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.

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

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.

Multivariate estimation for accurate and logically consistent forest-attributes maps at macroscales

Spatially explicit wall-to-wall forest-attributes information is critically important for designing management strategies resilient to climate-induced uncertainties. Multivariate estimation methods that link forest attributes and auxiliary variables at full-information locations can be used to estimate the forest attributes for locations with only auxiliary variables information. However, trade-offs between estimation accuracies versus logical consistency among estimated attributes may occur. This is particularly likely for macroscales (i.e., ≥1 Mha) with large forest-attributes variances and wide spacing between full-information locations. We examined these trade-offs for ∼390 Mha of Canada’s boreal zone using variable-space nearest-neighbours imputation versus two modelling methods (i.e., a system of simultaneous nonlinear models and kriging with external drift). We found logical consistency among estimated forest attributes (i.e., crown closure, average height and age, volume per hectare, species percentages) using (i) k ≤ 2 nearest neighbours or (ii) careful model selection for the modelling methods. Of these logically consistent methods, kriging with external drift was the most accurate, but implementing this for a macroscale is computationally more difficult. This extra cost is justified given the importance of assessing strategies under expected climate changes in Canada’s boreal forest and in other forest regions.

Comparison of various spatial interpolation methods for precipitation in TurkeyTürkiye’de yağışın farklı mekânsal enterpolasyon yöntemleriyle karşılaştırılması

Precipitation has a structure varying at spatial and temporal scale. Understanding this variation of precipitation has a significant role in the applications of hydrology, climatology, agriculture, ecology and other environmental sciences. It is difficult to make a correct forecast for precipitation and to reveal its spatial distribution in areas in which topography varies in a short distance and there is the insufficient number of stations. In recent years, geostatistical methods are commonly used in solving this problem. Geostatistical methods are preferred in studies, especially on modeling precipitation. Suggesting spatial distribution of precipitation with auxiliary variables explaining precipitation provides correct precipitation forecasts. The aim of this study is to create precipitation forecasting models with the help of precipitation in Turkey where topographic conditions change in a short distance and auxiliary variables such as coastal proximity, elevation, aspect and slope affecting precipitation and to select the correct precipitation forecasting model. The annual mean total precipitation values of 276 meteorological stations for the period of 1970–2014 were used for this purpose. The Kriging (Ordinary Kriging), Co-Kriging (Ordinary Co-Kriging) and Kriging with External Drift techniques were used in modeling precipitation.The Coefficient of Determination (R2), Root Mean Square Error (RMSE), Mean Absolute Error (MAE) and Mean Error (ME) performance measurement values were calculated by evaluating the results with Cross Validation. The precipitation model acquired from the Co-Kriging technique in which elevation was used as the auxiliary variable gave the performance results of R2 value as 0.64, RMSE (mm) value as 297.8, ME value as 247.8 and MAE value as 253.9. The precipitation model acquired from the Kriging with External Drift technique in which the coastal proximity was used as the auxiliary variable gave the results of R2 value as 0.64, RMSE (mm) value as 162.3, ME value as -0.246 and MAE value as 107.8. Although it has similarities with R2 values of the Co-Kriging technique, there is a difference in other performance measurements. The error estimation chart of the results of the Kriging with External Drift analysis in which auxiliary variables of coastal proximity and elevation were used together indicated lower values than the other analyses in terms of high and low estimation values in the study. Furthermore, when the performance results were evaluated with the precipitation estimation model created with the auxiliary variable of coastal proximity, small differences were observed as 0.01 in R2 and 3.9 in RMSE (mm) value. In accordance with these results, the Kriging with External Drift analysis in which the auxiliary variables of coastal proximity and elevation were used together is the most correct precipitation model created for the annual mean total precipitation estimation model in Turkey. ÖzetYağış, mekânsal ve zamansal ölçekte değişkenlik gösteren bir yapıya sahiptir. Yağışın bu değişkenliğini anlamak hidroloji, klimatoloji, ziraat, ekoloji ve diğer çevre bilimleri uygulamalarında önemli bir yer tutmaktadır. Topografyanın kısa mesafede değişim gösterdiği, istasyon sayısının yetersiz olduğu alanlarda yağışın doğru tahminini yapabilmek ve mekânsal dağılımını ortaya koymak zordur. Bu problem gidermede son yıllarda jeoistatistik yöntemler yaygın olarak kullanılmaktadır. Jeoistatistik yöntemler özellikle yağış modellemesini konu alan çalışmalarda tercih edilmektedir. Yağışı açıklayan yardımcı değişkenlerle birlikte yağışın mekânsal dağılımının ortaya konulması, doğru yağış tahminleri oluşturulmasını sağlamaktadır. Bu çalışmanın amacı, topografik koşulların kısa mesafede değiştiği Türkiye’de, yağış ve yağışı etkileyen kıyıya uzaklık, yükseklik, bakı ve eğim gibi yardımcı değişkenler yardımıyla yağış tahmin modelleri oluşturulması ve en doğru yağış tahmin modelinin seçilmesidir. Bu amaçla 276 meteoroloji istasyonunun 1970–2014 dönemine ait yıllık ortalama toplam yağış değerleri kullanılmıştır. Yağışın modellenmesinde Kriging (Ordinary Kriging), Co-Kriging (Ordinary Co-Kriging) ve Kriging with External Drift tekniklerinden faydalanılmıştır. Sonuçlar Çapraz Geçerlilik (Cross Validation) ile ölçülerek, Belirleyicilik Katsayısı (R2), Kök Ortalama Kare Hata (RMSE), Ortalama Mutlak Hata (MAE) ve Ortalama Hata (ME) performans ölçüm değerleri ile hesap edilmiştir. Yüksekliğin yardımcı değişken olarak kullanıldığı Co-Kriging tekniğinden elde edilen yağış modeli, R2 değeri 0.64, RMSE (mm) değeri, 297.8, ME değeri 247.8 ve MAE değeri, 253.9 performans sonuçları vermiştir. Kıyıya uzaklığın yardımcı değişken olarak kullanıldığı, Kriging with External Drift tekniğinden elde edilen yağış modeli R2 değeri 0.64, RMSE (mm) değeri, 162.3, ME değeri -0.246 ve MAE değeri 107.8 sonuçları vermiştir. Co-Kriging tekniğine ait R2 değerleri ile benzerlik göstermesine rağmen, diğer performans ölçümlerinde fark bulunmaktadır. Çalışmada, kıyıya uzaklık ve yükseklik yardımcı değişkeninin birlikte kullanıldığı Kriging with External Drift analizi sonucuna ait hata tahmin haritası yüksek ve düşük tahmin değerleri açısından diğer analizlere göre daha düşük değerler göstermiştir. Ayrıca performans sonuçları kıyıya uzaklık yardımcı değişkeni kullanılarak oluşturulmuş yağış tahmin modeliyle birlikte değerlendirildiğinde, R2 değerinde 0.01’lik, RMSE (mm) değerinde 3.9’luk küçük bir fark olduğu izlenmiştir. Bu sonuçlar doğrultusunda, kıyıya uzaklık ve yükseklik yardımcı değişkenlerinin birlikte kullanıldığı Kriging with External Drift, Türkiye’de yıllık ortalama toplam yağış tahmin modeli için oluşturulmuş en doğru yağış modelidir.