Applying the Method of Lagrange Multipliers to Derive an Estimator for Unsampled Soil Properties

2014 ◽  
Vol 11 (1) ◽  
pp. 15
Author(s):  
Set Foong Ng ◽  
Pei Eng Ch’ng ◽  
Yee Ming Chew ◽  
Kok Shien Ng
Keyword(s):  
Soil Properties ◽  
Lagrange Multipliers ◽  
Unbiased Estimator ◽  
Soil Property ◽  
Minimum Variance ◽  
Distance Method ◽  
True Value ◽  
A Site ◽  
Method Of Lagrange Multipliers ◽  
Inverse Distance

Soil properties are very crucial for civil engineers to differentiate one type of soil from another and to predict its mechanical behavior. However, it is not practical to measure soil properties at all the locations at a site. In this paper, an estimator is derived to estimate the unknown values for soil properties from locations where soil samples were not collected. The estimator is obtained by combining the concept of the ‘Inverse Distance Method’ into the technique of ‘Kriging’. The method of Lagrange Multipliers is applied in this paper. It is shown that the estimator derived in this paper is an unbiased estimator. The partiality of the estimator with respect to the true value is zero. Hence, the estimated value will be equal to the true value of the soil property. It is also shown that the variance between the estimator and the soil property is minimised. Hence, the distribution of this unbiased estimator with minimum variance spreads the least from the true value. With this characteristic of minimum variance unbiased estimator, a high accuracy estimation of soil property could be obtained.

Applying the Method of Lagrange Multipliers to Derive an Estimator for Unsampled Soil Properties

2014 ◽  
Vol 11 (1) ◽  
pp. 15
Author(s):  
Set Foong Ng ◽  
Pei Eng Ch’ng ◽  
Yee Ming Chew ◽  
Kok Shien Ng
Keyword(s):  
Soil Properties ◽  
Lagrange Multipliers ◽  
Unbiased Estimator ◽  
Soil Property ◽  
Minimum Variance ◽  
Distance Method ◽  
True Value ◽  
A Site ◽  
Method Of Lagrange Multipliers ◽  
Inverse Distance

Soil properties are very crucial for civil engineers to differentiate one type of soil from another and to predict its mechanical behavior. However, it is not practical to measure soil properties at all the locations at a site. In this paper, an estimator is derived to estimate the unknown values for soil properties from locations where soil samples were not collected. The estimator is obtained by combining the concept of the ‘Inverse Distance Method’ into the technique of ‘Kriging’. The method of Lagrange Multipliers is applied in this paper. It is shown that the estimator derived in this paper is an unbiased estimator. The partiality of the estimator with respect to the true value is zero. Hence, the estimated value will be equal to the true value of the soil property. It is also shown that the variance between the estimator and the soil property is minimised. Hence, the distribution of this unbiased estimator with minimum variance spreads the least from the true value. With this characteristic of minimum variance unbiased estimator, a high accuracy estimation of soil property could be obtained. 

scholarly journals Research trends of microplastics in the soil environment: Comprehensive screening of effects

2021 ◽  
Author(s):  
Shin Woong Kim ◽  
Matthias C. Rillig
Keyword(s):  
Soil Properties ◽  
Additional Data ◽  
Soil Property ◽  
Dry Weight ◽  
Current Data ◽  
Soil Biota ◽  
Soil Parameters ◽  
Soil Environment ◽  
Soil System ◽  
Sensitivity Distribution

AbstractWe collated and synthesized previous studies that reported the impacts of microplastics on soil parameters. The data were classified and integrated to screen for the proportion of significant effects, then we suggest several directions to alleviate the current data limitation in future experiments. We compiled 106 datasets capturing significant effects, which were analyzed in detail. We found that polyethylene and pellets (or powders) were the most frequently used microplastic composition and shape for soil experiments. The significant effects mainly occurred in broad size ranges (0.1–1 mm) at test concentrations of 0.1%–10% based on soil dry weight. Polyvinyl chloride and film induced significant effects at lower concentrations compared to other compositions and shapes, respectively. We adopted a species sensitivity distribution (SSD) and soil property effect distribution (SPED) method using available data from soil biota, and for soil properties and enzymes deemed relevant for microplastic management. The predicted-no-effect-concentration (PNEC)-like values needed to protect 95% of soil biota and soil properties was estimated to be between 520 and 655 mg kg−1. This study was the first to screen microplastic levels with a view toward protecting the soil system. Our results should be regularly updated (e.g., quarterly) with additional data as they become available.

scholarly journals A Comparison, Validation, and Evaluation of the S-world Global Soil Property Database

Land ◽  
2021 ◽  
Vol 10 (5) ◽  
pp. 544
Author(s):  
Jetse J. Stoorvogel ◽  
Vera L. Mulder
Keyword(s):  
Comparative Analysis ◽  
Soil Properties ◽  
Soil Property ◽  
Evaluation Criteria ◽  
Clay Content ◽  
Soil Database ◽  
Global Environmental ◽  
Global Soil ◽  
Mean Square Difference ◽  
Methodological Evaluation

Despite the increased usage of global soil property maps, a proper review of the maps rarely takes place. This study aims to explore the options for such a review with an application for the S-World global soil property database. Global soil organic carbon (SOC) and clay content maps from S-World were studied at two spatial resolutions in three steps. First, a comparative analysis with an ensemble of seven datasets derived from five other global soil databases was done. Second, a validation of S-World was done with independent soil observations from the WoSIS soil profile database. Third, a methodological evaluation of S-world took place by looking at the variation of soil properties per soil type and short distance variability. In the comparative analysis, S-World and the ensemble of other maps show similar spatial patterns. However, the ensemble locally shows large discrepancies (e.g., in boreal regions where typically SOC contents are high and the sampling density is low). Overall, the results show that S-World is not deviating strongly from the model ensemble (91% of the area falls within a 1.5% SOC range in the topsoil). The validation with the WoSIS database showed that S-World was able to capture a large part of the variation (with, e.g., a root mean square difference of 1.7% for SOC in the topsoil and a mean difference of 1.2%). Finally, the methodological evaluation revealed that estimates of the ranges of soil properties for the different soil types can be improved by using the larger WoSIS database. It is concluded that the review through the comparison, validation, and evaluation provides a good overview of the strengths and the weaknesses of S-World. The three approaches to review the database each provide specific insights regarding the quality of the database. Specific evaluation criteria for an application will determine whether S-World is a suitable soil database for use in global environmental studies.

Profile Soil Property Estimation Using a VIS-NIR-EC-Force Probe

2017 ◽  
Vol 60 (3) ◽  
pp. 683-692 ◽  
Author(s):  
Yongjin Cho ◽  
Kenneth A. Sudduth ◽  
Scott T. Drummond
Keyword(s):  
Soil Properties ◽  
Water Content ◽  
Bulk Density ◽  
Soil Property ◽  
Soil Strength ◽  
Reflectance Spectra ◽  
Land Resource ◽  
Strength Data ◽  
Soil Sensors ◽  
Combining Data

Abstract. Combining data collected in-field from multiple soil sensors has the potential to improve the efficiency and accuracy of soil property estimates. Optical diffuse reflectance spectroscopy (DRS) has been used to estimate many important soil properties, such as soil carbon, water content, and texture. Other common soil sensors include penetrometers that measure soil strength and apparent electrical conductivity (ECa) sensors. Previous field research has related these sensor measurements to soil properties such as bulk density, water content, and texture. A commercial instrument that can simultaneously collect reflectance spectra, ECa, and soil strength data is now available. The objective of this research was to relate laboratory-measured soil properties, including bulk density (BD), total organic carbon (TOC), water content (WC), and texture fractions to sensor data from this instrument. At four field sites in mid-Missouri, profile sensor measurements were obtained to 0.9 m depth, followed by collection of soil cores at each site for laboratory measurements. Using only DRS data, BD, TOC, and WC were not well-estimated (R2 = 0.32, 0.67, and 0.40, respectively). Adding ECa and soil strength data provided only a slight improvement in WC estimation (R2 = 0.47) and little to no improvement in BD and TOC estimation. When data were analyzed separately by major land resource area (MLRA), fusion of data from all sensors improved soil texture fraction estimates. The largest improvement compared to reflectance alone was for MLRA 115B, where estimation errors for the various soil properties were reduced by approximately 14% to 26%. This study showed promise for in-field sensor measurement of some soil properties. Additional field data collection and model development are needed for those soil properties for which a combination of data from multiple sensors is required. Keywords: NIR spectroscopy, Precision agriculture, Reflectance spectra, Soil properties, Soil sensing.

“Single Value” Soil Properties: A Study of the Significance of Certain Soil Constants. V. On the Changes Produced in a Soil by Oven Drying (With One Text-figure.)

1930 ◽  
Vol 20 (4) ◽  
pp. 541-548 ◽  
Author(s):  
J. R. H. Coutts
Keyword(s):  
Soil Properties ◽  
Soil Water ◽  
Soil Property ◽  
Sufficient Accuracy ◽  
Smooth Curves ◽  
Oven Drying ◽  
Satisfactory Degree ◽  
Different Types ◽  
Text Figure ◽  
Soil Colloids

1. It is shown that results for the loss in weight of a soil on oven heating can be obtained to a very satisfactory degree of accuracy when a Hearson electrically controlled oven is used.2. Results obtained by heating soils to temperatures ranging from 5° to 250° give smooth curves connecting loss in weight with rise in temperature; from which it is concluded that there is no sudden alteration in the structure of a soil when it is heated to 100°, and that the airdry moisture of a soil, as determined with sufficient accuracy by the usual methods, is a convenient empirical factor, but not a representation of any fundamental soil property.3. An examination is made of the factors contributing to the observed total loss in weight when the soil is heated, and an explanation offered of the contributions made by the different types of soil water and by the soil colloids. It is found that the conclusions drawn from this discussion confirm views developed earlier with regard to the behaviour of the water in the soil, and the absence of any sharp dividing line between the different classes into which the soil water is usually divided.

Measurement error-filtered machine learning in digital soil mapping

2021 ◽  
Author(s):  
Stephan van der Westhuizen ◽  
Gerard Heuvelink ◽  
David Hofmeyr
Keyword(s):  
Machine Learning ◽  
Measurement Error ◽  
Soil Property ◽  
Soil Mapping ◽  
Digital Soil Mapping ◽  
Simulation Studies ◽  
True Value ◽  
Linear Relationships ◽  
The Difference ◽  
The Relationship

<p>Digital soil mapping (DSM) may be defined as the use of a statistical model to quantify the relationship between a certain observed soil property at various geographic locations, and a collection of environmental covariates, and then using this relationship to predict the soil property at locations where the property was not measured. It is also important to quantify the uncertainty with regards to prediction of these soil maps. An important source of uncertainty in DSM is measurement error which is considered as the difference between a measured and true value of a soil property.</p><p>The use of machine learning (ML) models such as random forests (RF) has become a popular trend in DSM. This is because ML models tend to be capable of accommodating highly non-linear relationships between the soil property and covariates. However, it is not clear how to incorporate measurement error into ML models. In this presentation we will discuss how to incorporate measurement error into some popular ML models, starting with incorporating weights into the objective function of ML models that implicitly assume a Gaussian error. We will discuss the effect that these modifications have on prediction accuracy, with reference to simulation studies.</p>

scholarly journals Inverse distance weighting interpolated soil properties and their related landslide occurrences

2018 ◽  
Vol 195 ◽  
pp. 03013 ◽  
Author(s):  
Purwanto B. Santoso ◽  
Yanto ◽  
Arwan Apriyono ◽  
Rani Suryani
Keyword(s):  
Internal Friction ◽  
Slope Stability ◽  
Soil Properties ◽  
Hard Rock ◽  
Friction Angle ◽  
Inverse Distance Weighting ◽  
Central Java ◽  
Soil Cohesion ◽  
Distance Weighting ◽  
Inverse Distance

The causes of landslides can be categorized into three factors: climate, topographic, and soil properties. In many cases, thematic maps of landslide hazards do not involve slope stability analyses to predict the region of potential landslide risks. Slope stability calculation is required to determine the safety factor of a slope. The calculation of slope stability requires the soil properties, such as soil cohesion, the internal friction angle and the depth of hard-rock. The soil properties obtained from the field and laboratory investigation from the western part of Central Java were interpolated using Inverse Distance Weighting (IDW) to estimate the unknown soil properties in the gridded area. In this research, the IDW optimum parameter was determined by validation toward the percent bias. It was found that the IDW interpolation using higher weighting factor corresponds with a higher percent bias in case of the depth of hard-rock and soil cohesion, while the opposite was found for the internal friction angle. Validation to landslide incidents in western parts of Central Java shows that the majority of landslide incidents occur at depths of hard rock of 6 m-8 m, at soil cohesions of 0.0 kg/cm2-0.2 kg/cm2, and at internal friction angles of 30°-40°.

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