

Willis

et al. 2015

Journal of Nuclear Engineering and Radiation Science

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Recent experimental work has shown residual stress measurements in welded material to be difficult. To better assess the precision of residual stress measurement techniques, a measurement article was designed to allow repeated measurements of a nominally identical stress field. The measurement article is a long 316L stainless steel plate containing a machine-controlled eight-pass slot weld. Measurements of weld direction residual stress made with the contour method found high tensile stress in the weld and heat-affected zone, with a maximum near 450 MPa and compressive stress away from the weld, a typical residual stress profile for constrained welds. The repeatability standard deviation of repeated contour method residual stress measurements was found to be less than 20 MPa at most spatial locations away from the boundaries of the plate. The repeatability data in the weld are consistent with those from a previous repeatability experiment using the contour method in quenched aluminum bars. A finite-element simulation and neutron diffraction measurements were performed for the same weld and provided results consistent with the contour method measurements. Much of the material used in the work remains available for use in assessing other residual stress measurement techniques, or for an interlaboratory reproducibility study of the contour method.

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Section: Methodsmentioning

confidence: 99%

Assessment of Weld Residual Stress Measurement Precision: Mock-Up Design and Results for the Contour Method

Olson

Hill

Willis

et al. 2015

Journal of Nuclear Engineering and Radiation Science

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“…Some of these are reviewed by Hall and Barclay [1975], although others have been proposed since then [cf. Thorpe et al, 1979;Bethlamy, 1976;Pande et al, 1978].Attempts to evaluate and compare the different methods are much more rare. This is understandable for techniques that estimate spatial averages because of the lack of experimentally measured areal values.…”

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confidence: 99%

“…Some of these are reviewed by Hall and Barclay [1975], although others have been proposed since then [cf. Thorpe et al, 1979;Bethlamy, 1976;Pande et al, 1978].…”

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confidence: 99%

Objective analyses and mapping techniques for rainfall fields: An objective comparison

Creutin¹,

Obled²

1982

Water Resources Research

348

184

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Many methods have been proposed and applied individually to rainfall fields in order to estimate point or average values at ungauged sites. This paper reviews some of the usual as well as some of the more recent techniques. They are classified according to their fundamental principles, optimality criteria, and practical aspects. Some theoretical developments, mostly for the statistically based techniques, are offered, and the practical aspects are mainly directed to the particular case of rainfall fields. A case study is presented for a region with particularly high rainfall variability, providing a good sample of events for testing the sensitivity of the estimation to the different methods used. The identification of statistical structure functions, required by certain methods using regionalized variable concepts, is discussed in detail for the case considered. Method evaluation is based on a classical validation technique that divides the available stations into two separate networks, i.e., a base network is used to perform estimations at the stations of a test network for a set of independent storm events. Careful attention is paid to result interpretation and visualisation. Finally, conclusions are drawn as to which method should be implemented, taking into account cost-efficiency considerations.Many techniques have been proposed for mapping rainfall patterns and for evaluating the average rainfall over a watershed. Some of these are reviewed by Hall and Barclay [1975], although others have been proposed since then [cf. Thorpe et al., 1979;Bethlamy, 1976;Pande et al., 1978].Attempts to evaluate and compare the different methods are much more rare. This is understandable for techniques that estimate spatial averages because of the lack of experimentally measured areal values. However, most techniques may also be used for point values, where ground verification is possible. Point values are also of interest for contouring and for filling in gaps in records of existing stations. This paper proposes an objective comparison of methods estimating point values. The evaluation procedure itself relies on a simple validation technique commonly used in statistics. The methods evaluated are those which are or are becoming commonly used in surface hydrology.Although several other classification systems will be used throughout this paper, the various methods may first of all be separated into simple and sophisticated ones. In the first group are the following:1. The nearest neighbor method. The estimated value at any given point is taken as the observed value at the nearest neighboring station. This represents the simplest possible interpolation scheme and is in fact the basic principle of the Thiessen method, as demonstrated in the automated version proposed by Diskin [1970] and widely used in hydrology for average rainfall estimation. The arithmetic mean.This assumes that the rainfall depth is theoretically constant over a given region and can be estimated by the average of the observed values within this region.In the ...

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“…Areal interpolation methods transfer the discrete data to continuous data by constructing the quantity relationship between the target zone and source zones according to their spatial relationships (e.g., areal weighting, distance weighting) or some ancillary information (e.g., land use and land cover classes) [16]. This method has been widely applied to generate the surface data of rainfall and temperature [17,18]. The statistical modeling method is based on a functional relationship between dependent variables and independent variables.…”

Section: Introductionmentioning

confidence: 99%

Gridded Water Resource Distribution Simulation for China Based on Third-Order Basin Data from 2002

Wang

Zhou

et al. 2016

Sustainability

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Water resources are a key factor for regional sustainable development. However, the published water resource data in China is based on a large geographical scale, such as watershed units, and the data cannot reflect subtle differences in water resource distribution. The paper aimed to distribute water resources of the third-order basin of China into grid-cells of 1 km × 1 km. First, we used Moran's I index to analyze the spatial pattern of water resources of the third-order basin. Second, we constructed a spatial autocorrelation model between water resources of third-order basins and the associated factors. Third, we applied the model to simulate the gridded water resource distribution and evaluated the simulation accuracy. The results indicated that significant spatial autocorrelation existed among the water resources of third-order basins. Northern China was the low-value clustering area of water resources and Southeast China was the high-value clustering area of water resources. Slope and precipitation were the main factors that influenced the amount of water resources. The simulating accuracy of water resource distribution was very high, apart from some extremely arid regions (Gurbantunggut Desert, Kumtag Desert, and Hexi Desert). On the whole, the gridded water resource distribution map was valid and was helpful for regional water resource management.

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Areal interpolation of rainfall with a double Fourier series

Cited by 10 publications

References 1 publication

Assessment of Weld Residual Stress Measurement Precision: Mock-Up Design and Results for the Contour Method

Assessment of Weld Residual Stress Measurement Precision: Mock-Up Design and Results for the Contour Method

Objective analyses and mapping techniques for rainfall fields: An objective comparison

Gridded Water Resource Distribution Simulation for China Based on Third-Order Basin Data from 2002

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