Improving Initial Condition Adaptive Data Assimilation

Numerical forecasts of chaotic systems like the atmosphere are limited by the use of imperfect initial conditions. Lorenz (1965) pointed out that any minor discrepancies, between either the natural system and its model or the actual and the analyzed state of the system at the initial time of a forecast, will lead to a loss of predictability within a finite time period. The size of these discrepancies will, in general, determine the time period for which useful forecasts can be made. Improving the analysis of the atmosphere used as initial condition is hence one of the basic avenues through which progress can be made in NWP.

Although the regular and opportunity driven observations constitute the backbone of the global observing network, satellite derived atmospheric properties as discussed in the previous section are expected to be able to provide the accuracy, coverage, and resolution to improve our understanding of the dynamics of the atmosphere. Current remotely-sensed observations, therefore, provide the opportunity to assist the hurricane research community in addressing the deficiencies in initial conditions. The utilization of these data, however, will require either massive increase in our data processing capability, or a change in our approach. The selective extraction of observations (i.e., targeted observations) is, for example, one possible method to make maximal utilization of the satellite derived information.

3DOI scheme is used in many data assimilation studies (e.g., Daley, 1991), since it is less CPU intensive. The basic principle of the OI scheme is that an estimate of the value of a variable at a set of grid points can be created from a set of meteorological observations distributed irregularly throughout the analysis domain by forming an "optimal" linear combination of the observations closest to the grid point. However, the 3DOI analysis scheme provides a simple means for assimilating data. More sophisticated assimilation methods (such as three-dimensional or four-dimensional variational analysis, 3DVAR/4DVAR) may yield better results (e.g., Leslie et al., 1998).

For example, Figures 4 and 5 show one of the recent such studies in which temperature and dew point temperature soundings from the GOES satellite were selectively (i.e., targeted way) assimilated using a 3DOI scheme to improve the model initial condition (Boybeyi et al., 2007). The results show that by reducing uncertainties in the steering polar jet entrance flow region at initial time, the track

Fig. 4 Shown are; (left) 300-mb wind and height ETA analysis roughly overlaid on the enhanced infrared image of hurricane Floyd at 0000 UTC on September 15, 1999. The shaded area shows the high winds in the polar jet entrance steering flow region, (middle) the locations of about 1200 irregularly spaced GOES temperature and dew point temperature soundings superimposed on the observed Floyd track (hurricane symbols) and (right) OMEGA model forecasted tracks with the assimilation of the soundings at model initial time on 0000 UTC 9/14/2005 (dashed lines) and without the data assimilation (solid line)

Fig. 4 Shown are; (left) 300-mb wind and height ETA analysis roughly overlaid on the enhanced infrared image of hurricane Floyd at 0000 UTC on September 15, 1999. The shaded area shows the high winds in the polar jet entrance steering flow region, (middle) the locations of about 1200 irregularly spaced GOES temperature and dew point temperature soundings superimposed on the observed Floyd track (hurricane symbols) and (right) OMEGA model forecasted tracks with the assimilation of the soundings at model initial time on 0000 UTC 9/14/2005 (dashed lines) and without the data assimilation (solid line)

error was improved by about 30%. In a NWP model, the initial uncertainty is mainly associated with the low resolution of the observations. This problem is amplified further in hurricane initialization due to lack of observations over the ocean regions (Burpee et al., 1996; Aberson and Franklin, 1999).

Today, we are on the verge of having improvements in horizontal, vertical, and quantitative resolutions to provide 10 to 100 times more than is potentially useful for TC forecasting. This is due to the computational cost of data assimilation that is quadratic in both the model horizontal grid resolution and the number of observations used. Over the coming decade, we are likely to see a 10-fold increase in the forecast model resolution and a 10-100 fold increase in the amount of satellite data. This will result in a 104 to 106 fold increase in the cost of data processing, which will far outstrip the factor of 100 increase in computing power predicted by Moore's Law over the same period.

Targeted observations can provide a viable solution to the above noted problem. From a numerical modeling point of view, the prediction will be more sensitive over some areas as compared to others, or the inaccuracy of analysis over some locations will affect the forecast errors more than in other locations. Thereby, the concept of targeted data assimilation can improve forecast skill by reducing the uncertainties over some particular areas for specific weather systems at the initial stages. Forecasts of events with potentially large societal impact, such as tropical cyclones (hurricanes), are prime candidates for targeted observation studies, given there is substantial uncertainty in their forecasts. Many investigators also studied this concept for TC simulations (Joly et al., 1997; Gelaro et al., 1999; Bergot et al., 1999; Leutbecher 2003; and Kim et al., 2004).

Temperature Error Distribution below 850 mb level

Temperature Error Distribution below 850 mb level

□ RUN without RAOBs ■ RUN with RAOBs

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-10 -9 -8 -T -6 -5 -4 -S -2 -10 1 2 S 4 5 6 T 8 9 10 Model - Obs error, C

-10 -9 -8 -T -6 -5 -4 -S -2 -10 1 2 S 4 5 6 T 8 9 10 Model - Obs error, C

Dew Point Error Distribution below 850 mb level

Dew Point Error Distribution below 850 mb level

Model - Obs error, C

Fig. 5 Shows temperature (top) and dew point temperature (bottom) error distribution for the case presented in Fig. 2 below 850 mb level for hurricane Floyd case at model initial time (0000 UTC 9/ 14/1999) with and without the assimilation of the GOES soundings, respectively

Model - Obs error, C

Fig. 5 Shows temperature (top) and dew point temperature (bottom) error distribution for the case presented in Fig. 2 below 850 mb level for hurricane Floyd case at model initial time (0000 UTC 9/ 14/1999) with and without the assimilation of the GOES soundings, respectively

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