One of New Zealand's most disastrous examples of this knock-on effect was the 2016 Havelock North gastro outbreak, which may have affected more than 8000 people, and was implicated in at least four deaths.
But Lai said it wasn't known whether this heightened risk differed between typically wet and dry regions of New Zealand.
Along with historical rainfall records, he and colleagues analysed health data from a cohort of children born in 2009 and 2010.
They found children in areas with the lowest and highest long-term rainfall were even more likely to get sick - potentially because the ground absorbed less water in those areas, meaning more runoff ended up in the drinking water supply.
In these regions, they found the risk of hospitalisation was especially higher two days after heavy rainfall days.
Further, the researchers found there was a health risk well below MetService's working criteria of a "severe weather warning" - or when rainfall over an area of more than 1000sq m was forecast to exceed 100mm over 24 hours, or 50mm over six hours.
Rather, they found evidence of children becoming sick after rainfall totalling just 16.3mm over 24 hours.
In their study, just published in the journal Environment International, Lai and his colleagues pointed to global warming projections of more intense precipitation, against a background of increasing and severe droughts and flooding.
"The effects on child health world-wide are likely to be considerable, given diarrhoeal diseases are already a leading cause of morbidity and mortality," they said.
"We note also that hospitalisations, the focus of this study, include only a small fraction of all episodes of enteric disease among children."
Lai told the Herald that, in New Zealand's case, more thought could be given to how severe weather warnings should be set - especially in the context of public health.
"We should talk about whether a different approach to our warning system is needed to protect public health," he said, adding that boil water notices could even be issued as precautions.
The paper follows another major study, led by ESR, that used a DNA analysis to find the Havelock North outbreak might have been much more severe than first thought.
It suggested extra safeguards were needed to protect populations from such drinking water outbreaks, in light of expected increases in heavy rainfall events with climate change, but also further intensification of agriculture.
They suggested more work needed to be put into source protection, suitable water treatment, regular monitoring of water, and epidemiological surveillance of disease incidence.
The Government has already taken a raft of actions, including setting up an independent national regulator of drinking water supplies, and recently invested more than $760m to help councils upgrade run down water services.
