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SST record 17 km cell MDS
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2.6.1.1.5.3 Calculate Solar Angles

Solar and viewing angles required for cloud clearing are also determined at this stage. The angles are calculated at a series of tie points across the scan at increments of 25 km in the across-track co-ordinate x; these values are required for internal use within the processor, although only values at 50 km intervals are output to the product.

The following angles are calculated:

  • The azimuth of the sun at the pixel;
  • The elevation of the sun as seen from the pixel;
  • The azimuth of the sub-satellite point measured at the pixel.
  • The elevation of the satellite as seen from the pixel.

These quantities are required for use by the 1.6 micron cloud clearing test, to identify situations in which sun-glint might be present, while the solar elevation is also used to distinguish day and night measurements in cloud clearing and level 2 processing. The satellite azimuth and elevation are also used in the calculation of the topographic correction.

The solar and viewing angles are calculated at the centres and edges of the across-track bands defined in Section 2.3.1. . These correspond to a series of across-track positions separated by 25 km. Thus if we define an index k, the solar angles are calculated for nominal across-track co-ordinates

x = 25(k – 10) km

for k = 0, 20. In this formulation even values of k correspond to the band edges, and odd values of k to the band-centres. Internally within the processor values are calculated for both band centres and band edges and for every instrument scan, but only the band edge values on the granule rows are output to the product ADS.

Although defined at the nominal positions in the equation above, in practice the angles are calculated for specific instrument pixels. For each view and for every tenth instrument scan, and for each value of k, the instrument pixel whose across-track co-ordinate is closest to the nominal value given by equation (3.1) is identified, and its line of sight azimuth and elevation (measured at the satellite) are derived using the same algebra as in Section 2.6.1.1.5.1.1. . The calculation of the angles is then carried out using the standard ENVISAT mission CFI subroutine pp_target (Reference: Document PO-IS-GMV-GS-0559, PPF_POINTING Software User Manual) with the scan time and the line of sight azimuth and elevation as parameters.

Results for intermediate instrument scans are calculated by linear interpolation with respect to scan number for each across-track distance, and the results are regridded to the image rows in a similar way to the pixel data.

2.6.1.1.5.4 Calculate Topographic Corrections

For those scan pixels that coincide with tie points for which topographic corrections are required, and that are over land, the topographic height is determined from a digital terrain model and topographic corrections to the latitude and longitude are calculated.

2.6.1.1.5.4.1 Theoretical Basis

The pixel geolocation described in Section 2.6.1.1.5.1. finds the intersection of the line of sight from the instrument with the reference ellipsoid. If the land surface is elevated by an amount H above the reference surface, the intersection of the line of sight with the land surface, which is the true pixel position, is displaced towards the satellite in the direction of the projected line of sight by an amount that is proportional to the elevation H.

Let the unit vector from the pixel to the satellite be k = (kx, ky, kz). If the azimuth and elevation of the line of sight at the pixel are a, e respectively, then the components of the unit vector k are

eq 2.128

eq 2.129

eq 2.130

expressed in a local co-ordinate system in which the x axis is directed to the east, the y axis is directed to the north parallel to the local meridian, and the z axis is vertical.

The pixel position is displaced by linear amounts

eq 2.131

eq 2.132

The corrections in latitude and longitude are the corresponding angular displacements:

eq 2.133
,

eq 2.134
,

where φ is the latitude of the pixel. Here R and N are the two orthogonal radii of curvature of the Earth at latitude φ; N and R are the radii of curvature in prime vertical and in the meridian respectively, given by

eq 2.135
,

eq 2.136
,

eq 2.137
,

where e is the eccentricity of the reference ellipsoid, and the geodetic constant

eq 2.138
.

The quantity N cos φ is the radius of the parallel of latitude at φ.

2.6.1.1.5.4.2 Algorithm Description

The topographic corrections are computed for the same tie points as the image pixel latitude and longitude. This method makes use of the satellite viewing angles for the appropriate view and tie point previously computed. The topographic height is determined from a digital elevation model.

The nominal tie points are at across-track distances x = {-275, -250, -225, ... 275} km, corresponding to an across-track index k through x = 25(k – 11) km, k = (0, ... 22). However, if k = 0 or k = 22, no viewing angles will be available from the solar and viewing angles calculation, and so these cases are omitted.

The algorithm is applied to both nadir and forward view instrument scans. For each scan, the algorithm steps are as follows.

  • For each across-track distance for which a correction is required, the index p of the instrument pixel is found whose across-track co-ordinate is closest to the required across-track distance. The latitude φ and longitude λ of this pixel are found.
  • The local altitude (over land) or bathymetry (over sea), H, at latitude φ and longitude λ is extracted from the digital elevation model.
  • The pixel is regridded to the appropriate image row. Steps 4 and 5 are performed only if the pixel regrids to a tie row.
  • If H < 0 (note this includes the case that the pixel is over sea), the latitude and longitude corrections are set to zero and Step 5 is omitted.
  • If H ³ 0 the satellite azimuth and elevation corresponding to the pixel, calculated in the solar and viewing angles module (Section 2.6.1.1.5.3), are extracted and converted to radians, and the latitude and longitude corrections d φ, d λ are calculated using equations ( eq. 2.131 ) to ( eq. 2.138 ) in Section 2.6.1.1.5.4.1. above.

Note that the corrections are the quantities to be added to the nominal latitude and longitude to give the topographically corrected values.