Harold Ritchie

A System Simulation Approach to Ensemble Prediction

Abstract For many aspects of numerical weather prediction it is important to have good error statistics. Here one can think of applications as diverse as data assimilation, model improvement, and medium-range forecasting. In this paper, a method for producing these statistics from a representative ensemble of forecast states at the appropriate forecast time is proposed and examined. To generate the ensemble, an attempt is made to simulate the process of error growth in a forecast model. For different ensemble members the uncertain elements of the forecasts are perturbed in different ways. First the authors attempt to obtain representative initial perturbations. For each perturbation, an independent 6-h assimilation cycle is performed. For this the available observations are randomly perturbed. The perturbed observations are input to the statistical interpolation assimilation scheme, giving a perturbed analysis. This analysis is integrated for 6 h with a perturbed version of the T63 forecast model, using p...

Implementation of the Semi-Lagrangian Method in a High-Resolution Version of the ECMWF Forecast Model

Abstract In this article the implementation of the semi-Lagrangian method in a high-resolution version of the ECMWF forecast model is examined. Novel aspects include the application of the semi-Lagrangian scheme to a global model using the ECMWF hybrid coordinate in the vertical and its use in a baroclinic spectral model in conjunction with a reduced Gaussian grid in the horizontal. The former Eulerian vorticity-divergence formulation is first converted into a momentum-equation formulation that is considerably more economical, thanks in part to the incorporation of Legendre transform efficiencies that were previously demonstrated for the shallow-water equations. The semi-Lagrangian formulation is presented in detail, together with a discussion of computational aspects that are relevant for executing the high-resolution model efficiently on a modestly parallel supercomputer. The impact of formulation changes is assessed via numerical experiments on a set of 12 independent cases. In particular it is shown t...

A Semi-Lagrangian and Semi-Implicit Numerical Integration Scheme for Multilevel Atmospheric Models

Abstract A complete multilevel atmospheric model of the primitive meteorological equations is integrated at high spatial resolution with a large time step of 90 min. Numerical stability is achieved by associating a semi-Lagrangian technique with the commonly used semi-implicit algorithm. A detailed description of the method is given and some results are presented. From these runs, it seems possible to infer that the time truncation errors remain relatively small. Because of the 1arger time step, the semi-Lagrangian technique contributes to a significant enhancement of the efficiency of the semi-implicit integration scheme.

Seasonal predictions based on two dynamical models

Abstract Two dynamical models are used to perform a series of seasonal predictions. One model, referred to as GCM2, was designed as a general circulation model for climate studies, while the second one, SEF, was designed for numerical weather prediction. The seasonal predictions cover the 26‐year period 1969–1994. For each of the four seasons, ensembles of six forecasts are produced with each model, the six runs starting from initial conditions six hours apart. The sea surface temperature (SST) anomaly for the month prior to the start of the forecast is persisted through the three‐month prediction period, and added to a monthly‐varying climatological SST field. The ensemble‐mean predictions for each of the models are verified independently, and the two ensembles are blended together in two different ways: as a simple average of the two models, denoted GCMSEF, and with weights statistically determined to minimize the mean‐square error (the Best Linear Unbiased Estimate (BLUE) method). The GCMSEF winter and spring predictions show a Pacific/North American (PNA) response to a warm tropical SST anomaly. The temporal anomaly correlation between the zero‐lead GCMSEF mean‐seasonal predictions and observations of the 500‐hPa height field (Z500) shows statistically significant forecast skill over parts of the PNA area for all seasons, but there is a notable seasonal variability in the distribution of the skill. The GCMSEF predictions are more skilful than those of either model in winter, and about as skilful as the better of the two models in the other seasons. The zero‐lead surface air temperature GCMSEF forecasts over Canada are found to be skilful (a) over the west coast in all seasons except fall, (b) over most of Canada in summer, and (c) over Manitoba, Ontario and Quebec in the fall. In winter the skill of the BLUE forecasts is substantially better than that of the GCMSEF predictions, while for the other seasons the difference in skill is not statistically significant. When the Z500 forecasts are averaged over months two and three of the seasons (one‐month lead predictions), they show skill in winter over the north‐eastern Pacific, western Canada and eastern North America, a skill that comes from those years with strong SST anomalies of the El Niño/La Niña type. For the other seasons, predictions averaged over months two and three show little skill in Z500 in the mid‐latitudes. In the tropics, predictive skill is found in Z500 in all seasons when a strong SST anomaly of the El Niño/La Niña type is observed. In the absence of SST anomalies of this type, tropical forecast skill is still found over much of the tropics in months two and three of the northern hemisphere spring and summer, but not in winter and fall.

Semi-Lagrangian Advection on a Gaussian Grid

Abstract The treatment of advection is related to the stability, accuracy and efficiency of models used in numerical weather prediction. In order to remain stable, conventional Eulerian advection schemes must respect a Courant-Friedrichs-Lewy (CFL) criterion, which limits the size of the time step that can be used in conjunction with a given spatial resolution. In recent years, tests with gridpoint models have shown that semi-Lagrangian schemes permit the use of large time steps (roughly three to six times those permitted by the CFL criterion for the corresponding Eulerian models), without reducing the accuracy of the forecasts. This leads to improved model efficiency, since fewer steps are needed to complete the forecast. Can similar results be achieved in spectral models? This paper examines the semi-Lagrangian treatment of advection on the Gaussian grid used in spectral models. Interpolating and noninterpolating versions of the semi-Lagrangian scheme are applied to the problem of solid body rotation on...

Approximations and Sensitivity Experiments with a Baroclinic Semi-Lagrangian Spectral Model

Abstract This study examines the extensions that have been made to a basic semi-Lagrangian semi-implicit multilevel spectral primitive equation model in preparing it for use as an operational data assimilation and medium-range forecast model. The authors present an optimized formulation using accurate approximations to alternate trigonometric calculations for finding the upstream positions and performing the transformations for treating a vector form of the equation of motion in spherical geometry. The impact of the order of accuracy of the interpolators used in the semi-Lagrangian algorithms is also examined. It is shown that the recommended approximations have no significant meteorological consequences, but in a typical model step they reduce the time spent in the semi-Lagrangian calculations from about 50% to about 30%. Through a series of sensitivity tests, the authors establish the viability of the semi-Lagrangian semi-implicit method for spectral models with a more comprehensive physical parameteriz...

Application of the Semi-Lagrangian Method to a Spectral Model of the Shallow Water Equations

Abstract Previous tests with grid-point numerical weather prediction models have shown that semi-Lagrangian schemes permit the use of time steps that are much larger than those permitted by the Courant-Friedrichs-Lewy (CFL) stability criterion for the corresponding Eulerian models, without reducing the accuracy of the forecasts. Thus model efficiency is improved because fewer time steps are needed to complete the forecast. In a first step to see if similar results can be achieved in spectral models, Ritchie, in a previous study, applied interpolating and noninterpolating semi-Lagrangian treatments of advection to the problem of simple advection by a steady wind field on a Gaussian grid. This present paper combines these treatments of advection with the semi-implicit scheme in a spectral model of the shallow water equations expressed in vector momentum form. Model formulations are presented and intercomparison experiments are performed. It is shown that both interpolating and noninterpolating semi-Lagrangi...

On the Use of Coupled Atmospheric and Hydrologic Models at Regional Scale

Abstract. The purpose of this study is to present the possibilities offered by coupled atmospheric and hydrologic models as a new tool to validate and interpret results produced by atmospheric models. The advantages offered by streamflow observations are different from those offered by conventional precipitation observations. The dependence between basins and sub-basins can be very useful, and the integrating effect of the large basins facilitates the evaluation of stateof-the-art atmospheric models by filtering out some of the spatial and temporal variability that complicate the point-by-point verifications that are more commonly used. The streamflow predicted by the coupled atmospheric-hydrologic model versus the measured streamflow is sufficiently sensitive to clearly assess atmospheric model improvements resulting from increasing horizontal resolution and altering the treatment of precipitation processes in the model. A case study for several southern Ontario river basins is presented with the Watflood hydrologic model developed at the University of Waterloo. It is passively coupled to a nonhydrostatic mesoscale atmospheric model (mc2) that is integrated 318 HIGH PERFORMANCE COMPUTING SYSTEMS AND APPLICATIONS at horizontal resolutions of 35, 10 and 3 km. The Watflood model is also driven by radar derived precipitation amounts from King City Radar observations. It is demonstrated that the hydrological model is sufficiently sensitive and accurate to diagnose model and radar errors. This tool brings an additional degree of verification that will be very important in the improvement of technologies associated with atmospheric models, radar observations and the water resources management.

Eliminating the interpolation associated with the semi-Lagrangian scheme

Abstract There are several reasons why it is desirable to eliminate the interpolation associated with the conventional semi-Larangian scheme. Interpolation leads to smoothing and is also the most costly operation associated with the technique. Furthermore, its elimination produces a scheme that is more readily adaptable to a spectral model. In the conventional semi-Lagrangian method, in order to predict a field value at grid point (Xi, Yj) it is necessary to calculate the trajectory over one time step for the fluid element that arrives at (Xi, Yj). One then moves along this trajectory in order to extract the field value at an upstream location that generally lies between the grid points, and hence requires the use of interpolation formulae. This trajectory can be represented as a vector. In the new scheme, the trajectory vector is considered to be the sum of two other vectors—a first vector joining (Xi, Yj) to the grid point (Xu, Yu) nearest the upstream location, and a second vector joining (Xu, Yu) to t...

Impact of a Two-Way Coupling between an Atmospheric and an Ocean-Ice Model over the Gulf of St. Lawrence

The purpose of this study is to present the impacts of a fully interactive coupling between an atmospheric and a sea ice model over the Gulf of St. Lawrence, Canada. The impacts are assessed in terms of the atmospheric and sea ice forecasts produced by the coupled numerical system. The ocean-ice model has been developed at the Maurice Lamontagne Institute, where it runs operationally at a horizontal resolution of 5 km and is driven (one-way coupling) by atmospheric model forecasts provided by the Meteorological Service of Canada (MSC). In this paper the importance of two-way coupling is assessed by comparing the one-way coupled version with a two-way coupled version in which the atmospheric model interacts with the sea ice model during the simulation. The impacts are examined for a case in which the sea ice conditions are changing rapidly. Two atmospheric model configurations have been studied. The first one has a horizontal grid spacing of 24 km, which is the operational configuration used at the Canadian Meteorological Centre. The second one is a high-resolution configuration with a 4-km horizontal grid spacing. A 48-h forecast has been validated using satellite images for the ice and the clouds, and also using the air temperature and precipitation observations. It is shown that the two-way coupled system improves the atmospheric forecast and has a direct impact on the sea ice forecast. It is also found that forecasts are improved with a fine resolution that better resolves the physical events, fluxes, and forcing. The coupling technique is also briefly described and discussed.