Simplified Wind Speed and Temperature Models for Extreme Cold Weather Prediction

Recently, many regions of China have experienced extreme cold weather, significantly affecting daily life and the environment. Understanding and forecasting wind speed and temperature under such conditions is crucial because they influence climate patterns, energy consumption, traffic safety, and agriculture.

Wind Speed Model

Wind speed models are usually based on fluid dynamics principles, especially the Navier‑Stokes equations. For practical applications, a simplified model is often used. Here we present a basic one‑dimensional linear model describing wind speed variation over time.

A simplified wind speed model can use a one‑dimensional linear equation to describe the temporal change of wind speed. Let v(t) denote wind speed at time t , which can be expressed as:

dv/dt = -k·v + F , where k is a positive constant representing air resistance damping, and F denotes external driving forces such as temperature differences or terrain effects (e.g., sea‑land breezes or valley winds).

Temperature Model

Cold‑weather temperature models can be built by considering energy balance. Using a simplified heat‑balance model, temperature variation can be described. Let T(t) be temperature at time t , expressed as:

dT/dt = (Q_in - Q_out)/C , where Q_in and Q_out represent heat gained and lost per unit time, including solar radiation, ground heat exchange, and atmospheric cooling. C is the heat capacity, reflecting the system’s thermal inertia.

Combined Model

By coupling the wind speed and temperature models, we can analyze their interaction. For example, increased wind speed can enhance heat loss, affecting temperature, while temperature changes can alter air density and pressure distribution, influencing wind speed. This interaction is important for climate modeling.

Although these models simplify real‑world complexity, they provide useful tools for analyzing and predicting key variables under extreme weather conditions, aiding forecasts of wind and temperature changes and their societal impacts.