On Variational Ensemble Kalman Filtering

The Extended Kalman Filter (EKF) and four dimensional assimilation variational method (4D-VAR) are both advanced data assimilation methods. The EKF is impractical in large scale problems and 4D-VAR needs much effort in building the adjoint model. In this work we have formulated a data assimilation method that will tackle the above difficulties. The method will be later called the Variational Ensemble Kalman Filter (VEnKF). The method has been tested with the Lorenz95 model. Data has been simulated from the solution of the Lorenz95 equation with normally distributed noise. Two experiments have been conducted, first with full observations and the other one with partial observations. In each experiment we assimilate data with three-hour and six-hour time windows. Different ensemble sizes have been tested to examine the method. There is no strong difference between the results shown by the two time windows in either experiment. Experiment I gave similar results for all ensemble sizes tested while in experiment II, higher ensembles produce better results. In experiment I, a small ensemble size was enough to produce nice results while in experiment II the size had to be larger. Computational speed is not as good as we would want. The use of the Limited memory BFGS method instead of the current BFGS method might improve this. The method has proven succesful. Even if, it is unable to match the quality of analyses of EKF, it attains significant skill in forecasts ensuing from the analysis it has produced. It has two advantages over EKF; VEnKF does not require an adjoint model and it can be easily parallelized.

Software business expansion through distribution channel : Case M-Files - Denmark

The purpose of this study was to find out how a software company can successfully expand business to the Danish software market through distribution channel. The study was commissioned by a Finnish software company and it was conducted using a qualitative research method by analyzing external and internal business environment, and interviewing Danish ICT organizations and M-Files personnel. Interviews were semi-structured interviews, which were designed to collect comprehensive information on the existing ICT and software market in Denmark. The research used three external and internal analyzing frameworks; PEST analysis (market level), Porter´s Five Force analysis (industry level competition) and SWOT analysis (company level). Distribution channels theory was a base to understand why and what kind of distribution channels the case company uses, and what kind of channels target markets companies’ uses. Channel strategy and design were integrated to the industry level analysis. The empirical findings revealed that Denmark has very business friendly ICT environment. Several organizations have ranked Denmark´s information and communication technology as the best in the world. Denmark’s ICT and software market are relatively small, compared to many other countries in Europe. Danish software market is centralized. Largest software clusters are in the largest cities; Copenhagen, Aarhus, Odense and Aalborg. From these clusters, software companies can most likely find suitable resellers. The following growing trends are clearly seen in the software market: mobile and wireless applications, outsourcing, security solutions, cloud computing, social business solutions and e-business solutions. When expanding software business to the Danish market, it is important to take into account these trends. In Denmark distribution channels varies depending on the product or service. For many, a natural distribution channel is a local partner or internet. In the public sector solutions are purchased through a public procurement process. In the private sector the buying process is more straight forwarded. Danish companies are buying software from reliable suppliers. This means that they usually buy software direct from big software vendors or local partners. Some customers prefer to use professional consulting companies. These consulting companies can strongly influence on the selection of the supplier and products, and in this light, consulting companies can be important partners for software companies. Even though the competition is fierce in ECM and DMS solutions, Danish market offers opportunities for foreign companies. Penetration to the Danish market through reseller channel requires advanced solutions and objective selection criteria for channel partners. Based on the findings, Danish companies are interested in advanced and efficient software solutions. Interest towards M-Files solutions was clearly seen and the company has excellent opportunity to expand business to the Danish market through reseller channel. Since the research explored the Danish ICT and software market, the results of the study may offer valuable information also to the other software companies which are expanding their business to the Danish market.

Variational Ensemble Kalman Filtering in Hydrology

The current thesis manuscript studies the suitability of a recent data assimilation method, the Variational Ensemble Kalman Filter (VEnKF), to real-life fluid dynamic problems in hydrology. VEnKF combines a variational formulation of the data assimilation problem based on minimizing an energy functional with an Ensemble Kalman filter approximation to the Hessian matrix that also serves as an approximation to the inverse of the error covariance matrix. One of the significant features of VEnKF is the very frequent re-sampling of the ensemble: resampling is done at every observation step. This unusual feature is further exacerbated by observation interpolation that is seen beneficial for numerical stability. In this case the ensemble is resampled every time step of the numerical model. VEnKF is implemented in several configurations to data from a real laboratory-scale dam break problem modelled with the shallow water equations. It is also tried in a two-layer Quasi- Geostrophic atmospheric flow problem. In both cases VEnKF proves to be an efficient and accurate data assimilation method that renders the analysis more realistic than the numerical model alone. It also proves to be robust against filter instability by its adaptive nature.

Variational ensemble Kalman filtering applied to data assimilation problems in computational fluid dynamics

One challenge on data assimilation (DA) methods is how the error covariance for the model state is computed. Ensemble methods have been proposed for producing error covariance estimates, as error is propagated in time using the non-linear model. Variational methods, on the other hand, use the concepts of control theory, whereby the state estimate is optimized from both the background and the measurements. Numerical optimization schemes are applied which solve the problem of memory storage and huge matrix inversion needed by classical Kalman filter methods. Variational Ensemble Kalman filter (VEnKF), as a method inspired the Variational Kalman Filter (VKF), enjoys the benefits from both ensemble methods and variational methods. It avoids filter inbreeding problems which emerge when the ensemble spread underestimates the true error covariance. In VEnKF this is tackled by resampling the ensemble every time measurements are available. One advantage of VEnKF over VKF is that it needs neither tangent linear code nor adjoint code. In this thesis, VEnKF has been applied to a two-dimensional shallow water model simulating a dam-break experiment. The model is a public code with water height measurements recorded in seven stations along the 21:2 m long 1:4 m wide flume’s mid-line. Because the data were too sparse to assimilate the 30 171 model state vector, we chose to interpolate the data both in time and in space. The results of the assimilation were compared with that of a pure simulation. We have found that the results revealed by the VEnKF were more realistic, without numerical artifacts present in the pure simulation. Creating a wrapper code for a model and DA scheme might be challenging, especially when the two were designed independently or are poorly documented. In this thesis we have presented a non-intrusive approach of coupling the model and a DA scheme. An external program is used to send and receive information between the model and DA procedure using files. The advantage of this method is that the model code changes needed are minimal, only a few lines which facilitate input and output. Apart from being simple to coupling, the approach can be employed even if the two were written in different programming languages, because the communication is not through code. The non-intrusive approach is made to accommodate parallel computing by just telling the control program to wait until all the processes have ended before the DA procedure is invoked. It is worth mentioning the overhead increase caused by the approach, as at every assimilation cycle both the model and the DA procedure have to be initialized. Nonetheless, the method can be an ideal approach for a benchmark platform in testing DA methods. The non-intrusive VEnKF has been applied to a multi-purpose hydrodynamic model COHERENS to assimilate Total Suspended Matter (TSM) in lake Säkylän Pyhäjärvi. The lake has an area of 154 km2 with an average depth of 5:4 m. Turbidity and chlorophyll-a concentrations from MERIS satellite images for 7 days between May 16 and July 6 2009 were available. The effect of the organic matter has been computationally eliminated to obtain TSM data. Because of computational demands from both COHERENS and VEnKF, we have chosen to use 1 km grid resolution. The results of the VEnKF have been compared with the measurements recorded at an automatic station located at the North-Western part of the lake. However, due to TSM data sparsity in both time and space, it could not be well matched. The use of multiple automatic stations with real time data is important to elude the time sparsity problem. With DA, this will help in better understanding the environmental hazard variables for instance. We have found that using a very high ensemble size does not necessarily improve the results, because there is a limit whereby additional ensemble members add very little to the performance. Successful implementation of the non-intrusive VEnKF and the ensemble size limit for performance leads to an emerging area of Reduced Order Modeling (ROM). To save computational resources, running full-blown model in ROM is avoided. When the ROM is applied with the non-intrusive DA approach, it might result in a cheaper algorithm that will relax computation challenges existing in the field of modelling and DA.

Symmetristen komponenttien mallinnus

Tässä insinöörityössä suunniteltiin Helsingin ammattikorkeakoululle jakeluverkoissa tapahtuvien oikosulkujen symmetristen komponenttien laskutavan havainnollistamiseen sopiva sijaiskytkentä. Sijaiskytkennässä tärkeitä huomioitavia asioita olivat mm. jännitetaso, havainnollistavien muuntajien oikosulkukestoisuus, jatkokäyttö laboratoriotyönä ja yleinen havainnollistavuus. Työssä on aluksi perehdytty symmetristen komponenttien ja jakeluverkoissa tapahtuvien oikosulkujen teoriaan. Tämän jälkeen mitoitettiin tarvittavan kytkennän komponenttien jännite- ja virtakestoisuudet mahdolliset lisäkäytöt huomioiden. Näiden rajoitusten mukaan perusteella työtä ruvettiin toteuttamaan. Työssä tilattiin sähkön 40 V:n pääjännitetasolle alentava muuntaja syöttämään oikosulun kestävää muuntajaa, jolla simuloitiin jakeluverkon yleisimpiä vikatyyppejä. Jälkimmäiselle muuntajalle mitoitettiin ja hankittiin sisäistä impedanssia vastaava induktanssi. Tämän avulla rakennettiin kokonaisuus, jonka avulla voidaan simuloida kaikkia tapahtuvia oikosulkuja vastaavat sijaiskytkennät. Työhön jätettiin kehittämisvaraa ja muita laboratoriotyön rakentamismahdollisuuksia tulevien insinööritöiden tekijöille.