A Novel Simple Semi-Empirical Model for the Effective Earth Radius Factor

Palmer, Andrew J.; Baker, D.C.

doi:10.1109/tbc.2006.884737

Cited by 8 publications

(10 citation statements)

References 4 publications

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“…If the radio refractivity varies linearly with height h for the first few tenths of a kilometer above the earth's surface and doesn't vary in the horizontal direction, then the vertical refractivity gradient is given by [13][14][15]: dN dh = 77. 6 1 T dP dh + 4810…”

Section: Radio Refractivity and The Effective Earth Radius Factor (K-mentioning

confidence: 99%

“…For ease of geometrical analysis, these waves are represented as straight lines then compensation is done by assuming an imaginary earth radius, otherwise referred to as effective earth radius, r e [15]. The ratio between the effective and true earth radius is referred to as the effective earth radius factor (k-factor) and is given by [10,16,17]:…”

Section: Radio Refractivity and The Effective Earth Radius Factor (K-mentioning

confidence: 99%

“…The k-factor is a function of the vertical refractivity gradient, dN/dh, and can also be determined from [13,15,18]:…”

Section: Radio Refractivity and The Effective Earth Radius Factor (K-mentioning

confidence: 99%

“…The authors have worked on refractivity and k-factor statistics for various locations across the country using measurements from meteorological sensors either mounted on TV towers or ground measurements [2,3,5,10,18]. Palmer and Baker [13][14][15] have used regression analysis on data for summer inland rainfall areas of South Africa to develop a cumulative distribution model of the k-factor. Using this model they were also able to obtain contours of the k-factor exceeded 0.001 of the time annually.…”

Section: Previous Work On the Effective Earth Radius Factor In Africamentioning

confidence: 99%

“…where all parameters are as described in (14) and (15). The weighting in IDW is such that the sum of all the weights sum to unity [35]:…”

Section: Inverse Distance Weighting (Idw)mentioning

confidence: 99%

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Seasonal Distribution Modeling and Mapping of the Effective Earth Radius Factor for Microwave Link Design in South Africa

Nyete¹,

Afullo²

2013

PIER B

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Abstract-In this paper we present seasonal results of the effective earth radius factor distribution in South Africa using recently (2007)(2008)(2009) acquired radiosonde data from the South African Weather Service (SAWS) for seven locations in South Africa. Two data modeling methods are used to formulate the solution for the distribution of the effective earth radius factor.The seasonal effective earth radius factor statistics obtained from the radiosonde measurements are then interpolated, gridded and presented in contour maps to cover the rest of the country for the four seasons defined by ITU-R recommendation P.453-10. The Integral of Square Error is used to check the performance of the data modeling techniques while the Root Mean Square Error is used to compare the performance of the different interpolation methods used.

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Section: Radio Refractivity and The Effective Earth Radius Factor (K-mentioning

confidence: 99%

Section: Radio Refractivity and The Effective Earth Radius Factor (K-mentioning

confidence: 99%

“…The k-factor is a function of the vertical refractivity gradient, dN/dh, and can also be determined from [13,15,18]:…”

Section: Radio Refractivity and The Effective Earth Radius Factor (K-mentioning

confidence: 99%

Section: Previous Work On the Effective Earth Radius Factor In Africamentioning

confidence: 99%

“…where all parameters are as described in (14) and (15). The weighting in IDW is such that the sum of all the weights sum to unity [35]:…”

Section: Inverse Distance Weighting (Idw)mentioning

confidence: 99%

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Seasonal Distribution Modeling and Mapping of the Effective Earth Radius Factor for Microwave Link Design in South Africa

Nyete¹,

Afullo²

2013

PIER B

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General Formulas of Effective Earth Radius and Modified Refractive Index

Feng

Huang

2021

IEEE Access

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The effective earth radius can transform the curved ray path into a straight line, and the modified refractive index can transform the spherical ground into a plane. Using them can simplify the propagation modeling of electromagnetic waves in the atmosphere, so they are widely used in the calculation of long-range propagation of electromagnetic wave, and adopted by the ITU Recommendations and the IEEE Standards. In this paper, upon employing simple geometric methods, we provide general formulas for the effective earth radius and the modified refractive index, pointing out that they both originate from the use of conformal transformations. In turn, we prove that for both quantities the formulas contained in the ITU Recommendations and the IEEE Standards are special cases of the general formulas given in this paper. Our results provide a solid mathematical background to the concepts of effective earth radius and modified refractive index, and pave the way for their use beyond the propagation of electromagnetic waves in the earth atmosphere, e.g. to the propagation of other types of waves in generic media.INDEX TERMS Effective earth radius, modified refractive index, conformal transformation, wave propagation, ray tracing.

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Interpolation and mapping of the median k-factor for terrestrial link applications in South Africa

Nyete

Afullo

2013

2013 Africon

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In this paper, three years recent radiosonde data obtained from the South African Weather Service for seven locations in South Africa (Bethlehem, Bloemfontein, Cape Town, Durban, Polokwane, Pretoria and Upington) has been processed, analyzed and median k-factor values at a height of 200m above ground level processed. Due to the tedious nature of processing clear-air meteorological data, and the cost involved in launching radiosondes, two interpolation techniques have been employed in extending the k-factor statistics obtained to cover the whole of South Africa. A comparison of the interpolation methods is drawn by using the Mean Absolute Error and Root Mean Square Error criteria and then the interpolated and gridded values are presented in contour maps.

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A Novel Simple Semi-Empirical Model for the Effective Earth Radius Factor

Cited by 8 publications

References 4 publications

Seasonal Distribution Modeling and Mapping of the Effective Earth Radius Factor for Microwave Link Design in South Africa

Seasonal Distribution Modeling and Mapping of the Effective Earth Radius Factor for Microwave Link Design in South Africa

General Formulas of Effective Earth Radius and Modified Refractive Index

Interpolation and mapping of the median k-factor for terrestrial link applications in South Africa

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