[PP2-2-6-1] Vertical roughness component (RMS height)
The standard deviation of the surface height variation (or RMS height), denoted by s (or hRMS), describes the statistical variation of a random surface with height z(x). In case of an azimuthally symmetrical surface, the single-scale RMS height of the one dimensional case for discrete profile values is given by (1), where N is the number of samples, and z ̅ the mean surface height (2). As roughness depends not only on the soil surface properties but also the wavelength λ of the electromagnetic signal, the roughness parameters are scaled by the wave number k. Hence, the electromagnetic roughness ks for surface roughness parameter s is (2π/λ)*s (3). In order to determine if a random surface may be considered as electromagnetically smooth, one common definition is given by the Rayleigh roughness criterion, where s < λ / 8*cosθ, or ks < 0.8, at incidence angle θ = 0. This criterion has been revised for the microwave region, where the wavelength is usually of the order of the RMS height, called the Fraunhofer roughness criterion, where s < λ / 36*cosθ, or ks < 0.2, at incidence angle θ = 0. Additionally, surfaces are considered as electromagnetically rough for 1 < ks < 3.
Explanation
The standard deviation of the surface height variation (or RMS height), denoted by 
(or 
), describes the statistical variation of a random surface with height 
. In case of an azimuthally symmetrical surface, the single-scale RMS height of the one dimensional case for discrete profile values 
is given by:
, (1)
where 
is the number of samples, and 
the mean surface height:
. (2)
As roughness depends not only on the soil surface properties but also the wavelength 
of the electromagnetic signal, the roughness parameters are scaled by the wave number 
. Hence, the electromagnetic roughness 
for surface roughness parameter is
. (3)
In order to determine if a random surface may be considered as electromagnetically smooth, one common definition is given by the Rayleigh roughness criterion, where 
or 
, at incidence angle 
= 0. This criterion has been revised for the microwave region, where the wavelength is usually of the order of the RMS height, called the Fraunhofer roughness criterion, where 
or 
, at incidence angle = 0. Additionally, surfaces are considered as electromagnetically rough for 
.
External resources
- Henderson, F. M. & Lewis, A. J. (ed.) (1998). Principles & Applications of Imaging RADAR. Manual of Remote Sensing. Third Edition, Volume 2. John Wiley & Sons, USA.
-
Jagdhuber, T. (2012). Soil Parameter Retrieval under Vegetation Cover Using SAR Polarimetry. Dissertation, Institutional Repository of the University of Potsdam.
Jagdhuber, T. (2012). Soil Parameter Retrieval under Vegetation Cover Using SAR Polarimetry. Dissertation, Institutional Repository of the University of Potsdam. -
Ulaby, F. T., Long, D.G., Blackwell, W., Elachi, Ch., Fung, A., Ruf, C., Sarabandi, K., Zebker, H. H. and van Zyl, J. J. (2014). Microwave radar and radiometric remote sensing. University of Michigan. Press Ann Arbor. ISBN: 978-0-472-11935-6
Ulaby, F. T., Long, D.G., Blackwell, W., Elachi, Ch., Fung, A., Ruf, C., Sarabandi, K., Zebker, H. H. and van Zyl, J. J. (2014). Microwave radar and radiometric remote sensing. University of Michigan. Press Ann Arbor. ISBN: 978-0-472-11935-6
Learning outcomes
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1584 - Discuss what surface height variation (or RMS height) is
Discuss what surface height variation (or RMS height) is
Self assessment
Completed
Outgoing relations
- [PP2-2-6-1] Vertical roughness component (RMS height) subclassof [PP2-2-6] Surface roughness
Contributors
-
Anke Fluhrer
https://www.researchgate.net/profile/Anke_Fluhrer