During the early developmenTof numericalweather prediction, meteorologists noticed that theforecast skill in a focused area was limited by the initial conditions in a local region(Riehl et al., 1956).The improvement in forecast skill from adding observations in a local area may be no less than that inducedby addition of the observ ations in a wide area. Thisidea of adding additional observ ations in a local areato improve the forecast ability, is called targeted observ ation, or adaptive observ ation. To make a moreaccurate prediction at a future verification time(t_v)in a focused verification area, additional observ ationsare implemented at a future targeted time(t_a), wheret_a < t_v, in a sensitive area where the observ ations areexpected to have a great impacTon the forecasts inthe verification area, as shown in Fig. 1. The additional observ ations are assimilated by data assimilation system to provide a more reliable initial state forthe model. A detailed description of targeted observ ation can be found in Mu(2013).

Fig. 1.Schematic diagram of targeted observation. [FromMu et al., 2013]

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The theory and practice of numerical weatherprediction and climate projection indicate that, asidefrom the performance of numerical prediction models, successful forecasting depends on the quality of theinitial field. In particular, if the initial field containssignals of the occurrence and developmenTof the focused event, the amplitude of the initial error significantly affects the forecast. The key idea of targetedobserv ation, denoted as region A, is to look for thesensitive area of initial error. However, the sensitivearea of the precursor for the occurrence of an anomalyevent, denoted as region B, should also be investigated.Intuitively, region A should contain region B; however, these two regions may be significantly different uponfurther inspection. In this situation, although the targeted observation implemented in region A could reduce the forecast error, the forecast skill may be stillrelatively low because the signals are not well captured. However, if regions A and B are almost thesame, the targeted observation carried out in a localarea can noTonly find the precursor, but also reducethe initial error. This helps to improve the accuracyof the forecast and save on the huge costs caused bythe observ ation. Interestingly, Mu Mu and his grouphave found and proved that the two regions are almost the same when studying the predictabilities ofthe atmospheric and oceanic anomaly events such asthe El Niño-Southern Oscillation(ENSO), Kuroshiopath variations, and atmospheric blocking(Mu(2013)Mu and Jiang, 2011; Wang et al., 2013; Mu et al., 2014). Thisresult is a solid foundation for targeted observ ationsof the above events.

In the studies mentioned above, the conditionalnonlinear optimal perturbation(CNOP; Mu et al., 2003)approach was used. CNOP represents the initialperturbation that attains the largest nonlinear evolution at the prediction time. Because the linear approximation assumption is not used, the CNOP methodcan be considered an extension of the singular vector(LV)method in the nonlinear regime(Duan and Mu, 2009), and su±ciently represents the roles of nonlinear dynamics and physical processes. Here, we reviewthe use of the CNOP method in studies of the optimalprecursor(OPR) and optimally growing initial error(OGE)in the predictability of the ENSO, Kuroshiopath variations, and atmospheric blocking. The OPRrefers to the initial anomaly that most easily develops into some weather or climate events under specificconditions, while the OGE represents the initial errorwith the largest nonlinear evolution that results in anon-negligible forecast error. It has been found thatthe spatial patterns of the OPR and OGE are highlysimilar and have obvious localization characteristicsfor each anomaly event(Mu and Jiang, 2011; Wang et al., 2013; Mu et al., 2014). This means that additionalobserv ations over the sensitive area identified based onthe similarity and localization features can well capture the precursor signal and reduce the initial error, thus improving the forecast skill.

The CNOP method has been successfully used todetermine the sensitive areas of typhoon and heavyrain. F or example, Mu et al.(2009) and Qin and Mu(2011)have used the method to recognize the sensitive area of a typhoon. Wang and Tan(2009) and Tan et al.(2011)developed a fast algorithm to calculate the CNOP and determined the sensitive area forthe prediction of a typhoon. In addition, Liu et al.(2013)employed the CNOP method to identify thesensitive area for the targeted observation of a winter storm in the middle-lower branches of the Y angtzeRiver. These studies have been reviewed in Mu(2013);hence, we omit reviewing them here. The present paper will mainly summarize the obtained results aboutOPR and OGE in the predictability studies of ENSO, Kuroshio path variations, and atmospheric blockingduring recent years, and particularly focus on the similarity and localization characteristics of the spatialstructures of OPR and OGE and associated inspiration to the determination of the sensitive area of targeted observ ation, so as to provide scientific basis forthe implementation of the targeted observation of theaforementioned anomaly events.2. Sensitive area for the prediction of El NiñoThe roles of initial errors in ENSO predictability

have been investigated by many researchers. F or example, Moore and Kleeman(1996) and Xue et al.(1997)suggested that ENSO prediction is sensitive tothe initial condition. Chen et al.(2004)indicatedthat the spring predictability barrier(SPB)of ENSOcan be greatly overcome through improvemenTof theinitialization for the Zebiak-Cane model(Zebiak and Cane, 1987). Recently, Mu et al.2007(a, b) and Duanet al.(2009)demonstrated that ENSO predictions areclosely associated with the growth of initial errors resulted from nonlinear instability, and emphasized thatthe initial errors with particular structures could causethe prominent SPB. F urthermore, Duan and Zhang(2010) and Yu et al.(2012a)showed the importanceof initial errors by comparing them with the modelparameter errors. If the initial errors of a particular pattern could be filtered and more accurate initialfields obtained, the prediction skill of the model forthe ENSO may be well improved. T argeted observ ation may be one of the approaches that can filter outthose initial errors(Duan and Mu, 2009; Yu et al., 2009).

Mu et al.(2007b)used the Zebiak-Cane modelto investigate the initial error and found that theCNOP method represented the initial error that hadthe largest effecTon the ENSO prediction, namely, theOGE, which could yield a significant SPB for El Niñoevents. They also argued that although some otherinitial errors had the same magnitude as the CNOPs, these errors neither caused significant prediction uncertainties nor yielded apparent season-dependent evolution, and therefore failed to induce SPB for El Niñoevents. It is clear that a particular error pattern is necessary for the occurrence of SPB for El Niño events. Yu et al.(2009)further divided the CNOP-type initial error into two types using cluster analysis(Fig. 2). The first type of CNOP error(termed type-1OGE)possessed a thermocline depth anomaly component with a deepening along the equator, and anSST A structure with negative anomalies in the equatorial central to western Pacific and positive anomalies in the equatorial eastern Pacific. The other type(type-2 OGE)possessed a sign almosTopposite to theformer. Although the two OGEs had different patterns, they were both associated with a localized region, so predictions may be sensitive to this.

Fig. 2.(a, b)Type-1 and (c, d)type-2 OGEs for El Ni~ no events in the Zebiak-Cane model.(a, c)The sea surfacetemperature anomaly(SST A) and (b, d)the thermocline depth anomaly . [From Yu et al., 2009]

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On the other h and, the CNOP also played a rolein the OPRs for El Niño and La Ni~ na events(Fig. 3).Duan et al.(2013)calculated the CNOP-type initialanomaly and found that the OPR for El Niño is similar to the type-1 OGE of El Niño, namely, it possessesan SST A dipole over the equatorial central and eastern Pacific, plus positive thermocline depth anomaliesover the entire equatorial Pacific. Mu et al.(2014)also found that the OPR for La Ni~ na is similar to thetype-2 OGE. Hence, Mu et al.(2014)suggested thatthe OPR and OGE for El Niño share great similarities, localization, and evolution mechanisms. Thus, if additional observation instruments are deployed astargeted observation with limited coverage, the similarly large amplitude areas for the OPR and OGEshould be considered first, to better detect the earlysignals for ENSO events and meanwhile reduce the initial errors. The identified area may also represent thesensitive area for ENSO prediction.

Fig. 3.OPRs for(a, b)El Niña and (c, d)La Ni~ na.(a, c)The SST A and (b, d)the thermocline depth anomaly . [From Mu et al., 2014]>

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To test the validity of the aforementioned sensitive area, Yu et al.(2012b)divided the tropical Pacificinto six parts with equal numbers of grid points(Fig. 4). Domain 5 covers the equatorial central and easternPacific and has the large amplitude area of both theOPR and OGE for El Niño events. F or each domain, the CNOP-type initial error was computed and themaximum prediction error caused by the initial errorwas checked. It is found that the initial error in Domain 5 evolved more significantly than those in otherdomains. This reflected the fact that the SST initialerrors over the equatorial central and eastern Pacificmay have the biggest effecTon El Niño prediction.

Yu et al.(2012b)further investigated the effectsof the sensitive area on the improvemenTof ENSO forecast skill using 240 initial analysis fields obtained fromhindcasting experiments from January 1980 to December 1999 with a later version of the Zebiak-Cane model(Chen et al., 2004). They replaced the initial analysisfield in each of the six domains with the initial field ofthe El Niño event to eliminate the error of the initialfield for each domain, and examined the reduction offorecast error(Fig. 5). They found that the decreasein the prediction error was more significant when eliminating the initial error in domain 5 than in the otherdomains.

Fig. 4. Two kinds of CNOP initial errors:(a)type-1 and (b)type-2, over the tropical Paci¯c divided into sixregions labeled as domains 1-6. Large values of both kindsof errors occur mainly in domain 5. [From Yu et al., 2012b]

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Fig. 5. Root mean square errors for the Niño-3 SST Acaused by the original initial errors(squares connected bya black line) and six other sets of initial errors(labeledExps. 1-6). Each seTof new initial errors was generatedby eliminating errors in one of the six domains(Fig. 4)from the original initial errors. [From Yu et al., 2012b]

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The Kuroshio path variation south of Japan isa key problem in physical oceanography . Some researchers have attempted to predict the Kuroshio pathvariations because they have important effects on climate change, marine environment, and fisheries(Komori et al., 2003; Kamachi et al., 2004; Miyazawa et al., 2005; Usui et al., 2006; Wang et al., 2012). Similarto the above ENSO predictability studies, Wang et al.(2013)utilized the CNOP method to explore the OPR and OGE of Kuroshio path variations, and also foundthat the spatial patterns of the OPR and OGE sharedgreat similarities and obvious localization features.

Wang et al.(2013)employed the CNOP approachto investigate the OPR of the occurrence of Kuroshiolarge me and er within a 1.5-layer shallow-water model.Figure 6a shows the upper-layer thickness componentof the OPR and indicates that the spatial structuresof the OPR shared obvious localization characteristics and its large amplitude area was mainly locatedin the upstream region of the Kuroshio large me and er. Through investigating the evolution of the OPR, they found that the advection of potential vorticityplayed a vital role in the formation of the large me and er path. Simultaneously, they also calculated theOGEs for the prediction of Kuroshio path variations.The OGEs were divided into two types: type-1 and type-2 OGEs, as shown in Figs. 6b and 6c. It canbe seen that the OPR was similar to the two types ofOGEs: the similarity coe±cient between the OPR and type-1(type-2)OGE was negative(positive). Theyfurther found that the evolution process of the type-1 OGE was negatively correlated with thaTof OPR, resulting in the strength of the forecasted large me and er path to be underestimated. On the contrary, the evolution of the type-2 OGE was positively correlated with thaTof OPR, causing the amplitude of theforecasted large me and er to be overestimated. Theseresults reflect that the evolution mechanisms of theOPR and OGE were similar.

The similarity and localization features of theOPR and OGE inspired the above targeted observ ation studies of Kuroshio path variations. To determinethe sensitive area, Wang et al.(2013)computed thetotal energy distributions of the type-1 OGE(Fig. 7).Because the spatial structures of the OPR and OGEswere similar, the total energy distributions of the OPR and type-2 OGE were almost the same as those ofthe type-1 OGE. Figure 7 illustrates that the largeamplitude regions of the total energy of the type-1OGE were mainly located to the southeasTof Kyushu.Hence, the sensitive area was defined as a box, denotedas R3 in Fig. 7, big enough to contain the large amplitude of the total energy .

Fig. 6.The upper-layer thickness component of the OPR(a)for the Kuroshio large me and er, and (b)type-1 and (c)type-2 OGEs in prediction of the large me and er path(m). [F rom Wang et al., 2013

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Fig. 7.Spatial structure of the total energy for type-1OGE(shaded; m3s-2). The nine regions were used forthe ideal targeted observation experiments, and R3 wasthe sensitive area. The locations of these nine regions arelisted in Table 1. [From Wang et al., 2013]

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To examine the validity of the sensitive area, Wang et al.(2013)investigated the evolution of initiar and om errors in different areas. Figure 7 shows ninelocal regions with the same size(240 grid points), including the sensitive area R3 and eighTother arbitrarily chosen regions. These regions mainly cover thesouth of Japan and upstream of the Kuroshio extension. F orty r and om error fields were generated for eachregion. The generation process was follows: first, ar and om sequence with a normal distribution of variance σij was generated, wherei and j denote thevariables in the 1.5-layer shallow-water model and thegrid point, respectively . The r and om sequence wasdenoted as N(0; σ_ij), where i has the range 1-3 and j = 1-240. A r and om number selected from N(0; σ_ij)was regarded as the r and om error for the variable i atthe grid point j, creating a r and om error field for eachregion. To compare the evolution of the r and om error and the type-1 OGE, Wang et al.(2013)scaled ther and om error field, xr, so that its total energy equalsthaTof the type-1 OGE. The average kinetic energyof the forecast errors caused by the r and om errors islisted in Table 1 for each region. These results showthat the evolution of the initial errors depends on theirlocations. The forecast error caused by the error in thesensitive area R3 is the largest.

Table 1. Average values of kinetic energy of the forecast errors obtained from evolution of 40 r and om initial errors in each region(Wang et al., 2013)

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To investigate whether the targeted observ ationsimplemented over the sensitive area R3 improved theforecast skill of Kuroshio path variations, Wang etal.(2013)performed the following hindcasting experiments. First, 40 r and om initial errors over the wholemodel domain were obtained with the same amplitudeas the type-1 OGE. The averaged kinetic energy ofthe forecast errors caused by the r and om errors wasdenoted J₁. Second, the additional observ ations werecarried out for one of the nine regions, and so the r and om errors within that region were eliminated, without changing the errors outside of that region(Fig. 7).As a result, 40 r and om initial error fields were obtainedfor each region. The average kinetic energy of the prediction errors caused by the evolution of these r and omerror fields was denoted J₂. The improvemenTof theprediction due to the implementation of targeted observ ations was measured with the metric(J2-J₁)/J₁, where a negative number indicates a decrease of theforecast error. Table 2 shows the relative differences ofthe forecast errors for different areas. The reduction ofthe forecast error corresponding to the sensitive areais 43.59%, the largest among all the regions. This implies that if targeted observ ations were implementedover the sensitive area, the initial condition in this region would improve, and the precursor signal of theoccurrence of the Kuroshio path variations would bewell captured, greatly improving the forecast skill ofthe Kuroshio path variations.

Table. 2. Relative differences of the average kinetic energy of the forecast errors with and without implementingthe targeted observations(Wang et al., 2013)

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Blocking is a typical large-scale system, which hasa deep impacTon the regional weather and climate(Rex, 1950). Blocking prediction is extremely sensitive to the initial conditions, which leads to a limitedforecast skill. Therefore, improvemenTof the forecastskill of blocking events is one of the key problemsof medium-to-long term numerical weather forecasting(Tibaldi and Molteni, 1990; Kimoto et al., 1992; Frederiksen et al., 2004). We tried to assess whetherblocking events shared the great similarity betweenOPR and OGE, as found for the ENSO and Kuroshiopath variations.

Jiang and Wang(2010)calculated the OPR forthe Euro-Atlantic blocking with the CNOP method, based on a T21L3 quasi-geostrophic spectral model(Marshall and Molteni, 1993). Figure 8 presentsOPR as a baroclinic northeast-southwesTorientedwave train over the North American continent, whichis westward with heighTover the northward side ofthe Atlantic jet. In addition, the OPR displays localization characteristics in its spatial distribution.With time, the OPR propagated downward and amplified into a dipole blocking pattern over the Euro-Atlantic region. The energy source of the OPR evolution mainly came from the horizontal shear of thebasic state, and less from the baroclinic adjustment.

Fig. 8.OPR(contours; gpm)of Euro{Atlantic blocking for an optimization time of 3 days, and the climatological zonalwind(shaded; m s-1)over a 20-yr integration period from 1 December 1983 at(a)200, (b)500, and (c)800 hPa. [From Jiang and Wang, 2010]

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Mu and Jiang(2011)explored the OPR and OGEbased on 20 cases from 1985 to 1991. The compositeevolution of the OPR(Fig. 9)shows that the OPRwas a wave train upstream of the blocking region.With time, it propagated downward and amplified tobecome a high-over-low dipole structure. The OGEhad two types: type-1 OGE was a local CNOP whiletype-2 OGE was a global CNOP . With an optimization time of 3 days, the similarity coe±cient betweenthe OPR and type-1 OGE was 0.95, while that between the OPR and type-2 OGE was -0.87. Whenthe optimization time was extended to 4 days, the similarity reduced. The similarity coe±cient between theOPR and type-1 OGE was 0.85, and between OPR and type-2 OGE was only -0.69. As to the temporalevolution, the OPR had similar characteristics to thetype-1 OGE, and developed into a high-over-low dipolepattern. Type-2 OGEs also showed similar behavior, but with an opposite sign to blocking. In conclusion, OPR and OGE in blocking had similar spatial patterns, and similar evolutionary behavior.

Though a blocking event is an atmospheric process, the similarity between the OPR and OGE, and the localization characteristics appearing in the ENSO and Kuroshio path variations were also found in blocking processes. Therefore, by applying targeted observation in the sensitive region identified by the OGE, wecan reduce the possibility of OGE, capture the signalof the OPR, and improve the forecasting of a block-ing event. The validity of the targeted observation inblocking forecasting should be tested by using observation simulation system experiments.

Fig. 9.Composite nonlinear evolution of the OPR(gpm)for 20 cases at 500 hPa on(a)day 0, (b)day 1, (c)day 2, and (d)day 3. [From Mu and Jiang, 2011]

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This paper has reviewed the applications of theCNOP method to targeted observation studies of theENSO, Kuroshio path variations, and atmosphericblocking, while emphasizing the similarity betweenthe OPR and OGE and its applications to identifying the sensitive areas of the targeted observ ations ofthe events mentioned above. Specifically, the OGEsof the ENSO, Kuroshio path variations, and atmospheric blocking are all located in some specific areas. The localization areas of these OGEs may represent the sensitive areas of the targeted observ ation.Through ideal hindcasting experiments using targetedobservation studies of the ENSO and Kuroshio pathvariations, we proposed that additional observ ations inthe sensitive areas can help to improve forecast skills.As for atmospheric blocking, further numerical experiments are needed to investigate whether targeted observ ation in the sensitive areas would improve the related forecast skill.

Moreover, this paper has stressed the similaritybetween the OPR and OGE in the above events and their spatial localization characteristics, which canprovide useful information for the implementation oftargeted observ ation. If targeted observ ations are implemented in sensitive areas determined by the OGE, the probability of the appearance of the OGE can beeliminated, which can improve initial fields and reducethe prediction errors. Additionally, this method canprovide better guidance for building a local observ ation network, helping to capture OPR signals easily and increasing forecasting ability . The above resultshave illustrated that the similarity and spatial localization features of the OPR and OGE are of greatimportance for targeted observ ation. Are these features associated with most atmospheric and oceanicanomaly events? In order to answer this question, theOPR and OGE similarity and spatial localization fordifferent anomaly events should be investigated.

T argeted observation studies of atmospheric and oceanic anomaly events are challenging. However, with the rising capabilities of computers, effective multidisciplinary study, and collaboration of researchersfrom different fields, progress in this field is likely contributing and will contribute to the improvemenTofthe prediction of weather and climate.