Towards a data assimilation system for morphodynamic modeling: bathymetric data assimilation for wave property estimation

Data assimilation is mainly concerned with the proper management of uncertainties. The main objective of the present work is to implement and analyze a data assimilation technique capable of assimilating bathymetric data into a coupled flow, wave, and morphodynamic model. For the case presented here, wave significant height, wave direction of incidence, and wave peak period are being optimized based on bathymetric data taken from a twin experiment. An adjoint-free variational scheme is used. In this approach, a linear reduced order model (ROM) is constructed as an approximation of the full model. The ROM is an autoregressive model of order 1 (AR1) that preserves the parametrization. Since the ROM is linear, the construction of its adjoint is straightforward, making the implementation of 4D variational data assimilation effortless. The scheme is able to update the morphodynamic model satisfactorily despite the fact that the model shows nonlinear behavior even for very small perturbations of all three parameters. The size and direction of the perturbations necessary for constructing the ROM have a significant impact on the performance of the technique.     

Similarity Relations for C_{T}^2 in the Unstable Atmospheric Surface Layer: Dependence on Regression Approach,Observation Height and Stability Range

A great variety of similarity functions for the structure parameter of temperature ( \(C_{T}^2\) ) have been proposed in the literature. They differ in the way they were derived from the data and in the characteristics of the dataset used for their derivation (surface type, observation level, stability range). In this study, we use one single dataset (CASES-99 experiment) and investigate the impact on the similarity functions of applying various regression approaches, and measuring at different heights and within different stability ranges. We limit ourselves to similarity functions under unstable conditions, and evaluate only the most common shape that describes the relation with two coefficients ( \(f\left( z/L\right) =c_{1} \left( 1-c_{2} {z}/{L}\right) ^{-2/3}\) , where \(z\) is the height, and \(L\) is the Obukhov length and a measure of the stability, and \(c_{1}\) and \(c_{2}\) are the regression coefficients). The results show that applying various regression approaches has an impact on the regression coefficients \(c_{1}\) and \(c_{2}\) . Thus studies should always specify the regression approach when presenting similarity relations. We suggest use of an orthogonal distance regression method such that uncertainties in \(-z/L\) are also taken into account, to apply this to the logarithmic transformation of both dimensionless groups, and to use a weighted dataset such that unreliable data points have a smaller influence on the fit. Dividing the dataset into eight height ( \(z\) ) and eight stability ( \(-{1/L}\)  classes) classes, we show that the observation height and the stability range has an impact on the coefficients too. This implies that variations in \(c_{1}\) and \(c_{2}\) found in the literature may result from variations in the height and stability ranges among the datasets. Furthermore, application of the coefficients on a dataset obtained at a different height or within a different stability range has to be made with care. Finally, the variation in the coefficients between the classes indicates that the Monin–Obukhov similarity function for \(C_{T}^2\) is not sufficiently described by the two-coefficient function used here.     

Model-reduced gradient-based history matching

Gradient-based history matching algorithms can be used to adapt the uncertain parameters in a reservoir model using production data. They require, however, the implementation of an adjoint model to compute the gradients, which is usually an enormous programming effort. We propose a new approach to gradient-based history matching which is based on model reduction, where the original (nonlinear and high-order) forward model is replaced by a linear reduced-order forward model and, consequently, the adjoint of the tangent linear approximation of the original forward model is replaced by the adjoint of a linear reduced-order forward model. The reduced-order model is constructed with the aid of the proper orthogonal decomposition method. Due to the linear character of the reduced model, the corresponding adjoint model is easily obtained. The gradient of the objective function is approximated, and the minimization problem is solved in the reduced space; the procedure is iterated with the updated estimate of the parameters if necessary. The proposed approach is adjoint-free and can be used with any reservoir simulator. The method was evaluated for a waterflood reservoir with channelized permeability field. A comparison with an adjoint-based history matching procedure shows that the model-reduced approach gives a comparable quality of history matches and predictions. The computational efficiency of the model-reduced approach is lower than of an adjoint-based approach, but higher than of an approach where the gradients are obtained with simple finite differences.     

Infrasound produced by debris flow: propagation and frequency content evolution

Rapid mass movements such as avalanches, debris flows, and rock fall are periodic or episodic phenomena that occur in alpine regions. Recent studies have shown that debris flows generate characteristic signals in the low-frequency infrasonic spectrum (4–15 Hz). Infrasound can travel thousands of kilometers and can still be detectable. This characteristic provides a basis for the development of wide area automated monitoring systems that can operate in locations unaffected by the activity of the process. This study focuses on the infrasound vibrations produced by a debris flow at the Lattenbach torrent, Tyrol (Austria), and by two events at the Illgraben torrent, Canton of Valais (Switzerland). The Lattenbach torrent is a very active torrent, which is located in the west of Tyrol in a geologic fault zone between the Silvrettakristallin and the Northern Limestone Alps. It has a large supply of loose sediment. The Illgraben torrent, which is well known for its frequent sediment transport and debris flow activity, has been equipped with instruments for debris flow monitoring since the year 2000. This study shows that debris flow emits low-frequency infrasonic signals that can be monitored and correlated with seismic signals. During the passage of the debris flow, several surges were identified by ultrasonic gauges and detected in the time series and the running spectra of infrasonic data.     

Energy budget and imaging spectroscopy of a compact flare

We present the analysis of a compact flare that occurred on 26 February 2002 at 10:26 UT, seen by both RHESSI and TRACE. The size of the nearly circular hard X-ray source is determined to be 5.6 (±0.8)′′, using different methods. The power-law distribution of non-thermal photons is observed to extend down to 10 keV without flattening, and to soften with increasing distance from the flare kernel. The former indicates that the energy of the precipitating flare electron population is larger than previously estimated: it amounts to 2.6 (±0.8)×10³⁰ erg above 10 keV, assuming thick-target emission. The thermal energy content of the soft X-ray source (isothermal temperature of 20.8 (±0.9) MK) and its radiated power were derived from the thermal emission at low energies. TRACE has observed a low-temperature ejection in the form of a constricted bubble, which is interpreted as a reconnection jet. Its initial energy of motion is estimated. Using data from both satellites, an energy budget for this flare is derived. The kinetic energy of the jet bulk motion and the thermal and radiated energies of the flare kernel were more than an order of magnitude smaller than the derived electron beam energy. A movie is available on the CD-ROM accompanying this volume. Supplementary material to this paper is available in electronic form at http://dx.doi.org/10.1023/A:1022478300679     

Image compression by means of wavelet transform - application to solar observations

Images and spectra contain a large amount of data. Therefore the question arises, how this data can be decreased or compressed without losing important detail. The discrete wavelet transform is a tool which can be used to compress data because of its good approximation properties. It is very easy to implement and requires approximately the same amount of calculation as the fast Fourier transform. It has the advantage of giving information both in time and frequency. Since most of the coefficients in the transformed data are very small compared to the maximum values, which means that they do not contribute much to the transform, a large number of them can be neglected. Although some data get lost, the physical results deduced from the data remain the same, as is demonstrated by various examples. By this method it is even possible to compress data containing much noise to high-compression ratios.     

Field data and flow system response in clay (vertisol) shale terrain,north central Texas,USA

The water budget in clay shale terrain is controlled by a complex interaction between the vertisol soil layer, the underlying fractured rock, land use, topography, and seasonal trends in rainfall and evapotranspiration. Rainfall, runoff, lateral flow, soil moisture, and groundwater levels were monitored over an annual recharge cycle. Four phases of soil–aquifer response were noted over the study period: (1) dry‐season cracking of soils; (2) runoff initiation, lateral flow and aquifer recharge; (3) crack closure and down‐slope movement of subsurface water, with surface seepage; (4) a drying phase. Surface flow predominated within the watershed (25% of rainfall), but lateral flow through the soil zone continued for most of the year and contributed 11% of stream flow through surface seepage. Actual flow through the fractured shale makes up a small fraction of the water budget but does appear to influence surface seepage by its effect on valley‐bottom storage. When the valley soil storage is full, lateral flow exits onto the valley‐bottom surface as seasonal seeps. Well response varied with depth and hillslope position. FLOWTUBE model results and regional recharge estimates are consistent with an aquifer recharge of 1·6% of annual precipitation calculated from well heights and specific yield of the shale aquifer. Copyright © 2005 John Wiley & Sons, Ltd.