Section 5 - Template 3 : Grid point data - complex packing and spatial differencing

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Notes:

( 1) Spatial differencing is a pre-processing before group splitting at encoding time. It is intended to reduce the size of sufficiently smooth fields, when combined with a splitting scheme as described in Data Representation Template 5.2. At order 1, an initial field of values f is replaced by a new field of values g, where g₁ = f₁, g₂ = f₂ - f₁, ..., g_n = f_n - f_n-1. At order 2, the field of values g is itself replaced by a new field of values h, where h₁ = f₁, h₂ = f₂, h₃ = g₃ - g₂, ..., h_n = g_n - g_n-1. To keep values positive, the overall minimum of the resulting field (either g_min or h_min) is removed. At decoding time, after bit string unpacking, the original scaled values are recovered by adding the overall minimum and summing up recursively.

( 2) For differencing of order n, the first n values in the array that are not missing are set to zero in the packed array. These dummy values are not used in unpacking.

( 3) See Data Template 7.3 and associated notes for complementary information.