GSTools v1.3: A toolbox for geostatistical modelling in Python

Geostatistics as a subfield of statistics accounts for the spatial correlations encountered in many applications of e.g. Earth Sciences. Valuable information can be extracted from these correlations, also helping to address the often encountered burden of data scarcity. Despite the value of additional data, the use of geostatistics still falls short of its potential. This problem is often connected to the lack of user-friendly software hampering the use and application of geostatistics. We therefore present GSTools, a Python-based software suite for solving a wide range of geostatistical problems. We chose Python due to its unique balance between usability, flexibility, and efficiency and due to its adoption in the scientific community. GSTools provides methods for generating random fields, it can perform kriging and variogram estimation and much more. We demonstrate its abilities by virtue of a series of example application detailing their use.

SciKit-GStat 1.0: A SciPy flavoured geostatistical variogram estimation toolbox written in Python

Geostatistical methods are widely used in almost all geoscientific disciplines, i.e. for interpolation, re-scaling, data assimilation or modelling. 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 rather focus on the interpolation method or the result, 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 usage and interactivity and it is therefore usable with only a little or even no knowledge in 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 authors 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 at implementing new procedures, or even extending the core functionality as much as possible, to extend SciKit-GStat to uncovered use-cases. With broad documentation, user guide, tutorials and good unit-test coverage, SciKit-GStat enables the user to focus on variogram estimation, rather than implementation details.

GSTools: The Python toolbox for your geo-statistical project!

<p><span>Geo-scientific model development is lacking comprehensive open source tools, that are providing state-of-the art geo-statistic methods. To bridge this gap, we developed </span><span>a</span><span> geo-statistical toolbox named GSTools, which is a Python package providing an </span><span>abundance</span><span> of methods in a modern object oriented approach. Covered </span><span>use-cases</span><span> are:</span></p><ul><li> <p>covariance models (many readily provided and even user-defined models with a lot of functionality)</p> </li> <li> <p>random field generation (multigaussian and in-compressible vector fields)</p> </li> <li> <p>field transformations (boxcox, Zinn and Harvey, log-normal, binary)</p> </li> <li> <p>kriging (simple, ordinary, universal, external drift or detrended)</p> </li> <li> <p>variogram estimation (Cressie and Matheron estimators)</p> </li> <li> <p>I/O routines (interfaces to pyvista and meshio for mesh support)</p> </li> <li> <p>plotting routines (inspect your covariance model or random field on the fly)</p> </li> </ul><p><span>GSTools is developed openly within a GitHub organization </span><span>(</span>https://github.com/GeoStat-Framework<span>). O</span><span>n the one hand to be able to respond to the needs of the modeling community and integrate suggested functionalit</span><span>ies</span><span> and contributions,</span><span> on the other hand to guarantee stability and reliability of the code-base through continuous-integration features provided by the GitHub infrastructure</span><span>.</span></p><p>We will present several applications of the mentioned routines to demonstrate the interface and capabilities of GSTools.</p>

Spatially shifting temporal points: estimating pooled within-time series variograms for scarce hydrological data

Estimation of pooled within-time series (PTS) variograms is a frequently used technique for geostatistical interpolation of continuous hydrological variables in spatial data-scarce regions conditional that time series are available. The only available method for estimating PTS variograms averages semivariances, which are computed for individual time steps, over each spatial lag within a pooled time series. However, semivariances computed by a few paired comparisons for individual time steps are erratic and hence they may hamper precision of PTS variogram estimation. Here, we outlined an alternative method for estimating PTS variograms by spatializing temporal data points and shifting them. The data were pooled by ensuring consistency of spatial structure and stationarity within a time series, while pooling sufficient number of data points for reliable variogram estimation. The pooled spatial data point sets from different time steps were assigned to different coordinate sets on the same space. Then a semivariance was computed for each spatial lag within a pooled time series by comparing all point pairs separable by that spatial lag, and a PTS variogram was estimated by controlling the lower and upper boundary of spatial lags. Our method showed higher precision than the available method for PTS variogram estimation and was developed by using the freely available R open source software environment. The method will reduce uncertainty for spatial variability modeling while preserving spatiotemporal properties of data for geostatistical interpolation of hydrological variables in spatial data-scarce developing countries.