Spatial interpolation of Automatic Weather Station data

INTERNSHIP REPORT Spatial interpolation of Automatic Weather Station data GOYBET Thomas Internship supervisor : Dr. Mathias Bavay, WSL Institute for Snow and Avalanche Research SLF (Davos, Switzerland) University supervisor : Pr. Patrick Rairoux, Institute for Light and Matter (Lyon, France) 27/08/2025 ”But since our measurements and observations are nothing more than approximations to the truth, the same must be true of all calculations resting upon them” (Karl Friedrich Gauss, 1809) Abstract Spatial interpolation algorithms play a crucial role when working with Automatic Weather Station (AWS) data. Because AWS are limited in number and expensive to install in remote mountain regions, interpolation is necessary to extend their measurements to locations without direct observations. The performance of the spatial interpolation algorithms directly impacts the quality of the interpolated data and therefore the reliability of the results. In mountain environments, however, their performance can be constrained by complex topography and micrometeorological conditions. The quality of the input data, the number of AWS used, and their spatial distribution in elevation and distance strongly influence the outcome of the interpolation. To provide guidance on how to choose and configure the algorithms, a point-to-point interpolation study was carried out. The open-source library MeteoIO, developed by the WSL Institute for Snow and Avalanche Research SLF in Davos (Switzerland), was used to perform the interpolations. Based on the dense AWS network in the Davos region and a cleaned dataset, a set of recommendations has been established. These recommendations serve as guidelines to support the setup of spatial interpolations of AWS data in new study areas. Key words : Spatial interpolation, Automatic Weather Station (AWS), MeteoIO, INIshell, SNOWPACK, Meteorological field, Davos, SLF Acknowledgements First of all, I want to warmly thank Mathias for his supervision all along the internship and for the discussions we had from the first interview to the last days of the internship. He took the time to explain me the project several times, and to discuss the results I had and help me to improve my work. I hope our paths will cross again in the future. I also want to thank the Snow Processes group for including me in the meetings and giving me some advice during the presentations I did during some meetings. I want to thank my office mates, Anja and Sergi, with whom it was so comfortable to work in the same room. I was always impressed by their professionalism on the subjects they handle, and it makes me want to be as good as the experts they are one day . A big thank you goes to all the master students with whom I shared sports moments, lots of laughs and my thoughts, so thank you Marcel, Robin, Leah, Isa, both Yanniks, Alfred, Ida, Pia, Alesch, Arnod, Deborah, No¨ el, Florian, Chris, and all the others with whom we shared dinners. This Davos experience would not have been the same without you. At last, I want to thank Dr. Alain Miffre for his advice before the internship, and the Master of Ocean, Atmosphere and Climate Sciences program that allows me to dive into one of my dreams : working on Climate Sciences in Alpine regions, where I love to spend time. 1 CONTENTS CONTENTS Contents 1 Introduction 3 2 Methods 4 2.1 DataAvailability .................................... 4 2.2 MeteoIO......................................... 4 2.3 Workflow ........................................ 5 2.4 How to set up the recommendations . . . . . . . . . . . . . . . . . . . . . . . . . 6 3 Theory 7 3.1 Interpolationalgorithm ................................ 7 3.1.1 Non physical interpolation algorithm . . . . . . . . . . . . . . . . . . . . . 7 3.1.2 Interpolation algorithm for each parameter . . . . . . . . . . . . . . . . . 8 3.2 K-Combinations..................................... 9 3.3 Correlation factor R2.................................. 9 4 Results 10 5 Discussion 10 5.1 Spatial interpolation algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 5.2 Discussion for each recommendation . . . . . . . . . . . . . . . . . . . . . . . . . 12 5.2.1 Recommendation1............................... 12 5.2.2 Recommendation2............................... 12 5.2.3 Recommendation3............................... 14 5.2.4 Recommendation4............................... 15 5.2.5 Recommendation5............................... 15 6 Conclusion 16 A Appendix 17 A.1 IMIS Automatic Weather Station . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 A.2 Workflowscheme.................................... 18 A.3 Study case : Spatial interpolation for a snowpack . . . . . . . . . . . . . . . . . . 18 B References 21 2 1 INTRODUCTION 1 Introduction Environmental scientists often need some high quality and high resolution meteorological data for their projects to run physical models (Liston & all, 2006)[1]. But it can be a challenge that is not easy to solve. One way of getting some meteorological data may come from point measurements such as Automatic Weather Stations (AWS), and need to be spatially interpolated to the desired resolution. This way of getting meteorological data in Alpine areas was investigated during this internship, with a focus on the performances of the spatial interpolation algorithms integrated in the SLF product MeteoIO (Bavay & Egger, 2014)[2]. Some examples of spatial interpolation can be found in avalanche predictions (Morin & all, 2020) [3], (Monti & all, 2016) [4], avalanche danger level (Richter & all, 2021)[5], climate predictions for snow making and growing in modern ski resorts (Hanzer & all, 2020)[6], hydrological models (Carletti & all, 2022)[7] or river temperature future under climate change in Switzerland (Michel & all, 2022)[8]. As part of the first year of the Master of Ocean, Atmosphere and Climate Sciences program supported by Lyon 1 University and Ecole Centrale de Lyon in France, I did a 4-month internship under the supervision of Dr. Mathias Bavay at the WSL Institute for Snow and Avalanche Research SLF located in Davos, Switzerland, within the Snow and Atmosphere unit in the Snow Processes group. The goal of this internship is to provide a list of recommendations for the users of numerical models who need to perform spatial interpolation. To do so, I will be using the very rich and dense AWS network of Davos that counts 72 AWS and that started recording in 1975. This will allow me to explore many different configurations of station distributions in mountain areas. The reader will find the methods applied to establish the recommendations, the needed theory to do so, the result section with the 5 recommendations that were found, a discussion of the result section, some outlooks in the conclusion section and a study case in the appendix. 3 2 METHODS 2 Methods The method section highlights where the dataset is coming from, gives some insights about MeteoIO, highlights the chosen workflow, and highlights the way the recommendations were deduced. 2.1 Data Availability Davos has one of the most dense networks of AWS in the world, with more than 70 AWS in the area composed of IMIS AWS and non IMIS AWS. In 1996, the SLF and the Swiss Mountain cantons started to build IMIS weather stations, which are standardized AWS with a solar panel, and sensors to measure snow depth, air and surface temperature, as well as wind speed and direction, relative humidity, reflected short wave radiation, ground temperature, snow temperature at 25, 50 and 100 cm above the ground, and, at most stations, rainfall using a rain gauge. See a picture of it in appendix A.1. IMIS AWS files are generally well structured, with clear ownership. Although some metadata may be missing, such as imprecise coordinates or uncertain sensor heights, but these issues are relatively minor. In contrast, non-IMIS AWS presented far greater challenges: there was no standardization of parameter names, many coordinates were missing, large amounts of data were forgotten or inaccessible (sometimes left on old hard drives), some datasets lacked any context regarding their origin, and often no contact person was available. A huge work has been done by Dr. Mathias Bavay to clean all the files and make them standardized. He provided a clean dataset of 72 AWS data under the .smet format. A .smet file is a standard file for meteorological data composed of some metadata and the data itself. The metadata provides useful information about the AWS, such as the name of the station, the localization of the AWS given 2 coordinate systems, the altitude, the units, the name of the measured fields, the abbreviation used for each field, and as well some information about the data owner of the .smet file. The .smet files were prepared using the open source library MeteoIO, which will be introduced in section 2.2. The dataset is not yet published. Therefore, it is not present in the report. 2.2 MeteoIO MeteoIO was published by Bavay & Egger (2014)[2] and is an open-source library designed to process meteorological input and output data files. It is widely used both in research, as in this internship, and in operational contexts, for example by the avalanche forecasting team at SLF. One of its key roles is to transform raw input data into filtered, corrected, and standardized datasets. These efforts are illustrated for instance in Bavay & all (2020)[9], and reflects the bridge from research to operational needs. Many features are available in this library, but only the spatial interpolation feature was used in this study, since the input data are already cleaned and that the goal of the internship is to dive into the performances of the spatial interpolations. Each spatial interpolation algorithm has its default parametrization and can be changed if needed. In this study, the default parametrization will be applied in order to avoid introducing any bias into the algorithms. 4 2.3 Workflow 2 METHODS MeteoIO reads .ini files. We can either write the .ini files and give them to MeteoIO or use INIshell (Bavay & all, 2022)[10] which is a user-friendly interface for reading and writing .ini files. It is of particular help for the simplicity of navigation in MeteIO features and hides the complexity of the model. In this study, INIshell was used to understand the structure of the .ini files, to debug the workflow and to launch MeteoIO simulations. To perform spatial interpolations, MeteoIO requires as input a Digital Elevation Model (DEM) for the study area, here Davos. The DEM used in this work has a resolution of about 10 meters, which also defines the resolution of the interpolations. Since the objective is to perform point-to-point interpolations (see Section 2.3), such a resolution is sufficient. A finer DEM (1 to 2 meters) would not significantly improve the results but would drastically increase computational time. For most algorithms, the interpolation is performed only for the DEM cell containing the reference AWS, with elevation, slope, and aspect taken from the DEM rather than from the station itself. For algorithms where the surrounding terrain plays a role, such as the LISTON WIND algorithm for wind parameters, the interpolation is carried out over the whole DEM before extracting the target cell. In addition, this study relies on the virtual station (vstation) feature of MeteoIO (MeteoIO documentation)[19]. A vstation is defined as a point for which MeteoIO reconstructs time series by filtering and processing the input data, temporally interpolating them, and finally applying the selected spatial interpolation methods. The user provides the coordinates and elevation of the virtual point, as well as the parameters to interpolate, and MeteoIO outputs a .smet file containing both metadata and the interpolated data. Beyond research needs, vstations are also applied in operational contexts, for example in avalanche warning systems (Monti & all, 2016) [4]. In this study, vstations are systematically created at the exact locations of real AWS, enabling direct comparison between interpolated and observed values. Only the spatial interpolation feature will be used to reconstruct the data. This approach is central to our validation methodology, as it provides a robust assessment of algorithm performance. 2.3 Workflow To achieve the objective of this internship, a workflow was established to ensure reproducibility of the method and to avoid randomness. The key idea is to apply a Leave-One-Out CrossValidation approach: among the distributed AWS network, one station is temporarily excluded from the interpolation and treated as a vstation. Its coordinates are identical to those of the excluded reference AWS, which allows us to compare interpolated values against actual measurements at the same location, see figure 1. This setup provides a robust framework to evaluate how close the interpolated values are to real observations, using the correlation factor R2as a performance score for each spatial interpolation. The computation of R2will be detailed in section 3.3. Appendix A.2 shows a figure of the workflow that was automated. Its steps would be the following : 1. Choose one meteorological parameter : such as air temperature, relative humidity, radiations, etc. 5 2.4 How to set up the recommendations 2 METHODS 2. Choose a pool of stations to be used for the interpolation. The station must have the chosen parameter, otherwise they will not be used by the interpolation algorithm. The size of the pool of stations will increase or decrease the computational time of the simulation, depending on the pool size. 3. Choose one vstation : The vstation must be excluded from the station pool used to perform the interpolation algorithm. Otherwise, the results would be biased and appear artificially high, since many algorithms tend to predict the local value when a measured observation is already available at the interpolation point. The vstation must also contain the chosen parameter in its .smet file. 4. Create all the possible distinct combinations, regardless of the order of the stations, as it will not change anything in the interpolation. See section 3.2. 5. Write a .ini file for each combination. 6. Convert the .smet files from the interpolated data and the referenced station to .txt files with only the header with the reduced name of the field and the data. 7. Filter all the no data marked as -999. 8. Check that the two .txt files from the interpolated data and the referenced station have the exact same date and time step, so we can compare the data for a similar date. The goal of this step is to avoid comparing daytime data to nighttime data, for example. 9. Once the time steps are the same between the vstation .txt file and the reference station .txt file, we can compute the correlation factor R2for the predicted data and the real data. 10. Then we have a result file full of R2as the corresponding .ini files and we can start to learn some rules. The workflow was coded with Python and looped for each combinations of stations. The computational time was high, up to tens of hours or even to days. In order to reduce it, the Python code used was parallelized on the CPUs of the computer and a cluster with much more computational power called Hyperion [20] was used. This helped to reduce the computational time from hours to minutes. 2.4 How to set up the recommendations To set up a recommendation, some analysis was done on the result files at the end of the workflow. Three plots were made and had the same structure : The correlation factor R2as a function of the number of stations, the difference between the mean altitude of the selected stations for the interpolation and the altitude of the reference station, and the mean distance of the group of stations to the reference station. These plots highlighted the simulations with low and high R2and helped to understand what the common points for these simulations were. Once the common points were found, they were used to express recommendations, which are available in section 4. 6 3 THEORY Virtual station Input station Reference station Figure 1: Illustration of spatial interpolation at the vstation. Meteorological fields are interpolated to the location of the vstation, which shares the same coordinates as the reference station, enabling cross validation between observed and interpolated data. 3 Theory The theoretical part highlights the interpolation algorithms used during the internship, as well as the K-combinations that were used and how the correlation factor is described and interpreted in this study. 3.1 Interpolation algorithm Depending on the chosen parameter, several spatial interpolation algorithms can be used, but some are more constrained than others and may lead to dependencies. A first approach was statistical, which means that regardless of the physics of the parameter, many spatial interpolation algorithms were used, and the one that gave the best results was chosen. A second approach was to take into account the physics behind each parameter and show that the interpolation algorithm that is the closest to its physics will give higher correlation factors and should be used. The interpolation algorithms can be found in MeteoIO documentation [19]. In this subsection, a first part will be dedicated to the non-physical interpolation algorithm used, then a second part for each interpolation algorithm that matches the physics of the given parameter. In this study, the results of the second approach are presented. 3.1.1 Non physical interpolation algorithm It is possible to use no interpolation algorithm for a parameter by selecting the NONE option. This can be useful when a parameter only needs to be set up as input for another interpolation algorithm. 7 3.1 Interpolation algorithm 3 THEORY The NEAREST algorithm assigns the value of the nearest input station for the considered parameter to the virtual station. The average (AVG) algorithm calculates, for each time step, the average value of all input stations and uses it as the output value. The Inverse Distance Weighting (IDW) algorithm works as described in equation 1: ypred =Pi1 dαui Pi1 dα (1) where ypred is the predicted value, uiis the value from station iat the given time step, dis the distance between the reference station and the considered station, and αcontrols the weight of the distance. A larger αgives more influence to nearby stations. Inside MeteoIO, the default value of αis 1. If a physical interpolation algorithm fails due to overly strict constraints, IDW was used as a fallback. It is also worth noting that these statistical algorithms can be applied not only directly to the raw values but also in combination with altitudinal detrending. In this case, an elevation-dependent trend (e.g. lapse rate) is first computed and removed from the data, the detrended values are interpolated with the chosen algorithm, and the trend is then re-applied to reconstruct the interpolated series. This approach helps to better capture altitude-dependent processes and can improve interpolation performance in mountainous terrain. 3.1.2 Interpolation algorithm for each parameter The interpolation algorithms are greatly inspired by the ones inside the MicroMet model developed by Liston & all [1]. We know that air temperature TA changes in the altitude with a lapse rate in the troposphere. Therefore, a LAPSE algorithm will compute a linear regression for the data, detrend the temperature to sea-level, then compute the interpolation algorithm for this temperature whichever chosen spatial interpolation algorithm on the detrend data, then retrend the interpolated temperature to the altitude of the vstation. This is a more physical approach to interpolating the temperature. But this can lead to some problems, see the discussion in section 5.2.2. For relative humidity RH, the most suited interpolation algorithm is the one named LISTON RH. This algorithm first derives the dew point temperature for the given RH, then applies an interpolation algorithm to the dew point temperature, and the interpolated RH is again derived from the interpolated dew point temperature. Therefore, TA should be known and has to be interpolated. For pressure P, the most suited algorithm is the standard atmospheric pressure algorithm STD PRESS. This algorithm computes the pressure at the desired elevation if no pressure is measured. If one station measures it, then the offset between the local pressure and the standard atmosphere pressure is added to the computed pressure for the desired elevation. 8 5.2 Discussion for each recommendation 5 DISCUSSION 5.2.4 Recommendation 4 Recommendation 4 underlines favoring the largest possible number of valid stations to improve interpolation quality. But the stations used must have pass recommendations 1, 2, and 3. Figure 6(a) shows the evolution of the correlation factor for different numbers of stations for each interpolation. As mentioned in section 5.2.2, an interpolation with a lapse algorithm should have at least 2 stations in input. Figure 6(a) was filtered with the past recommendations and zoomed on 0.8 and 1.0 for the correlation factor. We see as well that 3 given stations for the interpolation are already enough to have a high performance of the interpolation. 5.2.5 Recommendation 5 Recommendation 5 points out limiting the distance of stations used to a maximum of 25 km from the interpolation point. It comes from the limitation of the spatial distribution of stations in the dataset. All the stations are in Davos area, therefore not too far from one another. Figure 6(b) shows the maximum distance between the 2 furthest stations is 25km, and the score for this interpolation is still high using a detrending algorithm. So the distance threshold is set at 25km. It might be possible that stations further away from the interpolation point work as long as they are in mountain area, but it has to be validated. Nevertheless, distance is a much more minor problem compared to altitude. It is much more important to check the altitude distribution of the stations than the distance. For the same setup as in figure 6(a), we observe in figure 6(b) that the distance has no impact on the scores distribution. 2 4 6 8 10 Number of station 0.800 0.825 0.850 0.875 0.900 0.925 0.950 0.975 1.000 Correletion factor R² Correlation factor as a function of the number of station Method : IDW_LAPSE Individuel scores Mean Mean + 3 Mean - 3 ((a)) Correlation factor as a function of the number of stations, zoomed on the range 0.8–1.0 of R2. 10000 12000 14000 16000 18000 20000 22000 24000 Mean distance to the reference station [m] 0.0 0.2 0.4 0.6 0.8 1.0 Correlation factor R² Correlation factor as a function of the mean distance of each simulations to the reference station Method : IDW_LAPSE Individual scores Mean Mean + 3 Mean - 3 ((b)) Correlation factor as a function of distance to the reference station. Figure 6: Correlation factor as a function of the number of stations (a) and the distance to the reference station (b). The interpolated parameter is the air temperature and the interpolation algorithm used is IDW LAPSE. In both figures, the blue dots represent the distribution of the scores for each number of stations, the red points and line show the mean score, and the orange area corresponds to the mean value ±3 times the standard deviation. 15 6 CONCLUSION 6 Conclusion Spatial interpolations are of very great in order to get meteorological data where they are not directly measured by Automatic Weather Stations, in order to make the most out of the already available AWS. This study showed that spatial interpolation performance can be of high quality if some conditions are fulfilled. The key messages resulting from this study are that for the time period of interest, the quality of the input data should be of high quality, and that the elevation distribution of the stations should be within some altitude ranges. The distance to the location of interpolation has less effect on the performances of the algorithms than the elevation. High performances of spatial interpolation were found for air temperature, relative humidity, and short and long waves radiations. Precipitation and wind fields are still research topics to tackle and may require other techniques to assess them, such as machine learning and deep learning. It is also important to notice that Davos is very particular for the unusually large number of weather stations that have been set up and are still running. In other places, where the density of AWS is less, the recommendations will help to choose an interpolation algorithm and lead to high quality interpolated data. The purpose of highlighting some recommendations is to use them in places where there are fewer Automatic Weather Stations. Therefore, it would be very useful to apply the recommendations somewhere where there are fewer AWS and check if we can improve the quality of the interpolations or validate what was already done. These recommendations can be also useful in more remote areas, in Alpine regions or in polar regions where it is hard to set up large AWS domain and where it is crucial to get high quality data to better assess Climate Change. As well, since the SLF has a purpose of warning and preventing avalanche natural hazards, it would be interesting to try these recommendations for modelling snow cover properties related to avalanche danger. 16 A APPENDIX A Appendix A.1 IMIS Automatic Weather Station Figure 7: IMIS snow station Belalp (canton Valais) at 2556 m: The four poles visible in front of the station carry a fence to protect the snow temperature sensors from wild animals and livestock in the summer period. Credits : https://www.slf.ch/en/avalanche-bulletin-and-snow-situation/ measured-values/description-of-automated-stations/ 17 A.2 Workflow scheme A APPENDIX A.2 Workflow scheme Figure 8: Scheme of the workflow. A.3 Study case : Spatial interpolation for a snowpack In order to evaluate the recommendations established in this work, spatial interpolations of selected meteorological parameters were performed for the winter 2023–2024, followed by an attempt to simulate the snowpack evolution. The simulations were carried out with the open-source SNOWPACK model, developed by the WSL Institute for Snow and Avalanche Research SLF (Lehning & all, 1999) [16]. SNOWPACK is designed to simulate the evolution of the snow cover and the ground surface based on meteorological data (air temperature, relative humidity, wind speed, precipitation, snow height, radiations, ground temperature). It models snow microstructure and the interactions between snow, the atmosphere, the soil, and the snowpack itself. It is widely used for both operational applications as for avalanche forecasting (Lehning & all, 1999) [16] and research purposes (Obleitner & Lehning, 2004)[17]. The purpose of this study case was not to conduct a depth analysis of SNOWPACK itself, but rather to test whether a realistic snowpack could be reconstructed over one winter using spatially interpolated data. For this, I used the example case provided in the SNOWPACK documentation, which contains an .ini configuration file and input data from a reference station. The set up of the .ini file would not be modified, except for the input stations and the spatial interpolation algorithms. The reference station chosen is located at Weissfluhjoch (Davos, 2556m elevation), at the SLF measurement site. The simulation was run for the 2023–2024 winter season. Based on the recommendations established during this internship, 12 surrounding AWS were selected to provide interpolated input for air temperature, relative humidity, and reflected shortwave radiation. Incoming shortwave radiation was derived from reflected shortwave values and the albedo, while incoming longwave radiation could not be interpolated due to insufficient coverage. Instead, the generator feature of MeteoIO was 18 A.3 Study case : Spatial interpolation for a snowpack A APPENDIX applied, using the ALL SKY option and the Unsworth model (MeteoIO documentation) [19]. Other required meteorological parameters such as wind speed, snow height, and ground temperature were taken directly from the reference station. First the interpolation would take place in MeteoIO, then this file would be merged with the reference file with the missing parameters (wind speed, snow height, precipitations). Initial results showed missing layers in the simulated profile, which reappeared once liquid precipitation data from the reference station were added. Figures 9(a) and 9(b) present the comparison between the reference snowpack and the interpolated one. ((a)) Snowpack of reference ((b)) Snowpack interpolated Figure 9: Comparison between a reference snowpack and an interpolated snowpack for winter 2023–2024 using the SNOWPACK model. The left y-axis shows the snow grain types (red = melting snow, red-black line = melt-freeze crust, green = new snow, pink = rounded grains, and the blue = faceted crystals, see Fierz & all, 2009 [18]), while the right y-axis indicates snow depth. The x-axis represents the time period from 01/09/2023 to 01/09/2024. Panel (a) displays the snowpack simulated with measurements from Weissfluhjoch, whereas panel (b) shows the snowpack simulated with interpolated air temperature, relative humidity, and reflected shortwave radiation, combined with measured snow height, wind speed, ground temperature, and precipitation at Weissfluhjoch. The results indicate that the general snowpack structure, from the first snow precipitations to the last melt, the height of the snow including its main layers, was reproduced reasonably well. However, some layers were missing, likely due to small discrepancies in interpolated temperature or humidity at key moments, preventing the formation of certain stratigraphic features. 19 A.3 Study case : Spatial interpolation for a snowpack A APPENDIX This highlights that, even when interpolation performance is high, fine-scale details may still be lost. Furthermore, the quality of wind speed, snow height, and precipitation data proved essential, as these variables strongly affect processes such as refreezing within the snowpack. Missing or inaccurate values led directly to missing layers. This underlines the importance of providing high-quality input data for wind, precipitation, and snow height when reconstructing snowpack profiles, which was a limiting factor in this study focused on the performance of spatial interpolations. 20 B References [1] Liston, G.E. & Elder, K., 2006. A meteorological distribution system for highresolution terrestrial modeling (MicroMet). Journal of Hydrometeorology, 7(2), pp.217–234. https : / / journals . ametsoc . org / view / journals / hydr / 7 / 2 / jhm486_1.pdf pages 3, 8 [2] Bavay, M. and Egger, T.: MeteoIO 2.4.2: a preprocessing library for meteorological data, Geosci. 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