Initial Condition vs Boundary Condition

Initial Condition vs Boundary Condition

Schamatic animation illustrating the difference between initial condition problem (ensemble drift and spread) and boundary condition problem (seasonality)

In modeling terms, the difference between weather and climate is what we call an initial condition problem versus a boundary condition problem. Initial conditions are the starting point, the initial state of variables like wind, temperatures, pressure, and moisture. Boundary conditions, in contrast, are values prescribed by the modeler. Examples include the intensity of solar radiation and composition of the atmosphere. Weather depends on initial conditions, while climate on decadal and longer time scales depends primarily on boundary conditions.

Imagine we are looking at two forecast model runs starting from the same initial value, representative of the spring or fall season in either the Northern or Southern Hemisphere: Let's force one set of forecasts with summer incoming solar radiation. The result is a prediction of temperature that oscillates up and down and gradually warms.

Now take that model and run it several more times with summer solar forcing, starting each run with slightly different initial conditions, just like weather forecasters do with model ensembles. The forecasts diverge with time, but stay within some gradually warming forecast envelope. The details of the forecast, just like weather, depend critically upon the initial conditions of the model run.

Next, repeat the process, but use winter solar forcing. It quickly becomes clear that the summer state is significantly warmer than the winter state.

The variance within the summer and winter ensembles results from slight changes in the initial conditions.

The difference between the summer and winter forecasts, or seasonality, results from a difference in boundary conditions.

animation of Earth orbiting Sun to explain seasons

If this were a location in the U.S., we know that it will be warmer in the summer, on average, than in the winter. The boundary condition that differs from summer to winter is the intensity and daily amount of incoming solar radiation reaching the Earth's surface, which is directly related to the tilt of the Earth with respect to the sun. Seasonality is a boundary condition. The Northern Hemisphere gets more sunlight in summer than in winter.

Evolution of a model variable and forecast error during model integration

On the other hand, the drift and spread between different forecasts within the summer and winter ensembles reflects a difference in initial conditions. This graphic illustrates how model forecasts continually drift away from the true state of the atmosphere. As a result, forecasters frequently re-initialize weather models to better match current observations, typically several times per day.

For climate models, it's the boundary conditions that matter. Initialization does not affect the long-term statistics that the models are designed to generate for periods of decades to centuries.