To assess medium-range forecasts of detailed spatial distributions of the daily mean temperature, an ensemble downscaling forecast experiment was conducted using the Japan Meteorological Agency (JMA) nonhydrostatic model (NHM) with horizontal resolutions of 25 km and 5 km. Special attention was paid to the anomalously cool summers over northeastern Japan caused by northeasterly winds called Yamase. The results are validated against the daily mean surface temperatures observed by the Automated Meteorological Data Acquisition System (AMeDAS) in the study area. Ensemble mean downscaling forecasts can successfully extract reliable signals with information about local circulations. The ensemble mean forecasts reduce the root mean square errors of the daily mean surface temperature by 15 % compared to single downscaling forecasts. The ensemble spreads also indicate the possibility of making probabilistic predictions that consider the effects of local circulations in addition to large-scale motions. The ensemble downscaling forecasts have 80 % larger spreads than the global forecasts with the JMA global spectral model at a resolution TL159L60 and approach the theoretical value. An empirical orthogonal function (EOF) analysis indicates that the predictability depends on the EOF modes. The predictable periods are 8 days for the homogeneous mode over northeastern Japan, 5 days for the Yamase mode (east-west mode), and 2 days for the north-south mode. The dynamical downscaling can properly predict the amplitudes of the EOF modes. In particular, the dynamical downscaling can predict 90 % of the Yamase mode, as compared to 20 % prediction of the global model for the same mode.
This study provides an overall understanding of the summertime synoptic variability of precipitation and moisture transport at mid-latitude from the eastern coastal region of China to the northwestern Pacific. Using satellite precipitation and reanalysis data, a clear relationship is found between upper tropospheric disturbances (Rossby waves), surface precipitation, and lower tropospheric humidity through July and August. The upper tropospheric disturbances are characterized by the undulation of the 1.5 PVU contours of potential vorticity (PV) on the 350 K isentropic surfaces. Case studies suggest that a precipitation band of several hundred kilometers wide and a thousand to several thousand kilometers long is formed very frequently on the equatorward and low-PV side of the northernmost 1.5 PVU contours, which meander together around 40°N. Lower tropospheric specific humidity is also enhanced there, and it falls sharply to the north of these contours. The synoptic situations associated with it include, but are not limited to, a common situation in which moist convection is enhanced ahead of upper-level troughs. These results are confirmed by a composite analysis over the 12 summers from 2001. A novel method of analyzing the forcing of the quasi-geostrophic potential enstrophy, in which boundary contributions are incorporated, reveals that upper tropospheric disturbances in the area are propagated predominantly from the west along the Asian jet, and that they exert a significant forcing onto near-surface levels, while the upward forcing from near-surface levels to upper tropospheric disturbances is weak. A Q-vector analysis shows that the upwelling associated with the precipitation bands is forced predominantly by confluence. This process is frontogenetic, and surface fronts are often formed therein. The upwelling is enhanced by latent heating. The latitudinal extent of humid air masses is affected not only by this circulation but by low-level flows induced by upper-level disturbances in a cooperative manner.
Month-to-month variation in the predictability of the stratospheric polar vortex in the Northern Hemisphere winter is examined on the basis of the systematic error and the ensemble spread of the North Pole temperature using a sevenyear archive of the operational ensemble one-month forecast dataset provided by the Japan Meteorological Agency. The systematic error defined by the ensemble mean error averaged over forecasts starting from each calendar month shows the following intraseasonal variability. In early winter, it has significantly large positive values of the North Pole temperature in the stratosphere, whereas in late winter, there is a significant negative bias in the upper stratosphere. The Eliassen-Palm (E-P) flux diagnosis reveals that the significant underestimation of the equatorward propagation of planetary waves in the stratosphere is related to the positive bias in early winter. On the other hand, the negative bias in late winter is not attributable to any systematic error of E-P flux. Hence, it is suggested that inadequate parameterization schemes for physical processes are responsible for the negative bias. An upper bound of the predictable period of the North Pole temperature is also assessed on the basis of monthly averaged ensemble spread using the logistic equation that describes the time evolution of small initial errors proposed by Lorenz. The estimated predictable period in the stratosphere attains a maximum value of 35 days in early winter, and gradually decreases with the seasonal march to 20 days in late winter, which is considerably longer than that in the troposphere (14 days).
Under strong nonlinear dynamics, the assumption of a Gaussian distribution for an ensemble may be strongly violated, and thus the mean of the ensemble cannot be the best estimate for the atmosphere. A mean recentering (MRC) scheme is proposed to handle a track ensemble that has a strong non-Gaussian distribution when the track prediction is conducted under a highly uncertain condition. The validity of the MRC scheme is confirmed using a case study of Typhoon Nanmadol in 2011, which moves northward initially but turns westward sharply at 0000UTC 24 August. Factors contributing to Nanmadol’s movement prediction include the saddle field between typhoons Nanmadol and Talas, the development of the subtropical high on the north side of both typhoons, and Nanmadol’s own circulation. The MRC scheme successfully improves the typhoon track prediction with a regional ensemble prediction system based on the Weather and Research Forecasting (WRF) model. The corrections from the MRC scheme allow the ensemble to capture the realistic behavior when the original ensemble track prediction is poor. Such ensemble adjustment can provide positive feedback to the background error covariance used in the ensemble-based data assimilation system. Results from the WRF-local ensemble transform Kalman filter (WRF-LETKF) system incorporated with the MRC scheme show that the ensemble track prediction can be significantly improved during the WRF-LETKF’s spin-up period when Nanmadol movement is highly uncertain. By dynamically adjusting the MRC scheme, the ensemble avoids suffering from the non-Gaussian and over-dispersive issues observed in the original ensemble prediction.
In ensemble Kalman filter methods, localization is applied for both avoiding the spurious correlations of distant observations and increasing the effective size of the ensemble space. The procedure is essential in order to provide quality assimilation in large systems; however a severe localization can cause imbalances that impact negatively on the accuracy of the analysis. We want to understand the fundamental properties of localized ensemble methods and to investigate an optimal localization expression which minimizes the analysis error. The novel analytical expression derived in this work depends on the observation error, the density of measurements, and the approximation error, i.e., the error that comes from working in the ensemble space. The mathematical results are tested with two numerical simulations using a toy model. We demonstrate that observations with different observation error or density need different localization length scales.
If the divergence in phase space of the evolution equation of a deterministic nonlinear system does not depend on the state variables (hereafter referred to as the divergence condition), the deterministic prediction starting from the mode of a probability density function (PDF) of the state variables remains the mode of the PDF at forecast time. For a system that does not satisfy the divergence condition, a condition for the forecast state to remain sufficiently close to the mode of the PDF is derived under assumption of a small forecast error. Calculation of the divergence in phase space for finite-dimensional analogs of several Eulerian equations of hydrodynamics shows that the divergence condition holds for the quasigeostrophic equations with lateral boundaries and the shallow water equations on a sphere. On the basis of the above results, a new formulation of four-dimensional variational data assimilation (4DVar) is presented. A Gaussian prior PDF at the beginning of an assimilation window is evolved up to the end of that window according to the Liouville equation. It is found that if the divergence condition holds, the cost function with the prior PDF thus evolved is equivalent to the conventional cost function of 4DVar. This result reveals that a non-Gaussian prior PDF which evolves according to the Liouville equation is implicitly used in 4DVar. Data assimilation experiments with toy models are conducted to demonstrate this advantage of 4DVar. The background error covariance at the beginning of the assimilation window is obtained from ensemble Kalman filter (EnKF). To alleviate the difficulty of multiple minima, when the convergence value of the cost function exceeds a certain threshold, the 4DVar analysis is replaced by the corresponding EnKF analysis. Results demonstrate that 4DVar cycles with the abovementioned modifications outperform EnKF cycles in terms of the accuracy of analysis in strong nonlinearity as well as in weak nonlinearity.
The ensemble Kalman filter (EnKF) approximates background error covariance by using a finite number of ensemble members. Although increasing the ensemble size consistently improves the EnKF analysis, typical applications of the EnKF to realistic atmospheric simulations are conducted with a small ensemble size due to limited computational resources. The finite ensemble size introduces a sampling error into the background error covariance, leading to a degradation of the accuracy of the analysis fields. As a representative of EnKF applications, a local ensemble transform Kalman filter (LETKF) was implemented on the K computer, the flagship supercomputer in Japan, which enables demanding computations with larger ensembles. This study investigated the performance of the LETKF on the K computer and evaluated the influence of sampling noise on the background error covariance estimated from 1000-member ensemble forecasting with the Japan Meteorological Agency nonhydrostatic model covering Japan with a 15-km horizontal resolution. The LETKF on the K computer achieved a high peak performance ratio of 14.7 % without special optimization, showing the suitability of the LETKF for high-performance parallel computing. The background error covariance estimated from 1000 ensemble members contained negligible sampling noise even at distant locations without covariance localization. The results indicated that for the case in the current study, an ensemble size of 500 would be large enough to approximate the error covariance under the configuration with a horizontal resolution of 15 km. The results also suggest that improving input/output performance will become a primary goal in the design of next-generation supercomputers.