PBPDA is a method to directly find the area where assimilating more data at the initial field will decrease the forecast error the most. The target area identified by this method was used as the true target area in this work. The three other methods are First Singular Vector (FSV), Ensemble Transform Kalman Filter (ETKF), and Conditional Nonlinear Optimal Perturbation (CNOP). FSV and ETKF are based on linear assumption while the PBPDA and CNOP do not.
The forecast metric used in this work is the difference total energy (DTE) of the 48-h forecast. The target area identified by PBPDA located to the north of the MCV center. CNOP located the target area to the northeast of the MCV center. The target area identified by the ETKF was collocated with the MCV center, while the FSV didn't have a target area near the MCV. Generally speaking, the target area identified by CNOP was closer to the one identified by PBPDA than FSV and ETKF. Besides the targeted area near the MCV, the CNOP also identified targeted areas to the north and northwest of the MCV center. The FSV identified one far to the northwest of the MCV.
The impact of the sensitive area identified by different methods was further examined through data assimilation using an observing system simulation experiment (OSSE). Using DTE as the forecast metric, all methods have significantly larger error reduction than no data assimilation experiments (NoDA). PBPDA had the highest reduction of the forecast error compared to other methods. CNOP and ETKF had similar error reduction though their targeted area had different locations. FSV had the largest forecast error. This result confirmed the results obtained in our previous work: Using DTE as the forecast metric, a difference in the location of identified targeted area does not make a significant difference in the improvement on the forecast. What really matters is the data assimilation itself instead of assimilating data in a particular area.
The impact of assimilating data in the targeted area identified using DTE as the forecast metric on the possible improvement in rainfall forecast was also examined. In terms of rainfall TS, all the four targeted areas produced a lower TS than the targeted area identified using rainfall as the forecast metric. CNOP and ETKF has similar TS and both are significantly higher than that of NoDA. The TS of FSV and PBPDA-DTE are no different from that of NoDA. This result also confirmed the results obtained in our previous work: Using rainfall as the forecast metric, a very accurate target area is required and a difference in the location of identified targeted area does make a significant difference in the improvement on the forecast.
Results of this work indicate that in operational practice of targeted observation, ETKF and CNOP could be better choices than FSV. They can not only more apparently decrease the forecast error in terms of the used norm but also improve the rainfall forecast.