Supplemental Material for Chapter 1

Helpful Figures for Chapter 1

This has figures relevant to issues discussed in class: the 500 hPa Geopotential height chart, the water vapor channel image showing convection along the equator and sinking (dark) regions in the subtropics, etc. You should be familiar with pages 3, 4, 24, 30, 36, 44, 45, 46, 48, 50, 51, 52, 53, 54, 55, 56.

Sources of Error in Weather Prediction

The validity of a weather forecast depends on:

(1) Model Initialization: how well the initial state of the atmosphere is known. A forecast involves running a model of the atmosphere from some initial state to a future state. The initial state at time = 0 is a blend of the previous forecast, and observations taken at time t = 0. This blending is referred to as data assimilation. Because forecast models tend to drift from reality (error growth), it is neccessary to periodically jolt the model closer to reality by assimilating observations. The model needs to know variables like temperature, pressure, water vapor mixing ratio, winds, cloudiness, etc et every grid point at the start of model run. These variables are determined from some blend of the previous forecast, and observations.

(2) Model Realism: how well the model replicates the real behavior of the atmosphere, i.e., how well it describes physical processes such as clouds (moist turbulence), dry turbulence, air-sea fluxes, wind circulations, radiation, etc. The main difficulty is that many of these processes are sub gridscale, i.e. most clouds are much smaller than a model grid box. The problem of accounting for the average effects of sub gridscale processes in a model is known as "parameterization". Models should be getting more realistic as computers become more powerful and model grid boxes get smaller, but progress in precipitation forecasts has been slow, especially in the tropics.

It is impossible to initialize a model from the observational network alone because it is not practical to make measurements of winds, temperature, humidity, and clouds everywhere on earth at the same time. Scientists use the measurements they do have, and information from the previous forecast. The process of coming up with an initial state that is most consistent both with all available measurements and the laws of physics is called data assimilation. This initial state is then run forward in time to make forecasts.

Data assimilation is very complicated - partly because it has to account for the possibility of errors in the measurements, partly because there are many regions which are poorly constrained by the observational network, and also because of the variation of temperature, wind, etc within grid cells. Usually, so a measurements can not be taken to be representative of an average within that cell. Satellite measurements are much better at providing global coverage. However, they usually have low horizontal and vertical resolution, and are typically subject to larger random errors.

Weather Forecasts versus Climate Forecasts

If there is no skill beyond 20 days in a weather forecast model, how can we ever expect to predict climate 100 years from now? The main reason is that prediction of the average state of the atmosphere (climate) should be easier than prediction of the state of the atmosphere at a particular time (the weather). Whereas weather is continuously fluctuating, climate changes occur much more slowly, usually in response to large scale forcings (like volcanoes, greenhouse gases, orbital changes, etc.),and hopefully in a way we can understand and predict. Secondly, errors in weather forecasts often arise from errors in the initial state. In climate forecasting, you are usally so far in the future that the initial state of the atmosphere often doesn't matter very much any more. You therefore lose one important source of error. Errors in climate forecasts can usually only arise from errors in the model physics (though seasonal forecasting often relies on sea surface temperature measurements at some initial time).

Climate models are usually forced to include more processes than weather forecast models. For example, it would not usually be necessary to couple an atmospheric model to an interactive ocean model to make a 1 week forecast (fixed sea surface temperatures should be good enough; hurricane forecasting may be an exception). In the case of a 6 month forecast, however, where sea surface temperatures would be expected to evolve in time over this period, an interactive ocean model would in general be necessary. Over even longer timescales, such as thousands of years, the climate would be expected to be influenced by changes in the ice sheets, and one might want to include an interactive cryosphere. The process of including ice sheet dynamics in 3d climate models is still relatively new, but may be important in climate of the upcoming century depending on how the Greenland ice sheet changes. Over longer timescales (tens of millions of years), plate tectonics (mountain building plus movement of continents) has a strong effect on climate

Forecast Time and Zone of Influence

If you are making a very short term forecast, e.g. 6 hours in advance, you only have to know the initial state of the atmosphere in a relatively small area around the forecast location. However, as the forecast time gets longer and longer, you need to characterize the initial state over a larger and larger area. E.g. the weather tomorrow might be influenced by a low pressure system now over Maine, but 4 days from now it might be influenced by a low pressure system now in Alberta. To make longer term forecasts, you need a global (or at least hemispheric) observing system to define your initial state. On weekly timescales, mid-latitude forecasts are often influenced by what is happening in the tropics. Weather really is a global phenomenon.

Chaos

Weather is deterministic in the sense that if we knew the exact state of the atmosphere at some initial time, and had a perfect model, we could predict weather in advance past 20 days. But as you predict out to longer forecast times, you have to know the initial state more accurately and over a larger spatial area (the "influence zone" gets bigger). 20 days appears to be a natural limit imposed by the best description of the initial state we could ever reasonably hope to ever achieve. Chaos is not "randomness" or "non-deterministic"; it is extreme sensitivity to initial conditions so that the behaviour of a system becomes, for all practical purposes, unpredictable beyond a certain time. This is what is sometimes known as the "butterfly effect". Strictly speaking, it refers only to weather and not to climate. And in practice, many errors in the initial state turn out to be irrelevant (i.e. do not grow in time). High sensitivity to initial conditions is more frequent in regions of high baroclinicity where storm genesis occurs, i.e. locations where wave amplitudes grow rapidly in time. These are naturally regions where the cost effectiveness of measurement stations is much higher than elsewhere.

Three types of precipitation: (1) Synoptic (2) Convective (3) Orographic

(1) Synoptic Precipitation is produced by low pressure systems. Most winter-time precipitation in mid-latitudes is synoptic precipitation associated with warm and cold fronts. This type of precipitation is produced by "baroclinicity" (horizontal temperature gradients). A highly baroclinic atmosphere has more more gravitational potential energy, which can be used to generate a circulation, and intensify low pressure systems. When the warm air rises up over the cold air in warm fronts, precipitation is generated.

(2) Convective precipitation is produced by some combination of warm, moist air at the surface, and cold air aloft. These conditions favour positive buoyancy of rising air parcels.

(3) Orographic Flow: vertical motion forced by horizontal flow hitting a mountain range generates precipitation on the upwind side of mountain ranges. very important on the western side of North America.