Interactive educational tools and outreach projects for learning about climate change, weather forecasting, and data assimilation

This page hosts a collection of interactive educational tools and outreach projects designed to support learning about climate change, weather forecasting, and data assimilation. The materials are intended for both secondary-school and university-level teaching, with the aim of making complex scientific concepts more accessible and engaging.

• Web application — Lorenz-63 and Data Assimilation Tool

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  This tool is designed for educational purposes and can be used to explore chaotic systems and understand how forecasts can be improved through the assimilation of observations. It combines the Lorenz-63 model with a simplified data-assimilation method.

  The Lorenz-63 model is a simplified dynamical system that exhibits chaotic behaviour, making it a useful example for studying the sensitivity of forecasts to their initial conditions. It consists of three ordinary differential equations:

  \[ \begin{aligned} \frac{dx}{dt} &= \sigma (y - x) \\ \frac{dy}{dt} &= x (\rho - z) - y \\ \frac{dz}{dt} &= xy - \beta z \end{aligned} \]

  The model provides an idealised representation of fluid convection and illustrates how small differences in the initial state can lead to increasingly different trajectories over time. In weather forecasting, this sensitivity to initial conditions is one of the reasons why forecast uncertainty increases with lead time. The Lorenz-63 system is therefore a classic example for introducing deterministic chaos and the limitations of predictability.

  The tool allows users to interact with the Lorenz-63 model and observe how a forecast evolves over time. Model parameters and initial conditions can be modified to investigate their effect on the forecast trajectory. The animation compares the true state with a forecast, allowing users to observe how initially similar trajectories progressively diverge.

  The data-assimilation component allows observations to be incorporated into the model in order to improve the forecast. Synthetic observations are generated by perturbing the true state according to the prescribed observation uncertainty, \(\sigma_{\text{obs}}\). Users can modify both the observation uncertainty and the observation interval to explore how these choices affect the analysis and subsequent forecast.

  The data-assimilation method is a simplified one-dimensional Kalman-filter formulation. The Kalman gain is defined as:

  \[ K = \frac{ \sigma^2_{\text{model}} }{ \sigma^2_{\text{model}} + \sigma^2_{\text{obs}} } \]

  Users can also modify \(\sigma_{\text{model}}\), which directly affects the Kalman gain and therefore the relative weight given to the model forecast and the observations.

  The analysis equations for the three Lorenz-63 components are:

  \[ \begin{aligned} x_a &= x_f + K(x_o - x_f) \\ y_a &= y_f + K(y_o - y_f) \\ z_a &= z_f + K(z_o - z_f) \end{aligned} \]

  These equations are used to compute the analysis, which then provides the initial conditions for the next forecast cycle. The user can therefore observe how repeated assimilation of observations helps keep the forecast closer to the true state.

  Questions for students

  • What is the difference between the true state and the forecast state?
  • Why is the true atmospheric state never known exactly in real forecasting applications?
  • Why does forecast skill generally decrease as lead time increases?
  • How does the forecast change when observations are assimilated?
  • What is the impact of observation uncertainty on the analysis and subsequent forecast?
  • What is the impact of the observation interval on the analysis and subsequent forecast?
  • What happens when \(\sigma_{\text{model}} \gg \sigma_{\text{obs}}\)?
  • What happens when \(\sigma_{\text{obs}} \gg \sigma_{\text{model}}\)?
  • What happens when \(\sigma_{\text{obs}} = \sigma_{\text{model}}\)?
  • Why is data assimilation useful in weather forecasting?
  • What other applications could benefit from data assimilation?

  How to use the tool

  Download the ZIP archive and extract it. Open the extracted folder and then open index.html in a web browser.

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• Project — Dal Meteo all'Emergenza Climatica: un percorso educativo tra scienza, consapevolezza e futuro

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  IT
  Il progetto “Dal Meteo all’Emergenza Climatica: un percorso educativo tra scienza, consapevolezza e futuro” , sviluppato in collaborazione con il professor Simone Napolitano, è un percorso interdisciplinare di circa 20 ore rivolto alla classe 2LD del Liceo Artistico “G. Romano” di Mantova. Il progetto integra Educazione civica, Scienze, Matematica e Informatica. L’obiettivo è sviluppare negli studenti una comprensione scientificamente fondata del cambiamento climatico, distinguendo in modo rigoroso meteo e clima, contrastando misconcezioni diffuse e potenziando competenze di analisi dei dati, valutazione critica delle fonti e cittadinanza attiva.

  Il percorso prevede un test diagnostico iniziale, una fase di ricerca cooperativa sul tema dell'emergenza climatica con produzione di elaborati multimediali e successiva discussione, e due lezioni dedicate a caos deterministico, affidabilità delle previsioni, fake news e lettura di grafici e indicatori provenienti da fonti quali IPCC, Copernicus, ECMWF e NASA. La valutazione avviene tramite una rubrica multidimensionale che considera contenuti, competenze e soft skills, evidenziando punti di forza e criticità, in particolare nell’uso delle fonti e nella comprensione delle relazioni causa–effetto. Il progetto si propone come modello replicabile nel biennio e ampliabile nel triennio con approfondimenti su teoria del caos e sistemi complessi.

  ENG
  The project “From Weather to the Climate Emergency: an educational pathway between science, awareness, and the future” , developed in collaboration with Professor Simone Napolitano, is an interdisciplinary programme of approximately 20 hours designed for class 2LD at the “G. Romano” Art High School in Mantua. It integrates Civic Education, Science, Mathematics, and Computer Science. The aim is to help students develop a scientifically grounded understanding of climate change by rigorously distinguishing between weather and climate, addressing common misconceptions, and strengthening skills in data analysis, critical evaluation of sources, and active citizenship.

  The programme includes an initial diagnostic test, a cooperative research phase on the climate emergency with the production and discussion of multimedia materials, and two lessons on deterministic chaos, forecast reliability, misinformation, and the interpretation of graphs and indicators from sources such as IPCC, Copernicus, ECMWF, and NASA. Assessment is carried out using a multidimensional rubric covering knowledge, competencies, and soft skills, with particular attention to the use of sources and understanding of cause-and-effect relationships. The project is intended as a replicable model for the first two years of secondary school and can be extended in later years through further study of chaos theory and complex systems.