Atmos — Weather, in perspective

WEATHER INTELLIGENCE—

Oxford

United Kingdom

—^°C

Reading the atmosphereLive forecast loading

A clearer view of the hours ahead.

↑ — High↓ — Low↗ — Gusts

↗ WIND

—km/h

At 10 metres

◒ HUMIDITY

—%

Relative humidity

☂ PRECIPITATION

—mm

Today’s total

☀ UV INDEX

—/ 11+

Daily maximum

LOOKING AHEAD

The next 24 hours

A LITTLE DAYLIGHT

Follow the sun

Sunrise—

Sunset—

— hours of daylight

THE BIGGER PICTURE

Your week, at a glance

Seven-day outlook

GO BEYOND THE FORECAST

What if you could look inside the model?

Explore solar forcing, thermal memory and Runge–Kutta integration in the forecast lab.

NUMERICAL WEATHER LABORATORY

A forecast you can take apart.

A corrected, browser-native evolution of the original temperature model. Tune thermal response and solar forcing, then compare against a held-out day of weather-model data.

Inside the atmosphere

Thermal relaxation 0.5 h⁻¹Previous-day memory 0.2 h⁻¹Solar heating 0.4 °C/h

Parameter fitting uses the day before the held-out reference. Moving the sliders afterward is exploratory tuning.

dT/dt = α(T_target − T)
+ m(T_previous − T)
+ β · solar(t)

Fourth-order Runge–Kutta · 5-minute steps · consistent hourly units

HOLD-OUT COMPARISON

Yesterday, reconstructed

RK4 modelReference24h persistence

Load a location to run the numerical experiment. The reference uses historical weather-model values from Open-Meteo, not station observations. This does not establish accuracy against measured weather.

THE SCIENCE, IN THE OPEN

Two forecasts. Different questions.

The overview answers “what weather is expected?” The laboratory asks “how does a simple numerical temperature model behave?”

01 / Live weather

Open-Meteo combines numerical weather prediction models to provide current conditions and hourly and daily forecasts. This app displays those predictions with their location, model time and data source.

Read the forecast documentation ↗

02 / An interpretable model

The laboratory evolves temperature from thermal relaxation, the previous day’s profile and a daylight heating term. It corrects the original notebook’s RK4 initialization, intermediate-stage evaluation, time units and calendar handling.

Parameters are fitted on an earlier day. The following day is held out for comparison with historical model values. The persistence baseline repeats the previous day at the same hour.

03 / What the scores mean

MAE measures average absolute temperature error. RMSE gives larger errors more weight. Skill is measured relative to 24-hour persistence. A negative skill score means the numerical model was worse on that reference day.

The experiment is small, uses model-derived reference data, and is not a validated weather forecasting service.

04 / Built to be explored

Everything runs in your browser. No accounts or API keys. Saved Oxford data is clearly marked with its acquisition date and can be explored when the live service is unavailable.

Explore the original notebook ↗

Created by Fyodor Amanov. original numerical-methods project retained in the repository.