Spatial and temporal variability of crop yield and some Rhodic Hapludox properties under no-tillage

Soil properties are closely related with crop production and spite of the measures implemented, spatial variation has been repeatedly observed and described. Identifying and describing spatial variations of soil properties and their effects on crop yield can be a powerful decision-making tool in specific land management systems. The objective of this research was to characterize the spatial and temporal variations in crop yield and chemical and physical properties of a Rhodic Hapludox soil under no-tillage. The studied area of 3.42 ha had been cultivated since 1985 under no-tillage crop rotation in summer and winter. Yield and soil property were sampled in a regular 10 x 10 m grid, with 302 sample points. Yields of several crops were analyzed (soybean, maize, triticale, hyacinth bean and castor bean) as well as soil chemical (pH, Soil Organic Matter (SOM), P, Ca2+, Mg2+, H + Al, B, Fe, Mn, Zn, CEC, sum of bases (SB), and base saturation (V %)) and soil physical properties (saturated hydraulic conductivity, texture, density, total porosity, and mechanical penetration resistance). Data were analyzed using geostatistical analysis procedures and maps based on interpolation by kriging. Great variation in crop yields was observed in the years evaluated. The yield values in the Northern region of the study area were high in some years. Crop yields and some physical and soil chemical properties were spatially correlated.

Automatic Mapping and Classification of Spatial Environmental Data

The paper deals with the development and application of the generic methodology for automatic processing (mapping and classification) of environmental data. General Regression Neural Network (GRNN) is considered in detail and is proposed as an efficient tool to solve the problem of spatial data mapping (regression). The Probabilistic Neural Network (PNN) is considered as an automatic tool for spatial classifications. The automatic tuning of isotropic and anisotropic GRNN/PNN models using cross-validation procedure is presented. Results are compared with the k-Nearest-Neighbours (k-NN) interpolation algorithm using independent validation data set. Real case studies are based on decision-oriented mapping and classification of radioactively contaminated territories.

Three-dimensional interpolation of soil data: fertility and pedomorphological features in southern Brazil

The graphical representation of spatial soil properties in a digital environment is complex because it requires a conversion of data collected in a discrete form onto a continuous surface. The objective of this study was to apply three-dimension techniques of interpolation and visualization on soil texture and fertility properties and establish relationships with pedogenetic factors and processes in a slope area. The GRASS Geographic Information System was used to generate three-dimensional models and ParaView software to visualize soil volumes. Samples of the A, AB, BA, and B horizons were collected in a regular 122-point grid in an area of 13 ha, in Pinhais, PR, in southern Brazil. Geoprocessing and graphic computing techniques were effective in identifying and delimiting soil volumes of distinct ranges of fertility properties confined within the soil matrix. Both three-dimensional interpolation and the visualization tool facilitated interpretation in a continuous space (volumes) of the cause-effect relationships between soil texture and fertility properties and pedological factors and processes, such as higher clay contents following the drainage lines of the area. The flattest part with more weathered soils (Oxisols) had the highest pH values and lower Al3+ concentrations. These techniques of data interpolation and visualization have great potential for use in diverse areas of soil science, such as identification of soil volumes occurring side-by-side but that exhibit different physical, chemical, and mineralogical conditions for plant root growth, and monitoring of plumes of organic and inorganic pollutants in soils and sediments, among other applications. The methodological details for interpolation and a three-dimensional view of soil data are presented here.

Spatial prediction of monthly wind speeds in complex terrain with adaptive general regression neural networks

This paper presents the general regression neural networks (GRNN) as a nonlinear regression method for the interpolation of monthly wind speeds in complex Alpine orography. GRNN is trained using data coming from Swiss meteorological networks to learn the statistical relationship between topographic features and wind speed. The terrain convexity, slope and exposure are considered by extracting features from the digital elevation model at different spatial scales using specialised convolution filters. A database of gridded monthly wind speeds is then constructed by applying GRNN in prediction mode during the period 1968-2008. This study demonstrates that using topographic features as inputs in GRNN significantly reduces cross-validation errors with respect to low-dimensional models integrating only geographical coordinates and terrain height for the interpolation of wind speed. The spatial predictability of wind speed is found to be lower in summer than in winter due to more complex and weaker wind-topography relationships. The relevance of these relationships is studied using an adaptive version of the GRNN algorithm which allows to select the useful terrain features by eliminating the noisy ones. This research provides a framework for extending the low-dimensional interpolation models to high-dimensional spaces by integrating additional features accounting for the topographic conditions at multiple spatial scales. Copyright (c) 2012 Royal Meteorological Society.

Spatial variability of the rainfall erosive potential in the State of Mato Grosso do Sul, Brazil

Information about rainfall erosivity is important during soil and water conservation planning. Thus, the spatial variability of rainfall erosivity of the state Mato Grosso do Sul was analyzed using ordinary kriging interpolation. For this, three pluviograph stations were used to obtain the regression equations between the erosivity index and the rainfall coefficient EI30. The equations obtained were applied to 109 pluviometric stations, resulting in EI30 values. These values were analyzed from geostatistical technique, which can be divided into: descriptive statistics, adjust to semivariogram, cross-validation process and implementation of ordinary kriging to generate the erosivity map.Highest erosivity values were found in central and northeast regions of the State, while the lowest values were observed in the southern region. In addition, high annual precipitation values not necessarily produce higher erosivity values.

A singular vector perspective of 4D-Var: Filtering and interpolation

Four-dimensional variational data assimilation (4D-Var) combines the information from a time sequence of observations with the model dynamics and a background state to produce an analysis. In this paper, a new mathematical insight into the behaviour of 4D-Var is gained from an extension of concepts that are used to assess the qualitative information content of observations in satellite retrievals. It is shown that the 4D-Var analysis increments can be written as a linear combination of the singular vectors of a matrix which is a function of both the observational and the forecast model systems. This formulation is used to consider the filtering and interpolating aspects of 4D-Var using idealized case-studies based on a simple model of baroclinic instability. The results of the 4D-Var case-studies exhibit the reconstruction of the state in unobserved regions as a consequence of the interpolation of observations through time. The results also exhibit the filtering of components with small spatial scales that correspond to noise, and the filtering of structures in unobserved regions. The singular vector perspective gives a very clear view of this filtering and interpolating by the 4D-Var algorithm and shows that the appropriate specification of the a priori statistics is vital to extract the largest possible amount of useful information from the observations. Copyright © 2005 Royal Meteorological Society

Reduced space optimal interpolation of daily rain gauge precipitation in Switzerland

The coarse spacing of automatic rain gauges complicates near-real- time spatial analyses of precipitation. We test the possibility of improving such analyses by considering, in addition to the in situ measurements, the spatial covariance structure inferred from past observations with a denser network. To this end, a statistical reconstruction technique, reduced space optimal interpolation (RSOI), is applied over Switzerland, a region of complex topography. RSOI consists of two main parts. First, principal component analysis (PCA) is applied to obtain a reduced space representation of gridded high- resolution precipitation fields available for a multiyear calibration period in the past. Second, sparse real-time rain gauge observations are used to estimate the principal component scores and to reconstruct the precipitation field. In this way, climatological information at higher resolution than the near-real-time measurements is incorporated into the spatial analysis. PCA is found to efficiently reduce the dimensionality of the calibration fields, and RSOI is successful despite the difficulties associated with the statistical distribution of daily precipitation (skewness, dry days). Examples and a systematic evaluation show substantial added value over a simple interpolation technique that uses near-real-time observations only. The benefit is particularly strong for larger- scale precipitation and prominent topographic effects. Small-scale precipitation features are reconstructed at a skill comparable to that of the simple technique. Stratifying the reconstruction method by the types of weather type classifications yields little added skill. Apart from application in near real time, RSOI may also be valuable for enhancing instrumental precipitation analyses for the historic past when direct observations were sparse.

DIAGNOSTIC TECHNIQUES OF LOCAL INFLUENCE IN SPATIAL ANALYSIS OF SOYBEAN YIELD

Modeling of spatial dependence structure, concerning geoestatistics approach, is an indispensable tool for fixing parameters that define this structure, applied on interpolation of values in places that are not sampled, by kriging techniques. However, the estimation of parameters can be greatly affected by the presence of atypical observations on sampled data. Thus, this trial aimed at using diagnostics techniques of local influence in spatial linear Gaussians models, applied at geoestatistics in order to evaluate sensitivity of maximum likelihood estimators and restrict maximum likelihood to small perturbations in these data. So, studies with simulated and experimental data were performed. Those results, obtained from the study of real data, allowed us to conclude that the presence of atypical values among the sampled data can have a strong influence on thematic maps, changing, therefore, the spatial dependence. The application of diagnostics techniques of local influence should be part of any geoestatistic analysis, ensuring that the information from thematic maps has better quality and can be used with greater security by farmers.

Soil CO2 emission estimated by different interpolation techniques

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Spatial distribution of trachoma cases in the City of Bauru, State of São Paulo, Brazil, detected in 2006: defining key areas for improvement of health resources

Introduction: The objective of this study was to analyze the spatial behavior of the occurrence of trachoma cases detected in the City of Bauru, State of São Paulo, Brazil, in 2006 in order to use the information collected to set priority areas for optimization of health resources. Methods: the trachoma cases identified in 2006 were georeferenced. The data evaluated were: schools where the trachoma cases studied, data from the 2000 Census, census tract, type of housing, water supply conditions, distribution of income and levels of education of household heads. In the Google Earth® software and TerraView® were made descriptive spatial analysis and estimates of the Kernel. Each area was studied by interpolation of the density surfaces exposing events to facilitate to recognize the clusters. Results: of the 66 cases detected, only one (1.5%) was not a resident of the city's outskirts. A positive association was detected of trachoma cases and the percentage of heads of household with income below three minimum wages and schooling under eight years of education. Conclusions: The recognition of the spatial distribution of trachoma cases coincided with the areas of greatest social inequality in Bauru City. The micro-areas identified are those that should be prioritized in the rationalization of health resources. There is the possibility of using the trachoma cases detected as an indicator of performance of micro priority health programs.

Spatial intra-annual variability of precipitation based on geostatistics. a case study for the Paraiba do Sul Basin, southeastern Brazil

The emphasis in this research is to evaluate the spatial distribution of the precipitation using a geostatistics approach. Seasonal time scales records considering DJF, MAM, JJA e SON periods performed the analysis. Procedures to evaluate the variogram selection and to produce kriging maps were performed in a GIS environment (ArcGIS®). The results showed that kriging method was very suitable to detect both large changes in the whole area as those local small and subtle changes. Kriging demonstrated be a powerful statistical interpolation method that might be very useful in regions with great complexity in climatology and geomorphology.

Spatial distribution of runoff depth from a watershed located in a cuesta relief area of São Paulo State, Brazil

This study was undertaken in a 1566 ha drainage basin situated in an area with cuesta relief in the state of São Paulo, Brazil. The objectives were: 1) to map the maximum potential soil water retention capacity, and 2) to simulate the depth of surface runoff in each geographical position of the area based on a typical rainfall event. The database required for the development of this research was generated in the environment of the geographical information system ArcInfo v.10.1. Undeformed soil samples were collected at 69 points. The ordinary kriging method was used in the interpolation of the values of soil density and maximum potential soil water retention capacity. The spherical model allowed for better adjustment of the semivariograms corresponding to the two soil attributes for the depth of 0 to 20 cm, while the Gaussian model enabled a better fit of the spatial behavior of the two variables for the depth of 20 to 40 cm. The simulation of the spatial distribution revealed a gradual increase in the depth of surface runoff for the rainfall event taken as example (25 mm) from the reverse to the peripheral depression of the cuesta (from west to east). There is a positive aspect observed in the gradient, since the sites of highest declivity, especially those at the front of the cuesta, are closer to the western boundary of the watershed where the lowest depths of runoff occur. This behavior, in conjunction with certain values of erodibility and depending on the land use and cover, can help mitigate the soil erosion processes in these areas.

Integration of spatial and temporal models to predict extreme water table depths

The objective of this work was to evaluate extreme water table depths in a watershed, using methods for geographical spatial data analysis. Groundwater spatio-temporal dynamics was evaluated in an outcrop of the Guarani Aquifer System. Water table depths were estimated from monitoring of water levels in 23 piezometers and time series modeling available from April 2004 to April 2011. For generation of spatial scenarios, geostatistical techniques were used, which incorporated into the prediction ancillary information related to the geomorphological patterns of the watershed, using a digital elevation model. This procedure improved estimates, due to the high correlation between water levels and elevation, and aggregated physical sense to predictions. The scenarios showed differences regarding the extreme levels - too deep or too shallow ones - and can subsidize water planning, efficient water use, and sustainable water management in the watershed.

SPATIAL VARIABILITY OF THE RAINFALL EROSIVE POTENTIAL IN THE STATE OF MATO GROSSO DO SUL, BRAZIL

Information about rainfall erosivity is important during soil and water conservation planning. Thus, the spatial variability of rainfall erosivity of the state Mato Grosso do Sul was analyzed using ordinary kriging interpolation. For this, three pluviograph stations were used to obtain the regression equations between the erosivity index and the rainfall coefficient EI30. The equations obtained were applied to 109 pluviometric stations, resulting in EI30 values. These values were analyzed from geostatistical technique, which can be divided into: descriptive statistics, adjust to semivariogram, cross-validation process and implementation of ordinary kriging to generate the erosivity map. Highest erosivity values were found in central and northeast regions of the State, while the lowest values were observed in the southern region. In addition, high annual precipitation values not necessarily produce higher erosivity values.

Effect of high order interpolation in the stability and efficiency of the time-integration process in vorticity-velocity CFD algorithms

The numerical solution of the incompressible Navier-Stokes Equations offers an effective alternative to the experimental analysis of Fluid-Structure interaction i.e. dynamical coupling between a fluid and a solid which otherwise is very complex, time consuming and very expensive. To have a method which can accurately model these types of mechanical systems by numerical solutions becomes a great option, since these advantages are even more obvious when considering huge structures like bridges, high rise buildings, or even wind turbine blades with diameters as large as 200 meters. The modeling of such processes, however, involves complex multiphysics problems along with complex geometries. This thesis focuses on a novel vorticity-velocity formulation called the KLE to solve the incompressible Navier-stokes equations for such FSI problems. This scheme allows for the implementation of robust adaptive ODE time integration schemes and thus allows us to tackle the various multiphysics problems as separate modules. The current algorithm for KLE employs a structured or unstructured mesh for spatial discretization and it allows the use of a self-adaptive or fixed time step ODE solver while dealing with unsteady problems. This research deals with the analysis of the effects of the Courant-Friedrichs-Lewy (CFL) condition for KLE when applied to unsteady Stoke’s problem. The objective is to conduct a numerical analysis for stability and, hence, for convergence. Our results confirmthat the time step ∆t is constrained by the CFL-like condition ∆t ≤ const. hα, where h denotes the variable that represents spatial discretization.