surfaceReflectivitySea

Normalized reflectivity of sea surface

Since R2022a

Description

Normalized reflectivity is the radar cross-section of a unit area of a sea surface. Multiplying by the total area of a surface or the illuminated area of a surface gives the total radar cross-section. Normalized reflectivity is also referred to as surface σ⁰ and is a function of frequency and grazing angle.

To compute the normalized reflectivity:

1. Create the surfaceReflectivitySea object and set its properties.

2. Call the object with arguments, as if it were a function.

To learn more about how System objects work, see What Are System Objects?

Creation

Syntax

refl = surfaceReflectivitySea

refl = surfaceReflectivitySea(Name=Value)

Description

refl = surfaceReflectivitySea creates a normalized reflectivity object, refl, for a sea surface. Use this object to generate a normalized radar cross section (NRCS). This syntax assumes a 'NRL' sea model with a sea state of zero.

refl = surfaceReflectivitySea(Name=Value) also creates a normalized reflectivity object for a sea surface with the specified property Name set to the specified Value. You can specify additional name-value pair arguments in any order as (Name1=Value1,...,NameN=ValueN).

Example: refl = surfaceReflectivitySea(Model="Hybrid",SeaState=2,Speckle="Rayleigh") creates a normalized reflectivity object for a sea surface using the Hybrid model with a SeaState of 2 and a Rayleigh Speckle type.

Properties

Unless otherwise indicated, properties are nontunable, which means you cannot change their values after calling the object. Objects lock when you call them, and the release function unlocks them.

If a property is tunable, you can change its value at any time.

For more information on changing property values, see System Design in MATLAB Using System Objects.

EnablePolarization — Enable polarization

false (default) | true

Enable polarization, specified as false or true.

• When true, the System object™ enables the specification of cross-polarization components to help form a complete polarimetric normalized radar cross-section (NRCS) reflectivity matrix σ⁰ of the form

  $${\sigma }^0=\left[\begin{array}{cc}{\sigma }_{HH}^0& {\sigma }_{HV}^0\\ {\sigma }_{VH}^0& {\sigma }_{VV}^0\end{array}\right]$$

  where σ⁰_HV and σ⁰_VH are the cross-polarization components specified by the ReflectivityHV and ReflectivityVH properties, respectively. The remaining components, σ⁰_HH and σ⁰_VV, are determined by the particular model set by the Model property.

• When false, the System object lets you specify the mean polarization using the Polarization property based on the selected Model.

CrossPolarization — Cross-polarization components

'Full' (default) | 'Symmetric'

Cross-polarization components, specified as 'Full' or 'Symmetric'.

When the CrossPolarization property is set to 'Full':

• If the Model property is not set to 'ConstantGamma', the ReflectivityHV and ReflectivityVH properties are applicable, and unique speckle values are generated for all reflectivity components (σ⁰_HH, σ⁰_HV, σ⁰_VH, and σ⁰_VV).

• If the Model property set to 'ConstantGamma', the CrossPolarization property only affects speckle generation.

When the CrossPolarization property is set to 'Symmetric' then reciprocity applies for monostatic geometry and the cross-polarization terms are equal, σ⁰_HV = σ⁰_VH.

• If the Model property is not 'ConstantGamma', only the ReflectivityHV property can be set. The ReflectivityVH property is assumed to be equal to the ReflectivityHV property. In addition, speckle values corresponding to the HV and VH components are equal.

• If the Model property is 'ConstantGamma', setting the CrossPolarization property to 'Symmetric' requires that the HV and VH components of the Gamma property are equal and the object returns equal HV and VH speckle values.

Dependencies

To enable this property, set the EnablePolarization property to true.

Data Types: char | string

Model — Sea reflectivity model

'NRL' (default) | 'APL' | 'GIT' | 'Hybrid' | 'Masuko' | 'Nathanson' | 'RRE' | 'Sittrop' | 'TSC' | 'ConstantGamma'

Sea reflectivity model, specified as 'NRL', 'APL', 'GIT', 'Hybrid', 'Masuko', 'Nathanson', 'RRE', 'Sittrop', 'TSC', or 'ConstantGamma'. The table.Sea Reflectivity Models summarize the sea surface models available in the radar simulation and their domain of application

SeaState — Sea state

1 (default) | nonnegative integer

Sea state, specified as a nonnegative integer from 0 – 8.

Data Types: double

Polarization — Polarization of reflectivity model

'H' (default) | 'V'

Polarization of reflectivity model, specified as 'H' for horizontal polarization or 'V' for vertical polarization.

Dependencies

To enable this property, set the EnablePolarization property to false and set the Model property to any value except 'ConstantGamma'.

Gamma — Sea gamma value

-40 (default) | real scalar

Gamma value used in the constant gamma clutter reflectivity model, specified as a scalar or 2-by-2 real-valued matrix. The gamma value depends on both sea state and operating frequency. Units are in dB.

• If EnablePolarization is false, specify Gamma as a scalar.

• If EnablePolarization is true, specify Gamma as a scalar or a 2-by-2 matrix, such that Gamma = [GammaHH GammaHV; GammaVH GammaVV]. When specified as a scalar, it is assumed that all polarimetric components are equal.

  To control the speckle values for the polarimetric Gamma case, set the CrossPolarization property to 'Full' for unique speckle values for all components or 'Symmetric' to set the speckle value for HV = VH.

Example: -25

Dependencies

To enable this property, set the Model property to ConstantGamma.

Data Types: double

ReflectivityHV — HV normalized radar cross section

zeros(91,2) (default) | Q-by-R real-valued matrix

Normalized radar cross section (NRCS), for the cross-polarized σ⁰_HV component, where HV represents horizontal transmission and vertical reception. Q corresponds to the number of angles in either the GrazingAngle or DepressionAngle property. R corresponds to the number of frequencies in the Frequency property. The σ⁰_HH and σ⁰_VV components are derived from the selected model designated by the Model property and associated properties. Units are m²/m².

Dependencies

To enable this property, set the EnablePolarization property to true and set the Model property is anything other than 'ConstantGamma'.

Data Types: double

ReflectivityVH — VH normalized radar cross section

zeros(91,2) (default) | Q-by-R real-valued matrix

Normalized radar cross section (NRCS), for the cross-polarized σ⁰_VH component, where VH represents horizontal transmission and vertical reception. Q corresponds to the number of angles in either the GrazingAngle or DepressionAngle property. R corresponds to the number of frequencies in the Frequency property. The σ⁰_HH and σ⁰_VV components are derived from the selected model designated by the Model property and associated properties. Units are m²/m².

Dependencies

To enable this property, set the CrossPolarization property to 'Full'.

Frequency — Radar frequency

[0 1e20] (default) | length-R row vector

Valid frequencies for the normalized reflectivity, specified as a length-R row vector. Frequency units are in Hz.

Example: [1e6,10e6]

Dependencies

To enable this property, set the EnablePolarization property to true and set the Model property to any value except 'Constant Gamma'.

Data Types: double

GrazingAngle — Grazing angles

[0:90] (default) | length-Q row vector

Grazing angles, as a length-Q row vector. Units are in degrees.

Example: [45:60]

Dependencies

To enable this property, set the EnablePolarization property to true and set the Model property any value except 'Constant Gamma'.

Data Types: double

Speckle — Speckle distribution type

'None' (default) | 'Lognormal' | 'Rayleigh' | 'Weibull'

Speckle distribution type, specified as 'None', 'Lognormal', 'Rayleigh', or 'Weibull'. Speckle is a multiplicative factor used to make clutter data appear noisier and is especially applicable to imaging applications.

Speckle is correlated with clutter RCS and is applied as I = σ*n, where σ represents the clutter RCS and n represents random numbers, which are often drawn from an independent identically-distributed unity mean noise statistical distribution.

• None – No speckle is applied.

• Lognormal – Speckle has a lognormal distribution. Define the distribution using the SpeckleMean and SpeckleStandardDeviation properties. Default values of these properties create speckle with a normalized mean lognormal distribution.

• Rayleigh – Speckle has a Rayleigh distribution. Define the distribution using the SpeckleScale property. The default value of this property creates speckle with a unit mean Rayleigh distribution.

• Weibull – Speckle has a Weibull distribution. Define the distribution using the SpeckleScale and SpeckleShape properties. The default values of these properties create speckle with a unit mean Rayleigh distribution.

Data Types: char | string

SpeckleMean — Mean of value of lognormal-distributed speckle

-0.5*log(2) (default) | scalar

Mean value of lognormal-distributed speckle, specified as a scalar.

Dependencies

To enable this property, set the Speckle property to 'Lognormal'.

Data Types: double

SpeckleStandardDeviation — Standard deviation of lognormal-distributed speckle

sqrt(log(2)) (default) | non-negative scalar

Standard deviation of lognormal-distributed speckle, specified as a non-negative scalar.

Dependencies

To enable this property, set the Speckle property to 'Lognormal'.

Data Types: double

SpeckleScale — Scale parameter for Weibull and Rayleigh speckle distribution

sqrt(4/π) (default) | non-negative scalar

Scale parameter for speckle for the Rayleigh and Weibull distributions, specified as a positive scalar.

Dependencies

To enable this property, set the Speckle property to 'Rayleigh' or 'Weibull'.

Data Types: double

SpeckleShape — Shape value for Weibull distribution

2 (default) | positive scalar

Shape value for the Weibull speckle distribution, specified as a positive scalar.

Dependencies

To enable this property, set the Speckle property to 'Weibull'.

Data Types: double

Usage

Syntax

nrcs = refl(graz,freq)

nrcs = refl(graz,freq,lookangle)

[nrcs,speck] = refl(___)

Description

nrcs = refl(graz,freq) returns the normalized radar cross section nrcs at grazing angle graz and frequency freq.

nrcs = refl(graz,freq,lookangle) also specifies the radar look angle lookangle with respect to the wind direction. To enable this syntax, set the Model property to 'APL', 'GIT', 'Hybrid', 'Masuko', 'Sittrop', or 'TSC'.

[nrcs,speck] = refl(___) also returns multiplicative speckle speck.

Input Arguments

graz — Grazing angle

nonnegative scalar | length-Q row vector of nonnegative values

Grazing angle of surface relative to radar, specified as a scalar or a length-Q row vector of nonnegative values. Grazing angles must lie between 0° and 90°. Units are in degrees.

freq — Transmitted frequencies

R-length vector of positive values

Transmitted frequencies, specified as a positive scalar or R-length vector of positive values. Units are in Hz.

Example: freq = 70e9

lookangle — Look angle with respect to wind direction

0 (default) | scalar

Look angle with respect to wind direction, specified as a scalar between 0° and 180°. The look angle is zero when looking upwind.

Dependencies

To enable this argument, set the Model property to 'APL', 'GIT', 'Hybrid', 'Masuko', 'Sittrop', or 'TSC'.

Data Types: double

Output Arguments

nrcs — Normalized surface reflectivity

real-valued Q-by-R matrix | real-valued 2-by-2-by-Q-by-R array

Normalized surface reflectivity , returned as a real-valued Q-by-R matrix or a real-valued 2-by-2-Q-by-R array. Q is the length of the grazing angle graz or, for land surfaces only, depression angle. R is the length of the frequency vector freq. nrcs is dimensionless but often expressed as m²/m². Normalized reflectivity is also called normalized radar cross section (NRCS).

• For the non-polarimetric reflectivity case, nrcs is returned as a real-valued Q-by-R matrix.

• For the polarimetric reflectivity case, nrcs is returned as a real-valued 2-b-2-byQ-by-R array. For each value of Q and R, NRCS forms a polarimetric normalized radar cross-section (NRCS) reflectivity matrix s of the form

  $${\sigma }^0=\left[\begin{array}{cc}{\sigma }_{HH}^0& {\sigma }_{HV}^0\\ {\sigma }_{VH}^0& {\sigma }_{VV}^0\end{array}\right]$$

  where S_HV and S_VH are the cross-polarization components specified by the ReflectivityHV and ReflectivityVH properties. The σ⁰_HH and σ⁰_VV components are derived from the specified model as set by the Model property

The returned normalized reflectivity for cross-polarization components σ⁰_HV and σ⁰_VH is calculated using nearest neighbor interpolation at a given grazing angle and frequency. To avoid interpolation errors, the normalized reflectivity values in the ReflectivityHV and ReflectivityVH properties should cover grazing angles from 0–90 degrees and all expected frequencies.

Dependencies

To enable the polarimetric reflectivity, set the EnablePolarization to true.

speck — Multiplicative speckle

Q-by-R matrix | 2-by-2-by-Q-by-R MATLAB^® array

Multiplicative speckle, returned as a Q-by-R matrix where Q is the length of the angles vector in graz and R is the length of the frequency vector in freq. For the polarimetric reflectivity case, speckle is returned as a 2-by-2-by-Q-by-R MATLAB array.

Data Types: double

Object Functions

To use an object function, specify the System object as the first input argument. For example, to release system resources of a System object named obj, use this syntax:

release(obj)

Common to All System Objects

step	Run System object algorithm
release	Release resources and allow changes to System object property values and input characteristics
reset	Reset internal states of System object

Examples

Create Sea Surface Reflectivity Model

Create a sea surface normalized reflectivity object using the default NRL model and a sea state of 6. Obtain the normalized reflectivity at a frequency of 1 GHz over grazing angles from 0.1 to 10 degrees and assume vertical polarization. Plot the normalize reflectivity as a function of grazing angle.

grazAng = 0.1:0.1:10;
freq = 1e9;
seastate = 6;
pol = 'V';
refl = surfaceReflectivitySea(SeaState = seastate,Polarization = pol);
nrcs = refl(grazAng,freq);
plot(grazAng,pow2db(nrcs))
grid on
xlabel('Grazing Angle (deg)')
ylabel('NRCS (dB m^2/m^2)')
title('NRL Model, Vertical Polarization')

Create Sea Surface Reflectivity Model with Default Values

Create a sea surface normalized reflectivity object using the default model parameters. Obtain the normalized reflectivity at a frequency of 1 GHz over grazing angles from 0.1 to 10 degrees and assume vertical polarization. Plot the normalize reflectivity as a function of grazing angle.

grazAng = 0.1:0.1:10;
freq = 1e9;
refl = surfaceReflectivitySea

refl = 
  surfaceReflectivitySea with properties:

    EnablePolarization: 0
                 Model: 'NRL'
              SeaState: 1
          Polarization: 'H'
               Speckle: 'None'

nrcs = refl(grazAng,freq);
plot(grazAng,pow2db(nrcs))
grid on
xlabel('Grazing Angle (deg)')
ylabel('NRCS (dB m^2/m^2)')
title('NRL Model, Vertical Polarization')

Create Reflective Sea Surface in Radar Scenario

Configure a radarscenario to simulate a reflective sea surface. Add a sea surface object to define the physical properties of the scenario surface. The surface is a simple 400-by-400 meter rectangle. Use the surfaceReflectivitySea function to create a GIT model with a sea state 3. Then, use the scenario seaSurface method to add the rectangular sea region and the radar reflectivity model to the scenario. Use a surface reference height of 16 meters.

scene = radarScenario(UpdateRate = 0, IsEarthCentered = false);
refl = surfaceReflectivitySea(Model = "GIT", SeaState = 3, Polarization = "V");
srf = seaSurface(scene,RadarReflectivity = refl, ...
    Boundary=[-200 200; -200 200],ReferenceHeight = 16)

srf = 
  SeaSurface with properties:

                WindSpeed: 10
            WindDirection: 0
                    Fetch: Inf
            SpectralModel: []
        RadarReflectivity: [1x1 surfaceReflectivitySea]
    ReflectionCoefficient: [1x1 radar.scenario.SurfaceReflectionCoefficient]
          ReflectivityMap: 1
          ReferenceHeight: 16
                 Boundary: [2x2 double]

Display Reflectivity Matrix for Sea Surface

Create a sea surface normalized reflectivity object using the NRL model and a sea state of 6. Specify the cross-polarization reflectivity. Obtain the NRCS at a frequency of 10 GHz over grazing angles from 1 to 10 degrees. Plot the reflectivities.

refl = surfaceReflectivitySea(Model='NRL',SeaState=6, ...
   EnablePolarization=true,CrossPolarization='full', ...
   GrazingAngle = 0:.1:90,Frequency = [100,1e6,11e6], ...
   ReflectivityHV=0.002*sind(0:.1:90)'*[1 1 1], ...
   ReflectivityVH=0.001*sind(0:.1:90)'*[1 1 1]);

Set the grazing angles and frequencies. Plot the reflectivities.

grazAng = 0.1:0.1:10;
freq = 10e9;
nrcs = refl(grazAng,freq);
plot(grazAng,pow2db(squeeze(nrcs(1,1,:))), ...
    grazAng,pow2db(squeeze(nrcs(2,2,:))), ...
    grazAng,pow2db(squeeze(nrcs(1,2,:))), ...
    grazAng,pow2db(squeeze(nrcs(2,1,:))))
legend('HH','VV','HV','VH');
grid on
xlabel('Grazing Angle (deg)')
ylabel('NRCS (dB m^2/m^2)')
title('NRL Model: Sea State 6')

More About

Sea Reflectivity Models

Model	Type	Grazing Angles	Frequency Range	Sea State	Settable Properties
'NRL' – Sea Clutter Model due to Gregers-Hansen and Mittal. (Default model) Naval Research Laboratory empirical model for sea reflectivity. The model does not include variation with azimuth or wind direction. The model matches experimental results with an absolute deviation of about 2.2 to 2.3 dB for grazing angles from 0.1° to 10°. A deviation of 2.6 dB can be seen for grazing angles above 10° and below 60°. See [1] and [2].	Empirical	0.1 – 60	0.5 – 35	0 – 6	SeaState Polarization Gamma Speckle SpeckleMean SpeckleStandardDeviation SpeckleScale SpeckleShape
'APL' – John Hopkins Applied Physics Laboratory ADSAM model. Derived wind velocity from sea state produces less conservative reflectivity values than GIT model at lower sea states. Takes into account wave height and wave speed. Differs from the GIT model by deriving wind velocity from sea state. See [3].	Semi-empirical	0.1 – 10	1 – 100	1 – 6	SeaState Polarization Gamma Speckle SpeckleMean SpeckleStandardDeviation SpeckleScale SpeckleShape
'GIT' – Georgia Institute of Technology Semi-empirical model based on multipath, wind speed, and wind direction factor. Takes into account wave height and wave speed. Derived wind velocity from sea state produces less conservative reflectivity values than GIT at lower sea states. See [4], [5], and [1].	Semi-empirical	0.1 – 10	1 – 100	1 – 6	SeaState Polarization Gamma Speckle SpeckleMean SpeckleStandardDeviation SpeckleScale SpeckleShape
'Hybrid' – Hybrid model that mixes work by Barton, Nathanson's tables, and GIT semi-empirical models. May be biased high in the low grazing angle regime. See [5].	Semi-empirical	0.1 – 30	0.5 – 35	0 – 5	SeaState Polarization Gamma Speckle SpeckleMean SpeckleStandardDeviation SpeckleScale SpeckleShape
'Masuko' – Empirical model applicable for medium grazing angles for X and Ka bands. See [6] and [4].	Empirical	30 – 60	X (8 – 12) Ka (26.5 – 40)	1 – 6	SeaState Polarization Gamma Speckle SpeckleMean SpeckleStandardDeviation SpeckleScale SpeckleShape
'Nathanson' – Empirical tables compiled from experimental data that are averages of all wind directions covering UHF to Ka. See [7].	Empirical	0.1 – 60	UHF (0.3 – 1), L (1 – 2), S(2 – 4), C(4 – 8), X(8 – 12), Ku(12 – 18), Ka(32 – 36)	0 – 6	SeaState Polarization Gamma Speckle SpeckleMean SpeckleStandardDeviation SpeckleScale SpeckleShape
'RRE' – Royal Radar Establishment model Averages over all wind directions. Used extensively in the UK for airborne radar performance assessment. See [4].	Mathematical	< 10	9 – 10	0 – 6	SeaState Polarization Gamma Speckle SpeckleMean SpeckleStandardDeviation SpeckleScale SpeckleShape
'Sittrop' – Empirical model for lower grazing angles and higher sea states for X-band. See [4].	Empirical	0.2 – 10	X (8 – 12)	0 – 7	SeaState Polarization Gamma Speckle SpeckleMean SpeckleStandardDeviation SpeckleScale SpeckleShape
'TSC' – Technology Service Corporation Empirical model. Based on fit to Nathanson tables. Similar to the GIT model but with values not falling off as rapidly in range Recommended for conservative performance prediction or when conditions are unknown. See [5].	Empirical	0.1 – 90	0.5 – 35	0 – 5	SeaState Polarization Gamma Speckle SpeckleMean SpeckleStandardDeviation SpeckleScale SpeckleShape
'ConstantGamma' – See the Constant Gamma Model for a description.	Mathematical				SeaState Gamma Speckle SpeckleMean SpeckleStandardDeviation SpeckleScale SpeckleShape

Constant Gamma Model

The constant-gamma model expresses a simple analytic relationship between the normalized radar cross-section and grazing angle.

σ = 10^(γ/10)sin(θ)

γ is defined by the Gamma property and θ is the grazing angle input argument graz given in degrees. The default value of Gamma is –40, which is representative of sea state 3.

Speckle Model

Speckle is modeled as an uncorrelated, multiplicative factor I = σ∙n, where σ represents the clutter RCS and n are independent identically distributed (IDD) mean noise samples with unity mean. Because speckle is correlated with underlying terrain RCS, it is usually applied to radar intensity. The speckle noise models include Weibull, Rayleigh, and lognormal.

References

[1] Gregers-Hansen, V. and Mittal, R. "An Improved Empirical Model for Radar Sea Clutter Reflectivity." NRL/MR/5310-12-9346, Apr. 27, 2012.

[2] Barton, David Knox. Radar Equations for Modern Radar. Artech House, 2013.

[3] Reilly, J. P., R. L. McDonald, and G. D. Dockery. "RF-Environment Models for the ADSAM Program." Report No. A1A97U-070, Laurel, MD: Johns Hopkins University Applied Physics Laboratory, August 22, 1997.

[4] Ward, Keith D., Simon Watts, and Robert J. A. Tough. Sea Clutter: Scattering, the K-Distribution and Radar Performance. IET Radar, Sonar, Navigation and Avionics Series 20. London: Institution of Engineering and Technology, 2006.

[5] Antipov, Irina. "Simulation of Sea Clutter Returns." Department of Defence, June 1998.

[6] Masuko, Harunobu, Ken'ichi Okamoto, Masanobu Shimada, and Shuntaro Niwa. "Measurement of Microwave Backscattering Signatures of the Ocean Surface Using X Band and K a Band Airborne Scatterometers." Journal of Geophysical Research 91, no. C11 (1986): 13065. https://doi.org/10.1029/JC091iC11p13065.

[7] Nathanson, Fred E., et al. Radar Design Principles: Signal Processing and the Environment. 2. ed., Repr, Scitech Publ, 2004.

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Version History

Introduced in R2022a