Source time functions of the Gonghe，China earthquake retrieved from long－period digital waveform data using empirical Green＇s function technique

An earthquake of Ms= 6, 9 occurred at the Gonghe, Qinghai Province, China on April 26, 1990. Three larger aftershocks took place at the same region, Ms= 5. 0 on May 7, 1990, Ms= 6. 0 on Jan. 3, 1994 and Ms= 5. 7on Feb. 16, 1994. The long-period recordings of the main shock from China Digital Seismograph Network (CDSN) are deconvolved for the source time functions by the correspondent0 recordings of the three aftershocks asempirical Green's functions (EGFs). No matter which aftershock is taken as EGF, the relative source time functions (RSTFs) Obtained are nearly identical. The RSTFs suggest the Ms= 6. 9 event consists of at least two subevents with approximately equal size whose occurrence times are about 30 s apart, the first one has a duration of 12 s and a rise time of about 5 s, and the second one has a duration of 17 s and a rise time of about & s. COmParing the RSTFs obtained from P- and SH-phases respectively, we notice that those from SH-phases are a slightly more complex than those from p-phases, implying other finer subevents exist during the process of the main shock. It is interesting that the results from the EGF deconvolution of long-Period way form data are in good agreement with the results from the moment tensor inversion and from the EGF deconvolution of broadband waveform data. Additionally, the two larger aftershocks are deconvolved for their RSTFs. The deconvolution results show that the processes of the Ms= 6. 0 event on Jan. 3, 1994 and the Ms= 5. 7 event on Feb. 16,1994 are quite simple, both RSTFs are single impulses.The RSTFs of the Ms= 6. 9 main shock obtained from different stations are noticed to be azimuthally dependent, whose shapes are a slightly different with different stations. However, the RSTFs of the two smaller aftershocks are not azimuthally dependent. The integrations of RSTFs over the processes are quite close to each other, i. e., the scalar seismic moments estimated from different stations are in good agreement. Finally the scalar seismic moments of the three aftershocks are compared. The relative scalar seismic moment Of the three aftershocks deduced from the relative scalar seismic moments of the Ms=6. 9 main shock are very close to those inverted directly from the EGF deconvolution. The relative scalar seismic moment of the Ms =6. 9 main shock calculated using the three aftershocks as EGF are 22 (the Ms= 6. 0 aftershock being EGF), 26 (the Ms= 5. 7 aftershock being EGF) and 66 (the Ms= 5. 5 aftershock being EGF), respectively. Deducingfrom those results, the relative scalar sesimic moments of the Ms= 6. 0 to the Ms= 5. 7 events, the Ms= 6. 0 tothe Ms= 5. 5 events and the Ms= 5. 7 to the Ms= 5. 5 events are 1. 18, 3. 00 and 2. 54, respectively. The correspondent relative scalar seismic moments calculated directly from the waveform recordings are 1. 15, 3. 43, and 3. 05.

Analysis of the regional spectral properties in northwestern South China Sea based on an empirical orthogonal function

This study presents an analysis of the spectral characteristics of remote sensing reflectance(Rrs)in northwestern South China Sea based on the in situ optical and water quality data for August 2018.Rrswas initially divided into four classes,classes A to D,using the max-classification algorithm,and the spectral properties of whole Rrs were characterized using the empirical orthogonal function(EOF)analysis.Subsequently,the dominant factors in each EOF mode were determined.The results indicated that more than 95%of the variances of Rrs are partly driven by the back-scattering characteristics of the suspended matter.The initial two EOF modes were well correlated with the total suspended matter and back-scattering coefficient.Furthermore,the first EOF modes of the four classes of Rrs(A-D Rrs-EOF1)significantly contributed to the total variances of each Rrs class.In addition,the correlation coefficients between the amplitude factors of class A-D Rrs-EOF1 and the variances of the relevant water quality and optical parameters were better than those of the unclassified ones.The spectral shape of class ARrs-EOF1 was governed by the absorption characteristic of chlorophyll a and colored dissolved organic matter(CDOM).The spectral shape of class B Rrs-EOF1 was governed by the absorption characteristic of CDOM since it exhibited a high correlation with the absorption coefficient of CDOM(ag(λ)),whereas the spectral shape of class C Rrs-EOF1 was governed by the back-scattering characteristics but not affected by the suspended matter.The spectral shape of class D Rrs-EOF1 exhibited a relatively good correlation with all the water quality parameters,which played a significant role in deciding its spectral shape.

A Simulated Annealing Algorithm for Training Empirical Potential Functions of Protein Folding

In this paper are reported the local minimum problem by means of current greedy algorithm for training the empirical potential function of protein folding on 8623 non-native structures of 31 globular proteins and a solution of the problem based upon the simulated annealing algorithm. This simulated annealing algorithm is indispensable for developing and testing highly refined empirical potential functions.

A NEW ONE-STEP BAND-LIMITED EXTRAPOLATION PROCEDURE USING EMPIRICAL ORTHOGONAL FUNCTIONS

A one-step band-limited extrapolation procedure is systematically developed under an a priori assumption of bandwidth. The rationale of the proposed scheme is to expand the known signal segment based on a band-limited basis function set and then to generate a set of Empirical Orthogonal Functions (EOF’s) adaptively from the sample values of the band-limited function set. Simulation results indicate that, in addi- tion to the attractive adaptive feature, this scheme also appears to guarantee a smooth result for inexact data, thus suggesting the robustness of the proposed procedure.

A Multivariate Empirical Orthogonal Function-Based Scheme for the Balanced Initial Ensemble Generation of an Ensemble Kalman Filter

The initial ensemble perturbations for an ensemble data assimilation system are expected to reasonably sample model uncertainty at the time of analysis to further reduce analysis uncertainty. Therefore, the careful choice of an initial ensemble perturbation method that dynamically cycles ensemble perturbations is required for the optimal performance of the system. Based on the multivariate empirical orthogonal function (MEOF) method, a new ensemble initialization scheme is developed to generate balanced initial perturbations for the ensemble Kalman filter (EnKF) data assimilation, with a reasonable consideration of the physical relationships between different model variables. The scheme is applied in assimilation experiments with a global spectral atmospheric model and with real observations. The proposed perturbation method is compared to the commonly used method of spatially-correlated random perturbations. The comparisons show that the model uncertainties prior to the first analysis time, which are forecasted from the balanced ensemble initial fields, maintain a much more reasonable spread and a more accurate forecast error covariance than those from the randomly perturbed initial fields. The analysis results are further improved by the balanced ensemble initialization scheme due to more accurate background information. Also, a 20-day continuous assimilation experiment shows that the ensemble spreads for each model variable are still retained in reasonable ranges without considering additional perturbations or inflations during the assimilation cycles, while the ensemble spreads from the randomly perturbed initialization scheme decrease and collapse rapidly.

Rupture process of November 6,1988,Lan-cang-Gengma,Yunnan,China,earthquake of M_s=7.6 using empirical Green’s function de-convolution method

The empirical Green's function deconvolution technique is applied to the November 6, 1988, Ms=7.6, Yunnan, China earthquake to study the rupture process of this event. An aftershock of Ms=6.3 is taken as the empirical Green's function. Recordings of these two events at six stations of China Digital Seismographic Network (CDSN) are employed. Deconvolution results show that this event is a relatively simple event. Directivity analysis indicates that the rupture was initiated at hypocenter and propagated bilaterally and nearly symmetrically towards the northwest and southeast directions with a total length of 70 km and a time duration of 19 s. The rupture velocity is estimated to be about 2.0 km/s.

NON-LINEAR DYNAMIC MODEL RETRIEVAL OF SUBTROPICAL HIGH BASED ON EMPIRICAL ORTHOGONAL FUNCTION AND GENETIC ALGORITHM

Aiming at the difficulty of accurately constructing the dynamic model of subtropical high, based on the potential height field time series over 500 hPa layer of T106 numerical forecast products, by using EOF（empirical orthogonal function） temporal-spatial separation technique, the disassembled EOF time coefficients series were regarded as dynamical model variables, and dynamic system retrieval idea as well as genetic algorithm were introduced to make dynamical model parameters optimization search, then, a reasonable non-linear dynamic model of EOF time-coefficients was established. By dynamic model integral and EOF temporal-spatial components assembly, a mid-/long-term forecast of subtropical high was carried out. The experimental results show that the forecast results of dynamic model are superior to that of general numerical model forecast results. A new modeling idea and forecast technique is presented for diagnosing and forecasting such complicated weathers as subtropical high.

Empirical orthogonal function analysis of short time series of sectional data in the tropical western Pacific

In this paper,some short time series of pnserved data pm sectopm 18°20′N in the tropical western Pacificwere reorganized to give mixed depth-time series,and processed by means of means of empirical orthogonal fonction analysis. It is indicated that the original form of element distribution could be obtained by linear combination of several main canonical distribution functions, and the intrinsic structure of element distribution on a certain section and its variation propertiescould be reveled by canonical distribution function and profiles in corresponding periods.

Estimation of Water Particle Velocities by Empirical Transfer Function

In previous and this studies it appears that the linear and nonlinear wave theory-can not accurately and easily predict the water particle velocities: Therefore, different from the theoretical considerations, in this study we have attempted to determine the transfer function empirically. Laboratory experiments were performed under various wave conditions. The empirical formulas of the transfer function of the wave height, angular frequency and water particle velocity were obtained on the basis of these test data by dimensional analysis and regression analysis. In intermediate and deep water depth conditions, the transfer function was only a function of a nondimensional parameter which is composed of the angular frequency, the depth of the velocity gauge under the still water level, water depth and the acceleration of gravity. Finally, the empirical formulas were compared with experimental data and observational data form present and Cavaleri's (1978) studies. The empirical formulas were found to be in sufficient correltion with these data.

ON THE MEASURABILITY FOR FUNCTIONAL OF EMPIRICAL PROCESSES

In this paper, we give some results for checking the measurability of functional of empirical processes, their direct applications concern with the measurability of statis-tics constructed by Projection pursuit technique, thus the results obtained provide a basis in theory for projection pursuit study.

Spatio-temporal variability of surface chlorophyll a in the Yellow Sea and the East China Sea based on reconstructions of satellite data of 2001-2020

Chlorophyll-a(Chl-a)concentration is a primary indicator for marine environmental monitoring.The spatio-temporal variations of sea surface Chl-a concentration in the Yellow Sea(YS)and the East China Sea(ECS)in 2001-2020 were investigated by reconstructing the MODIS Level 3 products with the data interpolation empirical orthogonal function(DINEOF)method.The reconstructed results by interpolating the combined MODIS daily+8-day datasets were found better than those merely by interpolating daily or 8-day data.Chl-a concentration in the YS and the ECS reached its maximum in spring,with blooms occurring,decreased in summer and autumn,and increased in late autumn and early winter.By performing empirical orthogonal function(EOF)decomposition of the reconstructed data fields and correlation analysis with several potential environmental factors,we found that the sea surface temperature(SST)plays a significant role in the seasonal variation of Chl a,especially during spring and summer.The increase of SST in spring and the upper-layer nutrients mixed up during the last winter might favor the occurrence of spring blooms.The high sea surface temperature(SST)throughout the summer would strengthen the vertical stratification and prevent nutrients supply from deep water,resulting in low surface Chl-a concentrations.The sea surface Chl-a concentration in the YS was found decreased significantly from 2012 to 2020,which was possibly related to the Pacific Decadal Oscillation(PDO).

Spatial and Temporal Differences of Climate Suitability of Ice and Snow Sports in Major Ski Tourism Destinations in China

Ice and snow tourism in China has grown significantly since the country successfully hosted the Beijing Winter Olympics.Climatic conditions profoundly impact the development of ice and snow tourism;however,most studies have focused on constructing different climate suitability indicators for ice and snow tourism to evaluate individual regions,lacking horizontal comparative studies across multiple regions.This study aims to enrich the connotation of climate suitability for ice and snow sports,establish an evaluation model based on snowfall amount,temperature,and wind speed,and use daily meteorological data from 1991 to 2021 to horizontally compare the climate suitability for ice and snow sports in major ski tourism destinations in China.This study boasts four major findings:1)the average ice and snow sports climate index of each region decreases over time,and the overall suitability of the climate for ice and snow sports is reducing;2)northern Xinjiang exhibits the most evident regional differentiation from‘very suitable’to‘generally suitable’;3)the spatial zoning of climate suitability for ice and snow sports exhibits heterogeneity,as northern Xinjiang is divided into two‘suitable and above’zones with rotating empirical orthogonal function(REOF).Correspondingly,the four provinces of Hebei,Heilongjiang,Jilin,and Liaoning are divided into three‘generally suitable and above’zones;4)snowfall amount is the main factor affecting the climate suitability of ice and snow sports in the major ski tourist destinations in China.

Spatiotemporal variations of parameters of internal solitary waves in the northern South China Sea

The dynamic parameters for internal solitary waves(ISWs)derived from the extended Korteweg-de Vries(eKdV)equation play an important role in the understanding and prediction of ISWs.The spatiotemporal variations of the dynamic parameters of the ISWs in the northern South China Sea(SCS)were studied based on the reanalysis of long-term temperature and salinity datasets.The results for spectrum analysis show that there are definite geographical differences for the periodic variation of the parameters:in shallow water,all parameters vary with a wave period of one year,while in deep water wave components of the parameters at other frequencies exist.Using wavelet analysis,the wavelet power spectral densities in deep water exhibited an inter-annual variation pattern.For example,the wave component of the dispersion coefficient with a wave period of about half a year reached its power peak once every two years.Based on previous work,this inter-annual variation pattern was deduced to be caused by dynamic processes.In further work on the regulatory mechanisms,empirical orthogonal function(EOF)decomposition was performed.It was found that the modes of the dispersion coefficient have different geographical distributions,explaining the reason why the wave components in different frequencies appeared in different locations.The numerical simulation results confirm that the variations in the parameters of the ISWs derived from the eKdV equation could affect the waveforms significantly because of changes in the polarity of the ISWs.Therefore,the periodic variations of the dynamic parameters are related to the geographical location because of dynamic processes operating.

Strong Convergence of Empirical Distribution for a Class of Random Matrices

Let {vij}, i, j = 1, 2, …, be i.i.d, random variables with Ev11 = 0, Ev11^2 = 1 and a1 = （ai1,…, aiM） be random vectors with {aij} being i.i.d, random variables. Define XN =（x1,…, xk） and SN =XNXN^T,where xi=ai×si and si=1/√N（v1i,…, vN,i）^T. The spectral distribution of SN is proven to converge, with probability one, to a nonrandom distribution function under mild conditions.

Synthesis of accelerations of the 1976 Tangshan earthquake(M_S 7.8)in near-and far-field by using semi-empirical method

In this paper a heterogeneous fault model of the Tangshan earthquake is suggested, which consists of two southern sub faults striking N30°E and two northern sub faults striking N50°E. Total length of the main shock fault is 114 km and seismic moment is about 1.4×10 20 N·m. The epicentre of the main shock is located at the southern part, near the intersection of the two bands. Accelerations of two aftershocks ( M L 5.5, M S 6.9 ) were used as empirical Green's functions to synthesize the accelerations of the main shock in near and far field. A method that small events and main shock are considered not satisfying the similarity relationship in the improved empirical Green's function is also applied in this paper. Peak values, duration and response spectra of synthesized accelerations in far field are in agreement with the observed records. The synthesized results in near field are also in agreement with the epicentral intensity distribution of the main shock. The results show that the peak acceleration of Tangshan earthquake in epicentral region exceeds 1.1 g. It is consistent with the peak accelerations recorded in some large earthquakes occurred in recent years.

Characteristics of the dynamic changes in active accumulated temperature in Sichuan,China in the last 51 years against the background of climate change

It is of utmost necessity to understand the dynamics of regional active accumulated temperature(AAT)to cope with the negative impacts of global warming on agroforestry development and food security and to provide a real-time and effective reference basis for regional agroforestry planning.The daily temperature data from 30 meteorological stations in Sichuan Province from 1970 to 2020,and sea surface temperature(SST)index data from the Atlantic Multiphase Oscillation(AMO)and Pacific Decadal Oscillation(PDO)were used for the study.Sichuan Province was divided into the western region(WS)and the eastern region(ES),considering 1000 m above sea level as the boundary.The spatiotemporal characteristics of≥0℃ and≥10℃ active accumulated temperature(AAT0,AAT10)in WS and ES were analyzed comprehensively using 5-day average sliding,empirical orthogonal function(EOF),ensemble empirical mode decomposition(EEMD),and multiple mutation tests.The results show that(1)AAT0 and AAT10 of WS ranged from 3034℃ to 3586℃ and 1971℃ to 2636℃,respectively,while the AAT0 and AAT10 of ES ranged from 5863℃ to 6513℃ and 4847℃ to 5875℃,respectively.The period around 1997 was a significant abrupt change,and the AAT in the province generally increased during the subsequent time period(2)AAT in the study area is mainly driven by the fluctuations of AMO,as reflected by the low-to-high variation of AAT coinciding with the jump of the cold-to-warm phase of AMO.Considering different time scale fluctuations in the past 51 years,the major cycle for both AAT0 and AAT10 in WS is 3.40 a,while the major cycles in ES are 3.64 a and 3.19 a,respectively with a sub-cycle of 7.29 a.AAT fluctuation has an insignificant periodic characteristic of 25.50 a on the interdecadal scale(3)The spatial heterogeneity of AAT in WS is prominent and is mainly reflected by the significantly warm conditions in the south of the WS region and relatively slight warm conditions in the north,as well as by the isolated cooling area in the form of"freezing point",i.e.,Xiaojin county.In contrast,the spatial variability of AAT in ES is more or less consistent,with the warming areas concentrated in the foothills of the western edge of the basin and a slight increase in AAT observed in the central part of the basin.

The Interannual Variability of Summer Rainfall in the Arid and Semiarid Regions of Northern China and Its Association with the Northern Hemisphere Circumglobal Teleconnection

Using the latest daily observational rainfall datasets for the period 1961–2008, the present study investigates the interannual variability of June–September （JJAS） mean rainfall in northern China. The regional characteristics of JJAS mean rainfall are revealed by a rotated empirical orthogonal function （REOF） analysis. The analysis identifies three regions of large interannual variability of JJAS rainfall： North China （NC）, Northeast China （NEC）, and the Taklimakan Desert in Northwest China （TDNWC）. Summer rainfall over NC is shown to have displayed a remarkable dry period from the late 1990s; while over NEC, decadal-scale variation with a significant decreasing trend in the last two decades is found, and over TDNWC, evidence of large interannual variability is revealed. Results also show that the interannual variability of JJAS rainfall in northern China is closely associated with the Northern Hemisphere circumglobal teleconnection （CGT）. Correlation coefficients between the CGT index and regional-averaged JJAS mean rainfall over NC and NEC were calculated, revealing values of up to 0.50 and 0.53, respectively, both of which exceeded the 99% confidence level.

Modeling the global ionospheric total electron content with empirical orthogonal function analysis

In the present work we model the global ionospheric total electron content (TEC) with the analysis of empirical orthogonal functions (EOF). The obtained statistical eigen modes, which makeup the modeled TEC, consist of two factors: the eigen vectors mapping TEC patterns at latitude and longitude (or local time LT), and the corresponding coefficients displaying the TEC variations in different time scales, i.e., the solar cycle, the yearly (annual and semiannual) and the diurnal universal time variations. It is found that the EOF analysis can separate the TEC variations into chief processes and the first two modes illustrate the most of the ionospheric climate properties. The first mode contains both the semiannual component which shows the semiannual ionospheric anomaly and the annual component which shows the annual or non-seasonal ionospheric anomaly. The second mode contains mainly the annual component and shows the normal seasonal ionospheric variation at most latitudes and local time sectors. The annual component in the second mode also manifests seasonal anomaly of the ionosphere at higher mid-latitudes around noontime. It is concluded that the EOF analysis, as a statistical eigen mode method, is resultful in analyzing the ionospheric climatology hence can be used to construct the empirical model for the ionospheric climatology.

Spatiotemporal Variations of Summer Rainfall over Eastern China during 1880-1999(1)

By applying rotated complex empirical orthogonal function (RCEOF) analysis on 1880-1999 summer rainfall at 28 selected stations over the east part of China, the spatio-temporal variations of China summer rainfall are investigated. Six divisions are identified, showing strong temporal variability, the middle and lower reaches of the Yangtze River, the Huaihe River, Southeast China, North China, Southwest China, and Northeast China. The locations of all divisions except Southwest China are in a good agreement with those of the rainband which moves northward from Southeast China to Northeast China from June-August. The phase relationship revealed by the RCEOF analysis suggests that rainfall anomalies in the middle and lower reaches of the Yangtze River, Southeast China, and Northeast China are all characterized by a stationary wave, while a traveling wave is more pronounced in the Huaihe River division, North China, and Southwest China. The fourth RCEOF mode indicates that rainfall anomalies can propagate from south of Northeast China across lower reaches of the Huanghe River and the Huaihe River to the lower reaches of the Yangtze River. A 20-25-year oscillation is found at the middle and lower reaches of the Yangtze River, the Huaihe River valley, North China, and Northeast China. The middle and lower reaches of the Yangtze River and Northeast China also show an approximately-60-year oscillation. Northeast China and the Huaihe River division are dominated by a 36-year and a 70-80-year oscillation, respectively. An 11-year oscillation is also evident in North China, with a periodicity similar to sunspot activity. The interdecadal variability in the middle and lower reaches of the Yangtze River, the Huaihe River valley, and North China shows a significant positive correlation with the solar activity.

Impact of Urbanization on Low-Temperature Precipitation in Beijing during 1960–2008

Daily precipitation and temperature records at 13 stations for the period 1960-2008 were analyzed to identify climatic change and possible effects of urbanization on low-temperature precipitation [LTP, precipitation of ≥ 0.1 mm d^-1 occurring under a daily minimum temperature （Tmin） of ≤ 0℃] in the greater Beijing region （B JR）, where a rapid process of urbaniza tion has taken place over the last few decades. The paper provides a climatological overview of LTP in B JR. LTP contributes 61.7% to the total amount of precipitation in B JR in the cold season （November-March）. There is a slight increasing trend [1.22 mm （10 yr）^-1] in the amount of total precipitation for the cold season during 1960-2008. In contrast, the amount of LTP decreases by 0.6 mm （10 yr）^-1. The warming rate of Train in B JR is 0.66℃ （10 yr）^-1. Correspondingly, the frequency of LTP decreases with increasing Tmin by -0.67 times per ℃. The seasonal frequency and amount of LTP in southeast B JR （mostly urban sites） are 17%-20% less than those in the northwestern （rural and montane sites）. The intensity of LTP for the urban sites and northeastern B JR exhibited significant enhancing trends [0.18 and 0.15 mm d^- 1 （10 yr）^- 1, respectively]. The frequency of slight LTP （〈0.2 mm d^-1） significantly decreased throughout B JR [by about -15.74% （10 yr）^-1 in the urban area and northeast B JR], while the contribution of the two heaviest LTP events to total LTP amount significantly increased by 3.2% （10 yr） ^-1.