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

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.

Comparison of different geostatistical approaches to estimate wind speed at hourly scale in the province of Granada (Southern Spain)

<p>Wind plays a key role in different processes of the earth system such as the earth's energy and water cycles. The use of the wind to produce clean energy as a substitute of other traditional systems may help to reduce the emission, and, therefore, to mitigate climate change. Wind is defined by two variables, direction and speed. This work is focused on the assessment of the second one. The aim is to estimate wind speed at ten meters (U<sub>10</sub>) fields in the province of Granada (Southern Spain). A grid with a spatial resolution of 300 m and an hourly temporal resolution has been adopted to estimate it for the period 1986 to 2016. Different geostatistical estimation approaches (ordinary kriging, kriging with external drift, regression and regression kriging) have been evaluated considering a monthly variogram model. Elevation showed a good correlation with wind speed and has been used as secondary variable for the external drift and the regression approaches. We have also tested mesoscale (U<sub>80</sub>) and logarithm transformations of U<sub>10</sub> for each of the geostatistical techniques. The performance of each transformation and geostatistical approach was assessed using a cross validation experiment. In general, geostatistical techniques that takes into account elevation as secondary information and approaches without transformation of data showed better accuracy. The regression kriging without transformation showed the lower mean error and mean squared error (0.03 m s<sup>-1 </sup>and 3.46 [m s<sup>-1</sup>]<sup>2</sup> respectively) for the considered period but other approaches such as kriging with external drift showed similar results (0.04 m s<sup>-1</sup> and 3.52 [m s<sup>-1</sup>]<sup>2</sup> respectively).</p><p>This research has been partially supported by the SIGLO-AN project from the Spanish Ministry of Science, Innovation and Universities (Programa Estatal de I+D+I orientada a los Retos de la Sociedad).</p>

High-Resolution Temperature Mapping by Geostatistical Kriging with External Drift from Large-Eddy Simulations

Detailed temperature maps are required in various applications. Any temperature interpolation over complex terrain must account for differences in land cover and elevation. Local circulations and other small-scale factors can also perturb the temperature. This study considers the surface air temperature T mapping with geostatistical kriging. The kriging methods are implemented for both T and temperature anomalies ΔT, defined as difference between T at a given location and T at the same elevation in the free atmosphere. The study explores the parallelized atmospheric large-eddy simulation (LES) model (PALM) as a source for variogram and external drift in the kriging methods. Ten kriging methods for the temperature mapping have been considered: ordinary kriging (OK) of T and ΔT with variogram derived from the observations (methods 1 and 2, correspondingly); OK of T and ΔT with variogram derived from LES data (3 and 4); universal kriging with external drift (KED) that utilizes the LES data (5 and 6); a weighted combination of KED of T and ΔT (method 7); and methods 5, 6, and 7 enhanced with additional “virtual” points in remote areas (methods 8, 9, and 10). These 10 methods are evaluated for eight typical weather situations observed in Bergen, Norway. Our results demonstrate considerable added value of the LES information for the detailed meteorological temperature mapping. The LES data improve both the variogram and the resulting temperature maps, especially in the remote mountain parts of the domain and along the coast.

DELINEATION OF HOMOGENEOUS ZONES BASED ON GEOSTATISTICAL MODELS ROBUST TO OUTLIERS

ABSTRACT Measures of the apparent electrical conductivity (ECa) of soil are used in many studies as indicators of spatial variability in physicochemical characteristics of production fields. Based on these measures, management zones (MZs) are delineated to improve agricultural management. However, these measures include outliers. The presence or incorrect identification and exclusion of outliers affect the variogram function and result in unreliable parameter estimates. Thus, the aim of this study was to model ECa data with outliers using methods based on robust approximation theory and model-based geostatistics to delineate MZs. Robust estimators developed by Cressie-Hawkins, Genton and MAD Dowd were tested. The Cressie-Hawkins semivariance estimator was selected, followed by the semivariogram cubic fit using Akaike information criterion (AIC). The robust kriging with an external drift plug-in was applied to fitted estimates, and the fuzzy k-means classifier was applied to the resulting ECa kriging map. Models with multiple MZs were evaluated using fuzzy k-means, and a map with two MZs was selected based on the fuzzy performance index (FPI), modified partition entropy (MPE) and Fukuyama-Sugeno and Xie-Beni indices. The defined MZs were validated based on differences between the ECa means using mixed linear models. The independent errors model was chosen for validation based on its AIC value. Thus, the results demonstrate that it is possible to delineate an MZ map without outlier exclusion, evidencing the efficacy of this methodology.

APLIKASI INVERSI POST-STACK DAN GEOSTATISTIK UNTUK KARAKTERISASI RESERVOAR BATUPASIR FORMASI LAKOTA LAPANGAN TEAPOT, WYOMING, USA

Penelitian menggunakan metode inversi post-stack dan geostatistik telah dilakukan pada Formasi Lakota Lapangan Teapot Dome, Wyoming, Amerika Serikat. Tujuan dilakukannya penelitian ini adalah untuk mengkarakterisasi reservoar Batupasir Formasi Lakota, hak milik RMOTC dan U.S.Department of Energy. Metode yang digunakan pada penelitian ini adalah inversi post-stack metode modelbased untuk mendapatkan nilai AI dari volume seismik dan aplikasi geostatistik menggunakan analisis variogram, Kriging with External Drift dan Simulasi Gaussian bertujuan untuk mendapatkan distribusi sifat fisis reservoar secara lateral dari data sumur. Hasil inversi modelbased menunjukkan nilai impedansi Formasi Lakota berada pada rentang 28000-36000 ft/s*g/cc yang mengindikasikan bahwa Formasi Lakota merupakan interbedded shaly sand. Pembuatan layering reservoar dari volume AI menjadi empat map bertujuan untuk mendapatkan persebaran sifat fisis reservoar yang lebih akurat menggunakan metode geostatistik. Hasil dari metode geostatistik menghasilkan nilai porositas total berada pada rentang 20 – 30 % dan Vshale memiliki rentang nilai 10 – 40 % pada keempat layer map tersebar pada daerah Barat Laut yang termasuk ke dalam zona tight (nilai AI > 30000 ft*s/g*cc). Daerah tersebut diindikasikan sebagai area yang berprospek dan rentang nilai sifat fisis tersebut diklasifikasikan sebagai karakteristik reservoar yang baik. Reservoar batupasir yang tersturasi gas berlokasi di sekitar sesar normal dengan orientasi Timur Laut – Barat Daya, yang dapat ditunjukkan dengan bright amplitude pada data seismik dan nilai impedansi rendah. Dua sesar normal mayor berorientasi Timur Laut – Barat Daya membentuk two way dip closure trap berpreran sebagai jebakan hidrokarbon gas pada Formasi Lakota yang telah terbukti dengan adanya sumur produksi 41-2-X-3, 53-LX-3 dan 56-LX-10 berdasarkan data produksi Lapangan Teapot.Kata Kunci: Formasi Lakota, Geostatistik, Inversi Post-stack, Shaly-sandThe research using post-stack inversion and geostatistical method has been conducted on Lakota Formation, Teapot Dome Field, Wyoming, USA. The aim is to obtain reservoir characteristics and physical properties of Lakota Sandstone, copyrights of RMOTC, U.S Department of Energy. The method used in this research consist of Post-stack inversion modelbased method to obtain Acoustic Impedance of seismic volume and geostastical method using variogram analysis, Kriging with External Drift and also Gaussian simulation to obtain physical properties distribution laterally from well data. The result of modelbased inversion shows the impedance value of Lakota Formation has the range 28000-36000 ft/s*g/cc. It indicates that Lakota Formation has interbedded shaly-sand characteristics. The inversion result is divided into four layers and sliced into four maps to obtain physical properties distributin of Lakota Formation more accurately. The result of geostatistical method yields Total Porosity value of four maps on Lakota Formation has 20 – 30 % and Vshale 10 – 40% scattered in Northwest area of Teapot Field represents a tight zone (Acoustic Impedance value > 30000 ft/s*g/cc), which is indicated as prospective area and also those physical properties values classified as good reservoar characteristics. Sandstone reservoir which saturated by gas is located around normal fault with Northeast – Southwest orientation. It can be seen by bright amplitude on seismic data and low impedance value. Two major normal fault with Northeast – Southwest orientation forming two way dip closure trap has the role of gas brine zone trap of Lakota Formation. The existing of gas zone was proven by production wells 41-2-X-3, 53-LX-3 dan 56-LX-10 from Teapot Production Data.Keywords: Geostatistics, Lakota Formation, Post-stack Inversion, Shaly-sand

Estimation of Housing Price Variations Using Spatio-Temporal Data

This paper proposes a hedonic regression model to estimate housing prices and the spatial variability of prices over multiple years. Using the model, maps are obtained that represent areas of the city where there have been positive or negative changes in housing prices. The regression-cokriging (RCK) method is used to predict housing prices. The results are compared to the cokriging with external drift (CKED) model, also known as universal cokriging (UCK). To apply the model, heterotopic data of homes for sale at different moments in time are used. The procedure is applied to predict the spatial variability of housing prices in multi-years and to obtain isovalue maps of these variations for the city of Granada, Spain. The research is useful for the fields of urban studies, economics, real estate, real estate valuations, urban planning, and for scholars.

Downscaling of Satellite OPEMW Surface Rain Intensity Data

This paper presents a geostatistical downscaling procedure to improve the spatial resolution of precipitation data. The kriging method with external drift has been applied to surface rain intensity (SRI) data obtained through the Operative Precipitation Estimation at Microwave Frequencies (OPEMW), which is an algorithm for rain rate retrieval based on Advanced Microwave Sounding Units (AMSU) and Microwave Humidity Sounder (MHS) observations. SRI data have been downscaled from coarse initial resolution of AMSU-B/MHS radiometers to the fine resolution of Spinning Enhanced Visible and InfraRed Imager (SEVIRI) flying on board the Meteosat Second Generation (MSG) satellite. Orographic variables, such as slope, aspect and elevation, are used as auxiliary data in kriging with external drift, together with observations from Meteosat Second Generation-Spinning Enhanced Visible and InfraRed Imager (MSG-SEVIRI) in the water vapor band (6.2 µm and 7.3 µm) and in thermal-infrared (10.8 µm and 8.7 µm). The validation is performed against measurements from a network of ground-based rain gauges in Southern Italy. It is shown that the approach provides higher accuracy with respect to ordinary kriging, given a choice of auxiliary variables that depends on precipitation type, here classified as convective or stratiform. Mean values of correlation (0.52), bias (0.91 mm/h) and root mean square error (2.38 mm/h) demonstrate an improvement by +13%, −37%, and −8%, respectively, for estimates derived by kriging with external drift with respect to the ordinary kriging.