André Robert

A stable numerical integration scheme for the primitive meteorological equations

Abstract A stable numerical integration scheme is applied to the non‐divergent barotropic vorticity equation. Integrations are performed with time steps ranging from 15 min to 4 h. The root‐mean‐square differences between the forecasts are calculated in order to measure the sensitivity of the predictions to the size of the time step. These experiments show that the truncation errors remain reasonably small with time steps as large as two hours. This scheme is then associated with the semi‐implicit algorithm in the integration of the shallow water equations. Integrations are carried out with large time steps and the resulting predictions are presented in order to demonstrate that the scheme is perfectly stable.

Statistical properties of sediment bed profiles in alluvial channels

The objective of this study is to investigate in detail the statistical properties of series of bed elevations measured on gravel-bed and sand-bed alluvial channels, in order to identify means of quantifying bed roughness effects on streamflow. The semivariogram is used as the basic statistical method for investigating roughness properties of bed profiles obtained from field work and laboratory experiments. For sand bedforms, the semivariograms include exponential and periodic components from which can be obtained reliable measures of bedform spacing and height, as well as information on the degree of regularity of bedform arrangement. Because of the irregular nature of gravel-bed profiles, the approach in this case uses the semivariogram to investigate fractal properties of series of bed elevations to determine scales of bed roughness associated with grain sizes and small-scale bedforms and to estimate the Hausdorff dimension corresponding to each scale. These superimposed scales of roughness may be responsible for the greater flow resistance generally observed in gravel-bed rivers rather than predicted from the theoretical friction equation.

Boundary roughness in coarse-grained channels

Riverbed configurations in natural environments are shaped by varying flows. Despite advances in understanding of riverbed forms and the related phenomenon of sediment transport, many issues remain to be investigated (Allen, 1983). Among these is the fact that bed forms are sources of boundary roughness which cannot be satisfactorily predicted because of a lack of knowledge of the factors determining the size and shape of sedimentary structures in alluvial channels. Riverbed forms create local acceleration and deceleration of the near-bed flow.

Identification and elimination of an inflow boundary computational solution in limited area model integrations

Abstract The linearized non‐divergent barotropic vorticity equation in one dimension is used for the study of a problem associated with the specification of lateral boundaries in limited area models. This problem presents itself in the form of a “pillow” that builds up near the inflow boundary of the model. Linear analysis shows that this pillow can easily be eliminated. Linear integrations carried out with a corrector seem to be reasonably accurate. Similar integrations with the linearized shallow water equations in one dimension also produce a pillow and the same corrector gives improved results. Additional runs are performed in order to show that some commonly used nesting strategies do not control this computational problem in a satisfactory manner. It seems that these strategies could be improved with an appropriate corrector.

A Historical Perspective on Numerical Weather Prediction: A 1987 Interview with André Robert

ABSTRACT In view of Andre Roberts outstanding scientific contributions, he was selected for a personal interview as part of the Oral History Project of the Canadian Meteorological Service. The interview covered a variety of topics including Andres education, early career, the beginnings of numerical weather prediction (NWP) in Canada, the evolution of NWP models at the Canadian Meteorological Centre, Andres general research methodology and his views on the impact and future of NWP. These phases are illustrated by many personal glimpses and anecdotes such as puzzles that his relatives challenged him with in his youth, his explanation of why “a lot of time in my life was spent trying to avoid reading literature”, and his expectation that “one day we are going to see forecasts of such a high quality that these will be even more accurate than the observations”. In addition to capturing Andres characteristically clear and unconventional insights, the contents also provide a very informative complement to t...

A C-grid Ocean General Circulation Model: Model Formulation and Frictional Parametrizations

ABSTRACT We describe the formation of an ocean circulation model using the Arakawa C-grid. The C-grid has been shown to give more accurate results than the B-grid in the treatment of geostrophic adjustment and linear convection. The model is formulated with β-plane geometry, and temperature is the only state variable. We include in the model a semi-implicit formulation of the Coriolis terms and a small scale dissipative term which depends on the horizontal divergence. The latter reduces the noise in the vertical motion field at coarse horizontal resolution. The results are compared to those obtained with other forms of frictional parametrizations.

Incompressible Homogeneous Fluids

ABSTRACT The four equations required for the study of motion in incompressible homogeneous fluids are given. Problems associated with the integration of these equations are examined. The balance equation and the vorticity equation are derived. Three integration procedures are described. The spatial finite difference discretization of these equations is examined. Integrations with the Crank-Nicolson scheme are presented.

An Anomaly in the Behaviour of the Time Filter Used with the Leapfrog Scheme in Atmospheric Models

ABSTRACT Integration techniques such as the explicit leapfrog scheme or the semi-implicit method carry out their calculations over three time levels. Because of this characteristic, these algorithms can produce computational modes that appear as superimposed onto the physical solution of the meteorological equations. These computational modes can cause problems and in order to avoid these problems or remove them, a common practice is to use a rime filter. The rime filter that is frequently used for this purpose efficiently damps the computational mode while it has little effect on the physical solution. This filter does not always behave exactly as expected and in some cases, strange results are observed. A series of simple numerical experiments are carried out in order to show that the filter can display an anomalous behaviour under certain conditions. An attempt is made to explain this behaviour by numerical analysis. This analysis gives some information as to how to avoid this anomalous behaviour in at...