Resolution issues in numerical models of oceanic and coastal circulation

The baroclinic and barotropic properties of ocean processes vary on many scales. These scales are determined by various factors such as the variations in coastline and bottom topography, the forcing meteorology, the latitudinal dependence of the Coriolis force, and the Rossby radius of deformation among others. In this paper we attempt to qualify and quantify scales of these processes, with particular attention to the horizontal resolution necessary to accurately reproduce physical processes in numerical ocean models. We also discuss approaches taken in nesting or down-scaling from global/basin-scale models to regional-scale or shelf-scale models. Finally we offer comments on how vertical resolution affects the representation of stratification in these numerical models.     

Rainfall stochastic disaggregation models: Calibration and validation of a multiplicative cascade model

The simulation of long time series of rainfall rates at short time steps remains an important issue for various applications in hydrology. Among the various types of simulation models, random multiplicative cascade models (RMC models) appear as an appealing solution which displays the advantages to be parameter parsimonious and linked to the multifractal theory. This paper deals with the calibration and validation of RMC models. More precisely, it discusses the limits of the scaling exponent function method often used to calibrate RMC models, and presents an hydrological validation of calibrated RMC models. A 8-year time series of 1-min rainfall rates is used for the calibration and the validation of the tested models. The paper is organized in three parts. In the first part, the scaling invariance properties of the studied rainfall series is shown using various methods (q-moments, PDMS, autocovariance structure) and a RMC model is calibrated on the basis of the rainfall data scaling exponent function. A detailed analysis of the obtained results reveals that the shape of the scaling exponent function, and hence the values of the calibrated parameters of the RMC model, are highly sensitive to sampling fluctuation and may also be biased. In the second part, the origin of the sensivity to sampling fluctuation and of the bias is studied in detail and a modified Jackknife estimator is tested to reduce the bias. Finally, two hydrological applications are proposed to validate two candidate RMC models: a canonical model based on a log-Poisson random generator, and a basic micro-canonical model based on a uniform random generator. It is tested in this third part if the models reproduce faithfully the statistical distribution of rainfall characteristics on which they have not been calibrated. The results obtained for two validation tests are relatively satisfactory but also show that the temporal structure of the measured rainfall time series at small time steps is not well reproduced by the two selected simple random cascade models.     

Sensitivity equations for hyperbolic conservation law-based flow models

The present paper focuses on the governing equations for the sensitivity of the variables to the parameters in flow models that can be described by one-dimensional scalar, hyperbolic conservation laws. The sensitivity is shown to obey a hyperbolic, scalar conservation law. The sensitivity is a conserved scalar except in the case of discontinuous flow solutions, where an extra, point source term must be added to the equations in order to enforce conservation. The propagation speed of the sensitivity waves being identical to that of the conserved variable in the original conservation law, the system of conservation laws formed by the original hyperbolic equation and the equation satisfied by the sensitivity is linearly degenerate. A consequence on the solution of the Riemann problem is that rarefaction waves for the variable of the original equation result in vacuum regions for the sensitivity. The numerical solution of the hyperbolic conservation law for the sensitivity by finite volume methods requires the implementation of a specific shock detection procedure. A set of necessary conditions is defined for the discretisation of the source term in the sensitivity equation. An application to the one-dimensional kinematic wave equation shows that the proposed numerical technique allows analytical solutions to be reproduced correctly. The computational examples show that first-order numerical schemes do not yield satisfactory numerical solutions in the neighbourhood of moving shocks and that higher-order schemes, such as the MUSCL scheme, should be used for sharp transients.     

A physically-based method for removing pits in digital elevation models

Spurious pits in digital elevation models (DEMs) are traditionally removed by filling depressions, often creating flat regions that lead to inaccurate estimation of landscape flow directions. In this study, a physical approach based on a simple landscape evolution model is proposed for DEM pit removal. This method, an alternative to traditional geometrical procedures, enforces more realistic slopes and flow directions on topography. The procedure is compared with the method most commonly used in the literature and distributed with commercial GIS software where, generally, elevations of a depression are increased up to the lowest value among neighbouring cells. Several tests are performed and parameters sensitivity is carried out in order to demonstrate the performance of the proposed model as compared to traditional methods.     

Influence of parameters selection in Chebyshev filters on the strong motion data processing

This contribution discusses the application of Chebyshev Type I filter for processing real earthquake records. Consideration is given to the effects of filtering parameters (passband amplitude ripple and order of the filter) on the time series, strong-motion parameters, Fourier Amplitude Spectrum of acceleration, and elastic displacement response spectra. Time histories of five earthquakes with different moment magnitudes have been examined (from stations located close to the epicenters). Data processing is based on application of bandpass Chebyshev filtering over frequency range with substantial signal to noise ratio (level of 3 or approximately 3 dB). Applying different filters, we have monitored several important strong-motion parameters: peak values of acceleration, velocity, and displacement; Arias intensity, acceleration/velocity spectrum intensity, significant duration, etc. Some new results and conclusions concerning the influence of Chebyshev filter in data processing of records have been summarized. The graphical and numerical outcomes obtained, as well as the comparison with a Butterworth causal filter, are included in the work. The results could be potentially useful to engineering seismologists who need to evaluate and better understand the merits of this type of filtering for strong-motion data processing.     

GIS morphometric indicators for the analysis of sediment dynamics in mountain basins

Watershed management and headwater reconstruction programs require a reliable knowledge of sediment dynamics. Geographical Information Systems (GIS) provide the framework for the implementation of different complex techniques for the assessment of shallow landsliding and erosion processes in mountain basins. This paper presents some morphometric indicators aimed at erosion and sediment delivery analysis. The proposed indicators can be easily derived from medium to fine resolution Digital Elevation Models (DEM). Applications conducted in Eastern Italian Alps have shown the adequateness of the proposed approach to address erosion and sediment-related problems. The analysis considered the classification of sediment source areas with regard to their activity, the comparison between drainage basins having different morphological characteristics and the topographic control on sediment transport capacity, with a particular attention to the identification of channel reaches characterised by a low sediment transport capacity.     

REAL-TIME FILTERING OF DATA FROM MOBILE,PASSIVE REMOTE INFRARED SENSORS WITH PRINCIPAL COMPONENT MODELS OF BACKGROUND

Real-time monitoring of pollutant levels from a mobile measuring platform requires fast,flexible dataanalysis methods.This paper reports a method for rapid analysis of passive remotely sensed infrared datawith the aid of a Kalman filter.The background spectra produced by emission from the atmosphere aremodelled at the start of the data collection sequence with a simple principal components model obtainedby eigenanalysis of the initial‘blank’data taken with the spectrometer.The species of interest areincluded in the state space model by a separate measurement of their infrared spectra.It is demonstratedthat for best filter performance in detecting the simulated pollutant species SF_6 in the atmosphere,a filtermodel with two principal components describing the emission background works best.The filter‘maps’of SF_6 closely follow the integrated spectral intensities measured after removal of suitable backgrounds.     

Difference between model parameter estimation and curve fitting

Within a single well, a least-squares model such as Ø = a +bT _sonic may be appropriate, insofar as random errors in core measurement and in sonic tool response are concerned. However, if several wells are in the reservoir, and if structural variation across the field exists, no single least-squares solution will adequately describe all wells with the same precision. Interpolation, via a cubic spline, is offered as an alternative to model this type of variation. However, to control both inter- and intra-well variability, a combination of least squares and interpolation is the model of choice.     

RECENT DEVELOPMENTS IN MULTIVARIATE CALIBRATION

With the goal of understanding global chemical processes,environmental chemists have some of the mostcomplex sample analysis problems.Multivariate calibration is a tool that can be applied successfully inmany situations where traditional univariate analyses cannot.The purpose of this paper is to reviewmultivariate calibration,with an emphasis being placed on the developments in recent years.The inverseand classical models are discussed briefly,with the main emphasis on the biased calibration methods.Principal component regression(PCR)and partial least squares(PLS)are discussed,along with methodsfor quantitative and qualitative validation of the calibration models.Non-linear PCR,non-linear PLSand locally weighted regression are presented as calibration methods for non-linear data.Finally,calibration techniques using a matrix of data per sample(second-order calibration)are discussed briefly.