DS-05 · Forecasting the James

Given upstream gauge readings and rainfall, can you predict James River stage at Richmond 12 hours ahead well enough to be useful to someone deciding whether to move a boat?

USGS National Water Information System instantaneous values (https://waterdata.usgs.gov/). NOAA precipitation (https://www.ncei.noaa.gov/products/land-based-station/global-historical-climatology-network-daily).

River stage is highly autocorrelated — a naive "same as now" model is very strong at 12 hours and students routinely fail to beat it. Flood events are rare and are the only ones that matter; a model trained on all data optimizes for tranquility. Upstream travel time is a real physical lag that must be discovered, not assumed.

A 12-hour-ahead stage forecast evaluated separately on ordinary conditions and on the highest-decile events, against persistence, with the discovered upstream lag reported.

CT: understanding why persistence is hard to beat. CR: finding the lag empirically via cross-correlation. CO: dividing gauge sites and merging findings. CM: a plain-language risk statement. CZ: flood warnings are life-safety — overconfidence has a cost.

A hydrologist, civil engineer, or emergency-management analyst reviews lag analysis at Checkpoint 1 and event-conditional evaluation at Checkpoint 2. School-supervised.

R1: horizon and site fixed and justified. R2: gauge outages handled. R3: persistence beaten, or the failure honestly reported. R4: rare-event performance reported separately — this is the whole assignment. R5: a boater could use it. R6: states clearly it is not a flood warning system.

(a) The student reports R² of 0.99, which persistence also achieves, and concludes the model works. (b) The student trains on all hours, never evaluates on flood events, and ships a model that is worst exactly when stage matters.