Effects of global brightening on primary production and hypoxia in Ise Bay, Japan

This work is concerned with the numerical solution of linear parabolic differential equations. We exploit the framework of analytic semigroups to understand the properties of the solution as well as to develop numerical algorithms. In the first chapter, we focus on the homogeneous problem. A short introduction to the theory of analytic semigroups is given, which forms the basis for the further development. We prove Besov regularity of the solution for each fixed time where the underlying spatial domain may have a non-smooth boundary and reentrant corners. Moreover, we exploit the Dunford-Cauchy representation of analytic semigroups to numerical evaluate the operator exponential. Essentially, a quadrature rule for a Banach space valued integrand over an infinite integration interval is presented. The error analysis which incorporates spatial discretisation errors also leads to an efficient algorithm which evaluates the solution to the homogeneous problem up to any prescribed target accuracy. In contrast to classical schemes (e.g. Implicit Euler) the algorithm allows us to do arbitrary large time steps and is inherently parallel. In the second chapter, the scope is extended to the inhomogeneous problem. After some results about the mapping properties of the solution operator L which maps the time dependent forcing term f to the solution u(t) = (Lf)(t) we present a new discretisation scheme. We utilise multi-wavelets to discretise the time direction. The coefficients of the wavelet decomposition become vector-valued and can in turn be discretised by a wavelet basis on the spatial domain. For this scheme to be successful, we have to show that the vector-valued coefficients decay sufficiently fast to permit a sparse approximation to the solution. This goal is accomplished under very weak regularity assumptions on the forcing term. Moreover, we outline an efficient algorithm which calculates the wavelet decomposition of the solution given the forcing term f in wavelet coordinates. This algorithm is based on the quadrature rule from the first chapter. The third chapter is devoted to applications in regularisation theory. The inverse problems to the homogeneous and the inhomogeneous problem are well-known to be ill-posed such that we have to apply some regularisation technique. After a short introduction to the classical theory, we present a modification of Tikhonov regularisation which is closely adapted to the eigenspaces of the ill-posed operator. While this eigenspaces are usually unknown, we develop an algorithm based on a contour integral which projects any given value onto certain selected eigenspaces. Moreover, this algorithm allows us to apply the inverse of the restriction of an analytic semigroup to certain eigenspaces which yields an economical regularisation scheme. Concerning the inhomogeneous problem, an adaptive discretisation is presented which proves useful in Tikhonov regularisation. In the fourth chapter numerical experiments for the algorithms from the preceding chapters as well as comparisons to classical methods are collected. The error analysis from the first chapter turns out to be rather sharp. Moreover, the algorithm based on quadrature outperforms a classical single step method of second order. The new discretisation scheme for the inhomogeneous problem leads to very few significant coefficients in the time decomposition which renders the scheme very appealing. This is exemplified in Tikhonov regularisation where we observe singularities in the solution which are resolved well by the adaptive solution scheme

Characteristics of suspended sediment material transport in the Ishikari Bay in snowmelt season

The present paper aims at studies of the suspended sediment transport in inner Ishikari Bay in snowmelt season using a numerical approach and field observation data. The sediment transport and bottom boundary layer models are coupled into the Princeton Ocean Model to compute suspended sediment concentration in the system. The following findings have been deduced: (1) The suspended sediment transport in the study area in snowmelt season is dominated by the sediment discharge from the Ishikari River. The effect of sediment resuspension due to wave current interaction is limited to a very shallow area along the coast. (2) A comparison between observed and computed suspended sediment concentrations shows that the model can reproduce reasonably well the general features of the dynamics of suspended sediment transport in Ishikari Bay in snowmelt season. (3) The suspended sediment matter (SSM) from the Ishikari River is mainly transported northward. The vertical structure of SSM concentration displays a slow sinking of sediment matter supplied to the water column from the surface i.e. high sediment concentration is seen in surface layers and it gradually deceases in the lower layers. (4) After two months of simulation, net erosion occurs in a narrow area nearshore. The average erosion depth in this area is 0.16 mm. Net deposition locates in a wider area north of the inner bay. The average deposition depth in this area is 0.04 mm

Phosphorus compounds in the dissolved and particulate phases in urban rivers and a downstream eutrophic lake as analyzed using 31P NMR

Phosphorus (P) discharges from human activities result in eutrophication of lakes. We investigated whether the forms of phosphorus (P) in rivers with high effluent loads flowing through urban areas of Sapporo, Japan, were transformed when transported downstream into a eutrophic lake, namely Lake Barato. We hypothesized that the inorganic P supplied from the rivers might be transformed to organic forms in the lake. The results showed that soluble reactive phosphorus (SRP) and particulate inorganic phosphorus (PIP) dominated in the river discharge to the lake. Suspended solids in the rivers were rich in iron (Fe) so PIP was associated with Fe. A comparison of the concentrations at the river mouth and 4.5 km downstream showed that the concentrations of SRP and PIP were lower at 4.5 km downstream than at the river mouth, whereas the concentrations of organic P (i.e., dissolved organic phosphorus and particulate organic phosphorus) were similar. The results from solution 31P nuclear magnetic resonance spectroscopy of lake water showed that pyrophosphate was only present in the particulate fraction, while orthophosphate diesters (DNA-P) were only present in the dissolved fraction. Riverine samples contained orthophosphate (ortho-P) only, while lake samples contained ortho-P, orthophosphate monoesters, and DNA-P. The results suggest that the P forms, particularly those of dissolved P, shifted from inorganic to organic forms as the water was discharged from the river to the lake

Incorporation characteristics of exogenous 15N-labeled thymidine, deoxyadenosine, deoxyguanosine and deoxycytidine into bacterial DNA.

Bacterial production has been often estimated from DNA synthesis rates by using tritium-labeled thymidine. Some bacteria species cannot incorporate extracellular thymidine into their DNA, suggesting their biomass production might be overlooked when using the conventional method. In the present study, to evaluate appropriateness of deoxyribonucleosides for evaluating bacterial production of natural bacterial communities from the viewpoint of DNA synthesis, incorporation rates of four deoxyribonucleosides (thymidine, deoxyadenosine, deoxyguanosine and deoxycytidine) labeled by nitrogen stable isotope (15N) into bacterial DNA were examined in both ocean (Sagami Bay) and freshwater (Lake Kasumigaura) ecosystems in July 2015 and January 2016. In most stations in Sagami Bay and Lake Kasumigaura, we found that incorporation rates of deoxyguanosine were the highest among those of the four deoxyribonucleosides, and the incorporation rate of deoxyguanosine was approximately 2.5 times higher than that of thymidine. Whereas, incorporation rates of deoxyadenosine and deoxycytidine were 0.9 and 0.2 times higher than that of thymidine. These results clearly suggest that the numbers of bacterial species which can incorporate exogenous deoxyguanosine into their DNA are relatively greater as compared to the other deoxyribonucleosides, and measurement of bacterial production using deoxyguanosine more likely reflects larger numbers of bacterial species productions