Approximate guaranteed estimates for matrices in linear regression problems with a small parameter

The problem of finding linear unbiased estimates of the linear operator of unknown matrices — components of the observations vector, is investigated. It is assumed that the observation vector additively depends on a random vector with zero expected value, and the unknown correlation matrix belongs to a known bounded set. For the introduced class of linear estimates, necessary and sufficient conditions for the existence of solutions of operator equations that determine the unknown parameters of the vector estimate, are proved. The form of the guaranteed mean square error of the estimate is introduced on the sets of constraints of the problem parameters. The influence on the linear unbiased estimate of small perturbations of known rectangular matrices, which are the composites of the observations vector components, is also investigated. The analytical form is given through the parameters of the perturbed set of singularities for the introduced special operators that depend on a small parameter, which determine the corresponding operator equations, as well as their approximate solutions, in the first approximation of the small parameter method. A test example of solving the problem of finding a linear unbiased estimate under the condition of perturbation of both linearly independent and linearly dependent known observation matrices is presented.

Regionally improved seasonal forecast of precipitation through Best estimation of winter NAO

We describe a methodology for ensemble member's weighting of operational seasonal forecasting systems (SFS) based on an enhanced prediction of a climate driver strongly affecting meteorological parameters over a certain region. We have applied it to the North Atlantic Oscillation (NAO) influence on the Iberian Peninsula winter precipitation. The first step in the proposed approach is to find the best estimation of winter NAO. Skill and error characteristics of forecasted winter NAO index by different Copernicus SFS are analysed in this study. Based on these results, a bias correction scheme is proposed and implemented for the ECMWF System 5 ensemble mean of NAO index, and then a modified NAO index pdf based on Gaussian errors is formulated. Finally, we apply the statistical estimation theory to achieve the Best linear unbiased estimate of winter NAO index and its uncertainty. For this purpose, two a priori estimates are used: the bias corrected NAO index Gaussian pdf from ECMWF System 5, and a skilful winter NAO index prediction based on teleconnection with snow cover advance with normal distributed errors. The second step of the proposed methodology is to employ the enhanced NAO index pdf estimates for ensemble member's weighting of a SFS based on a single dynamical model. The new NAO pdfs obtained in this work have been used to improve the skill of the ECMWF System 5 to predict both NAO index and precipitation over the Iberian Peninsula. We show the improvement of NAO prediction, and of winter precipitation forecasts over our region of interest, when members are weighted with the bias corrected NAO index Gaussian pdf based on ECMWF System 5 compared with the usual approach based on equiprobability of ensemble members. Forecast skill is further enhanced if the Best NAO index pdf based on an optimal combination of the two a priori NAO index estimates is used for ensemble member's weighting.

Analisis Faktor - Faktor Yang Mempengaruhi Pengeluaran Transportasi Rumah Tangga Indonesia

Transportasi merupakan bagian yang integrasi dengan kegiatan masyarakat, baik secara individu maupun kelompok. Penelitian ini menganalisis faktor-faktor yang mempengaruhi pengeluaran rumah tangga transportasi Indonesia. Faktor-faktor yang termasuk dalam penelitian ini adalah pengeluaran rumah tangga, pengeluaran pajak kendaraan, roda dua kepemilikan kendaraan bermotor, dan kapal motor. Metodologi yang digunakan dalam penelitian ini adalah metode kuantitatif yang dikembangkan dengan membangun sebuah model persamaan matematika. Data yang digunakan adalah Susenas 2010. Data kemudian diolah dengan menggunakan program pengolahan data SPSS. Dalam penelitian ini ditetapkan empat variabel independen, yaitu pengeluaran rumah tangga, pajak kendaraan bermotor, kepemilikan aset roda dua dan perahu motor. Hasil penelitian menunjukkan bahwa model ini telah memenuhi syarat Best Linear Unbiased Estimate. Dari hasil model yang dibangun, pengeluaran transportasi rumah tangga dipengaruhi oleh belanja rumah tangga, pajak kendaraan bermotor, dan kepemilikan aset. Untuk belanja rumah tangga dan pajak kendaraan bermotor memiliki hubungan yang positif. Berarti perubahan kedua variabel tersebut searah. Ta pi untuk kepemilikan kendaraan roda dua, aset dan kapal motor, memiliki hubungan yang berlawanan. Ini berarti bahwa jika ada perubahan dari dua variabel akan berdampak berbeda. Jika rumah tangga tidak memiliki aset akan menyebabkan kenaikan dalam pengeluaran biaya transportasi dan sebaliknya.

An Overlooked Issue of Variational Data Assimilation

The control variable transform (CVT) is a keystone of variational data assimilation. In publications using such a technique, the background term of the transformed cost function is defined as a canonical inner product of the transformed control variable with itself. However, it is shown in this paper that this practical definition of the cost function is not correct if the CVT uses a square root of the background error covariance matrix that is not square. Fortunately, it is then shown that there is a manifold of the control space for which this flaw has no impact, and that most minimizers used in practice precisely work in this manifold. It is also shown that both correct and practical transformed cost functions have the same minimum. This explains more rigorously why the CVT is working in practice. The case of a singular is finally detailed, showing that the practical cost function still reaches the best linear unbiased estimate (BLUE).

A non-Gaussian analysis scheme using rank histograms for ensemble data assimilation

One challenge of geophysical data assimilation is to address the issue of non-Gaussianities in the distributions of the physical variables ensuing, in many cases, from nonlinear dynamical models. Non-Gaussian ensemble analysis methods fall into two categories, those remapping the ensemble particles by approximating the best linear unbiased estimate, for example, the ensemble Kalman filter (EnKF), and those resampling the particles by directly applying Bayes' rule, like particle filters. In this article, it is suggested that the most common remapping methods can only handle weakly non-Gaussian distributions, while the others suffer from sampling issues. In between those two categories, a new remapping method directly applying Bayes' rule, the multivariate rank histogram filter (MRHF), is introduced as an extension of the rank histogram filter (RHF) first introduced by Anderson (2010). Its performance is evaluated and compared with several data assimilation methods, on different levels of non-Gaussianity with the Lorenz 63 model. The method's behavior is then illustrated on a simple density estimation problem using ensemble simulations from a coupled physical–biogeochemical model of the North Atlantic ocean. The MRHF performs well with low-dimensional systems in strongly non-Gaussian regimes.

A variational data assimilation system for soil–atmosphere flux estimates for the Community Land Model (CLM3.5)

This paper presents the development and implementation of a spatio-temporal variational data assimilation system (4D-var) for the soil–vegetation–atmosphere transfer model "Community Land Model" (CLM3.5), along with the development of the adjoint code for the core soil–atmosphere transfer scheme of energy and soil moisture. The purpose of this work is to obtain an improved estimation technique for the energy fluxes (sensible and latent heat fluxes) between the soil and the atmosphere. Optimal assessments of these fluxes are neither available from model simulations nor measurements alone, while a 4D-var data assimilation has the potential to combine both information sources by a Best Linear Unbiased Estimate (BLUE). The 4D-var method requires the development of the adjoint model of the CLM which is established in this work. The new data assimilation algorithm is able to assimilate soil temperature and soil moisture measurements for one-dimensional columns of the model grid. Numerical experiments were first used to test the algorithm under idealised conditions. It was found that the analysis delivers improved results whenever there is a dependence between the initial values and the assimilated quantity. Furthermore, soil temperature and soil moisture from in situ field measurements were assimilated. These calculations demonstrate the improved performance of flux estimates, whenever soil property parameters are available of sufficient quality. Misspecifications could also be identified by the performance of the variational scheme.

A variational data assimilation system for soil–atmosphere flux estimates for the Community Land Model (CLM3.5)

This article presents the development and implementation of a spatio–temporal variational data assimilation system (4D-var) for the soil–vegetation–atmosphere–transfer model "Community Land Model" (CLM3.5), along with the development of the adjoint code for the core soil-atmosphere transfer scheme of energy and soil moisture. The purpose of this work is to obtain an improved estimation technique for the energy fluxes (sensible and latent heat fluxes) between the soil and the atmosphere. Optimal assessments of these fluxes are neither available from model simulations nor measurements alone, while a 4D-var data assimilation has the potential to combine both information sources by a Best Linear Unbiased Estimate (BLUE). The 4D-var method requires the development of the adjoint model of the CLM which was established in this work. The new data assimilation algorithm is able to assimilate soil temperature and soil moisture measurements for one-dimensional columns of the model grid. Numerical experiments were first used to test the algorithm under idealised conditions. It was found that the analysis delivers improved results whenever there is a dependence between the initial values and the assimilated quantity. Furthermore, soil temperature and soil moisture from in situ field measurements were assimilated. These calculations demonstrate the improved performance of flux estimates, whenever soil property parameters are available of sufficient quality. Misspecifications could also be identified by the performance of the variational scheme.