Further linting of PFSes

Specifications/Surface-Temperature/README.md

@@ -10,6 +10,7 @@ The following files are the latest versions, and may include unreleased edits.
 The Markdown file is meant for editing through Pull Requests, all other files are for read-only purposes.
 
 - [**Markdown**](PFS.md)
+  - [Annex 1 - CARD4L Requirement Examples (Surface Temperature)](annex-1-card4l-requirement-examples.md)
 - Word (tbd)
 
 ## Released Version

Specifications/Synthetic-Aperture-Radar/annex-1.1-general-processing-roadmap.md

@@ -1,5 +1,5 @@
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-# **Annex 1.1: General Processing Roadmap**
+# Annex 1.1: General Processing Roadmap
 The radiometric interoperability of CEOS-ARD SAR products is ensured by a common processing chain during production. The recommended processing roadmap involves the following steps:
 
 - Apply the best possible orbit parameters to give the most accurate product possible. These will have been projected to an ellipsoidal model such as WGS84. To achieve the level of geometric accuracy required for the DEM-based correction, precise orbit determination will be required.
@@ -19,12 +19,12 @@ Table A1.1 lists possible sequential steps and existing software tools (e.g., Ga
 
 |**Step**|**Implementation option**|
 | :- | :- |
-|1\. Orbital data refinement|Check xml date and delivered format. RADARSAT-2, pre EDOT (July 2015) replace. Post July 2015, check if ‘DEF’, otherwise replace. (Gamma - RSAT2\_vec)|
-|2\. Apply radiometric scaling Look-Up Table (LUT) to Beta-Nought|<p>Specification of LUT on ingest. </p><p>(Gamma - par\_RSAT2\_SLC/SG)</p>|
-|3\. Generate covariance matrix elements|Gamma – COV\_MATRIX|
-|4\. Radiometric terrain normalisation|Gamma - geo\_radcal2|
-|5\. Speckle filtering (Boxcar or Sigma Lee)|Custom scripting|
-|6\. Geometric terrain correction/Geocoding|Gamma – gc\_map and geocode\_back|
-|7\. Create metadata|Custom scripting|
+|1. Orbital data refinement|Check xml date and delivered format. RADARSAT-2, pre EDOT (July 2015) replace. Post July 2015, check if ‘DEF’, otherwise replace. (Gamma - RSAT2\_vec)|
+|2. Apply radiometric scaling Look-Up Table (LUT) to Beta-Nought|<p>Specification of LUT on ingest. </p><p>(Gamma - par\_RSAT2\_SLC/SG)</p>|
+|3. Generate covariance matrix elements|Gamma – COV\_MATRIX|
+|4. Radiometric terrain normalisation|Gamma - geo\_radcal2|
+|5. Speckle filtering (Boxcar or Sigma Lee)|Custom scripting|
+|6. Geometric terrain correction/Geocoding|Gamma – gc\_map and geocode\_back|
+|7. Create metadata|Custom scripting|
 
 

Specifications/Synthetic-Aperture-Radar/annex-1.2-topographic-phase-removal.md

@@ -1,9 +1,9 @@
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-<a name="_heading=h.toui5ropweft"></a>
-# **A1.2: Topographic phase removal** 
+
+# A1.2: Topographic phase removal 
 InSAR analysis capabilities from CEOS-ARD SAR products are enabled with **[GSLC]** products, which is also the case when the Flattened Phase per-pixel data (item 3.7) are included in the **[NRB]** or **[POL]** products. This is made possible since the simulated topographic phase relative to a given reference orbit has been subtracted.
 
-From classical approach with SLC data, interferometric phase $\Delta \varphi_{1-2}$ between two SAR acquisitions is composed of a topographic phase $\Delta \varphi_{\text{Topo}\textunderscore1-2}$, a surface displacement phase $\Delta \varphi_{\text{Disp}\textunderscore1-2}$ and other noise terms $\Delta \varphi_{\text{Noise}\textunderscore1-2}$ (Eq. A1.1). The topographic phase consists to the difference in geometrical path length from each of the two antenna positions to the point on the SAR image ($\varphi_{\text{DEM}\textunderscore\text{SLC}}$) and is a function of their orbital baseline distance (Eq. A1.2). The surface displacement phase is related to the displacement of the surface that occurred in between the two acquisitions. The noise term is the function of the radar signal interaction with the atmosphere and the ionosphere during each acquisition and function of the system noise.
+From classical approach with SLC data, interferometric phase $`\Delta \varphi_{1-2}`$ between two SAR acquisitions is composed of a topographic phase $`\Delta \varphi_{\text{Topo}\textunderscore1-2}`$, a surface displacement phase $`\Delta \varphi_{\text{Disp}\textunderscore1-2}`$ and other noise terms $`\Delta \varphi_{\text{Noise}\textunderscore1-2}`$ (Eq. A1.1). The topographic phase consists to the difference in geometrical path length from each of the two antenna positions to the point on the SAR image ($`\varphi_{\text{DEM}\textunderscore\text{SLC}}`$) and is a function of their orbital baseline distance (Eq. A1.2). The surface displacement phase is related to the displacement of the surface that occurred in between the two acquisitions. The noise term is the function of the radar signal interaction with the atmosphere and the ionosphere during each acquisition and function of the system noise.
 
 $$\tag{Eq. A1.1}
 \Delta \varphi_{1-2} = \Delta \varphi_{\text{Topo}\textunderscore1-2} + \Delta \varphi_{\text{Disp}\textunderscore1-2} + \Delta \varphi_{\text{Noise}\textunderscore1-2}
@@ -15,58 +15,58 @@ $$\tag{Eq. A1.2}
 \Delta \varphi_{\text{Topo}\textunderscore1-2} = \varphi_{\text{DEM}\textunderscore\text{SLC}\textunderscore1} = \varphi_{\text{DEM}\textunderscore\text{SLC}\textunderscore2}
 $$
 
-Since CEOS-ARD products are already geocoded, it is important to remove the wrapped simulated topographic phase $\varphi_{\text{SimDEM}\textunderscore\text{SLC}}$ from the data in slant range (Eq. A1.3) during their production, before the geocoding step. The key here is to simulate the topographic phase relatively to a constant reference orbit, as done in a regular InSAR processing. There are two different ways to simulate the topographic phase: 
+Since CEOS-ARD products are already geocoded, it is important to remove the wrapped simulated topographic phase $`\varphi_{\text{SimDEM}\textunderscore\text{SLC}}`$ from the data in slant range (Eq. A1.3) during their production, before the geocoding step. The key here is to simulate the topographic phase relatively to a constant reference orbit, as done in a regular InSAR processing. There are two different ways to simulate the topographic phase: 
 
 1. The use of a virtual circular orbit above a nonrotating planet (Zebker et al., 2010) 
 2. The use of a specific orbit cycle or a simulated orbit of the SAR mission 
 
-In both cases, the InSAR topographic phase $\Delta \varphi_{\text{Topo}\textunderscore\text{OrbRef}-2}$ is simulated against the position of a virtual sensor $\Delta \varphi_{\text{Topo}\textunderscore\text{OrbRef}}$ lying on a reference orbit, instead of being simulated relatively to an existing reference SAR acquisition ($\varphi_{\text{DEM}\textunderscore\text{SLC}\textunderscore1}$). The use of a virtual circular orbit is a more robust approach since the reference orbit is defined at a fixed height above scene nadir and assuming the reference orbital height constant for all CEOS-ARD products. While with the second approach, the CEOS-ARD data producer must select a specific archived orbit cycle of the SAR mission or define a simulated one, from which the relative orbit, matching the one of the SAR acquisitions to be processed (to be converted to CEOS-ARD), is defined as the reference orbit. With this second approach, it is important to always use the same orbit cycle (or simulated orbit) for all the CEOS-ARD produced for a mission, in order to preserve the relevant compensated phase in between them. Providing absolute reference orbit number information in the metadata (item 1.7.15) allows users to validate the InSAR feasibility in between CEOS-ARD products.
+In both cases, the InSAR topographic phase $`\Delta \varphi_{\text{Topo}\textunderscore\text{OrbRef}-2}`$ is simulated against the position of a virtual sensor $`\Delta \varphi_{\text{Topo}\textunderscore\text{OrbRef}}`$ lying on a reference orbit, instead of being simulated relatively to an existing reference SAR acquisition ($`\varphi_{\text{DEM}\textunderscore\text{SLC}\textunderscore1}`$). The use of a virtual circular orbit is a more robust approach since the reference orbit is defined at a fixed height above scene nadir and assuming the reference orbital height constant for all CEOS-ARD products. While with the second approach, the CEOS-ARD data producer must select a specific archived orbit cycle of the SAR mission or define a simulated one, from which the relative orbit, matching the one of the SAR acquisitions to be processed (to be converted to CEOS-ARD), is defined as the reference orbit. With this second approach, it is important to always use the same orbit cycle (or simulated orbit) for all the CEOS-ARD produced for a mission, in order to preserve the relevant compensated phase in between them. Providing absolute reference orbit number information in the metadata (item 1.7.15) allows users to validate the InSAR feasibility in between CEOS-ARD products.
 
 $$ \tag{Eq. A1.3}
 \varphi_{\text{Flattended}\textunderscore\text{SLC}\textunderscore2} = \varphi_{\text{SLC}\textunderscore2} - \Delta\varphi_{\text{Topo}\textunderscore\text{OrbRef}-2} $$
 
 
-This procedure is equivalent to bring the position of the sensor platform of all the SAR acquisitions at the same orbital position (i.e., zeros baseline distance in between), which results in a Flattened phase  $\varphi_{\text{Flattended}\textunderscore\text{SLC}}$, independent of the local topography.
+This procedure is equivalent to bring the position of the sensor platform of all the SAR acquisitions at the same orbital position (i.e., zeros baseline distance in between), which results in a Flattened phase  $`\varphi_{\text{Flattended}\textunderscore\text{SLC}}`$, independent of the local topography.
 
 The phase subtraction could be performed by using a motion compensation approach (Zebker et al., 2010) or directly on the SLC data. Then the geometrical correction is performed on the Flattened SLC, which results in a **[GSLC]** product.
 #
 **[GSLC]** can also be saved as a **[NRB]** product by including the Flattened Phase per-pixel data (item 3.7) as follows:
 
-$$\text{NRB:} \quad \gamma_T^0 = |GSLC|^2 $$
+$$`\text{NRB:} \quad \gamma_T^0 = |GSLC|^2 `$$
 
-$$\text{Flattended Phase:} \quad \varphi_{\text{Flattended}} = \arg (GSLC) $$
+$$`\text{Flattended Phase:} \quad \varphi_{\text{Flattended}} = \arg (GSLC) `$$
 
 For **[POL]** product, the Flattened phase needs also to be subtracted from the complex number phase of the off-diagonal elements of the covariance matrix.
 
 Demonstration:
 
 From CEOS-ARD flattened SAR products, InSAR processing can be easily performed without dealing with topographic features and orbital sensor position, as for example with two **[GSLC]** products 
 
-$$ \varphi_{\text{Flattened}\textunderscore\text{GSLC}\textunderscore1} = \varphi_{\text{SLC}\textunderscore1} - \Delta\varphi_{\text{Topo}\textunderscore\text{OrbRef}-1} = \varphi_{\text{SLC}\textunderscore1} - \varphi_{\text{DEM}\textunderscore\text{OrbRef}} - \varphi_{\text{DEM}\textunderscore\text{SLC}\textunderscore1}$$
+$$` \varphi_{\text{Flattened}\textunderscore\text{GSLC}\textunderscore1} = \varphi_{\text{SLC}\textunderscore1} - \Delta\varphi_{\text{Topo}\textunderscore\text{OrbRef}-1} = \varphi_{\text{SLC}\textunderscore1} - \varphi_{\text{DEM}\textunderscore\text{OrbRef}} - \varphi_{\text{DEM}\textunderscore\text{SLC}\textunderscore1}`$$
 
-$$ \tag{Eq. A1.4} \varphi_{\text{Flattened}\textunderscore\text{GSLC}\textunderscore2} = \varphi_{\text{SLC}\textunderscore2} - \Delta\varphi_{\text{Topo}\textunderscore\text{OrbRef}-2} = \varphi_{\text{SLC}\textunderscore2} - \varphi_{\text{DEM}\textunderscore\text{OrbRef}} - \varphi_{\text{DEM}\textunderscore\text{SLC}\textunderscore2}$$
+$$` \tag{Eq. A1.4} \varphi_{\text{Flattened}\textunderscore\text{GSLC}\textunderscore2} = \varphi_{\text{SLC}\textunderscore2} - \Delta\varphi_{\text{Topo}\textunderscore\text{OrbRef}-2} = \varphi_{\text{SLC}\textunderscore2} - \varphi_{\text{DEM}\textunderscore\text{OrbRef}} - \varphi_{\text{DEM}\textunderscore\text{SLC}\textunderscore2}`$$
 
 
 The differential phase is
 
-$$ \tag{Eq. A1.5} \Delta \varphi_{\text{CARD}\textunderscore1-\text{CARD}\textunderscore2} =  \varphi_{\text{Flattened}\textunderscore\text{GSLC}\textunderscore1} - \varphi_{\text{Flattened}\textunderscore\text{GSLC}\textunderscore2} $$
+$$` \tag{Eq. A1.5} \Delta \varphi_{\text{CARD}\textunderscore1-\text{CARD}\textunderscore2} =  \varphi_{\text{Flattened}\textunderscore\text{GSLC}\textunderscore1} - \varphi_{\text{Flattened}\textunderscore\text{GSLC}\textunderscore2} `$$
 
 Which can be expanded using (Eq. A1.3)
 
-$$ \tag{Eq. A1.6} \Delta \varphi_{\text{CARD}\textunderscore1-\text{CARD}\textunderscore2} = (\varphi_{\text{SLC}\textunderscore1} - \varphi_{\text{DEM}\textunderscore\text{OrbRef}} - \varphi_{\text{DEM}\textunderscore\text{SLC}\textunderscore1}) - (\varphi_{\text{SLC}\textunderscore2} - \varphi_{\text{DEM}\textunderscore\text{OrbRef}} - \varphi_{\text{DEM}\textunderscore\text{SLC}\textunderscore2}) $$
+$$` \tag{Eq. A1.6} \Delta \varphi_{\text{CARD}\textunderscore1-\text{CARD}\textunderscore2} = (\varphi_{\text{SLC}\textunderscore1} - \varphi_{\text{DEM}\textunderscore\text{OrbRef}} - \varphi_{\text{DEM}\textunderscore\text{SLC}\textunderscore1}) - (\varphi_{\text{SLC}\textunderscore2} - \varphi_{\text{DEM}\textunderscore\text{OrbRef}} - \varphi_{\text{DEM}\textunderscore\text{SLC}\textunderscore2}) `$$
 
-$$ \tag{EQ. A1.7} \Delta \varphi_{\text{CARD}\textunderscore1-\text{CARD}\textunderscore2} = (\varphi_{\text{SLC}\textunderscore1} - \varphi_{\text{SLC}\textunderscore2}) - (\varphi_{\text{DEM}\textunderscore\text{SLC}\textunderscore1}) - \varphi_{\text{DEM}\textunderscore\text{SLC}\textunderscore2}) $$
+$$` \tag{EQ. A1.7} \Delta \varphi_{\text{CARD}\textunderscore1-\text{CARD}\textunderscore2} = (\varphi_{\text{SLC}\textunderscore1} - \varphi_{\text{SLC}\textunderscore2}) - (\varphi_{\text{DEM}\textunderscore\text{SLC}\textunderscore1}) - \varphi_{\text{DEM}\textunderscore\text{SLC}\textunderscore2}) `$$
 
-$$ \tag{EQ. A1.8} \Delta \varphi_{\text{CARD}\textunderscore1-\text{CARD}\textunderscore2} = \Delta\varphi_{\text{SLC}\textunderscore1-\text{SLC}\textunderscore2} - \Delta\varphi_{\text{Topo}\textunderscore1-2} $$
+$$` \tag{EQ. A1.8} \Delta \varphi_{\text{CARD}\textunderscore1-\text{CARD}\textunderscore2} = \Delta\varphi_{\text{SLC}\textunderscore1-\text{SLC}\textunderscore2} - \Delta\varphi_{\text{Topo}\textunderscore1-2} `$$
 
-Where $\Delta\varphi_{\text{SLC}\textunderscore1-\text{SLC}\textunderscore2}$ can be express as Eq. A1.1, which gives
+Where $`\Delta\varphi_{\text{SLC}\textunderscore1-\text{SLC}\textunderscore2}`$ can be express as Eq. A1.1, which gives
 
-$$ \tag{EQ. A1.9} \Delta \varphi_{\text{CARD}\textunderscore1-\text{CARD}\textunderscore2} = (\Delta \varphi_{\text{Topo}\textunderscore1-2} + \Delta \varphi_{\text{Disp}\textunderscore1-2} + \Delta \varphi_{\text{Noise}\textunderscore1-2}) - \Delta\varphi_{\text{Topo}\textunderscore1-2} $$
+$$` \tag{EQ. A1.9} \Delta \varphi_{\text{CARD}\textunderscore1-\text{CARD}\textunderscore2} = (\Delta \varphi_{\text{Topo}\textunderscore1-2} + \Delta \varphi_{\text{Disp}\textunderscore1-2} + \Delta \varphi_{\text{Noise}\textunderscore1-2}) - \Delta\varphi_{\text{Topo}\textunderscore1-2} `$$
 
 
 Consequently, the differential phase of two CEOS-ARD products doesn’t contain a topographic phase and is already unwrapped (at least over stable areas). It is only function of the surface displacement and of the noise term. Depending on the reference DEM and the satellite orbital state vector accuracies, some residual topographic phase could be present. Atmospheric (item 2.15) and ionospheric (item 2.16) phase corrections could be performed during the production of CEOS-ARD products, which reduces the differential phase noise in an InSAR analysis.
 
-$$ \tag{EQ. A1.9} \Delta \varphi_{\text{CARD}\textunderscore1-\text{CARD}\textunderscore2} = \Delta \varphi_{\text{Disp}\textunderscore1-2} + \Delta \varphi_{\text{Noise}\textunderscore1-2})$$
+$$` \tag{EQ. A1.9} \Delta \varphi_{\text{CARD}\textunderscore1-\text{CARD}\textunderscore2} = \Delta \varphi_{\text{Disp}\textunderscore1-2} + \Delta \varphi_{\text{Noise}\textunderscore1-2})`$$