Calibration of parameters of mathematical models is still a tough task in several engineering problems. Many of the models adopted for the numerical simulations of real phenomena, in fact, are of empirical derivation. Therefore, they include parameters which have to be calibrated in order to correctly reproduce the physical evidence. Thus, the success of a numerical model application depends on the quality of the performed calibration, which can be of great complexity, especially if the number of parameters is higher than one. Calibration is traditionally performed by engineers and researchers through manual trial-and-error procedures. However, since models themselves are increasingly sophisticated, it seems more proper to look at more advanced calibration procedures. In this work, in particular, an optimization technique for a multi-parameter calibration is applied to a two-phase depth-averaged model, already adopted in previous works to simulate morphodynamic processes, such as, for example, the dike erosion by overtopping.
Optimization methods are used to estimate parameters required for routing floods through open compound channels. Besides initial and boundary flow conditions, data required especially include, crosssectional area (A) of flow and conveyance (K) as functions of flow depth (y) for a representative crosssection of the study reach. Thus, instead of optimizing upon channel's geometric and hydraulic parameters, optimization is performed upon non-physical parameters in assumed A(y) and K(y) relationships. The optimization method selected for this application is the Nelder and Mead Simplex Algorithm. The objective function is expressed in terms of the relative differences between observed and simulated stages and discharges, which are evaluated based on the complete numerical solution of St Venant equations. This approach to formulating the optimization problem was applied to unsteady flow data sets for an experimental reach of the River Main in Northern Ireland. Based on statistical analysis, simulated and observed stages were found to be in good agreement. and Parametre potrebné pre kvantifikáciu transformácie povodňových vĺn v otvorených, zložených kanáloch, boli určené optimalizačnou metódou. Okrem počiatočných a okrajových podmienok sú potrebné ďalšie údaje, vrátane plochy priečneho rezu prúdom (A), ako aj vodivosť časti toku (K) ako funkcie hĺbky (y) pre reprezentatívny priečny rez. Namiesto optimalizácie geometrických a hydraulických parametrov kanála, optimalizácia sa vykonala pre nefyzické parametre, predpokladajúc závislosti A(y) a K(y). Vybranou metódou optimalizácie je Nelderov a Meadov Simplex Algoritmus. Funkcia je vyjadrená pomocou relatívnych rozdielov medzi pozorovanými a simulovanými vodnými stavmi a prietokmi, ktoré boli vyčíslené numerickým riešením rovníc St. Venanta. Tento spôsob formulácie optimalizačného problému bol aplikovaný na údaje pre neustálené prúdenie v experimentálnom priamom úseku rieky Main (River Main) v Severnom Írsku. Štatistickou analýzou bolo zistené, že simulované a merané vodné stavy boli veľmi blízke.
Inland waters are known to be laden with high levels of suspended particulate matter (SPM). Remotely sensed data have been shown to provide a true synoptic view of SPM over vast areas. However, as to date, there is no universal technique that would be capable of retrieving SPM concentrations without a complete reliance on time-consuming and costly ground measurements or a priori knowledge of inherent optical properties of water-borne constituents. The goal of this paper is to present a novel approach making use of the synergy found between the reflectance in the visual domain (~ 400-700 nm) with the near-infrared portion of the spectrum (~ 700-900 nm). The paper begins with a brief discourse of how the shape and spectral dependence of reflectance is determined by high concentrations of SPM. A modeled example is presented to mimic real-world conditions in fluvial systems, with specific absorption and scattering coefficients of the virtual optically active constituents taken from the literature. Using an optical model, we show that in the visual spectral domain (~ 400-700 nm) the water-leaving radiance responds to increasing SPM (0-100 g m-3) in a non-linear manner. Contrarily to the visual spectra, reflectance in the near infrared domain (~ 700-900 nm) appears to be almost linearly related to a broad range of SPM concentrations. To reduce the number of parameters, the reflectance function (optical model) was approximated with a previously experimentally verified exponential equation (Schiebe et al., 1992: Remote sensing of suspended sediments: the Lake Chicot, Arkansas project, Int. J. Remote Sensing, 13, 8, 1487-1509). The SPM term in Schiebe’s equation was expressed as a linear function of top-of-atmosphere reflectance. This made it possible to calibrate the reflectance in the visual domain by reflectance values from the near-IR portion of the spectrum. The possibility to retrieve SPM concentrations from only remote sensing data without any auxiliary ground mea-surements is tested on a Landsat ETM + scene acquired over a reservoir with moderately turbid water with SPM concentrations between 15-70 g m-3. The retrieved concentrations (on average) differ from in-situ measurement by ~ 10.5 g m-3. and Cieľom príspevku je prezentovať alternatívne spracovanie satelitných snímok na odhad koncentrácie suspendovaných sedimentov vo vodných útvaroch. Prvá časť článku sa venuje teórii a fyzikálnej podstate reflektancie a vplyvu prirodzene sa vyskytujúcich opticky aktívnych prvkov vo vode (suspendované sedimenty, pigmenty a rozpustené látky) na reflektanciu snímanú prostriedkami diaľkového prieskumu Zeme. Na modelovom príklade sme ukázali, že so zvyšovaním koncentrácie suspendovaných látok dochádza k saturácii signálu reflektancie.V druhej časti príspevku sme opísali spôsob využitia nelineárnosti vzťahu medzi reflektanciu vo viditeľnej časti (~ 400-700), a kvázi-linearitov v infračervenej časti (~ 700-900 nm) elektromegnetického spektra a koncentrácie suspendovaných sedimentov. Optimalizáciou tohto nelineárneho vzťahu sme odhadli koncentrácie suspendovaných sedimentov pre zdrž Hrušov pri Bratislave s RMSE 10.5 g m-3.