Forecasting urban temperatures through crowdsourced data from Citizen Weather Stations

Urban Climate 56 (2024) 102021 Available online 21 June 2024 2212-0955/© 2024 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Forecasting urban temperatures through crowdsourced data from Citizen Weather Stations Laura Romero Rodríguez a , * , MCarmen Guerrero Delgado b , Daniel Castro Medina a , Jos´ e S´ anchez Ramos b , Servando ´ Alvarez Domínguez b a Escuela Superior de Ingeniería, Departamento de M´ aquinas y Motores T´ ermicos, University of C´ adiz, Spain b Grupo Termotecnia, Escuela T´ ecnica Superior de Ingeniería, University of Seville, Spain ARTICLE INFO Keywords: Forecasting Crowdsourcing Urban temperatures CWS Prediction models ABSTRACT This work explores the potential of using crowdsourced data from Citizen Weather Stations (CWS) to forecast urban temperatures. Five case studies were selected (Madrid, London, Rome, Paris and Berlin), using data from the manufacturer Netatmo to gather the hourly temperatures of the years 2021 and 2022 for 776 CWS. A quality-control process was implemented to enhance data accuracy, and heat maps were generated. Multiple linear regression models were created for each CWS and month using only reference weather data as input, resulting in the development of accurate models (RMSE lower than 1.5 ◦C) for an average of 374 CWS. Then, reference weather predictions were used on the 2nd of April 2023 to forecast the hourly temperatures of those CWS for the period from the 3rd to the 9th of April (168 h). The outcomes showed that accurate CWS data and precise prediction models for the reference weather are crucial to improve the accuracy of the forecasts using crowdsourced data. The study demonstrates the potential benefits of using CWS data and simple models to forecast urban temperatures in a cost-efficient way even 168 h ahead, with implications for various sectors such as urban planning, energy consumptions, health impacts, or climate change adaptation strategies. 1. Introduction 1.1. Background Urban living has become increasingly prevalent in recent times. According to (Mathew et al., 2016), in early years of the twentieth century the world’s urban population was around 10% of the total population, which has risen to 50% (and will most probably keep increasing). Urbanisation involves the replacement of natural land surfaces with artificial materials, a transformation that can have detrimental effects on the environment. This process contributes to the emergence of the Urban Heat Island (UHI) effect, wherein urban areas exhibit elevated air temperatures compared to their rural counterparts. The intensified changes in land use, land cover, urban heat, emission of greenhouse gases, and cloud cover have also minimized the gap between daily maximum and minimum temperatures known as Diurnal Temperature Range (DTR), which has been found to decrease dramatically in the world during the past years (Sankalp et al., 2022). The reason is that night-time minimum temperatures have risen faster than day-time maximum * Corresponding author at: Departamento de M´ aquinas y Motores T´ ermicos, Escuela Superior de Ingeniería, Universidad de C´ adiz, Avda. Universidad de C´ adiz, n ◦10, 11519 Puerto Real, C´ adiz, Spain. E-mail address: [email protected] (L. Romero Rodríguez). Contents lists available at ScienceDirect Urban Climate journal homepage: www.elsevier.com/locate/uclim https://doi.org/10.1016/j.uclim.2024.102021 Received 7 March 2024; Received in revised form 10 June 2024; Accepted 16 June 2024 Urban Climate 56 (2024) 102021 2 temperatures, since the same amount of radiation forcing is concentrated in a shallower boundary layer at night, causing a more pronounced temperature effect with less air mass needing to be heated up. This issue has been discussed in detail in previous studies such as (Steeneveld et al., 2011a), (McNider et al., 2012) or (Zhou et al., 2022). 1.2. Urban temperatures One of the biggest challenges in atmospheric research is the provision of accurate air temperature observations in urban environments with sufficient spatial and temporal resolutions over long time periods. Essentially, urban temperatures can be mapped through several methods: ground-based weather stations, satellite remote sensing, mobile monitoring, and numerical simulations. However, all these approaches present drawbacks, including limited spatial coverage, surface-only measurements, limited time coverage or data availability respectively. Obtaining accurate and detailed air temperature data at the city-scale is often difficult due to limited weather stations, particularly in less developed cities (Ding et al., 2023). Many cities have only a few weather stations available, for instance at the airport. High spatio-temporal resolution of air temperature is crucial for studying the UHI and implementing effective mitigation strategies, especially at urban scale, which is why new methods are emerging to overcome current challenges. Air temperature modeling is also a paramount task for practical applications such as designing energy-efficient buildings, harnessing of solar energy, health-risk assessments, and weather prediction (Sanikhani et al., 2018). Additionally, the proportion of air-conditioning load in the total power load increases year by year, which is why meteorological factors such as temperature and humidity have significant influences on power load fluctuations (Wang et al., 2022). 1.3. Crowdsourced data As shown by (Chen et al., 2022), an in-depth understanding of air temperatures will help scientists to provide scientific evidence for policymakers, but this subject is still under-researched worldwide in many regions due to technical limitations. To study patterns of intra-urban air temperatures, it is necessary to have observations with a high spatial resolution (Feichtinger et al., 2020), but due to the high purchasing and maintainenance costs associated with meteorological measuring equipment, it is not common to find many professional weather stations in a city. Thus, utilizing networks of Citizen Weather Stations (CWS) is a recent trend to gather the data in a cost-efficient way. Before the term was widely known, previous studies had already used data from citizens, such as (Steeneveld et al., 2011b), who used observations from hobby meteorologists to quantify the UHI in several cities and villages in the Netherlands. CWS are basically networks of public sensors that provide anonymous weather observations from the home devices purchased by users. Each CWS may measure different parameters: air temperature, humidity, pressure, wind speed, wind direction and so on. The increasing number of citizens sharing their measurement data through CWS enables the utilization of crowdsourcing, an automated method for collecting extensive data from a diverse group of individuals, which presents exciting opportunities for atmospheric research (Napoly et al., 2018). The term crowdsourcing was initially introduced in an economic context and then expanded to refer to data obtained from non-traditional sources like public sensors, smartphone sensors or internet-connected devices. In fact, crowdsourcing is now increasingly finding itself as an established technique for collecting mass data in many scientific disciplines (Chapman et al., 2017). Crowdsourced data in atmospheric research offers advantages such as enhanced spatial resolution and broader coverage in urban areas. Thus, using information from such low-cost sensors has a great potential to overcome the challenges of in-situ measurements and statistical interpolation for urban heat maps (Zumwald et al., 2021). It also potentially allows for long-term measurements and proves to be a cost-effective alternative to traditional networks (Napoly et al., 2018). An example of a manufacturer of CWS widely used around the world is Netatmo (Netatmo, 2023), which will be further discussed in Section 2. Many research studies have used data from Netatmo. For instance, (Baniassadi et al., 2023) examined the association between nighttime temperatures and sleep quality in a sample of dwellings. In (Nielsen et al., 2024) the accuracy of rainfall observations was improved by merging Netatmo data with weather radar data. Similarly, (Lussana et al., 2023) assessed the precision of crowdsourced data from Netatmo comparing its data with observations of precipitation from nearby weather stations, observing that reference values were typically within the distribution of the CWS data. Also, (de Vos et al., 2020) employed both traditional sensing methods and opportunistic sensing networks to obtain temperature and precipitation measurements over the Amsterdam metropolitan area, using also data from Netatmo CWS. CWS however present an important drawback: the quality of the measurements. In fact, rigorous data quality assessment is the key challenge to fully benefit from these novel CWS datasets for urban climate research (Meier et al., 2017). The reason is that there is no control to ensure the quality of the gathered data, and hence data quality assessment is a crucial step before carrying out any analysis (Napoly et al., 2018). In this regard, (Chapman et al., 2023) evaluated the durability of Netatmo CWS data as opposed to just the data quality alone, revealing that expert input at the deployment stage greatly improved data quality. Nonetheless, the advantages of having high resolution measurements, or having observations where there are no measurements at all, cannot be ignored (Chapman et al., 2017). That is the reason why numerous studies have focused on data obtained from CWS. Some of these studies will be discussed in detail in Section 1.4.2 regarding temperature forecasting, and in Section 2 regarding the proposed quality-control scheme and the amount of data gathered. 1.4. Weather prediction Weather forecasts have always been an important service to the public. Precise fine-scale temperature forecasts are an important L. Romero Rodríguez et al. Urban Climate 56 (2024) 102021 3 tool in quantifying human comfort, health threats with extreme temperatures and energy consumptions (Chang et al., 2021). Day-to- day temperature forecasts are provided by numerous services, which make use of weather prediction models from regional to local scales. Seasonal climate prediction poses challenging and uncertain tasks, particularly in forecasting the sustained levels of various climate variables, including air temperature (Fister et al., 2023). Among the different parameters, the 2 m air temperature is an important meteorological parameter that has been the focus of meteorological forecasting (Hou et al., 2022). It is one of the most important outputs from numerical weather prediction models, and it is forecasted daily. This variable will be used in the present work. According to (Ramirez-Vergara et al., 2021), there are four groups of forecasting approaches: Numerical Weather Prediction (NWP) models, physical techniques, linear statistical models, and machine learning techniques. Their differences are related to their formulation, forecasting horizon, processing cost, and data acquisition and dependency. According to (Cho et al., 2022), NWP models are commonly used to forecast air temperatures, but they require post-processing, which may be done by using machine learning and deep learning techniques. Examples of NWP models include for instance ECMWF’s Integrated Forecasting System (IFS) or NOAA’s Global Forecast System (GFS). Also, gridded data of air temperatures may be provided using NWP models and data assimilation systems such as GFS, ERA5 or GLDAS. For instance, ERA5 is a reanalysis dataset that combines various observations and models to generate high-resolution atmospheric data on a global scale. However, the resolution is too coarse to capture the temperature heterogeneity with high spatial and temporal resolutions, which is why these methods are not suitable for urban scale applications. 1.4.1. Urban-scale forecasting models Forecasting accurate urban air temperatures at fine spatial and temporal scales remains a significant challenge for the meteorological community (Chang et al., 2021). That is the reason why, in recent years, the aim of predicting urban air temperatures led to the application of models based on different concepts, such as fuzzy theory, machine learning or statistical methods (Yu et al., 2021). Numerous investigations address challenges associated with forecasting air temperatures over extended periods, with the majority employing machine learning or artificial intelligence (AI) techniques (Fister et al., 2023). A very extensive review of the different machine learning strategies for temperature forecasting available in the literature is provided in (Cifuentes et al., 2020), presenting their advantages and disadvantages and identifying research gaps. Other examples are for instance the study by (Choi et al., 2021), based on linear Gaussian models and dimensionality reduction, which presented an approach to spatio-temporal high resolution mesoscale modeling of near-surface temperatures and applied it to regions with 1 km grid spacing. Also, a Gaussian mixture model clustering algorithm was used in (Boccalatte et al., 2023) to assess the urban heat island intensity. Short-term forecasting is usually referred to forecasting from 1-min-ahead (also known as nowcasting) to 1-day-ahead, while medium-term or long-term forecasting can be referred to few days ahead or even few months ahead (Dong et al., 2021). In forecasting, it should also be considered that including in the models as much available information as possible would not necessarily improve the forecast performance, since some of the variables may be noisy or have no significant relationship with the target output (Dong et al., 2021). The input variables may be either endogenous (same variable as the output variable, for instance the temperature) or exogenous (any other variables, such as wind or humidity). According to the findings in (Dong et al., 2021), there is a need to develop more accurate and scalable spatio-temporal weather forecasting models at individual building level, since they would impact the building control decisions: with more accurate weather information, it would be possible to predict the time and magnitude of the peak demands of buildings for instance. Thus, there is a need for timely and high-resolution temperature data for the sustainable planning and management of climate-resilient cities (Venter et al., 2020). In any case, the accuracy of forecasting models is crucial to achieve reliable air temperature predictions. In Section 4.3, specific results of the accuracy obtained by previous studies that focused on the forecasting of urban temperatures will be discussed in detail, in the context of the present study. 1.4.2. Temperature forecasting through CWS As mentioned in Section 1.3, to address data scarcity CWS are a current trend in scientific studies. CWS have also been utilized in the literature to perform air temperature forecasting. In fact, it was stated by (Chang et al., 2021) that low-cost weather stations could be an effective way to achieve a detailed temperature forecast in a heterogeneous urban environment. In (Uteuov et al., 2019), an approach to use CWS data to improve weather forecasting is suggested, proposing a data-driven model to correct numeric modeling for short-time forecasting. Also, (Zumwald et al., 2021) present an approach to model urban temperature using CWS, the quantile regression forest algorithm, open government data and remote sensing data. A methodology for anticipating temperature distributions in urban environments using Netatmo data is also shown in (Castro Medina et al., 2024). In addition, (Hassani et al., 2023) employed Netatmo data to predict daily ambient temperatures at nearly 1-km spatial resolution in Warsaw (Poland), comparing the predictions against observations from 5 meteorological reference stations. 1.5. Aim of this work The literature review has revealed the need to find accurate ways to forecast air temperatures at urban scale, due to the coarse spatial resolution of current forecasting methods which do not allow to capture microscale variations. Also, it is difficult to find dense monitoring networks in most cities due to the mentioned challenges. For these reasons, this work will explore the potential of utilizing crowdsourced temperature data for forecasting urban temperatures. Crowdsourced data has the drawback of data reliability (which may be mitigated through the implementation of a quality control process), but if offers the advantage of being cost-free and providing a high density of measurements in certain areas. In particular, the present study will focus on five case studies in Europe: Madrid, London, Rome, Paris and Berlin, utilizing data L. Romero Rodríguez et al. Urban Climate 56 (2024) 102021 4 from the CWS of the manufacturer Netatmo to gather temperature measurements. These cities are chosen to consider a diverse range of geographical locations with high population densities and enough CWS to provide ample data for analysis. In total 776 CWS are considered, gathering hourly temperature data for the years 2021 and 2022. To ensure data accuracy, a quality-control process inspired by previous literature will be implemented, thus establishing a reliable dataset for analysis and modeling. After the quality-control process, forecasting models will be developed using the hourly temperature data gathered in 2021. This is done to obtain the coefficients of the multiple linear regression models with lagged predictors that will be created, which depend on reference weather data obtained from the Open-Meteo platform for each case study. A validation of the developed models will then be carried out using the hourly data of 2022, comparing the predictions of the models with the actual temperature measurements. Then, the forecasting capabilities of the models will be explored by using them to predict the hourly urban temperatures up to 168 h ahead for a specific period in the future, using only the weather forecast for the reference weather as input. The manuscript is arranged in the following order: Section 2 explains the process to gather the data from the CWS, shows the case studies, the implemented quality-control procedure and illustrates the obtained measurements through heat maps. Then, Section 3 explains the development of the models, explains the obtention of the reference weather data and evaluates the accuracy of the developed models. In Section 4, the most precise models are used to forecast future urban temperatures up to 168 h ahead, the results are compared to previous literature and a summary of the outcomes of this work is provided. Last of all, Section 5 presents the conclusions of the study. 2. Data collection 2.1. CWS data: Netatmo The present work relies on crowdsourced temperature data, obtained from CWS that can be freely accessed. In particular, the data was obtained from the manufacturer Netatmo, using its Application Programming Interface (API). Netatmo is a widely used manufacturer of weather stations which allows its users around the world to monitor their indoor and outdoor atmospheric conditions in real-time, as well as share the measurements through a server. These weather stations may thus be categorized as CWS and belong to ‘the internet of things’, and their broad implementation in many cities allows to have access to a dense monitoring network. The Netatmo weather stations can measure various parameters such as temperature, air pressure, or humidity. CO 2 levels and noise may also be measured, but are not publicly available and cannot be downloaded through the API. In this study, only the temperature measurements of the Netatmo module located outdoors are used. This module is enclosed in an aluminum shell, and measures air temperature with an accuracy of ±0.3 ◦C. Once a user installs the device, the collected data is uploaded to the Netatmo server automatically at 5-min intervals if the user allows Netatmo to share their measurements. Then, the data can be accessed by anyone after registering on their developers’ webpage and calling the Netatmo API. In this work, the data was extracted from Netatmo by programming a Python script from scratch that used the following API calls to access the Netatmo servers: •\getpublicdata: This API is used only once for each case study, to define a certain area (indicating the latitude and longitude of the NE and SW corners of a rectangle) so as to retrieve the IDs of the weather stations within it. Only weather stations with temperature data are searched in our case. These IDs are saved in a list. •\getmeasure: It is used to retrieve data from a specific weather station. The device ID, module ID, type of data to be returned (temperature in our case), the scale (1 h in our case) as well as the begin date and end date (with UNIX time format) need to be indicated. A maximum of 1024 measurements may be retrieved in one API call. The process implemented in the Python script developed is explained as follows: first, an area is defined (a rectangle) using coordinates, and the \getpublicdata API is called. The API returns a JSON object, which is parsed to extract a list with the IDs of the available weather stations in the area. Then, the data of each weather station is collected by calling the \getmeasure API with the ID and the desired period. Since two years of hourly data are needed in the present work, the \getmeasure API needs to be called several times for each CWS. The following sections will provide a more detailed overview of the procedures involved in gathering the data for the case studies conducted in this research, including an in-depth exploration of the steps taken to guarantee data quality and an overview of the crowdsourced data acquired from Netatmo. 2.2. Quality control of temperature data Any approach that relies on crowdsourced data should implement a quality-control process to ensure that the measurements used are not erroneous due to several circumstances, among which may be included: •Missing values due to lack of wi-fi connection. •Intermittent failures of connection due to low battery power. •Inappropriate installation of the outdoor temperature sensor (placed indoors for instance). •Sensor not installed in a shaded place to minimize the effect of short-wave solar radiation. After carefully reviewing the available literature, several studies which carried out a data quality assessment after downloading L. Romero Rodríguez et al. Urban Climate 56 (2024) 102021 5 data from the Netatmo API were found: •(Meier et al., 2017) first developed a comprehensive data quality assessment based on 8 levels. •(Napoly et al., 2018) developed a routine that consisted of 7 levels: 4 levels to ensure the data quality (M1–M4) and 3 optional levels (O1–O3) dependent on the application. •(Zumwald et al., 2021) and (Feichtinger et al., 2020) applied a statistical control scheme combining the procedures developed by (Meier et al., 2017) and (Napoly et al., 2018). •(Venter et al., 2020) and (Uteuov et al., 2019) implemented the procedure developed by (Napoly et al., 2018). •(Chapman et al., 2017) just removed any observations that were found to be more than three standard deviations from the all station mean, since it was a night-time study. Table 1 outlines the data quality control process implemented in the present study after considering the previous literature. Each step is based on the data that remains after the completion of the previous step. The most important steps found in the literature to ensure temperature data quality from our point of view were selected. We did not implement the level C1 of (Meier et al., 2017) (positive and significant correlation between global radiation and air temperature difference) for instance, since our aim was to rely only on temperature measurements. Also, we did not correct the variations in altitude of the CWS and did not implement the linear interpolation of missing hourly values in (Napoly et al., 2018), since our intention was to rely only on the real observations. With regards to P3, which is based on M2 in (Napoly et al., 2018), we treated the upper tail of the distribution in a stricter way using 90% instead of 95%, since (Meier et al., 2017) showed that most common error sources in CWS data are related to indoor locations of stations or radiative errors in non-shaded areas. We did not implement either a specific step to identify indoor weather stations, since we observed that the issue could be temporal and in any case most values are eliminated automatically throughout the rest of the quality-control steps. In any case, a post-processing of the results could detect indoor weather stations in an easy way by looking at the deviation of the daily minimum and maximum temperature values. In addition, P4 in our case is based on level C2 in (Meier et al., 2017). However, the literature has evidenced that there are many systematic radiative errors when using crowdsourced data due to the location of the temperature sensors. Thus, we decided to be also more restrictive in this respect and eliminate values above or below 2 times the SD (Standard Deviation) of hourly temperatures with respect to the mean, instead of 3 times. Approximately 95.4% of the data would be retained in this way compared to the previous step. 2.3. Case studies and overview of the procedure The proposed procedure is illustrated by choosing as case studies certain areas of the city centers of 5 european cities: London, Madrid, Paris, Rome and Berlin. The whole process to gather all the available hourly Netatmo data of the years 2021 and 2022 in those areas, carried out using the programmed Python script explained in Section 2.1, is summarized in Fig. 1. Different area sizes were chosen for the cities to check whether the amount of CWS and their density affect the whole procedure. The defined areas as well as the number of CWS found in 2022 are shown in Fig. 2 and summarized in Table 2. As may be seen, the areas are varied, from 5.84 km 2 in Paris to 58.62 km 2 in Rome. Also, only 56 CWS were found in London while 356 were found in Berlin in a similar area. Therefore, these cases present very different CWS densities. The study in (Venter et al., 2020) stated that mapping accuracies dropped with <250 stations or 1 station per km 2 . In our case studies, the densities are thus higher. However, the distribution of the weather stations is not homogeneous, which may affect the spatial interpolations. Considering the total number of CWS available in all the cities (759 in 2021 and 776 in 2022) and the 8760 h in a year, 6,648,840 values of air temperature could theoretically be retrieved in 2021 and 6,797,760 in 2022. Table 1 Data quality control procedure implemented in the present study: P1 to P6. Process Description Based on P1 Gather all available temperature measurements for the period and area under study. Check and clean anomalous values. Level A0 in (Meier et al., 2017). P2 Eliminate weather stations that are included more than once for the same location, by checking the coincidence in latitude, longitude and altitude. The assumption is that they were not properly set-up by the owners. Level M1in (Napoly et al., 2018). P3 Eliminate extreme hourly values (below the 1% quantile and above the 90% quantile). This is performed independently for each hour of the period under study, comparing all measurements available in the area. Based on M2 in (Napoly et al., 2018), but 90% instead of 95%. P4 Eliminate the highest and lowest values when |Tcrowd −Tsensor| ≥2 ⋅ SD. This is performed independently for each hour of the period under study, comparing all measurements available in the area. Level C2 in (Meier et al., 2017) but considering 2 times the SD instead of 3 times. P5 Eliminate days that have >20% of empty data (5 h). Level A2 in (Meier et al., 2017) or O2 in (Napoly et al., 2018). P6 Eliminate months that have >20% of empty data (168 h). Level A3 in (Meier et al., 2017) or O3 in (Napoly et al., 2018). L. Romero Rodríguez et al. Urban Climate 56 (2024) 102021 6 2.4. Quality-control results As previously mentioned, any study based on crowdsourced data from CWS should implement a quality-control procedure to ensure that the measurements are valid. The procedure described in Section 2.2 was performed for all the case studies in the present work, with all the hourly data gathered for the years 2021 and 2022. Table 3 shows an example of the monthly results obtained for the quality-control process in Rome in 2022. As may be observed, initially (P1) >78% of hourly temperature data were available every month. Missing values could be due to weather stations later installed (since the IDs were retrieved in 2023) or lack of internet connection at certain times. Then, repeated weather stations were removed in several months in P2. P3 removed around 10% of the data by detecting extreme hourly values (below the 1% quantile and above the 90% quantile). In P4, around 3% of the data was removed for those hourly values which deviated greatly from the mean of the area. Last of all, in P5 and P6 days or months were removed for those CWS with >20% of missing values. In the end, for Rome in 2022, between 36% and 49% of the monthly data was retained (an average of 43% throughout the year). An illustration of the quality-control procedure is included in Fig. 3, showing the hourly temperatures in P1 and P4 for all the weather stations available during the period ranging from the 1st to the 7th of July 2022 in Rome. As may be seen, the procedure P1-P4 greatly smoothed the data and reduced unexplainable peaks due to the influence of solar radiation for instance. It becomes clear that the quality-control process is necessary, particularly to avoid the overestimation of urban temperatures, since it is very frequent for the users to install the outdoor modules in unshaded locations. In Table 4, the summary of the annual results for every case study and year after completing the quality-control process are shown. The main conclusions that may be drawn are the following: •P1: The percentage of available data at the beginning of the process ranged from 61% to 87% (an average of 77%). Overall, 71% of the data was available in 2021 and 83% in 2022. •P2: 5.7% of data was lost in Madrid due to repeated weather stations, and 4.5% was lost in Rome in 2021. In the rest of the case studies the data losses were negligible. •P3: eliminating values below the 1% percentile and above the 90% percentile resulted in a data loss between 9.0% and 12.4%. The total percentage is not exactly 11% due to two reasons. First, the percentages could be higher than 11% since several weather stations may have the same measurements. And second, since the percentiles are calculated in each hour separately, the amount of Fig. 1. Process flowchart for outdoor air temperature crowdsourcing. L. Romero Rodríguez et al. Urban Climate 56 (2024) 102021 7 available sensors varies. Therefore, since the percentages in Table 4 are calculated considering the total number of sensors in the city, the percentages could be lower than 11%. •P4: Eliminating values if |Tcrowd −Tsensor| ≥2 ⋅ SD meant a data loss between 2.3% and 3.5%. •P5: Between 7.9% and 14.6% of data was removed when days with >20% empty values were eliminated. •P6: Between 10.3% and 14.5% of data was removed when months with >20% empty values were eliminated. If we consider P4 as the step with clean data, between 50% (in London 2021) and 73% (in Paris 2022) of hourly temperature values were retained. Considering all case studies combined, in 2021 (training set) the available data in P4 was 58%, and in 2022 (validation set) the data available was 70%. These results after implementing the quality-control procedure are comparable to previous studies, which had variations of the implemented approach: in (Zumwald et al., 2021) 57% of the data was retained, in (Napoly et al., 2018) 57.41% for Toulouse and 58.54% for Berlin, in (Feichtinger et al., 2020) 55.3%, and in (Meier et al., 2017) 47.1%. An illustration of the whole quality-control procedure is also shown in Fig. 4 for the period from the 1st to the 7th of February 2021 in Berlin (a winter week). As stated for the case study in Rome during the summer, Fig. 4 shows that the whole quality-control procedure P1-P6 greatly smoothed the data, and even indoor sensors were automatically removed. It is also apparent that many CWS are placed by the users in unshaded locations, which affects the measurements even in winter. For this reason, the quality-control procedure should be more restrictive with the highest detected measurements, as was done here in P3 where values above the 90% quantile (instead of 95% as done in previous studies) were discarded. Fig. 2. Spatial distribution of the CWS in a) Madrid, b) Rome, c) Paris, d) London and e) Berlin. Table 2 Summary of case study characteristics. City Year Weather stations found Area [km2] Weather stations/km2 Minimum altitude [m] Maximum altitude [m] London 2021 54 37.03 1.5 2 55 2022 56 Madrid 2021 105 17.71 5.9 584 700 2022 104 Paris 2021 86 5.84 15.4 30 75 2022 90 Rome 2021 166 58.62 2.9 17 81 2022 170 Berlin 2021 348 38.86 9.2 30 66 2022 356 L. Romero Rodríguez et al. Urban Climate 56 (2024) 102021 8 Table 3 Example of monthly quality-control for all the CWS in Rome (2022). The percentages show the remaining data. In brackets, the changes compared to the previous step are shown. ROME 2022 P1 P2 P3 P4 P5 P6 January 82% 80% (-2.4 %) 70% (-9.8 %) 67% (-3.0 %) 58% (-9.4 %) 48% (-10.2 %) February 84% 82% (-2.4 %) 72% (-9.9 %) 69% (-2.9 %) 58% (-10.6 %) 49% (-9.7 %) March 84% 82% (-2.4 %) 72% (-10.0 %) 69% (-2.9 %) 58% (-10.6 %) 48% (-9.9 %) April 78% 76% (-2.4 %) 67% (-9.4 %) 64% (-2.7 %) 52% (-11.8 %) 42% (-9.7 %) May 79% 78% (-0.6 %) 68% (-9.7 %) 65% (-2.9 %) 51% (-14.0 %) 36% (-15.6 %) June 80% 80% (-0.0 %) 70% (-9.9 %) 67% (-3.1 %) 52% (-15.8 %) 36% (-15.1 %) July 82% 82% (-0.0 %) 72% (-9.8 %) 69% (-3.2 %) 51% (-17.1 %) 37% (-14.9 %) August 82% 82% (-0.0 %) 72% (-10.0 %) 69% (-3.0 %) 53% (-16.0 %) 40% (-13.1 %) September 81% 81% (-0.0 %) 71% (-10.1 %) 68% (-3.0 %) 54% (-14.0 %) 38% (-15.4 %) October 80% 80% (-0.0 %) 70% (-10.0 %) 67% (-3.0 %) 54% (-13.0 %) 43% (-10.7 %) November 83% 83% (-0.0 %) 73% (-10.3 %) 70% (-2.8 %) 60% (-10.2 %) 49% (-10.7 %) December 86% 86% (-0.0 %) 75% (-10.7 %) 73% (-2.6 %) 62% (-10.5 %) 48% (-14.6 %) Year 82% 81% (-0.8 %) 71% (-10.0 %) 68% (-2.9 %) 55% (-12.8 %) 43% (-12.5 %) Fig. 3. Illustration of the quality-control procedure for Rome (1st to 7th of July 2022), showing: a) temperatures in P1 (all measurements available), and b) temperatures in P4 (after several quality control steps). Table 4 Quality-control results for all the case studies. CITY YEAR CWS P1 P2 P3 P4 P5 P6 LONDON 2021 54 61% 61% (-0.0 %) 52% (-9.1 %) 50% (-2.3 %) 42% (-7.9 %) 31% (-10.9 %) 2022 56 77% 77% (-0.0 %) 66% (-10.7 %) 63% (-3.5 %) 54% (-9.0 %) 43% (-10.3 %) MADRID 2021 105 74% 69% (-5.7 %) 60% (-8.7 %) 58% (-2.4 %) 47% (-10.6 %) 35% (-12.4 %) 2022 104 87% 81% (-5.7 %) 71% (-9.9 %) 69% (-2.7 %) 57% (-11.9 %) 43% (-13.7 %) PARIS 2021 86 75% 74% (-1.1 %) 65% (-9.5 %) 62% (-2.8 %) 53% (-8.9 %) 40% (-12.3 %) 2022 90 87% 87% (-0.0 %) 77% (-10.6 %) 73% (-3.5 %) 62% (-11.3 %) 49% (-12.7 %) ROME 2021 166 76% 71% (-4.5 %) 62% (-9.0 %) 60% (-2.5 %) 50% (-9.9 %) 39% (-10.8 %) 2022 170 82% 81% (-0.8 %) 71% (-10.0 %) 68% (-2.9 %) 55% (-12.8 %) 43% (-12.5 %) BERLIN 2021 348 69% 80% (-0.0 %) 68% (-11.3 %) 65% (-3.1 %) 52% (-12.7 %) 40% (-12.7 %) 2022 356 82% 86% (-0.0 %) 74% (-12.4 %) 70% (-3.3 %) 56% (-14.6 %) 41% (-14.5 %) L. Romero Rodríguez et al. Urban Climate 56 (2024) 102021 9 It should also be noted that the urban environment is so complex that a specific CWS measurement cannot be generalized. If we wanted to find a representative weather station for a certain location, choosing large areas and then performing the quality-control procedure could potentially eliminate useful weather stations if their measurements greatly differ from the average. Thus, smaller areas should be chosen in such a situation. In any case, the results show that it is important to choose adequate parameters in the quality-control procedure, and that they may need to be adapted for each particular case study. In fact, an alternative would be to include a step that depends only on the behavior at each specific CWS, such as its rate of temperature change. Another option could be to distinguish night-time and day-time and be more restrictive during daylight hours. Fig. 4. Illustration of the quality-control procedure for Berlin (1st to 7th of February 2021), showing the temperatures in: a) P1(all measurements available), b) P2 (deleting repeated CWS), c) P3 (deleting extreme values), d) P4 (removing outliers after comparing all measurements), e) P5 (deleting days with insufficient data), f) P6 (deleting months with insufficient data). Fig. 5. Illustration of the implemented IDW method for the case study in Paris. On the right, a number of levels =1 is shown above, and a number of levels =2 is shown below. L. Romero Rodríguez et al. Urban Climate 56 (2024) 102021 16 models will be employed in the following sections to illustrate how they may be used to forecast the future temperatures at their corresponding CWS. To do this, the Weather Forecast API of Open-Meteo, mentioned in Section 3.2, is used to forecast the reference weather temperatures. This API can provide hourly 7-day weather forecasts worldwide just by indicating a location through its latitude and longitude, with models from multiple national weather providers. This means that it is possible to obtain a forecast of the hourly temperatures for the next 168 h. In addition, if desired, the API provides hourly data of the previous days as well. A period in April 2023 was chosen to try out the approach and the accuracy of the models in a real situation. The weather forecast for the reference weather of each case study was gathered on the 2nd of April 2023, and then the models with a RMSE <1.5 ◦C in April were used to forecast the hourly temperatures at their locations with a lead time up to 168 h (from the 3rd to the 9th of April 2023). The following sections will present the obtained results. 4.2. Testing the accuracy of the forecasted reference weather The first issue to consider in the proposed forecasting approach is the fact that it is necessary to provide a forecast for the reference weather temperatures, which introduces a source of uncertainty. It is not dependent on the development of the urban forecasting models, but on the accuracy of the forecast provided by the Open-Meteo API in this case. In turn, the Open-Meteo API depends on other data sources such as the European Centre for Medium-Range Weather Forecasts (ECMWF), NOAA, MeteoFrance or Deutscher Wetterdienst (DWD). As mentioned in the previous section, the period chosen to illustrate the procedure ranges from the 3rd to the 9th of April 2023. On the 2nd of April 2023, the Open-Meteo Weather Forecast API was called for the location of each case study city. With this, the forecast of the hourly reference weather temperatures from the 3rd to the 9th of April 2023 was obtained. Since the data of the previous 24 h is always needed in the models, the data of the 2nd of April was also gathered so as to be able to estimate the temperatures on the 3rd of April. Then, some days after this period, the real reference weather data was downloaded from the Historical Weather Open-Meteo API so as to carry out a validation. This API was the one used to train the models, explained in Section 3.2. Fig. 9 shows the validation of the reference weather forecast for each case study. As may be observed, the temperature forecasts were relatively good considering that the forecasting period covered the next 7 days with an hourly resolution, although at times the values differed. The RMSE obtained for London was 1.35 ◦C, for Paris 1.15 ◦C, for Madrid 1.87 ◦C, for Rome 1.45 ◦C and for Berlin 1.91 ◦C. 4.3. Hourly 7-days ahead forecasting results Using the reference weather forecast of the next 168 h provided by the Open-Meteo Weather Forecast API and the models developed in April which exhibited a RMSE <1.5 ◦C in the validation shown in Section 3.4, it was possible to obtain a temperature forecast for 304 of the CWS. To validate the temperature predictions, the real data of the Netatmo CWS were downloaded after the 9th of April 2023, once the forecasting period was over. The quality-control procedure up to P4 was also carried out with these data to avoid incorrect measurements. Table 7 shows a summary of the obtained results. Taking the example of Madrid for instance, the results reveal that initially 28 models were available in April with a RMSE lower than 1.5 ◦C to perform the forecasting. In fact, their average RMSE had been 1.32 for the validation period in 2022. Among those 28 weather stations, only 26 may be considered since the data of 2 of them could not be gathered from the Netatmo API after the forecasting period. The average RMSE of the 168 h forecast in Madrid amounts to 1.62 ◦C, with an average R 2 of 0.87. A total of 13 weather stations had a RMSE lower than 1.5 ◦C for the 168 h forecast, which means 50% of the CWS that were available. Similar conclusions may be drawn for the rest of the case studies. The diagram in Fig. 10 includes the distribution of the RMSE for the CWS temperature forecasts of all case studies, showing the average (cross), the median (horizontal line within the box), and the minimum and maximum values of the data that fall within 1.5 times the interquartile range from the first and third quartiles. Outliers are also shown. As previously done, the RMSE was calculated considering only times when both the predictions and the measurements for the validation were available. In the case of Madrid, Paris and Rome, the forecast at the CWS available showed accurate predictions, with most of the models achieving RMSE values around 1.5 ◦C. However, that is not the case of some of the CWS in Berlin and particularly in London, which showed worse results. Several outliers could also be identified, which were however a consequence of using CWS data which may present anomalies. In Fig. 11, some examples of the forecasted hourly temperatures are shown, both for accurate and inaccurate models. As may be observed, in general the models are quite capable of reproducing the real conditions at the locations of the CWS. This is true particularly when compared to the reference weather, which would be potentially the data used to make predictions if no models were Table 7 Results of urban temperature forecasting for the period from the 3rd to the 9th of April 2023. London Madrid Paris Rome Berlin RMSE of reference weather forecast 1.35 1.87 1.15 1.45 1.91 Number of CWS models in April (with RMSE <1.5 ◦C) 19 28 48 101 161 Number of CWS available for the forecast 16 26 30 89 143 Average RMSE of models in April (with RMSE <1.5 ◦C) 1.18 1.32 1.30 1.11 1.23 Average RMSE for the temperature forecast (168 h) 1.92 1.62 1.50 1.54 1.86 Average R 2 for the temperature forecast (168 h) 0.81 0.87 0.78 0.88 0.75 Number of CWS with a RMSE <1.5 ◦C for the temperature forecast (168 h) 8 13 21 44 15 L. Romero Rodríguez et al. Urban Climate 56 (2024) 102021 17 Fig. 10. Box plot illustrating the RMSE of urban temperature forecasting for all case studies. Box bottom: 25th percentile; horizontal line: median; cross: average; box top: 75th percentile. Whiskers extend to 1.5 times the interquartile range from the first and third quartiles. Outliers shown individually. Fig. 11. Example of accurate forecasting for CWS 48 in London, shown in a), and relatively inaccurate forecasting for CWS 150 in Berlin, shown in b). L. Romero Rodríguez et al. Urban Climate 56 (2024) 102021 18 available. Going back to the results presented in Table 7, if we now look at the total number of CWS initially available (304), the percentage of accurate forecasting models for the 7-day period is around 33% (101 of the CWS), with differences among the case studies. Nevertheless, if the limit was increased up to 2.2 ◦C, then 277 (91%) of the CWS available could be considered. Thus, it was possible to forecast the urban temperatures with a relatively good accuracy in a high percentage of the available CWS of the case studies. We should bear in mind however that a validation of the models was already carried out with hourly data of 2022. Thus, the decrease of precision of the models in this case is mostly due to the inaccuracy of the reference weather forecast. In any case, the results could still be improved. In Fig. 12, we may see for the case of Rome that the lower the RMSE of the models developed for April, the lower the RMSE of the 7-days forecasting. This tendency is also true for the rest of the case studies, if perhaps not so noticeable. This means that, as expected, the precision of the forecasting results may be improved by increasing the accuracy of the developed models. In turn, the percentage of accurate models may be increased by having better CWS measurements, so that more reliable data is available after the quality-control process to train the models. This means that the CWS should be placed by the users in unshaded locations, and that connection losses should be avoided. The accuracy of the reference weather forecast, mentioned in Section 4.2, is also very important. The 2 m air temperature used in the present study is an important meteorological variable, but even though numerical weather models are an important means of forecasting, they typically present forecasting errors (Hou et al., 2022). As mentioned in previous studies such as (Chang et al., 2021) or (Chakraborty et al., 2014), weather categories and patterns are major factors that influence temperature forecasting. This means that the accuracy of the forecasting may vary in sunny or rainy periods, which is why it is very important to train the models with a diverse dataset encompassing different weather conditions. The forecasting errors of the reference weather in our case were shown in Fig. 9. Looking again at the results shown in Table 7, with the average 7-days forecasting results for all case studies, we may see that in most cases the lower the RMSE of the reference weather forecast, the lower the average RMSE of the urban temperature forecast (up to 168 h ahead). Thus, we may conclude that, in the present study, it is very important to ensure the accuracy of the reference weather prediction. 4.4. Forecasting performance comparison with previous studies Comparing the results with those of previous studies, we may see that for instance in (Curceac et al., 2019) a non-parametric and a parametric approach were used to forecast hourly air temperatures, obtaining an average RMSE 1 h ahead around 0.7 ◦C, and 24 h ahead around 1.6 ◦C (requiring around 65 s to obtain the forecast). (Choi et al., 2021) obtained between 0.97 and 1.13 ◦C RMSE for 24- h ahead forecast in the case with most information available. In (Ozbek et al., 2021), for a 1 day-ahead prediction, the RMSE ranged between 1.3 and 4.4 ◦C for the models developed. Also, in (García-Duarte et al., 2022) different models were tested, obtaining a RMSE between 0.62 and 1.31 ◦C for 1 h ahead forecasting, and between 0.96 and 1.52 ◦C for 3 h ahead forecasting. (Kreuzer et al., 2020) tested deep neural networks, obtaining an average RMSE for hourly temperature forecasts up to 24 h in advance between 2.1 and 2.87 ◦C. Last of all, in (Lazzús et al., 2020) a method that combined ANN and genetic algorithms was used to forecast temperatures up to 6 h ahead, obtaining a RMSE of 0.99 ◦C for 1 h ahead forecasting, and 4.5 ◦C for 6 h ahead forecasting. Therefore, from these outcomes, we may conclude that the accuracy of the models proposed in this work are comparable to the previous literature or even better. This is true despite the simplicity of the models proposed and the longer forecasting horizon (up to 168 h ahead). This highlights the capability of the proposed approach to achieve accurate and reliable long-term temperature forecasts at urban scale. 4.5. Forecasting comparison in a city Last of all, we would like to emphasize the importance of having models to forecast urban temperatures at different locations within a city. Using as an example 4 of the developed models in Madrid and the same forecasting period in April 2023, Fig. 13 shows a comparison of the estimated temperatures at those CWS. It may be observed that, within the area under study in Madrid, there are various temperature profiles, with differences of temperature reaching up to 8 ◦C. Having the possibility of identifying these differences is paramount for urban planning and other disciplines, since it allows for instance to pinpoint the most critical locations during the day to avoid extreme temperatures, or to calculate the UHI intensities. It also becomes apparent that, if only the reference temperature had been considered (when there are no models available), the temperature predictions at specific locations would be very inaccurate due to the intricacies of the urban environment. 4.6. Forecasted heat maps To illustrate how the urban temperature forecasting may also be visualized in any area under study through heat maps, an example is shown in Fig. 14 for the temperature forecast of Rome on the 5th of April 2023 at 20 h. At that time, it was possible to forecast the temperature of 76 CWS, using the models previously developed for April that were accurate enough. The RMSE with respect to the real measurements amounted to 0.905 ◦C at that time. Considering that the forecasting was carried out on the 2nd of April 2023 (70 h before), the estimations are quite accurate, and allow to obtain a heat map that shows the coldest and warmest locations within the city. Nevertheless, it should be mentioned that the considerations that were previously raised are also applicable in this case. For instance, the higher the amount of CWS forecasts available, the higher the precision of the heat map estimation. L. Romero Rodríguez et al. Urban Climate 56 (2024) 102021 19 4.7. Summary of results and discussion In this section, the main results of the present work will be summarized. Five different case studies in Europe were considered, using temperature data from the CWS manufactured by the company Netatmo. A total of 776 CWS were available, with hourly temperature data for the years 2021 and 2022. Then, as prescribed in previous literature, a quality-control process was implemented, which is crucial given the inherent unreliability of data obtained from crowdsourcing alternatives. Considering all case studies combined, in 2021 the available hourly temperature data after the quality-control process was 58%, and in 2022 the available data was 70%. It should be however mentioned that, since percentages were used in the quality-control process to eliminate the outliers, extreme situations where for instance all weather stations are correct or all of them are incorrect are not considered. Thus, it would be recommendable in the future to include a step within the quality-control process that would depend only on the behavior at each specific CWS, such as its rate of temperature change. Once the data quality was ensured, the present work used the temperatures of 2021 to train models for each CWS and month, so as to be able to forecast the temperatures at their locations. As opposed to previous studies which are mostly based on complex machine Fig. 12. Example of comparison for all CWS available in Rome. Fig. 13. Comparison between the temperatures forecasted by the models of 4 CWS in Madrid. L. Romero Rodríguez et al. Urban Climate 56 (2024) 102021 20 learning models, this work proposed the development of multiple linear regression models with lagged predictors which only depend on reference weather temperatures. The data used as reference weather for the case studies were obtained from the platform Open- Meteo. Using the hourly data of 2022 to validate the models trained with data of 2021, it was possible to obtain an accurate prediction model (RMSE lower than 1.5 ◦C) for almost half of the total number of CWS (48%), with variations depending on the case study and month. The average RMSE value for the case studies was 1.39 ◦C. Then, those accurate models were used on the 2nd of April 2023 to forecast the hourly urban temperatures at each CWS for the period from the 3rd to the 9th of April 2023 (up to 7 days ahead, 168 h). The Weather Forecast API of Open-Meteo was utilized to forecast the reference weather temperatures, which were the input data needed for the models. Out of the 776 CWS initially considered across all case studies, it was possible to obtain an accurate temperature forecasting (RMSE lower than 1.5 ◦C) for only 101 of them (13%), which would increase up to 277 CWS (35.7%) if we considered those with RMSE lower than 2.2 ◦C. These results are comparable to previous literature, despite the simplicity of the proposed multiple linear regression models and the long forecasting horizon of 168 h. It was also observed that the higher the accuracy of the models developed, the lower the RMSE of the 7-day forecasting. Also, to improve the urban temperature forecasting with the proposed approach, it was found that it is very important to have access to accurate prediction models for the reference weather. As shown in (Huang and Ding, 2021), NWP models are essential for everyday life and quantitative weather prediction worldwide. However, they are computationally intensive, requiring continuous data assimilation from diverse sources and often needing supercomputers. When compared to NWP models, which solve complex physical equations governing atmospheric dynamics, our statistical method trained on historical CWS data requires significantly less computational power and offers faster prediction times once trained, although it necessitates a substantial training dataset and the resolution depends on the input data. In any case, NWP has made significant advancements in recent years. (Bauer et al., 2015) highlight that NWP models are frequently updated to improve model physics, data usage and computational efficiency. (Ronda et al., 2017) demonstrate that NWP can now forecast at urban scales with grid sizes as small as 100 m. Post-processing to correct model errors is also common practice (Qin et al., 2023). According to (Blunn et al., 2024), urban NWP air temperature errors are still typically 1–2 ◦C, and machine-learning postprocessing may help correct systematic biases and improve downscaling to higher resolutions. For all these reasons, both NWP models and our statistical approach have distinct advantages and disadvantages in predicting urban air temperatures. Integrating physicalbased models with statistical approaches or machine learning techniques for achieving robust and reliable predictions is thus a key area for future research. 5. Conclusions This research has demonstrated that cost-effective acquisition of extensive spatial and temporal temperature measurements in urban areas, along with accurate urban temperature forecasting, can be achieved by utilizing data from CWS and publicly available weather forecasts from sources such as ECMWF or NOAA. Existing methods often fail to capture microscale variations due to their coarse spatial resolution, highlighting the significance of the presented methodology in harnessing CWS data to capture localized temperature variations more accurately. The proposed approach, replicable globally where CWS data is available, was evaluated against previous literature regarding data collection, quality control procedures, and model accuracy. The developed models, when reliable CWS data and accurate reference weather forecasts are utilized, demonstrate strong accuracy compared to previous studies despite their simplicity. Notably, achieving a one-week forecasting horizon (up to 168 h ahead) with hourly resolution represents a novel achievement, not reported in prior literature with similarly satisfactory results. Fig. 14. Forecasted heat map for the 5th of April 2023 in Rome, performed 70 h ahead. L. Romero Rodríguez et al. Urban Climate 56 (2024) 102021 21 Moving forward, exploring more complex forecasting alternatives represents a promising avenue for future improvement. Additionally, even though this study is based on statistical modeling, further research should incorporate considerations of the physics and urban morphology underlying urban climate dynamics. This enhanced insight would improve temperature estimations and contribute to a comprehensive understanding of urban climate processes. Also, the findings of this study have important implications to predict the health impacts of urban temperature fluctuations, the energy consumption of buildings, inform about climate change adaptation strategies, or inform about urban planning and design decisions. Thus, this information may be beneficial to a wide range of stakeholders: urban planners, policymakers, health professionals, or even the general public, who could use the information to make informed decisions about their daily activities and behaviors. CRediT authorship contribution statement Laura Romero Rodríguez: Conceptualization, Investigation, Methodology, Software, Writing – original draft. MCarmen Guerrero Delgado: Formal analysis, Investigation, Validation. Daniel Castro Medina: Formal analysis, Methodology, Software. Jos´ e S´ anchez Ramos: Funding acquisition, Investigation, Supervision. Servando ´ Alvarez Domínguez: Conceptualization, Formal analysis, Methodology, Validation. Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Data availability Data will be made available on request. Acknowledgments This study has been funded by the projects “CONSTANCY - Resilient urbanisation methodologies and natural conditioning using imaginative nature-based solutions and cultural heritage to recover the street life” (Grant Agreement PID2020-118972RB-I00) and the project “NATURBEAM - Lighting the way to a greener future to restore urban habitability through nature-based solutions” (Grant Agreement TED2021-130416B-I00) by the Spanish Ministry of Science and Innovation. The authors would also like to express their gratitude to Jesús Barroso Casanova for his assistance in implementing the API calls for this research. References Baniassadi, A., Manor, B., Yu, W., Travison, T., Lipsitz, L., 2023. Nighttime ambient temperature and sleep in community-dwelling older adults. Sci. Total Environ. 899 https://doi.org/10.1016/j.scitotenv.2023.165623. Bauer, P., Thorpe, A., Brunet, G., 2015. The quiet revolution of numerical weather prediction. 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