Reply to “Standardized vs. customary ordinary cokriging…” by A. Papritz

Geoderma ◽  
2008 ◽  
Vol 146 (1-2) ◽  
pp. 397-399 ◽  
Author(s):  
T.F.A. Bishop ◽  
R.M. Lark
Keyword(s):  
Ordinary Cokriging

scholarly journals Integration of different-quality data in short-term mining planning

2015 ◽  
Vol 68 (2) ◽  
pp. 221-227 ◽  
Author(s):  
Cristina Paixão Araújo ◽  
João Felipe Coimbra Leite Costa
Keyword(s):  
Mineral Exploration ◽  
Quality Data ◽  
Imprecise Data ◽  
Short Term ◽  
Mining Operations ◽  
Different Types ◽  
Block Models ◽  
The Impact ◽  
Block Distribution ◽  
Ordinary Cokriging

AbstractDecisions, from mineral exploration to mining operations, are based on grade block models obtained from samples. This study evaluates the impact of using imprecise data in short-term planning. The exhaustive Walker Lake dataset is used and is considered as the source for obtaining the true grades. Initially, samples are obtained from the exhaustive dataset at regularly spaced grids of 20 × 20 m and 5 × 5 m. A relative error (imprecision) of ±25% and a 10% bias are added to the data spaced at 5 × 5 m (short-term geological data) in different scenarios. To combine these different types of data, two methodologies are investigated: cokriging and ordinary kriging. Both types of data are used to estimate blocks with the two methodologies. The grade tonnage curves and swath plots are used to compare the results against the true block grade distribution. In addition, the block misclassification is evaluated. The results show that standardized ordinary cokriging is a better methodology for imprecise and biased data and produces estimates closer to the true grade block distribution, reducing block misclassification.

scholarly journals Estimation of geotechnical parameters on the basis of geophysical methods and geostatistics

2017 ◽  
Vol 6 (2) ◽  
pp. 70-79 ◽  
Author(s):  
Aleksander Brom ◽  
Adrianna Natonik
Keyword(s):  
Spatial Correlation ◽  
Correlation Functions ◽  
Cross Validation ◽  
Geophysical Methods ◽  
Geophysical Investigation ◽  
Geotechnical Parameters ◽  
Geostatistical Modelling ◽  
Interpolation Methods ◽  
Ordinary Cokriging ◽  
Geotechnical Studies

AbstractThe paper presents possible implementation of ordinary cokriging and geophysical investigation on humidity data acquired in geotechnical studies. The Author describes concept of geostatistics, terminology of geostatistical modelling, spatial correlation functions, principles of solving cokriging systems, advantages of (co-)kriging in comparison with other interpolation methods, obstacles in this type of attempt. Cross validation and discussion of results was performed with an indication of prospect of applying similar procedures in various researches..

Use of ordinary cokriging with magnetic susceptibility for mapping lead concentrations in soils of an urban contaminated site

2019 ◽  
Vol 20 (3) ◽  
pp. 1357-1370 ◽  
Author(s):  
Nessa Golden ◽  
Chaosheng Zhang ◽  
Aaron Potito ◽  
Paul J. Gibson ◽  
Norma Bargary ◽  
...  
Keyword(s):  
Magnetic Susceptibility ◽  
Contaminated Site ◽  
Ordinary Cokriging

scholarly journals MODELLING EXTREME PRECIPITATION IN HAZARDOUS MOUNTAINOUS AREAS. CONTRIBUTION TO LANDSCAPE PLANNING AND ENVIRONMENTAL MANAGEMENT

2010 ◽  
Vol 18 (4) ◽  
pp. 329-342 ◽  
Author(s):  
Paulo Pereira ◽  
Marc Oliva ◽  
Edita Baltrėnaitė
Keyword(s):  
Thin Plate ◽  
Extreme Precipitation ◽  
Ordinary Kriging ◽  
Landscape Planning ◽  
Thin Plate Spline ◽  
Mountainous Areas ◽  
Local Polynomial ◽  
Radial Basis ◽  
Inverse Distance ◽  
Ordinary Cokriging

Extreme precipitation episodes are very common in Mediterranean area and can lead to serious and catastrophic environmental hazards. They have special incidence during autumn months, September, October and November (SON) with important impacts on society, leading frequently to significant economic losses and mortality. These events have special impact in mountainous areas where steep slopes enhance the effects of extreme precipitation. In mountainous areas rain gauge stations are sparse and normally in lower amount. Due to these reasons it is very important to map with higher accuracy the distribution of extreme precipitation. Also, in mountainous environments precipitation patterns can change in small distances that make the prediction more difficult, but also more important. A better prediction of areas with higher values of extreme precipitation will contribute to a better land use planning and avoid the effects of flash floods, land‐slides and soil erosion recognized as environmental problems. The aim of this paper is testing several well‐known interpolation methods, Inverse Distance Weight (IDW) with weighs of 1, 2, 3, 4 and 5, Local Polynomial (LP) with order 1 and 2, Radial Basis Methods (RBS), particularly Spline With Tension (SPT) and Thin Plate Spline (TPS), and Kriging techniques, Ordinary Kriging (OK) and Ordinary CoKriging (COK) in order to identify the less‐biased method to interpolate extreme precipitation calculated from the 95th percentile (P95) of SON precipitation in a mountainous area located in Portugal. The results show that extreme precipitation increases with the altitude and there are important differences between stations located at higher and lower altitudes. This relation is observed in the omni‐directional semi‐variograms calculated where we identified two major P95 areas coincident with higher elevations. The first one occurred at 12.19 km and the second at 23.57 km. The higher values of P95 are identified at Southeast and Northeast. In contrast, the lower P95 values are identified at Northwest due to lower altitudes and in the Northeast corner as a consequence of rain shadow effect. Prediction with precision of precipitation patterns in mountainous areas is difficult due to lack of data and the complex effect of topography in rainfall, however, it is of major importance in order to identify vulnerable areas. The findings observed in this study are a fundamental contribution to landscape planning and environmental management in areas with higher occurrence and vulnerability to extreme precipitation. Santrauka Gausūs krituliai, ypač būdingi Viduržemio jūros regionui, gali kelti rimtu pavoju aplinkai, lemti katastrofas. Krituliu poveikio zona ypač išsiplečia rudens laikotarpiu, t. y. rugsejo, spalio ir lapkričio (RSL) menesiais, neretai patiriama dideliu ekonominiu nuostoliu, žūsta ar kitaip nukenčia žmones. Statūs kalnu šlaitai sustiprina gausiu krituliu poveiki. Kalnuotose vietovese krituliu kiekio stebejimo stočiu nedaug, jos toli viena nuo kitos, todel labai aktualu tureti žemelapius, tiksliai nusakančius gausiu krituliu pasiskirstyma. Kalnuotose vietovese krituliu pobūdis skirtingu atstumu gali būti skirtingas, krituliu kieki numatyti sunkiau, tačiau tai itin svarbu. Tiksliau numatant vietoves, kur iškrinta daugiau krituliu, galima tikslingiau planuoti žemetvarka, išvengti staigiu potvyniu, nuošliaužu ir dirvožemio erozijos. Tyrimo tikslas buvo patikrinti kelis gerai žinomus interpoliacijos metodus – Inverse Distance Weight (IDW) su 1–5 svertinemis vertemis, Local Polynomial (LP), Radial Basis (RBS), ypač Spline With Tension (SPT), Thin Plate Spline (TPS), – bei Kriging technikas ir Ordinary Kriging (OK) bei Ordinary CoKriging (COK) metodus, siekiant parinkti tiksliausia, kuris leistu interpoliuoti gausius (95 %) kritulius RSL menesiais kalnuotoje Portugalijos teritorijoje. Nustatyta, kad krituliu kiekis dideja didejant altitudei. Reikšmingi krituliu skirtumai nustatyti stotyse, esančiose skirtinguose aukščiuose virš jūros lygio. Šis santykis pastebetas visomis kryptimis apskaičiuotose pusinese variogramose. Jose išsiskiria dvi teritorijos, kuriu P95 vertes didžiausios, ir akivaizdi sasaja su didelemis altitudemis. Pirmoji teritorija 12,19 km, o antroji 23,57 km aukštyje. Didžiausios P95 vertes pietryčiu ir šiaures rytu kryptimis, mažiausios – šiaures vakaru kryptimi, kur altitudes mažos, ir šiaures rytu teritorijos kampe del lietaus “šešelio” efekto. Tiksliai numatyti krituliu pobūdi kalnuotose teritori‐jose apsunkina duomenu trūkumas ir sudetinga topografijos itaka krituliams. Rezultatai ypač parankūs planuojant ir val‐dant dažniems ir gausiems krituliams jautrias teritorijas. Резюме Обильные осадки, особенно характерные для Средиземноморского региона, могут быть опасными для окружающей среды. Зона влияния осадков особенно увеличивается в осенний период – сентябре, октябре и ноябре. Осадки зачастую вызывают большие экономические убытки, гибнут или страдают люди. Влияние обильных осадков усиливают крутые горные склоны. В горных местностях станций наблюдения за количеством осадков немного и расположены они далеко друг от друга, поэтому необходимы карты, на которых было бы точно указано распределение обильных осадков. Характер осадков в горных местностях в зависимости от удаленности может значительно различаться, предвидеть количество осадков чрезвычайно сложно, однако это жизненно необходимо. Зная местности, на которых ожидается большее количество осадков, можно точнее планировать землеустройство, избежать внезапных наводнений, оползней и эрозии почв. Целью исследования было проверить несколько хорошо известных методов интерполяции – Inverse Distance Weight (IDW) с 1–5 значениями весомостей, Local Polynomial (LP), Radial Basis (RBS), особенно Spline With Tension (SPT), Thin Plate Spline (TPS), а также технику Kriging, методы Ordinary Kriging (OK) и Ordinary CoKriging (COK) с целью выявить наиболее точный, с помощью которого можно было бы интерполировать обильные (95%) осенние осадки в горных местностях Португалии. Установлено, что количество осадков увеличивается с увеличением амплитуды. Значительная разница в количестве осадков выявлена на станциях, находящихся на разной высоте от уровня моря. Это соотношение замечено на всех направлениях рассчитанных полувариограмм. На них выделяются две территории, на которых значения P95 наиболее велики и очевидна связь с большими амплитудами. Первая территория находится на высоте 12,19 км, вторая – 23,57 км. Наибольшие значения P95 отмечены в юго-восточном и северо-восточном, наименьшие – северо-западном направлениях, где амплитуды малы, и в углу северо-восточной территории из-за эффекта «тени» дождя. Точнее предвидеть характер осадков в горных местностях представляется затруднительным из-за недостатка данных и сложного влияния на осадки топографии. Результаты исследования окажутся особенно полезными при планировании и управлении территориями, подвергаемыми частым и обильным осадкам.

scholarly journals Cokriging Prediction Using as Secondary Variable a Functional Random Field with Application in Environmental Pollution

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1305 ◽  
Author(s):  
Ramón Giraldo ◽  
Luis Herrera ◽  
Víctor Leiva
Keyword(s):  
Particulate Matter ◽  
Wind Speed ◽  
Environmental Pollution ◽  
Random Field ◽  
Spatial Prediction ◽  
Proposed Model ◽  
Cross Correlations ◽  
Primary Variable ◽  
Secondary Variable ◽  
Ordinary Cokriging

Cokriging is a geostatistical technique that is used for spatial prediction when realizations of a random field are available. If a secondary variable is cross-correlated with the primary variable, both variables may be employed for prediction by means of cokriging. In this work, we propose a predictive model that is based on cokriging when the secondary variable is functional. As in the ordinary cokriging, a co-regionalized linear model is needed in order to estimate the corresponding auto-correlations and cross-correlations. The proposed model is utilized for predicting the environmental pollution of particulate matter when considering wind speed curves as functional secondary variable.

scholarly journals Improving Mean Annual Precipitation Prediction Incorporating Elevation and Taking into Account Support Size

Water ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 830
Author(s):  
Gabriele Buttafuoco ◽  
Massimo Conforti
Keyword(s):  
Spatial Distribution ◽  
Ordinary Kriging ◽  
Annual Precipitation ◽  
Mean Annual Precipitation ◽  
Block Kriging ◽  
Kriging With External Drift ◽  
Elevation Data ◽  
Support Size ◽  
Ordinary Cokriging ◽  
External Drift

Accounting for secondary exhaustive variables (such as elevation) in modelling the spatial distribution of precipitation can improve their estimate accuracy. However, elevation and precipitation data are associated with different support sizes and it is necessary to define methods to combine such different spatial data. The paper was aimed to compare block ordinary cokriging and block kriging with an external drift in estimating the annual precipitation using elevation as covariate. Block ordinary kriging was used as reference of a univariate geostatistical approach. In addition, the different support sizes associated with precipitation and elevation data were also taken into account. The study area was the Calabria region (southern Italy), which has a spatially variable Mediterranean climate because of its high orographic variability. Block kriging with elevation as external drift, compared to block ordinary kriging and block ordinary cokriging, was the most accurate approach for modelling the spatial distribution of annual mean precipitation. The three measures of accuracy (MAE, mean absolute error; RMSEP, root-mean-squared error of prediction; MRE, mean relative error) have the lowest values (MAE = 112.80 mm; RMSEP = 144.89 mm, and MRE = 0.11), whereas the goodness of prediction (G) has the highest value (75.67). The results clearly indicated that the use of an exhaustive secondary variable always improves the precipitation estimate, but in the case of areas with elevations below 120 m, block cokriging makes better use of secondary information in precipitation estimation than block kriging with external drift. At higher elevations, the opposite is always true: block kriging with external drift performs better than block cokriging. This approach takes into account the support size associated with precipitation and elevation data. Accounting for elevation allowed to obtain more detailed maps than using block ordinary kriging. However, block kriging with external drift produced a map with more local details than that of block ordinary cokriging because of the local re-evaluation of the linear regression of precipitation on block estimates.

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