A study of the influence of the coupling frequency and method on the prediction of a fast moving cyclone by ALADIN/LACE has been made on the case of 26/12/1999 storm. Although the operational ARPEGE which is used as the coupling model for ALADIN/LACE did a very good job and predicted the cyclone track and depth very well, the ALADIN/LACE operational forecast failed even to reproduce the cyclone forecast from the driving model.
This failure is attributed to an unfortunate combination of the small size and fast motion of the cyclone (its speed was about 110 km/h when entering the LACE domain) on one side and the too long coupling interval of 6 hours on the other side. Indeed, the cyclone entered the ALADIN/LACE integration domain on 1999/12/26 03UTC and passed through the thin model coupling zone (about 100 km wide) just between the coupling update (at 00 and 06 UTC). The signal was therefore lost and not captured by the internal domain solution.
In order to improve the forecast a set of several experiments was done:
The starting time for integration of all experiments mentioned above was 1999122512, operational reference is ALAD.
The aim was to enlarge C-zone twice. This was not fully possible to do because of the failure of the algorithm computing the relaxation weights in the coupling zone corners (subroutine SUEBICU). The maximum possible combination was NBZONL=12, NBZONG=10 (recall the default settings NBZONL=NBZONG=8). This brought basically no improvement of the cyclone forecast compared to the operational one. Hence, enlarging the C zone is not an issue.
It is quite evident and also proven, that using a shorter interval of the coupling brings positive influence to the resulting forecast because of more frequent update of the information on the in-flow boundary of integration domain. Currently used 6 hour interval is a compromise between the ''optimal'' coupling demand and the telecommunication constraints. Focusing on our extreme case one can see that forecast with 3 hours coupling interval is significantly better than the operational 6 hour interval in terms of both the localisation and the depth of small cyclone entering the LACE integration domain (see Fig. 4, Fig. 3).
The verifying analysis minimum was 974 hPa in the centre of that cyclone on 1999/12/26 at 06UTC (NW of France), while the observed minima were about 960 hPa!. Operational reference 6h LBC run gives value 988 hPa with no cyclone, just converging isobars. The 3h LBC test gives value a 976 hPa low precisely localised when compared to the observations.
6 hours later one can see first closed isobar 982.5 hPa in 6h LBC run, placed a little bit more to the east than in the 3h LBC run. The centre of the cyclone in latter case has 972.5 hPa with exact position. Corresponding analysis gives the minimum 974 hPa.
After further next 6 hours the pressure in the middle of cyclone rapidly grew to 980 hPa. The 3h LBC run starts to undershoot the pressure, it gives 972 hPa placed roughly 2.5° East from the observed cyclone centre. The 6 h LBC starts to have better forecast of minimal pressure but localisation of the centre is roughly 4° misplaced. This discrepancy probably comes from both the model's dynamics/physics and the lateral forcing of ARPEGE, which also undershoots the cyclone pressure in later hours of the forecast.
Another experiment with 1h coupling frequency (AA1H) was performed (just for the comparison with the experiments mentioned above). The position of small cyclone was forecasted well (the same as for AA3H) and the pressure was further lower in the cyclone centre, for example 969 hPa on 1999/12/26 at 12UTC.
At least for the time being. The quadratic temporal interpolation of LBC was coded already two years ago. After validation over some period it turned out, that from the scores point of view, the results were neutral. Since the computation required a little bit more CPU time and memory, it has never been used operationally. Nevertheless the algorithm has been kept in the code (LQCPL key).
Experiment made on the presented extreme case however shows that using LQCPL may bring a positive impact on the results because it provides a better interpretation of the coupling information between the coupling events (updates).
Comparing reference experiment AA6H (Fig. 3) with AQ6H (LQCPL=.TRUE.) (Fig. 2) one can see a first closed isobar in the AQ6H case already on 1999/12/26 at 09UTC, while in the AA6H case it was only 3 hours later. After next 3 hours AQ6H cyclone was 3.5 hPa deeper then AA6H with more precise localisation. Using LQCPL=.TRUE. the model processed the coupling information better and better generated the cyclone in the internal solution. Further on, an experiment AQ3H using both 3 hour frequency and quadratic interpolation performs as good as the one using 1 hour frequency (AA1H). This brings an important conclusion: further increase of the LBC update frequency beyond three hours may not be necessary when the quadratic interpolation is used.
Based on this conclusion we tried to move one step further to cubic polynomial interpolation. Results for the studied case were optimistic, the development of the cyclone was faster than for the quadratic interpolation. However the model run over a period of two weeks showed clear deterioration of skill scores. Therefore other experiments with higher order polynomials were abandoned. The problem is probably linked to the ``overshooting'' of interpolated values by higher-order polynomials. An example of used polynomials for interpolation can be seen on Fig. 1.
The scores of a two-week parallel test of ALADIN/LACE with the quadratic coupling are available at http://www.chmi.cz/meteo/ov/lace/aladin_lace/partests/aav/ showing a slight reduction of RMSE and bias of the geopotential in the troposphere.
Coupling files for ALADIN/LACE from the ARPEGE model are available only at some forecasting times, currently it is every 6 hours of the forecast. In the course of ALADIN/LACE forecast the lateral boundary update (the coupling) is however made in every time step. Therefore an interpolation in time is needed to obtain intermediate boundary values between the times the coupling files are available.
So far a simple linear interpolation between two consecutive coupling files has been used. Quadratic interpolation means that a piece-wise quadratic function is used for interpolating from two previous and one following coupling file (e.g. integration between 18 and 24 h will use the coupling files for 12, 18 and 24 hours). The only exception is the first interval (0-6 hours) which keeps the linear approach (since there is no ``-6h'' coupling file).
This interpolation is still far from advanced interpolations like the cubic splines which would require the knowledge of all interpolated values in advance. Because of operational constraints one can not wait for the last coupling file and start to integrate only after receiving it. Instead, the forecast starts immediately at the moment when the second coupling file is available and that is why the interpolation within 00 - 06 interval must be linear in any case. Later on the information from three LBC files is used in the quadratic interpolation. The resulting curve of interpolated values is certainly better than the normal linear one but of course yet not smooth in any mathematical sense.
The presented technique of the quadratic coupling improves the model ability to cope with the extreme cases of a fast moving cyclone while being rather neutral in a long-term skill. The algorithm entered the operational suite of ALADIN/LACE on 12 April 2000. The optimal operational target would be the combination of 3h frequency and piece-wise quadratic interpolation of LBC in time.
The method and its use is an intermediate result of the ongoing research carried on by the RC LACE Prague Team focusing on the coupling issues in ALADIN.
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