Empirical Regression Equations Research Articles

Fluxes and budgets of Cd, Zn, Cu, Cr and Ni in a remote forested catchment in Germany

The input of heavy metals by atmospheric deposition to forested watersheds substantially decreased during the last decades in many areas. The goal of our study was to identify the present sinks and sources of metals and factors influencing metal mobility at the catchment and soil profile scale. We determined concentrations and fluxes of Cd, Zn, Cu, Cr and Ni in precipitation, litterfall, soil solutions (Oi, Oe, Oa horizon percolates, 20 and 90 cm soil depth) and runoff in a forest ecosystem in NE-Bavaria, Germany for 1 year. The metal concentrations in solutions were mostly <10 μg l−1 beside Zn (<1200 μg l−1). The present total deposition was estimated at 1.0, 560, 30, 1.2 and 10.4 g ha−1 year−1 for Cd, Zn, Cu, Cr and Ni, respectively. The mass balance (total deposition minus runoff) at the catchment scale indicated actual retention of Zn, Cu and Ni, but an almost balanced budget for Cr and Cd. Considering the soil profile scale, the Oi horizon still acted as a sink, whereas the Oe and Oa horizons were presently sources for all metals. The solid–solution partitioning coefficients indicated higher mobility of Cd and Zn than of Cu, Cr and Ni in forest soils. In the mineral soil horizons, Kd values derived from field measurements were substantially larger than those predicted with empirical regression equations from Sauvé et al. (Environ Sci Technol 34:1125–1131, 2000; Environ Sci Technol 37:5191–5196, 2003). The mineral soil acted as a sink for all metals beside Cd. Dissolved organic C and pH influenced the metal mobility, as indicated by significant correlations to metal concentrations in Oa percolates and runoff. The solid–solution partitioning coefficients indicated higher mobility of Cd and Zn than of Cu, Cr and Ni in forest soils. Overall, the decreased deposition rates have obviously induced a source function of the Oe and Oa horizon for metals. Consequently, mobilization of metals from forest floor during heavy rain events and near surface flow conditions may lead to elevated concentrations in runoff.

Correspondence between the Campbell and van Genuchten Soil-Water-Retention Models

Two methods are presented that allow converting the van Genuchten (VG) soil-water-retention (SWR) model parameters to equivalent parameters of the Campbell (C) model. The first method builds on an available solution to convert the VG model to an equivalent Brooks-Corey (BC) model, but accounts for the fact that the effective water content of the BC model and the C model are not the same, because the C model lacks the residual water content parameter, θr. The second method (II) relies on a curve-fitting exercise (minimizing the differences between the VG and C-SWR curves) to derive simultaneously the optimal capacity-matching point and SWR-matching point. Results indicate that the second method outperforms the first method and yields an improved equivalence. To bypass the time-consuming curve-fitting exercise, based on Method II two empirical regression equations are presented that allow rapid calculation of the two C-parameters, air-entry and Campbell-b, by the corresponding VG-SWR parameters.

Estimating river flow effects on water ages by hydrodynamic modeling in Little Manatee River estuary, Florida, USA

The water age in a tidal river in Florida, Little Manatee River, has been investigated in this study by the application of a three-dimensional hydrodynamic model. In response to a pulse dye release in the upper end of the river boundary, the hydrodynamic model determines the water age for a given location by recording the time for the dye to reach the given river location. The hydrodynamic model uses horizontal curvilinear orthogonal grids to represent the complex river system that includes several bayous and tributaries. The model has was calibrated and verified in previous study by using two continuous data sets for a 6 month period. Satisfactory model verifications indicate that the hydrodynamic model is capable of quantifying the mixing and transport process for calculating the water age in the tidal river. For 17 freshwater inflow scenarios in the Little Manatee River, the hydrodynamic model was applied to simulate water ages along the main channel of the river at 2-km interval. Flow rates in the 17 scenarios varying from 0.26 to 76.56 m3/s cover the range of the observed flows in the Little Manatee River. Water ages from model predictions range from the minimum 1.2 days under the maximum 76.56 m3/s inflow condition to the 50 days under the minimum 0.26 m3/s inflow condition. Empirical regression equations at three selected stations, with the correlation coefficient R2 above 0.96, were derived from numerical model simulations to correlate water ages to freshwater inflows. The empirical water-age equation derived from hydrodynamic model simulations can be used to provide quick and low-cost estimations of water ages in response to various inflow scenarios for studying physical–chemical and biological processes in the river.

Effects of reducing river flow on pulse residence time in Little Manatee River, USA

Residence time is an important indicator for river environmental management. In this paper, a 3D hydrodynamic model has been successfully applied to Little Manatee River to characterize the mixing and transport process and residence time. The model employs horizontal curvilinear orthogonal grids to represent the complex river system that consists of branches and bayous. The model has been satisfactorily calibrated and verified by using two continuous data sets. The data sets consist of hourly observations of all forcing boundaries, including freshwater inputs, tides, winds, salinity and temperatures at bay boundary, and air temperatures for model simulations. The data sets also consist of hourly observations of water levels, salinity, and temperature at several river stations. The calibrated and verified hydrodynamic model was used to predict residence time in the Little Manatee River. Under the minimum flow of 0.312 m3/s, the pulse residence time (PRT) is 108 days. Model simulations were also conducted for 17 flow scenarios. Empirical regression equations have been satisfactorily derived to correlate PRT to freshwater inflow. Correlation coefficient R2 is 0.982 for PRT.

Removal of copper from aqueous solutions by adsorption onto chestnut shell and grapeseed activated carbons

Activated carbons prepared from chestnut shell and grapeseed were used as adsorbent for the removal of Cu (II) ions from aqueous solutions. Adsorption experiments were performed by varying initial metal ion concentration, temperature and pH. Freundlich and Langmuir isotherms were used to analyze the equilibrium data obtained at different adsorption conditions. It was observed that Freundlich isotherm provided better fit to the equilibrium data than Langmuir isotherm. Effects of temperature, pH and adsorbent surface area on the adsorption capacity constant of Freundlich and Langmuir isotherms were statistically investigated by using a two-level factorial design technique and empirical regression equations were developed. It was determined that the adsorption capacities of adsorbents increased with increasing temperature, pH and surface area. The SEM images of adsorbents before and after adsorption were compared.

Investigation into performance of a heat pipe with micro grooves fabricated by extrusion–ploughing process

Constrained by the micro geometry structure, a heat pipe with groove shaped capillary structure fabricated by the traditional method always shows smaller heat transfer limits. To solve this, a novel fabrication technique is of great importance. In this paper, we will discuss about heat pipes fabricated by a novel extrusion–ploughing process. Because of the extrusion from tools, two kinds of grooves, namely a leading groove and a secondary groove, are formed in this kind of heat pipe. This feature will polish the geometry structure of an ordinary heat pipe. Considering the fact of the parallel combination of these two kinds of grooves, improvement on the heat transfer performance can be expected. By experiments, the empirical mathematical regression equations relating the fabrication parameter to the geometry groove dimensions and the theoretical calculation of heat transfer limits are established here. The results show the heat pipe fabricated by the extrusion–ploughing process exhibits larger heat transfer limits when the work temperature ranges from 340 to 390 K.

Dielectric properties of a packed bed of the rhizome of P. Peltatum with an ethanol/water solution for radio frequency-assisted extraction of podophyllotoxin

The dielectric properties of a packed bed of the rhizome particles of Podophyllum peltatum and an ethanol/water solution were measured from 10 to 30 MHz using a precision LCR meter and a liquid test fixture. The effects of temperature, particle moisture content, volumetric concentration of ethanol and bed porosity on the dielectric constant, dielectric loss factor and power penetration depth were investigated. The dielectric constant of ethanol decreased with temperature but the effect of frequency was not significant. The dielectric constant of packed beds with 100% and 70% ethanol increased with the moisture content. For a packed bed with 30% ethanol, the dielectric constant was not significantly affected by particle moisture content. Frequency and temperature had no significant effect on the dielectric constant of the packed bed. The dielectric loss factor significantly increased with the particle moisture content for the beds with 100% and 70% ethanol but not with 30% ethanol. The dielectric loss factor was proportional to temperature directly and to frequency inversely. With 30% ethanol (and therefore 70% water) the dielectric loss factor of the bed dramatically increased compared to 70% and 100% ethanol. Porosity had a significant effect on the dielectric constant but not on the dielectric loss factor. The power penetration depth of a packed bed with 100% ethanol was significantly larger than that of the packed bed with 30% and 70% ethanol. Empirical regression equations were developed for simulation and design of an RF-assisted packed bed extraction of podophyllotoxin.

Calibration of the specific barrier model to Iranian plateau earthquakes and development of physically based attenuation relationships for Iran

Earthquake ground-motion relationships for soil and rock sites in Iran have been developed based on the specific barrier model (SBM) used within the context of the stochastic modeling and calibrated against up-to-date Iranian strong-motion data. A total of 171 strong-motion accelerograms recorded at distances of up to 200 km from 24 earthquakes with moment magnitudes ranging from Mw 5.2 to 7.4 are used to determine the region-specific source parameters of this model. Regression analysis was conducted using the “random effects” methodology that considers both earthquake-to-earthquake (inter-event) variability and within-earthquake (intra-event) variability to effectively handle the problem of weighting observations from different earthquakes. The minimization of the error function in each iteration of the “random effects” procedure was performed using the genetic algorithm method. The residuals are examined against available Iranian strong-motion data to confirm that the model predictions are unbiased and that there are no significant residual trends with distance and magnitude. No evidence of self-similarity breakdown is observed between the source radius and its seismic moment. To verify the robustness of the results, tests were performed to confirm that the results are unchanged if the number of observations is changed by removing different randomly selected datasets from the original database. Stochastic simulations, using the derived SBM, are then performed to predict peak ground-motion and response spectra parameters for a wide range of magnitudes and distances. The stochastic SBM predictions agree well with the new empirical regression equations proposed for Iran, Europe and Middle East in the magnitude–distance ranges well represented by the data. It has been shown that the SBM of this study provides unbiased ground-motion estimates over the entire frequency range of most engineering interests (1–10 Hz) for the Iranian earthquakes. Our results are also important for the assessment of hazards in other seismically active environments in the Middle East and Mediterranean regions.

An Improved Land Surface Emissivity Parameter for Land Surface Models Using Global Remote Sensing Observations

Abstract Because land surface emissivity (ɛ) has not been reliably measured, global climate model (GCM) land surface schemes conventionally set this parameter as simply constant, for example, 1 as in the National Oceanic and Atmospheric Administration (NOAA) National Centers for Environmental Prediction (NCEP) model, and 0.96 for bare soil as in the National Center for Atmospheric Research (NCAR) Community Land Model version 2 (CLM2). This is the so-called constant-emissivity assumption. Accurate broadband emissivity data are needed as model inputs to better simulate the land surface climate. It is demonstrated in this paper that the assumption of the constant emissivity induces errors in modeling the surface energy budget, especially over large arid and semiarid areas where ɛ is far smaller than unity. One feasible solution to this problem is to apply the satellite-based broadband emissivity into land surface models. The Moderate Resolution Imaging Spectroradiometer (MODIS) instrument has routinely measured spectral emissivities (ɛλ) in six thermal infrared bands. The empirical regression equations have been developed in this study to convert these spectral emissivities to broadband emissivity (ɛ) required by land surface models. The observed emissivity data show strong seasonality and land-cover dependence. Specifically, emissivity depends on surface-cover type, soil moisture content, soil organic composition, vegetation density, and structure. For example, broadband ɛ is usually around 0.96–0.98 for densely vegetated areas [(leaf area index) LAI &amp;gt; 2], but it can be lower than 0.90 for bare soils (e.g., desert). To examine the impact of variable surface broadband emissivity, sensitivity studies were conducted using offline CLM2 and coupled NCAR Community Atmosphere Models, CAM2–CLM2. These sensitivity studies illustrate that large impacts of surface ɛ occur over deserts, with changes up to 1°–2°C in ground temperature, surface skin temperature, and 2-m surface air temperature, as well as evident changes in sensible and latent heat fluxes.

Joint modeling of acoustic velocities and electrical conductivity from unified microstructure of rocks

A technique for the joint modeling of the electrical conductivity and acoustic velocities in porous rocks is proposed. The technique is based on the model of two‐component media, composed by grains, which constitute a solid frame and pores saturated by a fluid. For this model we used symmetrical effective medium approximation method that provides the simulation of the acoustic and electrical parameters for multicomponent systems with equally treated constituents. The individual element of each component as a pore or grain was approximated by an ellipsoid. The aspect ratios for grain and pore ellipsoids are introduced as a function of porosity. By applying this technique we performed the calculation of acoustic velocities and electrical conductivity for carbonate formations with a primary pore system. For such formations the experimentally determined acoustic and electrical parameters are described by the empirical regression equations for the P and S wave velocities versus porosity and Archie's law. The ellipsoid aspect ratios were obtained by minimizing the differences of both predicted P wave velocity and conductivity with experimental data. The results obtained demonstrate that electrical conductivity is more sensitive to the pore and grain geometry than acoustic velocities. To ensure the conductivity for the low porosities, the form of pores tends to a needle shape. The simulation technique developed is the base for the petrophysical inversion of well log data to reconstruct the microstructure of porous rocks.

Field Experiment Study of Transient Stratified Flow in an Estuary

An experimental study of stratified flow was conducted in this study. An electromagnetic measurement instrument, the S4 current meter, was used in field data collections of salinity and currents in the lower Apalachicola River estuary, Florida. The S4 current meter has an advantage in field deployments for long periods of time due to its preprogrammable capability for automatic data sampling and recording of fluid flow. Time series of surface and bottom salinity and currents obtained from field experiments were used to characterize the stratified flow at the measurement location in the Apalachicola River. Analysis of field data indicated that the river was strongly stratified. The stratification was affected by the upstream river flow and the downstream tidal variations. Stratification was stronger at high tide than at low tide. By removing the tidal signal using low-passing filtering, subtidal salinity, and currents were obtained to investigate the salinity stratification and currents responses to the changes of fresh water input. Subtidal vertical salinity and velocity profiles were presented at different flow conditions. At high flow conditions, both surface and bottom subtidal currents were in the seaward direction. At low flow conditions, the bottom subtidal currents were in the upstream direction due to the strong effects of density gradients. Empirical regression equations were obtained to quantify the effects of river flow on the subtidal salinity and the bottom currents. Regression analysis indicated good linear relationship between subtidal salinity stratification and the bottom currents.

Regression equations for determining the daily diffuse radiation as a function of daily beam radiation on a horizontal surface in the semi-arid Negev region of Israel

Global and normal incidence radiation intensities measured at two sites located in the semi-arid Negev region of Israel have been utilized to develop a set of monthly empirical regression equations for determining the diffuse radiation that simulate the data shown graphically in the classic paper by Liu and Jordan. This equation expresses K d , the ratio of the daily diffuse on a horizontal surface to the daily extraterrestrial radiation on a horizontal surface, as an exponential function of K D , the ratio of the daily beam on a horizontal surface to the daily extraterrestrial on a horizontal surface. The databases utilized in developing the equations consisted of measurements made in Beer Sheva and Sde Boker during the years 1990–1998 and 1990–1999, respectively. The monthly empirical regression equations were validated by using an independent set of data measured in Beer Sheva during the years 1983–1989. It was observed that a single set of monthly equations was capable of characterizing the Negev region of Israel. The statistical analysis of the results is presented and discussed in detail.

A practical approach to predict the duration of the growing season for European lakes

This work presents the first practically useful models to estimate the duration of the growing season (GS in days) for European lakes. GS is a fundamental parameter in limnology, where it is used, e.g., to calculate lake characteristic annual primary production (in g ww/m 2·yr) from measurement data in g C/l·day. We have presented two simple empirical regression equations where GS is estimated from latitude. We have also introduced a more comprehensive model. It is derived from a previously presented well calibrated and validated model predicting lake epilimnetic temperatures from readily available data on latitude, altitude, continentality (distance from the Sea) and lake volume. Operationally, the duration of the growing season (GS in days) is defined from the predicted number of days when epilimentic water temperatures are higher than 9°C. The two modelling approaches are based on different presuppositions and they have been derived and tested from different data-sets. A model comparison has shown that the overall correspondence in predicted GS-values between the methods is very good. Evidently, the more comprehensive model can provide more relevant GS-predictions for many lakes since it also accounts for differences among lakes in altitude, continentality and volume.

Predicting dry matter production of cauliflower ( Brassica oleracea L. botrytis) under unstressed conditions : I. Photosynthetic parameters of cauliflower leaves and their implications for calculations of dry matter production

Measurements of CO 2 exchange of cauliflower leaves were carried out in a field experiment which included two nitrogen fertilisation rates. Irradiance and CO 2 concentration were varied at the leaf level within a leaf cuvette and additionally a temperature treatment was applied to field grown plants moved into climate chambers. These measurements were used to estimate parameter values of a rectangular hyperbola describing cauliflower leaf CO 2 exchange as a function of irradiance and CO 2 concentration. The obtained parameter estimates were used to derive empirical regression equations with temperature and nitrogen content of the leaves as independent variables. The resulting relationships were applied within a simple photosynthesis–respiration based dry matter production model in order to derive functional relationships between light use efficiency and irradiance, leaf area index and temperature. The rectangular hyperbola was able to describe the gas exchange data as varied by irradiance and CO 2 concentration on the single leaf level with sufficient accuracy, but estimates of initial light use efficiency (about 25 μg J −1) were too high because of the bias emanating from the limited flexibility of this model. Light saturated photosynthesis rate ( P max) showed an optimum response to temperature and an increase with increasing nitrogen content of leaves. The initial slope α of the rectangular hyperbola showed no consistent responses to ambient temperature and nitrogen content of leaves. The respiration per unit leaf area β increased exponentially with increasing temperature, resulting in a Q 10 value of 1.86. Because only a limited number of plants was evaluated in this study, additional work is needed to further substantiate the results of the gas exchange measurements. The model analysis demonstrated that LUE is independent of the light integral over a range 5–10 MJ m −2 per day photosynthetically active radiation if one assumes an adaptation of P max within the canopy and over time according to the incident irradiance. Acclimatisation within the canopy and higher leaf area indices, LAI, reduce the decrease of LUE with irradiance but a substantial decline remains even for LAI values of 4.

Stochastic Modeling of California Ground Motions

Ground-motion relations are developed for California using a stochastic simulation method that exploits the equivalence between finite-fault models and a two-corner point-source model of the earthquake spectrum. First, stochastic simu- lations are generated for finite-fault ruptures, in order to define the average shape and amplitude level of the radiated spectrum at near-source distances as a function of earthquake size. The length and width of the fault plane are defined based on the moment magnitude of the earthquake and modeled with an array of subfaults. The radiation from each subfault is modeled as a Brune point source using the stochastic model approach; the subfault spectrum has a single-corner frequency. An earthquake rupture initiates at a randomly chosen subfault (hypocenter), and propagates in all directions along the fault plane. A subfault is triggered when rupture propagation reaches its center. Simulations are generated for an observation point by summing the subfault time series, appropriately lagged in time. Fourier spectra are computed for records simulated at many azimuths, placed at equidistant observation points around the fault. The mean Fourier spectrum for each magnitude, at a reference near- source distance, is used to define the shape and amplitude levels of an equivalent point-source spectrum that mimics the salient finite-fault effects. The functional form for the equivalent point-source spectrum contains two corner frequencies. Stochastic point-source simulations, using the derived two-corner source spectrum, are then performed to predict peak-ground-motion parameters and response spectra for a wide range of magnitudes and distances, for generic California sites. The sto- chastic ground-motion relations, given in the Appendix for rock and soil sites, are in good agreement with the empirical strong-motion database for California; the average ratio of observed to simulated amplitudes is near unity over all frequencies from 0.2 to 12 Hz. The stochastic relations agree well with empirical regression equations (e.g., Abrahamson and Silva, 1997; Boore et al., 1997; Sadigh et al., 1997) in the magnitude-distance ranges well represented by the data, but are better con- strained at large distances, due to the use of attenuation parameters based on regional seismographic data. The stochastic ground-motion relations provide a sound basis for estimation of ground motions for earthquakes of magnitude 4 through 8, at dis- tances from 1 to 200 km.

On the loss factor of wood during radio frequency heating

The radial direction loss factor of full-size western hemlock sapwood and heartwood, as well as western red cedar heartwood timbers was measured using the direct calorimetric method with a laboratory-scale radio frequency/vacuum dryer at the frequency of 13.56 MHz, moisture content range between 10 and 80%, temperature range between 25 and 55 °C, and root mean square (rms) electrode voltages of 0.8 and 1.1 kV, respectively. The results indicated that the moisture content, temperature, electric field strength and wood type significantly affected the loss factor. Empirical regression equations were derived based on the experimental data that made possible the calculation of the loss factor and power density within wood during RF heating.

Basin waves on a seafloor recording of the 1990 Upland, California, earthquake: Implications for ground motions from a larger earthquake

AbstractThe velocity and displacement time series from a recording on the seafloor at 74 km from the 1990 Upland earthquake (M = 5.6) are dominated by late-arriving waves with periods of 6 to 7 sec. These waves are probably surface waves traveling across the Los Angeles basin. Response spectra for the recording are in agreement with predictions from empirical regression equations and theoretical models for periods less than about 1 sec but are significantly larger than those predictions for longer periods. The longer-period spectral amplitudes are controlled by the late-arriving waves, which are not included in the theoretical models and are underrepresented in the data used in the empirical analyses. When the motions are scaled to larger magnitude, the results are in general agreement with simulations of wave propagation in the Los Angeles basin by Graves (1998).

Effects of supplementation on voluntary forage intake, diet digestibility, and animal performance

A data base was constructed to describe and estimate supplementation effects in nonlactating cattle consuming forage ad libitum. The data base included 66 publications on 126 forages (73 harvested and 53 grazed) and a total of 444 comparisons between a control, unsupplemented treatment and a supplemented treatment. Daily gains were reported for 301 comparisons and voluntary intake for 258. Direct measures of forage digestibility were reported for 202 comparisons, and total diet digestibility for 150. Supplements did not increase gain in all cases. Change in ADG due to supplement was not related closely to intake of supplemental TDN. Lowest increases in ADG were with native forages supplemented with molasses alone or with low intakes of molasses containing high levels of NPN. Greatest increases in gain were with improved forages, supplements with > 60% TDN, and supplemental CP intake > .05% of BW. Supplements decreased voluntary forage intake (VFI) when supplemental TDN intake was > .7% of BW, forage TDN:CP ratio was < 7 (adequate N), or VFI when fed alone was > 1.75% of BW. When supplements increased VFI, forage TDN: CP ratio was > 7 (N deficit), and VFI when fed alone was often low. There was little relationship between change in VFI and sources of supplemental CP and TDN. Supplements caused total diet TDN concentration to deviate from expected values by -10 to +5% of OM. When supplemental TDN intake was > .7% of BW, diet TDN concentration was always less than expected. There was little relationship between deviation from expected total diet TDN and type or composition of forages or supplements. Empirical multiple regression equations were developed to estimate effects of supplements on VFI and total diet TDN concentration. The most acceptable intake equation estimated VFI when fed with supplement (r2 = .84) That equation included VFI when fed alone, supplement intake, CP and TDN concentrations in forage and supplement, and classification codes describing forages and supplemental energy. The most acceptable equation for estimating total diet TDN concentration included only the expected total diet TDN concentration (r2 = .87). These equations may be used in nutritional models to account for associative effects.

Earthquake destructiveness potential factor and slope stability

This note presents a mathematical analysis procedure to estimate earthquake-induced displacements of embankments and slopes. It approximates the effects of the main seismic factors governing the stability of slopes by introducing the earthquake destructiveness potential factor Pd, which the authors claim to provide the most information on ground motion for the purpose of predicting the cumulative displacement of a slope. Pd is defined as the ratio between the Arias intensity and the square of the number of zero crossings per second of the accelerogram. Empirical regression equations were formulated for Pd in terms of the displacement of Newmark's rigid block vibrating horizontally with completely asymmetrical resistance; they were derived by analysing 310 horizontal components of actual accelerograms. In addition, graphs were obtained for calculating the seismic coefficients kc, which are needed to define the sliding surface, and the correction terms for estimating the displacements. This was done for the most important practical cases: (1) homogeneous infinite slope; (2) local plane slope failure; and (3) local log-spiral slope failure. Illustrative examples are given.

Lateral Flow Exchange in Transient Compound Channel Flow

Lateral flow exchange takes place between the main channel and the flood plain during the movement of a flood in a compound channel. An estimate of this lateral flow exchange is necessary in the application of transient one-dimensional coupled flow compound channel models. Two simplified theoretical equations are derived for flow exchange between the main channel and the flood plain in terms of the local channel and flood plain flow depths for fully and partially flooded flood plains with zero lateral slope. Data from numerical experiments support the trend of these equations reasonably well and empirical regression equations are proposed for practical purposes.