How flow, comfort and difficulty are calculated

A concrete example

Take a Semois whose baseline currently stands at 1.3 m³/s (late summer, low water), with a current flow of 1.3 m³/s (Semois K_base = 0.07). The wetness modulator is 1.3 / 1.3 = 1.0, giving a runoff coefficient K = 0.07 × 1.0 = 0.07. Tomorrow 16 mm of rain is forecast with a reliability of 75%, following 3.5 mm today.

The next day's calculation unfolds as follows : the decayed flow stays close to the baseline → 1.3 + (1.3 − 1.3) × 0.75 = 1.3 m³/s. The runoff adds (16 × 0.60 + 3.5 × 0.40) × 0.07 × 0.75 ≈ 0.64 m³/s. The next day's forecast is therefore about 1.9 m³/s (1.3 + 0.64) — a noticeable but realistic rise, compared with the old coefficients which, for this same scenario, would have announced more than 4 m³/s. Every number remains traceable : that is the whole point of a legible model.

The self-learning loop: how we measure our own errors

A transparent model must also be verifiable over time. Every forecast we publish is archived (calculation date, target day, forecast rain, predicted flow) are stored in our database. Each night, the previous day's forecasts are compared with the actually measured flow for that day, and record the gap. This memory of our own errors is what allowed us to identify, in mid-August 2026, the optimistic bias corrected above : without it, we would have had no objective way to know that the model was wrong, nor by how much. It also lets us keep refining every coefficient over the coming months, as the history grows.

Why a simple model rather than an « AI »?

Stacking an opaque neural network on top of this data would be tempting. We chose the opposite, and on purpose. A physical and interpretable model has three decisive advantages in a safety context : it is explainable (each output is justified by a formula), it fails predictably (we know why it is wrong, usually because of a bad rain forecast), and it stays robust even with a limited history, whereas a learned model would need years of data and could hallucinate aberrant values.

Each coefficient — the 1/3-2/3 weighting of the baseline, the 0.75 decay factor, the 60/40 split of the runoff — has a physical meaning and can be discussed, adjusted, audited. In our eyes, that is the condition for information on which one accepts to stake the safety of paddlers. Sophistication is not an end in itself : verifiable reliability is.

Archiving: the memory of the river

The whole model rests on one condition : having a clean history of the flow. With each refresh, the SPW measurement is recorded in our tables (etat_navigation_semois, and the equivalent for each river), keeping only physically plausible values. This memory, built day after day, is what allows us to compute a representative baseline and to adapt the model to the particularities of each watercourse. Without it, no serious forecast would be possible : a river can only be understood over time.

These archived data also feed our threshold tables and our open exports. The loop is virtuous : the richer the history, the more accurate the baseline, and the more the forecast matches the actual behaviour observed in the field.

Part 2 — Thermal comfort (windchill)

A favourable flow says nothing about the feel on the water. In a cool wind, the sensation of cold can be far more severe than the thermometer suggests : this is what's called windchill. We use the official wind chill formula adopted by weather services (the same one used by Environment Canada), which combines air temperature and wind speed :

Below 4.8 km/h, the wind's effect on heat loss is considered negligible : the felt temperature simply equals the air temperature. Above that, the formula reflects a real physical phenomenon : the wind strips away the thin layer of air warmed by the body, speeding up heat loss. Example : at 12°C with 25 km/h of wind, the felt temperature drops to around 8.3°C — a gap of nearly 4 degrees, which concretely changes the gear you need.

This felt temperature is only half the equation : we cross it with the actual water temperature, measured at the station, to determine a risk level and matching equipment advice :

• High hypothermia risk — felt temperature below 0°C or water below 8°C : full neoprene wetsuit mandatory, outing reserved for equipped experts.
• Cold water — felt temperature below 8°C or water below 12°C : life jacket mandatory, caution recommended.
• Storm reported : paddling not advised regardless of temperatures.
• Correct conditions — felt temperature below 15°C : standard gear, life jacket recommended.
• Ideal conditions — above that : light clothing, life jacket and water shoes are enough.

This is the engine that feeds the live felt-temperature figure shown on each river dashboard, next to water and air temperature.

Part 3 — Comfort Index and Difficulty Score

Beyond flow and felt temperature taken in isolation, we compute two summary indicators to answer, at a glance, the question "should I go out today ?". They rest on different logics, and we say so honestly : they are not two ways of measuring the same thing.

The Comfort Index (out of 100) starts from a perfect score and subtracts penalties based on the day's measured conditions :

The result is capped at 0 if the river is closed to navigation — comfort then no longer makes sense, and the index says so plainly. Example : open river, flow at 18 m³/s (within the ideal zone, no penalty), water at 10°C (−30), calm wind : the Comfort Index shows 70/100, and the "hypothermia risk" flag explains the drop.

The Difficulty Score (also out of 100, but where a high score signals a more demanding outing) follows a separate multi-factor logic : a "flow" sub-score (low, ideal, fast, or dangerous in flood) weighted at 60 %, combined with a "weather" sub-score (strong wind, precipitation, cold temperature) weighted at 40 % :

With a safety override : in case of a forecast storm or flood-level flow, the score jumps straight to 100, without waiting for the weighted average. The final score sorts the outing into four levels : easy (≤25), moderate (≤50), difficult (≤75) or very difficult / dangerous (>75). For transparency : our open-data export (JSON-LD Dataset) uses, to keep the export simple, an approximation of the difficulty score equal to 100 minus the Comfort Index ; the detailed multi-factor calculation above is the one used by our real-time weather analysis tools. Both remain consistent in spirit — a less comfortable river is, almost always, also the more difficult one.

The limits, stated honestly

No model can predict a river's future with certainty, and claiming otherwise would be dangerous. Here is what the flow forecast does not do : it does not capture the very localised storms that can swell a tributary within hours ; it depends entirely on the quality of the weather forecast, whose uncertainty grows with the horizon ; it ignores structure operations (dams, sluices) and certain snowmelt phenomena. Hence its reliability is excellent at 24 h and degrades beyond that.

We also resist the temptation to over-promise precision. A forecast expressed to the nearest tenth of a cubic metre per second can give a false sense of certainty ; in reality the meaningful information is the direction and magnitude of the change — is the river rising sharply, drifting back to normal, or holding steady? That is why our dashboards favour a readable trend over a spurious decimal, and why we always pair the number with a plain-language navigation status. Honesty about uncertainty is, in our view, part of the safety message itself : a paddler who understands that a three-day forecast is indicative, not guaranteed, makes better decisions than one lulled by a falsely precise figure.

Windchill, for its part, is a standard meteorological formula : it describes an average felt sensation, not your individual one (acclimatisation, physical effort or clothing all make it vary). The Comfort Index and the Difficulty Score are simple, deliberately legible rules : they replace neither a full weather bulletin, nor your own assessment of the terrain, nor a guide's experience. None of these three calculations knows your exact local conditions or your personal skill level.

Our golden rule, which we repeat everywhere : you book on a trend, but you paddle on a measurement. The forecast serves to plan an outing and to avoid a pointless trip ; the final decision to put in is always taken on the actual flow of the day, the measured felt temperature and the official navigation status. If conditions are not met, our cancellation policy protects you.

Why publish this method?

Because trust is built on transparency. When it comes to safety, an opaque figure is worth nothing : you must be able to know where it comes from and what it is worth. By documenting these three models, we let everyone — paddler, rescuer, journalist, fellow operator — understand, verify and challenge our work, including when we correct our own mistakes, as we did on 26 August 2026. This approach extends our commitment to open data built around the official SPW thresholds, which are already published and exportable. See also our changelog for the full history of changes.

These models can be improved and keep evolving with the seasons and with field observations. They come from years of paddling on the Semois and from daily monitoring of the region's hydrological data, and we offer this know-how freely in the service of your safety.