1. Introduction

    As time progresses, our society relies more and more heavily on climate data analysis and necessitates reliable weather measurement to create long-term climate models, daily weather forecasts or even vulnerabilities assessments  (Jones et al., (2009) ; Rummukainen, (2012 )). Weather forecasting and climatology first developed distinct traditions and data sources during the 19th century. This led to the emergence of climate modeling in the 1960s, bringing together the two fields and changing scientists' perspectives from a local to a global perspective (Barry and Chorley (2009); Edwards, (2010); Mauelshagen, (2014); Baker, (2017)). Forecasting the weather, however, was still difficult at the time because sampled weather balloons only began operating in the late 50's and records had poorly and inconsistent surface stations (Edwards, (2010); Kalnay, (2003). In the 1970s, climate modeling laboratories gained interest in energy and environmental policy, leading to an infrastructural overhaul (Edwards, (2010); Maraun and Widmann, (2018)). As the effects of global warming became all too apparent in the 1980s, scientists and policymakers established the Intergovernmental Panel on Climate Change (IPCC) to evaluate scientific data on climate change, its impact, and possible solutions (IPCC, (2009) ; Edwards, (2010) ; Baker, (2017)). In addition, from the 90's emerged a new source of global climate data through weather records reanalysis (Parker, (2016); Trenberth and Olson, (1988) ; Bengtsson and Shukla, (1988)) and nowadays, climate knowledge infrastructure is one of the most reliable source of data, constantly reviewed and reanalyzed with added metadata (Edwards, (2010)). 
Climate research and meteorology both rely on station observation and reanalysis techniques. Station observation provides real-world data, while reanalysis techniques provide consistent weather information on a global scale and over continuous time by integrating multiple observational data and numerical models (Edwards, (2010); Rummukainen, (2012); Hersbach et al., (2020)). In scientific research and application, it is often necessary to combine both to obtain more comprehensive meteorological data (Salcedo-Sanz et al., (2020); Schauberger et al., (2020)).  Simulation models rely on physical theory while numerical models were developed by weather forecasters to compute large-scale atmospheric movements and anticipate weather patterns (Parker, (2016)). Subsequently, climate scientists adopted similar methodologies to simulate the Earth's climate over extended periods, ranging from years to decades (Pitman, (2003); Jiao et al., (2021)). Additionally, by modifying the simulated variables and conditions, they utilize models to forecast how climate patterns will evolve as human activity affects the composition of the atmosphere and other climate-related systems.
In fact, three types of computer models are now used to understand global climate : simulation, reanalysis and data analysis models, however, this study is mainly focusing on the latest two. Reanalysis models originate from weather forecasting and are widely used datasets in studying weather and climate (Edwards, (2010); Doddy et al., (2021); Jiao et al., (2021)). Unlike pure simulations, these models simulate the weather and blend the results with actual weather observations to produce fully global, uniform data (Gleixner et al., (2020); Ghajarnia et al., (2022)). Reanalyses are valuable datasets for monitoring and comparing past and present climate conditions, testing the accuracy of past forecasts, driving numerical weather prediction (NWP) models, and identifying climate variations and change (Hersbach et al., (2020) ; Jiao et al., (2021)). Unlike data from instruments alone, climate statistics from reanalysis models cover the entire planet at all altitudes (Edwards, (2010)) and are increasingly used in various commercial sectors, including energy, agriculture, water resources, and insurance (Gleixner et al., (2020); Doddy et al., (2021)). On the other hand, data analysis models refer to the techniques, algorithms, and empirically derived adjustments used to process historical weather and climate records. These models are necessary as observing systems have undergone multiple changes over time and combining long-term records is still needed. In addition, data analysis models are employed to account for various factors such as instrument behaviors, data collection practices and weather station site changes and essential to adjust for the unevenness of observations in space and time. All in all, these techniques all are important to our society, being for forecasting, assessing current and future climate change but also mitigation. The data and models obtained can be used for seasonal drought prediction for example, which lead to better assessments, the development of new agricultural and water use policies or the creation of new infrastructures, more suitable or useful to the new climate condition, and so on (Bengtsson et al., (2007); Dee et al., (2014)). 
One of the tools using such reanalysis models, is ERA5:  in 2010, the European Center for Medium-Range Weather Forecasts (ECMWF) developed it as the fifth-generation Re-Analysis dataset and replaced the ERA-Interim dataset in 2019 (Hoffmann et al., (2019); Jiao et al., (2021); Ghajarnia et al., (2022)). ERA5 is a weather forecasting system that employs advanced techniques like four-dimensional variational data assimilation (4D-Var) and a high-resolution numerical weather model to provide more precise and accurate spatial and temporal resolution. Compared to its predecessors, ERA-Interim, ERA5 has a much higher resolution with 31km and hourly against 79km every 3 hours, making it more reliable (Hersbach  et al., (2020); McNicholl et al., (2021); Ghajarnia et al., (2022)). ERA5 uses a sophisticated numerical weather model that assimilates a diverse set of observational data to produce a comprehensive and high-quality representation of global atmospheric conditions (Jiao et al., (2021); Yu et al., (2021)).  ERA5 combines observations from different sources such as weather stations, satellites, and ocean buoys, with a numerical weather model to generate a detailed and consistent representation of the Earth's atmosphere (Cucchi et al., (2020)). This process is known as data assimilation, which involves adjusting the initial conditions of the weather model using observations to create a more accurate representation of the atmospheric state (Cucchi et al., (2020); Ghajarnia et al., (2022)). Over the past few decades, advancements in data assimilation techniques have significantly improved the accuracy of NWP forecasts (Kalnay, (2003); Parker, (2016)).  
In a recent paper, Velikou et al. (2022) conducted an investigation into the ERA5 dataset's reliability in replicating mean and extreme temperatures across Europe. The findings of the study suggest that ERA5 is highly reliable for climate investigation over Europe, as it captures the mean and extreme temperatures very well. The high correlations ranging from 0.995 to 1.000 indicate that ERA5 can capture the annual cycle very well, as supported by previous studies by Doddy et al. (2021) and Jiao et al. (2021). Furthermore, McNicholl et al. (2021) found that satellite temperature performs better in the temperate region compared to the tropical region. This suggests that the accuracy of satellite data is influenced by the time of year and climate region, with milder temperatures producing better estimates. 
These last years, ERA5 has become a widely used data source for temperature modeling due to its coverage of large land areas with regular latitude-longitude grids at 0.1° x 0.1° resolution. The reanalysis data also covers a period from 1950 to near-real-time hourly data, making it a valuable resource (Li et al., (2022); Essa et al., (2022)). While the gridded temperature derived from ERA5 reanalysis data provides the opportunity to interpolate temperature at arbitrary locations, this process can introduce errors and uncertainties, as noted in studies by Li et al. (2022) and Shi et al. (2021). To improve the accuracy of interpolated ERA5 temperature, a refinement method using an ANN model and measured station temperature was used to correct errors, as highlighted in studies by Li et al. (2022) and Hoffmann et al. (2019). However, the accuracy and biases of reanalysis datasets based on data assimilation continue to affect reanalysis tools, therefore it is essential to evaluate their performance (Yu et al., (2021); Li et al., (2022); Velikou et al., (2022)). In regard to that, this study, thus, aims to evaluate the accuracy of the ERA5 temperature dataset, doing so by analyzing the measurements of twenty-five stations in Frankfurt from September 2013 and September 2014. The main purpose is to identify any potential location errors resulting from incorrect latitude or longitude signs and, if necessary, make the appropriate corrections.