6. ANALYZED AND MODEL DATA

For a variety of reasons, many forecast centers changed from approximating the primitive equations with finite differences of data at grid points to exact differentials of spherical harmonics. They also changed from using pressure as a vertical coordinate to the `sigma' coordinate system. This quantity represents a transformed pressure coordinate and has several advantages. (It also has a few disadvantages.) The biggest advantage is that it is easier to deal with the lower boundary of the earth's surface because sigma levels approximately parallel the model's smoothed topography. Some recent model formulations use a hybrid pressure-sigma coordinate system where sigma is used in the troposphere and pressure in the stratosphere with a gradual transition in between.

Historically, there were considerable differences between operational models and climate models. For instance, early primitive equations operational models did not include radiation because, over short time periods, radiation effects were thought to be small. However, radiation is of fundamental importance for climate models. Many other physical approximations also differed between the models. Currently, there is little difference in either the numerics or physics used in operational and climate models. In fact, it is now generally accepted that poor representations of physical processes are a source of systematic forecast error (so it is important to have a good model climate if you want to accurately forecast the detailed evolution of the atmosphere over several days).

The process of establishing a dataset suitable for the initial conditions to an operational forecast model has been an integral part of the operational cycle since the first routine numerical forecasts. These datasets are the analyzed grids which have formed the basis for many atmospheric research studies. The procedure to develop these datasets has changed significantly over time to keep pace with model and computer improvements. Early analyzed grids were developed using a simple objective analysis method. Currently, they are produced using a four-dimensional (4-D) data assimilation system in which multivariate observed data are combined with a ``first guess'' using a statistically optimum scheme. The first guess is the best estimate of the current state of the atmosphere from previous analyses produced using the forecast model.

It must be emphasized that the operational analyses are performed under time constraints for weather forecasting purposes and not with the objective of providing a continuous picture of the atmosphere over time. Changes in the operational models, data handling techniques, the data available, initialization, and so on, which are implemented to improve the weather forecasts, may disrupt the continuity of the analyses. Some aspects, such as detailed analyses of the conditions at the surface of the earth, may be of less importance for weather forecasting while of great importance for diagnostic studies. Typically, the representation of orography in the operational models is greatly simplified (as it is in climate models).

The global atmospheric analyses produced as a result of four-dimensional data assimilation operationally consist of global fields of eastward and northward wind components (u, v), geopotential height (Z), virtual temperature (T), and relative humidity (RH) or, equivalently, specific humidity (q) as a function of pressure (p), latitude and longitude. In recent times, these quantities have been analyzed on the levels of the numerical weather prediction model used in the 4-D data assimilation to provide the first guess for the analyses. Generally, these are sigma levels where sigma = p/p_s, and p_s is the surface pressure defined on the model surface topography. Alternatively, the model levels are a hybrid between sigma and pressure coordinates, typically reverting to constant pressure above about 100 mb. Analyzed fields on standard constant pressure levels are produced by interpolation (e.g., at ECMWF by using tension splines or linearly). Actually, the changes in the analysis from one synoptic observation time to the next are interpolated to update the standard pressure level fields although the details as to how this has been done have changed with time. Horizontal divergence and vertical motion (w= vertical p-velocity) fields are produced diagnostically from the analyses. Once the fields have been analyzed, they are typically initialized using a procedure called nonlinear normal mode initialization (NNMI) to bring the mass and temperature fields into a dynamical balance with the velocity fields consistent with the predominant low frequency motions in the atmosphere. Thus, analyzed gridded datasets may be "initialized" or "uninitialized" (In some studies it is important to know which type of analyses are being used.).