Mapping minimum daily temperature in Spain using kriging with external drift

Presentación realizada en: 10th EUMETNET Data Management Workshop celebrado en St. Gallen, Suiza, del 28 al 30 de octubre de 2015.The spatial interpolation of daily temperature is often a complex process compared to the interpolation of monthly or annual data due to the necessity of dealing with local phenomenons, such as inversions, that frequently affect the daily temperatures, especially in mountainous regions. The objective of this study is to describe the methodology that it is being used in the Spanish Meteorological Agency for obtaining gridded fields of daily minimum temperature using a universal kriging method with with the altitude and the distance to the coast as an external drift. In this method, the vertical temperature gradient can vary from one point to another in the study region, so that temperature inversion effects can be properly considered in the interpolation process. A validation process is shown, including a comparison with other typical interpolation methods: regression kriging, ordinary kriging and inverse distance weighted. Finally, some examples of maps obtained by this method are shown, including several products generated for agroclimatological purposes by combining daily gridded maps, such as average number of frost days, mean first and last freezing date and average chill hours below different temperature thresholds

Pembangunan modul pembelajaran autocad dan kajian penerimaan pelajar. Satu kajian kes di Politeknik Kota Bharu

Modul Pengajaran dan Pembelajaran AutoCAD (MPP) merupakan satu media pengajaran yang mengandungi asas-asas mengenai komputer, perisian AutoCAD 2000 dan langkah-langkah berperingkat membuat lukisan teknikal menggunakan AutoCAD 2000. Kajian ini adalah bertujuan untuk menilai sejauh mana MPP ini boleh digunakan dalam proses pengajaran dan pembelajaran dalam aspek kesesuaian isi kandungan, sifat mesra pengguna dan kebolehlaksanaannya. Respondan untuk kajian ini ialah seramai 42 orang pelajar Diploma Kejuruteraan Elektrik Politeknik Kota Bharu. Untuk kajian ini instrumen yang digunakan ialah borang soal selidik di mana penilaian dilakukan berdasarkan persepsi responden terhadap MPP. Data-data yang dikumpulkan dianalisis menggunakan SPSS VI1.0 yang melibatkan skor min. Hasil kajian melaporkan dapatan yang diperolehi berkenaan penerimaan terhadap MPP. Hasil dapatan kajian menunjukkan penerimaan yang positif terhadap MPP oleh pelajar dan ianya mempimyai kebolehlaksanaan yang tinggi (skor min = 3.96) untuk diaplikasikan dalam proses pengajaran dan pembelajaran. Walaubagaimanapun pengkaji percaya MPP ini mempunyai ruang untuk penambahbaikan seperti saranan oleh penilai yang mengesahkan MPP ini agar ia lebih menarik dan sesuai digunakan pada masa depan

Extending Functional kriging to a multivariate context

Environmental data usually have a spatio-temporal structure; pollutant concentrations, for example, are recorded along time and space. Generalized Additive Models (GAMs) represent a suitable tool to model spatial and/or temporal trends of this kind of data, that can be treated as functional, although they are collected as discrete observations. Frequently, the attention is focused on the prediction of a single pollutant at an unmonitored site and, at this aim, we extend kriging for functional data to a multivariate context by exploiting the correlation with the other pollutants. In particular, we propose two procedures: the first one (FKED) combines the regression of a variable (pollutant), of primary interest on the other variables, with functional kriging of the regression residuals; the second one (FCK) is based on linear unbiased prediction of spatially correlated multivariate random processes. The performance of the two proposed procedures is assessed by cross validation; data recorded during a year (2011) from the monitoring network of the state of California (USA) are considered

Mapping monthly rainfall data in Galicia (NW Spain) using inverse distances and geostatistical methods

In this paper, results from three different interpolation techniques based on Geostatistics (ordinary kriging, kriging with external drift and conditional simulation) and one deterministic method (inverse distances) for mapping total monthly rainfall are compared. The study data set comprised total monthly rainfall from 1998 till 2001 corresponding to a maximum of 121 meteorological stations irregularly distributed in the region of Galicia (NW Spain). Furthermore, a raster Geographic Information System (GIS) was used for spatial interpolation with a 500×500 m grid digital elevation model. Inverse distance technique was appropriate for a rapid estimation of the rainfall at the studied scale. In order to apply geostatistical interpolation techniques, a spatial dependence analysis was performed; rainfall spatial dependence was observed in 33 out of 48 months analysed, the rest of the rainfall data sets presented a random behaviour. Different values of the semivariogram parameters caused the smoothing in the maps obtained by ordinary kriging. Kriging with external drift results were according to former studies which showed the influence of topography. Conditional simulation is considered to give more realistic results; however, this consideration must be confirmed with new data

Bootstrap based uncertainty bands for prediction in functional kriging

The increasing interest in spatially correlated functional data has led to the development of appropriate geostatistical techniques that allow to predict a curve at an unmonitored location using a functional kriging with external drift model that takes into account the effect of exogenous variables (either scalar or functional). Nevertheless uncertainty evaluation for functional spatial prediction remains an open issue. We propose a semi-parametric bootstrap for spatially correlated functional data that allows to evaluate the uncertainty of a predicted curve, ensuring that the spatial dependence structure is maintained in the bootstrap samples. The performance of the proposed methodology is assessed via a simulation study. Moreover, the approach is illustrated on a well known data set of Canadian temperature and on a real data set of PM$_{10}$ concentration in the Piemonte region, Italy. Based on the results it can be concluded that the method is computationally feasible and suitable for quantifying the uncertainty around a predicted curve. Supplementary material including R code is available upon request

Improving rainfall nowcasting and urban runoff forecasting through dynamic radar-raingauge rainfall adjustment

The insufficient accuracy of radar rainfall estimates is a major source of uncertainty in short-term quantitative precipitation forecasts (QPFs) and associated urban flood forecasts. This study looks at the possibility of improving QPFs and urban runoff forecasts through the dynamic adjustment of radar rainfall estimates based on raingauge measurements. Two commonly used techniques (Kriging with External Drift (KED) and mean field bias correction) were used to adjust radar rainfall estimates for a large area of the UK (250,000 km2) based on raingauge data. QPFs were produced using original radar and adjusted rainfall estimates as input to a nowcasting algorithm. Runoff forecasts were generated by feeding the different QPFs into the storm water drainage model of an urban catchment in London. The performance of the adjusted precipitation estimates and the associated forecasts was tested using local rainfall and flow records. The results show that adjustments done at too large scales cannot provide tangible improvements in rainfall estimates and associated QPFs and runoff forecasts at small scales, such as those of urban catchments. Moreover, the results suggest that the KED adjusted rainfall estimates may be unsuitable for generating QPFs, as this method damages the continuity of spatial structures between consecutive rainfall fields

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

Comparative assessment of global irradiation from a satellite estimate model (CM SAF) and on-ground measurements (SIAR): a Spanish case study

An analysis and comparison of daily and yearly solar irradiation from the satellite CM SAF database and a set of 301 stations from the Spanish SIAR network is performed using data of 2010 and 2011. This analysis is completed with the comparison of the estimations of effective irradiation incident on three different tilted planes (fixed, two axis tracking, north-south hori- zontal axis) using irradiation from these two data sources. Finally, a new map of yearly values of irradiation both on the horizontal plane and on inclined planes is produced mixing both sources with geostatistical techniques (kriging with external drift, KED) The Mean Absolute Difference (MAD) between CM SAF and SIAR is approximately 4% for the irradiation on the horizontal plane and is comprised between 5% and 6% for the irradiation incident on the inclined planes. The MAD between KED and SIAR, and KED and CM SAF is approximately 3% for the irradiation on the horizontal plane and is comprised between 3% and 4% for the irradiation incident on the inclined planes. The methods have been implemented using free software, available as supplementary ma- terial, and the data sources are freely available without restrictions

Spatial interpolation of hourly rainfall – effect of additional information, variogram inference and storm properties

Hydrological modelling of floods relies on precipitation data with a high resolution in space and time. A reliable spatial representation of short time step rainfall is often difficult to achieve due to a low network density. In this study hourly precipitation was spatially interpolated with the multivariate geostatistical method kriging with external drift (KED) using additional information from topography, rainfall data from the denser daily networks and weather radar data. Investigations were carried out for several flood events in the time period between 2000 and 2005 caused by different meteorological conditions. The 125 km radius around the radar station Ummendorf in northern Germany covered the overall study region. One objective was to assess the effect of different approaches for estimation of semivariograms on the interpolation performance of short time step rainfall. Another objective was the refined application of the method kriging with external drift. Special attention was not only given to find the most relevant additional information, but also to combine the additional information in the best possible way. A multi-step interpolation procedure was applied to better consider sub-regions without rainfall. <br><br> The impact of different semivariogram types on the interpolation performance was low. While it varied over the events, an averaged semivariogram was sufficient overall. Weather radar data were the most valuable additional information for KED for convective summer events. For interpolation of stratiform winter events using daily rainfall as additional information was sufficient. The application of the multi-step procedure significantly helped to improve the representation of fractional precipitation coverage