The term tribology, meaning the science and technology of friction, lubrication, and wear, is of recent origin (Lubrication Engineering Working Group, 1966), but its practical aspects reach back to prehistoric times. The importance of tribology has greatly increased during its long history, and modern civilization is surprisingly dependent on sound tribological practices.

The field of tribology affects the performance and life of all mechanical systems and provides for reliability, accuracy, and precision of many. Tribology is frequently the pacing item in the design of new mechanical systems. Energy loss through friction in tribo-elements is a major factor in limits on energy efficiency. Strategic materials are used in many tribo-elements to obtain the required performance.

This chapter describes the governing systems of equations that can serve as the basis for atmospheric models used for both operational and research applications. Even though most models employ similar sets of equations, the exact formulation can affect the accuracy of model forecasts and simulations, and can even preclude the existence in the model solution of certain types of atmospheric waves. Because these equations cannot be solved analytically, they must be converted to a form that can be. The numerical methods typically used to accomplish this are described in Chapter 3.

The equations that serve as the basis for most numerical weather and climate prediction models are described in all first-year atmospheric-dynamics courses. The momentum equations for a spherical Earth (Eqs. 2.1–2.3) represent Newton's second law of motion, which states that the rate of change of momentum of a body is proportional to the resultant force acting on the body, and is in the same direction as the force. The thermodynamic energy equation (Eq. 2.4) accounts for various effects, both adiabatic and diabatic, on temperature. The continuity equation for total mass (Eq. 2.5) states that mass is neither gained nor destroyed, and Eq. 2.6 is analogous, but applies only to water vapor. The ideal gas law (Eq. 2.7) relates temperature, pressure, and density. The variables have their standard meteorological meaning.

Background

Sometimes the standard dependent variables of NWP and climate models are all that are required for making decisions. But, frequently these meteorological variables influence some other physical process that also must be simulated before a weather-dependent decision can be made. As we will see, there are myriad examples of such situations. These models that are coupled with the atmospheric model may be referred to as special-applications models or secondary models. Examples include the following.

• Air-quality models

• Infectious-disease models

• Wave-height models

• Agricultural models

• River-discharge, or flood, models

• Wave-propagation models – sound and electromagnetic

• Wildfire-behavior and -prediction models

• Electricity-demand models

• Dust-elevation and -transport models

• Ocean-circulation models

• Ocean-drift models

• Aviation-hazard models – turbulence, icing, visibility

Sometimes the secondary model is embedded within the code of the atmospheric model, and the coupled system is run simultaneously. And, sometimes there are two distinct model codes that are run sequentially. When the code that represents the secondary process is run within the atmospheric model, the secondary process may interact with the atmospheric simulation. Or, the flow of data may be in one direction only, where the atmospheric variables are used in the secondary model without feedback. There are some secondary-model processes that have strong feedbacks to the atmosphere, and for their prediction there is of course a greater need to have a two-way exchange of information between the atmospheric and secondary models.

The surface processes whose numerical simulation is discussed here occur near both the land–atmosphere and the water–atmosphere interfaces. Over land, the movement of heat and water within the plant canopy and the ground beneath it must be represented in both weather- and climate-prediction models. Through this movement of heat and water across the land–atmosphere interface, properties of the land surface such as temperature and wetness are felt by the atmospheric boundary layer and the free atmosphere above. The atmosphere, in turn, affects the substrate and vegetation properties through radiation, precipitation, and controls on evapotranspiration. The effect of the surface on the frictional stress felt by the air moving over it is more the subject of boundary-layer meteorology and parameterizations rather than land-surface physics, so most of the discussion of this topic is found in Chapter 4. Over water, the interaction is complicated by the fact that the wind stress causes currents, waves, and vertical mixing of the water, which affect surface temperature and evaporation.

The skillful numerical prediction of atmospheric processes of many types and scales depends on the proper representation of surface–atmosphere interactions. For example, the prediction of convection relies on the accurate calculation by the model of surface fluxes of heat and water vapor. And, direct thermal circulations on the mesoscale, forced by horizontally differential heating at the surface, can dominate the local weather and climate near coastlines and sloping orography.

Background

What is verification?

Forecast verification involves evaluating the quality of forecasts. Various methods exist to accomplish this. In all cases, the process entails comparing model-predicted variables with observations of those variables. The term validation is sometimes used instead of verification, but the intended meaning is the same. That said, the root word “valid” may imply to some that a forecast can either be valid, or invalid, whereas obviously there is a continuous scale that measures forecast quality. Thus, the term verification is preferable to many, and will be employed here. Special verification measures that are most applicable to ensemble predictions have been discussed in Chapter 7. There is an extensive body of literature on the subject of model verification, and students and researchers should read beyond the summary material in this chapter to ensure that they understand underlying statistical concepts and that they use the verification metrics that are most appropriate for their needs.

Reasons for verifying model simulations and forecasts

There are multiple motivations for evaluating the quality of model forecasts or simulations.

• Most models are under continuous development, and the only way modelers can know if routine system changes, upgrades, or bug fixes improve the forecast or simulation quality is to objectively and quantitatively calculate error statistics.

• For physical-process studies, where the model is used as a surrogate for the real atmosphere, the model solution must be objectively verified using observations, and if the observations and model solution correspond well where the observations are available, there is some confidence that one can believe the model where there are no observations.

• […]

The current chapter summarizes various topics related to the numerical solution of the model equations, for resolvable scales of motion. This part of an atmospheric model that treats the resolvable scales is called the dynamical core, and is distinct from the representations of the subgrid-scale, parameterized physical processes. An especially important topic is how the numerical approximations that are used to solve the equations can affect the model solution. These nonphysical effects should be thoroughly understood by all model users. Even though basic concepts are described here, and examples provided, this presentation of numerical methods is far from exhaustive. A comprehensive text on this subject, such as Durran (1999), should be consulted if more depth is needed. Step-by-step derivations are frequently left to the reader.

Numerical methods used for solving the equations have naturally evolved over the last few decades, partly because of the results of research and partly because of changes in the available computational resources. Various factors are involved in the decision about the numerical methods to use for a particular modeling application, including computational efficiency (speed), accuracy, memory requirements, and code-structure simplicity. The last factor is especially important if the model is going to be used for research, especially by students. Simple methods that are not typically used in current operational models are sometimes described here for pedagogical purposes.

The following brief overview of concepts will help the reader to better understand the specialized material in later sections.

Background

The statistical post processing, or calibration, of operational NWP-model output is common because it can result in skill metrics that are equivalent to many years of improvement to the basic model. And, the greater skill is achieved at relatively little day-to-day expense, compared to other traditional approaches of trying to improve skill, such as through increasing the model resolution.

Historically, statistical post-processing methods were used to diagnose variables that could not be predicted directly by the low-resolution, early-generation NWP models. Standard model dependent variables associated with the large-scale conditions were statistically related to other poorly predicted or unpredicted weather variables such as freezing rain, fog, and cloud cover. However, many current-generation, high-resolution models can explicitly forecast such variables, and statistical correction methods are primarily employed to reduce systematic errors.

There is a variety of ways of classifying statistical post-processing methods. They may be categorized in terms of the statistical techniques used, as well as by the types of predictor data that are used for development of the statistical relationships. And, distinctions are made between static and dynamic methods. With static methods, statistical algorithms are developed for removing systematic error using a long training period that is based on the same version of the model, and the algorithms are applied without change for a significant period of time. Because of the computational expense associated with the calculation of the statistical relationships, models cannot be upgraded frequently because doing so requires recalculation of the relationships.

The aim of this chapter is to provide a few examples of some common methods for using models in research studies. Other chapters also discuss experimental designs in the context of the specific subject being discussed. For example, there are many places in Chapter 16 describing experimental methods related to modeling studies of climate change. The summary here is far from complete because experimental methods are obviously closely tied to the objectives of a research project, which can vary widely. Nevertheless, the methods summarized are in wide use, and their strengths and limitations should be understood.

Case studies for physical-process analysis

Model simulations, generally for short time periods, are often used to study some aspect of a meteorological phenomenon. Sometimes the purpose is to better understand the predictability of a process, in terms of the necessary physical-process parameterizations or initial conditions. This is treated in Section 10.7 on predictive-skill studies. More often, the purpose is to use the model to help better understand the dynamics or kinematics of a physical process. The model is integrated from an initialization that is based on observations at the beginning of the study period. A next step in the process is to confirm that a good correspondence exists between the model simulation and the observations that are available during the simulation period. Good verification of the model skill at these observation locations is typically considered to be justification for believing the simulation in the space and time gaps between the observations.

As we have seen in Chapter 3, solving the equations that govern the physical systems that we are modeling is an initial- and boundary-value problem. The lateral, upper, and lower boundary conditions are discussed in Chapters 3 and 5. In this chapter will be described the procedure by which observations are processed to define initial conditions for the model dependent variables, from which the model integration begins. This process is called model initialization. There are essentially two requirements for the initialization. First, the dependent variables defined on the model grid must faithfully represent conditions in the real atmosphere (e.g., fronts should be in the correct location), and second, the gridded mass-field variables (temperature, pressure) and momentum-field variables (velocity components) should be dynamically consistent, as defined by the model equations. An example of the mass–momentum consistency requirement is that, on the synoptic scale, the gridded initial conditions should be in approximate hydrostatic and geostrophic balance. If they are not, the model will generate potentially large-amplitude inertia–gravity waves after the initialization shock, and these nonphysical waves will be overlaid on the meteorological part of the model solution until the adjustment process is complete. The final adjusted condition will prevail after the inertia–gravity waves have been damped, or have propagated off the grid of a LAM. However, the model solution will be typically unusable during this adjustment period, which is one reason for the common, historical recommendation that model output not be used for about the first 12 h of the integration.

Background

The application of models for operational NWP has much in common with their use for answering physical-process questions, and for satisfying practical needs related to the assessment of air quality, evaluating the potential utility of new observing systems with OSSEs, and testing new numerical methods and physical-process parameterizations. Nevertheless, there are some issues that are unique to operational modeling. These will be addressed in this chapter.

It could be argued that the student of NWP should not need this kind of operationsoriented information because only large national modeling centers with experienced staff and large, fast computers are involved in operational prediction. However, there is a rapid growth in the use of operational regional models by consulting companies, universities, and regional governments to satisfy specialized needs. Thus, the student should become familiar with some of the concepts associated with the operational use of models.

Figure 12.1 illustrates the various components of a very simple operational modeling system. It should be kept in mind that the modeling systems that are operated by national weather services have very large infrastructures, and that the one summarized here is more consistent with the many modest-sized, specialized, operational-modeling systems that exist throughout the world. Some of these system components have been discussed before in earlier chapters, for example related to model initialization. To begin with, the system must have real-time connectivity to operational observational-data networks (top box in the figure), where this generally involves separate access to a number of different data providers.

The term climate modeling, as used here, includes (1) forecasts of climate with global AOGCMs that simulate the physical system's response to radiative-forcing scenarios that assume a specific trajectory for anthropogenic and natural gas and aerosol emissions, (2) initial-value simulations on seasonal to annual time scales, (3) the production of model-based analyses of the present climate, and (4) model experiments that evaluate the response of the climate system to anthropogenic changes in the landscape, say associated with continued urbanization or the expansion of agriculture. Thus, the term climate modeling refers to the use of a model to define the state of Earth's physical system on time scales of seasons to centuries. As we will see, the specifics of the modeling process depend on the time scale. Typically not included are monthly forecasts (e.g., Vitart 2004), which bridge the gap between medium-range forecasting and seasonal forecasting. If the AOGCM forecasts or the global-reanalysis data sets are used as input to a regional (mesoscale) model or a statistical procedure for correlating the large- and small-scale climate of a region, the process is called climate downscaling.

The material about the modeling of weather that has been presented so far in this book also has direct application to the problem of climate modeling. The climate is, after all, just the aggregate behavior of many thousands of individual weather events.