In this paper,the structure of systematic and random errors in marine survey net are discussed in detail and the adjustment method for observations of marine survey net is studied,in which the rank_defect characterist...In this paper,the structure of systematic and random errors in marine survey net are discussed in detail and the adjustment method for observations of marine survey net is studied,in which the rank_defect characteristic is discovered first up to now.On the basis of the survey_line systematic error model,the formulae of the rank_defect adjustment model are deduced according to modern adjustment theory.An example of calculations with really observed data is carried out to demonstrate the efficiency of this adjustment model.Moreover,it is proved that the semi_systematic error correction method used at present in marine gravimetry in China is a special case of the adjustment model presented in this paper.展开更多
A series of advantages of single difference (SD) and undifferenced (ZD) models are given as compared with the double difference (DD) model. However, rank defects exist in SD and ZD models. The reparameterization metho...A series of advantages of single difference (SD) and undifferenced (ZD) models are given as compared with the double difference (DD) model. However, rank defects exist in SD and ZD models. The reparameterization method is provided to resolve this rank defect problem by estimating some combinations of the unknowns rather than the unknowns themselves. The reparameterization of SD and ZD functional models is discussed in detail with their stochastic models. The theoretical confirmation of the equivalence of undifferenced and differenced models is described in a straightforward way. The relationship between SD and ZD residuals is given and verified for some special purposes, e.g. research on the stochastical properties of GPS observations.展开更多
In this paper,the role of constant optimal forcing(COF) in correcting forecast models was numerically studied using the well-known Lorenz 63 model.The results show that when we only consider model error caused by para...In this paper,the role of constant optimal forcing(COF) in correcting forecast models was numerically studied using the well-known Lorenz 63 model.The results show that when we only consider model error caused by parameter error,which also changes with the development of state variables in a numerical model,the impact of such model error on forecast uncertainties can be offset by superimposing COF on the tendency equations in the numerical model.The COF can also offset the impact of model error caused by stochastic processes.In reality,the forecast results of numerical models are simultaneously influenced by parameter uncertainty and stochastic process as well as their interactions.Our results indicate that COF is also able to significantly offset the impact of such hybrid model error on forecast results.In summary,although the variation in the model error due to physical process is time-dependent,the superimposition of COF on the numerical model is an effective approach to reducing the influence of model error on forecast results.Therefore,the COF method may be an effective approach to correcting numerical models and thus improving the forecast capability of models.展开更多
Consider heteroscedastic regression model Yni= g（xni） ＋ σniεni （1 〈 i 〈 n）, where σ2ni= f（uni）, the design points （xni, uni） are known and nonrandom, g（.） and f（.） are unknown functions defined on cl...Consider heteroscedastic regression model Yni= g（xni） ＋ σniεni （1 〈 i 〈 n）, where σ2ni= f（uni）, the design points （xni, uni） are known and nonrandom, g（.） and f（.） are unknown functions defined on closed interval [0, 1], and the random errors （εni, 1 ≤i≤ n） axe assumed to have the same distribution as （ξi, 1 ≤ i ≤ n）, which is a stationary and a-mixing time series with Eξi =0. Under appropriate conditions, we study asymptotic normality of wavelet estimators of g（.） and f（.）. Finite sample behavior of the estimators is investigated via simulations, too.展开更多
文摘In this paper,the structure of systematic and random errors in marine survey net are discussed in detail and the adjustment method for observations of marine survey net is studied,in which the rank_defect characteristic is discovered first up to now.On the basis of the survey_line systematic error model,the formulae of the rank_defect adjustment model are deduced according to modern adjustment theory.An example of calculations with really observed data is carried out to demonstrate the efficiency of this adjustment model.Moreover,it is proved that the semi_systematic error correction method used at present in marine gravimetry in China is a special case of the adjustment model presented in this paper.
文摘A series of advantages of single difference (SD) and undifferenced (ZD) models are given as compared with the double difference (DD) model. However, rank defects exist in SD and ZD models. The reparameterization method is provided to resolve this rank defect problem by estimating some combinations of the unknowns rather than the unknowns themselves. The reparameterization of SD and ZD functional models is discussed in detail with their stochastic models. The theoretical confirmation of the equivalence of undifferenced and differenced models is described in a straightforward way. The relationship between SD and ZD residuals is given and verified for some special purposes, e.g. research on the stochastical properties of GPS observations.
基金sponsored by the National Basic Research Program of China(Grant No.2012CB955202)the Knowledge Innovation Program of the Chinese Academy of Sciences(Grant No.KZCX2-YW-QN203)the National Natural Science Foundation of China(Grant No.41176013)
文摘In this paper,the role of constant optimal forcing(COF) in correcting forecast models was numerically studied using the well-known Lorenz 63 model.The results show that when we only consider model error caused by parameter error,which also changes with the development of state variables in a numerical model,the impact of such model error on forecast uncertainties can be offset by superimposing COF on the tendency equations in the numerical model.The COF can also offset the impact of model error caused by stochastic processes.In reality,the forecast results of numerical models are simultaneously influenced by parameter uncertainty and stochastic process as well as their interactions.Our results indicate that COF is also able to significantly offset the impact of such hybrid model error on forecast results.In summary,although the variation in the model error due to physical process is time-dependent,the superimposition of COF on the numerical model is an effective approach to reducing the influence of model error on forecast results.Therefore,the COF method may be an effective approach to correcting numerical models and thus improving the forecast capability of models.
基金supported by the National Natural Science Foundation of China under Grant No.10871146the Grant MTM2008-03129 from the Spanish Ministry of Science and Innovation
文摘Consider heteroscedastic regression model Yni= g（xni） ＋ σniεni （1 〈 i 〈 n）, where σ2ni= f（uni）, the design points （xni, uni） are known and nonrandom, g（.） and f（.） are unknown functions defined on closed interval [0, 1], and the random errors （εni, 1 ≤i≤ n） axe assumed to have the same distribution as （ξi, 1 ≤ i ≤ n）, which is a stationary and a-mixing time series with Eξi =0. Under appropriate conditions, we study asymptotic normality of wavelet estimators of g（.） and f（.）. Finite sample behavior of the estimators is investigated via simulations, too.
