A Proposal to Expand the Community of Users Able to Process Historical Rainfall Data by Means of the Today Available Open Source Libraries

The paper presents a software architecture based on open source technologies, implemented by the authors in an experience of processing spatio-temporal data gathered by rain gauges spread across two regions of central Italy. The interest in the automatic processing of data about precipitation is widespread, however, today only an inner circle of stakeholders can think of taking advantage of the available open source libraries because a strong programming skill is required to use them. It is opinion of the authors that the implemented software architecture is suitable for expanding the community of users able to process “by themselves” historical precipitation data. The centre of the architecture is the technology of the spatial database management systems. They offer full support for the creation and management of a spatial database suitable to store the rainfall data usually spread out in several files. Moreover, they allow adding to such a repository a large set of ad hoc “objects” oriented to carrying out spatio-temporal computations on the precipitation. The stakeholders are only required to familiarize with the database’s objects and invoke their execution. A large part of the paper is devoted to show how the adopted conceptual setting can assist nontechnical users in carrying out personalized computations on rain gauges data. The computing needs posed by the experience described in this paper are common to many other areas of high social impact that involve spatio-temporal data, hence we believe that the implemented framework can be exported to them, keeping unaltered operational effectiveness

Spatial prediction of species’ distributions from occurrence-only records: combining point pattern analysis, ENFA and regression-kriging

A computational framework to map species’ distributions (realized density) using occurrence-only data and environmental predictors is presented and illustrated using a textbook example and two case studies: distribution of root vole (Microtes oeconomus) in the Netherlands, and distribution of white-tailed eagle nests (Haliaeetus albicilla) in Croatia. The framework combines strengths of point pattern analysis (kernel smoothing), Ecological Niche Factor Analysis (ENFA) and geostatistics (logistic regression-kriging), as implemented in the spatstat, adehabitat and gstat packages of the R environment for statistical computing. A procedure to generate pseudo-absences is proposed. It uses Habitat Suitability Index (HSI, derived through ENFA) and distance from observations as weight maps to allocate pseudo-absence points. This design ensures that the simulated pseudo-absences fall further away from the occurrence points in both feature and geographical spaces. The simulated pseudo-absences can then be combined with occurrence locations and used to build regression-kriging prediction models. The output of prediction are either probabilitiesy of species’ occurrence or density measures. Addition of the pseudo-absence locations has proven effective — the adjusted R-square increased from 0.71 to 0.80 for root vole (562 records), and from 0.69 to 0.83 for white-tailed eagle (135 records) respectively; pseudo-absences improve spreading of the points in feature space and ensure consistent mapping over the whole area of interest. Results of cross validation (leave-one-out method) for these two species showed that the model explains 98% of the total variability in the density values for the root vole, and 94% of the total variability for the white-tailed eagle. The framework could be further extended to Generalized multivariate Linear Geostatistical Models and spatial prediction of multiple species. A copy of the R script and step-by-step instructions to run such analysis are available via contact author’s website

Gridovi fine prostorne rezolucije dnevnih visina snijega za Rumunjsku (2005.–2015.)

This study presents the spatial interpolation procedure from snow depth measurements at weather stations implying the following stages: (1) Spatial interpolation at 1 km × 1 km resolution of the mean multiannual values (2005-2015) corresponding to each month, computed from the data extracted from the climatological database; (2) Computation of the daily deviations against the multiannual monthly mean for every day and year over 2005–2015 and their spatial interpolation; (3) Spatio-temporal datasets were obtained through merging the two surfaces obtained in stages 1 and 2. The anomalies were considered to be the ratio between the daily snow depth values and the climatology. The spatial variability of the data used in the first stage was accounted for through the use of a series of predictors derived from the digital elevation model (DEM). To plot the maps with the climatological normals (multiannual means), the Regression-Kriging (RK) spatial interpolation method was used. In order to choose the optimum method applied in spatializing deviations, four interpolation methods were tested using a cross-validation procedure: Multiquadratic, Ordinary Kriging (separated and pooled variograms) and 3d Kriging.Ova studija prikazuje proceduru prostorne interpolacije mjerenja dubine snijega na meteorološkim postajama koja podrazumijeva sljedeće faze: (1) prostorna interpolacija pri rezoluciji od 1 km x 1 km srednjih višegodišnjih vrijednosti (2005.–2015.), koja se provodi s podacima iz klimatološke baze; (2) izračunavanje dnevnih odstupanja od višegodišnjeg mjesečnog srednjaka za svaki dan i godinu tijekom razdoblja od 2005. do 2015. i njihova prostorna interpolacija; (3) prostorno-vremenski skup podataka dobiven je združivanjem procjena dobivenih u fazi 1 i 2. Odstupanja su definirana kao omjeri dnevnih vrijednosti dubine snijeg i klimatološkog srednjaka. Prostorna varijabilnost podataka korištenih u prvoj fazi objašnjena je korištenjem niza prediktora izvedenih iz digitalnog modela visina (DEM). Karte klimatoloških normala (višegodišnji srednjaci) izrađene su metodom prostorne interpolacije zvanom regresijski kriging (RK). Za odabir optimalne metode za prostornu interpolaciju odstupanja, testirane su četiri metode interpolacije i ocijenjene pomoću postupka poprečne validacije: multikvadratična, obični kriging (razdvojeni i skupni variogrami) i 3D kriging

The design, deployment, and testing of kriging models in GEOframe with SIK-0.9.8

This work presents a software package for the interpolation of climatological variables, such as temperature and precipitation, using kriging techniques. The purposes of the paper are (1) to present a geostatistical software that is easy to use and easy to plug in to a hydrological model; (2) to provide a practical example of an accurately designed software from the perspective of reproducible research; and (3) to demonstrate the goodness of the results of the software and so have a reliable alternative to other, more traditional tools. A total of 11 types of theoretical semivariograms and four types of kriging were implemented and gathered into Object Modeling System-compliant components. The package provides real-time optimization for semivariogram and kriging parameters. The software was tested using a year's worth of hourly temperature readings and a rain storm event (11 h) recorded in 2008 and retrieved from 97 meteorological stations in the Isarco River basin, Italy. For both the variables, good interpolation results were obtained and then compared to the results from the R package gstat

Random Forest Spatial Interpolation

For many decades, kriging and deterministic interpolation techniques, such as inverse distance weighting and nearest neighbour interpolation, have been the most popular spatial interpolation techniques. Kriging with external drift and regression kriging have become basic techniques that benefit both from spatial autocorrelation and covariate information. More recently, machine learning techniques, such as random forest and gradient boosting, have become increasingly popular and are now often used for spatial interpolation. Some attempts have been made to explicitly take the spatial component into account in machine learning, but so far, none of these approaches have taken the natural route of incorporating the nearest observations and their distances to the prediction location as covariates. In this research, we explored the value of including observations at the nearest locations and their distances from the prediction location by introducing Random Forest Spatial Interpolation (RFSI). We compared RFSI with deterministic interpolation methods, ordinary kriging, regression kriging, Random Forest and Random Forest for spatial prediction (RFsp) in three case studies. The first case study made use of synthetic data, i.e., simulations from normally distributed stationary random fields with a known semivariogram, for which ordinary kriging is known to be optimal. The second and third case studies evaluated the performance of the various interpolation methods using daily precipitation data for the 2016–2018 period in Catalonia, Spain, and mean daily temperature for the year 2008 in Croatia. Results of the synthetic case study showed that RFSI outperformed most simple deterministic interpolation techniques and had similar performance as inverse distance weighting and RFsp. As expected, kriging was the most accurate technique in the synthetic case study. In the precipitation and temperature case studies, RFSI mostly outperformed regression kriging, inverse distance weighting, random forest, and RFsp. Moreover, RFSI was substantially faster than RFsp, particularly when the training dataset was large and high-resolution prediction maps were made

SciKit-GStat 1.0: a SciPy-flavored geostatistical variogram estimation toolbox written in Python

Geostatistical methods are widely used in almost all geoscientific disciplines, i.e., for interpolation, rescaling, data assimilation or modeling. At its core, geostatistics aims to detect, quantify, describe, analyze and model spatial covariance of observations. The variogram, a tool to describe this spatial covariance in a formalized way, is at the heart of every such method. Unfortunately, many applications of geostatistics focus on the interpolation method or the result rather than the quality of the estimated variogram. Not least because estimating a variogram is commonly left as a task for computers, and some software implementations do not even show a variogram to the user. This is a miss, because the quality of the variogram largely determines whether the application of geostatistics makes sense at all. Furthermore, the Python programming language was missing a mature, well-established and tested package for variogram estimation a couple of years ago. Here I present SciKit-GStat, an open-source Python package for variogram estimation that fits well into established frameworks for scientific computing and puts the focus on the variogram before more sophisticated methods are about to be applied. SciKit-GStat is written in a mutable, object-oriented way that mimics the typical geostatistical analysis workflow. Its main strength is the ease of use and interactivity, and it is therefore usable with only a little or even no knowledge of Python. During the last few years, other libraries covering geostatistics for Python developed along with SciKit-GStat. Today, the most important ones can be interfaced by SciKit-GStat. Additionally, established data structures for scientific computing are reused internally, to keep the user from learning complex data models, just for using SciKit-GStat. Common data structures along with powerful interfaces enable the user to use SciKit-GStat along with other packages in established workflows rather than forcing the user to stick to the author\u27s programming paradigms. SciKit-GStat ships with a large number of predefined procedures, algorithms and models, such as variogram estimators, theoretical spatial models or binning algorithms. Common approaches to estimate variograms are covered and can be used out of the box. At the same time, the base class is very flexible and can be adjusted to less common problems, as well. Last but not least, it was made sure that a user is aided in implementing new procedures or even extending the core functionality as much as possible, to extend SciKit-GStat to uncovered use cases. With broad documentation, a user guide, tutorials and good unit-test coverage, SciKit-GStat enables the user to focus on variogram estimation rather than implementation details