4c. Input to mcarats executable (c): Namelist mcarWld_nml_job...

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Namelist mcarWld_nml_job

Wld_nplcf -technical parameter-

integer, save :: Wld_nplcf = 0

Power exponent for local collision forcing (LCF), which forces collisions near the radiance detectors, by increasing extinction coefficients near the radiance detectors. The LCF is automatically deactivated if radiances are not target.

The LCF is effective when the 1st kind of radiances (Rad_mrkind = 1) are calculated. The formula of the 1st kind of radiance contribution has a term proportional to 1/r^2, where r is a distance between the collision point and radiance detector point. This type of local estimate has in general infinite variance. To reduce variance, LCF is useful. The power exponent should be 1 or 2 usually.

Scaled extinction coefficients (B_ext1) will be

B_ext1 = max(B_min, B_ext)

for original extinction coefficient B_ext, and the min extinction coefficient is

B_min = Wld_dtaumin / dz_lay * (zdif / Wld_rmlcf)**Wld_nplcf

where dz_lay is a layer geometrical thickness and zdif is height (z-coordinate) difference from the camera location. See also Wld_rmlcf and Wld_dtaumin.

Wld_rmlcf -technical parameter-

real(R_), save :: Wld_rmlcf = 100.0_R_

Scale length (m) for Local Collision-Forcing (LCF), which forces artificial collisions at locations near the radiance detectors. See also Wld_nplcf.

Wld_dtaumin -technical parameter-

real(R_), save :: Wld_dtaumin = 0.0_R_

This has different effects on extinction coefficient scaling, depending on target radiative quantities.

When fluxes and heating rates are target or the local collision forcing (LCF) is not used (Wld_nplcf = 0), Wld_dtaumin is a minimum layer optical thickness for collision forcing. If optical thickness of one layer is less than this threshold, then the collision-forcing method is used in that layer, and the scaled value of the optical thickness is set to Wld_dtaumin. Thus collision events are forced to occur with prescribed probability even in very optically thin layer.

When radiances are target and the LCF is used, then Wld_dtaumin is used for the LCF. See the description of Wld_nplcf for how each parameter is used in the code.

Namelist mcarAtm_nml_job

Several 1-D vertical profiles of some variables can be specified in this namelist. Data for 3-D distribution of properties for horizontally-inhomogneous layers are usually very large. Therefore, they should be read in from the external data file. The 1-D and 3-D profile data are mixed and used in the code. Please work with care for how they are mixed, which could be different by variable.

See here (in Chapter 3) for how homogeneous and inhomogeneous layers are defined.

Atm_idread

integer, save :: Atm_idread = 1

This controls how to import atmospheric dataset for the current job. Definition depends on the file format: binary or text. In both cases, if Atm_idread = 0, then namelist input for Atm_ext1d, Atm_omg1d, Atm_apf1d, and Atm_abs1d are all neglected. For the first job, Atm_idread should be > 0.

This variable also controls what dataset is read in from the external data file, Atm_inpfile, for the current job. Note that it is assumed that multiple datasets are possibly stored in the file as in the figure below.

Binary format : Atm_mfmt = 1

Variable Atm_idread is location index of data set to be read, in the 3-D atmospheric data file. One of data sets in the file can be chosen for each simulation job. The user can specify explicitly the data set index by this parameter or leave it as default value, which is 1 for the first job, and 0 for the subsequent jobs.

If Atm_idread = 0, then no new data set is read in for the current job, and atmospheric properties are the same as previous job. This is possible for second or subsequent job.

As described here, there are many ways to specify explicitly or implicitly the data set index for a job. For example,

• As default for all jobs

• Common single data set for all jobs

• To give explicitly all the indexes

• A combined aproach

where "-" denotes that no valye for Atm_idread is given in the namelist.

Text format: Atm_mfmt = 0

Variable Atm_idread is on/off flag for data import. If 0, no data is read in for the current job, and previously imported data are used again. If 1, then a new data set is read in from the file. For text format file, there is no possibility of random access as in binary format. Thus data sets are read in sequentially for each job.

Atm_dx, Atm_dy

real(R_), save :: Atm_dx = 1.0e+4_R_ ! X size of cell

real(R_), save :: Atm_dy = 1.0e+4_R_ ! Y size of cell

Cell sizes (m) along x and y-axes, respectively.

Atm_zgrd0

real(R_), save :: Atm_zgrd0(1:KNZ+1) = (/(10.0_R_*i, i = 1, KNZ+1)/)

Z-coordinate values (m) of layer boundaries. The bottom and top of a layer with index iz correspond to z=Atm_zgrd0(iz) and Atm_zgrd0(iz+1), respectively. The BOA (surface) corresponds to Atm_zgrd0(1), and TOA Atm_zgrd0(Atm_nz+1).

The following illustration shows the definitions of several geometrical parameters.

Atm_wkd0

real(R_), save :: Atm_wkd0(KNKD) = (/1.0_R_, (0.0_R_, i = 1, KNKD - 1)/) ! k-distribution weights

Weight coefficients of the correlated k-distribution. Give Atm_wkd0(1)=1 for monochromatic computation.

Atm_tmp1d

real(R_), save :: Atm_tmp1d(1:KNZ+1) = (/(300.0_R_, i = 1, KNZ+1)/)

Horizontally-averaged atmospheric temperatures (K) defined

• at layers [1:Atm_nz] if Atm_mtprof=0, or

• at layer interfaces [1:Atm_nz+1] if Atm_mtprof=1.

Used for thermal emission when Src_mtype = 2 or 3.

When Atm_mtprof=1, an interface of iz=1 corresponds to BOA, and that of iz=Atm_nz+1 corresponds to TOA. Note that Atm_tmp1d is atmospheric temperature even when iz=0 (BOA). The surface temperature should be given by different variables. For horizontally inhomogeneous layer, data of perturbation in temperature could be specified in external data file.

Atm_ext1d

real(R_), save :: Atm_ext1d(KNZ, KNP1D)

Extinction coefficients (/m) for each layer and each scattering component, one of which can be gas, aerosol, hydrometeor, or their mixture. Extinction coefficient Atm_ext1d(iz, ip1d) corresponds to a layer iz and a component ip1d. Note that optical properties specified by Atm_*1d variables are assumed be horizontally homogeneous in every atmospheric layers.

Atm_omg1d

real(R_), save :: Atm_omg1d(KNZ, KNP1D)

As Atm_ext1d, but for single scattering albedo.

Atm_apf1d

real(R_), save :: Atm_apf1d(KNZ, KNP1D)

As Atm_ext1d, but for phase function specification parameters. Phase functions are specified in the following way:

Atm_apf1d <= -2 : isotropic scattering phase function

-2 < Atm_apf1d <= -1 : Rayleigh scattering phase function

-1 < Atm_apf1d < 1 : Henyey-Greenstein phase function with asymmetry parameter of Atm_apf1d

1 <= Atm_apf1d : a tabulated phase function (given by the database file, see the namelist mcaSca_nml_init)

Note Atm_apf1d should be <= Sca_npf (# of phase functions read in from the file). Even when Atm_apf1d >= 1, this variable does not need to be integer. The phase function is assumed to follow an equation:

P = (1 - a) * P_tab(i) + a * P_tab(i+1)

where

i = int(Atm_apf1d)

a = Atm_apf1d - i

That is, the phase function is linearly interpolated between P_tab(i) and P_tab(i+1). Thus, for better accuracy, the parameter Atm_apf1d should be given, taking into account a relationship between the phase function and a physical property of particles. For example, note that the phase function is linear to the inverse of the effective radius (Re), as a first order approximation:

P ~ c + d / Re

Atm_abs1d

real(R_), save :: Atm_abs1d(KNZ, KNKD)

Horizontally-averaged absorption coefficients (/m) of purely-absorbing component, which can be gaseous mixture for instance. The correlated k-distribution is assumed. An element Atm_abs1d(iz, ikd) corresponds to a layer iz and a k-distribution index ikd. Note perturbations of the absorption coefficients in the horizontally inhomogeneous layers can be given by the data file (Atm_inpfile).

Scaling optical properties

Input extinction and absorption coefficients can be easily scaled by user-specified factors, as described below. The scaling is performed immediately after reading in the data (from the namelist file or from 3-D atmospheric data file). Variables, Atm_fext1d, Atm_fext3d, Atm_fabs1d, Atm_fabs3d, have been introduced in the namelist. These are useful for simple adjustments of input data. For example, someone could try two simulations easily: one for cloudy sky with 3-D cloud extinction, the other without the cloud (e.g., by setting Atm_fext3d = 0 for cloud).

Note that these parameters are effective only when Atm_idread >= 1. When Atm_idread = 0, no new dataset is read in, and no data scaling is applied.

Atm_fext1d

real(R_), save :: Atm_fext1d(KNP1D) = (/(1.0_R_, i = 1, KNP1D)/)

Scaling factor for Atm_ext1d(ip1d), where ip1d is component index. This is neglected when Atm_idread = 0: a new data set is not read in for the current job.

This provide a simple way to modify the original extinction coefficients given by Atm_ext1d. The data are modified just after reading in the namselist data, in the following way:

B_ext(iz, ip1d) = Atm_ext1d(iz, ip1d) * Atm_fext1d(ip1d)

for all iz = [1, Atm_nz].

Note the values of Atm_ext1d are untouched by this scaling and modified data are saved in a different variable array. Therefore, values of Atm_ext1d will be saved in the subsequent jobs.

Atm_fext3d

real(R_), save :: Atm_fext3d(KNP3D) = (/(1.0_R_, i = 1, KNP3D)/)

As Atm_fext1d, but for modifying Atm_ext3d, 3-D spatial distribution of extinction coefficients. This is neglected when Atm_idread = 0: a new data set is not read in for the current job.

The 3-D data are read in from the external data file (Atm_inpfile). The data are modified just after reading in the 3-D data, in the following way:

Atm_ext3d(ix, iy, iz3, ip3d) = Atm_ext3d(ix, iy, iz3, ip3d) * Atm_fext3d(ip3d)

for all iz3 = [1, Atm_nz3].

Note that a new data set is not always read in for each job and that the modification by Atm_fext3d is applied only when a new data set is read in. See also Atm_idread for when a new data set is read in for a job.

Atm_fabs1d

real(R_), save :: Atm_fabs1d = 1.0_R_

Scaling factor for Atm_abs1d. This is neglected when Atm_idread = 0: a new data set is not read in for the current job.

This provide a simple way to modify the original absorption coefficients given by Atm_abs1d. The data are modified just after reading in the namselist data, in the following way:

B_abs(iz, ikd) = Atm_abs1d(iz, ikd) * Atm_fabs1d

for all iz = [1, Atm_nz] and all ikd = [1, Atm_nkd].

Note the values of Atm_abs1d are untouched by this scaling and modified data are saved in a different variable array. Therefore, values of Atm_abs1d will be saved in the subsequent jobs.

Atm_fabs3d

real(R_), save :: Atm_fabs3d = 1.0_R_

As Atm_fabs1d, but for modifying Atm_abs3d, 3-D spatial distribution of absorption coefficients. This is neglected when Atm_idread = 0: a new data set is not read in for the current job.

The 3-D data are read in from the external data file (Atm_inpfile). The data are modified just after reading in the 3-D data, in the following way:

Atm_abs3d(ix, iy, iz3, ikd) = Atm_abs3d(ix, iy, iz3, ikd) * Atm_fabs3d

for all iz3 = [1, Atm_nz3] and all ikd = [1, Atm_nkd].

Note that a new data set is not always read in for each job and that the modification by Atm_fabs3d is applied only when a new data set is read in. See also Atm_idread for when a new data set is read in for a job.

Atm_taumin -technical parameter-

real(R_), save :: Atm_taumin = 2.0_R_

Minimum column optical thickness used for collision forcing. If actual column optical thickness is less than this threshold, then the collision forcing method is used, and the scaled value of the total optical thickness is set to Atm_taumin. Recommended value is between 1 and 10.

Atm_fsupg -technical parameter-

real(R_), save :: Atm_fsupg = 2.0_R_

Geometrical threshold parameter for automatic, adaptive super-cell formation for maximum cross section method. In the preprocess, super-cells are formed by merging cells until one of conditions are met. Cells are merged until super-cell size (m) is larger, on average, than

Atm_fsupg / E_max

where E_max is the maximum extinction coefficient (/m).

This is one of three conditions for adaptive super-cell formation. See also Atm_fsupi and Atm_nzzsup.

Atm_fsupi -technical parameter-

real(R_), save :: Atm_fsupi = 1.3_R_

Inhomogeneity threshold parameter for automatic, adaptive super-cell formation for maximum cross section method. Cells are merged when inhomogeneity of extinction coefficients within the super-cell is small enough, on average. If ratio of the maximum extinction coefficient (E_max) to super-cell average extinction coefficient (E_ave) is larger than Atm_fsupi, then cell merging will be stopped:

E_max / E_ave > Atm_fsupi

This is one of three conditions for adaptive super-cell formation. See also Atm_fsupg and Atm_nzzsup.

Atm_nzzsup -technical parameter-

integer, save :: Atm_nzzsup = 50

Possible max mumber of atmospheric layers merged into a single super-cell, in which the maximum cross section method is used.

Namelist mcarSfc_nml_job

Sfc_idread

integer, save :: Sfc_idread = 1

Location index of data set to be read, in the surface data file (Sfc_inpfile). Data set specification method is the same as Atm_idread. See Atm_idread for details.

Sfc_tmp

real(R_), save :: Sfc_tmp = 300.0_R_

Average surface temperature (K). Used for calculation of thermal emission when Src_mtype = 2 or 3. 2-D temperature perturbation can be specified by the external data file (Sfc_inpfile).

Sfc_mtype

integer, save :: Sfc_mtype = 1

Type index of globally constant surface BRDF. Used only when Sfc_inpfile = ' ', i.e. BRDF data are not given by the file, Sfc_inpfile. BRDF is assumed as follows:

0: black

1: Lambertian

2: Flx_diffuse-specular mixture (DSM) model

3: Rahman-Pinty-Verstraete (RPV) model

4: Li-Sparse-Ross-Thick (LSRT) model

Sfc_param

real(R_), save :: Sfc_param(Sfc_NPAR) = (/1.0_R_, 0.0_R_, 0.0_R_, 0.0_R_, 0.0_R_/)

BRDF parameters for globally constant surface properties. Used only when Sfc_inpfile = ' ', i.e. BRDF data are not given by the file, Sfc_inpfile. Definitions of Sfc_param(ipar) for respective ipar differs by the BRDF type, Sfc_mtype.

Sfc_mtype = 0 (black): No specification is required for Sfc_param, which is dummy parameter.

Sfc_mtype = 1 (Lambertian):

• Sfc_param(ipar=1): albedo

Sfc_mtype = 2 (DSM): The surface reflection is modeled by a microscopical mixture of diffuse and specular reflection.

• Sfc_param(ipar=1): diffuse albedo (A_d)

• Sfc_param(ipar=2): fraction of Flx_diffuse reflectors (f_d); Fraction of specular reflection is 1 - Sfc_param(ipar=2)

• Sfc_param(ipar=3): real part of refractive index of underlying material (e.g., water); Should be given as positive.

• Sfc_param(ipar=4): imaginary part of refractive index of underlying material (e.g., water); Should be given as positive.

• Sfc_param(ipar=5): variance of micro-scopic surface slope (tangent of the inclination angle). Give zero for flat surface. This is used for specular reflection. According to Cox and Munk's (1954) parameterization for ocean surface,

Sfc_param(ipar=5) = 0.00512 * V + 0.003.

where V is wind velocity (m/s) at 10 m above the ocean surface.

The DSM model albedo (A) and BRDF (R) follow

A = f_d * A_d + (1 - f_d) * A_s,

R = f_d * R_d + (1 - f_d) * R_s,

pi * R_d = cosQ * A_d

where A_s and R_s are albedo and BRDF for specular reflection.

Sfc_mtype = 3 (RPV): Rahman-Pinty-Verstraete (RPV) BRDF model

• Sfc_param(ipar=1): the first parameter, alpha

• Sfc_param(ipar=2): the exponent parameter, k

• Sfc_param(ipar=3): the asymmetry parameter, THETA

• Sfc_param(ipar=4): delta

The RPV BRDF, R, is given as

pi * R = alpha * [u0 * u1 / (u0 - 1) / (u1 - 1)]^(k - 1) * HG(THETA) * F(G)

where pi=3.141592653, u0 and u1 are respectively cosines of incidence and reflection vectors, and HG is the Heyney-Greenstein function. The function F is as follows:

F(G) = 1 + (1 + G)/(delta + G),

where G is a geometrical parameter.

Sfc_mtype = 4 (LSRT): Li-Sparse-Ross-Thick (LSRT) BRDF model

• Sfc_param(ipar=1): "k_L", weight of Lambertian reflection

• Sfc_param(ipar=2): "k_g", weight of geometrical optics reflection

• Sfc_param(ipar=3): "k_v", weight of volume scattering

The LSRT BRDF, R, is given by

pi * R = k_L * pi + k_g * K_geo + k_v * K_vol

where K_geo and K_vol are geometrical and volume scattering kernel functions.

Sfc_nudsm, Sfc_nurpv, Sfc_nulsrt -technical parameter-

integer, save :: Sfc_nudsm = 14

integer, save :: Sfc_nurpv = 8

integer, save :: Sfc_nulsrt = 14

Number of solar zenith angles for the look-up tables (LUTs) for DSM, RPV, and LSRT BRDF models, respectively. The LUTs contains parameters for albedo calculation and determination of reflection direction. In simulations, the parameters used are interpolated from the LUT. Thus larger Sfc_nudsm value achieves higher accuracy but requires larger memory for the LUTs.

Sfc_nqpot -technical parameter-

integer, save :: Sfc_nqpot = 24

Number of quadrature points for surface albedo pre-calculations for the BRDF models, DSM and RPV models. Used when creating the LUTs for albedo, which is calculated by integration of the BRDF over the hemisphere. Larger quadrature points can achieve accurate results but may take longer CPU time. Usually 10 is enough to achieve high accuracy as 0.5% (relative unit).

Sfc_rrmax -technical parameter-

real(R_), save :: Sfc_rrmax = 5.0_R_

Parameter for determination of random reflection direction by the BRDF models, DSM, RPV, and LSRT models. The rejection method is used for sampling. Smaller value needs less computer time, but the determined reflection direction is more approximate. If Sfc_rrmax is very large (>1.0e+8), then no such an approximation is used, and the simulation may require nearly infinite CPU time! Should be larger than or equally to 1. Default value is generally optimal.

Sfc_rrexp -technical parameter-

real(R_), save :: Sfc_rrexp = 0.5_R_

Parameter for determination of random reflection direction by the BRDF models, DSM and RPV models. Smaller value needs less computer time but the determined reflection direction is more approximate. If Sfc_rrexp=1, then no such an approximation is used, and the simulation may require nearly infinite CPU time! Should be between 0 and 1. Default value is generally optimal.

Namelist mcarSrc_nml_job

Src_mtype

integer, save :: Src_mtype(KNSRC) = (/(1, i = 1, KNSRC)/)

Flag for source type (0,1,2,3). Defines external and/or internal sources, as follows:

0: localized sources (the location, direction, and angular width should be specified)

1: solar sources (incidence from the top of atmosphere)

2: solar plus thermal emission sources

3: thermal emission sources

Src_wlen

real(R_), save :: Src_wlen(KNSRC) = (/(10.0_R_, i = 1, KNSRC)/)

Wavelength (micrometer) of light for thermal emission. This is used only when Src_mtype = 2 or 3. If the wavelength band width (Src_dwlen) is not zero, then Src_wlen is the lower limit of wavelength. See also Src_dwlen.

Src_dwlen

real(R_), save :: Src_dwlen(KNSRC) = (/(0.1_R_, i = 1, KNSRC)/)

Wavelength band width (micrometer). Zero is acceptable. When Src_dwlen=0, the simulation is completely monochromatic, and output quantities are spectral ones. Otherwise (Src_dwlen > 0), output quantities are spectrally averaged ones, and spectrally averaged thermal emission are calculated when Src_mtype = 2 or 3.

Note on output quantities and physical units:

a) Src_dwlen=0: spectral, monochromatic calculations, as the followings

• area-averaged spectral flux densities (e.g., W/m^2/micrometer),

• volume-averaged spectral heating rates (e.g., convergences, W/m^3/micrometer),

• spectral radiances (e.g., W/m^2/steradian/micrometer),

b) Src_dwlen > 0: spectrally-averaged calculations; Units are the same as above.

Src_flx

real(R_), save :: Src_flx(KNSRC) = (/(1.0_R_, i = 1, KNSRC)/)

Spectral or spectrally-averaged source flux density or power.

• When the solar source is present (Src_mtype = 1 or 2), Src_flx is the solar source spectral irradiance (W/m^2/micrometer) at the top of atmosphere. The Src_flx is defined as integrated on the plane normal to the center direction of the source emission. The top-of-atmosphere solar source irradiance on the horizontal plane should be, for collimated solar incidence (Src_qmax=0),

Src_flx * abs(cos(180 - Src_the))

• When the source is localized (Src_mtype = 0), Src_flx is the emitted spectral power (W/micrometer).

Even if Src_dwlen > 0, Src_flx should be spectrally-averaged quantity, averaged over the wavelength band. Then spectrally integrated solar source irradiance should be Src_dwlen*Src_flx, for example.

Src_qmax

real(R_), save :: Src_qmax(KNSRC) = (/(0.0_R_, i = 1, KNSRC)/)

Full cone angle (degrees) that determines angular width of solar or localized source, used only when Src_mtype = 0, 1 or 2. This should be 0.533133 (degree) for solar incidence at an annual-mean state of the sun-earth system. Give zero for cases in which sources are negligibly small or infinitely far.

Src_the, Src_phi

real(R_), save :: Src_the(KNSRC) = (/(120.0_R_, i = 1, KNSRC)/) ! zenith angle

real(R_), save :: Src_phi(KNSRC) = (/(0.0_R_, i = 1, KNSRC)/) ! azimuth angle

Zenith and azimuth angles (degrees), respectively, of the source emission direction vector. Used only when Src_mtype = 0, 1 or 2. Note the source direction is defined as transport direction of source light. If the source is solar light, then the transport direction corresponds to the sun-to-surface vector. Thus, the solar zenith angle should be (180 - Src_the).

Src_mphi

integer, save :: Src_mphi(KNSRC) = (/(0, i = 1, KNSRC)/)

Flag for random azimuth of source emission (0:no, 1:yes). If Src_mphi = 0, then the azimuth angles of the source vectors are set as Src_phi. Else if Src_mphi = 1, then the azimuth angles are set as random between 0 to 360 degrees.

Src_xpos, Src_ypos

real(R_), save :: Src_xpos(KNSRC) = (/(0.5_R_, i = 1, KNSRC)/) ! X relative position

real(R_), save :: Src_ypos(KNSRC) = (/(0.5_R_, i = 1, KNSRC)/) ! Y relative position

Coordinates that specifies the location of the localized source, used when Src_mtype=0.

Src_zloc

real(R_), save :: Src_zloc(KNSRC) = (/(0.0_R_, i = 1, KNSRC)/)

Z-coordinate that specifies the location of the localized source, used when Src_mtype=0.

Src_apsize

real(R_), save :: Src_apsize(KNSRC) = (/(0.0_R_, i = 1, KNSRC)/)

Aperture size, diameter (m) of the local source surface (or the surface of the outmost lens of the artificial source), when Src_mtype = 0. The localized source should be very small compared to the model domain, but non-zero finite size is allowed. If Src_apsize = 0, then it means the source is from a point. Otherwise, the source surface is assumed to be circular. Emission surface is assumed to be on a plane perpendicular to the emission center direction (with Src_the & Src_phi).

Namelist mcarRad_nml_job

Rad_mrproj

integer, save :: Rad_mrproj = 0

Flag for angular weighting, when radiances are averaged over finite solid angle (Rad_mrkind = 1 or 3). Options are as follows:

= 0 : w = 1, results are radiances simply averaged over solid angle

= 1 : w = cosQ for Q = angle from the camera center direction, results are weighted average

where w is a weighting function. Output radiance will be

R_out = integral{R(s) * w(s) * dS} / integral{w(s) * dS}

where R(s) is radiance in a direction s, and S is solid angle within the FOV.

Here are two examples. When FOV is a hemisphere (Rad_umax = 180 deg.),

Rad_mrproj = 0: R_out = hemispherical-mean radiance

Rad_mrproj = 1: R_out * pi = irradiance (radiative flux density)

Rad_zloc

real(R_), save :: Rad_zloc(KNRAD) = (/( 0.0_R_, i = 1, KNRAD)/)

Z coordinate, altitude (m) of the detector location.

The pixel mapping for radiance image is performed at the detector altitude. Note that this differs from the method that is used for image projection of satellite observation image pixels, which are mapped at the ground level (not at the satellite altitude). In the next version, more useful option will be added.

Rad_zref - new variable in v0.10.3

real(R_), save :: Rad_zref(KNRAD) = (/( 0.0_R_, i = 1, KNRAD)/)

Altitude (m) of the reference level. The output will be shifted to the appropriate position consistent with the input atmospheric distribution. Used only when Rad_mrkind=2. If Rad_the > 90, Rad_zref should be less than Rad_zloc. If Rad_the < 90, Rad_zref should be greater than Rad_zloc. This variable will be enabled in v0.10.3.

Rad_xpos, Rad_ypos

real(R_), save :: Rad_xpos(KNRAD) = (/( 0.5_R_, i = 1, KNRAD)/) ! X relative position

real(R_), save :: Rad_ypos(KNRAD) = (/( 0.5_R_, i = 1, KNRAD)/) ! Y relative position

Relative horizontal location along x and y-axes, respectively, for the detector. X and Y coordinates at the detector location are respectively

X_cam = Rad_xpos * Atm_dx * Atm_nx

Y_cam = Rad_ypos * Atm_dy * Atm_ny

Thus, Rad_xpos=0 corresponds to the X coordinate of 0, and Rad_xpos=1 corresponds to the uppermost X coordinate of the domain. If Rad_xpos or Rad_ypos is out of a range [0, 1], then they are reset in the code under the cyclic boundary condition. For example, Rad_xpos = 2.345 will be reset as 0.345, and -2.345 will be reset as 0.655.

Rad_rmin0, Rad_rmax0

real(R_), save :: Rad_rmin0(KNRAD) = (/(1.0e-17_R_, i = 1, KNRAD)/)

real(R_), save :: Rad_rmax0(KNRAD) = (/(1.0e+17_R_, i = 1, KNRAD)/)

Minimum and maximum distances (m), respectively, between emission point and the detector. Used only when Rad_mrkind = 1 or 2, in order to limit the distance between emission/scattering point and the detector. A view region is defined for each detector, and the distance R between the emission point and the detector should be

Rad_rmin0 < R < Rad_rmax0

Emissions from out of the view region are all excluded from sampling. Transmittance between the line of sight segment for 0 < R < Rad_rmin0 is artificially set at 1, which may result in bias of computed radiances.

Note current code has an intelligent way to automatically set the view region: Rad_rmin0, Rad_rmax0, and Rad_frmod are automatically set taking into account the domain size, detector location, and detector FOV. When Rad_mrkind = 2, default values are Rad_rmin0 = 0.0 and Rad_rmax0 = (a large enough value). Therefore, the user can leave the default setting as is. Alternatively set an explicit view region.

Basically, emission contributions from source emission, scattering, and reflection should be all sampled for calculating radiances. However, if the first kind of radiances are calculated (Rad_mrkind = 1), simulated images can be very noisy when Rad_rmin0 is too small, and scattering particles are present near the camera. This is because contribution function is proportional to 1/R^2. For that reason, emission near the camera should be excluded from sampling.

For simulation of physically-correct results, Rad_rmax0 should be infinity. However, such a simulation could be highly time consuming, so that an upper limit should be set.

The figure below schematically illustrates the geometry of the view region and the detector.

Figure. The geometry of the view region and the detector.

Rad_frmod

real(R_), save :: Rad_frmod = 0.3_R_

Factor for mode distance between emission point and the detector. Used only when the first kind of radiances are calculated (Rad_mrkind = 1). The mode distance (R_mod) will be

R_mod = [ (1 - Rad_frmod) * sqrt(Rad_rmin0) + Rad_frmod * sqrt(Rad_rmax0) ]**2

Contribution function for the first kind of radiance is proportional to 1/R^2. This mode distance is used for variance reduction. Emission contribution from a point far enough from the detector (R > R_mod), is scaled by the Russian roulette:

Zeta_new = Zeta_old * (R / R_mod), if Xi < R_mod / R

Zeta_new = 0, otherwise

where Xi is a random number. This reduces populations of sampling from points far from the detector, reducing calculation time.

Rad_the, Rad_phi, Rad_psi

real(R_), save :: Rad_phi(KNRAD) = (/(0.0_R_, i = 1, KNRAD)/) ! phi, angle around Z0

real(R_), save :: Rad_the(KNRAD) = (/(0.0_R_, i = 1, KNRAD)/) ! theta, angle around Y1

real(R_), save :: Rad_psi(KNRAD) = (/(270.0_R_, i = 1, KNRAD)/) ! psi, angle around Z2

Rotation angles (degrees) for the camera (detector) coordinates, which are defined by rotating the original X-Y-Z world coordinates, following Z-Y-Z rotation rule. Values can be in a range (-Inf, +Inf). Three rotations are operated in the correct order:

1: rotation about Z (Z-axis in (X,Y,Z) world coordinates) by Rad_phi

2: rotation about Y1 (Y-axis in (X1,Y1,Z1) coordinates) by Rad_theta

3: rotation about Z2 (Z-axis in (X2,Y2,Z2) coordinates) by Rad_psi

Finally camera coordinates are (Xc,Yc,Zc), and the Zc axis corresponds to the reverse radiance direction (when Rad_mrkind = 2) or the center direction of radiance image projection (when Rad_mrkind = 1 or 3). Angle between Zc axis direction and the original Z axis direction should be Rad_theta, and azimuth angle of Zc axis direction in the original world coordinate system (X,Y,Z) should be Rad_phi. Therefore, Rad_theta and Rad_phi denotes the zenith and azimuth angles, respectively, in degrees, of the radiance reverse direction or the center direction of radiance image projection. The direction is here defined as the reverse of light transport, i.e. camera to target direction.

Rad_psi is dummy when Rad_mrkind = 2, i.e., detector FOV is infinitesimal. Rad_psi should be appropriately set when Rad_mrkind = 1 or 3, because the angular distribution of radiance will be mapped in an image, definition of which requires the rotation angle Rad_psi.

Figure. The camera coordinates and world coordinates, where theta_rad = Rad_theta, phi_rad = Rad_phi, psi_rad = Rad_psi.

Camera coordinate system

The camera coordinates (Xc,Yc,Zc) are defined as described above, by the three angles (Rad_the, Rad_phi, Rad_psi). When Rad_mrkind = 2 (horizontal distribution of area-averaged radiances in specific direction), Zc axis is the single, specific direction. When Rad_mrkind = 1 or 3 (angular distribution of angle-averaged radiances), view directions are mapped in an image, which is defined for each camera. In the camera coordinate system, an arbitrary view direction (view point-to-target direction) is defined by the polar angle (theta_c) and the azimuth angle (phi_c), as illustrated in the figure below. The projection image coordinates are defined by U and V, as described below.

Figure. Camera coordinates and a view direction.

Rad_umax , Rad_vmax

real(R_), save :: Rad_umax(KNRAD) = (/(180.0_R_, i = 1, KNRAD)/) ! max angle along U coordinate

real(R_), save :: Rad_vmax(KNRAD) = (/(180.0_R_, i = 1, KNRAD)/) ! max angle along V coordinate

Maximum angles (degrees) of projection image coordinates, U and V, respectively, for each camera. Used only when Rad_mrkind = 1 or 3. Both should be <= 180 degrees. The pixel mapping method differs by Rad_mpmap.

Rad_mpmap = 1 (rectangular mapping)

U = theta_c * cos(phi_c) + Rad_umax / 2, in [0, Rad_umax]

V = theta_c * sin(phi_c) + Rad_vmax / 2, in [0, Rad_vmax]

Rad_mpmap = 2 (polar mapping)

U = theta_c * 2, in [0, Rad_umax]

V = phi_c, in [0, 360]

where theta_c and phi_c are the polar and azimuth angles in the camera coordinate system, of the view direction. Figures below show the image geometry schematically. See also Rad_qmax and [[a page>User's Guide v0.10/8]] for example applications. When Rad_mpmap = 2, Rad_vmax is not used.

Figure. Rectangular image mapping (Rad_mpmap=1).

Figure. Polar image mapping (Rad_mpmap=2).

Here is an example: Both show radiance angular distribution for an hemisphere, looking up a stratocumulus cloud deck. In both cases, Rad_umax = 180, and Rad_vmax = 180 (Rad_vmax is dummy when Rad_mpmap = 2).

Rad_qmax

real(R_), save :: Rad_qmax(KNRAD) = (/(180.0_R_, i = 1, KNRAD)/)

Maximum angle (degrees), full cone angle of the field of view (FOV) of the detector. Should be <= 180 degrees. If Rad_qmax = 180 degrees, the the FOV corresponds to a hemisphere, the normal of which corresponds to the direction with Rad_the and Rad_phi.

Rad_apsize

real(R_), save :: Rad_apsize(KNRAD) = (/(0.0_R_, i = 1, KNRAD)/)

Aperture size, diameter (m) of the detector surface (or the surface of the outmost lens of the detector). Used only when the first kind of radiances are calculated (Rad_mrkind = 1).

The detector size should be very small compared to the model domain, but non-zero finite size is allowed. If Rad_apsize = 0, then it means an infinitesimally small detector. Otherwise, the detector surface is assumed to be circular. Detector surface is assumed to be on a plane perpendicular to the FOV center direction.

Rad_wfunc0

real(R_), save :: Rad_wfunc0(KNZ, KNWF)

Weighting functions used when column averaged pathlengths are calculated (Rad_mplen=2). Unit is arbitrary. An element Rad_wfunc0(iz, iwf) corresponds to a layer index iz and a weighting function index iwf. The weighting function is used in the following formula: air mass factor (AMF),

AMF(iwf) = sum{ L(iz) * Rad_wfunc0(iz, iwf) } / sum{ Rad_wfunc0(iz, iwf) } / Dz(iz)

where the sum is for all layers, iz = [1, Atm_nz], and L is pathlength and Dz is layer depth.

Multiple weighting functions are useful for calculating multiple air mass factors for multiple gaseous species with different vertical profiles.

Rad_zetamin -technical parameter-

real(R_), save :: Rad_zetamin = 0.3_R_

Threshold for each radiance contribution function sampled by the local estimation method. Radiance contribution from each emission/scattering/reflection event is calculated as the normalized angular distribution function multiplied by transmittance between the event point and the detector.

Rad_difr0, Rad_difr1 -technical parameter-

real(R_), save :: Rad_difr0 = 30.0_R_

real(R_), save :: Rad_difr1 = 0.01_R_

Artificial diffusion coefficients for radiances. Default values are generally optimal.

What variables are actually used?

Different sets of variables are used depending on the kind of radiance (Rad_mrkind). The following table summarizes which variables are used for a given Rad_mrkind.

Here, "y" denotes that the variable is used, and "-" not used.

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