Scenario components

Surface component

Lambertian Surfaces (HOM00_LAM, HOM00_BLA, HOM00_WHI)

Lambertian surfaces are defined by one parameter, which is the magnitude of surface reflectance or BRF (unitless).

The spectral reflectance values for the lambertian model (LAM) has been obtained by applying a spectral convolution of the MSI spectral responses, the extraterrestrial solar spectrum and an isotropic reflectance spectrum of understorey vegetation.

This parameter depends on the spectral band used for the measurement. In addition to LAM values, black (BLA) and white (WHI) surface scenarios have been defined. These later ones are simulated using a Lambertian surface with a reflectance of 0 and 1 respectively.

Band	$\lambda_c$[$\Delta\lambda$]	WHI	BLA	LAM
M02	490 [65]	1.0	0.0	0.02173
M03	560 [35]	1.0	0.0	0.04439
M04	665 [30]	1.0	0.0	0.02806
M8A	865 [20]	1.0	0.0	0.21639
M11	1610[90]	1.0	0.0	0.09820
M12	2190[180]	1.0	0.0	0.04797

The corresponding JSON dotted notations is:

scenario.observations.surface.surface_parameters.reflectance

Anisotropic Surfaces (HOM00_RPV, HOM00_RLI)

RPV surface

The RPV surface is defined using its 3 parameters $\rho_0$, $k$ and $\Theta$.

These values describe the anisotropy reflectance of understorey vegetation similar to that used in HOM25 of RAMI-V phase and recalculated for MSI bands.

To define RPV parameters in MSI bands, an approach similar to that used in RAMI-V for HOM25 scene has been adopted. While $k$ and $\Theta$ have been defined a-priori, the $\rho_0$ parameter was varied to obtain, by bi-hemispherical integration of the RPV function, the same values of the LAM model, with a uncertainty of less than 1E-4 (bisection method was used to identify $\rho_0$).

Table 2 lists the spectral parametrs for the RPV model.

Band	$\rho_0$	$k$	$\Theta$
M02	0.013206	0.95	-0.10
M03	0.027059	0.95	-0.10
M04	0.017051	0.95	-0.10
M8A	0.129771	0.80	-0.05
M11	0.057726	0.80	-0.05
M12	0.027975	0.80	-0.05

The corresponding JSON dotted notations is:

scenario.observations.surface.surface_parameters.k
scenario.observations.surface.surface_parameters.theta
scenario.observations.surface.surface_parameters.rho_0

Ross-Li surface

The Ross-Thick Li-Sparse Reciprocal model is used to define a second anysotropical surface in RAMI4ATM using the associated $f_{iso}$, $f_{vol}$ and $f_{geo}$ parameters.

The RLI parameters presented in Table 2 were obtained by fitting the Ross-Li function over an array of BRF calculated by using the RPV model defined in [Table 2].

Band	$f_{iso}$	$f_{vol}$	$f_{geo}$
M02	0.024950	-0.002250	0.001513
M03	0.050877	-0.004504	0.003073
M04	0.032171	-0.002886	0.001949
M8A	0.209741	0.081384	0.004140
M11	0.095761	0.035598	0.002086
M12	0.046899	0.017130	0.001060

The corresponding JSON dotted notations is:

scenario.observations.surface.surface_parameters.f_iso
scenario.observations.surface.surface_parameters.f_vol
scenario.observations.surface.surface_parameters.f_geo

Homogeneous discrete canopies with isotropic background (HOM25_LAM, HOM35_LAM, HOM45_LAM)

All scenes share the same structural parameters in terms of extension (height and width), lead shape and dimension, leaf area index (LAI), leaf optical properties (R, T), except the LAD which is assumed to be Planophile (HOM25_LAM), erectophile (HOM35_LAM) and uniform (HOM45_LAM).

The background surface to be used under the vegetation component is lambertian and have the same optical characteristics of the HOM00_LAM model described above.

The structural properties of the scenes are summarized in [Table 4]. The LAD can be defined using Bunnik (1978) or Goel and Strebel (1984) distribution functions as defined here. The correlation between the distribution functions defined by Bunnik and those of Goel and Strebel parameterized with the $\mu$ and $\nu$ as given in the table, are of the order of 0.9989 for both the planophile and erectophile cases.

Three files are also given providing a deterministic way to define the canopies. Their columns contain the following informations for each leaf of the canopy: 1) the leaf radius (fixed to 0.05m), three columns with XYZ positions of the leaf centers in the scene (given in meters), and the direction cosines ($D_x$,$D_y$,$D_z$) of the angles formed by the leaf normal and the XYZ axes. The distributions of $\theta_Z$ characterizes the three canopies with different LAD as already discussed.

Properties	Planophile
Scene dimension	25 x 25 x 2.1 m
Leaf center (Xmin, Ymin, Zmin)	-12.500, -12.500, 0.100 m
Leaf center (Xmax, Ymax, Zmax)	-12.500, -12.500, 2.100 m
Scatterer Radius	0.05 m
Leaf area index	3 m2/m2
Height of canopy	2 m
Number of leaves	238732
Planophile LAD (HOM25_LAM)	$\mu$=2.531 $\nu$=1.096
Erectophile LAD (HOM35_LAM)	$\mu$=1.096 $\nu$=2.531
Uniform LAD ( HOM45_LAM)	$\mu$=1.0 $\nu$=1.0

The corresponding JSON dotted notations is:

scenario.observations.canopy.leaf_radius
scenario.observations.canopy.leaf_area_index
scenario.observations.canopy.height
scenario.observations.canopy.distribution_type
scenario.observations.canopy.distribution_mu
scenario.observations.canopy.distribution_nu

Leaf optical properties

Table 5 lists the reflectance and transmittance of the leaves for the six MSI spectral bands. They were calculated using [Equation 1]. The leaves are assumed to be flat object which bi-lambertian scattering properties.

Band	$\lambda_c$ [$\Delta\lambda$]	R	T
M02	490 [65]	0.06694	0.01950
M03	560 [35]	0.13230	0.08408
M04	665 [30]	0.05653	0.01692
M8A	865 [20]	0.49626	0.44153
M11	1610 [90]	0.33281	0.34079
M12	2202 [180]	0.18161	0.22086

The corresponding JSON dotted notations is:

scenario.observations.canopy.canopy_parameters.reflectance
scenario.observations.canopy.canopy_parameters.transmittance

Atmospheric components

Three main elements are combined to create complex atmospheres in RAMI4ATM. These are molecular scattering, molecular absorption, and aerosols.

An atmosphere type is therefore associated with each of the 7 possible combinations as shown in Figure 6:

Each atmosphere component has its own set of parameters with some variations. This means that there are multiple scenarios per atmosphere type.

The atmosphere is assumed plane-parallel.

An atmosphere type is therefore associated with each of the 7 possible combinations:

Description	Scenario JSON value	Priority
Rayleigh (molecular scattering only)	AtmosphereType.RAYLEIGH	1
Absorption	AtmosphereType.ABSORBING	1
Scattering and Absorption	AtmosphereType.SCATTERING_ABSORBING	1
Aerosols	AtmosphereType.AEROSOLS	2
Aerosols and Scattering	AtmosphereType.SCATTERING_AEROSOLS	2
Aerosols and Absorption	AtmosphereType.ABSORBING_AEROSOLS	2
Complete (Scattering, Absorption, and Aerosols)	AtmosphereType.COMPLETE	3

The corresponding JSON dotted notation is

scenario.observations.atmosphere.atmosphere_type

Molecular Scattering

Molecular Absorption

Model and Expert users may use the AFGL US-standard atmospheric profile option in their code with the possibility to rescale water vapour and ozone.

Only the "US standard" profile described in AFGL US-standard atmospheric profile is used in RAMI4ATM.
This atmospheric profile details the molecular concentration of 28 species at different altitudes.
For RAMI4ATM only the following 7 principal species are considered: H₂O, CO₂, O₃, N₂O, CO, CH₄, O₂.

This profile is available in most atmospheric models and is considered a standard in the field. It is recommended to use the provided atmospheric profile dataset. However, participants who already have their own definition of this profile in their model can use their own.

Various implementations of the AFGL US-standard atmospheric profile profile exist in radiative transfer models, accounting for the absorption of different molelcules.

Model users are encouraged to use the implementation shipped with their radiative transfer model.
Expert users can explicitely define the AFGL US-standard atmospheric profile.

The atmospheric profile data file includes 11 columns separated by whitespace. This data file provide the values of different atmospheric variables as a function of altitude. From left to right, these columns are:

• altitude in kilometers (km)
• air pressure in millibar (mb)
• air temperature in degrees Kelvin (K)
• air number density in inverse cubic centimeters (cm^-3)
• H₂O volume mixing ratio in parts per million per volume (ppmv)
• CO₂ volume mixing ratio in ppmv
• O₃ volume mixing ratio in ppmv
• N₂O volume mixing ratio in ppmv
• CO volume mixing ratio in ppmv
• CH₄ volume mixing ratio in ppmv
• O₂ volume mixing ratio in ppmv

In addition to the standard profile, atmospheric profiles with higher and lower concentrations of either water vapour and/or ozone are considered, to create the six variants of the molecular absorption block as described in [Table 7]. While the experiments for the standard values of $H_2O$ and $O_3$ should be performed in all the six S2-MSI spectral bands, those relevant to rescaled water vapour should be performed only in band M12, and those relevant to rescaled values of ozone only in M03, as indicated in [Table 7].

Description	H2O Scenario	O3 Scenario	Sentinel 2A bands
Standard value, no rescaling	14.274 kg/m2	0.746 10-2 kg/m2	M02, M03, M04, M8A, M11, M12
Dry atmosphere	4.208 kg/m2	0.746 10-2 kg/m2	M12
Wet atmosphere	41.591 kg/m2	0.746 10-2 kg/m2	M12
High Ozone concentration	14.274 kg/m2	0.895 10-2 kg/m2	M03
Low Ozone concentration	14.274 kg/m2	0.597 10-2 kg/m2	M03
Wet atmosphere, high Ozone	41.591 kg/m2	0.895 10-2 kg/m2	M03,M12

The corresponding JSON dotted notation for H₂O and O₃ rescaling is

scenario.observations.atmosphere.concentrations.H2O
scenario.observations.atmosphere.concentrations.O3

Aerosol

Desert dust particles are larger than the continental ones.

Each dataset may be used with a set of two different values for the optical thickness specified at 550nm.

There is only one possible vertical distribution for the aerosols: a single uniform layer of 2km high starting from the earth's surface.

The table shows the list of aerosol optical thickness values.

Description	AOD value ($\tau_{550}$)
Low AOD550	0.2
High AOD550	0.6

The corresponding JSON dotted notations are:

scenario.observations.atmosphere.aerosols.tau_550

Model users may use the Continental aerosol radiative properties and Desert aerosol radiative properties types shipped with their radiative transfer model.
Expert users are provided with two options:

• start from the particle microphysical properties, i.e. refractive properties data and particle radius distribution, compute the corresponding particle radiative properties and run their radiative transfer model with that input.
• directly use the particle radiative properties derived from the above-mentioned particle microphysical properties.

Particle microphysical properties

The microphysical properties of the aerosol particles are described by a refractive index data file and a particle radius distribution assuming spherical particles.

The refractive index data for the continental and desert particles are provided by the Continental aerosol refractive properties and Desert aerosol refractive properties data files, respectively.

The format of the refractive index data files is the following:

• the first column provides the wavelength in nanometers
• the second column provides the real part of the complex refractive index
• the third column provides the imaginary part of the complex refractive index

where $i$ is the imaginary number.

For each aerosol type, i.e. desert and continental, the aerosol particles population is divided into two groups: fine and coarse particles. For each group, the particle radius follows a lognormal particle radius distribution. The probability density function for the lognormal particle radius distribution is given by the following equation:

$$ n(r)= \frac {1} {r\sqrt{2\pi}\ln\sigma}exp{\left[-\frac{1}{2}\left(\frac{\ln(r/r_m)}{\ln\sigma}\right)^2\right]} $$

where $r_m$ and $\sigma$ are two parameters.
$r_m$ defines the median radius of the radius distribution.
The natural logarithm of $\sigma$ represents the standard deviation of the natural logarithm of the radius r.
The particle radius distribution of the entire particles population is specified as the linear combination of the two individual particle radius distributions:

$$ n(r)= w_{fine}n_{fine}(r)+w_{coarse}n_{coarse}(r) $$

The $r_m$ and $\sigma$ parameters, as well as the linear combination weights, are specificed for each aerosol type, i.e. desert and continental, in the table below:

Aerosol	mode	$w$ [dimensionless]	$r_m$ [microns]	$\sigma$ [dimensionless]
Desert	fine	0.99665597	0.0478666	1.87411
Desert	coarse	0.00332189	0.604127	1.75172
Continental	fine	0.99951414	0.0807989	1.50180
Continental	coarse	0.00046373	0.682651	2.10400

The corresponding JSON dotted notations are:

scenario.observations.atmosphere.aerosols.type.radiative_properties_dataset_name

Particle radiative properties

The Mie theory has been used to calculate aerosol particles radiative properties. The microphysical properties of the aerosol particles are described by a refractive index data file and a particle radius distribution.

The radiative properties of the desert and continental particles are provided by the Desert aerosol radiative properties and Continental aerosol radiative properties data files, respectively.

The format of these data files is the following:

• the first line lists the scattering angle cosine values
• the following lines are organised into groups of 4 lines where:
  • the first line provides the value of the wavelength in nanometers
  • the second line provides the value of the volume extinction coefficient in inverse kilometer, at the current wavelength
  • the third line provides the value of the single scattering albedo (dimensionless), at the current wavelength
  • the fourth line provides the values of the scattering phase function in inverse steradian, for all scattering angle cosine previsouly listed, at the current wavelength

The spectral variability of the aerosol single scattering properties should be estimated at any wavelength at which the radiative transfer equation is solved assuming a linear interpolation from wavelengths at wich the values of the refractive indices are provided.

Both fine and coarse particles are associated to the same refractive index data. Mie calculations are performed using 1000 particle radius values geometrically spaced between 0.001 and 100.0 micrometers.