An Efficient Accurate Direct Solution of Poisson''''s Equation for Computation of Meteorological Parameters

Poisson's equation is solved numerically by two direct methods, viz. Block Cyclic Reduction (BCR) method and Fourier Method. Qualitative and quantitative comparison between the numerical solutions obtained by two methods indicates that BCR method is superior to Fourier method in terms of speed and accuracy. Therefore. BCR method is applied to solve (?)2(?)= ζ and (?)2X= D from observed vorticity and divergent values. Thereafter the rotational and divergent components of the horizontal monsoon wind in the lower troposphere are reconstructed and are com pared with the results obtained by Successive Over-Relaxation (SOR) method as this indirect method is generally in more use for obtaining the streamfunction ((?)) and velocity potential (X) fields in NWP models. It is found that the results of BCR method are more reliable than SOR method.     

STUDY ON SST IN THE NORTHWESTERN PACIFIC OCEAN WITH SATELLITE OBSERVATIONS*

On the basis of extracting the clear brightness temperature in GMS-4 infrared data,the tests have been carried out by using three methods for SST retrieval in the northwestern Pacific Ocean in August 1993.Considering error amplification is the inherent feature in the single channel physical method,two statistical methods are developed.One is a single channel method.Its precision is 1.186℃,which is superior to that of other similar methods.The other is a multi-channel method using both TOVS and GMS-4 data.Its precision is 1.061℃,which is matched with that of other current multi-channel statistical methods(0.5-1.36℃).The retrieval SST distributions obtained by the two methods are in good agreement with conventional observations.     

NONLINEAR SCHRODINGER EQUATION IN THE ROTATIONAL BAROTROPIC ATMOSPHERE AND ATMOSPHERIC BLOCKING

In this paper,the WKB method is used to obtain the nonlinear Schr(?)dinger equation satisfied by nonlinearRossby wave in the rotational barotropic atmosphere.It is found that the nonlinear Schr(?)dinger equation hasan envelope solitary wave solution under the condition 1≤m≤2(m the zonal wavenumber),and the phasespeed of envelope solitary Rossby wave in the atmosphere is related to the square of its amplitude linearly,thatis,the larger the amplitude of envelope solitary Rossby wave,the smaller its propagation speed.Farthermore,the blocking high and cut-off low pressures which are consistent with the observations of blocking in the atmo-sphere are obtained by calculating envelope solitary Rossby wave,and the blocking structures persist more thanfive days,the results demonstrate that the envelope solitary Rossby wave is a possible mechanism about theformation,maintenance and breakout of blocking in the atmosphere.     

An Integrating VAP Method for Single-Doppler Radar Wind Retrieval

Some traditional methods, such as the velocity-azimuth display (VAD) and the velocity-azimuth processing (VAP), have been widely usedto retrieve the 3-D wind field from single-Doppler radar data because of their relative conceptual and practical simplicity. The advantage of VAD is that it is not affected by small-scale perturbations of the radial wind along the azimuth, to which the VAP method is very sensitive. Nevertheless, the spatial resolution of the VAD method is very poor compared to the VAP method. We show, in this study, that these two retrieval methods are actually related with each other and they are two special applications of a retrieval function based on the azimuthal uniform-wind assumption for a given azimuthal interval [θ1, θ2]. When using this retrieval function to retrieve wind fields, the azimuthal interval used in retrieval can be adjusted according to the requirement of smoothness or resolution. The larger (smaller) the azimuthal interval is, the coarser (finer) the horizontal resolution of retrieved wind field is, and the more insensitive (sensitive) the retrieval method is to small-scale perturbations. Because the full information within the azimuthal interval [θ1, θ2],instead of the information at two terminal points only, i.e., azimuths θ1 and θ2, is used to retrieve the wind fields, this method is referred to as the integrating VAP (IVAP) method, wherein the horizontal wind field is retrieved by using the Doppler velocity over the part of circumference, delimited by the given azimuthal interval times the scan radius. By contrast,the VAP method uses only the velocities at two terminal points of the given azimuthal interval. Therefore, the IVAP method has a filtering function, and the filtering rate can be controlled by adjusting the azimuthal interval. The filter such as that used in the pre-processing of the VAP method is no longer necessary for the IVAP method. When the retrieval azimuthal interval is as large as a whole circumference, the IVAP becomes the VAD. On the other hand, if only two neighboring azimuthal data are used, the IVAP becomes the VAP. The frequency response function of IVAP indicates that the IVAP method can filter out shortwaves, and a larger azimuthal interval leads to stronger filtering ability, therefore a smoother retrieved wind field. The shortwave filter function of the IVAP method is tested by an ideal experiment wherein the radar observations are artificially created by a uniform flow superposed with random disturbances. The VAP and IVAP methods are used in wind retrieval, respectively, and give different results for different azimuthal intervals (i.e., 6°, 12°, 24°, and 48°). Because the VAP method is sensitive to small disturbances, the retrieved winds have larger errors for all different azimuthal intervals. However, the retrieved wind by the IVAP method has smaller errors when the azimuthal interval is larger due to its shortwave filter function. An experiment for an idealized linear wind field is also carried out to demonstrate the effect of the retrieval azimuthal interval on the IVAP method. The results show that a short interval gives the retrieval close to the “true" wind field with a linear distribution. When increasing the interval, the retrieval is smoothed and can represent only the mean wind field.     

Statistical Downscaling Based on Dynamically DownscaledPredictors： Application to Monthly Precipitation in Sweden

A prerequisite of a successful statistical downscaling is that large-scale predictors simulated by the General Circulation Model (GCM) must be realistic. It is assumed here that features smaller than the GCM resolution are important in determining the realism of the large-scale predictors. It is tested whether a three-step method can improve conventional one-step statistical downscaling. The method uses predictors that are upscaled from a dynamical downscaling instead of predictors taken directly from a GCM simulation. The method is applied to downscaling of monthly precipitation in Sweden. The statistical model used is a multiple regression model that uses indices of large-scale atmospheric circulation and 850-hPa specific humidity as predictors. Data from two GCMs (HadCM2 and ECHAM4) and two RCM experiments of the Rossby Centre model (RCA1) driven by the GCMs are used. It is found that upscaled RCA1 predictors capture the seasonal cycle better than those from the GCMs, and hence increase the reliability of the downscaled precipitation. However, there are only slight improvements in the simulation of the seasonal cycle of downscaled precipitation. Due to the cost of the method and the limited improvements in the downscaling results, the three-step method is not justified to replace the one-step method for downscaling of Swedish precipitation.     

A New Method of Significance Testing for Correlation-Coefficient Fields and Its Application

Correlation-coefficient fields are widely used in short-term climate prediction research. The most frequently used significance test method for the correlation-coefficient field was proposed by Livezey, in which the number of significantcorrelation lattice(station) points on the correlation coherence map is used as the statistic. However, the method is based on two assumptions:(1) the spatial distribution of the lattice(station) points is uniform;and(2) there is no correlation between the physical quantities in the correlation-coefficient field. However, in reality, the above two assumptions are not valid.Therefore, we designed a more reasonable method for significance testing of the correlation-coefficient field. Specifically, a new statistic, the significant-correlation area, is introduced to eliminate the inhomogeneity of the grid(station)-point distribution, and an empirical Monte Carlo method is employed to eliminate the spatial correlation of the matrix.Subsequently, the new significance test was used for simultaneous correlation-coefficient fields between intensities of the atmospheric activity center in the Northern Hemisphere and temperature/precipitation in China. The results show that the new method is more reasonable than the Livezey method.     

ALGEBRAIC ROSSBY SOLITARY WAVE AND BLOCKING IN THE ATMOSPHERE

In this paper, the atmosphere is divided into two regions which are governed by different equations. Furthermore, multiple-scale method is used to obtain the Benjamin-Ono equation satisfied by the nonlinear Rossby wave in weak shear zonal flow. The equation has algebraic solitary wave solution, and the sta-tionary streamfunction fields in the atmosphere are calculated by using numerical method, and the results demonstrate that the stationary solution is antisymmetric dipoles with the anticyclone north of the cyclone, and the structure is similar to the equivalent modon obtained by Mcwilliains (1980), Because the modon obtained here is an algebraic solitary wave, the modon may be called “algebraic modon”, and the stationary algebraic modon is consistent with observations of blocking pattern in the atmosphere.     

A Comparison Study of the Contributions of Additional Observations in the Sensitive Regions Identified by CNOP and FSV to Reducing Forecast Error Variance for the Typhoon Morakot

The sensitive regions of conditional nonlinear optimal perturbations (CNOPs) and the first singular vector (FSV) for a northwest Pacific typhoon case are reported in this paper. A large number of probes have been designed in the above regions and the ensemble transform Kalman filter (ETKF) techniques are utilized to examine which approach can locate more appropriate regions for typhoon adaptive observations. The results show that, in general, the majority of the probes in the sensitive regions of CNOPs can reduce more forecast error variance than the probes in the sensitive regions of FSV. This implies that adaptive observations in the sensitive regions of CNOPs are more effective than in the sensitive regions of FSV. Furthermore, the reduction of the forecast error variance obtained by the best probe identified by CNOPs is twice the reduction of the forecast error variance obtained by FSV. This implies that dropping sondes, which is the best probe identified by CNOPs, can improve the forecast more than the best probe identified by FSV. These results indicate that the sensitive regions identified by CNOPs are more appropriate for adaptive observations than those identified by FSV.     

Optimal Perturbations Triggering Weather Regime Transitions: Onset of Blocking and Strong Zonal Flow

In this paper, the approach proposed by Mu and Jiang (2008) to obtain the optimal perturbations for triggering blocking (BL) onset is generalized to seek the optimal perturbations triggering onset of the strong zonal flow (SZF) regime. The BL and SZF regimes are characterized by the same dipole-like anomaly pattern superposed on the climatological flow, but with opposite sign. The results show that this method is also superior at finding the initial optimal perturbations triggering onset of the SZF regime, especially in the medium range. Furthermore, by comparing the two kinds of conditional nonlinear optimal perturbations (CNOPs) trig-gering onset of BL and SZF regimes, we find that in the linear approximation, there is symmetry in the sensitivities for BL and SZF onset, and the perturbations that optimally trigger onset of BL and SZF regimes at times when linear approximation is valid are also characterized by the same spatial pattern but with opposite sign. Whereas when the optimization time is extended to 6 days, the two kinds of CNOPs lose their out-of-phase behavior. The nonlinearity results in an asymmetry between the sensitivity for BL and SZF onset. Additionally, we find that the optimal perturbations have one common property, which is that the second baroclinic mode contributes more to the initial perturbations while the barotropic mode dominates the final structures.     

EVALUATION OF TEMPERATURE RECORDS OBTAINED BY AWS IN HAINAN PROVINCE AND ADJUSTMENT OF CLIMATOLOGICAL TIME SERIES

Based on the parallel air temperature data of automatic sounding and manual observations at 16 weather stations in Hainan province from 2004 to 2005, a comparative analysis and evaluation is made for validity according to relevant standards. The results indicate that there are daily and seasonal differences between temperature observations recorded by automatic weather stations (AWSs) and with conventional methods. The reasons for the differences are the systematic error, the sensitivity of the two types of instruments to the environmental temperature change, the difference of the observation time and the effect of solar radiation. Because the long-range data were obtained from manual observation, an empirical conversion formula between the temperature records obtained by the instruments is provided for continuous use of the climate data after the changes in instruments.     

A New Method for Aerosol Retrieval Based on Lidar Observations in Beijing

Lidar has been used extensively in the area of atmospheric aerosol measurement. Two unknowns at the reference altitude, the lidar ratio and the backscatter coefficient, need to be resolved from the lidar equation. In the actual application, these two values are difficult to obtain, particularly the backscatter coefficient. To better characterize the optical properties of aerosols, optical thickness, and attenuated backscatter obtained by other instruments are usually used as the input for joint inversion. However, this method is limited by location and time. In this study, the authors propose a new method for aerosol retrieval by using Mie scatter- ing lidar data to solve this problem. The authors take the horizontal aerosol extinction coefficient as the con- straint to begin the iteration until a self-consistent aerosol vertical profile was obtained. By comparing their results with Aerosol Robotic Network （AERONET） data, the authours determine that the aerosol extinction coefficient obtained by combining horizontal and vertical lidar observations is more pre- cise than that obtained by using the traditional Fernald method. This new method has been adopted for re- trieving the extinction coefficient of aerosols during the observation days.     

Nonlinear oscillations of semigeostrophic Eady waves in the presence of diffusivity

Analyses are performed to examine the physical processes involved in nonlinear oscillations of Eady baxoclinic waves obtained from viscous semigeostrophic models with two types of boundary conditions (free-slip and non-slip). By comparing with previous studies for the case of the free-slip boundary condition, it is shown that the nonlinear oscillations are produced mainly by the interaction between the baroclinic wave and zonal-mean state (total zonal-mean flow velocity and buoyancy stratification) but the timescale of the nonlinear oscillations is largely controlled by the diffusivity. When the boundary condition is non-slip, the nonlinear oscillations are further damped and slowed by the diffusive process. Since the free-slip (non-slip) boundary condition is the zero drag (infinite drag) limit of the more realistic drag boundary condition,the nonlinear oscillations obtained with the two types of boundary conditions are two extremes for more realistic nonlinear oscillations.     

Background Error Covariance Statistics of Hydrometeor Control Variables Based on Gaussian Transform

Use of data assimilation to initialize hydrometeors plays a vital role in numerical weather prediction(NWP).To directly analyze hydrometeors in data assimilation systems from cloud-sensitive observations,hydrometeor control variables are necessary.Common data assimilation systems theoretically require that the probability density functions(PDFs)of analysis,background,and observation errors should satisfy the Gaussian unbiased assumptions.In this study,a Gaussian transform method is proposed to transform hydrometeors to more Gaussian variables,which is modified from the Softmax function and renamed as Quasi-Softmax transform.The Quasi-Softmax transform method then is compared to the original hydrometeor mixing ratios and their logarithmic transform and Softmax transform.The spatial distribution,the non-Gaussian nature of the background errors,and the characteristics of the background errors of hydrometeors in each method are studied.Compared to the logarithmic and Softmax transform,the Quasi-Softmax method keeps the vertical distribution of the original hydrometeor mixing ratios to the greatest extent.The results of the D′Agostino test show that the hydrometeors transformed by the Quasi-Softmax method are more Gaussian when compared to the other methods.The Gaussian transform has been added to the control variable transform to estimate the background error covariances.Results show that the characteristics of the hydrometeor background errors are reasonable for the Quasi-Softmax method.The transformed hydrometeors using the Quasi-Softmax transform meet the Gaussian unbiased assumptions of the data assimilation system,and are promising control variables for data assimilation systems.     

Determination of Kolmogorov Entropy of Chaotic Attractor Included in One-Dimensional Time Series of Meteorological Data

The 1970-1985 day to day averaged pressure dataset of Shanghai and the extension method in phase space are used to calculate the correlation dimension D and the second-order Renyi entropy K2 of the approximation of Kolmogorov's entropy, the fractional dimension D = 7.7-7.9 and the positive value K2 - 0.1 are obtained. This shows that the attractor for the short-term weather evolution in the monsoon region of China exhibits a chaotic motion. The estimate of K2 yields a predictable time scale of about ten days. This result is in agreement with that obtained earlier by the dynamic-statistical approach.The effects of the lag time i on the estimate of D and K2 are investigated. The results show that D and K2 are convergent with respect to i. The day to day averaged pressure series used in this paper are treated for the extensive phase space with T = 5, the coordinate components are independent of each other; therefore, the dynamical character quantities of the system are stable and reliable.     

On Accurate Detection of Oceanic Features from Satellite IR Data Using ICSED Method

ICSED (Improved Cluster Shade Edge Detection) algorithm and other various methods to accurately and efficiently detect edges on satellite data are presented. Error rate criterion is used to statistically evaluate the performances of these methods in detecting oceanic features for both noise free and noise contaminated AVHRR (Advanced Very High Resolution Radiometer) IR image with Kuroshio. Also, practical experiments in detecting the eddy of Kuroshio with these methods are carried out for comparison. Results show that the ICSED algorithm has more advantages than other methods in detecting mesoscale features of ocean. Finally, the effectiveness of window size of ICSED method to oceanic features detection is quantitatively discussed.     

NUMERICAL STUDIES OF PLANETARY BOUNDARY LAYER PARAMETERIZATION SCHEMES ON SUPER TYPHOON SANBA (2012) DURING ITS INITIAL STAGE

The formation and development of typhoons are closely related to the disturbed low vortexes at the planetary boundary layer (PBL). The effects of five PBL parameterization schemes (PBL schemes hereinafter) on the trajectory, intensity, and distribution of physical quantities are studied using the mesoscale WRF model on Super Typhoon Sanba (2012) during its initial stage. Results show that the five PBL schemes exhibit significant different effects on the simulated intensity and path. The results simulated by QNSE and ACM2 without the Bogus method are close to the best track data in the numerical experiments. When the Bogus method is adopted, the simulated trajectories improve significantly because the initial field is close to the true data. Among the five PBL schemes, QNSE and ACM2 with the Bogus method present improved simulated path and intensity compared with the three other schemes. This finding indicates that the two schemes deal with the initial PBL process satisfactorily, especially in the formation and development of disturbed low vortexes. The differences in the treatment methods of the five PBL schemes affect the surface layer physical quantities and the middle and upper atmospheres during the middle to late periods of the typhoon. Although QNSE and ACM2 present better simulation results than other schemes, they exhibit a few differences in the internal structure of the typhoon. The results simulated by MYJ are worse, and this method may be unsuitable for studying the formation and development of typhoons.     

Analysis of the Weighted Mean Temperature of China Based on Sounding and ECMWF Reanalysis Data

Weighted mean temperature (Tm) is one of the most important conversion parameters for calculating precipitable water vapor by the signal path wet delay in ground-based GPS meteorology. This paper first discusses the Tmregression models for Hong Kong (HK) and the associated error statistics relative to the true values of Tmfrom the numerical method. The results show that there is little difference in precision between annual and seasonal Tmregression models for HK. The Bevis Tm-Ts(surface temperature) regression model is more suitable for northeastern China and the Qinghai-Tibetan Plateau than the local models. For areas lack of historical sounding data, the Kriging interpolation method and the ECMWF reanalysis product ERA-interim were employed to set up local Tm-Ts models. The results indicate that the Tmderived by the ERA-interim data coincides well with that by the sounding data, and the Kriging interpolation method can successfully obtain the coefficients of local Tm-Tsmodels, suggesting that these two approaches may serve as effective ways in the acquisition and localization of Tm.     

Water vapor transport around the Tibetan Plateau and its effect on summer rainfall over the Yangtze River valley

The water vapor transport around the Tibetan Plateau(TP) and its effect on the rainfall in the Yangtze River valley(YRV) in summer are investigated by decomposing the moisture transport into rotational and divergent components.Based on the ERA-Interim and PREC/L(Precipitation Reconstruction over Land) data from 1985 to 2014,the vertically integrated features of the two components are examined.The results show that the divergent part dominates the western TP while the rotational part dominates the rest of the TP,implying that moisture may be mostly locally gathered in the western TP but could be advected to/from elsewhere over the rest of the TP.The divergent and rotational moisture fluxes exhibit great temporal variability along the southern periphery of the TP,showing sensitivity of water vapor to the steep topography there.Correlation analysis reveals that it is over the southeastern corner of the TP and to its south that a significant correlation between rotational zonal moisture transport and summer rainfall in the YRV appears,suggesting that the southeastern corner of the TP may serve as a moisture transport bridge between the South Asian(Indian) monsoon and the East Asian monsoon.Further composite analysis indicates that anomalous eastward(westward) zonal water vapor transport from the South Asian monsoon via the southeastern corner of the TP favors more(less) precipitation in the YRV in summer.     

Effect of Nonlinear Dynamic Process on Formation and Breakdown of Blocking

With the L-P approximate method(variation of parameter method), a barotropic channel model in β-plane is used to study the effect of nonlinear interaction between two waves with different scales on the formation of blocking. The approximate analytical solution, which can describe the process of the blocking formation, maintenance and breakdown, has been obtained by using the method of aproximate expansion. The importance of nonlinear interaction between two waves with different scales is stressed in the solution. The result suggests that the nonlinear interaction is the main dynamic process of the blocking formation. Some required conditions of blocking formation are also discussed.     

Some Splitting Methods for Equations of Geophysical Fluid Dynamics

In this paper, equations of atmospheric and oceanic dynamics are reduced to a kind of evolutionary equation in operator form, based on which a conclusion that the separability of motion stages is relative is made and an issue that the tractional splitting methods established on the physical separability of the fast stage and the slow stage neglect the interaction between the two stages to some extent is shown. Also, three splitting patterns are summed up from the splitting methods in common use so that a comparison between them is carried out. The comparison shows that only the improved splitting pattern (ISP) can be in second order and keep the interaction well. Finally, the applications of some splitting methods on numerical simulations of typhoon tracks made clear that ISP owns the best effect and can save more than 80% CPU time.