6. Raluca RADU : "Extensive study of the coupling problem for a high resolution limited area model"”
Limited area models need information about the state of the atmosphere outside the integration area, so one of the inherent problems is the specification of the lateral boundary conditions. A number of studies have demonstrated that LBCs of LAMs can have a significant impact on the evolution of the predicted fields through the propagation of boundary errors onto the interior of the domain. As each prognostic variable is prescribed at each lateral boundary point, the result is over-determination (ill-posedness) and a consequence is partial reflections that propagate these errors back in the integration area. In order to introduce lateral boundary information coming from large scale model and to damp the reflection produced by limited area model, the Davies-Kallberg relaxation scheme (Davies 1976) is used in ALADIN. This method accepts its ill-posedness and tries to damp reflected spurious waves by using a relaxation zone. Coupling means that every time step the values of the ALADIN model, obtained without any influence of the coupling model, are combined with the values interpolated on the ALADIN grid starting from the coupling model.
During this first ALATNET stay the study has been concentrated on the study of the presently used relaxation scheme and on the improving of a new method for coupling. The investigation of weaknesses of the Davies-Kallberg scheme and possible enhancement of it was the first step. This was tested with 3D numerical experiments on Christmas storm from December 1999. In this case two deep cyclones developed in the middle Atlantic and passed quickly through Western Europe. Some integrations of standard ALADIN model, using hourly ARPEGE global model forecasts as coupling files and applying them as lateral boundary conditions for the LACE domain, were done. The purpose was to study the impact of coupling frequency by comparing the depth of the cyclone in the coupling and coupled model near the time of entering domain using MSLP post-processed fields and observing the entry time in the domain.
25.12.1999 Christmas storm case
Starting from the given data the model arrives to a surprising solution with 6 hours coupling frequency of updating the boundary files. For 18 hours forecast valid for 06UTC in 26.12.99 the cyclone is missing (Fig1a), meanwhile for 3 hours coupling frequency, the pressure field has the value 976 hPa (see Fig1b) and with hourly coupling frequency the same hour, the cyclone has the deepest value 974 hPa (Fig1c) and the closest to the forecasted field by ARPEGE (Fig1d), the reasonably good for that day.
27.12.1999 Christmas storm case
Using 6 hours coupling frequency in integration for 24 hours with coupling files from global model the plotted MSLP field has 984 hPa value for the second cyclone at 21 UTC for 27.12.99, for the same hour a value of 982 hPa using 3 hours coupling files frequency in integration of the model and the deepest value again was obtained using hourly coupling frequency 980 hPa, as in the case of the first storm. For the coupling field obtained directly from global model there is a minimum value 977 hPa from all of them. As we expected the closest value to reality in both cases was that one obtained through hourly frequency of coupling.
Discussion
Because the system was moving very fast it happened that it didn't appear in the coupling zone of the model at the coupling times. ALADIN has no chance to forecast the storm if the cyclone genesis process is outside its domain, as it gets any information through lateral boundary conditions on the existence of such a system. Even if the coupling model forecasts the system, the coupling scheme can fail to pass the information to the LAM, and this was the case. In addition, the forcing field is not the forecasted field of the coupling model for the given time, but the field obtained by temporal interpolation of two forecasts of the global models. If the system had no trace on the coupling zone (first time is outside the domain, next time is fully entered inside the domain), it cannot be forecasted by LAM. This can happen because the coupling model passes the information to the LAM only by its fields over the coupling zone at discrete times.
Next step is introduction and testing of spectral coupling, considered to be a solution for the problems described above, offered by the fact that ALADIN is a spectral model using Fourier expansions in both horizontal directions. Spectral coupling means blending of large scale spectral state vector with the state vector of the coupled model so that the blended state vector is equal to the large scale one for small wave-numbers and equal to the coupled one for large wave-numbers with a smooth transition in between. A spectral coupling scheme is built on the same analogy as the Davies relaxation scheme. It presents an additional coupling step to the present scheme.
New coupling scheme provides scale selection where large scales are dominated by the spectra of the coupling model and only small scales resolved by the forcing model are dominated by LAM. The potential advantage of spectral coupling is that scales resolved by the coupled model are forced to LAM, even if the location of the system of the given scale is inside the domain. Spectral coupling cannot eliminate spurious inward propagation through the lateral boundaries, without the damping by the standard Davies scheme all waves that exit on one side of the domain would freely enter on the opposite side, but using simultaneous Davies scheme and spectral coupling the advantages of both methods are combined.
This point required code development, which is going at the present moment. It looks reasonable to introduce this step after finishing semi-implicit scheme in spectral space but before applying horizontal diffusion. In principle the idea is to read the spectral coupling fields, introduction of a large scale buffer, make the time interpolation and blend ALADIN spectral fields with interpolated large scale ones by the use of the spectral alpha weight function. In order to avoid too strong external forcing we consider retuning of alpha function of grid-point coupling, and also we keep open the possibility not to apply the spectral coupling at every time step of integration of the model (introduction of step frequency).
References
Davies, 1976: "A lateral boundary formulation for multi-level prediction models" QJRMS, 102, 405-418
A. Mc Donald, 1997: "Lateral boundary conditions for operational regional forecast models" a review HIRLAM technical note no.32
R. Lehmann, 1993: "On the choice of relaxation coefficients for Davies lateral boundary scheme for regional weather prediction models", Meteorology and Atmospheric Physics, 52, 1-14
Gabor Radnoti, 2001: "An improved method to incorporate lateral boundary conditions in a spectral limited area model"
M. Janiskova, 1994: " Study of the coupling problem". ALADIN note
Figure1: Impact of coupling frequency on MSLP field forecasted for 18 hours valid for 26.12.99 06 UTC:
a) MSLP field of ALADIN using 6 hours coupling files, b) MSLP field of ALADIN using 3 hours coupling files, c) MSLP field of ALADIN using 1 hour coupling files, d) MSLP field of ARPEGE forecast.
7. André SIMON : "Study of the relationship between turbulent fluxes in deeply stable PBL situations and cyclogenetic activity"
The work is just starting. The very first and important progress is the discovery of the big bug in CYCORA_ter. Congratulations ! More news in the next Newsletter.
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