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.

Evaluation of approaches to estimate fish catches on Lake Victoria: a case study using CAS and frame data from Uganda

Since 2005, harmonized catch assessment surveys (CASs) have been implemented on Lake Victoria in the three riparian countries Uganda, Kenya, and Tanzania to monitor the commercial fish stocks and provide their management advice. The regionally harmonized standard operating procedures for CASs have not been wholly followed due to logistical difficulties. Yet the new approaches adopted have not been documented. This study investigated the alternative approaches used to estimate fish catches on the lake with the aim of determining the most reliable one for providing management advice and also the effect of current sampling routine on the precision of catch estimates provided. The study found the currently used lake-wide approach less reliable and more biased in providing catch estimates compared to the district based approach. Noticeable differences were detected in catch estimates between different months of the year. The study recommends future analyses of CAS data collected on the lake to follow the district based approach. Future CASs should also consider seasonal variations in the sampling design by providing for replication of sampling. The SOPs need updating to document the procedures that deviate from the original sampling design.

Use of short-term breath measures to estimate daily methane production by cattle

Methods to measure enteric methane (CH4) emissions from individual ruminants in their production environment are required to validate emission inventories and verify mitigation claims. Estimates of daily methane production (DMP) based on consolidated short-term emission measurements are developing, but method verification is required. Two cattle experiments were undertaken to test the hypothesis that DMP estimated by averaging multiple short-term breath measures of methane emission rate did not differ from DMP measured in respiration chambers (RC). Short-term emission rates were obtained from a GreenFeed Emissions Monitoring (GEM) unit, which measured emission rate while cattle consumed a dispensed supplement. In experiment 1 (Expt. 1), four non-lactating cattle (LW=518 kg) were adapted for 18 days then measured for six consecutive periods. Each period consisted of 2 days of ad libitum intake and GEM emission measurement followed by 1 day in the RC. A prototype GEM unit releasing water as an attractant (GEM water) was also evaluated in Expt. 1. Experiment 2 (Expt. 2) was a larger study based on similar design with 10 cattle (LW=365 kg), adapted for 21 days and GEM measurement was extended to 3 days in each of the six periods. In Expt. 1, there was no difference in DMP estimated by the GEM unit relative to the RC (209.7 v. 215.1 g CH4/day) and no difference between these methods in methane yield (MY, 22.7 v. 23.7 g CH4/kg of dry matter intake, DMI). In Expt. 2, the correlation between GEM and RC measures of DMP and MY were assessed using 95% confidence intervals, with no difference in DMP or MY between methods and high correlations between GEM and RC measures for DMP (r=0.85; 215 v. 198 g CH4/day SEM=3.0) and for MY (r=0.60; 23.8 v. 22.1 g CH4/kg DMI SEM=0.42). When data from both experiments was combined neither DMP nor MY differed between GEM- and RC-based measures (P>0.05). GEM water-based estimates of DMP and MY were lower than RC and GEM (P<0.05). Cattle accessed the GEM water unit with similar frequency to the GEM unit (2.8 v. 3.5 times/day, respectively) but eructation frequency was reduced from 1.31 times/min (GEM) to once every 2.6 min (GEM water). These studies confirm the hypothesis that DMP estimated by averaging multiple short-term breath measures of methane emission rate using GEM does not differ from measures of DMP obtained from RCs. Further, combining many short-term measures of methane production rate during supplement consumption provides an estimate of DMP, which can be usefully applied in estimating MY.

Optimizing PAT data transmission: assessing the accuracy of temperature summary data to estimate environmental conditions

Pop-up archival tags (PAT) provide summary and high-resolution time series data at predefined temporal intervals. The limited battery capabilities of PATs often restrict the transmission success and thus temporal coverage of both data products. While summary data are usually less affected by this problem, as a result of its lower size, it might be less informative. We here investigate the accuracy and feasibility of using temperature at depth summary data provided by PATs to describe encountered oceanographic conditions. Interpolated temperature at depth summary data was found to provide accurate estimates of three major thermal water column structure indicators: thermocline depth, stratification and ocean heat content. Such indicators are useful for the interpretation of the tagged animal's horizontal and vertical behaviour. The accuracy of these indicators was found to be particularly sensitive to the number of data points available in the first 100 m, which in turn depends on the vertical behaviour of the tagged animal. Based on our results, we recommend the use of temperature at depth summary data as opposed to temperature time series data for PAT studies; doing so during the tag programming will help to maximize the amount of transmitted time series data for other key data types such as light levels and depth.

FlorNExT®, a cloud computing application to estimate growth and yield of maritime pine (Pinus pinaster Ait.) stands in Northeastern Portugal

Aim of the study: To introduce and describe FlorNExT®, a free cloud computing application to estimate growth and yield of maritime pine (Pinus pinaster Ait.) even-aged stands in the Northeast of Portugal (NE Portugal). Area of study: NE Portugal. Material and methods: FlorNExT® implements a dynamic growth and yield modelling framework which integrates transition functions for dominant height (site index curves) and basal area, as well as output functions for tree and stand volume, biomass, and carbon content. Main results: FlorNExT® is freely available from any device with an Internet connection at: http://flornext.esa.ipb.pt/. Research highlights: This application has been designed to make it possible for any stakeholder to easily estimate standing volume, biomass, and carbon content in maritime pine stands from stand data, as well as to estimate growth and yield based on four stand variables: age, density, dominant height, and basal area. FlorNExT® allows planning thinning treatments. FlorNExT® is a fundamental tool to support forest mobilization at local and regional scales in NE Portugal. Material and methods: FlorNExT® implements a dynamic growth and yield modelling framework which integrates transition functions for dominant height (site index curves) and basal area, as well as output functions for tree and stand volume, biomass, and carbon content. Main results: FlorNExT® is freely available from any device with an Internet connection at: http://flornext.esa.ipb.pt/. Research highlights: This application has been designed to make it possible for any stakeholder to easily estimate standing volume, biomass, and carbon content in maritime pine stands from stand data, as well as to estimate growth and yield based on four stand variables: age, density, dominant height, and basal area. FlorNExT® allows planning thinning treatments. FlorNExT® is a fundamental tool to support forest mobilization at local and regional scales in NE Portugal.

Planar Odometry from a Radial Laser Scanner. A Range Flow-based Approach

In this paper we present a fast and precise method to estimate the planar motion of a lidar from consecutive range scans. For every scanned point we formulate the range flow constraint equation in terms of the sensor velocity, and minimize a robust function of the resulting geometric constraints to obtain the motion estimate. Conversely to traditional approaches, this method does not search for correspondences but performs dense scan alignment based on the scan gradients, in the fashion of dense 3D visual odometry. The minimization problem is solved in a coarse-to-fine scheme to cope with large displacements, and a smooth filter based on the covariance of the estimate is employed to handle uncertainty in unconstraint scenarios (e.g. corridors). Simulated and real experiments have been performed to compare our approach with two prominent scan matchers and with wheel odometry. Quantitative and qualitative results demonstrate the superior performance of our approach which, along with its very low computational cost (0.9 milliseconds on a single CPU core), makes it suitable for those robotic applications that require planar odometry. For this purpose, we also provide the code so that the robotics community can benefit from it.

A modified DEA model to estimate the importance of objectives with an application to agricultural economics

This paper demonstrates a connection between data envelopment analysis (DEA) and a non-interactive elicitation method to estimate the weights of objectives for decision-makers in a multiple attribute approach. This connection gives rise to a modified DEA model that allows us to estimate not only efficiency measures but also preference weights by radially projecting each unit onto a linear combination of the elements of the payoff matrix (which is obtained by standard multicriteria methods). For users of multiple attribute decision analysis the basic contribution of this paper is a new interpretation in terms of efficiency of the non-interactive methodology employed to estimate weights in a multicriteria approach. We also propose a modified procedure to calculate an efficient payoff matrix and a procedure to estimate weights through a radial projection rather than a distance minimization. For DEA users, we provide a modified DEA procedure to calculate preference weights and efficiency measures that does not depend on any observations in the dataset. This methodology has been applied to an agricultural case study in Spain.

Pesticide bioconcentration factor estimate in apples.

This work objective was to estimate the bioconcentration factor (BCF) of thirty six pesticides used in the Brazilian integrated apple production systems (IAP), in order to select priority pesticides to be monitored in apples. A hypothetical apple orchard was assumed and the model applied was according to Paraíba (2007) [Pesticide bioconcentration modeling for fruit trees. Chemosphere (66:1468-1475)]. The model relates BCF with plant and pesticide characteristics. The octanol-water partition coefficients of pesticides and their degradation rates in the soil were used. The following plant variables were considered: growth rate, total dry biomass, daily water transpiration rate, and total volume of water necessary to produce one kg of fresh fruit per plant. The pesticide stem-water partition coefficient and the transpiration stream concentration factor were calculated using equations that relate each coefficient with the octanol-water partition coefficient. The pesticide BCF in fruits is an important indicator of the pesticide affinity to fruits, and helps to improve the integrated production systems.

Aerial line transect survey to estimate abundance of marsh deer (Blastocerus dichotomus) (Illiger, 1815)

A população de cervo-do-pantanal (Blastocerus dichotomus) está drasticamente reduzida no Brasil. O nosso objetivo foi o de estimar a abundância do cervo-do-pantanal na bacia do Rio Paraná e discutir a metodologia aplicada. Os resultados darão suporte para uma análise do impacto do enchimento da represa de Porto Primavera sobre essa população. Sessenta e nove animais foram registrados através de sobrevôo utilizando-se a metodologia de transecção linear com amostragem das distâncias. Os dados não corrigidos resultaram em uma densidade estimada de 0,0035ind/ha e uma população de 636 indivíduos. A correção de g para os animais que não foram vistos apresentou uma densidade de 0,0049 ind/ha e uma abundância de 896 (CV=0,27) indivíduos. A metodologia foi aplicada com sucesso na estimativa de cervo-do-pantanal. Esse resultado é importante para avaliarmos a população do cervo-do-pantanal na área e para futuramente analisarmos o impacto do enchimento da represa.

Nested Sampling and its Applications in Stable Compressive Covariance Estimation and Phase Retrieval with Near-Minimal Measurements

Compressed covariance sensing using quadratic samplers is gaining increasing interest in recent literature. Covariance matrix often plays the role of a sufficient statistic in many signal and information processing tasks. However, owing to the large dimension of the data, it may become necessary to obtain a compressed sketch of the high dimensional covariance matrix to reduce the associated storage and communication costs. Nested sampling has been proposed in the past as an efficient sub-Nyquist sampling strategy that enables perfect reconstruction of the autocorrelation sequence of Wide-Sense Stationary (WSS) signals, as though it was sampled at the Nyquist rate. The key idea behind nested sampling is to exploit properties of the difference set that naturally arises in quadratic measurement model associated with covariance compression. In this thesis, we will focus on developing novel versions of nested sampling for low rank Toeplitz covariance estimation, and phase retrieval, where the latter problem finds many applications in high resolution optical imaging, X-ray crystallography and molecular imaging. The problem of low rank compressive Toeplitz covariance estimation is first shown to be fundamentally related to that of line spectrum recovery. In absence if noise, this connection can be exploited to develop a particular kind of sampler called the Generalized Nested Sampler (GNS), that can achieve optimal compression rates. In presence of bounded noise, we develop a regularization-free algorithm that provably leads to stable recovery of the high dimensional Toeplitz matrix from its order-wise minimal sketch acquired using a GNS. Contrary to existing TV-norm and nuclear norm based reconstruction algorithms, our technique does not use any tuning parameters, which can be of great practical value. The idea of nested sampling idea also finds a surprising use in the problem of phase retrieval, which has been of great interest in recent times for its convex formulation via PhaseLift, By using another modified version of nested sampling, namely the Partial Nested Fourier Sampler (PNFS), we show that with probability one, it is possible to achieve a certain conjectured lower bound on the necessary measurement size. Moreover, for sparse data, an l1 minimization based algorithm is proposed that can lead to stable phase retrieval using order-wise minimal number of measurements.

Échanges d’énergie et d’eau des écosystèmes nordiques dans un contexte de changement climatique

Le réchauffement climatique affecte fortement les régions nordiques du Canada où le dégel du pergélisol discontinu à sa limite sud est accompagné du mouvement de la limite des arbres vers le nord en zone de pergélisol continu. Ces altérations faites aux paysages de la Taïga des Plaines sont le point de départ de plusieurs rétroactions puisque les changements apportés aux caractéristiques de la surface (au niveau de l’albédo, l’humidité du sol et la rugosité de la surface) vont à leur tour entraîner des modifications biophysiques et éventuellement influencer l’augmentation ou la diminution subséquente des températures et de l’humidité de l’air. Seulement, il y a un nombre important de facteurs d’influence qu’il est difficile de projeter toutes les boucles rétroactives qui surviendront avec les présents changements climatiques en régions nordiques. Dans le but de caractériser les échanges d’eau et d’énergie entre la surface et l’atmosphère de trois sites des Territoires du Nord-Ouest subissant les conséquences de l’augmentation des températures de l’air, la méthode micro-météorologique de covariance des turbulences fut utilisée en 2013 aux sites de Scotty Creek (forêt boréale et tourbière nordique en zone de pergélisol sporadique-discontinu), de Havikpak Creek (forêt boréale nordique en zone de pergélisol continu) et de Trail Valley Creek (toundra arctique en zone de pergélisol continu). En identifiant les procédés biotiques et abiotiques (ex. intensité lumineuse, disponibilité en eau, etc.) d’évapotranspiration aux trois sites, les contrôles par l’eau et l’énergie furent caractérisés et permirent ainsi de projeter une augmentation de la limitation en eau, mais surtout en énergie du site de Trail Valley Creek. La répartition de l’énergie projetée est semblable à celle de Havikpak Creek, avec une augmentation de la proportion du flux de chaleur sensible au détriment de celui latent suite aux modifications des caractéristiques de la surface (albédo, rugosité et humidité du sol). L’augmentation relative du flux d’énergie sensible laisse présager une boucle rétroactive positive de l’augmentation des températures de l’air à ce site. Ensuite, en comparant des données modelées de la hauteur de la couche limite planétaire et des données provenant de profils atmosphériques d’Environnement Canada entre les trois sites, les changements de hauteur de cette couche atmosphérique furent aussi projetés. Trail Valley Creek pourrait connaître une hausse de la hauteur de sa couche limite planétaire avec le temps alors que Scotty Creek connaîtrait une diminution de celle-ci. Ces changements au niveau des couches atmosphériques liés à la répartition des flux d’énergie dans les écosystèmes se répercuteraient alors sur le climat régional de façon difficile à déterminer pour l’instant. Les changements apportés désignent une boucle rétroactive positive des températures de l’air à Trail Valley Creek et l’inverse à Scotty Creek. Les deux axes d’analyse arrivent donc aux mêmes conclusions et soulignent aussi l’importance de l’influence mutuelle entre le climat et les caractéristiques spécifiques des écosystèmes à la surface.

Inferences about Parameters of Trivariate Normal Distribution with Missing Data

Multivariate normal distribution is commonly encountered in any field, a frequent issue is the missing values in practice. The purpose of this research was to estimate the parameters in three-dimensional covariance permutation-symmetric normal distribution with complete data and all possible patterns of incomplete data. In this study, MLE with missing data were derived, and the properties of the MLE as well as the sampling distributions were obtained. A Monte Carlo simulation study was used to evaluate the performance of the considered estimators for both cases when ρ was known and unknown. All results indicated that, compared to estimators in the case of omitting observations with missing data, the estimators derived in this article led to better performance. Furthermore, when ρ was unknown, using the estimate of ρ would lead to the same conclusion.