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The resolution of such data is identified by the triangular truncation number which specifies the number of coefficients retained in the infinite sum. This number is stored in GRIB as the pentagonal resolution parameters, J, K and M:
ecCodes key | content | GRIB edition 1 | GRIB edition 2 |
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J | J pentagonal resolution parameter | Section 2 Octets 7-8 | Section 3 Octets 15-18 |
K | K pentagonal resolution parameter | Section 2 Octets 9-10 | Section 3 Octets 19-22 |
M | M pentagonal resolution parameter | Section 2 Octets 11-12 | Section 3 Octets 23-26 |
The pentagonal representation of resolution is general and the triangular representation used by ECMWF is a specific case with M = J = K. The truncation number, and hence the resolution of the data, can be obtained by querying the value of any one of these keys. Most usually, the value of J - or its alias pentagonalResolutionParameterJ - is used:
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It is not possible to relate the resolution of the spherical harmonic data directly to the resolution of the corresponding grid as this depends on the specific relationship between the spectral representation and the Gaussian grid used by the IFS. Three different relationships have been used by ECMWF over the years. For a triangular truncation of T, the corresponding Gaussian grid resolutions are:
Relationship | Gaussian grid resolution |
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linear | N = (T + 1) / 2 |
quadratic | N = 3 (T+1) / 4 |
cubic | N = T + 1 |
where N corresponds to the number of latitude lines between the poles and the equator. However, to determine which relationship was used when the data were produced requires interrogation of a corresponding grid point field.
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