This comprehensive text and reference work on numerical weather prediction, first published in 2002, covers not only methods for numerical modeling, but also the important related areas of data assimilation and predictability. It incorporates all aspects of environmental computer modeling including an historical overview of the subject, equations of motion and their approximations, a modern and clear description of numerical methods, and the determination of initial conditions using weather observations (an important science known as data assimilation). Finally, this book provides a clear discussion of the problems of predictability and chaos in dynamical systems and how they can be applied to atmospheric and oceanic systems. Professors and students in meteorology, atmospheric science, oceanography, hydrology and environmental science will find much to interest them in this book, which can also form the basis of one or more graduate-level courses.

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Atmospheric Modeling, Data Assimilation and Predictability

In 1996, version 2.5 of the Coupled Ocean–Atmosphere Response Experiment (COARE) bulk algorithm was published, and it has become one of the most frequently used algorithms in the air–sea interaction community. This paper describes steps taken to improve the algorithm in several ways. The number of iterations to solve for stability has been shortened from 20 to 3, and adjustments have been made to the basic profile stability functions. The scalar transfer coefficients have been redefined in terms of the mixing ratio, which is the fundamentally conserved quantity, rather than the measured water vapor mass concentration. Both the velocity and scalar roughness lengths have been changed. For the velocity roughness, the original fixed value of the Charnock parameter has been replaced by one that increases with wind speeds of between 10 and 18 m s−1. The scalar roughness length parameterization has been simplified to fit both an early set of NOAA/Environmental Technology Laboratory (ETL) experiments and...

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Bulk Parameterization of Air–Sea Fluxes: Updates and Verification for the COARE Algorithm

This paper describes the various physical processes relating near-surface atmospheric and oceanographic bulk variables ; their relationship to the surface fluxes of momentum, sensible heat, and latent heat ; and their expression in a bulk flux algorithm. The algorithm follows the standard Monin-Obukhov similarity approach for near-surface meteorological measurements but includes separate models for the ocean's cool skin and the diurnal warm layer, which are used to derive true skin temperature from the bulk temperature measured at some depth near the surface. The basic structure is an outgrowth of the Liu-Katsaros-Businger [Liu et al., 1979] method, with modifications to include a different specification of the roughness/stress relationship, a gustiness velocity to account for the additional flux induced by boundary layer scale variability, and profile functions obeying the convective limit. Additionally, we have considered the contributions of the sensible heat carried by precipitation and the requirement that the net dry mass flux be zero (the so-called Webb correction [Webb et al., 1980]). The algorithm has been tuned to fit measurements made on the R/V Moana Wave in the three different cruise legs made during the Coupled Ocean-Atmosphere Response Experiment. These measurements yielded 1622 fifty-min averages of fluxes and bulk variables in the wind speed range from 0.5 to 10 m s -1 . The analysis gives statistically reliable values for the Charnock [1955] constant (a = 0.011) and the gustiness parameter (β = 1.25). An overall mean value for the latent heat flux, neutral bulk-transfer coefficient was 1.11 x 10 -3 , declining slightly with increasing wind speed. Mean values for the sensible and latent heat fluxes were 9.1 and 103.5 W m -2 ; mean values for the Webb and rain heat fluxes were 2.5 and 4.5 W m -2 . Accounting for all factors, the net surface heat transfer to the ocean was 17.9 ± 10 W m -2 .

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Bulk parameterization of air‐sea fluxes for Tropical Ocean‐Global Atmosphere Coupled‐Ocean Atmosphere Response Experiment

A long-term global atmospheric reanalysis, named “Japanese 25-year Reanalysis (JRA-25)” was completed using the Japan Meteorological Agency (JMA) numerical assimilation and forecast system. The analysis covers the period from 1979 to 2004. This is the first long-term reanalysis undertaken in Asia. JMA's latest numerical assimilation system, and specially collected observational data, were used to generate a consistent and high-quality reanalysis dataset designed for climate research and operational monitoring and forecasts. One of the many purposes of JRA-25 is to enhance the analysis to a high quality in the Asian region.Six-hourly data assimilation cycles were performed, producing 6-hourly atmospheric analysis and forecast fields of various physical variables. The global model used in JRA-25 has a spectral resolution of T106 (equivalent to a horizontal grid size of around 120 km) and 40 vertical layers with the top level at 0.4 hPa. In addition to conventional surface and upper air observations, atmospheric motion vector (AMV) wind retrieved from geostationary satellites, brightness temperature from TIROS Operational Vertical Sounder (TOVS), precipitable water retrieved from orbital satellite microwave radiometer radiance and other satellite data are assimilated with three-dimensional variational method (3D-Var). JMA produced daily sea surface temperature (SST), sea ice and three-dimensional ozone profiles for JRA-25. A new quality control method for TOVS data was developed and applied in advance.Many advantages have been found in the JRA-25 reanalysis. Predicted 6-hour global total precipitation distribution and amount are well reproduced both in space and time. The performance of the long time series of the global precipitation is the best among the other reanalyses, with few unrealistic variations from degraded satellite data contaminated by volcanic eruptions. Secondly, JRA-25 is the first reanalysis to assimilate wind profiles around tropical cyclones reconstructed from historical best track information; tropical cyclones were analyzed properly in all the global regions. Additionally, low-level cloud along the subtropical western coast of continents is well simulated and snow depth analysis is also of a good quality. The article also covers material which requires attention when using JRA-25.

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The JRA-25 Reanalysis

A detailed description of the fourth-generation ECHAM model is presented. Compared to the previous version, ECHAM3, a number of substantial changes have been introduced in both the numerics and physics of the model. These include a semi-Lagrangian transport scheme for water vapour, cloud water and trace substances, a new radiation scheme (ECMWF) with modifications concerning the water vapour continuum, cloud optical properties and greenhouse gases, a new formulation of the vertical diffusion coefficients as functions of turbulent kinetic energy, and a new closure for deep convection based on convective instability instead of moisture convergence. Minor changes concern the parameterizations of horizontal diffusion, stratiform clouds and land surface processes. Also, a new dataset of land surface parameters have been compiled for the new model. The climatology of the model, derived from two extended AMIP simulations at T42L19 resolution, is documented and compared with ECMWF operational analyses. Some of the biases noted for the previous model version remain virtually unchanged. For example, the polar upper troposphere and lower stratosphere is much too cold, and the zonal wind errors become very large above the 200 hPa level. Furthermore, the low-frequency variability is still too small but the errors are reduced by about 50% compared to ECHAM3.

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The atmospheric general circulation model ECHAM-4: Model description and simulation of present-day climate

The vertical distribution of horizontal mean wind in the lowest 8 metres over a reservoir (1·6 km × 1 km) has been measured using sensitive anemometers freely exposed from a fixed mast in water 16 m deep, the fetch being more than 1 km. The resulting profiles are closely logarithmic, the small differences being systematic and possibly due to the thermal instability which existed when the measurements were made.

The usual law for wind profiles in neutral stability is 



where u is the wind speed at height z, k is von Karman's constant, log z (0) the intercept on the log z axis, and u* the so-called friction velocity defined by τ0 = pu, τ0 being the surface drag and rH the density of the air.

To characterize the profiles u*/k, their slope, was plotted in relation to z (0), their intercept; this allowed a direct comparison with other profiles, in particular those recently measured in a laboratory channel by Sibul. The agreement was better than expected and indicated that z (0) was comparatively independent of fetch and stability but was largely determined by u*. The relation between u* and z (0) agreed roughly with the simplest non-dimensional relation between them, gz (0)/u = constant, so that one is led to a generalized wind profile for flow over a water surface 



which specifies the drag, given the wind at one known height. An approximate value of the constant is 12·5.

This expression can be compared with earlier work. The better wind-profile observations show rough agreement; the experimental scatter is necessarily large since a water surface is aerodynamically much smoother than most land surfaces, precision anemometry in difficult circumstances being required to provide sufficiently precise values. Oceanographic measurements of the tilt of water surfaces are in fair agreement at high wind speeds but at low wind speeds the data are conflicting. The early results which imply that the drag-coefficient (u/u2) increases with decreasing wind speed in light winds are thought to be in error; some support for this belief comes from recent estimates of drag using a modified ageostrophic technique, which agree roughly among themselves and with the general expression.

Wind stress on a water surface

A note on empirical wind‐wave formulae

Swinbank's observations at Kerang (February 1962) are used to estimate the variation with the stability parameter ζ(≡ z/L) of the Monin-Obukhov universal function φM (≡ u,∗−1kz δu/δz).

A plot of Ri against ζ is used to derive the approximate variation of α (≡ φM/φH = KH/KM) with ζ.

Flux-gradient relations near the ground in unstable conditions

Information on eddy diffusion in the atmosphere at heights between one and two kilometres has been obtained from an analysis of observations made on pairs of smoke puffs by using a camera obscura.

The results are compared with a prediction of the Kolmogoroff similarity hypotheses.

H. Charnock

Papers

Wind stress on a water surface

A note on empirical wind‐wave formulae

Flux-gradient relations near the ground in unstable conditions

Note on eddy diffusion in the atmosphere between one and two kilometres