Tropical initial condition perturbations

In tropical areas physical processes may contribute significantly to perturbation growth. To determine singular vectors for such situations, linearised versions of important physical parametrizations included in the ECMWF model (vertical diffusion, subgrid-scale orographic effects, large-scale condensation, long-wave radiation and deep cumulus convection) are needed. The recent development of this package of linearized physics (Mahfouf 1999) has made it possible to extent the area of initial EPS perturbations to the tropical region.

Tropical singular vectors

The main difference between the tropical and extra-tropical singular vector computation is the use of the newly developed package of linear physics in the tropics. The norms used to define the perturbation growth are the same for both regions: the total energy norm is used at initial and final time.

Target areas

To benefit from tropical singular vectors in tropical cyclone ensemble forecasting, it is necessary to define target areas in the vicinity of tropical cyclone locations. The number of singular vectors' computations in the tropical region may vary from day to day depending how many target areas are defined. However, to limit the numerical costs, the maximum number of target areas is set to four:

i. the Carribean area (0°-25°N, 100°W-60°W) is always selected, since weather systems originating from the Carribean area may influence medium-range European forecasts;
ii. for each tropical systems with WMO classification index larger than 1 (hurricanes, typhoons, cyclones, severe tropical storms or tropical storm) in the tropical strip 25°S-25°N a 30°x40° target area centered at the system location and intersected by the strip 25°S-25°N is defined;
iii. if more than four areas have been defined, than merge the closest target areas to a maximum of four.

Multiple computations are required when several tropical cyclones coexist. In order to reduce the overall numerical costs of determining perturbations in the tropics, a multi-Gaussian sampling technique was adopted as described in Ehrendorfer (1999). For each tropical cyclone, 50 initial EPS perturbations are determined by sampling from the leading five singular vectors and added to the already existing perturbations.

Benefits of tropical perturbations

The tropical singular vectors have a clear impact on the EPS cyclone tracks. Figure 3 shows the tracks for cyclone ANDO of the 50 ensemble members for a forecast period of 4 days and starting from 4 January 2001. In the operational EPS, as shown in Figure 3a, all tracks follow the same route up to day 3 and there is a high probability that the cyclone will make landfall over La Reunion between days 2-3. The experimental EPS, however, makes this scenario less likely by indicating other possible cyclone tracks.

To investigate whether tropical perturbations are beneficial for the skill of the tropical cyclones tracks in the ensemble, distances between the ensemble tracks and the analysis for the tropical cyclone location have been computed for certain forecast periods and averaged over the 12 cases. Figure 4 gives the number of members, averaged over the 12 cases, closer to the analysed tropical cyclone location for selected distances and forecast periods. For a lead-time of 1 day, the EPS unperturbed control forecast is quite capable to position the tropical cyclone accurately. As seen from Fig. 4, initial perturbations may slightly deteriorate the skill of the ensembles members for this short forecast range. However, for longer lead times the number of skilful members is larger in the experimental ensemble.

Operational implementation

On the 21st of January 2002 tropical perturbations defined by singular vectors targeted to maximize total-energy inside an area centered on tropical storms were added to the operational EPS.

References

Barkmeijer, J., Buizza, R., Palmer, T. N., Puri, K., & Mahfouf, J.-F., 2001: Tropical singular vectors computed with linearized diabatic physics. Q. J. R. Meteorol. Soc., 127, 685-708.

Ehrendorfer, M., 1999: Prediction of the uncertainty of numerical weather forecasts: Problems and approaches. Proceedings of the ECMWF Workshop on Predictability, 20 - 22 October 1997, pp. 27-99.

Mahfouf, J.-F., 1999: Influence of physical processes on the tangent-linear approximation. Tellus, 51A, 147-166.

Puri, K., Barkmeijer, J. & Palmer, T. N., 1999: Ensemble prediction of tropical cyclones using targeted diabatic singular vectors. Q. J. R. Meteor. Soc., 127, 709-731.