Bathymetric modelin from satellite imagery via Single Band Algorithm (SBA) and Principal Components Analysis (PCA) in southern Caspian Sea

Remotely sensed imagery is proving to be a useful tool to estimate water depths in coastal zones. Bathymetric algorithms attempt to isolate water attenuation and hence depth from other factors by using different combinations of spectral bands. In this research, images of absolute bathymetry using two different but related methods in a region in the southern Caspian Sea coasts has been produced. The first method used a Single Band Algorithm (SBA) and assumed a constant water attenuation coefficient throughout the blue band. The second method used Principal Components Analysis (PCA) to adjust for varying water attenuation coefficients without additional ground truth data. PCA method (r=-0.672394) appears to match our control points slightly better than single band algorithm (r=-0.645404). It is clear that both methods can be used as rough estimates of bathymetry for many coastal zone studies in the southern Caspian Sea such as near shore fisheries, coastal erosion, water quality, recreation siting and so forth. The presented methodology can be considered as the first step toward mapping bathymetry in the southern Caspian Sea. Further research must investigate the determination of the nonlinear optimization techniques as well as the assessment of these models’ performance in the study area

Progressive augmentation of Reynolds stress tensor models for secondary flow prediction by computational fluid dynamics driven surrogate optimisation

Generalisability and the consistency of the a posteriori results are the most critical points of view regarding data-driven turbulence models. This study presents a progressive improvement of turbulence models using simulation-driven surrogate optimisation based on Kriging. We aim for the augmentation of secondary-flow reconstruction capability in a linear eddy-viscosity model without violating its original performance on canonical cases e.g. channel flow. Explicit algebraic Reynolds stress correction models (EARSCMs) for $k-\omega$ SST turbulence model are obtained to predict the secondary flow which the standard model fails to capture. The optimisation of the models is achieved by a multi-objective approach based on duct flow quantities, and numerical verification of the developed models is performed for various test cases. The results of testing new models on channel flow cases guarantee that new models preserve the performance of the original $k-\omega$ SST model. Regarding the generalisability of the new models, results of unseen test cases demonstrate a significant improvement in the prediction of secondary flows and streamwise velocity. These results highlight the potential of the progressive approach to enhance the performance of data-driven turbulence models for fluid flow simulation while preserving the robustness and stability of the solver.Comment: 23 pages, 20 figure

Influence of vertical distribution of phytoplankton on remote sensing signal of Case II waters : southern Caspian Sea case study

Reliable monitoring of coastal waters is not possible without using remote sensing data. On the other hand, it is quite difficult to develop remote sensing algorithms that allow one to retrieve water characteristics (like chlorophyll-a concentration) in optically complex coastal and inland waters (called also Case II waters) as the concentrations of optically active substances (phytoplankton, suspended matter, and colored dissolved organic matter) vary independently from each other and the range of variability is often high. Another problem related to developing remote sensing algorithms for retrieving concentrations of optically active substances in such complex waters is vertical distribution of these substances. For example, phytoplankton distribution in the water column is often characterized with maxima just below the surface mixed layer, and some phytoplankton species even have the capability to migrate in the water column and tend to form layers at depths optimal for their growth. Twenty-three field campaigns were performed during the spring-summer period in the coastal waters of the southern Caspian Sea where vertical distribution of phytoplankton was measured by means of chlorophyll-a fluorometer. There results showed that there is usually a chlorophyll-a maximum between 10 and 20 m where the concentration is about one order of magnitude higher than in the top mixed layer. The Hydrolight 5.0 radiative transfer model used to estimate if the vertical distribution of biomass have detectable impact on remote sensing signal in these waters. For that purpose, several stations with distinctly different chlorophyll-a profiles were selected and two simulations for each of those measuring stations was carried out. First the Hydrolight was run with the actual chlorophyll-a vertical distribution profile and second a constant chlorophyll-a value (taken as an average of measured chlorophyll-a in the surface layer) was used in the model simulation. The modelling results show that the “deep” chlorophyll maximum has negligible effect on the remote sensing reflectance spectra. Consequently, there is no need to take into account the vertical distribution of phytoplankton while developing remote sensing algorithms for the Caspian Sea coastal water

Multivalued SK-contractions with respect to b-generalized pseudodistances

A new class of multivalued non-self-mappings, called SK-contractions with respect to b-generalized pseudodistances, is introduced and used to investigate the existence of best proximity points by using an appropriate geometric property. Some new fixed point results in b-metric spaces are also obtained. Examples are given to support the usability of our main result

Best proximity point theorems for α-nonexpansive mappings in Banach spaces

In this paper, we discuss sufficient and necessary conditions for the existence of best proximity points for non-self-a-nonexpansive mappings in Banach spaces. We obtain convergence results under some assumptions, and we prove the existence of common best proximity points for a family of non-self-a-nonexpansive mappings