The impact of floodplain hydrology on the in-stream dissolved oxygen dynamics and the relation between dissolved oxygen and water temperature are investigated. This has been done by examining the time series of dissolved oxygen and water temperature coupled with meteorological and hydrological data obtained from two lowland rivers having contrasting hydrological settings. Spectral analysis of long-term oxygen variations in a vegetated river revealed a distinct scaling regime with slope ‘-1’ indicating a self-similar behaviour. Identical slopes were obtained for water temperature and water level. The same power-law behaviour was observed for an unvegetated river at small timescales revealing the underlying scaling behaviour of dissolved oxygen regime for different types of rivers and over various time scales. The results have shown that the oxygenation of a vegetated river is strongly related to its thermal regime and flow conditions. Moreover, analysis of short-term fluctuations in the unvegetated river demonstrated that physical factors such as rainfall and backwaters play a substantial role in the functioning of this ecosystem. Finally, the results show that the relation between water temperature and dissolved oxygen concentration at the diurnal timescale exhibits a looping behaviour on the variable plot. The findings of this study provide an insight into the sensitivity of rivers to changing hydro-physical conditions and can be useful in the assessment of environmental variability.
We consider autonomous systems where two scalar differential equations are coupled with the input-output relationship of the Preisach hysteresis operator, which has an infinite-dimensional memory. A prototype system of this type is an LCR electric circuit where the inductive element has a ferromagnetic core with a hysteretic relationship between the magnetic field and the magnetization. Further examples of such systems include lumped hydrological models with two soil layers; they can also appear as a component of the recently proposed models of population dynamics. We study dynamics of such systems near an equilibrium point. In particular, we show and examine a similarity in the behaviour of trajectories between the system with the Preisach memory operator and a planar slow-fast ordinary differential equation. The nonsmooth Preisach operator introduces a singularity into the system. Furthermore, we classify the robust equilibrium points according to their stability properties. Conditions for stability, instability and partial stability are presented. A robust partially stable point simultaneously attracts many trajectories and repels many trajectories (a behaviour which is not generic for smooth ordinary differential equations). We discuss implications of such local dynamics for the excitability properties of the system.
A good knowledge of hydraulic characteristics, particularly the retention curves, of the applied materials is necessary when studying the efficiency of a capillary barrier or numerically simulating flow of water in its layers. The main difficulties of their measurements originate in the fact that the coarse-grained soils of capillary barriers come from the state of residual moisture to the state of saturation within relatively small interval of pressure head. Hence, it is necessary to carry out the measurements in very fine steps of pressure head. Four materials of two capillary barriers are investigated in this paper. The tension apparatus according to Havlíček and Myslivec was used to measure their retention curves. Both branches of retention curves were measured in order to obtain data suitable for taking hysteresis into account. The method is described and the results are presented. Subsequently, the hydraulic characteristics of the materials are determined and their impact to the capillary barriers efficiency is investigated. The barriers were compared from the viewpoint of their efficiency using the measured data and tipping trough measurements made elsewhere. Explanation of the found differences was suggested and the effect of hysteresis was discussed., Dagmar Trpkošová and Jiří Mls., and Obsahuje bibliografii
Suspended sediment dynamics during hydrological events influenced by rainstorms and factors controlling changes in sediment dynamics were investigated in a small basin scale, since small basins can be considered as one of the most important sediment sources. The study focuses on the agricultural microbasin Rybárik, near Považská Bystrica (Western Slovakia). Suspended sediment concentrations were measured during discharge waves in the years 1987-1990, 1992, 2000 and 2001. The behaviour of suspended sediments in watercourses is not only a function of energy conditions, but also a function of sediment availability. The variations in sediment supply and sediment depletion result in so-called hysteresis effects. Thus, suspended sediment concentrations at rising and falling limbs are different for equal discharges. Positive and anti-clockwise hysteresis was observed at Rybárik basin. The procedure of separation of factors controlling sediment dynamics has given more realistic view on production and transport of suspended sediments. It is confirmed that spatial and temporal variability of sediment availability and suspended sediment dilution by the baseflow, mainly in the case of two or more waves following one after another control significantly suspended sediment dynamics. and Keďže malé povodia možno považovať za jeden z hlavných zdrojov sedimentov, na malom povodí bol skúmaný režim plavenín počas hydrologických udalostí spôsobených prívalovými zrážkami, a faktory ovplyvňujúce zmeny v dynamike plavenín. Štúdia bola vykonaná na poľnohospodárskom mikropovodí Rybárik pri Považskej Bystrici. Koncentrácie plavenín boli merané počas prietokových vĺn v rokoch 1987- 1990, 1992, 2000 a 2001. Režim plavenín vo vodných tokoch nie je funkciou len transportnej kapacity toku, ale aj dostupnosti sedimentov. Zmeny v zásobovaní a vyčerpávaní sedimentov spôsobujú tzv. hysterézny efekt. To znamená, že koncentrácie plavenín na stúpajúcej a klesajúcej vetve vlny sú rozdielne pri tých istých prietokoch. V povodí Rybárik bola pozorovaná pozitívna aj opačná hysteréza. Postup izolovania faktorov, ktoré ovplyvňujú dynamiku plavenín, prináša reálnejší obraz o tvorbe a transporte plavenín. Ukazuje sa, že zrieďovanie koncentrácií plavenín základným odtokom a časová a priestorová heterogenita územia z hľadiska dostupnosti sedimentov, predovšetkým v situácii tesne za sebou nasledujúcich prívalových vĺn, sa významne podieľajú na celkovej dynamike plavenín.
The paper deals with a scalar diffusion equation c ut = (F[ux])x+f, where F is a Prandtl-Ishlinskii operator and c, f are given functions. In the diffusion or heat conduction equation the linear constitutive relation is replaced by a scalar Prandtl-Ishlinskii hysteresis spatially dependent operator. We prove existence, uniqueness and regularity of solution to the corresponding initial-boundary value problem. The problem is then homogenized by considering a sequence of equations of the above type with spatially periodic data cε and ηε when the spatial period ε tends to zero. The homogenized characteristics c∗ and η∗ are identified and the convergence of the corresponding solutions to the solution of the homogenized equation is proved.
Two sets of triangular hydrographs were generated in a 12-m-long laboratory flume for two sets of initial bed conditions: intact and water-worked gravel bed. Flowrate ranging from 0.0013 m3 s–1 to 0.0456 m3 s–1, water level ranging from 0.02 m to 0.11 m, and cumulative mass of transported sediment ranging from 4.5 kg to 14.2 kg were measured. Then, bedload transport rate, water surface slope, bed shear stress, and stream power were evaluated. The results indicated the impact of initial bed conditions and flow unsteadiness on bedload transport rate and total sediment yield. Difference in ratio between the amount of supplied sediment and total sediment yield for tests with different initial conditions was observed. Bedload rate, bed shear stress, and stream power demonstrated clock-wise hysteretic relation with flowrate. The study revealed practical aspects of experimental design, performance, and data analysis. Water surface slope evaluation based on spatial water depth data was discussed. It was shown that for certain conditions stream power was more adequate for the analysis of sediment transport dynamics than the bed shear stress. The relations between bedload transport dynamics, and flow and sediment parameters obtained by dimensional and multiple regression analysis were presented.
The main objective of this study is to assess the effect of hysteresis of soil hydraulic properties on model predictions of soil water movement in a variably saturated soil. The model predictions are generated by the S1D model, which is based on numerical solution of one-dimensional Richards’ equation. The analysis is made for a loamy sand soil located in a small headwater catchment. The model is used to simulate the development of soil water pressure during three successive vegetation seasons. Three major simulation scenarios are formulated: the first scenario assumes no hysteresis in soil hydraulic properties, the second scenario involves a predefined hypothetical hysteresis, while the third scenario is based on optimized hysteresis, determined through the inverse modeling procedure. The analysis of the simulation results suggests that, in our case, ignoring hysteresis does not lead to any significant deviation of the model predictions from the observed soil water system responses. and Možnosti efektivně matematicky modelovat proudění vody v přirozených půdních formacích omezuje komplikovanost určení půdních hydraulických charakteristik, a to nejen s ohledem na jejich prostorovou a časovou variabilitu, ale také hysterezi. Příspěvek je zaměřen na testování vlivu hystereze na výsledky simulací proudění půdní vody v podmínkách malého horského povodí. Numerický model S1D, řešící Richardsovu rovnici v jednorozměrném tvaru, byl použit k výpočtu sezónního vývoje tlaku půdní vody. V simulacích byla alternativně uvažována hystereze retenční křivky. Odchylky mezi odezvami modelu a měřeními byly minimalizovány optimalizací scaling faktorů. Rozsáhlý srovnávací soubor uskutečněných optimalizací umožnil posoudit rozdíly modelové odezvy dvou hysterezních a jedné nehysterezní varianty a kvantifikovat dopad zanedbání hystereze na přesnost předpovědi modelu. Neuvažování hystereze v našem případě nezhoršuje schopnost modelu popsat změny půdní vlhkosti.
Certain financial market strategies are known to exhibit a hysteretic structure similar to the memory observed in plasticity, ferromagnetism, or magnetostriction. The main difference is that in financial markets, the spontaneous occurrence of discontinuities in the time evolution has to be taken into account. We show that one particular market model considered here admits a representation in terms of Prandtl-Ishlinskii hysteresis operators, which are extended in order to include possible discontinuities both in time and in memory. The main analytical tool is the Kurzweil integral formalism, and the main result proves the well-posedness of the process in the space of right-continuous regulated functions.