Pool temperature
Monte Sano Club pool temp, measured and forecasted (see below for the forecast model), plotted against plateau air. The dotted line is what the forecast said in advance — drag the advance selector to grade it.
How the forecast is built
The forecast is a lumped energy-balance model of the pool integrated forward in 1-hour steps. The water is treated as one well-mixed body that gains and loses heat four ways:
- Convection with the air — proportional to the water–air temperature difference.
- Shortwave (solar) gain during the day.
- Evaporation — a wind- and humidity-driven latent heat loss (Bowen-ratio form).
- Longwave radiation to the sky, stronger on clear nights than under cloud (humidity-dependent Brutsaert emissivity).
The pool's thermal time constant is roughly two to three days, so each forecast is re-anchored on the latest sensor reading every hour. That anchor dominates the first day or two; by five-plus days out it has decayed away and the forecast is, in effect, an integral of the weather forecast — which is why the error grows with lead.
What feeds it, and why
We run the model separately against the global weather models that
publish a usable solar forecast (GFS, ICON, and Open-Meteo's blend) and
average the resulting pool curves into the headline forecast
(POOL_ENSEMBLE). No single model is reliably best at
multi-day range; the ensemble mean cancels their independent errors.
For the solar term we use each model's own surface-shortwave (GHI)
forecast rather than deriving it from cloud cover. We used to estimate
sunshine as clear-sky × (1 − 0.75 × cloud%), but that
linear knockdown over-attenuates real sunshine — an overcast sky still
passes about 40% of clear-sky radiation, not 25% — and it was biasing
the forecast 2–3°F cold over the back half of the week. Switching to the
forecast radiation directly, and re-centering the surface-absorptivity
coefficient from 0.85 to 0.72, removed that bias. Beyond three days, the
solar and wind inputs are faded toward a seasonal climatology, since the
raw forecasts of those two stop beating climatology around then.
A 12-day backtest against the sensor put the central forecast within about a degree at 1–2 days, ~1°F at 3–5 days, and a touch over a degree at a week — roughly half the error of the previous cloud-based model from two days out. The plateau PWS solar sensors, for what it's worth, read about half of true irradiance, so they're not used here — only the model GHI forecasts and a satellite reanalysis are.