Trend-Surface Mapping in Geographical Research

Chorley, Richard J.; Haggett, Peter

doi:10.2307/621689

Cited by 129 publications

(30 citation statements)

References 44 publications

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“…The interpolation method is a widely used approach for generating raster data from the dispersed data of meteorological observation stations; it is simple and convenient, but it is unable to analyze the spatial variations in scattered data. TSA (Chorley & Haggett 1968, Gittins 1968) is a statistical method that is fully able to describe the variation in the spatial (or spatial-temporal) distribution of certain factors. It uses spatial coordinates as independent variables: abscissa and ordinate in a 2-dimensional TSA or longitude, latitude and elevation in a 3-dimensional TSA.…”

Section: Methodsmentioning

confidence: 99%

The Climate Information System of China

Shang

Gao²,

Da-yuan³

2001

Clim. Res.

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The Climate Information System of China (CISC) was built using Visual C++ and Java to perform 4 main functions: (1) to describe the variation in the spatial distribution of particular climatic variables with minimal digital information; (2) to separate the impacts of large-scale factors and local factors on climatic distribution and generate a raster database from the data collected from dispersed stations; (3) to share the climatic data on the Internet; and (4) to evaluate the impact of global change on Chinese water conditions under a number of prescribed climate scenarios. The establishment of CISC is described in detail. A digital elevation model and some meteorological (climatic) equations were used to calculate raster radiation data. Trend surface analysis and the interpolation method were used to analyze the spatial distribution of temperature, precipitation, relative humidity, sunshine fraction, and wind velocity and to generate the raster database. Penman's equation was amended and parameterized to calculate the potential evapotranspiration over China. An aridity index was calculated under present situations and 12 prescribed climate scenarios (raising mean temperature by 1.5, 3.0 and 4.5°C and changing precipitation by 0, +10, + 20 and -10%) to assess the sensitivity of Chinese water conditions to global change. Some Java applets were written to make it possible to share Chinese climate information on the Internet.

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Section: Methodsmentioning

confidence: 99%

The Climate Information System of China

Shang

Gao²,

Da-yuan³

2001

Clim. Res.

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“…The generalization in pattern description which the isopleth maps render may be further advanced by utilizing established trend-surface mapping programmes (Chorley & Haggett 1965). Trend-surface mapping refers to the fitting of mathematical polynomials to point reference data, and has mainly been developed in geological studies to facilitate interpretation of structural trends in rock deposits (Whitten 1963).…”

Section: Computer Graphic Techniquesmentioning

confidence: 99%

Computer graphic techniques in planning

Davies

1970

Planning Outlook

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“…Third, the topographic surface has appeared too complex for wide application of global polynomial approximations. As a result, only low-order orthogonal polynomials have been utilized in trend-surface analysis, a technique to reveal trend and residual components of the topographic surface [24,25]. However, the current progress in the theory and practice of polynomial approximation [26][27][28] suggests that it is now possible to solve such problems.…”

Section: Introductionmentioning

confidence: 99%

Digital terrain modeling with orthogonal polynomials

Florinsky¹,

Pankratov²

2015

JMLDA

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Background: Mathematical problems of digital terrain analysis include interpolation of digital elevation models (DEMs), DEM generalization and denoising, as well as computation of morphometric variables by calculation of partial derivatives of elevation. Traditionally, these procedures are based on numerical treatments of DEMs, two-dimensional (2D) discrete functions of elevation. Methods: We developed a spectral analytical method and algorithm based on high-order orthogonal expansions using the Chebyshev polynomials of the first kind with the subsequent Fejér summation. The method and algorithm are intended for analytical treatment of regularly spaced DEMs, such as DEM global approximation, generalization, and denoising as well as computation of morphometric variables by analytical calculation of partial derivatives. Results: To test the method and algorithm, a DEM of the Northern Andes containing 230,880 points (the elevation matrix 480×481) has been used. The DEMs were reconstructed with 480, 240, 120, 60, and 30 expansion coefficients. The first and the second partial derivatives of elevation were analytically calculated from the reconstructed DEMs. The models of 14 local morphometric variables were then computed with the derivatives. A set of maps of elevation and horizontal curvature (k h ) related to different number of expansion coefficients well illustrates data generalization effects, denoising, and removal of artifacts contained in the original DEM. Concluding Remarks:The test results demonstrated a good performance of the developed method and algorithm. They can be utilized as a universal tool for analytical treatment in digital terrain modeling. Keywords: Chebyshev polynomials; Fejér summation; generalization; denoising; partial derivatives DOI: 10.21469/22233792.1.12.01Цифровое моделирование рельефа с использованием ортогональных полиномов * И. В. Флоринский, А. Н. ПанкратовИнститут математических проблем биологии РАН Математические аспекты цифрового моделирования рельефа включают интерполя-цию цифровых моделей высот (ЦМВ), генерализацию и подавление шума в ЦМВ, а так-же расчет морфометрических характеристик на основе вычисления частных производных высоты. Эти процедуры традиционно основаны на численной обработке ЦМВ -дискрет-ных функций двух переменных. Авторы разработали спектрально-аналитический метод и алгоритм на основе ортогональных разложений высокого порядка с использованием многочленов Чебышёва I рода с последующим суммированием Фейера. Метод и алгоритм предназначены для аналитической обработки ЦМВ, включая глобальную аппроксимацию * The study was supported by RFBR grant 15-07-02484. I. V. Florinsky and A. N. Pankratov 1648 регулярных ЦМВ, генерализацию и подавление шума в ЦМВ, а также расчет морфо-метрических характеристик на основе аналитического вычисления частных производных. Для тестирования метода и алгоритма использовалась ЦМВ Северных Анд, включающая 230 880 точек (матрица высот 480×481). Цифровые модели высот были восстановлены с использованием 480, 240, 120, 60 и 30 коэффициентов...

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Trend-Surface Mapping in Geographical Research

Cited by 129 publications

References 44 publications

The Climate Information System of China

The Climate Information System of China

Computer graphic techniques in planning

Digital terrain modeling with orthogonal polynomials

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