The only option that comes to my mind is that you consider a social approach to the problem by asking the surrounding population for any particular sign of that date in terms of rain.

For example: An old woman may say that in 1 hour the rain filled a 1lt tray, etc.

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You have a gap. Make sure to note such in the footnotes or end notes.

The simplest advice I would offer is not to do field research where there is no data, especially research that needs tangible and not societal samples.

It is better to either change the period and duration of the search or the field of research

The presence of incomplete information will cause a defect in the research paper