Comment on hess-2021-86

Three-dimensional digital soil mapping of multiple soil properties at a field-scale using regression kriging

In the last two decades, machine learning (ML) methods have been widely used in digital soil mapping (DSM), but the regression kriging (RK) model which combines the advantages of the ML and kriging methods has rarely been used in DSM. In addition, due to the limitation of a single-model structure, many ML methods have poor prediction accuracy in undulating terrain areas. In this study, we collected the SOC content of 115 soil samples in a hilly farming area with continuous undulating terrain. According to the theory of soil-forming factors in pedogenesis, we selected 10 topographic indices, 7 vegetation indices, and 2 soil indices as environmental covariates, and according to the law of geographical similarity, we used ML and RK methods to mine the relationship between SOC and environmental covariates to predict the SOC content. Four ensemble models-random forest (RF), Cubist, stochastic gradient boosting (SGB), and Bayesian regularized neural networks (BRNNs)-were used to fit the trend of SOC content, and the simple kriging (SK) method was used to interpolate the residuals of the ensemble models, and then the SOC and residual were superimposed to obtain the RK prediction result. Moreover, the 115 samples were divided into calibration and validation sets at a ratio of 80%, and the tenfold cross-validation method was used to fit the optimal parameters of the model. From the results of four ensemble models: RF performed best in the calibration set (R2c = 0.834) but poorly in the validation set (R2v = 0.362); Cubist had good accuracy and stability in both the calibration and validation sets (R2c = 0.693 and R2v = 0.445); SGB performed poorly (R2c = 0.430 and R2v = 0.336); and BRNN had the lowest accuracy (R2c = 0.323 and R2v = 0.282). The results showed that the R2 of the four RK models in the validation set were 0.718, 0.674, 0.724, and 0.625, respectively. Compared with the ensemble models without superimposed residuals, the prediction accuracy was improved by 0.356, 0.229, 0.388, and 0.343, respectively. In conclusion, Cubist has high prediction accuracy and generalization ability in areas with complex topography, and the RK model can make full use of trends and spatial structural factors that are not easy to mine by ML models, which can effectively improve the prediction accuracy. This provides a reference for soil survey and digital mapping in complex terrain areas.

Comparison between geostatistical and machine learning models as predictors of topsoil organic carbon with a focus on local uncertainty estimation

One of the most robust empirical findings in political science is that in multiparty democracies cabinet ministries are distributed in rough proportion to parties’ legislative seat shares, a pattern known as Gamson’s Law. Yet existing research often overlooks the fact that portfolio and seat shares are compositional—mutually dependent parts of a whole. Standard methods treat them as unconstrained, risking bias, misleading uncertainty estimates, and flawed inference. Unfortunately, the most common strategy for handling compositions—the additive log-ratio (ALR) transformation combined with seemingly unrelated regression (SUR)—fails when the number and identity of compositional elements (like parties) vary across cases. We propose the isometric log-ratio (ILR) transformation—new to political science—as an alternative that both respects compositional geometry and adapts to differing compositional structures. Monte Carlo simulations show that ILR sharply outperforms standard approaches, reducing bias, improving coverage probability, and increasing statistical power. While we apply it to portfolio allocation, ILR provides a general solution for modeling compositional outcomes with other potential uses, including in electoral competition, where ALR+SUR has required strong assumptions or ad hoc adjustments. Using this improved methodology, we find that seat–portfolio proportionality is weaker overall than conventionally reported and varies substantially across governments.

Visible, near-infrared, and shortwave-infrared spectra as an input variable for digital mapping of soil organic carbon

A new class of [formula omitted]-transformations for the spatial analysis of Compositional Data

Evapotranspiration (ET) is a vital variable for land‐atmosphere interactions that links surface energy balance, water, and carbon cycles. The in situ techniques can measure ET accurately but the observations have limited spatial and temporal coverage. Modeling approaches have been used to estimate ET at broad spatial and temporal scales, while accurately simulating ET at regional scales remains a major challenge. In this study, we upscale ET from eddy covariance flux tower sites to the regional scale with machine learning algorithms. Five machine learning algorithms are employed for ET upscaling including artificial neural network, Cubist, deep belief network, random forest, and support vector machine. The machine learning methods are trained and tested at 36 flux towers sites (65 site years) across the Heihe River Basin and are then applied to estimate ET for each grid cell (1 km × 1 km) within the watershed and for each day over the period 2012–2016. The artificial neural network, Cubist, random forest, and support vector machine algorithms have almost identical performance in estimating ET and have slightly lower root‐mean‐square error than deep belief network at the site scale. The random forest algorithm has slightly lower relative uncertainty at the regional scale than other methods based on three‐cornered hat method. Additionally, the machine learning methods perform better over densely vegetated conditions than barren land or sparsely vegetated conditions. The regional ET generated from the machine learning approaches captured the spatial and temporal patterns of ET at the regional scale.

Available accurate and reliable precipitation data are so important in water resources management and planning. In this study,to determine the best method of regional precipitation estimate in Khuzestan province, estimated daily precipitation data from the best interpolation method and APHRODIT Daily Grid Precipitation data during the 2000-2007 years were compared with 44 meteorological stations. Four interpolation methods i.e. Inverse Distance Weighted, Ordinary Kriging, Cokriging, and Regression Kriging were assessed to determine the most appropriate interpolation method for daily precipitation.For the variography analysis in Kriging models, five variogram models including spherical, exponential, linear, linear to sill and Gaussian fitted on the precipitation data. Near neighbor method was used to compare APHRODIT Daily Precipitation data with station recorded data. Cross validation technique was employed to evaluate the interpolation methods and the most appropriate method was determined based on Root Mean Square Error,Mean Bias Error, Mean Absolute Error indices and regression analysis. The result of error evaluation of interpolation methods showed that regression Kriging method has the highest accurate to interpolation of daily precipitation data in Khuzestan province. Therefore, regression-based interpolation methods which using covariates would be improved precipitation evaluate accurate in the area. Comparison of error indices and regression analysis of regression Kriging interpolation method and estimate of APHRODITE show that on most days the accurately estimate of regression Kriging is higher than the APHRODITE. Therefore to understanding of spatial distribution and estimate of daily precipitation data in Khuzestan Province, Regression Kriging interpolation method is more accurate than available APHRODITE data

Spatially continuous and accurate estimation of forest aboveground biomass (AGB) is essential for understanding carbon storage, ecosystem health, and biodiversity. Forests of the southeastern United States (US) represent about 40% of the nation’s forest area and one of the most significant carbon sequestration and storage potentials in the US. The availability of data from more recent and long-standing Earth-observing missions, like spaceborne light detection and ranging data from NASA’s Ice, Cloud, and land Elevation Satellite-2 (ICESat-2) and imagery from Landsat satellites, present an exemplary opportunity to characterize vegetation structure and AGB. Despite this potential, the extent to which data from these ongoing missions can be used synergistically for AGB estimation at the regional scale is not well known. This study served to better understand the combined utility of Landsat and ICESat-2 for developing a large-area AGB mapping framework. Specifically, this work served to: (1) determine the best modeling technique for estimating field-derived AGB using ICESat-2 and Landsat-derived variables, among machine learning (random forest (RF) and support vector machine (SVM)) and geostatistical approaches (random forest regression kriging (RFRK) and support vector machine regression kriging (SVMRK)), and (2) create a high-resolution (30 m) baseline AGB map for the year 2020 across ~254,266 km² of forests of the southeastern US. Canopy height information from ICESat-2, Landsat-8 imagery and imagery-derived variables, digital elevation models, and canopy cover were used to model AGB. Resulting models yielded R2 values ranging from 0.34 to 0.61, and RMSEs between 22 and 31 Mg/ha. Evidently, AGB estimated using the SVMRK model was substantially better than the other models (R2 = 0.61 and RMSE = 23.99 Mg/ha), highlighting its potential for broad-scale AGB mapping. Overall, this work highlights a feasible approach for deriving spatially comprehensive AGB information for southeastern US forests and provides a high-resolution AGB baseline product to support regional-scale monitoring.

Spatial prediction of soil organic matter in the presence of different external trends with REML-EBLUP

The availability of canopy height information in the Ice, Cloud, and Land Elevation Satellite-2’s (ICESat-2’s) land and vegetation product, or ATL08, presents opportunities for developing full-coverage products over broad spatial scales. The primary goal of this study was to develop a 30-meter canopy height map over the southeastern US, for the Southeastern Plains ecoregion and the Middle Atlantic Coastal Plains ecoregion. More specifically, this work served to compare well-known modeling approaches for upscaling canopy information from ATL08 to develop a wall-to-wall product. Focusing on only strong beams from nighttime acquisitions, the h_canopy parameter was extracted from ATL08 data. Landsat-8 bands and derived vegetation indices (normalized difference vegetation index, enhanced vegetation index, and modified soil-adjusted vegetation index) along with National Land Cover Database’s canopy cover and digital elevation models were used to extrapolate ICESat-2 canopy height from tracks to the regional level. Two different modeling techniques, random forest (RF) and regression kriging (RK), were applied for estimating canopy height. The RF model estimated canopy height with a coefficient of determination (R2) value of 0.48, root-mean-square error (RMSE) of 4.58 m, mean absolute error (MAE) of 3.47 and bias of 0.23 for independent validation, and an R2 value of 0.38, RMSE of 6.39 m, MAE of 5.04 and bias of −1.39 when compared with airborne lidar-derived canopy heights. The RK model estimated canopy heights with an R2 value of 0.69, RMSE of 3.49 m, MAE of 2.61 and bias of 0.03 for independent validation, and an R value of 0.68, R2 value of 0.47, RMSE of 5.96m, MAE of 4.52 and bias of −1.81 when compared with airborne lidar-derived canopy heights. The results suggest feasibility for the implementation of the RK method over a larger spatial extent and potential for combining other remote sensing and satellite data for future monitoring of canopy height dynamics.

수문학, 기상학 및 기후학 등에서 필수적인 자료중의 하나인 지상기온 자료는 최근 보건, 생물, 환경 등의 다양한 분야로까지 활용영역이 확대되고 있어 그 중요성이 커지고 있으나 지상관측을 통한 지상기온자료의 취득은 시공간적인 제약이 크기 때문에 실측된 기온자료는 시공간 해상도가 낮아 높은 해상도가 요구되는 연구 분야에서는 활용성에 큰 제약을 갖게 된다. 이를 극복하기 위한 하나의 대안으로 상대적으로 높은 시공간 해상도를 가지고 있는 위성영상자료에서 얻을 수 있는 지표면온도 자료를 이용하여 지상기온을 추정하는 많은 연구들이 수행되어 왔다. 본 연구는 이러한 연구의 일환으로써 기상청에서 제공하고 있는 AWS(Automatic Weather Station)에서 취득된 2010년 지상 온도 자료(AWS data)를 바탕으로 대표적인 지표면 온도자료인 MODIS Land Surface temperature(LST data:MOD11A1)와 지상기온에 영향을 미칠 수 있는 Land Cover Data, DEM(digital elevation model) 등의 보조 자료와 함께 다양한 지구통계 기법들을 이용하여 남한 지역의 지상기온을 추정하였다. 추정 전 2010년 전체(365일) LST자료와 AWS자료와의 차이에 대한 RMSE(Root Mean Square Error)값의 계절별 피복별 분석결과 계절에 따른 RMSE값의 변동계수는 0.86으로 나타났으나 피복에 따른 변동계수는 0.00746으로 나타나 계절별 차이가 피복별 차이보다 큰 것으로 분석 되었다. 계절별 RMSE 값은 겨울철이 가장 낮은 것으로 나타났으며 AWS자료와 LST자료와 보조자료를 이용한 선형 회귀분석결과에서도 겨울철의 결정 계수가 가장 높은 0.818로 나타났으며, 여름철의 경우에는 0.078로 나타나 계절별 차이가 매우 크게 나타났다. 이러한 결과를 바탕으로 지구통계 기법들의 대표적인 방법론인 크리깅 방법 중 일반적으로 많이 사용되고 있는 정규 크리깅, 일반 크리깅, 공동 크리킹, 회귀 크리깅을 이용하여 지상기온을 추정한 후 모델의 정확도를 판단할 수 있는 교차 검증을 실시한 결과 정규 크리깅과 일반 크리깅에 의한 RMSE 값은 1.71, 공동 크리깅과 회귀 크리깅에 의한 RMSE 값은 각각 1.848, 1.63으로 나타나 회귀 크리깅 방법에 의한 추정의 정확도가 가장 높은 것으로 분석되었다. Near surface air temperature data which are one of the essential factors in hydrology, meteorology and climatology, have drawn a substantial amount of attention from various academic domains and societies. Meteorological observations, however, have high spatio-temporal constraints with the limits in the number and distribution over the earth surface. To overcome such limits, many studies have sought to estimate the near surface air temperature from satellite image data at a regional or continental scale with simple regression methods. Alternatively, we applied various Kriging methods such as ordinary Kriging, universal Kriging, Cokriging, Regression Kriging in search of an optimal estimation method based on near surface air temperature data observed from automatic weather stations (AWS) in South Korea throughout 2010 (365 days) and MODIS land surface temperature (LST) data (MOD11A1, 365 images). Due to high spatial heterogeneity, auxiliary data have been also analyzed such as land cover, DEM (digital elevation model) to consider factors that can affect near surface air temperature. Prior to the main estimation, we calculated root mean square error (RMSE) of temperature differences from the 365-days LST and AWS data by season and landcover. The results show that the coefficient of variation (CV) of RMSE by season is 0.86, but the equivalent value of CV by landcover is 0.00746. Seasonal differences between LST and AWS data were greater than that those by landcover. Seasonal RMSE was the lowest in winter (3.72). The results from a linear regression analysis for examining the relationship among AWS, LST, and auxiliary data show that the coefficient of determination was the highest in winter (0.818) but the lowest in summer (0.078), thereby indicating a significant level of seasonal variation. Based on these results, we utilized a variety of Kriging techniques to estimate the surface temperature. The results of cross-validation in each Kriging model show that the measure of model accuracy was 1.71, 1.71, 1.848, and 1.630 for universal Kriging, ordinary Kriging, cokriging, and regression Kriging, respectively. The estimates from regression Kriging thus proved to be the most accurate among the Kriging methods compared.

"The pattern of variation in soil and landform properties in relation to environmental covariates are closely related to soil type distribution. The aim of this study was to apply digital soil mapping techniques to analysis of the pattern of soil property variation in relation to environmental covariates under periglacial conditions at Keller Peninsula, Maritime Antarctica. We considered the hypothesis that covariates normally used for environmental correlation elsewhere can be adequately employed in periglacial areas in Maritime Antarctica. For that purpose, 138 soil samples from 47 soil sites were collected for analysis of soil chemical and physical properties. We tested the correlation between soil properties (clay, potassium, sand, organic carbon, and pH) and environmental covariates. The environmental covariates selected were correlated with soil properties according to the terrain attributes of the digital elevation model (DEM). The models evaluated were linear regression, ordinary kriging, and regression kriging. The best performance was obtained using normalized height as a covariate, with an R2 of 0.59 for sand. In contrast, the lowest R2 of 0.15 was obtained for organic carbon, also using the regression kriging method. Overall, results indicate that, despite the predominant periglacial conditions, the environmental covariates normally used for digital terrain mapping of soil properties worldwide can be successfully employed for understanding the main variations in soil properties and soil-forming factors in this region."

Can pedotransfer functions based on environmental variables improve soil total nutrient mapping at a regional scale?

This study introduces a novel groundwater pollution index (GPI) formulated through compositional data analysis (CoDa) and robust principal component analysis (RPCA) to enhance groundwater quality assessment. Using groundwater quality monitoring data from sites impacted by the 2010–2011 foot-and-mouth disease outbreak in South Korea, CoDa uncovers critical hydrochemical differences between leachate-influenced and background groundwater. The GPI was developed by selecting key subcompositional parts (NH4+-N, Cl-, and NO3--N) using RPCA, performing the isometric log-ratio (ILR) transformation, and normalizing the results to environmental standards, thereby providing a more precise and accurate assessment of pollution. Validated against government criteria, the GPI has shown its potential as an alternative assessment tool, with its reliability confirmed by receiver operating characteristic curve analysis. This study highlights the essential role of CoDa, especially the ILR -transformation, in overcoming the limitations of traditional statistical methods that often neglect the relative nature of hydrochemical data. Our results emphasize the utility of the GPI in significantly advancing groundwater quality monitoring and management by addressing a methodological gap in the quantitative assessment of groundwater pollution.