Forecast error growth: A dynamic-stochastic model

Area of Science:

• Atmospheric sciences
• Meteorology
• Data science

Background:

• Numerical weather prediction (NWP) models have historically used simple error growth models.
• Existing models capture key properties but can be improved with advanced techniques.

Purpose of the Study:

• To propose a novel dynamic-stochastic scalar model for forecast error growth.
• To incorporate multiplicative noise within a nonlinear stochastic differential equation (SDE).

Main Methods:

• Developed a nonlinear stochastic differential equation (SDE) incorporating multiplicative noise.
• Analyzed the SDE's properties, including error growth curves and stationary distribution.
• Fitted the model to operational NWP error growth data.

Main Results:

• The proposed SDE model demonstrates well-posedness and positivity of solutions.
• The model shows good agreement with both mean and probabilistic aspects of NWP error growth.
• The model's dynamic-stochastic approach offers a robust framework for error prediction.

Conclusions:

• The new dynamic-stochastic error growth model provides an accurate representation of NWP error dynamics.
• This modeling approach has potential applications beyond meteorology in various predictive sciences.