Uncertainty bounds of a fitted curve from an observational datasets (water level VS discharge)

“Daily” river discharge/flow were hard to observe/obtain, so in practical, hydrologist takes several data at site which are water level and discharge datasets. They fit the data into a curve called rating curve. But the data is uncertain due to many factors. Im trying to look at certain framework to quantify the uncertainty bounds but couldn’t really understand. Im interested in this one paper that quantify uncertainty in that on-site stage-discharge measurement dataset. I have the sample for stage/water level-discharge dataset for you to show me exactly what this paper done for their datasets. Preferable using R language. Or if you have any solutions even if it is simple for quantifying the uncertainty, let me know.