Lab Interpolation
Compilation of methods for air temperature interpolation across Austria.
The Zentralanstalt für Meteorologie und Geodynamik (ZAMG) operates one of the densest meteorological networks worldwide. Since October 2021, the ZAMG Data Hub provides free access to high-quality weather and climate data via NetCDF and CSV files. For this analysis I have collected daily mean air temperature data from all the available stations on November 10, 2021. Simple data engineering was performed to drop all the stations with NaN values, as well as a relate operation to merge the data with the metadata to include latitute, longitue and air temperature values into a single CSV file. In total, 248 stations were identified as operational.
Source: https://data.hub.zamg.ac.at/
Spatial distribution of weather stations measuring air temperature in Austria on November 10, 2021.
Method 1. Inverse distance weighting (IDW) using 2 and 2.5 as power values and a variable search radius to consider the closest 12 points. The stretch symbology was chosen with a histogram equalization to enhance the visualization.
Figure 1. IDW with a power value 2 (left), and IDW with a power value 2.5 (right).
Method 2. Kriging (Ordinary and Universal). The Ordinary method was calculated with a spherical semivariogram model, whereas the Universal method employed a linear drift semivariogram model. The stretch symbology was chosen with a percent clip type to enhance the visualization.
Figure 2. Ordinary Kriging (left), and Universal Kriging (right).
Method 3. Empirical Bayesian kriging (EBK) in ArcGIS online.
Figure 3. EBK (left), and error values (right).
Method 4. Empirical Bayesian Kriging (EBK) in ArcGIS Pro using 100 simulations of a power semivariogram model and a smooth circular search neighborhood with a smoothing factor of 0.2. The stretch symbology was chosen with a histogram equalization to enhance the visualization.
Figure 4. EBK interpolation using ArcGIS Pro.
Table 1. Statistics of the interpolation methods in comparison to the original dataset.
Discussion. Interpolation quality assessment depends on the applied methodology. For instance, the Empirical Bayesian Kriging accounts for the uncertainty by estimating the weight of repeating simulations. This process creates a large number of semivariograms, which measure the statistical correlation between the data points as a function of distance. Various semivariogram models exist, differing in speed, performance and accuracy, such examples include linear, gaussian, exponential, circular and spherical, among others (Fig 5). To get reliable results the chosen semivariogram must match the behavior of the studied phenomena.
Figure 5. Semivariogram models for Kriging interpolation.
To evaluate interpolation results I suggest to take a random set of known measurements (20%) to act as validation values. For example, if 248 data points are available, I would only use 200 points for interpolation and 48 for verification, then perform a statistical analysis such as the root mean square error (RMSE) between the predicted and real values. Another suggestion to evaluate temperature interpolation is to use numerical weather prediction model outputs for cross-referencing. My third suggestion is to utilize independent datasets such as WegenerNet (Fuchsberger J., et al 2021) or crowdsourced data from personal weather stations, which are typically denser than automatic weather stations.
Limitations. ArcGIS Online uses the EBK method, however it only offers a default and unmodifiable parametrization. Therefore, ArcGIS Pro was used to perform the IDW, EBK, and Kriging analyses. Another limitation is related to the utilized dataset, since the measurements are constrained to Austria, the interpolation is not exempted of experiencing edge related problems.
