Spatio-temporal interpolation of climate elements using geostatistics and machine learning

Abstract

High resolution daily maps for climate elements are a valuable source of information and serve as aninput for climatology, meteorology, agriculture, hydrology, ecology, and many other research areasand disciplines. Spatio-temporal interpolation methods are o en used for creation of daily mapsfor climate elements. In this research, already existing spatio-temporal geostatistical interpolationmethods and newly developed spatio-temporal interpolation methods based on machine learning algorithms are applied to and evaluated on climate element case studies. A spatio-temporal regressionkriging model for global land areas for mean daily temperature is simpli ed by using only a geometric temperature trend, digital elevation model, and topographic wetness index (without MODISLST) as covariates and adapted for Croatian territories for the year 2008 in this dissertation. eleave-one-out and 5-fold cross-validation show that the accuracy of the model a er adaptation is97.8% in R2 and 1.2 ◦C in RMSE, which is an improvement of 3.4% in R2 and 0.7 ◦C in RMSE. eadapted daily mean temperature model also outperforms previously developed models for Croatiaand shows similar or be er accuracy in comparison with models for other local areas. e resultsshow that the spatio-temporal regression kriging model for global land areas can be adapted to localareas using a national weather station network, thus providing more accurate daily mean temperature maps at a 1 km spatial resolution. e proposed adapted geostatistical model for Croatia stillprovides larger prediction errors in mountainous regions making it convenient for application inagricultural areas that are at lower altitudes.A di erent approach to spatial or spatio-temporal interpolation of climate elements is to usemachine learning algorithms together with spatial covariates. A novel Random Forest Spatial Interpolation (RFSI) methodology for spatial or spatio-temporal interpolation is proposed and evaluatedin this dissertation. e RFSI methodology is based on the Random Forest algorithm that uses innovative spatial predictors: observations at n nearest locations and distances to them. e RFSImethodology is applied and evaluated in three case studies. In the rst, a synthetic (simulated) casestudy, the accuracy of RFSI is compared with the accuracy of ordinary kriging, Random Forest forspatial prediction (RFsp), inverse distance weighting, nearest neighbour, and trend surface mappinginterpolation methods. In this case study, RFSI outperforms nearest neighbour and trend surfacemapping and has similar accuracy as RFsp and inverse distance weighting. RFSI is outperformed byordinary kriging because this case study is created by geostatistical simulation and consequentiallyordinary kriging is an optimal interpolation method in this case. In the following two real-world casestudies, a daily precipitation for Catalonia for the 2016–2018 period and a daily mean temperaturefor Croatia for the year 2008, the accuracy of RFSI is compared with the accuracy of spatio-temporalregression kriging, inverse distance weighting, standard Random Forest and RFsp using a nestedviiUNIVERSITY OF BELGRADEFaculty of Civil EngineeringDepartment of Geodesy and Geoinformaticsk-fold leave-location-out cross-validation and RFSI outperformed all of them. RFSI is recommendedfor the interpolation of complex variables due to Random Forest’s ability to model non-linear relations between covariates and target variables. RFSI can be used for spatial or spatio-temporalinterpolation of any environmental variable.Next, a MeteoSerbia1km dataset — a rst gridded dataset for daily climate elements (maximum,minimum, and mean temperature, mean sea level pressure, and total precipitation) at a 1 km spatialresolution for Serbian territories for the 2000–2019 period — is created using RFSI methodologyfor spatio-temporal interpolation. Additionally, monthly and annual summaries and daily, monthly,and annual long term means maps of the climate elements are generated by aggregating the dailyMeteoSerbia1km maps. e nested 5-fold leave-location-out cross-validation is used to access theaccuracy of the MeteoSerbia1km daily dataset. e accuracy is high for daily temperature variablesand sea level pressure and lower for daily precipitation which was expected due to its complexity.MeteoSerbia1km daily maps are further compared with the 10-km E-OBS daily maps and show highcorrelation with them except for daily precipitation. e automation of the RFSI methodology is implemented within the R package meteo, in theform of four new R functions for creation, prediction, tuning, and cross-validation processes of RFSImodel.

Gridovani podaci dnevnih klimatskih elemenata visoke rezolucije predstavljaju znacajan izvor in- ˇformacija koje se koriste kao ulazni podaci za analize u klimatologiji, meteorologiji, poljoprivredi,hidrologiji, ekologiji i ostalim istraziva ˇ ckim oblastima i disciplinama. Prostorno-vremenske inter- ˇpolacione metode cesto se koriste za kreiranje gridovanih dnevnih klimatskih elemenata. Glob- ˇalni model prostorno-vremenskog regresionog kriginga za srednje dnevne temperature iznad povrsi ˇZemlje je pojednostavljen koristeci samo geometrijski temperaturni trend, digitalni model terena ´i topografski indeks vlaznosti (bez MODIS LST snimaka) kao prediktore i kalibrisan za podru ˇ cje ˇHrvatske koristeci podatke iz 2008 godine u ovoj disertaciji. Na osnovu prostorne kros-validacije, ´tacnost kalibrisanog modela iznosi R ˇ 2=97.8% i RMSE=1.2 ◦C, sto je pobolj ˇ sanje od 3.4% i 0.7 ˇ ◦C uodnosu na globalni model. Prilagodeni model srednjih dnevnih temperatura nadmasuje ostale ve ˇ c´razvijene modele za podrucje Hrvatske u pogledu ta ˇ cnosti i ima sli ˇ cnu ili ve ˇ cu ta ´ cnost u odnosu na ˇmodele za druga lokalna podrucja ili dr ˇ zave. Rezultati pokazuju da se globalni model prostorno- ˇvremenskog regresionog kriginga moze prilagoditi lokalnim podru ˇ cjima koriste ˇ ci mre ´ zu nacional- ˇnih meteoroloskih stanica i tako proizvesti gridovane podatke srednjih dnevnih temperatura ve ˇ ce ´tacnosti sa prostornom rezolucijom od 1 km. Kalibrisani model za podru ˇ cje Hrvatske jo ˇ s uvek ima ˇmanju tacnost u planinskim predelima, ˇ sto ga ˇ cini pogodnim za primenu u poljoprivrednim po- ˇdrucjima koja su na ni ˇ zim nadmorskim visinama. ˇAlgoritmi masinskog u ˇ cenja kombinovani sa inovativnim prostornim prediktorima predstavljaju ˇnovi oblik modela za prostornu ili prostorno-vremensku interpolaciju, koji mogu da se koriste i zainterpolaciju klimatskih elemenata. U ovoj disertaciji je predstavljena i testirana inovativna RandomForest Spatial Interpolation (RFSI) metodologija za prostornu ili prostorno-vremensku interpolaciju.RFSI metodologija je bazirana na Random Forest algoritmu masinskog u ˇ cenja koji koristi inovativne ˇprostorne prediktore: opazanja na ˇ n najblizih lokacija i rastojanja do njih. RFSI metodologija je ˇprimenjena i testirana na tri studije slucaja. U prvoj sinteti ˇ ckoj studiji, koja predstavlja simulirani ˇset podataka, tacnost RFSI metodologije je pore ˇ dena sa tacno ˇ sˇcu obi ´ cnog kriging-a, ˇ Random Forestfor spatial prediction (RFsp) metode, metode inverznih distanci (eng. inverse distance weighting), najblizeg suseda (eng. ˇ nearest neighbour) i mapiranja povrsi trenda (eng. ˇ trend surface mapping). Uovom slucaju, RFSI je pokazao ve ˇ cu ta ´ cnost u pore ˇ denju sa metodama najblizeg suseda i mapiranja ˇpovrsi trenda i sli ˇ cnu ta ˇ cnost kao RFsp i metoda inverznih distanci. Obi ˇ cni kriging je o ˇ cekivano dao ˇbolje rezultate od RFSI metodologije iz razloga sto je simulirani set podataka kreiran geostatisti ˇ ckom ˇsimulacijom i samim tim obicni kriging predstavlja optimalnu metodu interpolacije u ovom slu ˇ caju. ˇU ostale dve studije slucaja, koje se odnose na dnevne koli ˇ cine padavina za podru ˇ cje Katalonije ˇza 2016–2018 period i srednje dnevne temperature za podrucje Hrvatske za 2008 godinu, ta ˇ cnost ˇixUNIVERZITET U BEOGRADUGradevinski fakultetOdsek za geodeziju i geoinformatikuRFSI metodologije je poredena sa tacno ˇ sˇcu prostorno-vremenskog regresionog kriginga, metode in- ´verznih distanci, standardnom Random Forest i RFsp metodom koristeci ugnje ´ zdenu prostornu kros- ˇvalidaciju. RFSI metodologija je pokazala najbolje rezultate u ovim studijama. RFSI metodologija sepreporucuje za interpolaciju slo ˇ zenih parametara zbog osobine ˇ Random Forest algoritma da moze da ˇmodelira nelinearne veze izmedu prediktora i modeliranog parametra. RFSI metodologija se takodemoze koristiti za prostornu ili prostorno-vremensku interpolaciju bilo kog drugog parametra ˇ zivotne ˇsredine.Koristeci RFSI metodologiju za prostorno-vremensku interpolaciju, kreiran je MeteoSerbia1km ´set podataka koji predstavlja prvi set gridovanih dnevnih klimatskih elemenata (maksimalne, minimalne i srednje temperature, atmosferskog pritiska na nivou mora i kolicine padavina) sa pros- ˇtornom rezolucijom od 1 km za podrucje Srbije za period 2000–2019. Agregacijom dnevnih gri- ˇdovanih podataka dodatno su kreirani gridovani podaci mesecnih i godi ˇ snjih proseka (ukupne ˇkolicine za padavine) i gridovani podaci dnevnih, mese ˇ cnih i godi ˇ snjih dugoro ˇ cnih proseka kli- ˇmatskih elemenata. Tacnost dnevnih MeteoSerbia1km gridovanih podaka je ocenjena pomo ˇ cu ´ugnjezdene prostorne kros-validacije. Ta ˇ cnost dnevnih temperatura i atmosferskog pritiska na ˇnivou mora je visoka, dok je tacnost dnevnih padavina o ˇ cekivano ne ˇ sto manja zbog slo ˇ zenosti samih ˇpadavina. Dnevni MeteoSerbia1km gridovani podaci su takode poredeni sa E-OBS setom dnevnihgridovanih podataka sa prostornom rezolucijom od 10 km i pokazuju visok stepen korelacije, osimza padavine.RFSI metodolgija je automatizovana i implementirana u okviru R paketa meteo, kroz cetiri ˇnove R funkcije za procese kreiranja, predikcije, kalibrisanja i kros-validacije RFSI modela.