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Xuguang Wang and Ting Lei

Abstract

A four-dimensional (4D) ensemble–variational data assimilation (DA) system (4DEnsVar) was developed, building upon the infrastructure of the gridpoint statistical interpolation (GSI)-based hybrid DA system. 4DEnsVar used ensemble perturbations valid at multiple time periods throughout the DA window to estimate 4D error covariances during the variational minimization, avoiding the tangent linear and adjoint of the forecast model. The formulation of its implementation in GSI was described. The performance of the system was investigated by evaluating the global forecasts and hurricane track forecasts produced by the NCEP Global Forecast System (GFS) during the 5-week summer period assimilating operational conventional and satellite data. The newly developed system was used to address a few questions regarding 4DEnsVar. 4DEnsVar in general improved upon its 3D counterpart, 3DEnsVar. At short lead times, the improvement over the Northern Hemisphere extratropics was similar to that over the Southern Hemisphere extratropics. At longer lead times, 4DEnsVar showed more improvement in the Southern Hemisphere than in the Northern Hemisphere. The 4DEnsVar showed less impact over the tropics. The track forecasts of 16 tropical cyclones initialized by 4DEnsVar were more accurate than 3DEnsVar after 1-day forecast lead times. The analysis generated by 4DEnsVar was more balanced than 3DEnsVar. Case studies showed that increments from 4DEnsVar using more frequent ensemble perturbations approximated the increments from direct, nonlinear model propagation better than using less frequent ensemble perturbations. Consistently, the performance of 4DEnsVar including both the forecast accuracy and the balances of analyses was in general degraded when less frequent ensemble perturbations were used. The tangent linear normal mode constraint had positive impact for global forecast but negative impact for TC track forecasts.

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Qin Xu, Ting Lei, and Shouting Gao

Abstract

Maximum nonmodal growths of total perturbation energy are computed for symmetric perturbations constructed from the normal modes presented in Part I. The results show that the maximum nonmodal growths are larger than the energy growth produced by any single normal mode for a give optimization time, and this is simply because the normal modes are nonorthogonal (measured by the inner product associated with the total perturbation energy norm). It is shown that the maximum nonmodal growths are produced mainly by paired modes, and this can be explained by the fact that the streamfunction component modes are partially orthogonal between different pairs and parallel within each pair in the streamfunction subspace. When the optimization time is very short (compared with the inverse Coriolis parameter), the nonmodal growth is produced mainly by the paired fastest propagating modes. When the optimization time is not short, the maximum nonmodal growth is produced almost solely by the paired slowest propagating modes and the growth can be very large for a wide range of optimization time if the parameter point is near the boundary and outside the unstable region. If the parameter point is near the boundary but inside the unstable region, the paired slowest propagating modes can contribute significantly to the energy growth before the fastest growing mode becomes the dominant component.

The maximum nonmodal growths produced by paired modes are derived analytically. The analytical solutions compare well with the numerical results obtained in the truncated normal mode space. The analytical solutions reveal the basic mechanisms for four types of maximum nonmodal energy growths: the PP1 and PP2 nonmodal growths produced by paired propagating modes and the GD1 and GD2 nonmodal growths produced by paired growing and decaying modes. The PP1 growth is characterized by the increase of the cross-band kinetic energy that excessively offsets the decrease of the along-band kinetic and buoyancy energy. The situation is opposite for the PP2 growth. The GD1 (or GD2) growth is characterized by the reduction of the initial cross-band kinetic energy (or initial along-band kinetic and buoyancy energy) due to the inclusion of the decaying mode.

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Lei Wang, Xiaojun Yuan, Mingfang Ting, and Cuihua Li

Abstract

Recent Arctic sea ice changes have important societal and economic impacts and may lead to adverse effects on the Arctic ecosystem, weather, and climate. Understanding the predictability of Arctic sea ice melting is thus an important task. A vector autoregressive (VAR) model is evaluated for predicting the summertime (May–September) daily Arctic sea ice concentration on the intraseasonal time scale, using only the daily sea ice data and without direct information of the atmosphere and ocean. The intraseasonal forecast skill of Arctic sea ice is assessed using the 1979–2012 satellite data. The cross-validated forecast skill of the VAR model is found to be superior to both the anomaly persistence and damped anomaly persistence at lead times of ~20–60 days, especially over northern Eurasian marginal seas and the Beaufort Sea. The daily forecast of ice concentration also leads to predictions of ice-free dates and September mean sea ice extent. In addition to capturing the general seasonal melt of sea ice, the model is also able to capture the interannual variability of the melting, from partial melt of the marginal sea ice in the beginning of the period to almost a complete melt in the later years. While the detailed mechanism leading to the high predictability of intraseasonal sea ice concentration needs to be further examined, the study reveals for the first time that Arctic sea ice can be predicted statistically with reasonable skill at the intraseasonal time scales given the small signal-to-noise ratio of daily data.

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