By sampling perturbed state vectors from each ensemble prediction run at properly selected time levels in the vicinity of the analysis time, the recently proposed time-expanded sampling approach can enlarge the ensemb...By sampling perturbed state vectors from each ensemble prediction run at properly selected time levels in the vicinity of the analysis time, the recently proposed time-expanded sampling approach can enlarge the ensemble size without increasing the number of prediction runs and, hence, can reduce the computational cost of an ensemble-based filter. In this study, this approach is tested for the first time with real radar data from a tornadic thunderstorm. In particular, four assimilation experiments were performed to test the time-expanded sampling method against the conventional ensemble sampling method used by ensemble- based filters. In these experiments, the ensemble square-root filter （EnSRF） was used with 45 ensemble members generated by the time-expanded sampling and conventional sampling from 15 and 45 prediction runs, respectively, and quality-controlled radar data were compressed into super-observations with properly reduced spatial resolutions to improve the EnSRF performances. The results show that the time-expanded sampling approach not only can reduce the computational cost but also can improve the accuracy of the analysis, especially when the ensemble size is severely limited due to computational constraints for real-radar data assimilation. These potential merits are consistent with those previously demonstrated by assimilation experiments with simulated data.展开更多
In the Ensemble Kalman Filter（EnKF） data assimilation-prediction system,most of the computation time is spent on the prediction runs of ensemble members.A limited or small ensemble size does reduce the computational...In the Ensemble Kalman Filter（EnKF） data assimilation-prediction system,most of the computation time is spent on the prediction runs of ensemble members.A limited or small ensemble size does reduce the computational cost,but an excessively small ensemble size usually leads to filter divergence,especially when there are model errors.In order to improve the efficiency of the EnKF data assimilation-prediction system and prevent it against filter divergence,a time-expanded sampling approach for EnKF based on the WRF（Weather Research and Forecasting） model is used to assimilate simulated sounding data.The approach samples a series of perturbed state vectors from Nb member prediction runs not only at the analysis time（as the conventional approach does） but also at equally separated time levels（time interval is △t） before and after the analysis time with M times.All the above sampled state vectors are used to construct the ensemble and compute the background covariance for the analysis,so the ensemble size is increased from Nb to Nb＋2M×Nb=（1＋2M）×Nb） without increasing the number of prediction runs（it is still Nb）.This reduces the computational cost.A series of experiments are conducted to investigate the impact of △t（the time interval of time-expanded sampling） and M（the maximum sampling times） on the analysis.The results show that if t and M are properly selected,the time-expanded sampling approach achieves the similar effect to that from the conventional approach with an ensemble size of（1＋2M）× Nb,but the number of prediction runs is greatly reduced.展开更多
This paper proposes a new personal tour planning problem with time-dependent satisfactions, traveling and activity duration times for sightseeing. It is difficult to represent the time-dependent model using general st...This paper proposes a new personal tour planning problem with time-dependent satisfactions, traveling and activity duration times for sightseeing. It is difficult to represent the time-dependent model using general static network models, and hence, Time-Expanded Network (TEN) is introduced. The TEN contains a copy to the set of nodes in the underlying static network for each discrete time step, and it turns the problem of determining an optimal flow over time into a classical static network flow problem. Using the proposed TEN-based model, it is possible not only to construct various variations with time of costs and satisfactions flexibly in a single network, but also to select optimal departure places and accommodations according to the tour route with tourist’s favorite places and to obtain the time scheduling of tour route, simultaneously. The proposed model is formulated as a 0 - 1 integer programming problem which can be applied by existing useful combinatorial optimization and soft computing algorithms. It’s also equivalently transformed into several existing tour planning problems using some natural assumptions. Furthermore, comparing the proposed model with some previous models using a numerical example with time-dependent parameters, both the similarity of these models in the static network and the advantage of the proposed TEN-based model are obtained.展开更多
基金supported by ONR Grants N000140410312 and N000141010778 to CIMMS,the University of Oklahomaby the radar data assimilation projects No. 2008LASW-A01 and No.GYHY200806003 at the Institute of Atmospheric Physics,Chinese Academy of SciencesProvided to CIMMS by NOAA/Office of Oceanic and Atmospheric Research under NOAA-University of Oklahoma Coopera-tive Agreement #NA17RJ1227,U.S. Department of Commerce
文摘By sampling perturbed state vectors from each ensemble prediction run at properly selected time levels in the vicinity of the analysis time, the recently proposed time-expanded sampling approach can enlarge the ensemble size without increasing the number of prediction runs and, hence, can reduce the computational cost of an ensemble-based filter. In this study, this approach is tested for the first time with real radar data from a tornadic thunderstorm. In particular, four assimilation experiments were performed to test the time-expanded sampling method against the conventional ensemble sampling method used by ensemble- based filters. In these experiments, the ensemble square-root filter （EnSRF） was used with 45 ensemble members generated by the time-expanded sampling and conventional sampling from 15 and 45 prediction runs, respectively, and quality-controlled radar data were compressed into super-observations with properly reduced spatial resolutions to improve the EnSRF performances. The results show that the time-expanded sampling approach not only can reduce the computational cost but also can improve the accuracy of the analysis, especially when the ensemble size is severely limited due to computational constraints for real-radar data assimilation. These potential merits are consistent with those previously demonstrated by assimilation experiments with simulated data.
基金Supported by the National Natural Science Foundation of China (40805044)Natural Science Foundation of Gansu Province(1010RJZA118)Fundmental Research Fund for Central Universities Science and Technology Development Program of China(lzujbky-2010-12)
文摘In the Ensemble Kalman Filter（EnKF） data assimilation-prediction system,most of the computation time is spent on the prediction runs of ensemble members.A limited or small ensemble size does reduce the computational cost,but an excessively small ensemble size usually leads to filter divergence,especially when there are model errors.In order to improve the efficiency of the EnKF data assimilation-prediction system and prevent it against filter divergence,a time-expanded sampling approach for EnKF based on the WRF（Weather Research and Forecasting） model is used to assimilate simulated sounding data.The approach samples a series of perturbed state vectors from Nb member prediction runs not only at the analysis time（as the conventional approach does） but also at equally separated time levels（time interval is △t） before and after the analysis time with M times.All the above sampled state vectors are used to construct the ensemble and compute the background covariance for the analysis,so the ensemble size is increased from Nb to Nb＋2M×Nb=（1＋2M）×Nb） without increasing the number of prediction runs（it is still Nb）.This reduces the computational cost.A series of experiments are conducted to investigate the impact of △t（the time interval of time-expanded sampling） and M（the maximum sampling times） on the analysis.The results show that if t and M are properly selected,the time-expanded sampling approach achieves the similar effect to that from the conventional approach with an ensemble size of（1＋2M）× Nb,but the number of prediction runs is greatly reduced.
文摘This paper proposes a new personal tour planning problem with time-dependent satisfactions, traveling and activity duration times for sightseeing. It is difficult to represent the time-dependent model using general static network models, and hence, Time-Expanded Network (TEN) is introduced. The TEN contains a copy to the set of nodes in the underlying static network for each discrete time step, and it turns the problem of determining an optimal flow over time into a classical static network flow problem. Using the proposed TEN-based model, it is possible not only to construct various variations with time of costs and satisfactions flexibly in a single network, but also to select optimal departure places and accommodations according to the tour route with tourist’s favorite places and to obtain the time scheduling of tour route, simultaneously. The proposed model is formulated as a 0 - 1 integer programming problem which can be applied by existing useful combinatorial optimization and soft computing algorithms. It’s also equivalently transformed into several existing tour planning problems using some natural assumptions. Furthermore, comparing the proposed model with some previous models using a numerical example with time-dependent parameters, both the similarity of these models in the static network and the advantage of the proposed TEN-based model are obtained.
