Geostatistical analysis of rainfall

Rainfall can be modeled as a spatially correlated random field superimposed on a background mean value; therefore, geostatistical methods are appropriate for the analysis of rain gauge data. Nevertheless, there are certain typical features of these data that must be taken into account to produce useful results, including the generally non-Gaussian mixed distribution, the inhomogeneity and low density of observations, and the temporal and spatial variability of spatial correlation patterns. Many studies show that rigorous geostatistical analysis performs better than other available interpolation techniques for rain gauge data. Important elements are the use of climatological variograms and the appropriate treatment of rainy and nonrainy areas. Benefits of geostatistical analysis for rainfall include ease of estimating areal averages, estimation of uncertainties, and the possibility of using secondary information (e.g., topography). Geostatistical analysis also facilitates the generation of ensembles of rainfall fields that are consistent with a given set of observations, allowing for a more realistic exploration of errors and their propagation in downstream models, such as those used for agricultural or hydrological forecasting. This article provides a review of geostatistical methods used for kriging, exemplified where appropriate by daily rain gauge data from Ethiopia.

Evaluation of satellite-based and model re-analysis rainfall estimates for Uganda

The dependence of much of Africa on rain fed agriculture leads to a high vulnerability to fluctuations in rainfall amount. Hence, accurate monitoring of near-real time rainfall is particularly useful, for example in forewarning possible crop shortfalls in drought-prone areas. Unfortunately, ground based observations are often inadequate. Rainfall estimates from satellite-based algorithms and numerical model outputs can fill this data gap, however rigorous assessment of such estimates is required. In this case, three satellite based products (NOAA-RFE 2.0, GPCP-1DD and TAMSAT) and two numerical model outputs (ERA-40 and ERA-Interim) have been evaluated for Uganda in East Africa using a network of 27 rain gauges. The study focuses on the years 2001 to 2005 and considers the main rainy season (February to June). All data sets were converted to the same temporal and spatial scales. Kriging was used for the spatial interpolation of the gauge data. All three satellite products showed similar characteristics and had a high level of skill that exceeded both model outputs. ERA-Interim had a tendency to overestimate whilst ERA-40 consistently underestimated the Ugandan rainfall.

Geostatistical radar-raingauge combination with nonparametric correlograms: methodological considerations and application in Switzerland

Modelling spatial covariance is an essential part of all geostatistical methods. Traditionally, parametric semivariogram models are fit from available data. More recently, it has been suggested to use nonparametric correlograms obtained from spatially complete data fields. Here, both estimation techniques are compared. Nonparametric correlograms are shown to have a substantial negative bias. Nonetheless, when combined with the sample variance of the spatial field under consideration, they yield an estimate of the semivariogram that is unbiased for small lag distances. This justifies the use of this estimation technique in geostatistical applications. Various formulations of geostatistical combination (Kriging) methods are used here for the construction of hourly precipitation grids for Switzerland based on data from a sparse realtime network of raingauges and from a spatially complete radar composite. Two variants of Ordinary Kriging (OK) are used to interpolate the sparse gauge observations. In both OK variants, the radar data are only used to determine the semivariogram model. One variant relies on a traditional parametric semivariogram estimate, whereas the other variant uses the nonparametric correlogram. The variants are tested for three cases and the impact of the semivariogram model on the Kriging prediction is illustrated. For the three test cases, the method using nonparametric correlograms performs equally well or better than the traditional method, and at the same time offers great practical advantages. Furthermore, two variants of Kriging with external drift (KED) are tested, both of which use the radar data to estimate nonparametric correlograms, and as the external drift variable. The first KED variant has been used previously for geostatistical radar-raingauge merging in Catalonia (Spain). The second variant is newly proposed here and is an extension of the first. Both variants are evaluated for the three test cases as well as an extended evaluation period. It is found that both methods yield merged fields of better quality than the original radar field or fields obtained by OK of gauge data. The newly suggested KED formulation is shown to be beneficial, in particular in mountainous regions where the quality of the Swiss radar composite is comparatively low. An analysis of the Kriging variances shows that none of the methods tested here provides a satisfactory uncertainty estimate. A suitable variable transformation is expected to improve this.

An investigation into the impact of using various techniques to estimate Arctic surface air temperature anomalies

Time series of global and regional mean Surface Air Temperature (SAT) anomalies are a common metric used to estimate recent climate change. Various techniques can be used to create these time series from meteorological station data. The degree of difference arising from using five different techniques, based on existing temperature anomaly dataset techniques, to estimate Arctic SAT anomalies over land and sea ice were investigated using reanalysis data as a testbed. Techniques which interpolated anomalies were found to result in smaller errors than non-interpolating techniques relative to the reanalysis reference. Kriging techniques provided the smallest errors in estimates of Arctic anomalies and Simple Kriging was often the best kriging method in this study, especially over sea ice. A linear interpolation technique had, on average, Root Mean Square Errors (RMSEs) up to 0.55 K larger than the two kriging techniques tested. Non-interpolating techniques provided the least representative anomaly estimates. Nonetheless, they serve as useful checks for confirming whether estimates from interpolating techniques are reasonable. The interaction of meteorological station coverage with estimation techniques between 1850 and 2011 was simulated using an ensemble dataset comprising repeated individual years (1979-2011). All techniques were found to have larger RMSEs for earlier station coverages. This supports calls for increased data sharing and data rescue, especially in sparsely observed regions such as the Arctic.

Representing the Arctic in global surface temperature time series of recent climate change

The Arctic is an important region in the study of climate change, but monitoring surface temperatures in this region is challenging, particularly in areas covered by sea ice. Here in situ, satellite and reanalysis data were utilised to investigate whether global warming over recent decades could be better estimated by changing the way the Arctic is treated in calculating global mean temperature. The degree of difference arising from using five different techniques, based on existing temperature anomaly dataset techniques, to estimate Arctic SAT anomalies over land and sea ice were investigated using reanalysis data as a testbed. Techniques which interpolated anomalies were found to result in smaller errors than non-interpolating techniques. Kriging techniques provided the smallest errors in anomaly estimates. Similar accuracies were found for anomalies estimated from in situ meteorological station SAT records using a kriging technique. Whether additional data sources, which are not currently utilised in temperature anomaly datasets, would improve estimates of Arctic surface air temperature anomalies was investigated within the reanalysis testbed and using in situ data. For the reanalysis study, the additional input anomalies were reanalysis data sampled at certain supplementary data source locations over Arctic land and sea ice areas. For the in situ data study, the additional input anomalies over sea ice were surface temperature anomalies derived from the Advanced Very High Resolution Radiometer satellite instruments. The use of additional data sources, particularly those located in the Arctic Ocean over sea ice or on islands in sparsely observed regions, can lead to substantial improvements in the accuracy of estimated anomalies. Decreases in Root Mean Square Error can be up to 0.2K for Arctic-average anomalies and more than 1K for spatially resolved anomalies. Further improvements in accuracy may be accomplished through the use of other data sources.

Designing a sampling scheme to reveal correlations between weeds and soil properties at multiple spatial scales

Weeds tend to aggregate in patches within fields and there is evidence that this is partly owing to variation in soil properties. Because the processes driving soil heterogeneity operate at different scales, the strength of the relationships between soil properties and weed density would also be expected to be scale-dependent. Quantifying these effects of scale on weed patch dynamics is essential to guide the design of discrete sampling protocols for mapping weed distribution. We have developed a general method that uses novel within-field nested sampling and residual maximum likelihood (REML) estimation to explore scale-dependent relationships between weeds and soil properties. We have validated the method using a case study of Alopecurus myosuroides in winter wheat. Using REML, we partitioned the variance and covariance into scale-specific components and estimated the correlations between the weed counts and soil properties at each scale. We used variograms to quantify the spatial structure in the data and to map variables by kriging. Our methodology successfully captured the effect of scale on a number of edaphic drivers of weed patchiness. The overall Pearson correlations between A. myosuroides and soil organic matter and clay content were weak and masked the stronger correlations at >50 m. Knowing how the variance was partitioned across the spatial scales we optimized the sampling design to focus sampling effort at those scales that contributed most to the total variance. The methods have the potential to guide patch spraying of weeds by identifying areas of the field that are vulnerable to weed establishment.

Estimation or simulation? That is the question

The issue of smoothing in kriging has been addressed either by estimation or simulation. The solution via estimation calls for postprocessing kriging estimates in order to correct the smoothing effect. Stochastic simulation provides equiprobable images presenting no smoothing and reproducing the covariance model. Consequently, these images reproduce both the sample histogram and the sample semivariogram. However, there is still a problem, which is the lack of local accuracy of simulated images. In this paper, a postprocessing algorithm for correcting the smoothing effect of ordinary kriging estimates is compared with sequential Gaussian simulation realizations. Based on samples drawn from exhaustive data sets, the postprocessing algorithm is shown to be superior to any individual simulation realization yet, at the expense of providing one deterministic estimate of the random function.

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.

Transfer function-noise modeling and spatial interpolation to evaluate the risk of extreme (shallow) water-table levels in the Brazilian Cerrados

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Mapeamento de áreas de risco à saúde pública por meio de métodos geoestatísticos

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

Using geostatistical analysis to evaluate the presence of Rotylenchulus reniformis in cotton crops in Brazil: Economic implications

In recent years, the productivity of cotton in Brazil has been progressively decreasing, often the result of the reniform nematode Rotylenchulus reniformis. This species call reduce crop productivity by up to 40%. Nematodes can be controlled by nematicides but, because of expense and toxicity, application of nematicides to large crop areas may be undesirable. In this Work. a methodology using geostatistics for quantifying the risk of nematicide application to small crop areas is proposed. This risk, in economic terms, can be compared to nematicide cost to develop an optimal strategy for Precision Farming, Soil (300 cm(3)) was sampled in a regular network from a R. reniformis-infested area that was a cotton monoculture for 20 years. The number of nematodes in each sample was counted. The nematode number per volume of soil was characterized using geostatistics, and 100 conditional simulations were conducted. Based on the simulations, risk maps were plotted showing the areas where nematicide should be applied in a Precision Farming context. The methodology developed can be applied to farming in countries that ale highly dependent on agriculture, with useful economic implications.

Variabilidade espacial de atributos químicos de um argissolo para aplicação de insumos à taxa variável em diferentes formas de relevo

A agricultura de precisão implica análise da variabilidade espacial de fatores de produção e a aplicação de insumos de forma localizada. Várias são as causas que condicionam a variabilidade espacial dos solos, sendo o relevo um dos fatores mais importantes. O presente estudo teve por objetivo analisar a variabilidade espacial dos atributos químicos do solo e a elaboração de mapas de necessidade de aplicação de insumos de forma localizada, em áreas com diferentes formas de relevo. Duas parcelas de 1 ha cada foram delimitadas em áreas com topografia côncava e convexa. Foram retiradas, em cada área, 242 amostras de solos em 121 pontos, nas profundidades de solo de 0,00-0,20 m e 0,20-0,40 m. Os resultados de análise química foram submetidos às análises da estatística descritiva, geoestatística e interpolação por krigagem. A área convexa apresentou maior variabilidade espacial do solo em relação a área côncava. A adoção da agricultura de precisão possibilitou economia de aproximadamente 25 kg ha-1 de P2O5 na área côncava.

Spatial variability of soil CO2 emission in a sugarcane area characterized by secondary information

Soil CO2 emission (FCO2) is governed by the inherent properties of the soil, such as bulk density (BD). Mapping of FCO2 allows the evaluation and identification of areas with different accumulation potential of carbon. However, FCO2 mapping over larger areas is not feasible due to the period required for evaluation. This study aimed to assess the quality of FCO2 spatial estimates using values of BD as secondary information. FCO2 and BD were evaluated on a regular sampling grid of 60 m × 60 m comprising 141 points, which was established on a sugarcane area. Four scenarios were defined according to the proportion of the number of sampling points of FCO2 to those of BD. For these scenarios, 67 (F67), 87 (F87), 107 (F107) and 127 (F127) FCO2 sampling points were used in addition to 127 BD sampling points used as supplementary information. The use of additional information from the BD provided an increase in the accuracy of the estimates only in the F107, F67 and F87 scenarios, respectively. The F87 scenario, with the approximate ratio between the FCO2 and BD of 1.00:1.50, presented the best relative improvement in the quality of estimates, thereby indicating that the BD should be sampled at a density 1.5 time greater than that applied for the FCO2. This procedure avoided problems related to the high temporal variability associated with FCO2, which enabled the mapping of this variable to be elaborated in large areas.

Spatial analysis of the distribution of Spodoptera frugiperda (J.E. Smith) (Lepidoptera: Noctuidae) and losses in maize crop productivity using geostatistics

A lagarta-do-cartucho, Spodoptera frugiperda (J.E. Smith), é uma das principais pragas do milho nas Américas. O estudo de sua distribuição espacial é fundamental para a utilização de estratégias de controle, otimização de técnicas de amostragens, determinação de danos econômicos e incorporação de um programa de agricultura de precisão. em uma área cultivada com milho foram realizadas amostragens com intervalo semanal, correspondendo ao estádio vegetativo que compreende desde a germinação até o pendoamento. Foram amostradas 10 plantas ao acaso por parcela, no total de 2000 plantas em cada amostragem. A produtividade foi obtida através da colheita de todas as parcelas que eram pesadas separadamente no campo e em cada parcela foram coletadas 15 espigas aleatoriamente para estimar o comprimento e o diâmetro médio. As análises espaciais, utilizando geoestatística, mostraram que o modelo esférico apresentou o melhor ajuste às lagartas pequenas. À medida que as lagartas foram se desenvolvendo sua distribuição foi tornando aleatória, representada por um modelo ajustado por uma reta, não tendo sido detectado nenhum tipo de dependência espacial nos pontos de amostragem. A produtividade e o diâmetro e comprimento da espiga foram descritos por modelos esféricos, indicando uma variabilidade espacial nos parâmetros de produtividade na área cultivada. A geoestatística mostrou-se promissora para a aplicação de métodos precisos no controle integrado de pragas.

Soil CO2 emission estimated by different interpolation techniques

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