Data-assimilatie bij dynamische milieuverontreinigingsproblemen

Data-assimilatie methoden zijn bruikbare instrumenten ten behoeve van monitoring en diagnostiek van de milieukwaliteit. Bij deze methoden wordt informatie verkregen uit een milieukwaliteitsmeetnet geincorporeerd met een kwaliteitsmodel. Op deze manier wordt de in de algemene praktijk voorkomende schaarsheid aan metingen aangevuld door middel van modeluitkomsten (model-interpolatie). Anderzijds wordt voorkomen dat modeluitkomsten en metingen twee totaal verschillende diagnoses opleveren (model-calibratie). Dit rapport behandelt de mogelijke toepasbaarheid van twee zulke data-assimilatie methoden. Beide methoden worden met elkaar vergeleken. De eerste, een optimum interpolatietechniek bekend onder de naam Kriging, is eenvoudig en levert acceptabele nauwkeurigheid. Echter, ten opzichte van de andere techniek zijn meer metingen vereist. Bovendien gaat deze methode uit van aannamen met betrekking tot isotropie der data en de zogenaamde intrinsieke hypothese. De aanname met betrekking tot isotropie kan, maar dan ten koste van nog meer metingen, afgezwakt worden. De intrinsieke hypothese is essentieel. Aan beide aannamen wordt in de praktijk meestal matig of slecht voldaan. De aanname in de tweede methode, Kalman filter-techniek, met betrekking tot de data zijn realistischer. Het blijkt dat deze methode ook met veel minder metingen nog goed toepasbaar is. Daar tegenover staat dat het Kalman filter rekentechnisch (CPU-tijd en data-opslag) zware eisen stelt. Volgens Chandrasekhar kan men deze methode, onder zekere veronderstellingen met betrekking tot de modelstructuur, modificeren zodat hij, onder behoud van de typische filter eigenschap, rekentechnisch veel minder veeleisend is. Aan deze veronderstellingen wordt in de onderhavige problematiek voldaan.Integration of data with environmental quality models is a key element for the estimation of dynamic spatial concentration patterns. Therefore, data assimilation methods are useful tools to assist in monitoring and controlling environmental quality. This report discusses the applicability of two such data assimilation methods for the estimation and prediction of air pollution. First, a computational effective time-invariant Kalman filter is developed by using a Chandrasekhar-type filter algorithm. Then, as an alternative, a more simple data assimilation method based on Kriging is proposed. The two data assimilation methods are compared in a number of experiments. It appeared that the Kriging approach is only valid if the isotropic and intrinsic hypothesis is satisfied. However, this assumption may not be realistic in many practical problems. In addition, it requires a relatively large number of measurements to produce reliable predictions. Kalman filtering provides a more accurate estimation and is more widely applicable. However, it suffers from computational burden. For real life applications in the next research phase, it is promising that a recently developed Chandrasekhar-type Kalman filter approach can be incorporated to improve computational effectiveness significantly.RIV

Dataverwerking in grondwaterkwaliteitsmodellen met behulp van Kriging. Deel I

As part of a research program directed towards the development of data assimiliation procedures for environmental models, in this report kriging techniques to integrate models and monitoring networks are studied. Simulated data are obtained from a random concentration field Z(x,t) which is generated as a sum of a deterministic component mu (x,t) giving the main trend of Z (x,t) and a stochastic component e (x) giving the natural variation of Z (x,t) around mu (x,t) with zero mean, constant variance and high spatial correlation. The deterministic part mu (x,t) with known mu (x,0) is formed as a superposition of a constant background concentration field and a rotating cone interpreted as the representation of a local pollution. To integrate models and data simple kriging and universal kriging techniques are implemented and compared. In each experiment the number of observations N is varied, as well as the spatial observation pattern which may be regular or irregular. Every case is subdivided into the situations that the spatial correlation structure, i.e. the semivariogram, is known or not. The method for fitting a semivariogram model is also investigated. In particular, some drawbacks existing in a popularly used cost criterion of weighted least squares method for fitting a semivariogram model are pointed out, and a new cost criterion is proposed. The simulation study illustrates the advantages of the proposed new cost criterion. Further, for a specified underlying realization of a stochastic process, different semivariogram models are employed for kriging. Since the real concentration is known in all these cases, the data assimilation methods are quantitatively compared with the real concentration field. In the next research phases emphasis will be on the elaboration of data assimilation procedures, the testing of their applicability in practice under various conditions, and if necessary and feasible the incorporation of more physics-based information into procedures.RIV

A population-based model to describe geometrical uncertainties in radiotherapy: applied to prostate cases

Local motions and deformations of organs between treatment fractions introduce geometrical uncertainties into radiotherapy. These uncertainties are generally taken into account in the treatment planning by enlarging the radiation target by a margin around the clinical target volume. However, a practical method to fully include these uncertainties is still lacking. This paper proposes a model based on the principal component analysis to describe the patient-specific local probability distributions of voxel motions so that the average values and variances of the dose distribution can be calculated and fully used later in inverse treatment planning. As usually only a very limited number of data for new patients is available; in this paper the analysis is extended to use population data. A basic assumption (which is justified retrospectively in this paper) is that general movements and deformations of a specific organ are similar despite variations in the shapes of the organ over the population. A proof of principle of the method for deformations of the prostate and the seminal vesicles is presented

Quantifying bedform migration using multi-beam sonar

The migration rates of both medium and very large dunes in a part of the North Sea were determined from high-resolution multi-beam echo soundings. From the bathymetric maps, crest positions were determined and compared. From changes in the positions of these crests relative to fixed markers, the migration rates within a tidal cycle and on a seasonal timescale were calculated. The sediment transport rates derived from the migration of the bedforms compare well with theoretical estimates of the residual transport in the area