Notes written from memory by Anders Persson (ECMWF) on 16 September 1999. The reader is encouraged to read P. D. Thompson's paper “Charney and the Revival of Numerical Weather Prediction”, reproduced, together with Charney's letters to Thompson in Lindzen et al., (1990).

History of NWP

In late 1945 Vladimir Zworykin, the “Father of Television”, who worked at RCA, joined with John von Neumann, the “Father of the Computer”, to suggest the use of the computer in meteorology. Zworykin's interest was in weather modification, and von Neumann's was in fluid dynamics. They also had the dream of connecting the TV and the computer into something we today know as a PC or Workstation. Their dream came partially true in Sweden in around 1955 when for the first time a forecast map that was made directly and automatically without any human intervention was produced on a screen (oscilloscope) (see Bergthorsson and Döös, (1955), Bergthorsson et al., (1955), also the Rossby Memorial Volume).

In early 1946 von Neumann contacted Rossby's group. They told von Neumann why a zonally averaged dynamical model would not work, and instead suggested a barotropic model which had been manually tested by Victor Starr in his 1941 book on weather forecasting for a 72-h forecast at 700 hPa. Von Neumann was not satisfied with the simple barotropic approach and in speeches in the spring of 1946 presented more ambitious plans. Von Neumann and Zworykin also appeared at the annual meeting of the AMS (see Bulletin of AMS (1946)).

If the numerical model forecasts are skillful, the forecast variables should be strongly related to the weather parameters of interest to the “person in the street” and for other important applications. These include precipitation (amount and type), surface wind, and surface temperature, visibility, cloud amount and type, etc. However, the model output variables are not optimal direct estimates of local weather forecasts. This is because models have biases, the bottom surface of the models is not a good representation of the actual orography, and models may not represent well the effect of local forcings important for local weather forecasts. In addition, models do not forecast some required parameters, such as visibility and probability of thunderstorms.

In order to optimize the use of numerical weather forecasts as guidance for human forecasters, it has been customary to use statistical methods to “post-process” the model forecasts and adapt them to produce local forecasts. In this appendix we discuss three of the methods that have been used for this purpose.

Model Output Statistics (MOS)

This method, when applied under ideal circumstances, is the gold standard of NWP model output post-processing (Glahn and Lowry, 1972, Carter et al., 1989). MOS is essentially multiple linear regression, where the predictors hnj are model forecast variables (e.g., temperature, humidity, or wind at any grid point, either near the surface or in the upper levels), and may also include other astronomical or geographical parameters (such as latitude, longitude and time of the year) valid at time tn.

Introduction

In general, the public is not aware that our daily weather forecasts start out as initial-value problems on the major national weather services supercomputers. Numerical weather prediction provides the basic guidance for weather forecasting beyond the first few hours. For example, in the USA, computer weather forecasts issued by the National Center for Environmental Prediction (NCEP) in Washington, DC, guide forecasts from the US National Weather Service (NWS). NCEP forecasts are performed by running (integrating in time) computer models of the atmosphere that can simulate, given one day's weather observations, the evolution of the atmosphere in the next few days. Because the time integration of an atmospheric model is an initial-value problem, the ability to make a skillful forecast requires both that the computer model be a realistic representation of the atmosphere, and that the initial conditions be known accurately.

NCEP (formerly the National Meteorological Center or NMC) has performed operational computer weather forecasts since the 1950s. From 1955 to 1973, the forecasts included only the Northern Hemisphere; they have been global since 1973. Over the years, the quality of the models and methods for using atmospheric observations has improved continuously, resulting in major forecast improvements.

Figure 1.1.1(a) shows the longest available record of the skill of numerical weather prediction. The “S1” score (Teweles and Wobus, 1954) measures the relative error in the horizontal gradient of the height of the constant pressure surface of 500 hPa (in the middle of the atmosphere, since the surface pressure is about 1000 hPa) for 36-h forecasts over North America.

Introduction

In Chapter 2 we derived the equations that govern the evolution of the atmosphere, and in Chapter 3 we discussed the numerical discretizations that allow the numerical integration of those equations on a computer. The discretization of the continuous governing equation is limited by the model resolution, i.e., by the size of the smallest resolvable scale. We have seen that in a finite difference scheme, the smallest scales of motion that can be (poorly) resolved are those which have a wavelength of two grid sizes. In spectral models, the motion of the smallest wave present in the solution is more accurately computed, but for these and for any type of numerical discretization there is always a minimum resolvable scale. Current climate models typically have a horizontal resolution of the order of several hundred kilometers, global weather forecast models have resolutions of 50–100 km, and regional mesoscale models of 10–50 km. Storm-scale models have even higher resolution, with grid sizes of the order of 1–10 km. In the vertical direction, model resolution and vertical extent have also been increased substantially, with current models having typically between 10 and 50 vertical levels, and extending from the surface to the stratosphere or even the mesosphere. As computer power continues to increase, so does the resolution of atmospheric models.

Despite the continued increase of horizontal and vertical resolution, it is obvious that there are many important processes and scales of motion in the atmosphere that cannot be explicitly resolved with present or future models.

Introduction to atmospheric predictability

In his 1951 paper on NWP, Charney indicated that he expected that even as models improved there would still be a limited range to skillful atmospheric predictions, but he attributed this to inevitable model deficiencies and finite errors in the initial conditions. Lorenz (1963a, b) discovered the fact that the atmosphere, like any dynamical system with instabilities, has a finite limit of predictability (which he estimated to be about two weeks) even if the model is perfect, and even if the initial conditions are known almost perfectly. He did so by performing what is now denoted an “identical twin” experiment: he compared two runs made with the same model but with initial conditions that differed only very slightly. Just from round-off errors, he found that after a few weeks the two solutions were as different from each other as two random trajectories of the model.

Lorenz (1993) described how this fundamental discovery took place: His original goal had been to show that statistical prediction could not match the accuracy attainable with a nonlinear dynamical model, and therefore that NWP had a potential for predictive skill beyond that attainable purely through statistical methods. He had acquired a Royal-McBee LGP-30 computer, with a memory of 4K words and a speed of 60 multiplications per second, which for the late 1950s was very powerful.

Introduction

In previous chapters we saw that NWP is an initial/boundary value problem: given an estimate of the present state of the atmosphere (initial conditions), and appropriate surface and lateral boundary conditions, the model simulates (forecasts) the atmospheric evolution. Obviously, the more accurate the estimate of the initial conditions, the better the quality of the forecasts. Currently, operational NWP centers produce initial conditions through a statistical combination of observations and short-range forecasts. This approach has become known as “data assimilation”, whose purpose is defined by Talagrand (1997) as “using all the available information, to determine as accurately as possible the state of the atmospheric (or oceanic) flow.”

There are several excellent reviews of this subject, which has become an important science in itself. The book Atmospheric data analysis by Daley (1991) is a comprehensive description of methods for atmospheric data analysis and assimilation. Ghil and Malanotte-Rizzoli (1991) have written a rigorous discussion of present data assimilation methods with special emphasis on sequential methods. Talagrand (1997) gives an elegant introductory overview of current methods of data assimilation, and Zupanski and Kalnay (1999) also provide a short introduction to the subject. The book Data assimilation in meteorology and oceanography: Theory and practice (Ghil et al., editors, 1997) contains a wealth of important papers on current methods for data assimilation. An earlier but still useful book is Dynamic meteorology: Data assimilation methods (Bengtsson et al., editors, 1981). Thiebaux and Pedder (1987) provided a description of spatial interpolation methods applied to meteorology.

During the 50 years of numerical weather prediction the number of textbooks dealing with the subject has been very small, the latest being the 1980 book by Haltiner and Williams. As you will soon realize, the intervening years have seen impressive development and success. Eugenia Kalnay has contributed significantly to this expansion, and the meteorological community is fortunate that she has applied her knowledge and insight to writing this book.

Eugenia was born in Argentina, where she had exceptionally good teachers. She had planned to study physics, but was introduced to meteorology by a stroke of fate; her mother simply entered her in a competition for a scholarship from the Argentine National Weather Service! But a military coup took place in Argentina in 1966 when Eugenia was a student, and the College of Sciences was invaded by military forces. Rolando Garcia, then Dean of the College of Sciences, was able to obtain for her an assistantship with Jule Charney at the Massachusetts Institute of Technology. She was the first female doctoral candidate in the Department and an outstanding student. In 1971, under Charney's supervision, she finished an excellent thesis on the circulation of Venus. She recalls that an important lesson she learned from Charney at that time was that if her numerical results did not agree with accepted theory it might be because the theory was wrong.

Previous chapters have described coastal landforms and discussed morphodynamic frameworks for interpreting the pattern of adjustments for different coastal types. The range of adjustments is complex and individual coasts change at varying rates and in varying directions. The level of uncertainty about what will happen in the future increases as the time scale increases. Although coastal landforms and the natural processes of erosion and deposition that shape them are the focus of this book, this natural pattern of adjustment is increasingly influenced directly and indirectly by human activities. Many coasts have been substantially modified by local structural and ecological changes brought about intentionally or unintentionally by humans. The impact of human activities can be felt beyond the local scale. Climate change as a result of the enhanced greenhouse effect and the associated threat of accelerated sea-level rise imply human impact on a global scale at an unprecedented rate. These impacts are added to natural pattens of change.

No coast is now likely to be beyond the influence of humans who have become a force ‘as powerful as many natural forces of change, stronger than some and sometimes as mindless as any’ (Meyer, 1996, p. 2).

This chapter is concerned with coral reefs and associated carbonate environments on tropical and subtropical coasts. Reefs are dynamic geomorphological systems demonstrating a complex interplay between physical and biological processes. They form solid limestone, simultaneously producing, breaking down and redistributing sediments of different sizes to construct a range of landforms. As a result of their ability to build rigid, wave-resistant structures, corals modify the environment in which they live, as expressed by Darwin in the quotation above. Reefs contain a variety of interacting subsystems operating over a broader range of time scales than generally seen on rocky coasts, comprising construction, destruction and various responses to extreme perturbations, such as storms.