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1. Particle Linear Depolarization Ratio Implementation
======================================================

The most important improvement included in the SCC v4.0 is the implementation of a new optical product which is the particle linear depolarization ratio.

1.1 Background
--------------

The calculation of the volume linear depolarization ratio profile (*VLDR*) and particle linear depolarization ratio profile (*PLDR*) needs two different steps:

#. the calibration of the polarization sensitive lidar channels;
#. the calculation of the *VLDR* or *PLDR* itself.

The SCC allows the user to make both the above points. In particular the calibration step is made by a completely new module called **scc\_calibrator** which computes the *apparent calibration factor* :math:`\beta^*` out of the pre-processed data provided by the standard **ELPP** (Earlinet Lidar Pre-Processor) module and it records it in the SCC database (SCC\_DB). Once logged into the SCC\_DB this factor can be used whenever it is necessary.

The raw lidar calibration measurements should be put in a NetCDF file which has the same structure as the “standard” raw SCC NetCDF input file (for more details see sections 2 and 3.2).

New signal types have been introduced to take into account special channel configurations used for calibration purposes.

Moreover new product types for both calibration and *PLDR* calculation have been defined. As, in principle, it is possible to calculate the *PLDR* only when the aerosol backscatter coefficient profile is available the following new products have been defined:

#. *Linear polarization calibration (factor* h) *(product\_type\_id=6);*
#. *Raman backscatter and linear depolarization ratio
   (product\_type\_id=7);*
#. *Elastic backscatter and linear depolarization ratio
   (product\_type\_id=8).*

The first product in the above list is used only for calibration while the other two are used for the calculation of *PLDR*. Basically, in most of the cases, the products 2 and 3 are equivalent to the corresponding backscatter product types with the exception that also the following new variables are available:

.. code-block:: python

   double VolumeDepol(Length) ;
   double ErrorVolumeDepol(Length) ;
         ErrorVolumeDepol:long\_name = "absolute error of VolumeDepol" ;
   double ParticleDepol(Length) ;
   double ErrorParticleDepol(Length) ;
         ErrorParticleDepol:long\_name = "absolute error of ParticleDepol" ;

1.2 Polarization calibration
----------------------------

An important point is the definition of reliable *PLDR* calibration procedures. Within EARLINET the following calibration procedures are currently used:

 a) Rayleigh calibration;
 b) +45 calibration method, or D90 calibration method (made by +45 and -45 measurements);
 c) 3 signals (total, cross and parallel).

It is well known that method a) could produce easily large errors on *PLDR* which cannot be controlled. For this reason only the methods b) and c) can be used to provide reliable polarization calibrations and so only those methods will be implemented in the SCC.

For what it concerns the method c) it, basically, requires to solve the equation:

.. math::
   \alpha_s P_s + \alpha_p P_p = P

in two different of atmospheric layers with considerably different *VLDR*. So to calibrate in this way the implementation of automatic layer identification in the SCC is required. As at moment this feature is not yet available within the SCC *ONLY* the method b) is considered.

1.3 SCC procedure to calculate the PLDRP
----------------------------------------

According to what mentioned before the SCC calculates the *PLDR* through the following steps:

#. The user needs to create a new system configuration in the SCC\_DB    including only lidar channels used for the calibration. One (or more) *Linear polarization calibration (product\_type\_id=6)* product should be associated to this new configuration (see section 3.2 for more details);

#. This new system configuration should contain only the polarization channels in the configuration used for the calibration (for example rotated in the polarization plane of +45 degrees). A channel in calibration measurement configuration should have a *DIFFERENT* channel ID from the channel ID corresponding to the same channel in standard measurement configuration. For example, if a system has two polarization channels which in standard measurement configuration correspond to the channel ID=1 and 2 respectively, the same physical channels under calibration measurement configuration should correspond to different channel IDs (let's say ID=3 and 4 for the +45 degrees polarization rotated channels and ID=5 and 6 for the -45 degrees polarization rotated ones in case D90 calibration method is used). Moreover, the polarization channels should be labeled correctly using the new signal types available (*+45elPT, +45elPR, -45elPT, -45elPR, +45elPTnr, +45elPTfr, +45elPRnr, +45elPRfr, -45elPTnr, -45elPTfr, -45elPRnr, -45elPRfr).* For more details see section 3.2;

#. In SCC v4.0 the polarization channels are *NOT* labeled on the base of their polarization state (as it was done in the SCC v3.11) but *ALWAYS* as transmitted and reflected channels. So the channels that in SCC v3.11 were labeled as *elCP, elCPnr, elCPfr, elPP, elPPnr elPPfr* will be labeled in SCC v4.0 as *elPR, elPRnr elPRfr elPT, elPTnr elPTfr* where the letter *T* stands from transmitted and the letter *R* for reflected.

:WARNING: In switching from the SCC v3.11 to SCC v4.0 the following modifications have been made on *ALL* channels of *ALL* registered configurations:
   *elPP→elPR*

   *elCP→elPT*

   *elPPnr→elPRnr*

   *elPPfr→ elPRfr*

   *elCPnr→ elPTnr*

   *elCPfr→ elPTfr*

 Please be sure these modifications reflect to your actual lidar setup(cross channels are transmitted and parallel channels are reflected);

4. The user needs to submit a file (same format as raw SCC input file) containing the raw data for the lidar channels defined at the point 1 (see section 3.2 for more details);
#. The file at point 2 is pre-processed by **ELPP** module which applies the standard pre-processing procedures applied to “standard” lidar data;
#. The pre-processed files are then processed by the new modules **scc\_calibrator** which calculates :math:`\eta^*` *the apparent calibration factor* and logs it into the SCC\_DB;
#. The user needs to create a new system configuration in the SCC\_DB (which should be different from the one used for the calibration) and associate it the new product *Raman backscatter and linear depolarization ratio product\_type\_id=7)* or *Elastic backscatter and linear depolarization ratio (product\_type\_id=8).* Alternatively the calculation of those products can be added to an already existing lidar configuration as long as it is different from the calibration one;
#. The product defined at point 5 should be linked to the product containing the polarization calibration (defined at point 1) in a way that the *apparent calibration factor* can be selected from the SCC\_DB (see section 3.3 and in particular figure 3.4);
#. The user needs to submit another SCC raw data file containing the “standard” measurements;
#. Finally **ELPP** and **ELDA** will produce a b-file containing backscatter coefficient profile and *PLDR*. In particular this calculation is made in two different steps: from the pre-processed lidar polarization signals, and taking into account the *apparent calibration factor* and the *calibration factor correction K* (defined as option of *Linear polarization calibration* product\ *)* written into the SCC\_DB, an “apparent” *VLDR* :math:`\delta^*` is calculated. Even if :math:`\delta^*` is a calibrated quantity it can be still affected by possible systematic errors due to not perfect optics or alignment of the system;

#. To take into account these errors a corrected *VLDR* (:math:`\delta`) is calculated using the *polarization cross-talk correction parameters* *G* and *H* calculated on the base of Müller matrix formalism. These cross-talk correction parameters (*G* and *H*) are stored in the SCC\_DB for each lidar channels (see section 3.1 in particular figure 3.2). Finally the *PLDR* is calculated using the backscatter coefficient profile and the molecular LDRP calculated by ELPP considering the center wavelength and bandwidth of the channels interference filter.

The *apparent calibration factor* :math:`\eta^*` is calculated by the **scc\_calibrator** module as the geometrical mean of the ratio of the +/-45 degrees reflected to the +/- 45 degrees transmitted signals within an altitude calibration range defined by the users in the raw data input files.

In case of +45 calibration method :math:`\eta^*` is calculated by:

.. math::
   \eta^* = \frac{I_R}{I_T}(+45)

While in case of D90 calibration method:

.. math::
   \eta^* = \sqrt{\frac{I_R}{I_T}(+45) \frac{I_R}{I_T}(-45)}

**ELDA** module calculates the “apparent” *VLDR*:

.. math::
   \delta^* = \frac{K}{\eta^*} \cdot \frac{I_R}{I_T}

the *VLDR*

.. math::
   \delta = \frac{\delta^*(G_T + H_T)-(G_R + H_R)}{(G_R - H_R) - \delta^*(G_T - H_T)}

and the *PLDR*

.. math::
   \delta_{\alpha} = \frac{(1 + \delta_m)\delta R - (1 + \delta)\delta_m}{(1 + \delta_m)R - (1 + \delta)}

where:

 - :math:`\eta^*` is the *apparent calibration factor* calculated by **scc\_calibrator**

 - *K* is the *calibration factor correction* defined as polarization product option

 - :math:`I_T` and :math:`I_R` are the transmitted and the reflected signals in the polarization detection set-up

 - :math:`G_{T,R}` and :math:`H_{T,R}` are *polarization cross-talk correction parameters* for the transmitted and reflected signals used to correct for systematic errors. Both these factors are defined in the SCC\_DB for each lidar channel.

 - :math:`\delta_m` is the molecular linear depolarization ratio calculated by ELPP

 - *R* is the backscatter ratio

Please note once again that the polarization channels are described in terms of transmitted and reflected signals. This means that according to different lidar instrumental configurations, the transmitted or the reflected channel can contain total, perpendicular or parallel polarized signals.

In order to retrieve the backscatter profile the total signal must be obtained combining the transmitted and reflected polarized signals. The following formula is used:

.. math::
   I_{total} \propto \frac{\eta^*}{K}H_R I_T - H_T I_R

The formulas above are general and can be adapted to all possible polarization lidar configurations selecting the right polarization cross-talk correction parameters (see Table 1.1).

Let's suppose, for example, we have the perpendicular polarized lidar signal on the transmitted channel and the parallel polarized on reflected channel. For an ideal system (no diattenuation and cross-talk) we have:

.. math::
   G_T=1 , \qquad H_T=-1, \qquad G_R=1, \qquad H_R=1

If, on the other hands, we have the perpendicular polarized lidar signal on reflected channel and the total polarized on the transmitted for and ideal system we have:

.. math::
   G_T=1 , \qquad H_T=0, \qquad G_R=1, \qquad H_R=-1


**Table 1.1:** Polarization cross-talk correction parameters for ideal systems

+----------------------+-----------------------------+-----------------+-----------------+-----------------+
| Laser polarization   | Detected in lidar channel                                                         |
+                      +-----------------------------+-----------------+-----------------+-----------------+
|                      | Transmitted                                   | Reflected                         |
+                      +-----------------------------+-----------------+-----------------+-----------------+
|                      | :math:`G_T`                 | :math:`H_T`     | :math:`G_R`     | :math:`H_R`     |
+----------------------+-----------------------------+-----------------+-----------------+-----------------+
| total                | 1                           | 0               | 1               | 0               |
+----------------------+-----------------------------+-----------------+-----------------+-----------------+
| parallel             | 1                           | 1               | 1               | 1               |
+----------------------+-----------------------------+-----------------+-----------------+-----------------+
| cross                | 1                           | -1              | 1               | -1              |
+----------------------+-----------------------------+-----------------+-----------------+-----------------+

The *apparent calibration factor (:math:`\eta^*`), *the calibration factor correction* (*K*) and the *polarization cross-talk correction parameters* are stored by **ELPP** module in the intermediate NetCDF files using the following variables:

testing the inline code :code:`test`

 - :code:`Polarization_Channel_Gain_Factor` (*apparent calibration factor* - :math:`\eta^*` )
 - :code:`Polarization_Channel_Gain_Factor_Correction` (*calib. factor corr.* – *K*)
 - :code:`G_T`
 - :code:`H_T`
 - :code:`G_R`
 - :code:`H_R`

Finally new usecases have been defined to take into account all the possible lidar configurations. The details on that are provided as a separate file.

2. Changes of the SCC input format
==================================

The following minor changes have been applied to raw SCC data format:

#. The optional variable *ID\_Range* has been *REMOVED*;
#. The *OPTIONAL* variable :code:`int Signal\_Type(channels)` has been added. The possible values are the same available in the SCC\_DB:

      :code:`0` :math:`\rightarrow` :code:`elT`

      :code:`1` :math:`\rightarrow` :code:`elTnr`

      :code:`2` :math:`\rightarrow` :code:`elTfr`

      :code:`3` :math:`\rightarrow` :code:`vrRN2`

      :code:`4` :math:`\rightarrow` :code:`vrRN2nr`

      :code:`5` :math:`\rightarrow` :code:`vrRN2fr`

      :code:`6` :math:`\rightarrow` :code:`elPR`

      :code:`7` :math:`\rightarrow` :code:`elPT`

      :code:`8` :math:`\rightarrow` :code:`pRRlow`

      :code:`9` :math:`\rightarrow` :code:`pRRhigh`

      :code:`10` :math:`\rightarrow` :code:`elPRnr`

      :code:`11` :math:`\rightarrow` :code:`elPRfr`

      :code:`12` :math:`\rightarrow` :code:`elPTnr`

      :code:`13` :math:`\rightarrow` :code:`elPTfr`

      :code:`14` :math:`\rightarrow` :code:`vrRH2O`

      :code:`15` :math:`\rightarrow` :code:`pRRhighnr`

      :code:`16` :math:`\rightarrow` :code:`pRRhighfr`

      :code:`17` :math:`\rightarrow` :code:`pRRlownr`

      :code:`18` :math:`\rightarrow` :code:`pRRlowfr`

      :code:`19` :math:`\rightarrow` :code:`vrRH2Onr`

      :code:`20` :math:`\rightarrow` :code:`vrRH2Ofr`

      :code:`21` :math:`\rightarrow` :code:`elTunr`

      :code:`22` :math:`\rightarrow` :code:`+45elPT`

      :code:`23` :math:`\rightarrow` :code:`+45elPR`

      :code:`24` :math:`\rightarrow` :code:`-45elPT`

      :code:`25` :math:`\rightarrow` :code:`-45elPR`

      :code:`26` :math:`\rightarrow` :code:`+45elPTnr`

      :code:`27` :math:`\rightarrow` :code:`+45elPTfr`

      :code:`28` :math:`\rightarrow` :code:`+45elPRnr`

      :code:`29` :math:`\rightarrow` :code:`+45elPRfr`

      :code:`30` :math:`\rightarrow` :code:`-45elPTnr`

      :code:`31` :math:`\rightarrow` :code:`-45elPTfr`

      :code:`32` :math:`\rightarrow` :code:`-45elPRnr`

      :code:`33` :math:`\rightarrow` :code:`-45elPRfr`

   :WARNING: It this variable is found in the SCC input file the corresponding settings in the SCC database will be *overwritten*. Unless you don't have any valid reason to overwrite the database value this variable should not be used.

3. The variables:

   .. code-block:: python

      double Pol\_Calib\_Range\_Min(channels)
      double Pol\_Calib\_Range\_Max(channels)

 have been added. Both these variable are *MANDATORY* for any calibration raw dataset. These variable should be included only the polarization calibration measurements and should specify the altitude range (meters) in which the polarization calibration should be made. For more details see section 3.3;

4. The variable :code:`Depolarization_Factor` has been *REMOVED*.

 The SCC v3.11 used this variable to get polarization calibration factor for the calculation of the total signal out of cross and parallels ones. As the SCC v4.0 is able to calculate the same parameter by itself, the use of this variable is *NOT* possible anymore. The recommended way to get a valid and quality assured depolarization calibration factor is to submit to the SCC v4.0 a polarization calibration dataset and let the SCC to calculate such factor.

 To make this change more smooth and to provide the users with the possibility to continue to analyze their data with the SCC v4.0 even if a calibration dataset has not been submitted yet, it will be possible for a *LIMITED* period of time to submit the calibration constant via the SCC web interface. The SCC will keep track of the used calibration method (automatic or manual).

 :WARNING: After this transition period *ONLY* automatic calibration will be allowed!

5. The new *OPTIONAL* variable:

      :code:`string channel\_string\_ID(channels)`

 has been introduced.

 Starting from SCC v4.0 the lidar channel can be identified not only by using integers (as it happened until SCC v3.11) but also by using strings.

 The procedure implemented in the SCC v4.0 to recognize the lidar channel within the raw lidar data is fully backward compatible (old format files are accepted as they are by SCC v4.0).

 :WARNING: Please note that the definition of the new string variable requires netCDF-4 format! The type *string* is not supported in netCDF-3 format!

Real Example
============

This section describes all the practical steps the users need to follow
to switch from SCC v3.11 to new SCC v4.0.

**IMPORTANT:**

If your lidar system is not equipped with any polarization channels *NO*
changes are required. In this case, the SCC v4.0 should work using the
same input files and the same database configurations you have used with
the SCC v3.11. Anyway as in the SCC v4.0 several bugs have been fixed,
it is recommended to re-run all the measurement IDs you have submitted.
For doing that you just need to reprocess all your data without the need
to submit raw data files already uploaded on the server.

The practical example reported below describes the modifications
required to use the SCC v4.0 for lidar systems equipped with
polarization channels.

Modification of polarization channel parameters
-----------------------------------------------

In what it follows it is assumed you already have registered one or more
lidar configurations in the SCC database and that such configurations
have been already used to produce optical products (aerosol extinction
and/or backscatter coefficients) by means of the SCC v3.11.

Let's assume your 3+2 system is registered in the SCC database and the
settings used by the SCC v3.11 are the ones summarized in table 3.1.

**Table 3.1:** Example of configuration in SCC v3.11

+----------------+--------------+----------------+-------------+-----------+
| Channel Name   | Channel ID   | Channel Type   | nighttime   | daytime   |
+----------------+--------------+----------------+-------------+-----------+
| 355            | 1            | elT            |            |          |
+----------------+--------------+----------------+-------------+-----------+
| 387            | 2            | vrRN2          |            |           |
+----------------+--------------+----------------+-------------+-----------+
| 532 cross      | 3            | elCP           |            |          |
+----------------+--------------+----------------+-------------+-----------+
| 532 parallel   | 4            | elPP           |            |          |
+----------------+--------------+----------------+-------------+-----------+
| 607            | 5            | vrRN2          |            |           |
+----------------+--------------+----------------+-------------+-----------+
| 1064           | 6            | elT            |            |          |
+----------------+--------------+----------------+-------------+-----------+

We assume there are 2 system configurations called “nighttime” and
“daytime”. The nighttime configuration contains all the available lidar
channels (in order to calculate, for example, the aerosol extinction at
355 and 532nm and the aerosol backscatter at 355, 532 and 1064nm) while
in daytime conditions only elastic channels are used (only elastic
backscatter coefficients are generated).

To make these settings working with SCC v4.0 it is needed to modify
*ONLY* the products properties involving the polarization channels (532
cross and parallel). All the products not involving the polarization
channels *DO NOT* need any modification and should work in the SCC v4.0
exactly as they did in SCC v3.11. In the example above the aerosol
extinction and backscatter coefficient at 355nm, the extinction at 532nm
as well as the backscatter coefficient at 1064nm do not required any
modification. Let's focus on the modifications needed for the
calculation of backscatter at 532nm.

|image0| How to select signal types

The first modification concerns the settings of the channel type for the
532 cross and 532 parallel polarization channels. Starting from SCC v4.0
polarization channels are identified as transmitted and reflected
polarization channels and not on the base of their polarization state.
So suppose if we suppose the cross polarized channel is transmitted by a
polarizer beam splitter cube and the parallel is reflected the value
reported in table 3.1 should be modified as they appear in table 3.2. So
using the SCC web interface, the signal type of the 532 cross channel
should be changed from elCP to elPT and and in the same way the 532
parallel channel should be changed from elPP to elPR (see figure 3.1).

**Table 3.2:** The same of table 3.1 but with new channel types
introduced in SCC v4.0

+----------------+--------------+----------------+-------------+-----------+
| Channel Name   | Channel ID   | Channel Type   | nighttime   | daytime   |
+----------------+--------------+----------------+-------------+-----------+
| 355            | 1            | elT            |            |          |
+----------------+--------------+----------------+-------------+-----------+
| 387            | 2            | vrRN2          |            |           |
+----------------+--------------+----------------+-------------+-----------+
| 532 cross      | 3            | **elPT**       |            |          |
+----------------+--------------+----------------+-------------+-----------+
| 532 parallel   | 4            | **elPR**       |            |          |
+----------------+--------------+----------------+-------------+-----------+
| 607            | 5            | vrRN2          |            |           |
+----------------+--------------+----------------+-------------+-----------+
| 1064           | 6            | elT            |            |          |
+----------------+--------------+----------------+-------------+-----------+

The other change about the polarization channels required to run the SCC
v4.0 is the definition of the polarization crosstalk parameters for all
the polarization channels available. Such parameters can be defined for
each polarization channel using the SCC web interface (see figure 3.2).
In particular among the channel parameters there is a new tab called
*Polarization crosstalk parameters* where it is possible to insert the
values from for the parameters *G* and *H* and the corresponding
statistical and systematic errors if available. In case you have
measured *G* and *H* for your polarization channels please insert the
corresponding values there. Otherwise you can insert the ideal values as
reported in table 1.1.

|image1| *Polarization crosstalk parameters* tab in channel properties
(SCC v4.0).

Definition of new calibration configuration and product
-------------------------------------------------------

In this section we will see how to set the polarization calibration
parameters: the calibration constant (called h\ :sup:`\*` in section
1.3) and the correction to calibration constant (called K in section
1.3).

In order to provide such parameters you need to define a new system
configuration to be used *only* for calibration purposes. Such new
configuration should include the polarization channels in the
measurement configuration used for the calibration. Let's suppose we
want to use the D90 calibration method.

In this case we need to define a new configuration (called for example
“depol\_calibration”) as reported in the table 3.3. As you can see the
configuration “depol\_calibration” includes 4 “new” channels. Actually
the channels “532 cross +45 degrees” (channel ID=10) and “532 cross -45
degrees” (channel ID=12) refer to the same physical channel “532 cross”
reported with channel ID=3 in table 3.2. Anyway we need to define two
new channel IDs to identify the “532 cross” channel in the two
polarization rotated configurations (+45 and -45 degrees) needed to
apply the D90 calibration method. The same is true for the “532
parallel” channel. The polarization rotated channels should be labeled
with the corresponding signal type as reported in table 3.3 (see figure
3.1).

**Table 3.3:** Polarization calibration configurations assuming D90
calibration method

+----------------------------+--------------+----------------+----------------------+
| Channel Name               | Channel ID   | Channel Type   | depol\_calibration   |
+----------------------------+--------------+----------------+----------------------+
| 532 cross +45 degrees      | 10           | +45elPT        |                     |
+----------------------------+--------------+----------------+----------------------+
| 532 parallel +45 degrees   | 11           | +45elPR        |                     |
+----------------------------+--------------+----------------+----------------------+
| 532 cross -45 degrees      | 12           | -45elPT        |                     |
+----------------------------+--------------+----------------+----------------------+
| 532 parallel -45 degrees   | 13           | -45elPR        |                     |
+----------------------------+--------------+----------------+----------------------+

Finally we should add to the configuration “depol\_calibration” a
product “\ *Linear polarization calibration”* to be used for the
calibration. According to the example given above and to the usecase
document attached we should use an usecase=4 for this example.

Other “\ *Linear polarization calibration”* options to be specified are
reported in figure 3.3. The most important factor you should insert here
is the *Pol calibration correction factor* (K). The ideal value for this
parameter is 1. Anyway if you have measured the parameter K please fill
in the measured value and the corresponding measurement errors.

|image2| Options for *Linear polarization calibration product*.

As you can see it is possible to fill in only the K correction factor
and not the calibration constant h\ :sup:`\*`.

Actually for a *LIMITED* period of time it will be possible to fill in
also the constant h\ :sup:`\*` using a temporary tab called
*Polarization calibration constant*. This has been done to provide the
users with the possibility to continue to use the SCC even if an
automatic calibration made by the SCC was not submitted yet. Anyway
after a transition period it will be *not* possible to provide
calibration constant using this procedure and the parameter h\ :sup:`\*`
can be calculated *ONLY* by the SCC as result of the submission of a
proper calibration raw input dataset. The format of this input file is
the same as the standard SCC input file. The only difference is that is
should contain calibration measurements instead of standard
measurements. Following our example, such file should contain the
measurement performed at +45 and -45 degrees at 532nm. Also the channel
IDs in the file should reflect the ones reported in table 3.3.

Moreover this raw input file has to contain the variables:

*double Pol\_Calib\_Range\_Min(channels)*

*double Pol\_Calib\_Range\_Max(channels) *

where to specify the altitude ranges in meters in which the polarization
calibration should be done.

According to the table 3.3 this file should be something similar to:

dimensions:

channels = 4 ;

nb\_of\_time\_scales = 1 ;

points = 16380 ;

scan\_angles = 1 ;

time = UNLIMITED ; // (3 currently)

variables:

int channel\_ID(channels) ;

double Background\_Low(channels) ;

double Background\_High(channels) ;

int id\_timescale(channels) ;

double Laser\_Pointing\_Angle(scan\_angles) ;

int Molecular\_Calc ;

int Laser\_Pointing\_Angle\_of\_Profiles(time, nb\_of\_time\_scales) ;

int Raw\_Data\_Start\_Time(time, nb\_of\_time\_scales) ;

int Raw\_Data\_Stop\_Time(time, nb\_of\_time\_scales) ;

int Laser\_Shots(time, channels) ;

double Raw\_Lidar\_Data(time, channels, points) ;

double Pressure\_at\_Lidar\_Station ;

double Temperature\_at\_Lidar\_Station ;

double Pol\_Calib\_Range\_Min(channels) ;

double Pol\_Calib\_Range\_Max(channels) ;

// global attributes:

:System = "mysystem" ;

:Longitude\_degrees\_east = 15.723771 ;

:RawData\_Start\_Time\_UT = "220000" ;

:RawData\_Start\_Date = "20130620" ;

:Measurement\_ID = "20130620po00" ;

:Altitude\_meter\_asl = 760. ;

:RawData\_Stop\_Time\_UT = "230333" ;

:Latitude\_degrees\_north = 40.601039 ;

data:

channel\_ID = 10, 11, 12, 13 ;

Background\_Low = 30000, 30000, 30000, 30000 ;

Background\_High = 50000, 50000, 50000, 50000 ;

id\_timescale = 0, 0, 0, 0 ;

Laser\_Pointing\_Angle = 0 ;

Molecular\_Calc = 0 ;

Laser\_Pointing\_Angle\_of\_Profiles =

0,

0,

0 ;

Raw\_Data\_Start\_Time =

0,

300,

600 ;

Raw\_Data\_Stop\_Time =

210,

510,

810 ;

Laser\_Shots =

1200, 1200, 1200, 1200,

1200, 1200, 1200, 1200,

1200, 1200, 1200, 1200 ;

Pressure\_at\_Lidar\_Station = 1010 ;

Temperature\_at\_Lidar\_Station = 14 ;

Pol\_Calib\_Range\_Min = 1000, 1000, 1000, 1000 ;

Pol\_Calib\_Range\_Min = 2000, 2000, 2000, 2000 ;

Raw\_Lidar\_Data = …...;

The file above assume the following calibration measurements have been
done:

1. First +45 degrees acquisition followed by a corresponding -45 degrees
   acquisition

   a. Measurement at +45 degrees

Start Time: 20130620 22:00:00

Stop Time: 20130620 22:01:00

Shots: 1200

a. Measurement at -45 degrees

Start Time: 20130620 22:02:30

Stop Time: 20130620 22:03:30

Shots: 1200

1. Second +45 degrees acquisition followed by a corresponding -45
   degrees acquisition

   a. Measurement at +45 degrees

Start Time: 20130620 22:05:00

Stop Time: 20130620 22:06:00

Shots: 1200

a. Measurement at -45 degrees

Start Time: 20130620 22:07:30

Stop Time: 20130620 22:08:30

Shots: 1200

1. Third +45 degrees acquisition followed by a corresponding -45 degrees
   acquisition

   a. Measurement at +45 degrees

Start Time: 20130620 22:10:00

Stop Time: 20130620 22:11:00

Shots: 1200

a. Measurement at -45 degrees

Start Time: 20130620 22:12:30

Stop Time: 20130620 22:13:30

Shots: 1200

As you can see there are 3 cycles of consecutive measurements at +45 and
-45 degrees. That's way the dimension time is set to 3.

The first +/-45 degrees measurement starts at “20130620 22:00:00” (start
time of the first +45 measurement) and stops at “20130620 22:03:30”
(stop time of the fist -45 measurement). As a consequence, according to
the values of the global attributes RawData\_Start\_Date and
RawData\_Start\_Time\_UT we have to set:

Raw\_Data\_Start\_Time[0]=0 (start of the first +45 measurement in
seconds since RawData\_Start\_Time\_UT)

Raw\_Data\_Stop\_Time[0]=210 (stop of the first -45 measurement in
seconds since RawData\_Start\_Time\_UT)

Following a similar procedure for the other 2 cycles we have:

Raw\_Data\_Start\_Time[1]=300 (start of the second +45 measurement in
seconds since RawData\_Start\_Time\_UT)

Raw\_Data\_Stop\_Time[1]=510 (stop of the second -45 measurement in
seconds since RawData\_Start\_Time\_UT)

Raw\_Data\_Start\_Time[2]=600 (start of the third +45 measurement in
seconds since RawData\_Start\_Time\_UT)

Raw\_Data\_Stop\_Time[2]=810 (stop of the third -45 measurement in
seconds since RawData\_Start\_Time\_UT)

Moreover, according to the order of the channels in the channel\_ID
variable, the Raw\_Lidar\_Data array should be filled as it follows:

Raw\_Lidar\_Data[0][0][points] → 1\ :sup:`st` measured transmitted
signal at +45 degrees

Raw\_Lidar\_Data[0][1][points] → 1\ :sup:`st` measured reflected signal
at +45 degrees

Raw\_Lidar\_Data[0][2][points] → 1\ :sup:`st` measured transmitted
signal at -45 degrees

Raw\_Lidar\_Data[0][3][points] → 1\ :sup:`st` measured reflected signal
at -45 degrees

Raw\_Lidar\_Data[1][0][points] → 2\ :sup:`nd` measured transmitted
signal at +45 degrees

Raw\_Lidar\_Data[1][1][points] → 2\ :sup:`nd` measured reflected signal
at +45 degrees

Raw\_Lidar\_Data[1][2][points] → 2\ :sup:`nd` measured transmitted
signal at -45 degrees

Raw\_Lidar\_Data[1][3][points] → 2\ :sup:`nd` measured reflected signal
at -45 degrees

Raw\_Lidar\_Data[2][0][points] → 3\ :sup:`rd` measured transmitted
signal at +45 degrees

Raw\_Lidar\_Data[2][1][points] → 3\ :sup:`rd` measured reflected signal
at +45 degrees

Raw\_Lidar\_Data[2][2][points] → 3\ :sup:`rd` measured transmitted
signal at -45 degrees

Raw\_Lidar\_Data[2][3][points] → 3\ :sup:`rd` measured reflected signal
at -45 degrees

Once this file has been created it needs to be submitted to the SCC and
linked to the configuration “depol\_calibration”. The result of the SCC
analysis on this file will be the calculation of the calibration
constant h\ :sup:`\*` that will be logged into the SCC database and can
be used to calibrate Raman/Elastic backscat ter products (see section
3.3).

**Definition of “Raman/Elastic backscatter and linear depolarization ratio”**
-----------------------------------------------------------------------------

In order to calculate the *PLDR* we need to modify the polarization
related products linked to the “standard” measurement configurations
(the configuration called “nighttime” and/or “daytime” in table 3.2).

Let's suppose we have defined the following products (defined already in
SCC v3.11):

**Table 3.4:** Example of products configuration in SCC v3.11

+-----------------------+--------------+-----------------------+-------------+-----------+
| Product Name          | Product ID   | Product Type          | nighttime   | daytime   |
+-----------------------+--------------+-----------------------+-------------+-----------+
| Raman backscatter     | 1            | Raman backscatter     |            |           |
|                       |              |                       |             |           |
| 355nm                 |              |                       |             |           |
+-----------------------+--------------+-----------------------+-------------+-----------+
| Extinction            | 2            | Extinction            |            |           |
|                       |              |                       |             |           |
| 387nm                 |              |                       |             |           |
+-----------------------+--------------+-----------------------+-------------+-----------+
| Raman backscatter     | 3            | Raman backscatter     |            |           |
|                       |              |                       |             |           |
| 532nm                 |              |                       |             |           |
+-----------------------+--------------+-----------------------+-------------+-----------+
| Extinction            | 4            | Extinction            |            |           |
|                       |              |                       |             |           |
| 532nm                 |              |                       |             |           |
+-----------------------+--------------+-----------------------+-------------+-----------+
| Elastic backscatter   | 5            | Elastic backscatter   |             |          |
|                       |              |                       |             |           |
| 355nm                 |              |                       |             |           |
+-----------------------+--------------+-----------------------+-------------+-----------+
| Elastic backscatter   | 6            | Elastic backscatter   |             |          |
|                       |              |                       |             |           |
| 532nm                 |              |                       |             |           |
+-----------------------+--------------+-----------------------+-------------+-----------+
| Elastic backscatter   | 7            | Elastic backscatter   |            |          |
|                       |              |                       |             |           |
| 1064nm                |              |                       |             |           |
+-----------------------+--------------+-----------------------+-------------+-----------+

Product ID=1, 2, 4, 5, 7 do not need any modification as they do not
involve polarization channels. The only product that need to be modified
are the Product ID=3 and 6. To produce b532 files containing also *PLDR*
we need to modify the “nighttime” and “daytime” configurations to
include a product of type “Raman bakscatter and linear depolarization
ratio” or “Elastic bakscatter and linear depolarization ratio”
respectively. So the configuration reported in table 3.4 should be
changed to match what is included in table 3.5.

**Table 3.5:** The same of table 3.4 but with new product types
introduced in SCC v4.0

+-----------------------+--------------+-----------------------------------------------------------+-------------+-----------+
| Product Name          | Product ID   | Product Type                                              | nighttime   | daytime   |
+-----------------------+--------------+-----------------------------------------------------------+-------------+-----------+
| Raman backscatter     | 1            | Raman backscatter                                         |            |           |
|                       |              |                                                           |             |           |
| 355nm                 |              |                                                           |             |           |
+-----------------------+--------------+-----------------------------------------------------------+-------------+-----------+
| Extinction            | 2            | Extinction                                                |            |           |
|                       |              |                                                           |             |           |
| 387nm                 |              |                                                           |             |           |
+-----------------------+--------------+-----------------------------------------------------------+-------------+-----------+
| Raman backscatter     | 10           | **Raman backscatter and linear depolarization ratio**     |            |           |
|                       |              |                                                           |             |           |
| 532nm                 |              |                                                           |             |           |
+-----------------------+--------------+-----------------------------------------------------------+-------------+-----------+
| Extinction            | 4            | Extinction                                                |            |           |
|                       |              |                                                           |             |           |
| 532nm                 |              |                                                           |             |           |
+-----------------------+--------------+-----------------------------------------------------------+-------------+-----------+
| Elastic backscatter   | 5            | Elastic backscatter                                       |             |          |
|                       |              |                                                           |             |           |
| 355nm                 |              |                                                           |             |           |
+-----------------------+--------------+-----------------------------------------------------------+-------------+-----------+
| Elastic backscatter   | 11           | **Elastic backscatter and linear depolarization ratio**   |             |          |
|                       |              |                                                           |             |           |
| 532nm                 |              |                                                           |             |           |
+-----------------------+--------------+-----------------------------------------------------------+-------------+-----------+
| Elastic backscatter   | 7            | Elastic backscatter                                       |            |          |
|                       |              |                                                           |             |           |
| 1064nm                |              |                                                           |             |           |
+-----------------------+--------------+-----------------------------------------------------------+-------------+-----------+

As you can see in table 3.5, the old product IDs=3 and 6 (present in
table 3.4) have been replaced with the new product ID=10 and 11 to
guarantee the calculation of *PLDR*.

It is important to set among the product options of the product ID=10
and 11 which calibration product we want to use for calibration (see
section 3.2). This can be done using the SCC web interface setting the
appropriate setting in the tab *Polarization calibration products* (see
figure 3.4). According to the current example you should set here the
calibration product defined in section 3.2.

|image3| How to link a product to calibrate with a calibration product.

**WARNING:** Please not that also *Raman/Elastic backscatter products*
need to be linked to a calibration product because the calibration
constant and the corresponding correction factor is needed to calculate
the total signal out of the two polarization components even if the
*PLDR* is not involved in the product calculation.

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