The Application of Statistical and Mathematical Models of a Morphometric Study of Dry Valleys: Nessah Valley in Saudi Arabia PDF

Keywords

Nessah Valley, Saudi Arabia, Morphometric study, Statistical and mathematical techniques, Geodesic, Cartisi

Abstract

This paper deals with the application of numerous statistical and mathematical techniques used during a morphometric study that was conducted at Nessah mountain pass. The study focuses on building a Terrain Model (TM)made of two parts: the Digital Terrain Model, which represents the earth digitally, the other being the Terrain Mathematical Model, this model represents the mathematical and statistical functions that correspond with the morphometric study requirements of the valley, and consequently interacts with the digital data via a computer modeling process The research was enhanced, affected and enriched with results obtained from the application of the mathematical and statistical techniques, not only of its field measurements, but also in the analysis. The data was used to determine the various morphometric characteristics, (water, morphic topographical and river density) and to find out the correlation relationships between them that will establish the related planometric drawings. This has been achieved through the following research stages - Enhancing the field work through the adjustment of Geodesic observation by the least squares - Assigning correlation power between the meteorology and the morphometric characteristics. Determination of their function significance level via the application of Pearson's correlation equations, and the partial correlation application of the statistical test known as (t Test) - Detection of the most appropriate equations to represent the scope in the main valley and its feeders by the application of simple and compound regression equations (polynomial until the 4 grade) - To assign the geodesic, cartisic and local coordinates mathematically, their interconversion within suphroad international basics. the basics of the complete cosines direction to the basic local geodesic reference. - To establish a morphometric base to extract the various morphometric characteristics (water, morphic, topographical, and river density characteristics). This was conducted by the application of solid, analytical geometry rules to find out the four basic components of such rules, these are the distance, directions, areas and heights. - To find out the correlation links between relations of the dual and multi morphometric characteristics and nine other characteristics, after specifying which variants are fixed and which are secondary through the alteration between them through partial correlation. The best regression equation between the nine morphometric characteristics have been specified and the mathematics of the matrixes have been employed to determine the basics of the compound regression equations. To specify the equation error used to adjust the morphometric forms. The application of Azimuth rules in distance, directions, accumulative calculations and the specification of the various coordinates in the planometric drawings operations of the mountain pass borders and its main course and its feeders.