Mathematics and Hydrology Questions 2025

At the recent workshop between mathematical and flood risk communities, participants were asked early in the workshop to pose those questions they were interested in answering. Some of the responses are recorded below.

We did some filtering of the questions into general subject areas (biased to maths).

One group indicated whether the “flow” of the question was directed from Hydrology to Maths (H to M) or vice versa.

1. (H to M) How can we compare models to assess fitness-for-purpose?
2. (M to H) What (else) can you extract or derive from models to enable comparison? [reduced order models of dynamics]
3. (M to H) Why would SHETRAN (a physics-based model) perform worse than LSTM (ML)?
4. Does NSE do an effective job in distinguishing good or bad models? And parameter sets?
5. What techniques/approaches exist for robust model comparison?

1. Can insight of ML + blended models lead to development of better low-dimensional models?

1. (M to H) How are hydrologists destroying mass?
2. (H to M) What scaling laws exist? (e.g. for whole hydrological systems)
3. (M to H) Could viewing hydrology as an inverse problem give us insights about the influence of catchment features?
4. (M to H) What is the minimum amount of data to solve the inverse problem?

1. (H to M) How do we estimate extreme events from limited data?
2. (H to M) How can we better quantify uncertainty? And how do we assess the priorities for investment of a fixed budget to reduce uncertainty in decisions?
3. (H to M) Is it more useful to collect a small amount of data everywhere or a lot in a few places?
4. Are there new data collection methods that could be utilised?
5. How to evaluate flows given uncertainties?
6. What metrics do you use for high flows?
7. How/can you use ML in low data environments?
8. What techniques exist for collapsing spatial information?
9. What rainfall data do you use? How do you measure discharge? Does it matter?