scholarly journals Test of Some Aspects of Modelling the Sorption of Hydrophobic Compounds in Soils

2002 ◽  
Vol 20 (3) ◽  
pp. 231-242 ◽  
Author(s):  
Bogusław Buszewski ◽  
Radosław Zbytniewski
Keyword(s):  
Goodness Of Fit ◽  
Podzolic Soil ◽  
Least Squares Method ◽  
Sorption Isotherms ◽  
Domain Model ◽  
Linear Transformations ◽  
Equilibrium Studies ◽  
Soil Matrix ◽  
Model Calculations ◽  
Hydrophobic Compounds

A study was carried out on the sorption of the herbicide linuron in podzolic soil (one of the typical soils of Poland), the sorption isotherms being obtained using batch equilibrium studies. Modelling sorption phenomena involving the interactions of chemicals and particularly herbicides is very difficult because of the strong heterogeneity of the soil matrix. The present work presents the results of applying the most common models, i.e. Freundlich and Linear, as well as the newer concept of the Dual Reactive Domain model. The data obtained were validated using various statistical and chemometric methods. The results suggest that applying the non-linear least-squares method to obtain isotherm parameters gave a much better description of the sorption phenomena than often obtained using linear transformations of the adsorption equations. The study also showed that appropriate weighting schemes should be included in any model calculations. To test the goodness-of-fit of the model to the experimental data both the correlation coefficient and the Residual Root Mean Square Error were obtained. The models were also compared using the Extra Sum of Squares Principle statistical test.

scholarly journals Trends of HCl, ClONO<sub>2</sub>, and HF column abundances from ground-based FTIR measurements in Kiruna (Sweden) in comparison with KASIMA model calculations

2011 ◽  
Vol 11 (10) ◽  
pp. 4669-4677 ◽  
Author(s):  
R. Kohlhepp ◽  
S. Barthlott ◽  
T. Blumenstock ◽  
F. Hase ◽  
I. Kaiser ◽  
...  
Keyword(s):  
Annual Cycle ◽  
Middle Atmosphere ◽  
Least Squares Method ◽  
Transport Model ◽  
Montreal Protocol ◽  
Positive Trend ◽  
Model Data ◽  
Model Calculations ◽  
The Difference ◽  
Total Column

Abstract. Trends of hydrogen chloride (HCl), chlorine nitrate (ClONO2), and hydrogen fluoride (HF) total column abundances above Kiruna (Northern Sweden, 67.84° N, 20.41° E) derived from nearly 14 years (1996–2009) of measurement and model data are presented. The measurements have been performed with a Bruker 120 HR (later Bruker 125 HR) Fourier transform infrared (FTIR) spectrometer and the chemistry-transport model (CTM) used was KASIMA (KArlsruhe SImulation model of the Middle Atmosphere). The total column abundances of ClONO2 and HF calculated by KASIMA agree quite well with the FTIR measurements while KASIMA tends to underestimate the HCl columns. To calculate the long-term trends, a linear function combined with an annual cycle was fitted to the data using a least squares method. The precision of the resulting trends was estimated with the bootstrap resampling method. For HF, both model and measurements show a positive trend that seems to decrease in the last few years. This suggests a stabilisation of the HF total column abundance. Between 1996 and 2009, KASIMA simulates an increase of (+1.51±0.07) %/yr which exceeds the FTIR result of (+0.65±0.25) %/yr. The trends determined for HCl and ClONO2 are significantly negative over the time period considered here. This is expected because the emission of their precursors (chlorofluorocarbons and hydrochlorofluorocarbons) has been restricted in the Montreal Protocol in 1987 and its amendments and adjustments. The trend for ClONO2 from the FTIR measurements amounts to (−3.28±0.56) %/yr and the one for HCl to (−0.81±0.23) %/yr. KASIMA simulates a weaker decrease: For ClONO2, the result is (−0.90±0.10) %/yr and for HCl (−0.17±0.06) %/yr. Part of the difference between measurement and model data can be explained by sampling and the stronger annual cycle indicated by the measurements. There is a factor of about four between the trends of HCl and ClONO2 above Kiruna for both measurement and model data.

scholarly journals Method to generate growth and degrowth models obtained from differential equations applied to agrarian sciences

2018 ◽  
Vol 39 (6) ◽  
pp. 2659 ◽  
Author(s):  
André Luiz Pinto dos Santos ◽  
Guilherme Rocha Moreira ◽  
Cicero Carlos Ramos de Brito ◽  
Frank Gomes-Silva ◽  
Maria Lindomárcia Leonardo da Costa ◽  
...  
Keyword(s):  
Differential Equations ◽  
Goodness Of Fit ◽  
Least Squares Method ◽  
Growth Curves ◽  
Information Criterion ◽  
Coefficient Of Determination ◽  
Absolute Deviation ◽  
Marquardt Algorithm ◽  
Maturation Rate ◽  
Biological Interpretation

This study aims to propose a method to generate growth and degrowth models using differential equations as well as to present a model based on the method proposed, compare it with the classic linear mathematical models Logistic, Von Bertalanffy, Brody, Gompertz, and Richards, and identify the one that best represents the mean growth curve. To that end, data on Undefined Breed (UB) goats and Santa Inês sheep from the works of Cavalcante et al. (2013) and Sarmento et al. (2006a), respectively, were used. Goodness-of-fit was measured using residual mean squares (RMS), Akaike information criterion (AIC), Bayesian information criterion (BIC), mean absolute deviation (MAD), and adjusted coefficient of determination . The models’ parameters (?, weight at adulthood; ?, an integration constant; ?, shape parameter with no biological interpretation; k, maturation rate; and m, inflection point) were estimated by the least squares method using Levenberg-Marquardt algorithm on the software IBM SPSS Statistics 1.0. It was observed that the proposed model was superior to the others to study the growth curves of goats and sheep according to the methodology and conditions under which the present study was carried out.

scholarly journals The validation of a generalized Hooke's law for coronary arteries

2008 ◽  
Vol 294 (1) ◽  
pp. H66-H73 ◽  
Author(s):  
Chong Wang ◽  
Wei Zhang ◽  
Ghassan S. Kassab
Keyword(s):  
Experimental Data ◽  
Blood Vessels ◽  
Coronary Arteries ◽  
Goodness Of Fit ◽  
Least Squares Method ◽  
Boundary Value ◽  
Hooke’S Law ◽  
Material Constants ◽  
Biphasic Model ◽  
Hooke's Law

The exponential form of constitutive model is widely used in biomechanical studies of blood vessels. There are two main issues, however, with this model: 1) the curve fits of experimental data are not always satisfactory, and 2) the material parameters may be oversensitive. A new type of strain measure in a generalized Hooke's law for blood vessels was recently proposed by our group to address these issues. The new model has one nonlinear parameter and six linear parameters. In this study, the stress-strain equation is validated by fitting the model to experimental data of porcine coronary arteries. Material constants of left anterior descending artery and right coronary artery for the Hooke's law were computed with a separable nonlinear least-squares method with an excellent goodness of fit. A parameter sensitivity analysis shows that the stability of material constants is improved compared with the exponential model and a biphasic model. A boundary value problem was solved to demonstrate that the model prediction can match the measured arterial deformation under experimental loading conditions. The validated constitutive relation will serve as a basis for the solution of various boundary value problems of cardiovascular biomechanics.

A hysteresis model suitable for numerical simulation of moisture content in wood

Holzforschung ◽  
2007 ◽  
Vol 61 (2) ◽  
pp. 175-181 ◽  
Author(s):  
Henrik Lund Frandsen ◽  
Staffan Svensson ◽  
Lars Damkilde
Keyword(s):  
Relative Humidity ◽  
Moisture Content ◽  
Sorption Isotherms ◽  
Ambient Air ◽  
Domain Model ◽  
Hysteresis Phenomenon ◽  
Hysteresis Model ◽  
Worst Case ◽  
Different Temperatures ◽  
History Of

Abstract The equilibrium moisture content in wood depends not only on the current relative humidity in ambient air, but also on the history of relative humidity variations. This hysteresis dependence of sorption in wood implies that in the worst case the moisture content for a given relative humidity may deviate by 30–35%. While researchers seem to have reached a general agreement on the hypothesis for the sorption hysteresis phenomenon, only a few models describing the phenomenon are available. Current models such as the independent domain model have numerical deficiencies and drawbacks. This paper presents a new hysteresis model, which mathematically resolves in closed-form expressions, with the current relative humidity and moisture content as the only input parameters. Furthermore, the model has the advantage of being applicable to different sorption isotherms, i.e., different species and different temperatures. These features make the model relatively easy to implement into a numerical method such as the finite element method.

scholarly journals Fitting a logistic growth model to yield traits of lettuce cultivars growing in summer

2020 ◽  
Vol 14 (1) ◽  
Author(s):  
Fernanda Carini ◽  
Alberto Cargnelutti-Filho ◽  
Jéssica Maronez De Souza ◽  
Rafael Vieira Pezzini ◽  
Cassiane Ubessi ◽  
...  
Keyword(s):  
Confidence Intervals ◽  
Growth Model ◽  
Iterative Process ◽  
Logistic Model ◽  
Goodness Of Fit ◽  
Least Squares Method ◽  
Logistic Growth ◽  
Model Parameters ◽  
Yield Traits ◽  
Logistic Growth Model

The objective of this study was to fit a logistic model to fresh and dry matters of leaves and fresh and dry matters of shoots of four lettuce cultivars to describe growth in summer. Cultivars Crocantela, Elisa, Rubinela, and Vera were evaluated in the summer of 2017 and 2018, in soil in protected environment and in soilless system. Seven days after transplantation, fresh and dry leaf matters and fresh and dry shoot matters of 8 plants were weighed every 4 days. The model parameters were estimated using the software R, using the least squares method and iterative process of Gauss-Newton. We also estimated the confidence intervals of the parameters, verified the assumptions of the models, calculated the goodness-of-fit measures and the critical points, and quantified the parametric and intrinsic nonlinearities. The logistic growth model fitted well to fresh and dry leaf and shoot matters of cultivars Crocantela, Elisa, Rubinela, and Vera and is indicated to describe the growth of lettuce.

scholarly journals Linear modeling and regression for exponential engineering functions by a generalized ordinary least squares method

2014 ◽  
Vol 3 (2) ◽  
pp. 174
Author(s):  
Yaser Abdelhadi
Keyword(s):  
Least Squares ◽  
Least Squares Method ◽  
Simulated Data ◽  
Ordinary Least Squares ◽  
Parametric Estimation ◽  
Linear Least Squares ◽  
Linear Modeling ◽  
Linear Transformations ◽  
Data Points ◽  
Ordinary Least Squares Method

Linear transformations are performed for selected exponential engineering functions. The Optimum values of parameters of the linear model equation that fits the set of experimental or simulated data points are determined by the linear least squares method. The classical and matrix forms of ordinary least squares are illustrated. Keywords: Exponential Functions; Linear Modeling; Ordinary Least Squares; Parametric Estimation; Regression Steps.

scholarly journals A QBO-signal in mesospheric water vapor measurements at ALOMAR (69.29° N, 16.03° E) and in model calculations by LIMA over a solar cycle

2009 ◽  
Vol 9 (1) ◽  
pp. 883-903 ◽  
Author(s):  
G. R. Sonnemann ◽  
P. Hartogh ◽  
S. Li ◽  
M. Grygalashvyly ◽  
U. Berger
Keyword(s):  
Water Vapor ◽  
Solar Cycle ◽  
Middle Atmosphere ◽  
Transport Processes ◽  
Domain Model ◽  
Time Interval ◽  
High Latitudes ◽  
Model Calculations ◽  
The Real ◽  
Mixing Ratios

Abstract. Microwave water vapor measurements between 40 and 80 km over a solar cycle (1996–2006) were carried out in high latitudes at ALOMAR (69.29° N, 16.03° E), Norway. Three larger interuptions in the winters of 1996/97 and 2005/06, and from spring 2001 to spring 2002, a few smaller interruptions of monitoring occurred during this period. The observed year-to-year variability is not directly related to the solar activity. The analysis of the observations by the Fast Fourier Transform (FFT) method revealed peaks close to two years, particularly in the upper monitoring domain. Model calculations by means of the real date model LIMA, Leibniz-Institute Middle Atmosphere model, reflect essential patterns of the water vapor variation. The FFT-analysis of the calculated water vapor mixing ratios also showed peaks of around two years. The real period of the QBO during the monitoring period ranged quite close to two years within the time interval considered, with the exception of the years 2001/02 when the period was essentially longer. Although the QBO is a phenomenon occurring in the zonal wind of the tropical stratosphere, we suppose an influence of the QBO on the water vapor distribution of the mesosphere of high latitudes controlled by transport processes. A possible link could be given by the planetary wave activity triggered by the QBO.

scholarly journals Modelling the growth of rearing cattle

2021 ◽  
Author(s):  
Hanna Unterauer ◽  
Norbert Brunner ◽  
Manfred Kühleitner
Keyword(s):  
Goodness Of Fit ◽  
Linear Growth ◽  
Mean Squared Error ◽  
Least Squares Method ◽  
Information Criterion ◽  
Squared Error ◽  
Akaike Criterion ◽  
Linear Growth Model ◽  
Bp Model ◽  
Scientific Growth

Scientific growth literature often uses the models of Brody, Gompertz, Verhulst, and von Bertalanffy. The versatile five-parameter Bertalanffy-Pütter (BP) model generalizes them. Using the least-squares method, we fitted the BP model to mass-at-age data of 161 calves, cows, bulls, and oxen of cattle breeds that are common in Austria and Southern Germany. We used three measures to assess the goodness of fit: R-squared, normalized root-mean squared error, and the Akaike information criterion together with a correction for sample size. Although the BP model improved the fit of the linear growth model considerably in terms of R-squared, the better fit did not, in general, justify the use of its additional parameters, because most of the data had a non-sigmoidal character. In terms of the Akaike criterion, we could identify only a small core of data (15%) where sigmoidal models were indispensable.    

scholarly journals A Least Squares Estimation Method for the Linear Learning Model

1978 ◽  
Vol 15 (1) ◽  
pp. 145-153
Author(s):  
Berend Wierenga
Keyword(s):  
Least Squares ◽  
Simulation Study ◽  
Goodness Of Fit ◽  
Least Squares Method ◽  
Estimation Method ◽  
Learning Model ◽  
New Method ◽  
Data Sets ◽  
Goodness Of Fit Test ◽  
Chi Square

The author presents a new method for estimating the parameters of the linear learning model. The procedure, essentially a least squares method, is easy to carry out and avoids certain difficulties of earlier estimation procedures. Applications to three different data sets are reported, as well as results from a goodness-of-fit test. A simulation study was carried out to validate the method. The outcomes are compared with those obtained from the minimum chi square estimation method. The results of the new method appear to be satisfactory.

Moisture Sorption Characteristics of Dakuwa (Nigerian Cereal/Groundnut Snack)

2013 ◽  
Vol 9 (4) ◽  
pp. 499-504 ◽  
Author(s):  
Ocheme Boniface Ocheme ◽  
Chukwuma Charles Ariahu ◽  
Emmanuel Kongo Ingbian
Keyword(s):  
Moisture Content ◽  
Equilibrium Moisture Content ◽  
Goodness Of Fit ◽  
Sorption Isotherms ◽  
Moisture Sorption ◽  
Sorption Data ◽  
Moisture Contents ◽  
Monolayer Moisture ◽  
Increasing Temperature ◽  
Sorption Characteristics

AbstractThe moisture sorption characteristics of dakuwa at 10, 20, 30 and 400°C were studied. The experimental sorption data obtained were applied to BET, GAB, Oswin and Henderson equations to test fitness of the equations to moisture sorption of dakuwa. The sorption isotherms of dakuwa were type III isotherms (J shaped), and the equilibrium moisture content increased with increasing water activity but decreased with increasing temperature. The BET and GAB monolayer moisture contents all decreased with increasing temperature. For adsorption, the BET monolayer was higher (3.163–4.158 g/100 g solid) than that of GAB (2.931–3.728 g/100 g solid), but for desorption, the GAB monolayer (4.792–7.741 g/100 g solid) was higher than that of BET (3.962–4.480 g/100 g solid). Evaluation of goodness of fit of models revealed that moisture sorption of dakuwa was best modelled by GAB equation.

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