The Ensemble Kalman Filter: theoretical formulation and practical implementation

The purpose of this paper is to provide a comprehensive presentation and interpretation of the Ensemble Kalman Filter (EnKF) and its numerical implementation. The EnKF has a large user group, and numerous publications have discussed applications and theoretical aspects of it. This paper reviews the important results from these studies and also presents new ideas and alternative interpretations which further explain the success of the EnKF. In addition to providing the theoretical framework needed for using the EnKF, there is also a focus on the algorithmic formulation and optimal numerical implementation. A program listing is given for some of the key subroutines. The paper also touches upon specific issues such as the use of nonlinear measurements, in situ profiles of temperature and salinity, and data which are available with high frequency in time. An ensemble based optimal interpolation (EnOI) scheme is presented as a cost-effective approach which may serve as an alternative to the EnKF in some applications. A fairly extensive discussion is devoted to the use of time correlated model errors and the estimation of model bias.Responsible Editor: Jörg-Olaf Wolff     

Experimental investigation of drag coefficients of gobi surfaces

The response of gobi surfaces to the near-surface air flow can be characterized quantitatively by drag coefficients. By using wind tunnel tests, an attempt is made to define the relationship between the drag coefficients of gobi surfaces and gravel size and coverage. It is concluded that the drag coefficients of gobi surfaces tend to be constants when gravel coverage is over 40%-50%. Consequently, we think that the gobi deflation planes expanding vastly in the arid Northwestern China are aerodynamically stable, at least not the supplying sources of current dust storms, and therefore the emphasis on dust storm control should be paid on the so-called "earth gobi" that has low gravel coverage. The prediction model for drag coefficients of gobi surfaces has been developed by regressing drag coefficients on gravel size and coverage, the predicted results are in reasonably good agreement with wind tunnel results (R 2 = 0.94). The change of drag coefficients with gravel friction Reynolds number implies that the development extent of drag effect increases with gravel size and coverage.     

Centrifuge modeling of PGD response of buried pipe

A new centrifuge based method for determining the response of continuous buried pipe to PGD is presented. The physical characteristics of the RPI‘s 100 g-ton geotechnical centrifuge and the current lifeline experiment split-box are described: The split-box contains the model pipeline and surrounding soil and is manufactured such that half can be offset, in flight, simulating PGD. In addition, governing similitude relations which allow one to determine the physical characteristics, (diameter, wall thickness and material modulus of elasticity) of the model pipeline are presented. Finally, recorded strains induced in two buried pipes with prototype diameters of 0.63 m and 0.95 m (24 and 36 inch) subject to 0.6 and 2.0 meters (2 and 6 feet) of full scale fault offsets and presented and compared to corresponding FE results.     

Measurement of six degree-of-freedom ground motion by using eight accelerometers

A new integrated measuring system with eight force-balance accelerometers is proposed to obtain a direct measurement of six degree-of freedom （DOF） ground motions, including three rotational and three actual translational acceleration components without gyroscopes. In the proposed measuring system, the relationship between the output from eight force-balance accelerometer and the six DOF motion of the measuring system under an earthquake are described by differential equations. These equations are derived from the positions and directions of the eight force-balance accelerometers in the measuring system. The third-order Runge-Kutta algorithm is used to guarantee the accuracy of the numerical calculation. All the algorithms used to compute the six DOF components of the ground motion are implemented in a real-time in Digital Signal Processor （DSP）. The distortion of the measured results caused by position and direction errors of the accelerometers in the measuring system are reduced by multiplying a compensation coefficient C to the output and subtracting static zero drift from the measured results, respectively.     

Treatment of ground-motion predictive relationships for the reference seismic hazard map of Italy

In the framework of the 2004 reference seismic hazard map of Italy the amplitude of the strong-motion (expressed in terms of Peak Horizontal Acceleration with 10% probability of non-exceedence in 50 years, referred to average hard ground conditions) was computed using different predictive relationships. Equations derived in Italy and in Europe from strong-motion data, as well as a set of weak and strong-motion based empirical predictive relationships were employed in a logic tree procedure, in order to capture the epistemic uncertainty affecting ground-motion attenuation. This article describes the adjustments and conversions required to eliminate the incompatibilities amongst the relations. Particularly significant are distance conversions and style-of-faulting adjustments, as well as the problems related to the use of regional relations, such as the selection of a reference depth, the quantification of random variability and the strong-motion prediction. Moreover, a regional attenuation relationship specific for volcanic areas was also employed, allowing a more realistic evaluation of seismic hazard, as confirmed by the attenuation of macroseismic intensities.     

Climatological distribution of lightning density observed by satellites in China and its circumjacent regions

The 0.5°×0.5°grid resolution distribution of lightning density in China and its circumjacent regions have been analyzed by using the satellite-borne OTD (Apr 1995-Mar 2000) and LIS (Dec 1997-Mar 2003) databases. It is shown that: (i) Firstly, the variability of the lightning density (LD) is particularly pronounced over the different subareas, 9 times greater over the south than the north side of Himalayas Mountains, 2.5 times greater over the eastern than the western area of China. While the maximum and minimum LD are respectively 31.4fl/km2/a (in Guangzhou region) and less than 0.2fl/km2/a (in the desert of western China). Secondly, the LD of China's continent regularly varies with latitude and distance off coast, which is consistent with annual mean precipitation in varying trend. In conclusion, the Qinghai-Tibet Plateau, the China's three-step staircase topography and the latitude are three important factors affecting macro-scale characteristics of the LD distribution, (ii) The regional differences     

Heating status of the Tibetan Plateau from April to June and rainfall and atmospheric circulation anomaly over East Asia in midsummer

Based on the 1958-1999 monthly averaged reanalysis data of the National Center for Environmental Prediction (NCEP)/National Center for Atmospheric Research (NCAR) and the rainfall data of 160 Chinese surface stations, the relationship between rainfall and the atmospheric circulation anomaly over East Asia (EA) in July and the sensible heating (SH) over the Tibetan Plateau (TP) from April to June (AMJ) is investigated by using the rotational experimental orthogonal function (REOF) method. The results show that the TP is an isolated heating source in this period. The lagged correlation analysis between the first rotational principal component (RPC) of SH over the TP in May and rainfall of EA in July demonstrates that strong SH over the TP before July leads to a positive rainfall anomaly over the TP, the valley between the Yangtze River and Huaihe River, and the regions south and southeast of the TP, and the Sichuan Basin and Yunnan-Guizhou Plateau, but less rainfall anomaly over the regions north, northeas     

Middle and Late Devonian microbial carbonates,reefs and mounds in Guilin,South China and their sequence stratigraphic,paleoenvironmental and paleoclimatic significance

The importance of calcimicrobes and microbialite in carbonate platform and reefal environments has been stressed in recent literature. Burne and Moore[1] introduced the term microbialite to describe the clotted, laminated and undifferentiated fabrics formed by mi-crobial communities. Microbialites are organosedi-mentary deposits that have accreted as a result of ben-thic (prokaryotic or eukaryotic) communities, trapping and binding detrital sediment[1]. Microbial organisms and microbialite are…     

The secular variation of inner zone high energy proton environment in the SAA

The main portion of the inner radiation belt en-countered by spacecraft in low-Earth orbits (LEOs) is concentrated over the South Atlantic Anomaly (SAA) where satellites observed the highest particle flux. The anomaly arises from the Earth’s magnetic field being less intense in the region centered near the east of the Atlantic coast of South America. The trapped radiation belt particles therefore have their lowest mirroring altitudes over the center region of the SAA. Drift shells in t…