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Evaluating regression-kriging for mid-infrared spectroscopy prediction of soil properties in western Kenya-East Africa
Abstract
In this study, the utility of regression-kriging was investigated in building prediction models for soil properties using mid-infrared (7498 to 600 cm− 1) spectral data for soil samples collected from Nyando, Nzoia and Yala catchment areas in Kenya, sampled at 0–20 cm and 20–50 cm depths. Using a systematic technique, 158 samples were selected for analysis of a number of soil properties of interest using wet chemistry methods. We randomly divided the dataset into two groups: 118 samples in the calibration and 40 samples in the holdout validation set. The calibration set was first used to develop partial least squares regression (PLS) models for all the soil properties. Residuals from these models were used to generate semivariograms, which revealed a strong spatial dependence as determined by the ratio of nugget to sill for nitrogen, 9%; Al, 12%; and B, 36%, but with weak spatial dependence for exchangeable Ca (ExCa), 100%; and carbon, 76%. The fitted theoretical semivariograms were used to fit regression-kriging models. Lastly, both the PLS and regression-kriging models were assessed with the validation set and their prediction performance evaluated by R² and root mean square error (RMSE). The results showed that regression kriging method gave lower RMSE values for all the evaluated soil properties except for ExCa, B and exchangeable acidity, with the best predictions, compared with the PLS model, obtained for ExMg (R², 0.93 vs 0.88; RMSE, 6.1 vs 8.4 cmolc kg− 1) and total nitrogen (R² = 0.92 vs R² = 0.74; RMSE, 0.11%, RMSE = 0.2%). In this study, regression-kriging, which takes into account spatial variation normally ignored by other methods, improved use of infrared spectroscopy for predicting soil properties.
... Digital soil mapping (DSM) quantitatively analyzes the relationship between soil attributes and the surrounding environment through neighborhood analysis and mathematical modeling methods and predicts the spatial distribution pattern of the soil-landscape continuum [10,11], which can reduce the cost of sampling and analysis to a certain extent and has been widely recognized and applied [11][12][13]. At present, three main types of quantitative methods were used in DSM: (i) geostatistical models that do not consider deterministic trends, such as ordinary kriging (OK) [14,15]; (ii) identifying the random spatial correlation changes and employing a mixed method to determine the trend, such as regression kriging (RK) [16,17]; and (iii) machine learning models based on feature space who do not explicitly consider the relevant changes in random space; for example, radial basis function neural network (RBFNN), support vector machine (SVM), and random forest (RF) [18][19][20]. Soil is a spatiotemporal continuum with high variability, and the effect of soil-forming factors on soil is nonlinear during the formation and development of soil [21]. ...
... The regression kriging (RK) model is an extension of the OK model, and its observations are regarded as the sum of drift and residual [44,45]. RK first uses MLR to predict the soil attributes based on the auxiliary predictors retained via stepwise regression analysis, then makes an OK prediction for the residual of soil attributes predicted via MLR, and finally adds the regression prediction value and the OK prediction value of the residual to obtain the prediction value of soil attributes [16,17]. ...
... The RK method can not only make full use of neighborhood information for OK interpolation when the residual term has spatial autocorrelation but also effectively establishes a global regression model according to the relationship between SOM and environmental variables [42,45]. Earlier studies have revealed that the RK method significantly weakens the smoothing effect and improves the prediction accuracy compared with OK interpolation [16,17]. The RBFNN network has a simple structure and fast convergence speed, which can effectively overcome the shortcomings of many adjustment parameters and easily fall into local minimum [31]. ...
Accurately mapping the spatial distribution and variation of soil organic matter (SOM) is of great significance for guiding regional soil management. However, the applicability and prediction performance of machine learning techniques in dryland agroecosystems still needs to be further studied. In this study, we collected a total of 733 topsoil samples from the farmland in Xiao County, Anhui Province, which is a typical dryland agroecosystem in the Huang-Huai-Hai Plain. Then, the environmental covariates were selected, and the ordinary kriging (OK), multiple linear stepwise regression (MLR), regression kriging (RK), radial basis function neural network (RBFNN), and random forest (RF) models were conducted to map the SOM content, and the optimal model was ascertained. The results demonstrated that the alkali-hydrolyzable nitrogen (26.11%), available potassium (17.73%), mean annual precipitation (13.26%), and pH (11.80%) were the main controlling factors affecting the spatial distribution of SOM in the study area. Meanwhile, the introduction of environmental covariates can effectively improve the SOM prediction accuracy, and the RF model (R2 = 0.48, MAE = 2.38 g kg−1, MRE = 12.99%, RMSE = 3.14 g kg−1) has a better performance than the RFBNN, MLR, RK, and OK methods. Although there are local differences in the spatial distribution of SOM predicted by the five methods, the overall spatial distribution of SOM was characterized by the low concentration area (13.44–20.00 g kg−1) distributed in the central and northwest of study area, and the high concentration area (24.00–28.95 g kg−1) distributed in the southeast. Overall, our study demonstrated that machine learning-based models could accurately predict the SOM content in dryland agroecosystem, and the produced maps function as baseline maps for sustainable agricultural management.
... About 10% of the whole sample set was chosen following a procedure adapted from Kennard and Stone (1969) and implemented in the prospectr package (Forkuor et al., 2017;Sila et al., 2017). The data from conventional soil analyses were used for developing best fitted models using infrared (IR) spectra to estimate soil fertility properties. ...
... For each soil property, cross-validation procedures using partial least-squares regression (PLSR) were developed using soil reference data (about 10% of the whole sample) and infrared spectral data. The exact number of soil samples for cross-validation of each soil property is presented in Table 3. PLSR is a common, simple and ease-of-use multivariate regression method that has demonstrated a good capacity for estimating physical and chemical properties resulting from the soil spectra (Terhoeven-Urselmans et al., 2010;Sila et al., 2017;Adeline et al., 2017). The cross-validation data was split into two: (1) training set (70%); (2) testing set (30%). ...
... This finding is in the same line with previous studies using MIR-PLSR method. For example, studies by Terhoeven-Urselmans et al. (2010), and Sila et al. (2017) demonstrated good and similar model accuracy for predicting soil pH H 2 O 1:2 (R 2 = 0.80). In contrary, Janik et al. (1998) reported poor soil pH prediction using pH H 2 O 1:5 (R 2 = 0.56). ...
Assessment and monitoring of soil resources is needed for ensuring environmental sustainability of rice production in sub-Saharan Africa (SSA). Diffuse reflectance spectroscopy has the potential to offer means to evaluate and monitor soils at large scale in an efficient, affordable and timely manner. However, its accuracy for predicting chemical and physical properties of soils under rice cultivation is little known. The objectives of this study were to i) determine physical and chemical soil fertility properties which can be accurately analyzed using near infrared (NIR) (700–2500 nm), mid-infrared (MIR) (2500–16,670 nm), or a combination of both (NIR-MIR) (700–16,670 nm) spectral libraries, ii) compare their prediction potential for identifying the most suitable spectral range for simultaneous analysis of soil fertility properties, and iii) assess degrees of variation of 29 soil fertility properties for 2845 soil samples collected from 42 study sites in 20 SSA countries. Diffuse reflectance spectroscopy data were obtained using a Fourier-transform infrared spectrometer (FT-IR) Tensor 27 with a high-throughput screening (HTS-XT) extension unit. About 10% of the whole sample set was chosen for conventional wet chemistry soil analysis, and was used for developing best fitted models with partial least squares regression (PLSR) that can estimate soil fertility properties using infrared (IR) spectra. The prediction performances were evaluated by R2, RMSE and RPIQ. Good prediction models (0.75 < R2 ≤ 0.86 and 1.36 ≤ RPIQ ≤ 3.78) were obtained for 13 soil properties consisting of pH H2O 1:2, exchangeable Ca, exchangeable Mg, sum of exchangeable cations, CEC, ECEC, base saturation percentage, total N, total organic C, clay content, silt content, phosphorus sorption index (PSI) and extractable Al. Satisfactory predictions (0.53 ≤ R2 ≤ 0.75 and 0.59 ≤ RPIQ ≤ 2.56) were obtained for pH H2O 1:2.5, exchangeable K, extractable Mn, Cu, and B, and sand content. NIR, MIR, and combined NIR-MIR diffuse reflectance spectroscopy demonstrate the best prediction potential for 14, 21, and 76% of the studied soil fertility properties, respectively. Except soil pH, most of soil properties are moderate to highly variable (CV = 21–131%). On average, soils in rice fields are characterized by moderate acidity, and low total N, available P and B. In conclusion, the combined NIR-MIR diffuse reflectance spectroscopy can offer an alternative to conventional wet chemistry methods for assessing soil fertility properties in rice fields in SSA, except for those having poor prediction potentials.
... Soil and plant NPK nutrient concentrations were predicted from spectral measurements data for all the samples using calibration models [37,57]. Wet-chemical reference values were calibrated to the smoothed first derivative spectra by conducting partial least square regression analysis using the "soil. ...
... Even though previous studies showed poor prediction for phosphorus [77,79], it is clear that MIR spectra contain useful information about NPK nutrient limitations in general. These findings demonstrate the potential of using MIR spectra for the assessment of nutrient deficiencies and can be embedded in the implementation of PFS approach for smallholder nutrient management strategies [57,80]. The main advantage of this technique is the reduction of cost and rapidness, especially when a target population has many soil and plant samples, to be analysed for large areas [81]. ...
Adept use of fertilizers is critical if sustainable development goal two of zero hunger and agroecosystem resilience are to be achieved for African smallholder agroecosystems. These heterogeneous systems are characterized by poor soil health mainly attributed to soil nutrient depletion. However, conventional methods do not take into account spatial patterns across geographies within agroecosystems, which poses great challenges for targeted interventions of nutrient management. This study aimed to develop a novel population-based farm survey approach for diagnosing soil nutrient deficiencies. The approach embraces principles of land health surveillance of problem definition and rigorous sampling scheme. The advent of rapid soil testing techniques, like infrared spectroscopy, offers opportune avenues for high-density soil and plant characterization. A farm survey was conducted on 64 maize fields, to collect data on soil and plant tissue nutrient concentration and grain yield (GY) for maize crops, using hierarchical and purposive sampling. Correlations between soil test values with GY and biomass were established. The relationship between GY, soil NPK, and the tissue nutrient concentrations was evaluated to guide the setting up of localized critical soil test values. Diagnosis Recommendation Integrated System (DRIS) indices for total nitrogen (N), total phosphorus (P), and total potassium (K) were used to rank and map the prevalence of nutrient limitations. A positive correlation existed between plant tissue nutrient concentration with GY with R² values of 0.089, 0.033, and 0.001 for NPK, respectively. Soil test cut-off values were 0.01%, 12 mg kg⁻¹, 4.5 cmolc kg⁻¹ for NPK, respectively, which varied slightly from established soil critical values for soil nutrient diagnostics. N and K were the most limiting nutrients for maize production in 67% of sampled fields. The study demonstrates that a population-based farm survey of crop fields can be a useful tool in nutrient diagnostics and setting priorities for site-specific fertilizer recommendations. A larger-scale application of the approach is warranted.
... At each sampling point, soil samples were collected from two layers, 0-20 cm and 20-60 cm, and then were measured to determine the actual soil salinity, so as to establish inversion models with the EC a . Then, the inverted soil salinity was fitted to semi-variance functions to determine the effects of structural and random factors in the spatial variations of soil salinity [26,27]. Afterwards, to obtain the spatial Agronomy 2023, 13, 2246 4 of 15 distribution of soil salinity over the entire experimental field, the block kriging method was cross-validated and then applied using GS+ software (version 10.0.) to interpolate soil salinity values at locations that were not sampled by EM38-MK2 [28]. ...
Flood irrigation is often applied in the arid regions of Northwest China to facilitate the leaching of salts accumulated in the soil during cotton growth in the previous season. This will, in turn, affect the temporal and spatial patterns of soil salinity, and thus cotton germination. To reveal the salinity of the two soil layers (0–20 cm and 20–60 cm), so as to determine the optimal cotton sowing timing, an electronic ground conductivity meter (EM38-MK2) was employed to measure the soil apparent electrical-conductivity (ECa) on different days: 4 days prior to flood irrigation, and, respectively, 6, 10, 15, 20, and 45 days after flood irrigation. Moreover, geostatistical analysis and block kriging interpolation were employed to analyze the spatial-temporal variations of soil salinity introduced by flood irrigation. Our results indicate that: (1) soil salinity in the two layers on different days can be well inverted from binary first-order equations of ECa at two coils (i.e., ECa1.0 and ECa0.5), demonstrating the feasibility of applying EM38-MK2 to estimate soil salinity in the field; and (2) soil salinity in the 0–20 cm layer significantly decreased during the first 15 days after flood irrigation with the greatest leaching rate of 88.37%, but tended to increase afterwards. However, the salinity in the 20–60 cm layer was persistently high before and after flood irrigation, with merely a brief decrease during the first 10 days after flood irrigation at the highest leaching rate of 40.74%. (3) The optimal semi-variance models illustrate that, after flood irrigation, the sill value (C0 + C) in the 0–20 cm layer decreased sharply, but the 20–60 cm Range of the layer significantly increased, suggesting that flood irrigation not only reduces the spatial variability of surface soil salinity, but also enhances spatial dependence in the 20–60 cm layer. (4) The correlation of the soil salinity between the two soil layers was very poor before flood irrigation, but gradually enhanced during the first 15 days after flood irrigation. Overall, for the study year, the first 15 days after flood irrigation was an optimal timing for cotton sowing when the leaching effects during flood irrigation were most efficient, and overrode the effects of evaporation and microtopography. Although not directly applicable to other years or regions, the electromagnetic induction surveys and spatiotemporal analysis of soil salinity can provide a rapid and viable guide to help determine optimal cotton sowing timing.
... When numerous measurements are required for soil taxonomy and mapping, wet chemistry frequently necessitates a large amount of sample preparation and sophisticated apparatus, which is usually insufficient (Viscarra . Also, traditional wet chemistry has disadvantages such as physical damage to the soil system's nature (Waruru et al., 2014) and generation of toxic wastes (environmentally harmful) that must be disposed off properly (Sila et al., 2017). Soil infrared techniques are promising and have demonstrated several advantages over wet chemistry methods, making it more extensively used in the soil research community, notably in soil analysis. ...
Updating soil information systems (SIS) requires advanced technologies to support the time and cost-effective and environment-friendly soil data. The use of mid- infrared (MIR) Spectroscopy as alternative to wet chemistry has been tested. The MIR spectral library is a useful technique for predicting soil attributes with high accuracy, efficiency, and low cost. The Hungarian MIR spectral library contained data on 2200 soil samples from 10 counties representing the first Soil Information and Mentoring System (SIMS) survey. Archived soil samples were prepared and scanned based on Diffuse Reflectance Infrared spectroscopy (DRIFT) technique and spectra data were saved in the fourier transform infrared (FTIR) spectrometer OPUS software. Preprocessed filtering methods, outlier detection methods and calibration sample selection methods were applied for spectral library. MIR calibration models were built for soil attributes using Partial Least Square Regression (PLSR) method. Coefficient determination (R2), The Root Mean Squared Error (RMSE) and Ratio of Performance to Deviation (RPD) were used to assess the goodness of calibration and validation models. MIR spectral library had the ability to significantly estimate soil properties such as SOC, CaCO3, sand, clay and silt through various scale models (national, county and soil type). The findings showed that our spectral library soil estimations are precise enough to provide information on national, county and soil type levels enabling a wide range of soil applications that demand huge amounts of data such as soil survey, precision agriculture and digital soil mapping.
... For example, the states or territories of Australia were used as categorical variables to account for any variance in the modelling of Australian soil spectra resulting from geography 30 . Sila et al. 31 used regression-kriging to predict soil properties with mid-infrared spectra of soil samples, where residuals from a regression fit were informed using variograms. Geographically weighted regression (GWR) might be a useful tool for modelling spectra and accounting for the geographic relationships and spatial non-stationarity in the data 32 . ...
Soil properties, such as organic carbon, pH and clay content, are critical indicators of ecosystem function. Visible–near infrared (vis–NIR) reflectance spectroscopy has been widely used to cost-efficiently estimate such soil properties. Multivariate modelling, such as partial least squares regression (PLSR), and machine learning are the most common methods for modelling soil properties with spectra. Often, such models do not account for the multiresolution information presented in the vis–NIR signal, or the spatial variation in the data. To address these potential shortcomings, we used wavelets to decompose the vis–NIR spectra of 226 soils from agricultural and forested regions in south-western Western Australia and developed a wavelet geographically weighted regression (WGWR) for estimating soil organic carbon content, clay content and pH. To evaluate the WGWR models, we compared them to linear models derived with multiresolution data from a wavelet decomposition (WLR) and PLSR without multiresolution information. Overall, validation of the WGWR models produced more accurate estimates of the soil properties than WLR and PLSR. Around 3.5–49.1% of the improvement in the estimates was due to the multiresolution analysis and 1.0–5.2% due to the integration of spatial information in the modelling. The WGWR improves the modelling of soil properties with spectra.
... To develop predictive models of plant nutrients concentrations, second-derivative spectral data were cross-validated against plant laboratory reference data (n = 149) using partial least-squares regression (PLSR) Sila et al., 2017;Terhoeven-Urselmans et al., 2010). The data were split into two: (1) training set (70%) was used for calibration and (2) testing set (30%) was used for validation. ...
Determination of the concentration of nutrients in the plant is key information for evaluating crop nutrient removal, nutrient use efficiency, fertilizer recommendations guidelines, and in turn for improving food security and reducing environmental footprints of crop production. Diffuse infrared (IR) reflectance spectroscopy is a powerful, rapid, cheap, and less pollutant analytical tool that could be substituted for traditional laboratory methods for the determination of the concentration of nutrients in plants. However, its accuracy for predicting the concentration of nutrients in rice plants is poorly known. This study aimed i) to determine macro- and micronutrients concentration that can be accurately predicted by near-infrared (NIR, 7498–4000 cm⁻¹), mid-infrared (MIR, 4000–600 cm⁻¹), or their combination (NIR-MIR, 7498–600 cm⁻¹) spectra, ii) to identify the most suitable spectral range with the best prediction potential for the simultaneous analysis of nutrients concentrations in rice plants (straw and paddy) and iii) to assess the influence of agro-ecological zone and production system on nutrients concentrations in straw and paddy (unhulled grains) samples. Second-derivative spectra were fitted against plant laboratory reference data using partial least-squares regression (PLSR) to estimate six macronutrients (N, P, K, Ca, Mg, and S) and seven micronutrients (Na, Fe, Mn, B, Cu, Mo, and Zn) concentration in paddy and rice straw samples collected at harvest from 1628 farmers’ fields in 20 sub-Saharan African (SSA) countries. The modeling prediction potential was assessed by coefficient of determination (R²), root mean square error (RMSE), mean absolute error (MAE), and ratio of performance to interquartile distance (RPIQ). Good prediction models (0.75 < R² ≤ 0.95) were obtained for 7 nutrients concentrations consisting of N, P, K, Ca, Mg, Mn, and Cu. Satisfactory predictions (0.62 ≤ R² ≤ 0.75) were obtained for S, Fe, and B. NIR, MIR, and combined NIR-MIR diffuse reflectance spectroscopy demonstrated the best prediction potential for 3, 1, and 6 of these 10 well-predicted nutrients concentrations, respectively. All nutrients concentrations both in straw and paddy were moderate to highly variable (CV = 15–111%). Agro-ecological zone and production system had a significant impact on most nutrients concentrations both in rice straw and paddy. N, P, and K concentrations in rice in irrigated lowland (IL) fields were higher than in rainfed lowland (RL) and upland (RU). From the studied fields, 2%, 16%, and 16% of straw samples were deficient in N, P, and K, respectively. K deficiency occurred in all three production systems, whereas P deficiency mainly occurred in the rainfed upland systems. Overall, the combined NIR-MIR diffuse reflectance spectroscopy has a good potential to be applied as an alternative method in the determination of macronutrient concentrations in rice plants. Further investigation on the relationships between soil attributes, rice productivity, and nutrients concentration data determined in this study is needed for providing fundamental information for site-specific soil management and fertilizer recommendations in SSA.
... In Kenya, Mora-Vallejo et al. (2008), used regression kriging to predict SOC and clay with an accuracy of 0.21% and 8.61%, respectively. Additionally In Kenya, Sila et al. (2017), predicted exchangeable Mg and N with an accuracy of 6.1 −1 and 0.11%, respectively. They found that, in general, RK gives a lower RMSE than partial least squares regression. ...
This research serves as a preliminary study to map the whole Sandspruit catchment in the Western Cape, South Africa for hydrological modelling and agricultural management. This study represents the first study in South Africa evaluating feature selection techniques combined with supervised machine learning to map soil spatial variability. The objectives of this study were i) to evaluate feature selection techniques to objectively choose environmental covariates, ii) to evaluate multiple supervised predictive models to determine soil spatial variability, iii) and to determine which regions require a higher soil density for further research. Eighty-four environmental covariates, four feature selection techniques, ten regression models, and nine classification models were used to determine the soil special variability of gravel, sand, silt, clay, soil organic matter, soil associations, great groups, presents of a bleached A horizon, depth class, and USDA textural class. The top performing regression models were then subjected to regression kriging (RK). For regression models, satisfactory results were achieved for gravel (RMSE = 8.9 and R2 = 0.77) and sand (RMSE = 4.8 and R2 = 0.66) content with RK and support vector machines, respectively. Silt (RMSE = 4.3 R2 = 0.48), clay (RMSE = 2.5 R2 = 0.43), and SOC (RMSE = 0.32 R2 = 0.44) achieved moderate results with quantile regression, random forest, and cubist models, respectively. For classification, satisfactory results were achieved for soil associations (kappa = 0.64 accuracy =74%), presence of a bleached A horizon (kappa = 0.7 accuracy = 88%), and soil depth (kappa = 0.48 accuracy = 74%) using stochastic gradient boosting (SGB), linear discriminatory analysis, and SGB, respectively. Soil texture showed moderate results (kappa = 0.43 accuracy = 66%) with multinomial ridge regression. Finally, uncertainty maps show the highest uncertainty on slope positions. In conclusion, this study shows the importance of feature selection and predictive model combinations when determining soil spatial variability of each soil attribute. Finally, this study produced DSM at a resolution that can be used for environmental models as well as small scale farming.
... The geostatistical method is a subset of statistics that specializes in analysis and interpretation of spatially (and temporally) referenced data, often employed to estimate the values of variables between data points and quantify the variance structure, to characterize the spatial distribution, and to track trend changes of soil attributes (Maliva 2016;Sila et al. 2017;Zhang et al. 2017). This approach is used to first identify and analyze the spatial structure of the variables of concern (i.e., ECa), and then to interpolate the values of variables from neighboring values, taking into consideration their spatial structure. ...
Over the past five decades, increased pressure caused by the rapidly growing population has resulted in a reclamation of agricultural and urban buffer zones along China's coastline. However, information about the spatio–temporal variation of soil salinity in these reclaimed regions is limited. As such, obtaining this information is crucial for mapping the variation in saline areas and to identify suitable salinity management strategies. In this study, we employed EM38 data to conduct digital soil mapping of spatio–temporal variation and map these variations of different site-specific zones. The results indicated that the distribution of soil salinity was heterogeneous in the middle of, and that the leaching of salts was significant at the edges of, the study field. Afterwards, fuzzy-k means algorithm was used to divide the site-specific management zones within the time series apparent soil electrical conductivity (ECa) data and the spatial correlations of variation. We concluded that two management zones are optimal to guide precision management. Zone A had an average salinity level of about 165 mS m⁻¹, in which salt-tolerant crops, such as cotton and barley can grow normally, while crops such as soybean and cowpeas may be planted using leaching and increasing the mulching film methods to reduce the accumulation of salt in surface soil. In Zone B, there was a low salinity level with a mean of 89 mS m⁻¹ for ECa, which allows for rice, wheat, and a wide range of vegetables to be grown normally. In such situations, measures such as an optimized combination of irrigation and drainage, as well as soil amendment can be taken to adjust and control the salt content. Particularly, flattening the land with a large-scale machine was used to improve the ability of micro-topography to influence salt migration; rice and other dry, land crops were planted in rotation in combination with utilizing salt-leaching multiple times to speed up desalinization.
Reducing carbon dioxide (CO2) anthropogenic emissions is an essential goal for combating climate change, and firms and policymakers must be aware of the main polluting areas of intervention for health, economic and environmental improvement, and mapping emissions is a relevant instrument to measure their geospatial distribution in order to reach that goal. Verified carbon emissions within the European Union mechanisms are a direct source of information that has not been previously used for mapping purposes. Through the application of universal kriging techniques, the proposed model shows the spatial variations of CO2 industrial emissions in the Spanish provinces and the contribution of the most polluting sectors, helping to understand the spatial CO2 emission dynamics in order to establish adequate environmental policies.
It has been reported that persistent cyanide pollution occurs in artisanal small-scale gold mining (ASGM) catchment areas in Burkina Faso. In the present study, logistic regression (LR) and Regression Kriging (RK) methods were applied to predict cyanide pollution hazard at the catchment level as well as to determine the most vulnerable areas to prioritize for restoration of degraded ecosystems. Soil samples were collected from two ASGM sites in Burkina Faso: the northern Zougnazagmiline site and the southern Galgouli site. Free cyanide (FCN) concentration in each sample was measured and the use of the LR and RK methods identified the relationships between pollution sources and pathways. However, RK was able to identify more areas with a high cyanide hazard than LR. Nevertheless, the two methods reveal that the cyanidation zones and catchments outlets within the two catchments are where the highest risk of cyanide pollution occurs, with probabilities of 0.8 and 1 in Zougnazagmiline and Galgouli, respectively.
There is a need for up-to-date assessments and maps of soil properties and land health at scales relevant for decision-making and management, including for properties that are dynamic and hence change in response to management. Also, there is a need for approaches to soil mapping that capture the ever increasing effects that humans are having on the environment in general and specifically on soil properties worldwide. In this paper, we develop models for digital soil mapping based on remote sensing data from the Moderate Resolution Imaging Spectroradiometer (MODIS) platform for Africa. The article presents maps of soil organic carbon (SOC), pH, sand and sum of exchangeable bases, as well as prevalence of root-depth restrictions in the upper 50 cm of the soil profile. Prediction models were developed based on spatially balanced field survey data, representing all major climate zones on the continent. The prediction models for soil property mapping performed well, with overall RMSEP values of 10.6, 0.34, 9.1, and 6.5 for SOC, pH, sand, and sum of bases, respectively. The accuracy of the prediction model for root-depth restrictions was 77%, with an AUC of 0.85 and Cohen's kappa value of 0.52 when averaged across predictions run on independent test data. The methods and maps developed can provide much improved identification of soil and land health constraints, and spatial targeting of land management interventions at various scales, informing both policy and practice.
80% of arable land in Africa has low soil fertility and suffers from physical soil problems. Additionally, significant amounts of nutrients are lost every year due to unsustainable soil management practices. This is partially the result of insufficient use of soil management knowledge. To help bridge the soil information gap in Africa, the Africa Soil Information Service (AfSIS) project was established in 2008. Over the period 2008-2014, the AfSIS project compiled two point data sets: the Africa Soil Profiles (legacy) database and the AfSIS Sentinel Site database. These data sets contain over 28 thousand sampling locations and represent the most comprehensive soil sample data sets of the African continent to date. Utilizing these point data sets in combination with a large number of covariates, we have generated a series of spatial predictions of soil properties relevant to the agricultural management-organic carbon, pH, sand, silt and clay fractions, bulk density, cation-exchange capacity, total nitrogen, exchangeable acidity, Al content and exchangeable bases (Ca, K, Mg, Na). We specifically investigate differences between two predictive approaches: random forests and linear regression. Results of 5-fold cross-validation demonstrate that the random forests algorithm consistently outperforms the linear regression algorithm, with average decreases of 15-75% in Root Mean Squared Error (RMSE) across soil properties and depths. Fitting and running random forests models takes an order of magnitude more time and the modelling success is sensitive to artifacts in the input data, but as long as quality-controlled point data are provided, an increase in soil mapping accuracy can be expected. Results also indicate that globally predicted soil classes (USDA Soil Taxonomy, especially Alfisols and Mollisols) help improve continental scale soil property mapping, and are among the most important predictors. This indicates a promising potential for transferring pedological knowledge from data rich countries to countries with limited soil data.
The soil science community is facing a growing demand of regional, continental, and worldwide databases in order to monitor the status of the soil. However, the availability of such data is very scarce. Cost-effective tools to measure soil properties for large areas (e.g., Europe) are required. Soil spectroscopy has shown to be a fast, cost-effective, environmental-friendly, nondestructive, reproducible, and repeatable analytical technique. The main aim of this paper is to describe the state of the art of soil spectroscopy as well as its potential to facilitating soil monitoring. The factors constraining the application of soil spectroscopy as an alternative to traditional laboratory analyses, together with the limits of the technique, are addressed. The paper also highlights that the widespread use of spectroscopy to monitor the status of the soil should be encouraged by (1) the creation of a standard for the collection of laboratory soil spectra, to promote the sharing of spectral libraries, and (2) the scanning of existing soil archives, reducing the need for costly sampling campaigns. Finally, routine soil analysis using soil spectroscopy would be beneficial for the end users by a reduction in analytical costs, and an increased comparability of results between laboratories. This ambitious project will materialize only through (1) the establishment of local and regional partnerships among existent institutions able to generate the necessary technical competence, and (2) the support of international organizations. The Food and Agriculture Organization (FAO) of United Nations and the Joint Research Centre of the European Commission are well placed to promote the use of laboratory and field spectrometers for monitoring the state of soils.
Heterogeneity in soil fertility in these smallholder systems is caused by both inherent soil-landscape and human-induced variability across farms differing in resources and practices. Interventions to address the problem of poor soil fertility in Africa must be designed to target such diversity and spatially heterogeneity. Data on soil management and soil fertility from six districts in Kenya and Uganda were gathered to understand the determinants of soil heterogeneity within farms. Analysis of the variance of soil fertility indicators across 250 randomly selected farms (i.e., 2607 fields), using a mixed model that considered site, sampling frame, farm type, and field as random terms, revealed that the variation in soil organic C (6.5-27.7 g kg(-1)), total N (0.6-3.0 g kg(-1)), and available P (0.9-27 mg kg(-1)) was mostly related to differences in the inherent properties of the soils across sites (50 to 60% of total variance). Exchangeable K+ (0.1-1.1 cmol((+)) kg(-1)), Ca2+ (1.5-14.5 cmol((+)) kg(-1)), Mg2+ (0.6-3.7 cmol((+)) kg(-1)), and pH (5.1-6.9) exhibited larger residual variability associated with field-to-field differences within farms (30 to 50%). Soil fertility indicators decreased significantly with increasing distance from the homesteads. When this variable was included in the model, the unexplained residual variances-associated with soil heterogeneity within farms-were 38% for soil C; 32% for total N; 49% for available P; 56, 49, and 38% for exchangeable K+, Ca2+ and Mg2+, respectively; and 49% for the pH. In allocating nutrient resources, farmers prioritized fields they perceived as most fertile, reinforcing soil heterogeneity. Categorization of fields within a farm with respect to distance from the homestead, and soil fertility classes as perceived by farmers, were identified as entry points to target soil fertility recommendations to easily recognizable, distinct entities.
Current methods for assessing soil organic carbon (SOC) stocks are generally not well suited for understanding variations in SOC stocks in landscapes. This is due to the tedious and time-consuming nature of the sampling methods most commonly used to collect bulk density cores, which limits repeatability across large areas, particularly where information is needed on the spatial dynamics of SOC stocks at scales relevant to management and for spatially explicit targeting of climate change mitigation options. In the current study, approaches were explored for (i) field-based estimates of SOC stocks and (ii) mapping of SOC stocks at moderate to high resolution on the basis of data from four widely contrasting ecosystems in East Africa. Estimated SOC stocks for 0–30 cm depth varied both within and between sites, with site averages ranging from 2 to 8 kg m−2. The differences in SOC stocks were determined in part by rainfall, but more importantly by sand content. Results also indicate that managing soil erosion is a key strategy for reducing SOC loss and hence in mitigation of climate change in these landscapes. Further, maps were developed on the basis of satellite image reflectance data with multiple R-squared values of 0.65 for the independent validation data set, showing variations in SOC stocks across these landscapes. These maps allow for spatially explicit targeting of potential climate change mitigation efforts through soil carbon sequestration, which is one option for climate change mitigation and adaptation. Further, the maps can be used to monitor the impacts of such mitigation efforts over time.
Soil-water properties vary widely with soil composition and texture, but measurements are often time consuming and expensive to determine using traditional laboratory methods. Mid-infrared (MIR) spectroscopy is sensitive to soil composition, allowing multivariate calibrations to be derived between volumetric soil water retention and MIR spectra. Mid-infrared partial least squares (PLS) models can be derived from the spectra of soils and reference data, and can be used to predict the water retention solely from the MIR spectra of unknown samples. Regressions between laboratory-determined volumetric water retentions, θv, at matric suctions from 1 to 1500 kPa and values predicted by MIR PLS analysis are presented for a broad variety of surface soils from southern Australia. Cross-validation produced coefficient of determination values ranging from 0.67 to 0.87 and standard error of cross-validation in the range 4.1 to 3.2. Prediction robustness was tested using an independent set of samples for values of θv at field capacity (10-kPa suction) and permanent wilting point (1500-kPa suction). The prediction standard error for the test set was higher than for cross-validation. This was attributed to a mismatch between spectra for the test set and those of the calibration samples, resulting in a reduced ability of the calibration samples to model the test set spectra. The MIR PLS prediction method performed at least as well as some pedotransfer functions and was shown to be a rapid and inexpensive method for the prediction of volumetric soil moisture content for a range of soil types at a range of matric suctions.
Near-infrared reflectance spectroscopy (NIRS) is a cost-effective and environmentally friendly technique of soil analysis that is particularly advantageous in intensive soil sampling and soil nutrient management as well. This study evaluated the potential of NIRS for predicting P, K, Ca, Mg, Cu, Zn, Mn, Fe, and Al extracted by Mehlich 3. We used 150 air-dried samples collected from a 15-ha site dominated by Orthic Humic Gleysol and Gleyed Dystric Brunisol soils. Calibration equations were developed using modified partial least squares regression. The accuracy of NIRS prediction was evaluated using the coefficient of determination (R2), the ratio of performance deviation (RPD), and the ratio of error range (RER). Reliable calibrations were found for Ca, Cu, and Mg (R2 ≥0.7, RPD ≤1.75, and RER ≥8). Less-reliable calibrations were found for Al, Fe, K, Mn, P, and Zn (R2 <0.7, RPD ≥1.75, and RER ≥8). In the validation with independent samples, acceptable regression coefficients (i.e., 0.85 ≥ slope ≥1.2) were only found for Ca, Mg, and Mn. We presumed that the pH of the Mehlich 3 extractant (2.5±0.1) may affect the solubility of most of these nutrients, regardless the soil texture and, consequently, the potential of NIRS to predict them. The more a nutrient was correlated to clay content, the more it was likely predictable by NIRS. The prediction models obtained for Al, Ca, Cu, Fe, K, Mg, and Mn could still be used for screening purposes in cases where high accuracy is not required. These NIRS prediction models should be validated across larger geographic areas of geological homogeneity.
Globally applicable calibrations to predict standard soil properties based on infrared spectra may increase the use of this reliable technique. The objective of this study was to evaluate the ability of mid-infrared diffuse reflectance spectroscopy (4000-602 cm(-1)) to predict chemical and textural properties for a globally distributed soil spectral library. We scanned 971 soil samples selected from the International Soil Reference and Information Centre database. A high-throughput diffuse reflectance accessory was used with optics that exclude specular reflectance as a potential source of error. Archived data on soil chemical and physical properties were calibrated to first derivative spectra using partial least-squares regression. Good predictions for the spatially independent validation set were achieved for pH value, organic C content, and cation exchange capacity (CEC) (n = 291, r(2) of linear regression of predicted against measured values >= 0.75 and ratio of standard deviation of measured values to root mean square error of prediction (RPD) >= 2.0). The root mean square errors of prediction (RMSEP) were 0.75 pH units, 9.1 g organic C kg(-1) and 5.5 cmol(c) CEC kg(-1). Satisfactory predictions (r(2) = 0.65-0.75, RPD = 1.4-2.0) were obtained for exchangeable Mg concentration and clay content. The respective RMSEPs were 4.3 cmol(c) kg(-1) and 126 g kg(-1). Poorer predictions (r2 = 0.61 and 0.64) were achieved for sand and exchangeable Ca contents. Although RMSEP values are large relative to laboratory analytical errors, our results suggest a marked potential for the global spectral library as a tool for advice on land management, such as the classification of new samples into basic soil fertility classes based on organic C and clay contents, CEC, and pH. Further research is needed to test the stability of this global calibration on new data sets.
Near infrared diffuse reflectance spectrophotometry, within the wavelength range 1100 to 2500 nm, was investigated for use in the simultaneous prediction of the moisture, organic C, and total N contents of air‐dried soils. An infraAlyzer 500 C (Technicon Instruments Corp.) scanning spectrophotometer was used to obtain near infrared reflectance of soils at 2‐nm intervals. Calibration equations for each of the soil constituents studied were based upon selection of the best combination of three wavelengths in a multiple regression analysis. The wavelengths selected for moisture, organic C, and total N, respectively, were 1926, 1954, and 2150 nm, 1744, 1870 and 2052 nm, and 1702, 1870 and 2052 nm. The standard errors of prediction for finely ground samples (<0.25 mm) from the top layers (0‐0.1, 0.1‐0.2, 0.2‐0.3, 0.3‐0.6 m) were 0.58, 0.16, and 0.014% for moisture, organic C, and total N, respectively. The standard errors of prediction, however, were much larger for coarsely ground soils (<2 mm), soils containing low amounts of organic C (<0.3%) and total N (<0.03%), and for those with a wide range in colors. Within a narrow range in soil color and at moderate amounts of organic matter (0.3–2.5%C), the near infrared reflectance technique provides a rapid, nondestructive, and simultaneous measurement of moisture, organic C and total N in soils
Recent developments in infrared spectroscopy
and computer software, together with decreasing spectrometer costs, have
resulted in an increase in the potential for soil analysis. Infrared
spectroscopy in both the near and mid infrared ranges allows rapid acquisition
of soil information at quantitative and qualitative, or indicator, levels for
use in agriculture and environmental monitoring. In this paper, we describe
how mid infrared diffuse reflectance analysis can provide results comparable
in accuracy with many traditional extractive and digestion laboratory methods
in soil studies, with the possibility of either replacing or enhancing them.
Examples are given for estimation of lime requirement, organic carbon,
exchangeable cations, air-dry moisture, clay content and biological
indicators. Infrared methodology appears to have advantages in facilitating
some soil analyses that are otherwise very time-consuming or expensive, or
where spatially dense data is required.
Climate change and land use change are two forces influencing the hydrology of watersheds and their ability to provide ecosystem services, such as clean and well-regulated streamflow and control of soil erosion and sediment yield. The Soil Water Assessment Tool, SWAT a distributed, watershed-scale hydrological model was used with 18 scenarios of rainfall, temperature and infiltration capacity of land surface to investigate the spatial distribution of watershed services over the 3587 km(2) Nyando basin in Western Kenya and how it is affected by these two forces. The total annual water yield varied over the 50 sub-basins from 35 to 600 mm while the annual sediment yield ranged From 0 to 104 tons ha(-1). Temperature change had a relatively minor effect on streamflow and sediment yield compared to change in rainfall and land surface condition. Improvements in land surface condition that result in higher infiltration are an effective adaptation strategy to moderate the effects of climate change on supply of watershed services. Spatial heterogeneity in response to climate and land use change is large, and hence it is necessary to understand it if interventions to modify hydrology or adapt to climate change are to be effective.
This paper discusses the characteristics of regression-kriging (RK), its strengths and limitations, and illustrates these with a simple example and three case studies. RK is a spatial interpolation technique that combines a regression of the dependent variable on auxiliary variables (such as land surface parameters, remote sensing imagery and thematic maps) with simple kriging of the regression residuals. It is mathematically equivalent to the interpolation method variously called “Universal Kriging” (UK) and “Kriging with External Drift” (KED), where auxiliary predictors are used directly to solve the kriging weights. The advantage of RK is the ability to extend the method to a broader range of regression techniques and to allow separate interpretation of the two interpolated components. Data processing and interpretation of results are illustrated with three case studies covering the national territory of Croatia. The case studies use land surface parameters derived from combined Shuttle Radar Topography Mission and contour-based digital elevation models and multitemporal-enhanced vegetation indices derived from the MODIS imagery as auxiliary predictors. These are used to improve mapping of two continuous variables (soil organic matter content and mean annual land surface temperature) and one binary variable (presence of yew). In the case of mapping temperature, a physical model is used to estimate values of temperature at unvisited locations and RK is then used to calibrate the model with ground observations. The discussion addresses pragmatic issues: implementation of RK in existing software packages, comparison of RK with alternative interpolation techniques, and practical limitations to using RK. The most serious constraint to wider use of RK is that the analyst must carry out various steps in different software environments, both statistical and GIS.
A methodological framework for spatial prediction based on regression-kriging is described and compared with ordinary kriging and plain regression. The data are first transformed using logit transformation for target variables and factor analysis for continuous predictors (auxiliary maps). The target variables are then fitted using step-wise regression and residuals interpolated using kriging. A generic visualisation method is used to simultaneously display predictions and associated uncertainty. The framework was tested using 135 profile observations from the national survey in Croatia, divided into interpolation (100) and validation sets (35). Three target variables: organic matter, pH in topsoil and topsoil thickness were predicted from six relief parameters and nine soil mapping units. Prediction efficiency was evaluated using the mean error and root mean square error (RMSE) of prediction at validation points. The results show that the proposed framework improves efficiency of predictions. Moreover, it ensured normality of residuals and enforced prediction values to be within the physical range of a variable. For organic matter, it achieved lower relative RMSE than ordinary kriging (53.3% versus 66.5%). For topsoil thickness, it achieved a lower relative RMSE (66.5% versus 83.3%) and a lower bias than ordinary kriging (0.15 versus 0.69 cm). The prediction of pH in topsoil was difficult with all three methods. This framework can adopt both continuous and categorical soil variables in a semi-automated or automated manner. It opens a possibility to develop a bundle algorithm that can be implemented in a GIS to interpolate soil profile data from existing datasets.
In this paper, we implement and compare the accuracy of ordinary kriging, lognormal ordinary kriging, inverse distance weighting (IDW) and splines for interpolating seasonally stable soil properties (pH, electric conductivity and organic matter) that have been demonstrated to affect yield production.The choice of the exponent value for IDW and splines as well as the number of the closest neighbours to include was decided from the root mean squared error (RMSE) statistic, obtained from a cross-validation procedure. Experimental variograms were fitted with the exponential, spherical, Gaussian and linear models using weighted least squares. The model with the smallest residual sum of squares (RSS) was further interrogated to find the number of neighbours that returned the best cross-validation result.Overall, all of the methods gave similar RMSE values. On this experimental field, ordinary kriging performed best for pH in the topsoil and lognormal ordinary kriging gave the best results when applied to electrical conductivity in the topsoil. IDW interpolated subsoil pH with the greatest accuracy and splines surpassed kriging and IDW for interpolating organic matter.In all uses of IDW, the power of one was the best choice, which may due to the low skewness of the soil properties interpolated. In all cases, a value of three was found to be the best power for splines. Lognormal kriging performed well when the dataset had a coefficient of skewness larger than one. No other summary statistics offered insight into the choice of the interpolation procedure or its parameters. We conclude that many parameters would be better identified from the RMSE statistic obtained from cross-validation after an exhaustive testing.
Analysis and interpretation of spatial variability of soils is a keystone in site-specific farming. Soil survey maps may have up to 0.41-ha inclusions of dissimilar soils within a mapping unit. The objectives of this study were to determine the degree of spatial variability of soil physical properties and variance structure, and to model the sampling interval of alluvial floodplain soils. Soil profiles (n = 209) from 18 parallel transects were sampled with a mean separation distance of 79.4 m. Each profile was classified into surface, subsurface, and deep horizons. Structural analysis of soil bulk density (rho(b)), sand, clay, saturated hydraulic conductivity (K(s)), volumetric water content (theta(v)) at seven pressure potentials (psi(a)) (-1, -10, -33, -67, -100, -500, and -1500 kPa) were modeled for the three horizons. Variance of soil physical properties varied from as low as 0.01% (rho(b)) to as high as 1542% (K(s)). The LSD test indicated significant (P < 0.05) differences in sand, clay, rho(b), K(s), and theta(v) at various psi(a). Geostatistical analyses illustrated that the spatially dependent stochastic component was predominant over the nugget effect. Structured semivariogram functions of each variable were used in generating fine-scale kriged contour maps. Overall autocorrelation, Moran's I, indicated a 400-m sampling range would be adequate for detection of spatial structure of sand, silt, clay, and a 100-m sampling range for soil hydraulic properties and rho(b). The magnitude and spatial patterns soil physical property variability have implications for variable rate applications and design of soil sampling strategies in alluvial floodplain soils.
Aluminum (Al) is the most abundant metal in the earths crust, comprising about 7% of its mass. Since many plant species are sensitive to micromolar concentrations of Al, the potential for soils to be A1 toxic is considerable. Fortu- nately, most of the A1 is bound by ligands or occurs in other nonphytotoxic forms such as aluminosilicates and precip- itates. However, solubilization of this A1 is enhanced by low pH and A1 toxicity is a major factor limiting plant production on acid soils. Soil acidification can develop naturally when basic cations are leached from soils, but it can be accelerated by some farming practices and by acid rain (Kennedy, 1986). Strategies to maintain production on these soils include the application of lime to raise the soil pH and the use of plants that are tolerant of acid soils. Although A1 toxicity has been identified as a problem of acid soils for over 70 years, our knowledge about the primary sites of toxicity and the chain of events that finally affects plant growth remains largely speculative. In this paper we review recent progress that has been made in our understanding of A1 toxicity and the mechanisms of A1 tolerance in plants.
The fifteen chapters of this book analyse the living community-based water laws in Africa, Latin America and Asia and critically examine the interface between community-based water laws, formal water laws and a variety of other key institutional ingredients of on-going water resources management reform.
The diffuse reflectance spectroscopic technique provides a convenient means of obtaining mid-infrared spectra of soils, as an alternative to the pressed halide disc method. Advantages and drawbacks of the DRIFT technique are discussed and compared with those for the KBr pressed disc method for a range of Australian soils. Useful sample concentrations for DRIFT spectra range from 1-100%, i.e. much higher than for typical pressed halide discs. This high sample concentration leads to an apparent enhancement of relatively weak band intensities, providing increased information content for soil characterization. Some neat soils and soil minerals, however, show severe distortion of strongly absorbing bands at high sample concentrations, generally at frequencies below 1100 cm-1. This results in some bands having an 'inverted' appearance. Bands due to organic components are clearly visible in the range 3100-2800 cm-l. Mineral components of soils often show a group of broad, weak-medium intensity bands in the 2600-1650 cm-1 region due to overtone and combination vibrations. These bands, enhanced in DRIFT spectra, are useful for characterization purposes. For example, bands in the region near 2600-2500 cm-1 are diagnostic features for the identification of calcite and dolomite, while those in the region 2000-1650 cm-1 are characteristic of quartz and kaolinite.
Foresters have always relied on a knowledge of chemical and physical properties of soils to assess capacity of sites to support productive forests. Recently, the need for assessing soil properties has expanded because of growing public interest in determining consequences of management practices on the quality of soil relative to sustainability of forest ecosystem functions in addition to plant productivity. The concept of soil quality includes assessment of soil properties and processes as they relate to ability of soil to function effectively as a component of a healthy ecosystem. Specific functions and subsequent values provided by forest ecosystems are variable and rely on numerous soil physical, chemical, and biological properties and processes, which can differ across spatial and temporal scales. Choice of a standard set of specific properties as indicators of soil quality can be complex and will vary among forest systems and management objectives. Indices of forest soil quality which incorporate soil chemical, physical, and biological properties will be most readily adopted if they are sensitive to management-induced changes, easily measured, relevant across sites or over time, inexpensive, closely linked to measurement of desired values, and adaptable for specific ecosystems. This paper traces development of the concept of soil quality, explores use of soil chemical and physical properties as determinants of forest soil quality, and presents challenges and opportunities for forest soil scientists to play a relevant role in assessment and advancement of sustainable forest management by developing the concept of soil quality as an indicator of sustainability.
Many of the cultivated soils of sub‐Saharan Africa typically have a surface horizon low in clay and with a low cation exchange capacity (CEC). In these soils, CEC is largely due to the soil organic matter (SOM). Measurements made on long‐term trials show that changes in CEC and SOM are positively correlated to one another, but not of same magnitude, suggesting that not all of the SOM plays an equal role as regards the soil CEC. To study the influence of the different SOM size fractions on the CEC, soils with or without application of manure or compost coming from trials in Chad and Côte d'Ivoire were separated without destruction of the SOM into five organo‐mineral fractions: “coarse sand”;, “fine sand”;, “coarse silt”;, “fine silt”;, and “clay”; made up of particles of sizes between 2,000 and 200, 200 and 50, 50 and 20, 20 and 2, and 2 and 0 μm, respectively. Fractionation was carried out by mechanical dispersion of the soil, wet sieving of the fractions larger than 20 μm, and decanting of the “clay”; and “fine silt”; fractions. The CEC of these fractions increases inversely with their size. The “clay”; fraction which contains half of the SOM contributes about 80% of the CEC of the soils. The CEC of the fractions is largely a function of their carbon (C) content, but the organic CEC per unit C of the “clay”; fraction appears to be four times greater than that of the other fractions (1,000 as against 270 cmolc kg). Applications of manure or compost increase the CEC of the soils by increasing the soil C only when this C increase concerns the fine fractions of the SOM.
Reflectance spectroscopy techniques in the ultraviolet, visible, near-infrared and mid-infrared regions are alternatives for many traditional laboratory methods for measuring soil properties. However, debate exists over whether the near-infrared (700-2500 nm) or the mid-infrared (MIR, 2500-25000 nm) region of the electromagnetic spectrum is more useful for predicting soil properties. Therefore, the aim of this study was to compare UV-VIS-NIR and MIR spectroscopic techniques to predict several soil properties. A total of 415 surface and subsurface soil samples were collected from widely spread locations within New South Wales and south-eastern Queensland of Australia to model the proposed hypothesis. Principal component regression analysis (PCR) was used to develop calibration and validation models from soil spectra and reference laboratory values. The models developed using MIR spectra achieved higher prediction accuracy (regression coefficient, r2 = 0.62-0.85) for pH, organic carbon, clay, sand, CEC, and exchangeable Ca and Mg than that obtained by UV-VIS-NIR spectra (r2 = 0.28-0.76). PCR models were also developed for the combined spectral regions (UV-VIS-NIR+MIR). The models developed using combined spectra were also found to predict pH, organic carbon, clay, sand, CEC, and exchangeable Ca and Mg with acceptable accuracy (r 2 = 0.59-0.79). The results of this study indicate that MIR spectra are better than UV-VIS-NIR spectra for estimation of common soil properties.
Science-based approaches to agricultural and environmental management are needed to accelerate development progress in the world's poorest countries. We present a diagnostic surveillance framework modelled on medical diagnostic approaches for evidence-based management of agriculture and environment in developing countries. Infrared (IR) spectroscopy can play a pivotal role in making the surveillance framework operational, by providing a rapid, low cost and highly reproducible diagnostic screening tool. We review the wide applicability of IR spectroscopy for setting up measurement systems for the management of soils, crops, agricultural inputs, livestock health, agricultural products and water quality. IR spectroscopy is already being used in the design of soil surveillance systems, but the principles are generally applicable. A new evidence-based interpretation approach to plant analysis, combining plant and soil IR spectroscopy measurements, is proposed. Finally, an idealised design is proposed for making IR spectroscopy-based diagnostic surveillance operational in developing countries over the next ten years. Large area surveillance frameworks for agricultural and environmental problems will deploy integrated spectral indicators of soil, crop and livestock health and water quality. Spectral indicators will help to quantify risk factors associated with problems and assess intervention impacts. Smallholder farmers will have access to IR spectroscopy-based analysis of soils, crops and inputs through a network of hand-held or mobile IR spectroscopy units. Agricultural processing industries will make extensive use of IR spectroscopy on the factory floor to add value to agricultural produce and improve food safety. Regional centres of scientific and technological excellence will be required to support (i) high quality laboratory reference analyses, (ii) development of IR spectroscopy calibration databases and interpretation systems and (iii) up-grading of scientific and technical skills through training and education. Key challenges for adoption of this design include (i) building human capacity in science- and technology-based approaches, (ii) development of rugged low cost IR spectroscopy instrumentation and (iii) development of decision support systems to interpret IR spectroscopy data into management recommendations.
Mid-infrared diffuse reflectance spectroscopy (MIR-DRS, 2500 to 25 000 nm) can provide rapid, cheap and relatively accurate predictions for a number of soil properties. This paper examines the ability of MIR-DRS to predict various soil chemical properties with emphasis on the elucidation of possible mechanisms of prediction. Three datasets from the states of Queensland, New South Wales, and Victoria, Australia were used in this study. MIR is able to predict fundamental soil properties related to soil matrix or solid constituents and soil solution concentrations which are in equilibrium with the solid phases. Basic soil organic and mineral constituents are well predicted: cation exchange capacity, clay content, organic and total C, and total N. Chemical properties that are related to the mineral and organic components can also be predicted, including: total K, total P, elemental Fe, Si, and Al. Soil pH appears to be related to the soil constituents from its relationship with the exchange sites. Due to the differences in the origins of the soil and in the laboratory measurement procedures, calibration functions from one region do not perform well on another one. Local calibration is preferred to avoid the measurement biases between laboratories, and the calibrated functions are more specific to the soil types in an area.
In this paper we develop the mathematical and statistical structure of PLS regression. We show the PLS regression algorithm and how it can be interpreted in model building. The basic mathematical principles that lie behind two block PLS are depicted. We also show the statistical aspects of the PLS method when it is used for model building. Finally we show the structure of the PLS decompositions of the data matrices involved.
Mid-infrared spectroscopy (MIRS) is assumed to be superior to near-infrared spectroscopy (NIRS) for the prediction of soil constituents, but its usefulness is still not sufficiently explored. The objective of this study was to evaluate the ability of MIRS to predict the chemical and biological properties of organic matter in soils and litter. Reflectance spectra of the mid-infrared region including part of the near-infrared region (7000–400 cm–1) were recorded for 56 soil and litter samples from agricultural and forest sites. Spectra were used to predict general and biological characteristics of the samples as well as the C composition which was measured by 13C CPMAS-NMR spectroscopy. A partial least-square method and cross-validation were used to develop equations for the different constituents over selected spectra ranges after several mathematical treatments of the spectra. Mid-infrared spectroscopy predicted well the C : N ratio: the modeling efficiency EF was 0.95, the regression coefficient (a) of a linear regression (measured against predicted values) was 1.0, and the correlation coefficient (r) was 0.98. Satisfactorily (EF ≥ 0.70, 0.8 ≤ a ≤ 1.2, r ≥ 0.80) assessed were the contents of C, N, and lignin, the production of dissolved organic carbon, and the contents of carbonyl C, aromatic C, O-alkyl C, and alkyl C. However, the N mineralization rate, the microbial biomass and the alkyl–to–aromatic C ratio were predicted less satisfactorily (EF < 0.70). Limiting the sample set to mineral soils did generally not result in improved predictions. The good and satisfactory predictions reported above indicate a marked usefulness of MIRS in the assessment of chemical characteristics of soils and litter, but the accuracies of the MIRS predictions in the diffuse-reflectance mode were generally not superior to those of NIRS.
Compositional data are very common in the earth sciences. Nevertheless, little attention has been paid to the spatial interpolation of these data sets. Most interpolators do not necessarily satisfy the constant sum and nonnegativity constraints of compositional data, nor take spatial structure into account. Therefore, compositional kriging is introduced as a straightforward extension of ordinary kriging that complies with these constraints. In two case studies, the performance of compositional kriging is compared with that of the additive logratio-transform. In the first case study, compositional kriging yielded significantly more accurate predictions than the additive logratio-transform, while in the second case study the performances were comparable.
Databases identifying spatial distributions of soil properties are needed to implement site-specific management practices. This study examined spatial patterns for nine soil chemical properties in two adjacent fields, one in a corn (Zea mays L.)-soybean [Glycine max (L.) Merr.] rotation with inorganic fertilizer and the other in a 5-yr corn-soybean-corn-oat (Avena sativa L.)-meadow rotation with organic nutrient sources. We established sampling grids in both fields and collected soil cores to a depth of 30 cm. Soil properties with strong spatial correlations (low nugget variance/total variance ratio) and the maximum distance to which those properties were correlated (range) differed for the two fields. Soil pH, exchangeable Ca, total organic C, and total N were strongly correlated and had range values greater than 182 m in the conventional field. Bray P and exchangeable Mg were strongly correlated with range values of less than 100 m within the other. Low nugget/total variance ratios and small range values for P and Mg suggest patchy distributions, probably from long-term animal manure and municipal sludge application. Since most variance was structural in the organic field, placing sampling points closer together would improve data precision. In contrast, a relatively coarse sampling grid with fewer sampling points spaced further apart appears adequate for the conventional field. To develop accurate sampling strategies for precision agriculture, long-term field management histories should be documented since the practices appear to affect both the properties that are strongly correlated and the range to which the correlation exists.
Geostatistical prediction and simulation are being increasingly used in the earth sciences and engineering to address the imperfect knowledge of attributes that fluctuate over large areas or volumes—pollutant concentration, electromagnetic fields, porosity, thickness of a geological formation. Central to the application of such techniques is the need to know the spatial continuity, knowledge that is commonly condensed in the form of covariance or semivariogram models. Their preparation is subdivided here into the following steps: (1) Data editing, (2) Exploratory data analysis, (3) Semivariogram estimation, (4) Directional investigation, (5) Simple modeling, (6) Nested modeling. I illustrate these stages practically with a real data set from a geophysical survey from Elk County, Kansas, USA. The applicability of the approach is not limited by the physical nature of the attribute of interest.
Several methods involving spatial prediction of soil properties from landform attributes are compared using carefully designed validation procedures, The methods, tested against ordinary kriging and universal kriging of the target variables, include multi-linear regression, isotopic cokriging, heterotopic cokriging and regression-kriging models A, B and C. Prediction performance by ordinary kriging and universal kriging was comparatively poor as the methods do not use covariation of the predictor variable with terrain attributes. Heterotopic cokriging outperformed isotopic cokriging because the former utilised more of the local information from the covariables. The combined regression-kriging methods generally performed well. Both the regression-kriging model C and heterotopic cokriging performed well when soil variables were predicted into a relatively finer gridded digital elevation model (DEM) and when all the local information was utilised. Regression-kriging model C generally performed best and is, perhaps, more flexible than heterotopic cokriging. Potential for further research and developments rests in improving the regression part of model C.
Historically, our understanding of the soil and assessment of its quality and function has been gained through routine soil chemical and physical laboratory analysis. There is a global thrust towards the development of more time- and cost-efficient methodologies for soil analysis as there is a great demand for larger amounts of good quality, inexpensive soil data to be used in environmental monitoring, modelling and precision agriculture. Diffuse reflectance spectroscopy provides a good alternative that may be used to enhance or replace conventional methods of soil analysis, as it overcomes some of their limitations. Spectroscopy is rapid, timely, less expensive, non-destructive, straightforward and sometimes more accurate than conventional analysis. Furthermore, a single spectrum allows for simultaneous characterisation of various soil properties and the techniques are adaptable for ‘on-the-go’ field use. The aims of this paper are threefold: (i) determine the value of qualitative analysis in the visible (VIS) (400–700 nm), near infrared (NIR) (700–2500 nm) and mid infrared (MIR) (2500–25,000 nm); (ii) compare the simultaneous predictions of a number of different soil properties in each of these regions and the combined VIS–NIR–MIR to determine whether the combined information produces better predictions of soil properties than each of the individual regions; and (iii) deduce which of these regions may be best suited for simultaneous analysis of various soil properties. In this instance we implemented partial least-squares regression (PLSR) to construct calibration models, which were independently validated for the prediction of various soil properties from the soil spectra. The soil properties examined were soil pHCa, pHw, lime requirement (LR), organic carbon (OC), clay, silt, sand, cation exchange capacity (CEC), exchangeable calcium (Ca), exchangeable aluminium (Al), nitrate–nitrogen (NO3–N), available phosphorus (PCol), exchangeable potassium (K) and electrical conductivity (EC). Our results demonstrated the value of qualitative soil interpretations using the loading weight vectors from the PLSR decomposition. The MIR was more suitable than the VIS or NIR for this type of analysis due to the higher incidence spectral bands in this region as well as the higher intensity and specificity of the signal. Quantitatively, the accuracy of PLSR predictions in each of the VIS, NIR, MIR and VIS–NIR–MIR spectral regions varied considerably amongst properties. However, more accurate predictions were obtained using the MIR for pH, LR, OC, CEC, clay, silt and sand contents, P and EC. The NIR produced more accurate predictions for exchangeable Al and K than any of the ranges. There were only minor improvements in predictions of clay, silt and sand content using the combined VIS–NIR–MIR range. This work demonstrates the potential of diffuse reflectance spectroscopy using the VIS, NIR and MIR for more efficient soil analysis and the acquisition of soil information.
Efficient tools to measure within-field spatial variation in soil are important when establishing agricultural field trials and in precision farming. The object of the study was to investigate if a combination of two techniques, principal component analysis (PCA) and geostatistics, could reveal spatial soil variation from near infrared reflectance (NIR) spectroscopy data and thereby replace more conventional, viz. laborious and expensive, soil analyses. NIR spectrum is known to reveal information about important soil chemical, physical and biological properties and has been used in soil science for years. Three soil variables, total carbon (Tot-C), clay content and pH, were used as reference variables. The study was carried out on one site (200×160 m) in eastern Sweden with a Eutric Cambisol soil type where a sampling grid of 20×20 m was established. From the grid nodes, 99 samples were collected to a depth of 10 cm. The soil was analyzed by NIR and the data were decomposed by PCA. The first two principal components (PC 1 and PC 2) explained 85% of the total variance and therefore these two PCs were selected for further assessment of spatial variation by variography and kriging. PC 1 showed the strongest spatial dependence with a range of 148 m and a nugget close to zero. The variogram for PC 1 was robust and the kriging map expressed a clear pattern. The range of spatial correlation varied between the three reference soil variables. Tot-C expressed a low spatial dependence with a high proportion of nugget, whereas clay content and pH expressed spatial dependence at a range of 54 and 46 m, respectively. Neither of the traditional soil variables showed as strong spatial dependence as PC 1 of NIR. The advantage of the NIR–PCA strategy is that the first PCs will capture the spectral bands that express the largest variation regardless of what the NIR bands correlate to and, hence, PC 1 will always explain the variation of the soil properties that in each specific case have the largest influence on the PCA model. In conclusion, the NIR–PCA strategy seems to be an efficient and reliable strategy to use when determining the soil spatial variation in a field.
PLS-regression (PLSR) is the PLS approach in its simplest, and in chemistry and technology, most used form (two-block predictive PLS). PLSR is a method for relating two data matrices, X and Y, by a linear multivariate model, but goes beyond traditional regression in that it models also the structure of X and Y. PLSR derives its usefulness from its ability to analyze data with many, noisy, collinear, and even incomplete variables in both X and Y. PLSR has the desirable property that the precision of the model parameters improves with the increasing number of relevant variables and observations.This article reviews PLSR as it has developed to become a standard tool in chemometrics and used in chemistry and engineering. The underlying model and its assumptions are discussed, and commonly used diagnostics are reviewed together with the interpretation of resulting parameters.Two examples are used as illustrations: First, a Quantitative Structure–Activity Relationship (QSAR)/Quantitative Structure–Property Relationship (QSPR) data set of peptides is used to outline how to develop, interpret and refine a PLSR model. Second, a data set from the manufacturing of recycled paper is analyzed to illustrate time series modelling of process data by means of PLSR and time-lagged X-variables.
Mid-infrared (mid-IR) spectroscopy experiments were conducted to detect added nitrate in various soil types both in the laboratory and field. Soil pastes from ten different soils, including sandy loam, clay, and peat soils, were analysed for soil nitrate contents using the Fourier transform infrared (FTIR) attenuated total reflectance (ATR) technique. Nitrate concentrations for the laboratory experiments varied from approximately 0–1000 ppm. NO3-N while concentrations for the field experiments varied from approximately 0–140 ppm. NO3-N. Three-dimensional plots were created by graphing the wavelet deconvoluted values at 32 scales for each sample. From each plot, the volume of the nitrate peak was determined and correlated to nitrate concentrations. Results of the laboratory experiments indicated values for the coefficient of determination R2 as high as 0·99 and standard errors as low as 24 ppm. NO3-N for soil-specific calibrations. Results of the field experiments gave values for R2 as high as 0·98 and standard errors as low as 5 ppm NO3-N for soil-specific calibrations. An alternative technique to determine nitrate content was developed in which wavelet analysis was used to identify a few wavenumbers at which interferences from other ions were minimal. This method produced calibration equations that were soil independent and gave superior results to those obtained based on correlating wavelet deconvoluted volumes to nitrate concentrations.
Spectrophotometric data often comprise a great number of numerical components or variables that can be used in calibration models. When a large number of such variables are incorporated into a particular model, many difficulties arise, and it is often necessary to reduce the number of spectral variables. This paper proposes an incremental (Forward–Backward) procedure, initiated using an entropy-based criterion (mutual information), to choose the first variable. The advantages of the method are discussed; results in quantitative chemical analysis by spectrophotometry show the improvements obtained with respect to traditional and nonlinear calibration models.
There has been growing interest in the use of diffuse infrared reflectance as a quick, inexpensive tool for soil characterization. In studies reported to date, calibration and validation samples have been collected at either a local or regional scale. For this study, we selected 3768 samples from all 50 U.S. states and two tropical territories and an additional 416 samples from 36 different countries in Africa (125), Asia (104), the Americas (75) and Europe (112). The samples were selected from the National Soil Survey Center archives in Lincoln, NE, USA, with only one sample per pedon and a weighted random sampling to maximize compositional diversity. Applying visible and near-infrared (VNIR) diffuse reflectance spectroscopy (DRS) to air-dry soil (< 2 mm) with auxiliary predictors including sand content or pH, we obtained validation root mean squared deviation (RMSD) estimates of 54 g kg− 1 for clay, 7.9 g kg− 1 for soil organic C (SOC), 5.6 g kg− 1 for inorganic C (IC), 8.9 g kg− 1 for dithionate–citrate extractable Fe (FEd), and 5.5 cmolc kg− 1 for cation exchange capacity (CEC) with NH4 at pH = 7. For all of these properties, boosted regression trees (BRT) outperformed PLS regression, suggesting that this might be a preferred method for VNIR-DRS soil characterization. Using BRT, we were also able to predict ordinal clay mineralogy levels for montmorillonite and kaolinite, with 88% and 96%, respectively, falling within one ordinal unit of reference X-ray diffraction (XRD) values (0–5 on ordinal scale). Given the amount of information obtained in this study with ∼4 × 103 samples, we anticipate that calibrations sufficient for many applications might be obtained with large but obtainable soil-spectral libraries (perhaps 104–105 samples). The use of auxiliary predictors (potentially from complementary sensors), supplemental local calibration samples and theoretical spectroscopy all have the potential to improve predictions. Our findings suggest that VNIR soil characterization has the potential to replace or augment standard soil characterization techniques where rapid and inexpensive analysis is required.
Soil fertility depletion in smallholder agricultural systems in sub-Saharan Africa presents a formidable challenge both for food production and environmental sustainability. A critical constraint to managing soils in sub-Saharan Africa is poor targeting of soil management interventions. This is partly due to lack of diagnostic tools for screening soil condition that would lead to a robust and repeatable spatially explicit case definition of poor soil condition. The objectives of this study were to: (i) evaluate the ability of near infrared spectroscopy to detect changes in soil properties across a forest-cropland chronosequence; and (ii) develop a heuristic scheme for the application of infrared spectroscopy as a tool for case definition and diagnostic screening of soil condition for agricultural and environmental management. Soil reflectance was measured for 582 topsoil samples collected from forest-cropland chronosequence age classes namely; forest, recently converted, RC (17 years) and historically converted, HC (ca.70 years). 130 randomly selected samples were used to calibrate soil properties to soil reflectance using partial least-squares regression (PLSR). 64 randomly selected samples were withheld for validation. A proportional odds logistic model was applied to chronosequence age classes and 10 principal components of spectral reflectance to determine three soil condition classes namely; “good”, “average” and “poor” for 194 samples. Discriminant analysis was applied to classify the remaining 388 “unknown” samples into soil condition classes using the 194 samples as a training set. Validation r2 values were: total C, 0.91; total N, 0.90; effective cation exchange capacity (ECEC), 0.90; exchangeable Ca, 0.85; clay content, 0.77; silt content, 0.77 exchangeable Mg, 0.76; soil pH, 0.72; and K, 0.64. A spectral based definition of “good”, “average” and “poor” soil condition classes provided a basis for an explicitly quantitative case definition of poor or degraded soils. Estimates of probabilities of membership of a sample in a spectral soil condition class presents an approach for probabilistic risk-based assessments of soil condition over large spatial scales. The study concludes that reflectance spectroscopy is rapid and offers the possibility for major efficiency and cost saving, permitting spectral case definition to define poor or degraded soils, leading to better targeting of management interventions.
Geographical information systems could be improved by adding procedures for geostatistical spatial analysis to existing facilities. Most traditional methods of interpolation are based on mathematical as distinct from stochastic models of spatial variation. Spatially distributed data behave more like random variables, however, and regionalized variable theory provides a set of stochastic methods for analysing them. Kriging is the method of interpolation deriving from regionalized variable theory. It depends on expressing spatial variation of the property in terms of the variogram, and it minimizes the prediction errors which are themselves estimated. We describe the procedures and the way we link them using standard operating systems. We illustrate them using examples from case studies, one involving the mapping and control of soil salinity in the Jordan Valley of Israel, the other in semi-arid Botswana where the herbaceous cover was estimated and mapped from aerial photographic survey.
Geostatistics is essential for environmental scientists. Weather and climate vary from place to place, soil varies at every scale at which it is examined, and even man-made attributes - such as the distribution of pollution - vary. The techniques used in geostatistics are ideally suited to the needs of environmental scientists, who use them to make the best of sparse data for prediction, and top plan future surveys when resources are limited. Geostatistical technology has advanced much in the last few years and many of these developments are being incorporated into the practitioner's repertoire. This second edition describes these techniques for environmental scientists. Topics such as stochastic simulation, sampling, data screening, spatial covariances, the variogram and its modeling, and spatial prediction by kriging are described in rich detail. At each stage the underlying theory is fully explained, and the rationale behind the choices given, allowing the reader to appreciate the assumptions and constraints involved.
The spatial variation of soil nutrients in topsoil (0-20 cm) was analyzed using semivariogram in the Zunhua County of Hebei Province, China. The effect on semivariogram with randomly deleted data and kriged estimates using various reduced sample sizes was also analyzed. The semivariograms of available N, total N, available P, organic matter were best described by a spherical model, except for available K, which best fitted a complex structure of exponential model and linear with sill model. The ratio of nugget to total sample variance ranged from 34.4% to 68.4%, indicating the spatial correlation of tested soil nutrients on a large scale was moderately dependent. Among five soil nutrients, available nitrogen and available phosphorus had the shortest spatial correlation range (5 km and 5.5 km), available K had the longest range (25.5 km), whereas total nitrogen and organic matter had intermediate spatial correlation range (14.5 km and 8.5 km). The semivariograms of available N, total N, available P, and organic matter were insensitive to a 50%-60% reduction in original sampling density, while for available K, it is up to 70%. The estimated spatial distributions of total N by kriging, under various reduced sample sizes, all correlated significantly (P = 0.001) with those obtained from original data. The results showed that the semivariogram was a relatively robust tool when used in a large region and sufficient spatial variation information could be retained regardless of a higher deletion proportion of the original data. The original sample data could be reduced by kriging and the estimates showed no loss of spatial information, however, the results may be unreliable unless a clearly identified semivariogram model could be obtained. The results may provide useful information for determining the appropriate sampling densities for these scales of soil survey.
The use of mid-infrared attenuated total reflectance (ATR) spectroscopy enables direct measurement of nitrate concentration in soil pastes, but strong interfering absorbance bands due to water and soil constituents limit the accuracy of straightforward determination. Accurate subtraction of the water spectrum improves the correlation between nitrate concentration and its nu3 vibration band around 1350 cm(-1). However, this correlation is soil-dependent, due mostly to varying contents of carbonate, whose absorbance band overlaps the nitrate band. In the present work, a two-stage method is developed: First, the soil type is identified by comparing the "fingerprint" region of the spectrum (800-1200 cm(-1)) to a reference spectral library. In the second stage, nitrate concentration is estimated using the spectrum interval that includes the nitrate band, together with the soil type previously identified. Three methods are compared for estimating nitrate concentration: integration of the nitrate absorbance band, cross-correlation with a reference spectrum, and principal component analysis (PCA) followed by a neural network. When using simple band integration, the use of soil specific calibration curves leads to determination errors ranging from 5.5 to 24 mg[N]/kg[dry soil] for the mineral soils tested. The cross-correlation technique leads to similar results. The combination of soil identification with PCA and neural network modeling improves the predictions, especially for soils containing calcium carbonate. Typical prediction errors for light non-calcareous soils are about 4 mg[N]/kg[dry soil], whereas for soils containing calcium carbonate they range from 6 to 20 mg[N]/kg[dry soil], which is less than four percent of the concentration range investigated.
Fundamentals of semivariogram estimation, modeling , and usage
- R A Olea
Olea, R.A., 1994. Fundamentals of semivariogram estimation, modeling, and usage. In:
Stochastic Modeling and Geostatistics, pp. 27-35.
R: A Language and Environment for Statistical Computing. R Found
R Development Core Team, 2012. R: A Language and Environment for Statistical
Computing. R Found. Stat. Comput., Vienna Austria3-900051-07-0.