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I am calculating changes in precipitation using the Delta method, wherein the relative changes are calculated thus:

Delta change = (modelled Future climatology (2050s) - modelled historical climatology (1981-2010)) / modelled historical climatology (1981-2010))

This Delta (or anomaly) data is added to the actual observations to produce a final bias corrected future projection for Precipitation using: Future projection = Observed climatology (1981-2010) * (1 + Delta change).

My problem is that there are some very large numbers being produced in the dataset (presumably due to dry areas having unrealistically large relative differences calculated between future and present). How can I account for this? They mention it in this paper: https://www.nature.com/articles/s41597-019-0343-8 but I don't follow exactly what they did:

We note that in very dry areas (i.e. monthly historical precipitation close to zero) relative changes could produce unreasonably large relative precipitation increases (e.g. Sahara Desert). To avoid this, we made two adjustments: (1) we set a threshold of 0.1 mm month−1 both for current and future GCM values, which prevents indetermination in Eq. 2; and (2) we truncate the top 2% of anomaly values to the 98th percentile value in the empirical probability distribution for each anomaly gridded dataset

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(1) we set a threshold of 0.1 mm month−1 both for current and future GCM values = they masked out all grid cells with less than 0.1 mm month−1 precipitation. That way they're avoiding dividing by very small numbers in what you correctly identified as dry areas

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(2) we truncate the top 2% of anomaly values to the 98th percentile value in the empirical probability distribution for each anomaly gridded dataset = for each delta dataset (or anomaly gridded dataset) they set all grid cells with anomalies greater than the 98th percentile to the value of the 98th percentile. Presumably to catch any outliers that were not addressed with the masking of dry areas.

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  • $\begingroup$ Thanks for your feedback. In relation to (1) we set a threshold of 0.1 mm month−1 both for current and future GCM values = they masked out all grid cells with less than 0.1 mm month−1 precipitation. That way they're avoiding dividing by very small numbers in what you correctly identified as dry areas. When you say they masked them out....Do you mean they are replaced with an 'NA' as opposed to any real number? $\endgroup$
    – matlabcat
    Commented Sep 13, 2021 at 11:00
  • $\begingroup$ Having looked at this further, it seems that using NA's will cause a problem of indetermination when calculating the relative changes for the Delta change. I wonder did they set every value below 0.1 to 0.1? That doesn't seem like a robust approach either..as you would be creating precipitation data where there was none before. $\endgroup$
    – matlabcat
    Commented Sep 13, 2021 at 12:50
  • $\begingroup$ Yes setting every value <0.1 to 0.1 doesn't seem right. I'd probably simply avoid calculating precipitation Deltas for those masked grid cells and set those grid cells to zero afterwards. $\endgroup$
    – Alex
    Commented Sep 15, 2021 at 8:56

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