Complex mathematical model for studying wave processes in flow-through systems of open channels and water bodies

Complex two- and one-dimensional mathematical model and numerical method for studying wave processes in flow-through systems of open channels and water bodies are developed. The mathematical model is based on one-dimensional cross-section-averaged hydrodynamic equations (Saint-Venant equations), as well as on two-dimensional models averaged for channel or stream width (longitudinal-vertical model). Numerical method is developed with the use of implicit difference schemes. The area of practical application of developed models is studied. Preliminary analysis and comparison of results of numerical modeling of hydrodynamical regimes from conjugated (combined) model with the results obtained only from two-(one-) dimensional models have demonstrated effectiveness of mathematical model developed.     

A mathematical model of microclimate

Climatologists will be interested in a mathematical model of microclimate which is bieng developed by the fluid-mechanics group at the Institute of Limnology (Leningrad). The model is designed for two main types of application: microclimatic simulations; and microclimatic interpretations of large-scale weather forecasts.     

A simple mathematical model of airflow in waving plant canopies

A simple mathematical model is proposed, which combines the effects of mean wind speed, plant spacing and the drag coefficients of individual plants to calculate the fluctuating airflow within a waving crop canopy. The model is non-linear and is only amenable to analytical treatment when linearized; however, the full non-linear version can be solved on an analogue computer.The linear and non-linear results show unexpectedly good agreement, and the success of the linearization allows clear conclusions to be drawn about the relationship between the elasticity, geometry and mean wind speed through a stand of plants and the fluctuating components of airflow and stalk motion.Finally, the analytical results are in qualitative agreement with wind-tunnel results from two model canopies with different characteristics.     

Application of a water balance model to estimating hay growth in the peace river region

Abstract

A model that uses daily climate data for calculating hay crop growth in the Peace River region of British Columbia was developed and evaluated using data obtained over four growing seasons. The performances of the ratio of growth to transpiration and the ratio of growth to transpiration (J) divided by vapour pressure deficit (VPD) in estimating crop growth were compared. Transpiration was calculated by subtracting evaporation losses from the soil and foliage from the calculated evapotranspiration. Evapotranspiration was calculated using solar radiation and air temperature, and a one‐layer root zone water balance model, which accounted for soil water supply limitation. Soil water storage measurements showed that the water balance model worked well. The model provided satisfactory estimates of growing season yield of above‐ground dry matter. The use of the ratio of growth toT/ vpd showed no improvement in growth estimation over the ratio of growth to transpiration.     

Distributional changes in rainfall and river flow in Sarawak,Malaysia

Climate change may not change the rainfall mean, but the variability and extremes. Therefore, it is required to explore the possible distributional changes of rainfall characteristics over time. The objective of present study is to assess the distributional changes in annual and northeast monsoon rainfall (November-January) and river flow in Sarawak where small changes in rainfall or river flow variability/distribution may have severe implications on ecology and agriculture. A quantile regression-based approach was used to assess the changes of scale and location of empirical probability density function over the period 1980-2014 at 31 observational stations. The results indicate that diverse variation patterns exist at all stations for annual rainfall but mainly increasing quantile trend at the lowers, and higher quantiles for the month of January and December. The significant increase in annual rainfall is found mostly in the north and central-coastal region and monsoon month rainfalls in the interior and north of Sarawak. Trends in river flow data show that changes in rainfall distribution have affected higher quantiles of river flow in monsoon months at some of the basins and therefore more flooding. The study reveals that quantile trend can provide more information of rainfall change which may be useful for climate change mitigation and adaptation planning.     

On closure of a turbulent flow model in ducts and stream channels in a way alternative to a calibrating method

It is shown that correction factors in turbulent motion models can be determined in a way alternative to a calibration method from a synergetic criterion of equilibrium between a body and environment—an extremum of a local effect of counteraction to the integral effect in the relaxation process of body transition into an equilibrium state.     

A nonstationary nocturnal drainage flow model

The evolution and structure of the steady state of an idealized nocturnal drainage flow over a large uniformly-sloping surface are studied using a nonstationary model with a height-dependent eddy diffusivity profile and a specified surface cooling rate. The predicted mean velocity and temperature profiles are compared with Prandtl's stationary analytical solutions based on the assumption of a constant eddy diffusivity in the drainage layer. The effects of important physical parameters, such as the slope angle, surface cooling, atmospheric stability, and surface roughness, on the steady drainage flow are investigated.Affiliated with Oak Ridge Associated Universities (ORAU).     

A simple model of drainage flow in a valley

A model of the drainage flow in a valley under calm conditions has been developed on the basis of the conservation laws of mass, momentum, and heat. The inflow of mass and heat from side-slopes is incorporated, and the momentum and sensible heat exchanges between valley drainage flow and valley floor are parameterized.The characteristic velocity of valley drainage flow is expressed in terms of the following parameters: three potential temperature differences representing the temperature field in the valey; topographic parameters of the valley; mean bulk coefficients representing the aerodynamic conditions of the valley floor; and the stability of the ambient atmosphere. The characteristic thickness includes additional parameters of side-slope flow.That the model satisfactorily predicts the characteristic thickness and velocity is shown from comparison with observations from valleys several hundred meters to a few hundred kilometers long.     

A Markov-chain particle dispersion model based on air flow data: Extension to large water droplets

An analysis is presented which gives the adjustment to a Markov-chain particle dispersion model to account for the effect of drag between heavy particles (e.g., rain splash droplets, spray droplets) and the surrounding air parcels for which turbulence statistics are known.     

A thermomechanical model of ice flow in West Antarctica

 This study uses a three-dimensional thermo-mechanical model to investigate the internal flow dynamics of the West Antarctic Ice Sheet (WAIS). The model allows ice thickness, flow and temperature to interact freely. Its domain is prescribed as that of the present-day grounded WAIS. Realistic present-day climatic and topographical boundary conditions are employed. The analysis of a series of experiments pays particular attention to the location and dynamics of concentrations of ice flow (ice streams). Underlying topographic troughs are crucial in determining the strength and location of these concentrations of flow. The flow pattern generated by subglacial troughs is made more distinct by the inclusion of ice flow/temperature coupling. The inclusion of sliding leads to the generation of limit cycles in the ice flow. They are concentrated around the present-day ice streams B and C of the Siple Coast and have a period of 5 to 10 ky. There appears to be competition between several preferred ice flow pathways in this area. The two end members of the flow regime are a strong ice stream C with a weakened ice stream A/B complex, and strong ice streams A and B with a dormant ice stream C. Ice streams appear to require ice discharges above a certain threshold in order to maintain frictional heat generation and fast flow. Individual ice streams can therefore interact through changes in catchment-area size: a reduction in catchment area reduces the volume of ice entering a stream and can cause stagnation as the amount of frictional heating falls. Received: 22 July 1997/Accepted: 27 July 1998     

Assessment of concentration of radionuclides in river water and bottom sediments

The results of modeling of ^{89, 90}Sr, ¹³⁷Cs, and ^{239, 240}Pu migration in the Techa River are compared with observed data. It is shown that taking into account of the process of mass exchange between the main stream of a river and underflow is important for adequate modeling of migration and accumulation of radiative substances in a river. It is difficult to obtain results of modeling corresponding to the observed data if the process is neglected. Taking into account the mass exchange is especially important in developing models for long enough rivers that were polluted by radionuclides during long time. Authors believe that, in future, the considered aspects of modeling radioactive substances in rivers can be generalized on chemical polluting substances with similar physical and chemical properties, for example, heavy metals, phenols, etc.     

A simple parameterization of sub-grid scale open water for climate models

The effects of small fractions ( < 30%) of open water covering a grid element are currently neglected even in atmospheric general circulation models (AGCMs) which incorporate complex land surface parameterization schemes. Here, a method for simulating sub-grid scale open water is proposed which permits any existing land surface model to be modified to account for open water. This new parameterization is tested as an addition to an advanced land surface scheme and, as expected, is shown to produce general increases in the surface latent heat flux at the expense of the surface sensible heat flux. Small changes in temperature are associated with this change in the partitioning of available energy which is driven by an increase in the wetness of the grid element. The sensitivity of the land surface to increasing amounts of open water is dependent upon the type of vegetation represented. Dense vegetation (with a high leaf area index) is shown to complicate the apparently simple model sensitivity and indicates that more advanced methods of incorporating open water into AGCMs need to be considered and compared against the parameterization suggested here. However, the sensitivity of one land surface model to incorporating open water is large enough to warrant consideration of its incorporation into climate models.     

Global river discharge and water temperature under climate change

Climate change will affect hydrologic and thermal regimes of rivers, having a direct impact on freshwater ecosystems and human water use. Here we assess the impact of climate change on global river flows and river water temperatures, and identify regions that might become more critical for freshwater ecosystems and water use sectors. We used a global physically based hydrological-water temperature modelling framework forced with an ensemble of bias-corrected general circulation model (GCM) output for both the SRES A2 and B1 emissions scenario. This resulted in global projections of daily river discharge and water temperature under future climate. Our results show an increase in the seasonality of river discharge (both increase in high flow and decrease in low flow) for about one-third of the global land surface area for 2071–2100 relative to 1971–2000. Global mean and high (95th percentile) river water temperatures are projected to increase on average by 0.8–1.6 (1.0–2.2) °C for the SRES B1–A2 scenario for 2071–2100 relative to 1971–2000. The largest water temperature increases are projected for the United States, Europe, eastern China, and parts of southern Africa and Australia. In these regions, the sensitivities are exacerbated by projected decreases in low flows (resulting in a reduced thermal capacity). For strongly seasonal rivers with highest water temperatures during the low flow period, up to 26% of the increases in high (95th percentile) water temperature can be attributed indirectly to low flow changes, and the largest fraction is attributable directly to increased atmospheric energy input. A combination of large increases in river temperature and decreases in low flows are projected for the southeastern United States, Europe, eastern China, southern Africa and southern Australia. These regions could potentially be affected by increased deterioration of water quality and freshwater habitats, and reduced water available for human uses such as thermoelectric power and drinking water production.     

Gust factors over open water and built-up country

Data are presented of the gust factorG =u ^max/, both at 8-m height over a lake and up to 80-m height at the edge of a town. It is argued that, due to the presence of trends in long-period averages, the use of arithmetic or least-squareG-averages leads to overestimation of the dependence ofG on wind speedu, and medianG-values are preferable. A simple non-spectral model for gustiness at high wind speeds in the constant-stress layer is proposed and checked. The model relatesG to surface roughness and height above surface for gust wavelengths up to 200 m. The gust factor concept is shown to be inadequate for characterizing thunderstorm gustiness.     

A semi-analytical model of barotropic and baroclinic flows for an open Panama Gateway

A semi-analytical model of the Panama throughflow is presented. The model expresses the throughflow transport as a function of deep water formation in the North Pacific and in the North Atlantic, and of the Panama Gateway depth. The model is derived from the integral of the momentum equation along a circumpolar path, and can be interpreted from the point of view of the vorticity balance. The important conditions are whether the deep water, whose location is considered to be above the bottom water formed around Antarctica, originates from the North Atlantic or from the North Pacific, and whether the Panama Gateway is shallower than the lower boundary of the deep water. The present model indicates that the barotropic transport through the Panama Gateway is eastward, except for the case where the deep water is formed in the North Pacific and the sill of the Panama Gateway is shallow. The baroclinic structure of the Panama throughflow depends on whether the deep water is formed in the North Pacific or in the North Atlantic. These qualitative implications of the model are consistent with recent numerical studies and proxy-based paleoceanographic studies. Numerical experiments performed in the present study reinforce confidence in the semi-analytical model.     

Climate-induced changes in river water temperature in North Iberian Peninsula

With the surface air temperature (SAT) data at 37 stations on Central Yunnan Plateau (CYP) for 1961–2010 and the Defense Meteorological Satellite Program/Operational Linescan System (DMSP/OLS) nighttime light data, the temporal-spatial patterns of the SAT trends are detected using Sen’s Nonparametric Estimator of Slope approach and MK test, and the impact of urbanization on surface warming is analyzed by comparing the differences between the air temperature change trends of urban stations and their corresponding rural stations. Results indicated that annual mean air temperature showed a significant warming trend, which is equivalent to a rate of 0.17 °C/decade during the past 50 years. Seasonal mean air temperature presents a rising trend, and the trend was more significant in winter (0.31 °C/decade) than in other seasons. Annual/seasonal mean air temperature tends to increase in most areas, and higher warming trend appeared in urban areas, notably in Kunming city. The regional mean air temperature series was significantly impacted by urban warming, and the urbanization-induced warming contributed to approximately 32.3–62.9 % of the total regional warming during the past 50 years. Meantime, the urbanization-induced warming trend in winter and spring was more significant than that in summer and autumn. Since 1985, the urban heat island (UHI) intensity has gradually increased. And the urban temperatures always rise faster than rural temperatures on the CYP.     

利用环境同位素技术研究沈阳浑河与地下水的水力联系

查明地下水与河水之间的水力联系,是研究浑河污染水体对地下水环境影响的前提。采用环境同位素技术研究浑河沿岸地下水演化规律,沿浑河冲洪积扇地下水流动方向取地下水样13个、河水样3个。结果表明:通过对水样进行D(氘)、18O分析,查明了浑河与地下水之间的水力联系,确定了河水对地下水的补给宽度,定量计算了河水对沿岸地下水的贡献比例。从浑河的上游至下游,河水对地下水的贡献比例由大变小,平均约为50%;河水对地下水强补给带位于浑河以南约1 km的范围内,二者的水力联系密切。     

一个描述河陆风变化的数值模式及其数值实验

本文设计了一个包括水平及垂直扩散、牛顿冷却的二维46层非弹性运动方程模式来模拟及研究河陆风的变化。在模式中包括了太阳辐射;地-气系统的长波辐射;地表面、河表面向大气的感热与潜热输送以及地表面向土壤层的热传导等物理过程。 本模式采用分解算法及隐式时间差分方案,计算结果表明,这个模式无论对稳定层结或不稳定层结其计算都是稳定的,且所需计算时间也是很节省的,其计算结果是符合实际的。     

A second-order closure model for flow through vegetation

By splitting the turbulent kinetic energy into two wavebands and adopting as the turbulence timescale the ratio k/ of the kinetic energy in the low-frequency band to its turnover-rate, the second-order closure scheme of Launder et al. (1975) has been adapted for flow through vegetation. Predictions of the model compare satisfactorily with observations of the mean windspeed and (somewhat less satisfactorily) with the turbulent velocity variances in two very different canopies.     

A simple model of drainage flow on a slope

The concept of a cold air ‘Parcel’ is introduced for describing the bulk properties of drainage flow. By means of a model based on the momentum and sensible heat transports under calm conditions, the thickness h and velocity u of the Parcel are derived in simple forms. It is shown that h and u correspond to the inversion height and maximum velocity of actual drainage flow. The governing parameters for h and u are the length and vertical drop of the slope, potential temperature difference between the ambient atmosphere and the Parcel, aerodynamic condition of the slope surface expressed by the mean bulk coefficients, and ambient stability. The mean bulk coefficients depend on the roughness lengths for the velocity and potential temperature profiles and are decreasing functions of the slope length. The Parcel Model agrees qualitatively with Manins and Sawford's (1979) model under neutral ambient stratification. But agreement is not so good under stable conditions. The thickness and velocity of drainage flow predicted by the Parcel Model agree with observations on slopes several tens of meters to several hundred kilometers long.