Correction of resistance to penetration by pedofunctions and a reference soil water content

The soil penetration resistance is an important indicator of soil compaction and is strongly influenced by soil water content. The objective of this study was to develop mathematical models to normalize soil penetration resistance (SPR), using a reference value of gravimetric soil water content (U). For this purpose, SPR was determined with an impact penetrometer, in an experiment on a Dystroferric Red Latossol (Rhodic Eutrudox), at six levels of soil compaction, induced by mechanical chiseling and additional compaction by the traffic of a harvester (four, eight, 10, and 20 passes); in addition to a control treatment under no-tillage, without chiseling or additional compaction. To broaden the range of U values, SPR was evaluated in different periods. Undisturbed soil cores were sampled to quantify the soil bulk density (BD). Pedotransfer functions were generated correlating the values of U and BD to the SPR values. By these functions, the SPR was adequately corrected for all U and BD data ranges. The method requires only SPR and U as input variables in the models. However, different pedofunctions are needed according to the soil layer evaluated. After adjusting the pedotransfer functions, the differences in the soil compaction levels among the treatments, previously masked by variations of U, became detectable.

Pedotransfer functions to estimate water retention parameters of soils in northeastern Brazil

Pedotransfer functions (PTF) were developed to estimate the parameters (α, n, θr and θs) of the van Genuchten model (1980) to describe soil water retention curves. The data came from various sources, mainly from studies conducted by universities in Northeast Brazil, by the Brazilian Agricultural Research Corporation (Embrapa) and by a corporation for the development of the São Francisco and Parnaíba river basins (Codevasf), totaling 786 retention curves, which were divided into two data sets: 85 % for the development of PTFs, and 15 % for testing and validation, considered independent data. Aside from the development of general PTFs for all soils together, specific PTFs were developed for the soil classes Ultisols, Oxisols, Entisols, and Alfisols by multiple regression techniques, using a stepwise procedure (forward and backward) to select the best predictors. Two types of PTFs were developed: the first included all predictors (soil density, proportions of sand, silt, clay, and organic matter), and the second only the proportions of sand, silt and clay. The evaluation of adequacy of the PTFs was based on the correlation coefficient (R) and Willmott index (d). To evaluate the PTF for the moisture content at specific pressure heads, we used the root mean square error (RMSE). The PTF-predicted retention curve is relatively poor, except for the residual water content. The inclusion of organic matter as a PTF predictor improved the prediction of parameter a of van Genuchten. The performance of soil-class-specific PTFs was not better than of the general PTF. Except for the water content of saturated soil estimated by particle size distribution, the tested models for water content prediction at specific pressure heads proved satisfactory. Predictions of water content at pressure heads more negative than -0.6 m, using a PTF considering particle size distribution, are only slightly lower than those obtained by PTFs including bulk density and organic matter content.

Pedotransfer functions to estimate retention and availability of water in soils of the state of Santa Catarina, Brazil

Studies on water retention and availability are scarce for subtropical or humid temperate climate regions of the southern hemisphere. The aims of this study were to evaluate the relations of the soil physical, chemical, and mineralogical properties with water retention and availability for the generation and validation of continuous point pedotransfer functions (PTFs) for soils of the State of Santa Catarina (SC) in the South of Brazil. Horizons of 44 profiles were sampled in areas under different cover crops and regions of SC, to determine: field capacity (FC, 10 kPa), permanent wilting point (PWP, 1,500 kPa), available water content (AW, by difference), saturated hydraulic conductivity, bulk density, aggregate stability, particle size distribution (seven classes), organic matter content, and particle density. Chemical and mineralogical properties were obtained from the literature. Spearman's rank correlation analysis and path analysis were used in the statistical analyses. The point PTFs for estimation of FC, PWP and AW were generated for the soil surface and subsurface through multiple regression analysis, followed by robust regression analysis, using two sets of predictive variables. Soils with finer texture and/or greater organic matter content retain more moisture, and organic matter is the property that mainly controls the water availability to plants in soil surface horizons. Path analysis was useful in understanding the relationships between soil properties for FC, PWP and AW. The predictive power of the generated PTFs to estimate FC and PWP was good for all horizons, while AW was best estimated by more complex models with better prediction for the surface horizons of soils in Santa Catarina.

Pedotransfer functions to predict water retention for soils of the humid tropics: a review

Over the past three decades, pedotransfer functions (PTFs) have been widely used by soil scientists to estimate soils properties in temperate regions in response to the lack of soil data for these regions. Several authors indicated that little effort has been dedicated to the prediction of soil properties in the humid tropics, where the need for soil property information is of even greater priority. The aim of this paper is to provide an up-to-date repository of past and recently published articles as well as papers from proceedings of events dealing with water-retention PTFs for soils of the humid tropics. Of the 35 publications found in the literature on PTFs for prediction of water retention of soils of the humid tropics, 91 % of the PTFs are based on an empirical approach, and only 9 % are based on a semi-physical approach. Of the empirical PTFs, 97 % are continuous, and 3 % (one) is a class PTF; of the empirical PTFs, 97 % are based on multiple linear and polynomial regression of n th order techniques, and 3 % (one) is based on the k-Nearest Neighbor approach; 84 % of the continuous PTFs are point-based, and 16 % are parameter-based; 97 % of the continuous PTFs are equation-based PTFs, and 3 % (one) is based on pattern recognition. Additionally, it was found that 26 % of the tropical water-retention PTFs were developed for soils in Brazil, 26 % for soils in India, 11 % for soils in other countries in America, and 11 % for soils in other countries in Africa.

Assessment of pedotransfer functions for estimating soil water retention curves for the amazon region

Knowledge of the soil water retention curve (SWRC) is essential for understanding and modeling hydraulic processes in the soil. However, direct determination of the SWRC is time consuming and costly. In addition, it requires a large number of samples, due to the high spatial and temporal variability of soil hydraulic properties. An alternative is the use of models, called pedotransfer functions (PTFs), which estimate the SWRC from easy-to-measure properties. The aim of this paper was to test the accuracy of 16 point or parametric PTFs reported in the literature on different soils from the south and southeast of the State of Pará, Brazil. The PTFs tested were proposed by Pidgeon (1972), Lal (1979), Aina & Periaswamy (1985), Arruda et al. (1987), Dijkerman (1988), Vereecken et al. (1989), Batjes (1996), van den Berg et al. (1997), Tomasella et al. (2000), Hodnett & Tomasella (2002), Oliveira et al. (2002), and Barros (2010). We used a database that includes soil texture (sand, silt, and clay), bulk density, soil organic carbon, soil pH, cation exchange capacity, and the SWRC. Most of the PTFs tested did not show good performance in estimating the SWRC. The parametric PTFs, however, performed better than the point PTFs in assessing the SWRC in the tested region. Among the parametric PTFs, those proposed by Tomasella et al. (2000) achieved the best accuracy in estimating the empirical parameters of the van Genuchten (1980) model, especially when tested in the top soil layer.

Revisiting Field Capacity (FC): variation of definition of FC and its estimation from pedotransfer functions

Taking into account the nature of the hydrological processes involved in in situ measurement of Field Capacity (FC), this study proposes a variation of the definition of FC aiming not only at minimizing the inadequacies of its determination, but also at maintaining its original, practical meaning. Analysis of FC data for 22 Brazilian soils and additional FC data from the literature, all measured according to the proposed definition, which is based on a 48-h drainage time after infiltration by shallow ponding, indicates a weak dependency on the amount of infiltrated water, antecedent moisture level, soil morphology, and the level of the groundwater table, but a strong dependency on basic soil properties. The dependence on basic soil properties allowed determination of FC of the 22 soil profiles by pedotransfer functions (PTFs) using the input variables usually adopted in prediction of soil water retention. Among the input variables, soil moisture content θ (6 kPa) had the greatest impact. Indeed, a linear PTF based only on it resulted in an FC with a root mean squared residue less than 0.04 m³ m-3 for most soils individually. Such a PTF proved to be a better FC predictor than the traditional method of using moisture content at an arbitrary suction. Our FC data were compatible with an equivalent and broader USA database found in the literature, mainly for medium-texture soil samples. One reason for differences between FCs of the two data sets of fine-textured soils is due to their different drainage times. Thus, a standardized procedure for in situ determination of FC is recommended.

PEDO-TRANSFER FUNCTIONS FOR ESTIMATING SOIL BULK DENSITY IN CENTRAL AMAZONIA

Under field conditions in the Amazon forest, soil bulk density is difficult to measure. Rigorous methodological criteria must be applied to obtain reliable inventories of C stocks and soil nutrients, making this process expensive and sometimes unfeasible. This study aimed to generate models to estimate soil bulk density based on parameters that can be easily and reliably measured in the field and that are available in many soil-related inventories. Stepwise regression models to predict bulk density were developed using data on soil C content, clay content and pH in water from 140 permanent plots in terra firme (upland) forests near Manaus, Amazonas State, Brazil. The model results were interpreted according to the coefficient of determination (R2) and Akaike information criterion (AIC) and were validated with a dataset consisting of 125 plots different from those used to generate the models. The model with best performance in estimating soil bulk density under the conditions of this study included clay content and pH in water as independent variables and had R2 = 0.73 and AIC = -250.29. The performance of this model for predicting soil density was compared with that of models from the literature. The results showed that the locally calibrated equation was the most accurate for estimating soil bulk density for upland forests in the Manaus region.

Redes neurais e suas aplicações em calibração multivariada

Neural Networks are a set of mathematical methods and computer programs designed to simulate the information process and the knowledge acquisition of the human brain. In last years its application in chemistry is increasing significantly, due the special characteristics for model complex systems. The basic principles of two types of neural networks, the multi-layer perceptrons and radial basis functions, are introduced, as well as, a pruning approach to architecture optimization. Two analytical applications based on near infrared spectroscopy are presented, the first one for determination of nitrogen content in wheat leaves using multi-layer perceptrons networks and second one for determination of BRIX in sugar cane juices using radial basis functions networks.

A primeira lei da termodinâmica dos processos homogêneos

Thermodynamics of homogeneous processes, which corresponds to the very special situation in thermodynamics of continuous media, is used to discuss the first law. An important part of this work is the exposition of some typical mathematical errors, frequently found in the traditional presentation of thermodynamics. The concepts of state and process functions are discussed, as well as reverse and reversible processes, temporality and its implications on thermodynamics, energy reservoirs and symmetry. Our proposal is to present the first law by using a time dependent viewpoint coherent with mechanics and the foundations of that viewpoint.

Sintonização de estados quânticos: um estudo numérico do oscilador harmônico quântico

The quantum harmonic oscillator is described by the Hermite equation.¹ The asymptotic solution is predominantly used to obtain its analytical solutions. Wave functions (solutions) are quadratically integrable if taken as the product of the convergent asymptotic solution (Gaussian function) and Hermite polynomial,¹ whose degree provides the associated quantum number. Solving it numerically, quantization is observed when a control real variable is "tuned" to integer values. This can be interpreted by graphical reading of Y(x) and |Y(x)|², without other mathematical analysis, and prove useful for teaching fundamentals of quantum chemistry to undergraduates.

Mathematical equation correction to spectral and transport interferences in high-resolution continuum source flame atomic absorption spectrometry: determination of lead in phosphoric acid

In this work, a new mathematical equation correction approach for overcoming spectral and transport interferences was proposed. The proposal was applied to eliminate spectral interference caused by PO molecules at the 217.0005 nm Pb line, and the transport interference caused by variations in phosphoric acid concentrations. Correction may be necessary at 217.0005 nm to account for the contribution of PO, since Atotal217.0005 nm = A Pb217.0005 nm + A PO217.0005 nm. This may be easily done by measuring other PO wavelengths (e.g. 217.0458 nm) and calculating the relative contribution of PO absorbance (A PO) to the total absorbance (Atotal) at 217.0005 nm: A Pb217.0005 nm = Atotal217.0005 nm - A PO217.0005 nm = Atotal217.0005 nm - k (A PO217.0458 nm). The correction factor k is calculated from slopes of calibration curves built up for phosphorous (P) standard solutions measured at 217.0005 and 217.0458 nm, i.e. k = (slope217.0005 nm/slope217.0458 nm). For wavelength integrated absorbance of 3 pixels, sample aspiration rate of 5.0 ml min-1, analytical curves in the 0.1 - 1.0 mg L-1 Pb range with linearity better than 0.9990 were consistently obtained. Calibration curves for P at 217.0005 and 217.0458 nm with linearity better than 0.998 were obtained. Relative standard deviations (RSD) of measurements (n = 12) in the range of 1.4 - 4.3% and 2.0 - 6.0% without and with mathematical equation correction approach were obtained respectively. The limit of detection calculated to analytical line at 217.0005 nm was 10 µg L-1 Pb. Recoveries for Pb spikes were in the 97.5 - 100% and 105 - 230% intervals with and without mathematical equation correction approach, respectively.

Mathematical models to describe the volumetric shrinkage rate of red beans during drying

The present study aimed to determine the volumetric shrinkage rate of bean (Phaseolus vulgaris L.) seeds during air-drying under different conditions of air, temperature and relative humidity, and to adjust several mathematical models to the empiric values observed, and select the one that best represents the phenomenon. Six mathematical models were adjusted to the experimental values to represent the phenomenon. It was determined the degree of adjustment of each model from the value of the coefficient of determination, the behavior of the distribution of the residuals, and the magnitude of the average relative and estimated errors. The rate of volumetric shrinkage that occurred in bean seeds during drying is between 25 and 37%. It basically depends on the final moisture content, regardless of the air conditions during drying. The Modified Bala & Woods' model best represented the process.

Mathematical model to estimate of the deterioration of wooden poles in contact with soil used in rural areas

In São Paulo State, mainly in rural areas, the utilization of wooden poles is observed for different purposes. In this context, wood in contact with the ground presents faster deterioration, which is generally associated to environmental factors and, especially to the presence of fungi and insects. With the use of mathematical models, the useful life of wooden structures can be predicted by obtaining "climatic indexes" to indicate, comparatively among the areas studied, which have more or less tendency to fungi and insects attacks. In this work, by using climatological data of several cities at São Paulo State, a simplified mathematical model was obtained to measure the aggressiveness of the wood in contact with the soil.

Mathematical analysis of maximum power generated by photovoltaic systems and fitting curves for standard test conditions

The rural electrification is characterized by geographical dispersion of the population, low consumption, high investment by consumers and high cost. Moreover, solar radiation constitutes an inexhaustible source of energy and in its conversion into electricity photovoltaic panels are used. In this study, equations were adjusted to field conditions presented by the manufacturer for current and power of small photovoltaic systems. The mathematical analysis was performed on the photovoltaic rural system I-100 from ISOFOTON, with power 300 Wp, located at the Experimental Farm Lageado of FCA/UNESP. For the development of such equations, the circuitry of photovoltaic cells has been studied to apply iterative numerical methods for the determination of electrical parameters and possible errors in the appropriate equations in the literature to reality. Therefore, a simulation of a photovoltaic panel was proposed through mathematical equations that were adjusted according to the data of local radiation. The results have presented equations that provide real answers to the user and may assist in the design of these systems, once calculated that the maximum power limit ensures a supply of energy generated. This real sizing helps establishing the possible applications of solar energy to the rural producer and informing the real possibilities of generating electricity from the sun.

Mathematical modeling applied to the growth of tilapia in net cages in the sub middle of the São Francisco river

This study aimed to apply mathematical models to the growth of Nile tilapia (Oreochromis niloticus) reared in net cages in the lower São Francisco basin and choose the model(s) that best represents the conditions of rearing for the region. Nonlinear models of Brody, Bertalanffy, Logistic, Gompertz, and Richards were tested. The models were adjusted to the series of weight for age according to the methods of Gauss, Newton, Gradiente and Marquardt. It was used the procedure "NLIN" of the System SAS® (2003) to obtain estimates of the parameters from the available data. The best adjustment of the data were performed by the Bertalanffy, Gompertz and Logistic models which are equivalent to explain the growth of the animals up to 270 days of rearing. From the commercial point of view, it is recommended that commercialization of tilapia from at least 600 g, which is estimated in the Bertalanffy, Gompertz and Logistic models for creating over 183, 181 and 184 days, and up to 1 Kg of mass , it is suggested the suspension of the rearing up to 244, 244 and 243 days, respectively.