APPENDIX A: Terms and Definitions

The following provides definitions for some of the terms used in numerical weather prediction and forecast guidance discussions. Many other sources of these definitions are available, such as Thompson (1961), Hess (1979), Haltiner and Williams (1980), etc.

Baroclinic Models: Baroclinic models are dynamic models formulated with the assumption that the wind can change with height. As a result, these models must account for multiple levels. One advantage of baroclinic models is that they better represent the instantaneous structure of the atmosphere than barotropic models. Another advantage is that baroclinic models account for vertical variations in wind, temperature, etc. NOGAPS, OTCM, NORAPS, MFM, QLM, JTYM, and GSM are all baroclinic models.
Barotropic Models: Barotropic models are dynamic models formulated with the assumption that the atmospheric structure does not vary with height. Hence, these models are single level models. One advantage of barotropic models is that they are relatively simple. Examples of barotropic models include BAM, FBAM, MBAM, SBAM, and SANBAR.
Boundary Layer: This is a transitional area between two distinct regions with different physical properties (e.g., air and water). In atmospheric modeling, the boundary layer is usually considered to be the layer of air adjacent to the Earth's surface. There are basically two ways to represent the boundary layer in a numerical prediction model. One way is to provide sufficient levels near the Earth's surface to resolve the boundary layer. Another way is to apply boundary layer parameterization methods so that the boundary layer processes can be approximately represented with model variables.
Finite Difference Methods: These are methods for approximating derivatives in the equations of motion. Continuous derivatives in differential equations are replaced by finite difference approximations at a discrete set of points in space and time. The resulting set of equations, with appropriate restrictions, can then be solved by algebraic methods.
A finite difference model is one which employs finite difference methods. The resolution of a finite difference model is determined by the spacing of the discrete set of points (grid points) used to approximate the derivatives.
Fine Mesh Models: Fine mesh models are "high spatial resolution" models. Due to the large amount of computer processing time necessary to run these high resolution models, it is impractical to reduce the grid length uniformly over the entire globe or model domain. An alternative is to superimpose a fine mesh over one or more limited areas of the larger coarse mesh. Another alternative is to use nest model technique that is to superimpose a "finer" mesh over the "fine" mesh of "coarse" mesh model. These introduce the problem of providing lateral boundary conditions on the periphery of the fine mesh during the course of the integration period.
Lateral Boundary Conditions of Regional Numerical Weather Prediction Model: Lateral boundary conditions are the conditions must be satisfied along the boundaries of a limited domain (regional) model. Boundary values should be assigned in such a manner as to allow a smooth transition, for example, from the coarse resolution of a global model to the higher resolution of a regional model. The method used to derive the boundary conditions must guard against the introduction of severe changes in model variables along the boundaries.
Model Resolution: Model resolution is usually defined as the distance between grid points in the model and is of primary interest to modelers and operational forecasters. In general, increased model resolution allows for definition of smaller scale features. In data rich areas, this increased resolution allows for more accurate depiction of small scale phenomena.
As a general rule, at least 5 grid points (or 4 grid intervals) are needed to define a wave-like weather phenomenon; even through 2-grid-interval sampling is minimum requirement for a wave phenomenon. For example, a model with a horizontal resolution of 125 km can resolve only horizontal phenomena of 500 km or greater. Vertical resolution defines the resolution between the earth's surface and the top of the model. In many cases vertical resolution is variable. For example, a model with 21 vertical levels may have 7 levels in the region below the 850-hPa level. In this case, processes in the boundary layer will be much better represented than if the levels were evenly spaced in the vertical.
Multi-variate Optimum Interpolation (MVOI): The MVOI is a method for producing a dynamically consistent blending of observations and model forecasts for use as initial conditions for forecast models. The MVOI technique combines first guess fields (usually 6 hour or 12 hour model forecasts) with a wide variety of observational data to generate an analysis of the present state of the atmosphere. An important feature of MVOI is that it minimizes the error in the analysis by accounting for errors in both observations and first guess fields (Goerss and Phoebus, 1992).
One Way Influence Models: These are fine mesh models which use information from a coarse mesh model, but do not influence the coarse mesh model. The simplest procedure is to interpolate the coarse mesh variables to the fine mesh boundaries at each time step of the coarse mesh. The coarse mesh points falling in the interior of the fine mesh are ignored in the fine mesh calculations, and the fine mesh calculations have no influence on the coarse mesh prediction.
The One Way Influence Tropical Cyclone Model (OTCM) is an example of a one way influence model because it uses information from NOGAPS, but it does not influence NOGAPS.
Primitive Equations Models: Mathematical models which use the primitive equation system to approximate the dynamic, thermodynamic and static state of the atmosphere were called primitive equation models. Early primitive equation models used a system of six equations; three prognostic equations (the x and y components of the momentum equation, and the thermodynamic energy equation) and three diagnostic equations (the continuity equation, the hydrostatic approximation, and the equation of state) (Holton, 1979). Most models in use these days are primitive equation models.
Regression Methods: These are statistic methods that provide formula linking a predictand with predictors. These models can be used in data analyses, and applied to prediction problems. The most commonly used regression methods consist of three iterative phases: problem definition and data collection, minimization and verification.

(a). Problem definition and data collection: This is the phase in which the available data are collected and analyzed to hypothesize the physical principles (e.g., environmental steering) governing a phenomenon (e.g., tropical cyclone motion). These physical principles can vary from something as simple as persistence extrapolated into the future to something as complex as relationships between dynamic fields and recurvature of a tropical cyclone (TC). These relationships must be converted into mathematical equations.

(b). Minimization: This is a process to obtain weights for various predictors in the formula developed in the previous phase. It begins with acquisition of a suitable data set which contains data for the predictors and predictand. Relative weights for predictors are determined which minimize errors in predictions. For example, it may be determined that, given a formula which predicts 6-hour TC motion speed based on both past 12- and 24-hour speeds, assigning the heavier weight to the 12 hour vice the 24 hour average storm speed yields the best results. Once the weights are assigned, this formula defines our statistical model.

(c). Verification: This is the phase in which the statistical model developed in the other two phases is tested with independent data (data other than that used to develop the model). Verification is accomplished by comparing results from the independent data runs with those of alternative methods. For example, if the statistical TC track model was developed using 1945-1994 TC track data, then an independent data set could be formed from 1995 or 1996 tracks.
Spectral Models: A spectral forecast model is a model that uses continuous basis functions, such as trigonometric functions, to represent model parameters in space (usually horizontal space). Not all meteorological parameters are suitable for spectral representation. For example, precipitation is a discrete phenomenon that is difficult to represent in a spectral wave form. These discrete phenomena may be better represented using a finite difference method (i.e., grid point model).
A few advantages of spectral methods are that they can be computational efficient, provide for elimination of computational instability, and make some derived quantities easy to compute. Some disadvantages are that discrete phenomena are not suitable for spectral representation, computational efficiency decreases quickly as model resolution is increased, and output from spectral models must be transformed to a grid ("transform grid") for graphical display.
From a forecaster's standpoint, model resolution is more important than the computational methods used in a model because model resolution is related to the scale of weather phenomena that a model can represent. The following formula can be used to estimate the distance X between grid points on the transform grid of a spectral model:
X (in km) = 40,000 * COSINE (degree latitude) / (4*(N+1)),
where N is the model truncation wave number. For example, in a T79 spectral model (The letter "T" in T79 indicates a triangular truncation, a type of wave number truncation currently used in spectral models), we have X = 40000 / (4*(79+1)) = 125 km at the equator where COSINE(0) is equal to 1. This is roughly equivalent to 1.25 degrees longitude spacing at the equator. Therefore, equatorial weather phenomena with wave lengths shorter than 500 km are not represented in the T79 spectral model.
A similar formula can also be used to estimate the distance X between grid points on the transform grid of a spectral model:
X (in km) = 40,000 * COSINE (degree latitude) / (3*(N+1)),
this formula provides similar distance value as the first formula.
If the maximum wind zone associated with a mature TC has an average width of about 50 km, what is the minimum model resolution sufficient to resolve the maximum wind zone of a TC in the equatorial zone? The answer is approximately a T800 spectral model. Fast computers, alternative computation methods and physics formulations are required in such models.
Currently even the fastest computers cannot run a T800 global model in a reasonable period of time. Therefore, for TC structure studies, we must use high resolution fine mesh models to resolve TC structure.
Synthetic Tropical Cyclone Observations: These are synthetically generated observations which are intended to represent a TC in a model analysis. Tropical cyclone warning positions are often used to help place the synthetic observations in the analysis. This process is commonly called "tropical cyclone bogus process". Trinh and Krishnamurti (1992) identified that TC bogus includes three factors: TC size and location, TC intensity, and initial TC motion vector.
At FNMOC, the TC bogus is a set of synthetic surface and upper-air observations to 400 hPa. These observations are symmetric around the TC warning center position with an observation at the center, four at 220 km, four at 440 km, and four at 660 km from the forecast center.

Section 4

Appendix B

Chapter 5