Downslope flow models of a Bingham liquid: Implications for lava flows

It is widely recognized that lavas behave as Bingham liquids, which are characterized by a yield stress σ and a plastic viscosity η. We consider two models describing downslope flows of a Bingham liquid with different aspect ratios A (= flow height/flow width): model 1 with A 1 and model 2 with A ≈ 1. Sufficiently uphill with respect to the front, such flows can be considered as laminar and locally isothermal. For both models, we obtain analytically the steady-state solution of the Navier-Stokes equations and the constitutive equation for a Bingham liquid. We study the flow height and velocity as functions of flow rate, rheological parameters and ground slope. It is found that such flows remain in the Newtonian regime at low yield stresses (σ 10³dyne/cm²), but the transition to the Bingham regime also depends on flow rate and occurs at higher values of σ for higher flow rates: for instance, a high aspect ratio flow (model 2) is still very close to the Newtonian regime at σ = 10⁴ dyne/cm², if the flow rate is greater than 10⁵ g/s. In the Bingham regime, flow heights are generally greater and flow velocities are smaller than in the Newtonian regime; moreover, flow heights are independent of flow rate, so that a change in flow rate results exclusively in a velocity change. After assuming a specific temperature dependence of σ and η between the solidus and the liquidus temperatures of an ideal Bingham liquid (1000°C and 1200 °C respectively), flow heights and velocities are examined as functions of temperature along the flow. Several effects observed in lava flows are predicted by these models and allow a more quantitative insight into the behaviour of lava flows.     

Soil water content and salinity determination using different dielectric methods in saline gypsiferous soil / Détermination de la teneur en eau et de la salinité de sols salins gypseux à l'aide de différentes méthodes diélectriques

Abstract

Measurements of dielectric permittivity and electrical conductivity were taken in a saline gypsiferous soil collected from southern Tunisia. Both time domain reflectometry (TDR) and the new WET sensor based on frequency domain reflectometry (FDR) were used. Seven different moistening solutions were used with electrical conductivities of 0.0053–14 dS m^?1. Different models for describing the observed relationships between dielectric permittivity (K _a ) and water content (θ), and bulk electrical conductivity (EC _a ) and pore water electrical conductivity (EC _p ) were tested and evaluated. The commonly used K _a –θ models by Topp et al. (1980) and Ledieu et al. (1986) cannot be recommended for the WET sensor. With these models, the RMSE and the mean relative error of the predicted θ were about 0.04 m³ m^?3 and 19% for TDR and 0.08 m³ m^?3 and 54% for WET sensor measurements, respectively. Using the Hilhorst (2000) model for EC _p predictions, the RMSE was 1.16 dS m^?1 and 4.15 dS m^?1 using TDR and the WET sensor, respectively. The WET sensor could give similar accuracy to TDR if calibrated values of the soil parameter were used instead of standard values.     

Treatment of anchor pixels in the METRIC model for improved estimation of sensible and latent heat fluxes

Abstract

Reliable estimation of sensible heat flux (H) is important in energy balance models for quantifying evapotranspiration (ET). This study was conducted to evaluate the value of adding the Priestley-Taylor (PT) equation to the METRIC (Mapping Evapotranspiration at high Resolution with Internalized Calibration) model. METRIC was used to estimate energy fluxes for 10 Landsat images from the 2005, 2006 and 2007 crop growing seasons in south-central Nebraska, USA, where each image owing to recent rainfall exhibited high residual moisture content even at the hot pixel. The METRIC model performed satisfactorily for net radiation (R_n ) and soil heat flux (G) estimation with a root mean square error (RMSE) of 52 and 24 W m^-2, respectively. A RMSE of 122 W m^-2 for H indicated the limitation of the METRIC model in estimating H for high residual moisture content of the hot pixel (Alfalfa reference ET fraction, ET _r F > 0.15). The modified METRIC model (wet METRIC or wMETRIC) incorporating the PT equation was applied to calculate H at the anchor pixels (hot and cold) for high residual moisture content of the hot pixel. The α coefficient of the PT equation was locally calibrated using hourly meteorological data from an automatic weather station and R_n and G data from a Bowen ratio flux tower. The mean α coefficient value was 1.14. The wMETRIC model reduced the RMSE of H from 122 to 64 W m^-2 and that of latent heat flux, LE, from 163 to 106 W m^-2. The RMSE of daily ET decreased from 1.7 to 1.1 mm d^-1 with wMETRIC. The results indicate that treatment of anchor pixels for high residual moisture content with the PT approach gives improved estimation of H, LE and daily ET. It is recommended that the wMETRIC model be used for estimating ET if the hot pixel has high residual moisture (i.e. reference ET fraction > 0.15).

Citation Singh, R. K. & Irmak, A. (2011) Treatment of anchor pixels in the METRIC model for improved estimation of sensible and latent heat fluxes. Hydrol. Sci. J. 56(5), 895–906.     

Subglacial drainage system structure and morphology of Brewster Glacier,New Zealand

A global positioning system and ground penetrating radar surveys is used to produce digital elevation models of the surface and bed of Brewster Glacier. These are used to derive maps of subglacial hydraulic potential and drainage system structure using three different assumptions about the subglacial water pressure (P_w): (i) P_w = ice overburden; (ii) P_w = half ice overburden; (iii) P_w = atmospheric. Additionally, 16 dye‐tracing experiments at 12 locations were performed through a summer melt season. Dye return curve shape, together with calculations of transit velocity, dispersivity and storage, are used to infer the likely morphology of the subglacial drainage system. Taken together, the data indicate that the glacier is underlain by a channelised but hydraulically inefficient drainage system in the early summer in which water pressures are close to ice overburden. By mid‐summer, water pressures are closer to half‐ice overburden and the channelised drainage system is more hydraulically efficient. Surface streams that enter the glacier close to the location of major subglacial drainage pathways are routed quickly to the channels and then to the glacier snout. Streams that enter the glacier further away from the drainage pathways are routed slowly to the channels and then to the snout because they first flow through a distributed drainage system. Copyright © 2008 John Wiley & Sons, Ltd.     

Forecasting Hourly Roadside Particulate Matter in Taipei County of Taiwan Based on First‐Order and One‐Variable Grey Model

In this study, seven types of first‐order and one‐variable grey differential equation model (abbreviated as GM (1, 1) model) were used to forecast hourly roadside particulate matter (PM) including PM₁₀ and PM_2.5 concentrations in Taipei County of Taiwan. Their forecasting performance was also compared. The results indicated that the minimum mean absolute percentage error (MAPE), mean squared error (MSE), root mean squared error (RMSE), and maximum correlation coefficient (R) was 11.70%, 60.06, 7.75, and 0.90%, respectively when forecasting PM₁₀. When forecasting PM_2.5, the minimum MAPE, MSE, RMSE, and maximum R‐value of 16.33%, 29.78, 5.46, and 0.90, respectively could be achieved. All statistical values revealed that the forecasting performance of GM (1, 1, x⁽⁰⁾), GM (1, 1, a), and GM (1, 1, b) outperformed other GM (1, 1) models. According to the results, it revealed that GM (1, 1) was an efficiently early warning tool for providing PM information to the roadside inhabitants.     

Predictive equation for longitudinal dispersion coefficient

Dye tracing field data were collected in small, steep streams in Ontario and used to calculate longitudinal dispersion coefficients for these headwater streams. A predictive equation for longitudinal dispersion coefficient is developed using combined data sets from five steeper head – water streams and 24 milder and larger rivers. The predictive equation relates the longitudinal dispersion coefficient to hydraulic and geometric parameters of the stream and has been developed using multiple regression analysis. The newly developed equation shows impressive accuracy of predictions for longitudinal dispersion coefficient (R² = 0.86, RMSE = 25, Nash–Sutcliffe coefficient E_ns = 0.86 and Index of Agreement D = 0.96) for both small, steep headwater streams as well as large, mild rivers. The Froude number has been introduced as a third key parameter to capture the effect of slope of the reach – in addition to the aspect ratio and bed material surface roughness – on the longitudinal dispersion coefficient. The pronounced improvement in the accuracy of the prediction is due to the addition of the Froude number to capture the effect of the slope of the reach on longitudinal dispersion coefficient. Copyright © 2014 John Wiley & Sons, Ltd.     

Developing an empirical model of canopy water flux describing the common response of transpiration to solar radiation and VPD across five contrasting woodlands and forests

A modified Jarvis–Stewart model of canopy transpiration (E_c) was tested over five ecosystems differing in climate, soil type and species composition. The aims of this study were to investigate the model's applicability over multiple ecosystems; to determine whether the number of model parameters could be reduced by assuming that site‐specific responses of E_c to solar radiation, vapour pressure deficit and soil moisture content vary little between sites; and to examine convergence of behaviour of canopy water‐use across multiple sites. This was accomplished by the following: (i) calibrating the model for each site to determine a set of site‐specific (SS) parameters, and (ii) calibrating the model for all sites simultaneously to determine a set of combined sites (CS) parameters. The performance of both models was compared with measured E_c data and a statistical benchmark using an artificial neural network (ANN). Both the CS and SS models performed well, explaining hourly and daily variation in E_c. The SS model produced slightly better model statistics [R² = 0.75–0.91; model efficiency (ME) = 0.53–0.81; root mean square error (RMSE) = 0.0015–0.0280 mm h^‐1] than the CS model (R² = 0.68–0.87; ME = 0.45–0.72; RMSE = 0.0023–0.0164 mm h^‐1). Both were highly comparable with the ANN (R² = 0.77–0.90; ME = 0.58–0.80; RMSE = 0.0007–0.0122 mm h^‐1). These results indicate that the response of canopy water‐use to abiotic drivers displayed significant convergence across sites, but the absolute magnitude of E_c was site specific. Period totals estimated with the modified Jarvis–Stewart model provided close approximations of observed totals, demonstrating the effectiveness of this model as a tool aiding water resource management. Analysis of the measured diel patterns of water use revealed significant nocturnal transpiration (9–18% of total water use by the canopy), but no Jarvis–Stewart formulations are able to capture this because of the dependence of water‐use on solar radiation, which is zero at night. Copyright © 2012 John Wiley & Sons, Ltd.     

Solar Photocatalytic Decolorization and Detoxification of Industrial Batik Dye Wastewater Using P(3HB)‐TiO2 Nanocomposite Films

Solar photocatalytic decolorization and detoxification of batik dye wastewater using titanium dioxide (TiO₂) immobilized on poly‐3‐hydroxybutyrate (P(3HB)) film was studied. The effects of initial dye concentration, catalyst concentration, P(3HB) film thickness, and fabrication methods of the nanocomposite films were evaluated against methylene blue, a standard organic dye. It was observed that 0.4 g of P(3HB)‐40 wt% TiO₂ removed 96% of the color under solar irradiation. P(3HB) and TiO₂, mixed concurrently in chloroform followed by stirring for 24 h showed a more even distribution of the photocatalyst on the polymer surface and yielded almost 100% color removal. The photocatalytic films were able to completely decolorize real industrial batik dye wastewater in 3 h and induced a chemical oxygen demand (COD) reduction of 80%. Reusability of the 0.4 g P(3HB)‐40 wt% TiO₂ film in decolorizing the batik dye wastewater was also possible as it gave a high consistent value of decolorization percentage (>80%) even after the sixth repeated usage. Recovery step of the photocatalysts was also not required in this simple treatment system. The decolorized batik dye wastewater had less/no toxic effects on mosquito larvae, Aedes aegypti, and microalgae, Scenedesmus quadricauda indicating simultaneous detoxification process along with the decolorization process.     

Estimation of the Maximum Earthquake Magnitude, <Emphasis Type="Italic">m</Emphasis><Subscript>max</Subscript>

This paper provides a generic equation for the evaluation of the maximum earthquake magnitude m_max for a given seismogenic zone or entire region. The equation is capable of generating solutions in different forms, depending on the assumptions of the statistical distribution model and/or the available information regarding past seismicity. It includes the cases (i) when earthquake magnitudes are distributed according to the doubly-truncated Gutenberg-Richter relation, (ii) when the empirical magnitude distribution deviates moderately from the Gutenberg-Richter relation, and (iii) when no specific type of magnitude distribution is assumed. Both synthetic, Monte-Carlo simulated seismic event catalogues, and actual data from Southern California, are used to demonstrate the procedures given for the evaluation of m_max.The three estimates of m_max for Southern California, obtained by the three procedures mentioned above, are respectively: 8.32 ± 0.43, 8.31 ± 0.42 and 8.34 ± 0.45. All three estimates are nearly identical, although higher than the value 7.99 obtained by Field et al. (1999). In general, since the third procedure is non-parametric and does not require specification of the functional form of the magnitude distribution, its estimate of the maximum earthquake magnitude m_max is considered more reliable than the other two which are based on the Gutenberg-Richter relation.     

Applicability of cosmic-ray neutron sensor for measuring soil moisture at the agricultural-pastoral ecotone in northwest China

Accurate monitoring of soil moisture is crucial in hydrological and ecological studies. Cosmic-ray neutron sensors (CRNS) measure area-average soil moisture at field scale, filling a spatial scale gap between in-situ observations and remote sensing measurements. However, its applicability has not been assessed in the agricultural-pastoral ecotone, a data scarce semi-arid and arid region in Northwest China (APENC). In this study, we calibrated and assessed the CRNS (the standard N₀ method) estimates of soil moisture. Results show that Pearson correlation coefficient, R_P, and the root mean square error (RMSE) between the CRNS soil moisture and the gravimetric soil moisture are 0.904 and less than 0.016 m³ m⁻³, respectively, indicating that the CRNS is able to estimate the area-average soil moisture well at our study site. Compared with the in-situ sensor network measurements (ECH2O sensors), the CRNS is more sensitive to the changes in moisture in its footprint, which overestimates and underestimates the soil moisture under precipitation and dry conditions, respectively. The three shape parameters a₀, a₁, a₂ in the standard calibration equation (N₀ method) are not well suited to the study area. The calibrated parameters improved the accuracy of the CRNS soil moisture estimates. Due to the lack of low gravimetric soil moisture data, performance of the calibrated N₀ function is still poor in the extremely dry conditions. Moreover, aboveground biomass including vegetation biomass, canopy interception and widely developed biological soil crusts adds to the uncertainty of the CRNS soil moisture estimates. Such biomass impacts need to be taken into consideration to further improve the accuracy of soil moisture estimation by the CRNS in the data scarce areas such as agricultural-pastoral ecotone in Northwest China.

     

Artificial Neural Network Prediction of Tropospheric Ozone Concentrations in Istanbul,Turkey

Tropospheric (ground‐level) ozone has adverse effects on human health and environment. In this study, next day's maximum 1‐h average ozone concentrations in Istanbul were predicted using multi‐layer perceptron (MLP) type artificial neural networks (ANNs). Nine meteorological parameters and nine air pollutant concentrations were utilized as inputs. The total 578 datasets were divided into three groups: training, cross‐validation, and testing. When all the 18 inputs were used, the best performance was obtained with a network containing one hidden layer with 24 neurons. The transfer function was hyperbolic tangent. The correlation coefficient (R), mean absolute error (MAE), root mean squared error (RMSE), and index of agreement or Willmott's Index (d₂) for the testing data were 0.90, 8.78 µg/m³, 11.15 µg/m³, and 0.95, respectively. Sensitivity analysis has indicated that the persistence information (current day's maximum and average ozone concentrations), NO concentration, average temperature, PM₁₀, maximum temperature, sunshine time, wind direction, and solar radiation were the most important input parameters. The values of R, MAE, RMSE, and d₂ did not change considerably for the MLP model using only these nine inputs. The performances of the MLP models were compared with those of regression models (i.e., multiple linear regression and multiple non‐linear regression). It has been found that there was no significant difference between the ANN and regression modeling techniques for the forecasting of ozone concentrations in Istanbul.     

A comparative study on the rheology and wave dissipation of kaolinite and natural Hendijan Coast mud, the Persian Gulf

The objective of this paper is to investigate the rheological behavior of kaolinite and Hendijan mud, located at the northwest part of the Persian Gulf, and the dissipative role of this muddy bed on surface water waves. A series of laboratory rheological tests was conducted to investigate the rheological response of mud to rotary and cyclic shear rates. While a viscoplastic Bingham model can successfully be applied for continuous controlled shear-stress tests, the rheology of fluid mud displays complex viscoelastic behavior in time-periodic motion. The comparisons of the behavior of natural Hendijan mud with commercial kaolinite show rheological similarities. A large number of laboratory wave-flume experiments were carried out with a focus on the dissipative role of the fluid mud. Assuming four rheological models of viscous, Kelvin-Voigt viscoelastic, Bingham viscoplastic, and viscoelastic-plastic for fluid mud layer, a numerical multi-layered model was applied to analyze the effects of different parameters of surface wave and muddy bed on wave attenuation. The predicted results based on different rheological models generally agree with the obtained wave-flume data implying that the adopted rheological model does not play an important role in the accuracy of prediction.     

GRID METHOD OF DETERMINING MEAN FLOW-DISTANCE IN A DRAINAGE BASIN

Summary

The basin characteristics Σal or L _ca are useful in hydrologic studies, but existing methods of determining them are either tedious or somewhat inaccurate. The grid method presented herein lessens the amount of tedious labor and provides an accurate measure of either Σal or L _ca . An adaptation of the method could be used to compute the lag time for the basin.     

A method of estimating the stress exponent in the flow law for rocks using fold shape

On the basis of experiment and theory, we expect rocks to deform in a linear fashion when diffusive processes control deformation, and nonlinearly in most other situations. The geometric characteristics of buckle folds in layered materials are dependent on rheological parameters, and in particular depend strongly on the stress exponent,n _L , of the stiff layers involved. Thus, information about the deformation rocks have undergone and their rheological state during deformation can be obtained by studying fold shapes and strain distributions. This is important because there is uncertainty in extrapolating laboratory-derived flow laws to the very slow natural strain rates and large strains found in nature.We have studied the development of buckle folds in linear and nonlinear materials using finite-element modeling, and interpolated the numerical results to construct plots relating several geometric parameters to variations in power-law exponent,n _L , and viscosity ratio,m, of layer to matrix. Such plots allow for a comparison of the results of numerical models with data for many natural and experimentally-produced folds, and there is consistency among the data for folds produced in physical models, using both linear and nonlinear materials and the numerical simulations. data for folds from the Appalachian Mountains, the Alps and elsewhere, however, suggest high values ofn _L in the flow laws for a number of rock types. The unexpectedly high estimates ofn _L suggest that other factors, such as strain softening or anisotropy, may influence fold shape, and thus complicate the estimation of the rheological properties of rocks.     

A numerical method for simulating non-Newtonian fluid flow and displacement in porous media

Flow and displacement of non-Newtonian fluids in porous media occurs in many subsurface systems, related to underground natural resource recovery and storage projects, as well as environmental remediation schemes. A thorough understanding of non-Newtonian fluid flow through porous media is of fundamental importance in these engineering applications. Considerable progress has been made in our understanding of single-phase porous flow behavior of non-Newtonian fluids through many quantitative and experimental studies over the past few decades. However, very little research can be found in the literature regarding multi-phase non-Newtonian fluid flow or numerical modeling approaches for such analyses.For non-Newtonian fluid flow through porous media, the governing equations become nonlinear, even under single-phase flow conditions, because effective viscosity for the non-Newtonian fluid is a highly nonlinear function of the shear rate, or the pore velocity. The solution for such problems can in general only be obtained by numerical methods.We have developed a three-dimensional, fully implicit, integral finite difference simulator for single- and multi-phase flow of non-Newtonian fluids in porous/fractured media. The methodology, architecture and numerical scheme of the model are based on a general multi-phase, multi-component fluid and heat flow simulator — TOUGH2. Several rheological models for power-law and Bingham non-Newtonian fluids have been incorporated into the model. In addition, the model predictions on single- and multi-phase flow of the power-law and Bingham fluids have been verified against the analytical solutions available for these problems, and in all the cases the numerical simulations are in good agreement with the analytical solutions. In this presentation, we will discuss the numerical scheme used in the treatment of non-Newtonian properties, and several benchmark problems for model verification.In an effort to demonstrate the three-dimensional modeling capability of the model, a three-dimensional, two-phase flow example is also presented to examine the model results using laboratory and simulation results existing for the three-dimensional problem with Newtonian fluid flow.     

An Analytical Study for the Dispersion of Pollutants in a Finite Layer under Low Wind Conditions

A steady-state three-dimensional analytical model for the dispersion of a pollutant from a continuously emitting point source in a finite inversion layer has been proposed. The advection along the mean wind and the diffusion in all three directions have been accounted. A closed-form analytical solution of the proposed problem has been obtained using the method of integral transform and the same happens out to be non-Gaussian. Various limiting cases including the crosswind integrated concentration and the standard Gaussian-plume formula have been deduced from the solution obtained.The present model has been evaluated using Hanford diffusion experiment (DORAN et al., 1984) in stable conditions and IIT diffusion experiment (SINGH et al., 1991) in unstable conditions. The dispersion parameters have been computed using the various sigma schemes in accordance with the available observations. The proposed model has performed reasonably well with the data from both the diffusion experiments considered here.     

Performance evaluation of satellite-based approaches for the estimation of daily air temperature and reference evapotranspiration

Different satellite-based radiation (Makkink) and temperature (Hargreaves-Samani, Penman-Monteith temperature, PMT) reference evapotranspiration (ET_o) models were compared with the FAO56-PM method over the Cauvery basin, India. Maximum air temperature (T_max) required in the ET_o models was estimated using the temperature–vegetation index (TVX) and an advanced statistical approach (ASA), and evaluated with observed T_max obtained from automatic weather stations. Minimum air temperature (T_min) was estimated using ASA. Land surface temperature was employed in the ET_o models in place of air temperature (T_a) to check the potency of its applicability. The results suggest that the PMT model with T_a as input performed better than the other ET_o models, with correlation coefficient (r), averaged root mean square error (RMSE) and mean bias error (MBE) of 0.77, 0.80 mm d^?1 and ?0.69 for all land cover classes. The ASA yielded better T_max and T_min values (r and RMSE of 0.87 and 2.17°C, and 0.87 and 2.27°C, respectively).     

Estimation of soil hydraulic properties and their uncertainty: comparison between laboratory and field experiment

Often the soil hydraulic parameters are obtained by the inversion of measured data (e.g. soil moisture, pressure head, and cumulative infiltration, etc.). However, the inverse problem in unsaturated zone is ill‐posed due to various reasons, and hence the parameters become non‐unique. The presence of multiple soil layers brings the additional complexities in the inverse modelling. The generalized likelihood uncertainty estimate (GLUE) is a useful approach to estimate the parameters and their uncertainty when dealing with soil moisture dynamics which is a highly non‐linear problem. Because the estimated parameters depend on the modelling scale, inverse modelling carried out on laboratory data and field data may provide independent estimates. The objective of this paper is to compare the parameters and their uncertainty estimated through experiments in the laboratory and in the field and to assess which of the soil hydraulic parameters are independent of the experiment. The first two layers in the field site are characterized by Loamy sand and Loamy. The mean soil moisture and pressure head at three depths are measured with an interval of half hour for a period of 1 week using the evaporation method for the laboratory experiment, whereas soil moisture at three different depths (60, 110, and 200 cm) is measured with an interval of 1 h for 2 years for the field experiment. A one‐dimensional soil moisture model on the basis of the finite difference method was used. The calibration and validation are approximately for 1 year each. The model performance was found to be good with root mean square error (RMSE) varying from 2 to 4 cm³ cm^?3. It is found from the two experiments that mean and uncertainty in the saturated soil moisture (θ_s) and shape parameter (n) of van Genuchten equations are similar for both the soil types. Copyright © 2010 John Wiley & Sons, Ltd.     

A Statistical Estimation Model for the Impact Force of Dry Granular Flow Against Rigid Barrier

The impact force on retaining structure, which is caused by granular flow comprised of dry particles originated from shallow landslide failure, still lacks systematic studies. In order to support the potential design requirement of structure used to resist this kind of impact, a series of dry granular impact experiments are conducted on one rigid barrier model. According to parametric analysis results, one nonlinear regression model is proposed to correlate total normal impact force at critical time (F_cr) with its influential parameters. Further, we complete a systematic statistics analysis and obtain a subsequent optimum regression equation based on the proposed model. According to experience and dimension balance, the equation is modified and finally transformed into one non-dimensional equation, which shows good agreement between predicted and observed results.