On the uncertainty of stream networks derived from elevation data: the error propagation approach

DEM error propagation methodology is extended to the derivation of vector-based objects (stream networks) using geostatistical simulations. First, point sampled elevations are used to fit a variogram model. Next 100 DEM realizations are generated using conditional sequential Gaussian simulation; the stream network map is extracted for each of these realizations, and the collection of stream networks is analyzed to quantify the error propagation. At each grid cell, the probability of the occurrence of a stream and the propagated error are estimated. The method is illustrated using two small data sets: Baranja hill (30 m grid cell size; 16 512 pixels; 6367 sampled elevations), and Zlatibor (30 m grid cell size; 15 000 pixels; 2051 sampled elevations). All computations are run in the open source software for statistical computing R: package geoR is used to fit variogram; package gstat is used to run sequential Gaussian simulation; streams are extracted using the open source GIS SAGA via the RSAGA library. The resulting stream error map (Information entropy of a Bernoulli trial) clearly depicts areas where the extracted stream network is least precise – usually areas of low local relief and slightly convex (0–10 difference from the mean value). In both cases, significant parts of the study area (17.3% for Baranja Hill; 6.2% for Zlatibor) show high error (H>0.5) of locating streams. By correlating the propagated uncertainty of the derived stream network with various land surface parameters sampling of height measurements can be optimized so that delineated streams satisfy the required accuracy level. Such error propagation tool should become a standard functionality in any modern GIS. Remaining issue to be tackled is the computational burden of geostatistical simulations: this framework is at the moment limited to small data sets with several hundreds of points. Scripts and data sets used in this article are available on-line via the www.geomorphometry.org website and can be easily adopted/adjusted to any similar case study

Hybrid kriging methods for interpolating sparse river bathymetry point data

Terrain models that represent riverbed topography are used for analyzing geomorphologic changes, calculating water storage capacity, and making hydrologic simulations. These models are generated by interpolating bathymetry points. River bathymetry is usually surveyed through cross-sections, which may lead to a sparse sampling pattern. Hybrid kriging methods, such as regression kriging (RK) and co-kriging (CK) employ the correlation with auxiliary predictors, as well as inter-variable correlation, to improve the predictions of the target variable. In this study, we use the orthogonal distance of a (x, y) point to the river centerline as a covariate for RK and CK. Given that riverbed elevation variability is abrupt transversely to the flow direction, it is expected that the greater the Euclidean distance of a point to the thalweg, the greater the bed elevation will be. The aim of this study was to evaluate if the use of the proposed covariate improves the spatial prediction of riverbed topography. In order to asses such premise, we perform an external validation. Transversal cross-sections are used to make the spatial predictions, and the point data surveyed between sections are used for testing. We compare the results from CK and RK to the ones obtained from ordinary kriging (OK). The validation indicates that RK yields the lowest RMSE among the interpolators. RK predictions represent the thalweg between cross-sections, whereas the other methods under-predict the river thalweg depth. Therefore, we conclude that RK provides a simple approach for enhancing the quality of the spatial prediction from sparse bathymetry data

Prostorno mapiranje kemijskih svojstava tla koristeći multivarijatnu geostatistiku. Studija s oraničnih tala u istočnoj Hrvatskoj

The spatial variability of soil chemical properties is affected by factors of soil formation and human activities. Understanding their spatial variability will improve agricultural production, reduce environmental problems (e.g., soil pollution, offsite effects), and achieve sustainable agroecosystems. The main objective was to study the spatial variability of pH, soil organic matter, available phosphorus, and available potassium using univariate and multivariate methods in cropland fields in eastern Croatia. For the study, 169 (0-30 cm) soil samples were collected in a 911 ha study area. The results showed that soils had slightly acidic pH, adequate available phosphorus and potassium values for crop production, and low soil organic matter concentration. The variability was high in available phosphorus and low in pH. Soil pH, soil organic matter, available phosphorus, and potassium nugget/sill ratio was 0.00, 2.79, 18.68, and 22.08, respectively. Auxiliary variables increased the accuracy of the predictions. Soil organic matter levels were below the recommendable, and this is very likely an anthropogenic effect, even though the intrinsic process influences soil organic matter. The heterogeneous distribution of phosphorus and potassium highlighted the necessity of fertilization in some areas. For the sustainability of agroecosystems, adaptable site-specific soil management strategies need to be implemented.Prostorna varijabilnost kemijskih svojstava tla uvjetovana je pedogenetskim čimbenicima i ljudskom aktivnošću. Razumijevanje prostorne varijabilnosti poboljšati će poljoprivrednu proizvodnju, smanjiti okolišne probleme (npr. zagađenje tla, off-site učinci), i postići održivost agroekosustava. Glavni cilj rada je istraživanje prostorne varijabilnosti pH, organske tvari i biljci pristupačnog fosfora i kalija, koristeći univarijatne i multivarijatne metode na oraničnim tlima u istočnoj Hrvatskoj. Za rad je prikupljeno 169 (0-30 cm) uzoraka tla s površine od 911 ha. Rezultati pokazuju da su tla blago kisela, adekvatnog sadržaja biljci pristupačnog fosfora i kalija za biljnu proizvodnju i niskog sadržaja organske tvari tla. Varijabilnost je visoka kod biljci pristupačnog fosfora i niska kod pH tla. pH tla, organska tvar te biljci pristupačan fosfor i kalij imaju nuget/sill omjer 0.00, 2.79, 18.68, i 22.08. Pomoćni podaci povećali su preciznost predikcije. Identificiran je sadržaj organske tvari tla ispod preporučljive razine i to vrlo vjerojatno radi antropogenog utjecaja, iako i pedogenetska svojstva utječu na organsku tvar tla. Heterogena distribucija fosfora i kalija istaknula je nužnost za gnojidbom u nekim područjima. Za održivost agroekosustava potrebno je provesti prilagodljive strategije korištenja i upravljanja tlima na svakoj pojedinoj lokaciji

Aylık yağışın konumsal dağılımının modellenmesinde farklı enterpolasyon yöntemlerinin karşılaştırmalı analizi

For many water resources planning and management studies such as water budget and hydrological modeling, it is very important to estimate areal precipitation from point observation stations. There are many deterministic and geostatistical methods for determining the spatial distribution of precipitation. In this study, the most widely used methods, inverse distance weighting (IDW), Simple Kriging (SK) and Co-Kriging (CK) are applied. It is the main objective of the study that Geographic Information Systems (GIS) techniques are used to compare widely preferred interpolation methods and to model the spatial distribution of monthly precipitation values for prediction in ungauged areas in Akarcay Sinanpasa and Suhut sub-basins, Turkey. At the same time, the effects of number of stations, basin area, characteristics and secondary data usage such as elevation on model performance are investigated. The IDW, a deterministic method and the SK-CK, geostatistical methods are compared with each other by cross validation technique and the applicability of the interpolation techniques for the study areas is analyzed. According to the cross validation test results of IDW, SK and CK methods, the mean RMSE (root mean square error) values of Sinanpasa sub-basin are respectively 13,76 mm, 9,32 mm and 8,72 mm while these values are 9,43 mm, 7,82 mm and 7,90 mm for Suhut sub-basin. Then, uncertainty analysis by means of PSE (prediction standard error) is applied to SK-CK methods with clear advantages over the IDW method and with the close RMSE values. In consideration of the results of the uncertainty analysis, the SK method with the mean PSE values 10,30 mm and 8,54 mm has a little superiority to the CK method whose average PSE values are 11,03 mm and 9,02 mm for both Sinanpasa and Suhut sub-basins, respectively. When the findings are evaluated, it can be seen that all three methods can be used for the study areas. The determination of the spatial distribution of precipitation in this way is considered to be beneficial for many water resources engineering studies in areas of ungauged/sparsely gauged.Su bütçesi ve hidrolojik modelleme gibi birçok su kaynakları planlama ve yönetim çalışmaları için noktasal yağış gözlemlerinden alansal yağışın tahmin edilmesi çok önemlidir. Yağışın konumsal dağılımının belirlenmesi için deterministik ve jeoistatistik birçok yöntem bulunmaktadır. Bu çalışmada en yaygın kullanılan uzaklığın tersi ile ağırlıklandırma (IDW), Simple Kriging (SK) ve CoKriging (CK) yöntemleri uygulanmıştır. Akarçay Sinanpaşa ve Şuhut alt havzalarında, Coğrafi Bilgi Sistemleri (CBS) teknikleri ile yaygın olarak tercih edilen enterpolasyon yöntemlerinin karşılaştırılması ve aylık yağış değerlerinin konumsal dağılımının ölçüm yapılmayan alanlarda tahmin yapılması için modellenmesi çalışmanın ana amacını oluşturmaktadır. Aynı zamanda istasyon sayısı, havza alanı, karakteristikleri ve yükseklik gibi ikincil veri kullanımının model performansları üzerindeki etkileri araştırılmıştır. Deterministik bir yöntem olan IDW ve jeoistatistik yöntemler olan SK-CK yöntemlerinin çapraz doğrulama tekniği ile performansları test edilerek karşılaştırılmış ve çalışma alanları için enterpolasyon tekniklerinin kullanılabilirliği incelenmiştir. IDW, SK ve CK yöntemlerinin çapraz doğrulama test sonuçlarına göre Sinanpaşa alt havzası için sırasıyla RMSE (karesel ortalama hata) değerleri 13,76 mm, 9,32 mm ve 8,72 mm iken; Şuhut alt havzası için 9,43 mm, 7,82 mm ve 7,90 mm'dir. IDW yöntemine kıyasla açık üstünlükleri olan ve yakın RMSE değerlerine sahip SK-CK yöntemlerine, ek olarak PSE (tahmin standart hatası) ile belirsizlik analizi uygulanmıştır. Belirsizlik analizi sonuçlarına göre hem Sinanpaşa hem de Şuhut alt havzaları için SK yöntemi sırasıyla 10,30 mm ve 8,54 mm PSE değerleriyle, 11,03 mm ve 9,02 mm PSE değerlerine sahip CK yöntemine az da olsa üstünlük sağlamıştır. Elde edilen bulgulara göre her üç yönteminde çalışma alanları için kullanılabilir olduğu görülmektedir. Bu şekilde yağışın konumsal dağılımının belirlenmesinin ölçüm yapılmayan veya kıt ölçüm yapılan alanlarda birçok su kaynakları mühendisliği çalışmaları için faydalı olacağı düşünülmektedir

Spatial prediction of soil properties in two contrasting physiographic regions in Brazil

This study compared the performance of ordinary kriging (OK) and regression kriging (RK) to predict soil physical-chemical properties in topsoil (0-15 cm). Mean prediction of error and root mean square of prediction error were used to assess the prediction methods. Two watersheds with contrasting soil-landscape features were studied, for which the prediction methods were performed differently. A multiple linear stepwise regression model was performed with RK using digital terrain models (DTMs) and remote sensing images in order to choose the best auxiliary covariates. Different pedogenic factors and land uses control soil property distributions in each watershed, and soil properties often display contrasting scales of variability. Environmental covariables and predictive methods can be useful in one site study, but inappropriate in another one. A better linear correlation was found at Lavrinha Creek Watershed, suggesting a relationship between contemporaneous landforms and soil properties, and RK outperformed OK. In most cases, RK did not outperform OK at the Marcela Creek Watershed due to lack of linear correlation between covariates and soil properties. Since alternatives of simple OK have been sought, other prediction methods should also be tested, considering not only the linear relationships between covariate and soil properties, but also the systematic pattern of soil property distributions over that landscape

Mapping of aluminum concentration in bauxite mining residues using sentinel-2 imagery

open6siThis research was funded by Cop-Piles Project, from the RawMatCop Programme (2018–2019), funded by the European Commission and EIT RawMaterial, grant agreement number 271/G/Gro/COPE/17/10036.There is a growing interest in the characterization of mining residues, both for environmental assessments and critical raw materials recovery. The lack of sufficient in situ samples hampers an effective geostatistical modelling of material concentrations variability. This paper proposes a method to characterize the aluminum spatial variability in a mine residue from remote sensing data and imprecise information from daily dumping procedures. The method is proposed for the mapping of aluminum within a Greek bauxite residue, using Sentinel-2 imagery. The spatial correlation between metal concentrations and remote sensing indicators (e.g., spectral band ratios) is the premise for mapping aluminum varieties. The proposed method is based on Conditional Gaussian Co-Simulation, where Sentinel-2 images can be used as auxiliary variables. Simulation results are compared with the Co-kriging estimation method. To perform the Co-kriging estimation, the same conditions as simulation are used (same inputs, models, and neighborhoods). Simulation results quantified the metals variability in mining residues, presenting the metal concentration of piled materials in two time periods. For results validation and selecting the best map, fourteen validation samples were used. For the best representative maps of aluminum concentration, a correlation coefficient of about 0.7 between the validation data and obtained aluminum concentration map was obtained.openKasmaeeyazdi S.; Mandanici E.; Balomenos E.; Tinti F.; Bonduà Stefano; Bruno R.Kasmaeeyazdi S.; Mandanici E.; Balomenos E.; Tinti F.; Bonduà Stefano; Bruno R

Spatio-temporal modeling of soil characteristics for soilscape reconstruction

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