Modeling Weather and Climate

The Prediction of Weather and Climate

Numerical models of weather and climate are based on the fundamental mathematical equations which describe the physics and dynamics of the movements and processes taking place in the atmosphere, the ocean, the ice and the land.

Types of interactions used in a weather forecast Model

These models are:

• Very complex
• Deal with huge quantity of data
• Require a very large number of calculations

Therefore, these models need fast computers with large memory systems.

A 10-day weather prediction takes roughly 4 hours to complete.

First, the individual elements that make up the model must be specified along with measurable quantities that define the state of each element.

The state of each element, or block, in our model is specified for a given instant of time by a series of numbers that define its temperature, pressure, density, humidity, wind direction and speed, and so on.

We begin the operation of our model by specifying all these numbers for every block in the model. This is the initial condition of the model and defines the state of the model at the starting time.

Sample of the equations that control the behavior of the atmosphere

From here on, the model runs itself. The mathematical laws governing the interactions between elements allow us to calculate how the temperature, pressure, etc., of any block will change due to the influence of its neighbors .

We do this for each block, updating the conditions in the block to reflect the effects of the interactions.

At this point we have a slightly changed model from the initial condition, and we can repeat the process, calculating a new set of changes based on the new state of the model.

These can then be used to produce a third version of the model, and so on, as long as we wish to continue the process.

What we end with is a numerical model that evolves with time, hopefully mirroring changes that take place in the actual atmosphere.

A sketch of a General Circulation Model (CGM), note that the grid cells can be of very different dimensions.

State of the atmosphere at time t temperature, winds, etc.

equations that describe the behavior of the atmosphere

State of the atmosphere at time t + dt temperature, winds, etc.

equations that describe the behavior of the atmosphere

State of the atmosphere at time t + 2 * dt temperature, winds, etc.

Unfortunately errors in the initial conditions (possibly from incorrect observations) tend to amplify with time. Past 10-15 days the forecast "skill" is often lower than persistence.

How a weather forecast is made? Links to models - U. of U.

Model sensitivity to initial conditions

How can we trust a model of the atmosphere to predict the climate as much as 100 years into the future if we do not trust similar models to predict the weather 10 days in advance?

• Weather Forecast needs to be very accurate to be useful -> people want to know if it will rain or not 2 days from now.
• Climate Modeling is not concerned with a single event but whether it can generate a realistic average of individual events. NOT important exactly where or on what day it rains, as long as it rains a reasonable amount over the country as a whole during a given month or season.

Climate models are used to study:

• changes in chemical composition of the atmosphere: doubling CO₂, sulfate aerosols;
• changes in the orbital parameters: simulating past climates;
• study the variability of present climate: very long simulations to study the occurrence of El Ninos for example;
• changes in land use: deforestation or desertification;
• climate in other planets.

Models make calculations at widely separated points:

• Weather forecast models: about 30 miles apart (10 days computed in about 4 hours);
• Climate models: about 150 miles apart (2 months to complete a simulation of 100 years);