Residual Standard Deviation Research Articles

“Site response analysis considering strain compatible site period”

In practice it is common to estimate site effects using a single proxy, or single variable such as 30m shear wave velocity (VS30) or site period. Many studies have investigated merits of proposed proxies with contradicting recommendations. Yet, most studies indicate the single proxy approach is less than ideal, resulting in large uncertainty. To provide a better understanding of components that drive site response, we performed a parameterized study on 19 shallow soil profiles with VS ranging from 150m/s to 400m/s. We propagated 74 input motions through each soil column using one-dimensional equivalent-linear method to produce 1406 site response analyses. The resulting amplification factors (the ratio of surface to base motion) were then analyzed statistically to identify trends. The mean amplification factor, averaged from 74 records, was used to isolate and quantify the effects of VS on site response. Based on analysis of record-to-record trends, we identified two separate mechanisms through which nonlinearity affects site response including “damping increase” and “site period shift”. The interaction of these two mechanisms makes amplification-shaking intensity models highly depth-dependent. The residual standard deviation of amplification factor based on depth-independent models was found to be up to three times larger than the corresponding standard deviation based on depth-specific models. We found strain compatible site period a promising site parameter that complements the predictive information obtained from VS. Finally, a simplified procedure providing a five-point estimate of site transfer function is outlined. The proposed procedure can fill the gap in current practice for an intermediate solution between the numerically rigorous solution and the single proxy approach. Implementation of this procedure is demonstrated in an example.

Automated system measuring triple oxygen and nitrogen isotope ratios in nitrate using the bacterial method and N2O decomposition by microwave discharge

RationaleTriple oxygen and nitrogen isotope ratios in nitrate are powerful tools for assessing atmospheric nitrate formation pathways and their contribution to ecosystems. N2O decomposition using microwave‐induced plasma (MIP) has been used only for measurements of oxygen isotopes to date, but it is also possible to measure nitrogen isotopes during the same analytical run.MethodsThe main improvements to a previous system are (i) an automated distribution system of nitrate to the bacterial medium, (ii) N2O separation by gas chromatography before N2O decomposition using the MIP, (iii) use of a corundum tube for microwave discharge, and (iv) development of an automated system for isotopic measurements. Three nitrate standards with sample sizes of 60, 80, 100, and 120 nmol were measured to investigate the sample size dependence of the isotope measurements.ResultsThe δ17O, δ18O, and Δ17O values increased with increasing sample size, although the δ15N value showed no significant size dependency. Different calibration slopes and intercepts were obtained with different sample amounts. The slopes and intercepts for the regression lines in different sample amounts were dependent on sample size, indicating that the extent of oxygen exchange is also dependent on sample size. The sample‐size‐dependent slopes and intercepts were fitted using natural log (ln) regression curves, and the slopes and intercepts can be estimated to apply to any sample size corrections. When using 100 nmol samples, the standard deviations of residuals from the regression lines for this system were 0.5‰, 0.3‰, and 0.1‰, respectively, for the δ18O, Δ17O, and δ15N values, results that are not inferior to those from other systems using gold tube or gold wire.ConclusionsAn automated system was developed to measure triple oxygen and nitrogen isotopes in nitrate using N2O decomposition by MIP. This system enables us to measure both triple oxygen and nitrogen isotopes in nitrate with comparable precision and sample throughput (23 min per sample on average), and minimal manual treatment. Copyright © 2016 John Wiley & Sons, Ltd.

Sufficiency Economy Philosophy and Firm Risks

Using data from Thailand, we designed and created our Sufficiency Economy Philosophy score (SEP score) that measures the extent to which a firm is aligned with Sufficiency Economy Philosophy. We find that our SEP score has a negative relationship with firm-specific risk measured by the standard deviation of residuals from the market model. However we find no relationship between SEP score with neither market risk nor other measures of firms’ performance. The findings support the notion that alignment with Sufficiency Economy Philosophy could reduce risk without sacrificing performance, it leads to sustainability, and that Sufficiency Economy Philosophy practices are well aligned with shareholders’ interests.

Individualized Prediction of Changes in 6-Minute Walk Distance for Patients with Duchenne Muscular Dystrophy.

BackgroundDeficits in ambulatory function progress at heterogeneous rates among individuals with Duchenne muscular dystrophy (DMD). The resulting inherent variability in ambulatory outcomes has complicated the design of drug efficacy trials and clouded the interpretation of trial results. We developed a prediction model for 1-year change in the six minute walk distance (6MWD) among DMD patients, and compared its predictive value to that of commonly used prognostic factors (age, baseline 6MWD, and steroid use).MethodsNatural history data were collected from DMD patients at routine follow up visits approximately every 6 months over the course of 2–5 years. Assessments included ambulatory function and steroid use. The annualized change in 6MWD (Δ6MWD) was studied between all pairs of visits separated by 8–16 months. Prediction models were developed using multivariable regression for repeated measures, and evaluated using cross-validation.ResultsAmong n = 191 follow-up intervals (n = 39 boys), mean starting age was 9.4 years, mean starting 6MWD was 351.8 meters, and 75% had received steroids for at least one year. Over the subsequent 8–16 months, mean Δ6MWD was -37.0 meters with a standard deviation (SD) of 93.7 meters. Predictions based on a composite of age, baseline 6MWD, and steroid use explained 28% of variation in Δ6MWD (R2 = 0.28, residual SD = 79.4 meters). A broadened prognostic model, adding timed 10-meter walk/run, 4-stair climb, and rise from supine, as well as height and weight, significantly improved prediction, explaining 59% of variation in Δ6MWD after cross-validation (R2 = 0.59, residual SD = 59.7 meters).ConclusionsA prognostic model incorporating timed function tests significantly improved prediction of 1-year changes in 6MWD. Explained variation was more than doubled compared to predictions based only on age, baseline 6MWD, and steroid use. There is significant potential for composite prognostic models to inform DMD clinical trials and clinical practice.

Residual standard deviation: Validation of a new measure of dual-task cost in below-knee prosthesis users

We developed and evaluated properties of a new measure of variability in stride length and cadence, termed residual standard deviation (RSD). To calculate RSD, stride length and cadence are regressed against velocity to derive the best fit line from which the variability (SD) of the distance between the actual and predicted data points is calculated. We examined construct, concurrent, and discriminative validity of RSD using dual-task paradigm in 14 below-knee prosthesis users and 13 age- and education-matched controls. Subjects walked first over an electronic walkway while performing separately a serial subtraction and backwards spelling task, and then at self-selected slow, normal, and fast speeds used to derive the best fit line for stride length and cadence against velocity. Construct validity was demonstrated by significantly greater increase in RSD during dual-task gait in prosthesis users than controls (group-by-condition interaction, stride length p=0.0006, cadence p=0.009). Concurrent validity was established against coefficient of variation (CV) by moderate-to-high correlations (r=0.50–0.87) between dual-task cost RSD and dual-task cost CV for both stride length and cadence in prosthesis users and controls. Discriminative validity was documented by the ability of dual-task cost calculated from RSD to effectively differentiate prosthesis users from controls (area under the receiver operating characteristic curve, stride length 0.863, p=0.001, cadence 0.808, p=0.007), which was better than the ability of dual-task cost CV (0.692, 0.648, respectively, not significant). These results validate RSD as a new measure of variability in below-knee prosthesis users. Future studies should include larger cohorts and other populations to ascertain its generalizability.

Estimation of the effects of selection on French Large White reproductive performance using frozen semen.

Genetic trends for male and female sexual development and components of litter size and weight at birth (LB) as well as traits related to sow lifetime productivity were estimated in a French Large White (LW) pig population using frozen semen. Two experimental groups (EXP = L77 and L98) were produced by inseminating LW sows with either stored frozen semen from 17 LW boars born in 1977 (EXP = L77) or with semen from 23 LW boars born in 1998 (EXP = L98). In each group, about 100 males were measured for testicular development and bulbo-urethral gland development, and 90 gilts were checked for puberty, among which about 50 gilts were measured for their first ovulation rate at puberty (ORP). The females were then mated to 15 randomly chosen males for each group for 6 successive parities and measured for total number born (TNB), number born alive (NBA), litter weight at birth (LWB), and interval from weaning to first estrus as well as ovulation rate at fertilization (ORF = ovulation rate of gestating sows) on a subset of litters. The data were analyzed using mixed linear models including the fixed effects of EXP, of finishing (sexual development traits) or farrowing group, and parity (LB traits); the random effects of birth litter (sexual development traits) or sow (LB traits); and, when relevant, age or BW as covariates. The homogeneity of residual variances across EXP was also tested. For each trait, the genetic trend was estimated as twice the difference between L98 and L77. Limited differences were observed for sexual development traits, except for ORF, which increased by 0.17 ± 0.06/yr. The residual SD of NBA (2.7 vs. 2.0; = 0.004) and LWB (3.1 vs. 2.5; = 0.03) were larger in L98 sows than in L77 sows. Positive trends were observed for all litter traits (0.22 ± 0.07 ova, 0.12 ± 0.04 piglet, 0.09 ± 0.04 piglet, and 0.23 ± 0.06 kg/yr for ORF, TNB, NBA, and LWB, respectively) but at the expense of a degradation of prenatal and farrowing survival. A negative trend was also observed for length of productive life (-8.9 ± 3.9 d/yr). These results suggest that gains in productivity were associated with a loss of robustness.

대량 데이터를 위한 제한거절 기반의 회귀부스팅 기법

The purpose of this study is to challenge a computational regression-type problem, that is handling large-size data, in which conventional metamodeling techniques often fail in a practical sense. To solve such problems, regression-type boosting, one of ensemble model techniques, together with bootstrapping-based re-sampling is a reasonable choice. This study suggests weight updates by the amount of the residual itself and a new error decision criterion which constructs an ensemble model of models selectively chosen by rejection limits. Through these ideas, we propose AdaBoost.RMU.R as a metamodeling technique suitable for handling large-size data. To assess the performance of the proposed method in comparison to some existing methods, we used 6 mathematical problems. For each problem, we computed the average and the standard deviation of residuals between real response values and predicted response values. Results revealed that the average and the standard deviation of AdaBoost.RMU.R were improved than those of other algorithms.

Low-complexity prediction of frequency-rich biosignals for lossless compression in wearable technologies.

Wearable technologies that store, monitor and analyse a range of biosignals are an area of significant growth and interest for both industry and academia. The rate of data generation in these devices poses a considerable challenge with regards to the bandwidths of wireless transmission protocols, local storage capacities and the on-board power consumption requirements. This issue is particularly acute for frequency-rich biosignals containing significant higher frequency components that are un-served by conventional compression techniques. This paper proposes a low-complexity predictor, based on a low-order infinite impulse response bandpass filter, to accurately predict such biosignals for use in lossless compression. Experimental evaluation of the method demonstrates that it outperforms conventional predictors with an average 25 % reduction in predictor residual standard deviation. The predictor described here enables high-bandwidth wearable sensors that can be employed in systems with reduced power consumption for transmission, storage and compression leading to considerable improvements in user experience by reducing device mass and increasing battery life.

Modelling, characterisation and uncertainties of stabilised pseudoelastic shape memory alloy helical springs

The thermo-mechanical behaviour of pseudoelastic shape memory alloy helical springs is of concern discussing stabilised and cyclic responses. Constitutive description of the shape memory alloy is based on the framework developed by Lagoudas and co-workers incorporating two modifications related to hardening and sub-loop functions designated by Bézier curves. The spring model takes into account both bending and torsion of the spring wire, thus representing geometrical non-linearities. Simplified models are explored showing that a single point in the wire cross section is enough to represent the global spring behaviour in spite of complex stress–strain distributions. The experiments are carried out considering different deflection amplitudes, frequencies and ambient temperatures, which influence the spring behaviour to different extents. The model is fitted against a calibration data set resulting in 1.3% residual standard deviation relative to the full range force. Compared to the validation data set, the errors are below 10% relative to the full range of the complex modulus. Uncertainty analysis of the model parameters using a Markov chain Monte Carlo technique shows low to high parameter correlation, and the relative uncertainties are less than ±12%. Both the heat capacity and the convection coefficient are clearly identifiable from the performed experiments.

Rapid, sensitive, and reproducible screening of liquid milk for adulterants using a portable Raman spectrometer and a simple, optimized sample well.

We have developed a powerful general spectroscopic method for rapidly screening liquid milk for adulterants by combining reflective focusing wells simply fabricated in aluminum with a small, portable Raman spectrometer with a focusing fiber optic probe. Hemispherical aluminum sample wells were specially designed to optimize internal reflection and sampling volume by matching the focal length of the mirror to the depth of focus of the laser probe. The technique was tested on milk adulterated with 4 different nitrogen-rich compounds (melamine, urea, dicyandiamide, and ammonium sulfate) and sucrose. No sample preparation of the milk was needed, and the total analysis time was 4min. Reliable sample presentation enabled average reproducibility of 8% residual standard deviation. The limit of detection interval measured from partial least squares calibrations ranged between 140 and 520mg/L for the 4 N-rich compounds and between 7,000 and 36,000mg/L (0.7-3.6%) for sucrose. The portability of the system and the reliability and reproducibility of this technique open opportunities for general, reagentless screening of milk for adulterants at the point of collection.

Chemical applicability domain of the Local Lymph Node Assay (LLNA) for skin sensitisation potency. Part 2. The biological variability of the murine Local Lymph Node Assay (LLNA) for skin sensitisation

The Local Lymph Node Assay (LLNA) is the most common in vivo regulatory toxicology test for skin sensitisation, quantifying potency as the EC3, the concentration of chemical giving a threefold increase in thymidine uptake in the local lymph node. Existing LLNA data can, along with clinical data, provide useful comparator information on the potency of sensitisers. Understanding of the biological variability of data from LLNA studies is important for those developing non-animal based risk assessment approaches for skin allergy. Here an existing set of 94 EC3 values for 12 chemicals, all tested at least three times in the same vehicle have been analysed by calculating standard deviations (SD) for logEC3 values. The SDs range from 0.08 to 0.22. The overall SD for the 94 logEC3 values is 0.147. Thus the 95% confidence limits (2xSD) for LLNA EC3 values are within a factor of 2, comparable to those for physico-chemical measurements such as partition coefficients and solubility. The residual SDs of Quantitative Mechanistic Models (QMMs) based on physical organic chemistry parameters are similar to the overall SD of the LLNA, indicating that QMMs of this type are unlikely to be bettered for predictive accuracy.

Screening for Adulterants in Liquid Milk Using a Portable Raman Miniature Spectrometer with Immersion Probe.

A portable Raman system with an immersion fiber optic probe was assessed for point-of-collection screening for the presence of adulterants in liquid milk. N-rich adulterants and sucrose were measured in this proof-of-concept demonstration. Reproducibility, limit of detection range and other figures of merit such as specificity, sensitivity, ratio of predicted to standard deviation, standard error of prediction and root mean squared error for cross validation were determined from partial least squares (PLS) and partial least squares with discriminant analysis (PLS-DA) calibrations of milk mixtures containing 50-1000 ppm (parts per million) of melamine, ammonium sulphate, Dicyandiamide, urea and sucrose. The spectra were recorded by immersing the fiber optic probe directly in the milk solutions. Despite the high scattering background which was easily and reliably estimated and subtracted, the reproducibility for four N-rich compounds averaged to 11% residual standard deviation (RSD) and to 5% RSD for sucrose. PLS calibration models predicted the concentrations of separate validation sets with standard errors of prediction of between 44 and 76 ppm for the four N-rich compounds and 0.17% for sucrose. The sensitivity and specificity of the PLS-DA calibration were 92% and 89%, respectively. The study shows promise for use of portable mini Raman systems for routine rapid point-of-collection screening of liquid milk for the presence of adulterants, without the need for sample preparation or addition of chemicals.

Extraction of full energy peak of 137Cs from in situ NaI (Tl) gamma-ray spectrum

A Levenberg–Marquardt Gaussian fitting algorithm has been used for analyzing the overlap of three peaks (the 583-keV peak of 208Tl, the 609-keV peak of 214Bi, and the 662-keV peak of 137Cs) using an in situ NaI (Tl) scintillation spectrometer. The algorithm, in addition, was compared with a genetic algorithm used for multiple deconvolution. The three fitted peak areas (583, 609, and 662 keV) were calculated from the measured gamma-ray spectra obtained from a simulation experiment in which a 137Cs source was buried at different soil depths (from 18 to 38 cm). The application of the Levenberg–Marquardt algorithm yielded similar results compared to the genetic algorithm. A lack-of-fit test showed that the fitting is good when the instrumental noise levels were estimated from replicated analyses. The relative fitting error of the total net area and the residual standard deviation were within 5 % and 0.04, respectively, and the goodness of the fitting was better than 0.98. While the methods used in this paper give high performance, the results may lead to incorrect estimation when the signal-to-noise ratio is smaller than −30 dB. This study is useful for the determination of radioactive specific activity of 137Cs by in situ spectrometry.

Accuracy of dual energy X-ray absorptiometry (DXA) in assessing carcass composition from different pig populations

The accuracy of dual energy X-ray absorptiometry (DXA) in assessing carcass composition from pigs with diverse characteristics was examined in the present study. A total of 648 pigs from three different sire breeds, two sexes, two slaughter weights and three different diets were employed. DXA estimations were used to predict the dissected/chemical yield for lean and fat of carcass sides and primal cuts. The accuracy of the predictions was assessed based on coefficient of determination (R2) and residual standard deviation (RSD). The linear relationships for dissected fat and lean for all the primal cuts and carcass sides were high (R2>0.94, P<0.01), with low RSD (<1.9%). Relationships between DXA and chemical fat and lean of pork bellies were also high (R2>0.94, P<0.01), with RSD <2.9%. These linear relationships remained high over the full range of variation in the pig population, except for sire breed, where the coefficient of determination decreased when carcasses were classified based on this variable.

Bowhead whale localization using asynchronous hydrophones in the Chukchi Sea.

This paper estimates bowhead whale locations and uncertainties using non-linear Bayesian inversion of their modally-dispersed calls recorded on asynchronous recorders in the Chukchi Sea, Alaska. Bowhead calls were recorded on a cluster of 7 asynchronous ocean-bottom hydrophones that were separated by 0.5-9.2 km. A warping time-frequency analysis is used to extract relative mode arrival times as a function of frequency for nine frequency-modulated whale calls that dispersed in the shallow water environment. Each call was recorded on multiple hydrophones and the mode arrival times are inverted for: the whale location in the horizontal plane, source instantaneous frequency (IF), water sound-speed profile, seabed geoacoustic parameters, relative recorder clock drifts, and residual error standard deviations, all with estimated uncertainties. A simulation study shows that accurate prior environmental knowledge is not required for accurate localization as long as the inversion treats the environment as unknown. Joint inversion of multiple recorded calls is shown to substantially reduce uncertainties in location, source IF, and relative clock drift. Whale location uncertainties are estimated to be 30-160 m and relative clock drift uncertainties are 3-26 ms.

Analysis of CNC machining based on characteristics of thermal errors and optimal design of experimental programs during actual cutting process

The compensation of thermal errors plays a critical role in developing the machine tools of intelligent computer numerically controlled (CNC). According to the international standards, the testing, modeling, and compensation of thermal error of CNC machine tools are carried out only in a so-called idling state where the spindle is free running without any workload. However, in practical applications, machine tools are often applied in the actual cutting state with more influence factors, such as cutting parameters, cooling liquid, and cutting force. Subsequently, the thermal characteristics at idling state and actual cutting state are compared and analyzed in this paper. It was found that the thermal error compensation model under idling state is not precise enough to be applied in actual cutting state. Also, further research finds that different combinations of cutting parameters, such as spindle speed and feed rate, also have influences on the accuracy of prediction and robustness of thermal error model under actual cutting state. Therefore, the cutting parameters of spindle speed, feed rate, depth of cut, and ambient temperature are studied with the usage of the Taguchi method. Through calculating signal-to-noise ratio (SN) of each combination through residual standard deviation of thermal error model, the combination of optimal cutting parameters can be obtained. The resultant analysis shows that the thermal error model under the combination of optimal cutting parameters demonstrates higher accuracy of prediction and better robustness.

Bowhead whale localization and environmental inversion using asynchronous hydrophones

This paper estimates bowhead whale locations and environmental properties using Bayesian inversion of the modal dispersion of whale calls recorded on asynchronous recorders in the shallow waters of the northeastern Chukchi Sea, Alaska. Bowhead calls were recorded on a Y-shaped cluster of seven autonomous ocean-bottom hydrophones, separated by up to 9.2 km. We use a warping time-frequency analysis to obtain frequency-dependent relative mode arrival times for nine frequency-modulated whale calls. Trans-dimensional inversion is applied to invert mode arrival times for the whale location, water sound-speed profile, subbottom layering and geoacoustic parameters, source instantaneous frequency (IF), relative recorder clock drifts, and residual error standard deviation, all with estimated uncertainties. Joint inversion of multiple calls is found to substantially reduce uncertainties on whale location, source IF, and clock drifts. Estimated whale location uncertainties are 30–160 m and clock drift uncertainties a...

Assessment of the accuracy of estimation of gestational age in cattle from placentome size using inverse regression

AIMS: To assess, in dairy cows between 60–160 days of gestation, whether the agreement between actual gestational age and that predicted by placentome size could be improved by using individual placentome measurements rather than a single average, and to identify how increasing the number of placentomes measured improved the prediction.METHODS: Data were obtained from 58 cows examined using transrectal ultrasonography every 10 days between 60–130 days, and every 15 days between 130–160 days of gestation. For each cow, four to six placentomes in each of the pregnant and non-pregnant horns were examined from the region of the uterus near to the cervix. A mixed-effects model, which included cow as a random effect, and a simple linear regression which ignored within-cow correlation, were fitted to the data. Inverse regression was used to compare the 95% prediction bands obtained for estimating gestational age using the means of three, five or eight placentome measurements.RESULTS: The fit of the mixed effects model was better than a simple linear regression (p<0.001) but the fitted lines from the two models were very similar. Using the simple regression model, for a mean placentome length of 15 mm estimated gestational age was 100 days, with 95% CI of 68–131 days for measurement of three placentomes, and 80–120 days for eight placentomes.CONCLUSIONS: The agreement between placentome size and gestational age was improved by increasing the number of placentomes measured. Direct comparison of these CI with those for other published fetal measures was not possible as similar prediction bands have not previously been calculated for fetal measures; however one study reported a residual SD which had been calculated using size measurements as the predictor variable and age as the response variable. Using these data 95% CI were calculated to be ±9 days for crown-rump length and ±25 days for uterine diameter. These are likely to be an underestimate of the true CI and do not take account of the increase in variance of the difference between predicted and actual gestational age as gestational age increases.CLINICAL RELEVANCE: Placentome measurement may be useful for estimating fetal age in late gestation. Further research is required to better establish the agreement between gestational age and the fetal measurements which are currently used to estimate fetal age.

Heparin Reversal After Cardiopulmonary Bypass: Are Point-of-Care Coagulation Tests Interchangeable?

Protamine is used to neutralize heparin after patient separation from cardiopulmonary bypass (CPB). Different bedside tests are used to monitor the adequacy of heparin neutralization. For this study, the interchangeability of the activated coagulation time (ACT) and thromboelastometry (ROTEM; Tem Innovations GmbH, Basel, Switzerland) clotting time (CT) ratios in children undergoing cardiac surgery was assessed. Single-center, retrospective, cohort study between September 2010 and January 2012. University children's hospital. The study comprised children 0 to 16 years old undergoing elective cardiac surgery with CPB. Exclusion criteria were preoperative coagulopathy, Jehovah's witnesses, and children in a moribund condition (American Society of Anesthesiologists score 5). None. After heparin neutralization with protamine, the ratio between ACT, with and without heparinase, and the CT measured with INTEM/HEPTEM (intrinsic test activated with ellagic acid was performed without heparinase [INTEM] and with heparinase [HEPTEM]) using tests of ROTEM were calculated. Agreement was evaluated using Cohen's kappa statistics, Passing-Bablok regression, and Bland-Altman analysis. Among the 173 patients included for analysis, agreement between both tests showed a Cohen's kappa statistic of 0.06 (95% CI: -0.02 to 0.14; p = 0.22). Bland-Altman analysis showed a bias of 0.01, with a standard deviation of 0.13, and limits of agreement between -0.24 and 0.26. Passing-Bablok regression showed a systematic difference of 0.40 (95% CI: 0.16-0.59) and a proportional difference of 0.61 (95% CI: 0.42-0.86). The residual standard deviation was 0.11 (95% CI: -0.22 to 0.22), and the test for linearity showed p = 0.10. ACT, with or without heparinase, and the INTEM/HEPTEM CT ratios are not interchangeable to evaluate heparin reversal after pediatric patient separation from CPB. Therefore, the results of these tests should be corroborated with the absence/presence of bleeding and integrated into center-specific treatment algorithms.

Three-dimensional geostatistical modeling of soil organic carbon: A case study in the Qilian Mountains, China

For mapping soil properties in three dimensions the simplest option is to choose a series of depth intervals, and to calibrate a two-dimensional (2-D) model for each interval. The alternative is to calibrate a full three dimensional (3-D) model that describes the variation in lateral and vertical direction. In 3-D modeling we must anticipate possible changes with depth of the effects of environmental covariates on the soil property of interest. This can be achieved by including interactions between the environmental covariates and depth. Also we must anticipate possible non-stationarity of the residual variance with depth. This can be achieved by fitting a 3-D correlation function, and multiplying the correlation between two points by the residual standard deviations at these two points that are a function of depth. In this paper various 3-D models of the natural logarithms of SOC are compared with 2-D depth-interval specific models. Five environmental covariates are used as predictors in modeling the lateral trend. In the 3-D models also depth was used as a predictor, either categorical, with categories equal to the depth intervals (3-Dcat), or continuous (3-Dcon). The covariance of the residuals in 3-D is modeled by a sum-metric covariance function. Both stationary and non-stationary variance models are fitted. In the non-stationary variance models the residual standard deviations are modeled either as a stepwise function or as a linear function of depth. In the 2-D models the regression coefficients differed largely between the depth intervals. In the 3-Dcat model extreme values for the regression coefficients were leveled out, and in the 3-Dcon model only the coefficients of NDVI and aspect changed with depth. The 3-Dcon model with a residual standard deviation that is a stepwise function of depth had the largest residual log-likelihood and smallest AIC among all 3-D models. Based on the cross-validation root mean squared error (RMSE) there was no single best model. Based on the mean and median of the standardized squared error (MSSE, MedSSE) the 2-D models outperformed all 3-D models. Overestimation of the prediction error variance by the kriging variance was less strong with the non-stationary variance models compared to the stationary variance models. 3-D modeling is required for realistic geostatistical simulation in spatial uncertainty analyses.