Using a mesoscale ensemble to predict forecast error and perform targeted observation

Using NCEP short range ensemble forecast（SREF） system,demonstrated two fundamental on-going evolutions in numerical weather prediction（NWP） are through ensemble methodology.One evolution is the shift from traditional single-value deterministic forecast to flow-dependent（not statistical） probabilistic forecast to address forecast uncertainty.Another is from a one-way observation-prediction system shifting to an interactive two-way observation-prediction system to increase predictability of a weather system.In the first part,how ensemble spread from NCEP SREF predicting ensemble-mean forecast error was evaluated over a period of about a month.The result shows that the current capability of predicting forecast error by the 21-member NCEP SREF has reached to a similar or even higher level than that of current state-of-the-art NWP models in predicting precipitation,e.g.,the spatial correlation between ensemble spread and absolute forecast error has reached 0.5 or higher at 87 h（3.5 d） lead time on average for some meteorological variables.This demonstrates that the current operational ensemble system has already had preliminary capability of predicting the forecast error with usable skill,which is a remarkable achievement as of today.Given the good spread-skill relation,the probability derived from the ensemble was also statistically reliable,which is the most important feature a useful probabilistic forecast should have.The second part of this research tested an ensemble-based interactive targeting（E-BIT） method.Unlike other mathematically-calculated objective approaches,this method is subjective or human interactive based on information from an ensemble of forecasts.A numerical simulation study was performed to eight real atmospheric cases with a 10-member,bred vector-based mesoscale ensemble using the NCEP regional spectral model（RSM,a sub-component of NCEP SREF） to prove the concept of this E-BIT method.The method seems to work most effective for basic atmospheric state variables,moderately effective for convective instabilities and least effective for precipitations.Precipitation is a complex result of many factors and,therefore,a more challenging field to be improved by targeted observation.

Exploring sensitive area in the tropical Indian Ocean for El Niño prediction: implication for targeted observation

Based on initial errors of sea temperature in the tropical Indian Ocean that are most likely to induce spring predictability barrier(SPB)for the El Niño prediction,the sensitive area of sea temperature in the tropical Indian Ocean for El Niño prediction starting from January is identified using the CESM1.0.3(Community Earth System Model),a fully coupled global climate model.The sensitive area locates mainly in the subsurface of eastern Indian Ocean.The effectiveness of applying targeted observation in the sensitive area is also evaluated in an attempt to improve the El Niño prediction skill.The results of sensitivity experiments indicate that if initial errors exist only in the tropical Indian Ocean,applying targeted observation in the sensitive area in the Indian Ocean can significantly improve the El Niño prediction.In particular,for SPB-related El Niño events,when initial errors of sea temperature exist both in the tropical Indian Ocean and the Pacific Ocean,which is much closer to the realistic predictions,if targeted observations are conducted in the sensitive area of tropical Pacific,the prediction skills of SPB-related El Niño events can be improved by 20.3%in general.Moreover,if targeted observations are conducted in the sensitive area of tropical Indian Ocean in addition,the improvement of prediction skill can be increased by 25.2%.Considering the volume of sensitive area in the tropical Indian Ocean is about 1/3 of that in the tropical Pacific Ocean,the prediction skill improvement per cubic kilometer in the sensitive area of tropical Indian Ocean is competitive to that of the tropical Pacific Ocean.Additional to the sensitive area of the tropical Pacific Ocean,sensitive area of the tropical Indian Ocean is also a very effective and cost-saving area for the application of targeted observations to improve El Niño forecast skills.

Identifying the sensitive areas in targeted observation for predicting the Kuroshio large meander path in a regional ocean model

With the Regional Ocean Modeling System(ROMS),this paper investigates the sensitive areas in targeted observation for predicting the Kuroshio large meander(LM)path using the conditional nonlinear optimal perturbation approach.To identify the sensitive areas,the optimal initial errors(OIEs)featuring the largest nonlinear evolution in the LM prediction are first calculated;the resulting OIEs are localized mainly in the upper 2500 m over the LM upstream region,and their spatial structure has certain similarities with that of the optimal triggering perturbation.Based on this spatial structure,the sensitive areas are successfully identified,located southeast of Kyushu in the region(29°–32°N,131°–134°E).A series of sensitivity experiments indicate that both the positions and the spatial structure of initial errors have important effects on the LM prediction,verifying the validity of the sensitive areas.Then,the effect of targeted observation in the sensitive areas is evaluated through observing system simulation experiments.When targeted observation is implemented in the identified sensitive areas,the prediction errors are effectively reduced,and the prediction skill of the LM event is improved significantly.This provides scientific guidance for ocean observations related to enhancing the prediction skill of the LM event.

ENSO Predictions in an Intermediate Coupled Model Influenced by Removing Initial Condition Errors in Sensitive Areas： A Target Observation Perspective

Previous studies indicate that ENSO predictions are particularly sensitive to the initial conditions in some key areas（socalled ＂sensitive areas＂）. And yet, few studies have quantified improvements in prediction skill in the context of an optimal observing system. In this study, the impact on prediction skill is explored using an intermediate coupled model in which errors in initial conditions formed to make ENSO predictions are removed in certain areas. Based on ideal observing system simulation experiments, the importance of various observational networks on improvement of El Ni n？o prediction skill is examined. The results indicate that the initial states in the central and eastern equatorial Pacific are important to improve El Ni n？o prediction skill effectively. When removing the initial condition errors in the central equatorial Pacific, ENSO prediction errors can be reduced by 25%. Furthermore, combinations of various subregions are considered to demonstrate the efficiency on ENSO prediction skill. Particularly, seasonally varying observational networks are suggested to improve the prediction skill more effectively. For example, in addition to observing in the central equatorial Pacific and its north throughout the year,increasing observations in the eastern equatorial Pacific during April to October is crucially important, which can improve the prediction accuracy by 62%. These results also demonstrate the effectiveness of the conditional nonlinear optimal perturbation approach on detecting sensitive areas for target observations.

Identification of the sensitive area for targeted observation to improve vertical thermal structure prediction in summer in the Yellow Sea

The sensitive area of targeted observations for short-term(7 d)prediction of vertical thermal structure(VTS)in summer in the Yellow Sea was investigated.We applied the Conditional Nonlinear Optimal Perturbation(CNOP)method and an adjoint-free algorithm with the Regional Ocean Modeling System(ROMS).We used vertical integration of CNOP-type temperature errors to locate the sensitive areas,where reduction of initial errors is expected to yield the greatest improvement in VTS prediction for the selected verification area.The identified sensitive areas were northeast−southwest orientated northeast to the verification area,which were possibly related to the southwestward background currents.Then,we performed a series of sensitivity experiments to evaluate the effectiveness of the identified sensitive areas.Results show that initial errors in the identified sensitive areas had the greatest negative effect on VTS prediction in the verification area compared to errors in other areas(e.g.,the verification area and areas to its east and northeast).Moreover,removal of initial errors through deploying simulated observations in the identified sensitive areas led to more refined prediction than correction of initial conditions in the verification area itself.Our results suggest that implementation of targeted observation in the CNOP-based sensitive areas is an effective method to improve short-term prediction of VTS in summer in the Yellow Sea.

The Initial Errors in the Tropical Indian Ocean that Can Induce a Significant “Spring Predictability Barrier” for La Nina Events and Their Implication for Targeted Observations

Initial errors in the tropical Indian Ocean(IO-related initial errors) that are most likely to yield the Spring Prediction Barrier(SPB) for La Ni?a forecasts are explored by using the CESM model.These initial errors can be classified into two types.Type-1 initial error consists of positive sea temperature errors in the western Indian Ocean and negative sea temperature errors in the eastern Indian Ocean,while the spatial structure of Type-2 initial error is nearly opposite.Both kinds of IO-related initial errors induce positive prediction errors of sea temperature in the Pacific Ocean,leading to underprediction of La Nina events.Type-1 initial error in the tropical Indian Ocean mainly influences the SSTA in the tropical Pacific Ocean via atmospheric bridge,leading to the development of localized sea temperature errors in the eastern Pacific Ocean.However,for Type-2 initial error,its positive sea temperature errors in the eastern Indian Ocean can induce downwelling error and influence La Ni?a predictions through an oceanic channel called Indonesian Throughflow.Based on the location of largest SPB-related initial errors,the sensitive area in the tropical Indian Ocean for La Nina predictions is identified.Furthermore,sensitivity experiments show that applying targeted observations in this sensitive area is very useful in decreasing prediction errors of La Nina.Therefore,adopting a targeted observation strategy in the tropical Indian Ocean is a promising approach toward increasing ENSO prediction skill.

An Adaptive Local Grid Nesting-based Genetic Algorithm for Multi-earth Observation Satellites' Area Target Observation

The Scheduling of the Multi-EOSs Area Target Observation(SMEATO)is an EOS resource schedul-ing problem highly coupled with computational geometry.The advances in EOS technology and the ex-pansion of wide-area remote sensing applications have increased the practical significance of SMEATO.In this paper,an adaptive local grid nesting-based genetic algorithm(ALGN-GA)is proposed for developing SMEATO solutions.First,a local grid nesting(LGN)strategy is designed to discretize the target area into parts,so as to avoid the explosive growth of calculations.A genetic algorithm(GA)framework is then used to share reserve information for the population during iterative evolution,which can generate high-quality solutions with low computational costs.On this basis,an adaptive technique is introduced to determine whether a local region requires nesting and whether the grid scale is sufficient.The effectiveness of the proposed model is assessed experimentally with nine randomly generated tests at different scales.The results show that the ALGN-GA offers advantages over several conventional algorithms in 88.9%of instances,especially in large-scale instances.These fully demonstrate the high efficiency and stability of the ALGN-GA.

Recent Advances in China on the Predictability of Weather and Climate

This article summarizes the progress made in predictability studies of weather and climate in recent years in China,with a main focus on advances in methods to study error growth dynamics and reduce uncertainties in the forecasting of weather and climate.Specifically,it covers(a)advances in methods to study weather and climate predictability dynamics,especially those in nonlinear optimal perturbation methods associated with initial errors and model errors and their applications to ensemble forecasting and target observations,(b)new data assimilation algorithms for initialization of predictions and novel assimilation approaches to neutralize the combined effects of initial and model errors for weather and climate,(c)applications of new statistical approaches to climate predictions,and(d)studies on meso-to small-scale weather system predictability dynamics.Some of the major frontiers and challenges remaining in predictability studies are addressed in this context.

Effects of Dropsonde Data in Field Campaigns on Forecasts of Tropical Cyclones over the Western North Pacific in 2020 and the Role of CNOP Sensitivity

Valuable dropsonde data were obtained from multiple field campaigns targeting tropical cyclones,namely Higos,Nangka,Saudel,and Atsani,over the western North Pacific by the Hong Kong Observatory and Taiwan Central Weather Bureau in 2020.The conditional nonlinear optimal perturbation(CNOP)method has been utilized in real-time to identify the sensitive regions for targeting observations adhering to the procedure of real-time field campaigns for the first time.The observing system experiments were conducted to evaluate the effect of dropsonde data and CNOP sensitivity on TC forecasts in terms of track and intensity,using the Weather Research and Forecasting model.It is shown that the impact of assimilating all dropsonde data on both track and intensity forecasts is case-dependent.However,assimilation using only the dropsonde data inside the sensitive regions displays unanimously positive effects on both the track and intensity forecast,either of which obtains comparable benefits to or greatly reduces deterioration of the skill when assimilating all dropsonde data.Therefore,these results encourage us to further carry out targeting observations for the forecast of tropical cyclones according to CNOP sensitivity.

The Time and Regime Dependencies of Sensitive Areas for Tropical Cyclone Prediction Using the CNOP Method

This study examines the time and regime dependencies of sensitive areas identified by the conditional nonlinear optiflml perturbation （CNOP） method for forecasts of two typhoons. Typhoon Meari （2004） was weakly nonlinear and is herein referred to as the linear case, while Typhoon Matsa （2005） was strongly nonlinear and is herein referred to as the nonlinear case. In the linear case, the sensitive areas identified for special forecast times when the initial time was fixed resembled those identified for other forecast times. Targeted observations deployed to improve a special time forecast would thus also benefit forecasts at other times. In the nonlinear case, the similarities among the sensitive areas identified for different forecast times were more limited. The deployment of targeted observations in the nonlinear case would therefore need to be adapted to achieve large improvements for different targeted forecasts. For both cases, the closer the forecast time, the higher the similarities of the sensitive areas. When the forecast time was fixed, the sensitive areas in the linear case diverged continuously from the verification area as the forecast period lengthened, while those in the nonlinear case were always located around the initial cyclones. The deployment of targeted observations to improve a special forecast depends strongly on the time of deployment. An examination of the efficiency gained by reducing initial errors within the identified sensitive areas confirmed these results. In general, the greatest improvement in a special time forecast was obtained by identifying the sensitive areas for the corresponding forecast time period.

Impact of Different Guidances on Sensitive Areas of Targeting Observations Based on the CNOP Method

The conditional nonlinear optimal perturbations（CNOPs） obtained by a fast algorithm are applied to determining the sensitive area for the targeting observation of Typhoon Matsa in 2005 using an operational regional prediction model-the Global/Regional Assimilation and PrEdiction System（GRAPES）.Through a series of sensitivity experiments,several issues on targeting strategy design are discussed,including the effectivity of different guidances to determine the sensitive area（or targeting area） and the impact of sensitive area size on improving the 24-h forecast.In this study,three guidances are used along with the CNOP to find sensitive area for improving the 24-h prediction of sea level pressure and accumulated rainfall in the verification region.The three guidances are based on winds only;on winds,geopotential height,and specific humidity;and on winds,geopotential height,specific humidity,and observation error,respectively.The distribution and effectivity of the sensitive areas are compared with each other,and the results show that the sensitive areas identified by the three guidances are different in terms of convergence and effectivity.All the sensitive areas determined by these guidances can lead to improvement of the 24-h forecast of interest. The second and third guidances are more effective and can identify more similar sensitive areas than the first one.Further,the size of sensitive areas is changed the same way for three guidances and the 24-h accumulated rainfall prediction is examined.The results suggest that a larger sensitive area can result in better prediction skill,provided that the guidance is sensitive to the size of sensitive areas.

Application of Conditional Nonlinear Optimal Perturbation to Targeted Observation Studies of the Atmosphere and Ocean

This paper reviews progress in the application of conditional nonlinear optimal perturbation to targeted observation studies of the atmosphere and ocean in recent years, with a focus on the E1 Nifio-Southern Oscillation （ENSO）, Kuroshio path variations, and blocking events. Through studying the optimal precursor （OPR） and optimally growing initial error （OGE） of the occurrence of the above events, the similarity and localization features of OPR and OGE spatial structures have been found for each event. Ideal hindcasting experiments have shown that, if initial errors are reduced in the areas with the largest amplitude for the OPR and OGE for ENSO and Kuroshio path variations, the forecast skill of the model for these events is significantly improved. Due to the similarity between patterns of the OPR and OGE, additional observations implemented in the same sensitive region would help to not only capture the precursors, but also reduce the initial errors in the predictions, greatly increasing the forecast abilities. The similarity and localization of the spatial structures of the OPR and OGE during the onset of blocking events have also been investigated, but their application to targeted observation requires further study.

A Fast Algorithm for Solving CNOP and Associated Target Observation Tests

Conditional Nonlinear Optimal Perturbation （CNOP） is a new method proposed by Mu et al. in 2003, which generalizes the linear singular vector （LSV） to include nonlinearity. It has become a powerful tool for studying predictability and sensitivity among other issues in nonlinear systems. This is because the CNOP is able to represent, while the LSV is unable to deal with, the fastest developing perturbation in a nonlinear system. The wide application of this new method, however, has been limited due to its large computational cost related to the use of an adjoint technique. In order to greatly reduce the computational cost, we hereby propose a fast algorithm for solving the CNOP based on the empirical orthogonal function （EOF）. The algorithm is tested in target observation experiments of Typhoon Matsa using the Global/Regional Assimilation and PrEdiction System （GRAPES）, an operational regional forecast model of China. The effectivity and feasibility of the algorithm to determine the sensitivity （target） area is evaluated through two observing system simulation experiments （OSSEs）. The results, as expected, show that the energy of the CNOP solved by the new algorithm develops quickly and nonlinearly. The sensitivity area is effectively identified with the CNOP from the new algorithm, using 24 h as the prediction time window. The 24-h accumulated rainfall prediction errors （ARPEs） in the verification region are reduced significantly compared with the ＂true state,＂ when the initial conditions （ICs） in the sensitivity area are replaced with the ＂observations.＂ The decrease of the ARPEs can be achieved for even longer prediction times （e.g., 72 h）. Further analyses reveal that the decrease of the 24-h ARPEs in the verification region is attributable to improved simulations of the typhoon＇s initial warm-core, upper level relative vorticity, water vapor conditions, etc., as a result of the updated ICs in the sensitivity area.

Increasingly important role of numerical modeling in oceanic observation design strategy: A review

Oceanic observation design is of considerable significance and has made remarkable progress during the past several decades.This study addresses the critical role of numerical modeling in oceanic observation design.Following a brief introduction of the characteristics of existing oceanic observation design studies,we present the advantages of the model-based observation design strategy and further review its decisive contribution.To demonstrate the effectiveness of this strategy,the targeted observation applications using the conditional nonlinear optimal perturbation(CNOP)approach for improving the Kuroshio predictions are introduced.Finally,the authors present their consideration for correcting model errors by targeted observations of sensitive model parameters and mitigating the model-dependency problem by utilizing multiple modeling systems.Suggestions on using observing system simulation experiments to validate the designed observations and extending the model-based observation design strategy into observing oceanic climatological mean states are also discussed.

Recent Progress in Applications of the Conditional Nonlinear Optimal Perturbation Approach to Atmosphere-Ocean Sciences

The conditional nonlinear optimal perturbation(CNOP for short) approach is a powerful tool for predictability and targeted observation studies in atmosphere-ocean sciences. By fully considering nonlinearity under appropriate physical constraints, the CNOP approach can reveal the optimal perturbations of initial conditions, boundary conditions, model parameters, and model tendencies that cause the largest simulation or prediction uncertainties. This paper reviews the progress of applying the CNOP approach to atmosphere-ocean sciences during the past five years. Following an introduction of the CNOP approach, the algorithm developments for solving the CNOP are discussed.Then, recent CNOP applications, including predictability studies of some high-impact ocean-atmospheric environmental events, ensemble forecast, parameter sensitivity analysis, uncertainty estimation caused by errors of model tendency or boundary condition, are reviewed. Finally, a summary and discussion on future applications and challenges of the CNOP approach are presented.

Reducing the Prediction Uncertainties of High-Impact Weather and Climate Events： An Overview of Studies at LASG

This paper summarizes recent progress at the State Key Laboratory of Numerical Modeling for Atmospheric Sci- ences and Geophysical Fluid Dynamics （LASG）, Institute of Atmospheric Physics, Chinese Academy of Sciences in studies on targeted observations, data assimilation, and ensemble prediction, which are three effective strategies to re- duce the prediction uncertainties and improve the forecast skill of weather and climate events. Considering the limita- tions of traditional targeted observation approaches, LASG researchers have developed a conditional nonlinear op- timal perturbation-based targeted observation strategy to optimize the design of the observing network. This strategy has been employed to identify sensitive areas for targeted observations of the E1 Nifio-Southern Oscillation, Indian Ocean dipole, and tropical cyclones, and has been demonstrated to be effective in improving the forecast skill of these events. To assimilate the targeted observations into the initial state of a numerical model, a dimension-reduced- projection-based four-dimensional variational data assimilation （DRP-4DVar） approach has been proposed and is used operationally to supply accurate initial conditions in numerical forecasts. The performance of DRP-4DVar is good, and its computational cost is much lower than the standard 4DVar approach. Besides, ensemble prediction, which is a practical approach to generate probabilistic forecasts of the future state of a particular system, can be used to reduce the prediction uncertainties of single forecasts by taking the ensemble mean of forecast members. In this field, LASG researchers have proposed an ensemble forecast method that uses nonlinear local Lyapunov vectors （NLLVs） to yield ensemble initial perturbations. Its application in simple models has shown that NLLVs are more useful than bred vectors and singular vectors in improving the skill of the ensemble forecast. Therefore, NLLVs rep- resent a candidate for possible development as an ensemble method in operational forecasts. Despite the consider- able efforts made towards developing these methods to reduce prediction uncertainties, much challenging but highly important work remains in terms of improving the methods to further increase the skill in forecasting such weather and climate events.

Moving scanning emitter tracking by a single observer using time of interception:Observability analysis and algorithm

The target motion analysis（TMA） for a moving scanning emitter with known fixed scan rate by a single observer using the time of interception（TOI） measurements only is investigated in this paper.By transforming the TOI of multiple scan cycles into the direction difference of arrival（DDOA） model,the observability analysis for the TMA problem is performed.Some necessary conditions for uniquely identifying the scanning emitter trajectory are obtained.This paper also proposes a weighted instrumental variable（WIV） estimator for the scanning emitter TMA,which does not require any initial solution guess and is closed-form and computationally attractive.More importantly,simulations show that the proposed algorithm can provide estimation mean square error close to the Cramer-Rao lower bound（CRLB） at moderate noise levels with significantly lower estimation bias than the conventional pseudo-linear least square（PLS） estimator.