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When data are packed in GRIB using the simple packing method, the values are packed by storing differences from the reference value (the minimum of all the values) to a specified fixed number of bits referred to as the "bits per value" (ecCodes key: bitsPerValue).  Thus the packing introduces a discretisation of the values with an associated packing error (ecCodes key:  packingError) such that:

\mathrm{\mathbf{packed\ value}} - \mathrm{\mathbf{packing\ error}} < \mathrm{\mathbf{true\ value}} =\leq \mathrm{\mathbf{packed\ value}} \pm+ \mathrm{\mathbf{packing\ error}}

The packing error depends on the range of vafieldslues field values and the number of bits per value used to pack the values.

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• All accumulations start with a zero value at step=0
• The values at all points are packed exactly

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• The model values increase at all points except the north west
• Not all values can be represented exactly using 8 bits per value
• In particular, the value of 0.031250 at the southern point is exactly the packing error and its packed value becomes 0.062500
• In this case, the packed values are all multiples of 2*packing error=0.0625 so values of 4.55, 5.9 and 2.2 are not stored precisely

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• Only the model value at the north east point increases

• The increase in the range of values increases the packing error by a factor of 2

• Now all packed values are multiples of 2*packing error=0.125

• The value at the central point of 4.55 is now packed as 4.5 compared to a packed value of 4.5625 at the previous step - a negative accumulation of -0.0625
• The value at the south west point of 2.2 is now packed as 2.25 compared to a packed value of 2.1857 at the previous step - a positive accumulation of +0.0625

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• Again only the model value at the north east point increases further from 20.0 to 40.0
• The increase in the range of values increases the packing error.
• Now all packed values are multiples of 2*packing error=0.25
• The model value at the eastern point is unchanged at 5.9 but now its packed value is 6.0 giving an apparent positive accumulation  of +0.125

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For accumulated fields, such as precipitation, the GRIB packing can have a strange affect on the totals, even when the data are used on the native model reduced Gaussian grid.  In some cases, the values concerned are sufficiently small that the issue can be ignored, but for others - for example when looking at the frequency of zero rain, or light drizzle on forecast day 10 - action is needed. The figures below highlight the issue is and its impacts:

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