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\papertype{Original Article}

\title{Detecting Location Errors with ERA5 Pseudo Stations}


\author[1]{Clara Bezeau}
\author[2]{Elizabeth Geissel}
\author[3]{Emily Hayes}
\author[4]{Gertrude Miria}
\author[5]{Connor Platt}
\author[6]{William Whelan}
\author[7]{Teng Yang}
\author[8]{Peter Thorne}

\affil[1]{Maynooth University}
\affil[2]{Maynooth University}
\affil[3]{Maynooth University}
\affil[4]{Maynooth University}
\affil[5]{Maynooth University}
\affil[6]{Maynooth University}
\affil[7]{Maynooth University}
\affil[8]{Affiliation not available}



\runningauthor{Clara Bezeau}

\begin{document}

\maketitle
\selectlanguage{english}
\begin{abstract}
Significant efforts are made to eliminate biases from models and
observations, especially at operational~centres. However, these biases
still significantly impact the quality of assimilated data products. In
the case of numerical weather prediction, residual biases can result in
suboptimal utilization of available data or even render them unusable.
In climate research based on re-analyzed datasets, it can be difficult
to distinguish between accurate signals and trends from inaccurate ones
caused by biases in models and data.This study used a detection
algorithm written in the R language to perform statistical computing and
data analysis. The algorithm was applied to a synthetic study utilizing
pseudo-stations based on ERA5 to simulate and detect instrumental
effects. Rather than using observational data from real-world sources,
the study generated artificial scenarios to guarantee the quality of the
data assessment.ERA5 is a well-known atmospheric reanalysis product that
was used to create simulated or pseudo-weather stations. These stations
were designed to mimic actual stations but were generated
computationally to enable controlled experimentation. The study
constructed twenty-five pseudo-stations in Frankfurt, Germany, within
the latitude 49--50\selectlanguage{ngerman}° and longitude 8--9° in the Northern Hemisphere. The
study utilized the ERA5 land surface dataset of hourly 2-m air
temperature of September in 2013 and 2014. The study tool significantly
improves data quality assessment by evaluating the synthetic dataset's
precision, dependability, and general robustness. It introduces a range
of factors to assess the degree to which the data quality can be
enhanced and maintained, including station movements, errors, and
noise.To determine the likelihood of the threshold correlation occurring
at our confirmed noise threshold, the correlation values occurring at
1.53 for each locational trial were extracted. Our threshold correlation
was evaluated to see if it occurred within a likely range of
correlations occurring at 1.53 degrees of noise, where 0.9744052 is less
than 0.9744667 but greater than 0.9781093.~This process helps improve
detection methods for data anomalies, contributing to advancements in
data quality assessment.%
\end{abstract}\selectlanguage{ngerman}%




\textbf{Keywords}: ERA5, Weather Station Validation, Statistical
Noise,~RStudio, Confidence Threshold

\section*{}

{\label{450396}}

\section*{\texorpdfstring{1. Introduction
\emph{}}{1. Introduction }}

{\label{450396}}

~~~~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~\emph{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 \emph{et al.}, (2020)). In scientific research and
application, it is often necessary to combine both to obtain more
comprehensive meteorological data (Salcedo-Sanz~\emph{et al.}, (2020);
Schauberger~\emph{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~\emph{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~\emph{et al.},
(2021); Jiao~\emph{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~\emph{et
al.}, (2020); Ghajarnia~\emph{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~\emph{et al.}, (2020) ; Jiao~\emph{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~\emph{et al.},
(2020); Doddy~\emph{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 \emph{et al.},
(2007); Dee~\emph{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~\emph{et al.}, (2019);~Jiao~\emph{et al.},
(2021); Ghajarnia~\emph{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~\emph{et
al}., (2021); Ghajarnia~\emph{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~\emph{et al.},
(2021);~Yu~\emph{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~\emph{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~\emph{et
al.}, (2020); Ghajarnia~\emph{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 \emph{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 \emph{et al.} (2021) and Jiao \emph{et al.} (2021). Furthermore,
McNicholl \emph{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\selectlanguage{ngerman}° x 0.1°\textbf{~}resolution. The
reanalysis data also covers a period from 1950 to near-real-time hourly
data, making it a valuable resource (Li~\emph{et al.}, (2022);
Essa~\emph{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~\emph{et al.} (2022) and
Shi~\emph{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~\emph{et al.} (2022) and Hoffmann~\emph{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~\emph{et al.}, (2021); Li~\emph{et al.},
(2022); Velikou~\emph{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.\textbf{~} ~\textbf{~} ~

\section*{}

{\label{274877}}

\section*{2. Methodology}

{\label{274877}}

\subsection*{~~~~2.1 Study Location and Air
Temperature}

{\label{369377}}

Frankfurt, Germany, is situated in Central Europe inland at geographical
coordinates of 50.116 degrees latitude and 8.684 degrees longitude and
sits at an elevation of 117 meters. The topography within a 3-kilometer
radius of Frankfurt am Main city is mostly flat, with a maximum
elevation change of 83 meters and an average elevation above sea level
of 114 meters.~Based on data from 1985--2015, the city experiences a
peak in temperature in July and August, then slowly decreases to its
minimum in December and January. September, thus, still shows warm
weather, and while September 2013 stays quite stable with a peak in the
early days, September 2014 is warmer and a bit more variable. However,
if we compare the extreme temperatures throughout the year, we can
observe similar results. Unstable weather, locally both in time and in
topography, could be a slight difficulty to test station accuracy as
temperatures can be as much as 4-5°C different from day to day,
according to records.\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Fig7/Fig7}
\caption{{Map showing the global distribution of all known weather stations. Note
the relatively high station density in Europe, hence our choice of study
in Frankfurt.~
{\label{147044}}%
}}
\end{center}
\end{figure}

Appropriate data from the .nc file, such as time, coordinates and
temperature values, were extracted and converted into .csv format. This
was due to the accessible format of .csv files. Csv files are commonly
used for the storage and distribution of data. Analysis of the ERA5 was
initiated once in this format. Originally two variables were selected
for analysis (2m temperature~ and surface pressure), however upon
initiation of analysis, a single variable, temperature,~ proved to be
sufficient.

Each coordinate within a quarter degree of the chosen window (latitude
49--50\selectlanguage{ngerman}° and longitude 8--9°) was extracted and assigned to a variable
name. This allowed for individual analysis per coordinate or location.
The quality and distribution for each location was then assessed. For
the purposes of reanalysis in this study, the city of Frankfurt was
divided into 25 distinct locations, which are tabulated below:

\emph{Table 1: Co-ordinates of each of the 25 locations in nearby
regions to Frankfurt}\selectlanguage{english}
\begin{longtable}[]{@{}llll@{}}
\toprule
\textbf{Station location} & \textbf{Longitude~} & \textbf{Latitude~} &
\textbf{Name of location}\tabularnewline
\textbf{01} & \selectlanguage{ngerman}\textbf{8°E} & \selectlanguage{ngerman}\textbf{50°N} & \textbf{Oestrich -
Winkel}\tabularnewline
\textbf{02} & \selectlanguage{ngerman}\textbf{8.25°E} & \selectlanguage{ngerman}\textbf{50°N} &
\textbf{Mainz}\tabularnewline
\textbf{03} & \selectlanguage{ngerman}\textbf{8.5° E} & \selectlanguage{ngerman}\textbf{50° N} & \textbf{Hasslock
(East)}\tabularnewline
\textbf{04} & \selectlanguage{ngerman}\textbf{8.75° E} & \selectlanguage{ngerman}\textbf{50° N} &
\textbf{Gotzehain}\tabularnewline
\textbf{05} & \selectlanguage{ngerman}\textbf{9° E} & \selectlanguage{ngerman}\textbf{50° N} &
\textbf{Zellhausen}\tabularnewline
\textbf{06} & \selectlanguage{ngerman}\textbf{8° E} & \selectlanguage{ngerman}\textbf{49.75°N} & \textbf{Nack
(Northwest)}\tabularnewline
\textbf{07} & \selectlanguage{ngerman}\textbf{8.25° E} & \selectlanguage{ngerman}\textbf{49.75°N} &
\textbf{Dittelsheim-Hessloch}\tabularnewline
\textbf{08} & \selectlanguage{ngerman}\textbf{8.5° E} & \selectlanguage{ngerman}\textbf{49.75°N} &
\textbf{Gernsneim}\tabularnewline
\textbf{09} & \selectlanguage{ngerman}\textbf{8.75° E} & \selectlanguage{ngerman}\textbf{49.75°N} &
\textbf{Webern}\tabularnewline
\textbf{10} & \selectlanguage{ngerman}\textbf{9° E} & \selectlanguage{ngerman}\textbf{49.75°N} & \textbf{Nack
(North)}\tabularnewline
\textbf{11} & \selectlanguage{ngerman}\textbf{8° E} & \selectlanguage{ngerman}\textbf{49.5°N} & \textbf{Hertlinghausen
(West)}\tabularnewline
\textbf{12} & \selectlanguage{ngerman}\textbf{8.25° E} & \selectlanguage{ngerman}\textbf{49.5°N} & \textbf{Weisenheim am
Sand}\tabularnewline
\textbf{13} & \selectlanguage{ngerman}\textbf{8.5° E} & \selectlanguage{ngerman}\textbf{49.5°N} &
\textbf{Wohlgelegen}\tabularnewline
\textbf{14} & \selectlanguage{ngerman}\textbf{8.75° E} & \selectlanguage{ngerman}\textbf{49.5°N} & \textbf{Lampenhain
(West)}\tabularnewline
\textbf{15} & \selectlanguage{ngerman}\textbf{9°E} & \selectlanguage{ngerman}\textbf{49.5°N} &
\textbf{Soitzberg}\tabularnewline
\textbf{16} & \selectlanguage{ngerman}\textbf{8°E} & \selectlanguage{ngerman}\textbf{49.25°N} &
\textbf{Dernbach}\tabularnewline
\textbf{17} & \selectlanguage{ngerman}\textbf{8.25°E} & \selectlanguage{ngerman}\textbf{49.25°N} &
\textbf{Oberlustadt}\tabularnewline
\textbf{18} & \selectlanguage{ngerman}\textbf{8.5°E} & \selectlanguage{ngerman}\textbf{49.25°N} &
\textbf{Waghausel}\tabularnewline
\textbf{19} & \selectlanguage{ngerman}\textbf{8.75°E} & \selectlanguage{ngerman}\textbf{49.25°N} &
\textbf{Muhlhausen}\tabularnewline
\textbf{20} & \selectlanguage{ngerman}\textbf{9°E} & \selectlanguage{ngerman}\textbf{49.25°N} & \textbf{Ehrstadt (North
East)}\tabularnewline
\textbf{21} & \selectlanguage{ngerman}\textbf{8°E} & \selectlanguage{ngerman}\textbf{49°N} & \textbf{Schleithal (North
West)}\tabularnewline
\textbf{22} & \selectlanguage{ngerman}\textbf{8.25°E} & \selectlanguage{ngerman}\textbf{49°N} & \textbf{Neuburg am
Rhein}\tabularnewline
\textbf{23} & \selectlanguage{ngerman}\textbf{8.5°E} & \selectlanguage{ngerman}\textbf{49°N} &
\textbf{Grotzingen}\tabularnewline
\textbf{24} & \selectlanguage{ngerman}\textbf{8.75°E} & \selectlanguage{ngerman}\textbf{49°N} &
\textbf{Kleinvillars}\tabularnewline
\textbf{25} & \selectlanguage{ngerman}\textbf{9°E} & \selectlanguage{ngerman}\textbf{49°N} &
\textbf{Hohenhaslach}\tabularnewline
\bottomrule
\end{longtable}

\par\null

\subsection*{~~~~~2.2 ERA5}

{\label{369377}}

ERA5 is a dataset created by the European Centre for Medium-Range
Weather Forecasts (ECMWF) and managed by Copernicus Climate Change
Services (C3S). To produce a more precise spatial and temporal
resolution compared to ERA-Interim, ERA5 uses advanced techniques like
4D-Var and a high-resolution numerical weather model (Hersbach ~\emph{et
al.}, (2020)). ERA5 assimilates a broad range of observational data,
including satellite measurements, ground-based weather stations, and
ocean buoys, thus, improving the accuracy of the initial conditions used
in weather models. This dataset plays a significant role in weather
forecasting by assimilating observational data, offering high-resolution
information, maintaining consistency in data records, providing global
coverage, and aiding in model validation. All of these factors
contribute to the accuracy and reliability of temperature forecasts
(Hersbach~\emph{et al.}, (2020) ; Yu ~\emph{et al.}, (2021) ;
McNicholl~\emph{et al.}, (2022)).

\subsection*{~~~~2.3 Air Temperature and
ERA5}

Several studies have assessed ERA5 efficiency both in terms of air
temperature data and air temperature trends (Almeida and Coelho, (2023)
; Yilmaz, (2023)). According to them, ERA5 has a tendency to slightly
underestimate air temperature in some regions, possesses~ a greater
accuracy with simulations across flatter areas in contrast to locations
of high altitude and complex, uneven terrain patterns (Almeida and
Coelho, (2023)). While it may be best to be cautious for short term
environmental studies, it is overall really effective to describe air
temperature in Europe (Almeida and Coelho, (2023)). Focusing more on
temperature trends, ERA5 is shown to be consistent with observed trends
with a better accuracy over long term period, its trends can be on
average slightly higher than observed but to a negligible level of
difference (Yilmaz, (2023)). Factors such as time period, location of
study, biases in ground observation and inhomogeneities can introduce
trends and variability in the dataset that are inconsistent with
observed values (Almeida and Coelho, (2023)). In light of these points,
Almeida and Coelho (2023) suggest carrying out assessments of reanalysis
datasets under different climatic conditions to eliminate as much
uncertainty as possible,~ however, all in all, studies still agree that
ERA5 can be highly trusted with air temperature.~Therefore the data must
be simulated to determine if an outlying data point is truly incorrect
(whether from an alternate data set or a typo), if it is genuinely a
novel change in data (e.g., freak events, creating a novel area for
research), or if it is due to an unrecorded change in station location.~
A step-by-step approach used in the data manipulation, calibration and
verification of this process is shown below.~

\subsection*{~~~~2.4 Analysis Method~}

{\label{941270}}

We used the Copernicus Climate Change Service (C3S) Climate Data Store
(\url{https://climate.Copernicus.eu/climate-reanalysis}) to obtain
hourly 2-m air temperature from ERA5-Land surface, which the European
Centre provides for Medium-Range Weather Forecasts (ECMWF). The data was
downloaded on December 7, 2023, in NetCDF format (CDS, n.d.) for a
single month in September 2013 and September 2014; it was available at
0.250 (31 km) gridded resolution in the latitude 49--50 degrees and
longitude 8--9 degrees.\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Fig2/Fig2}
\caption{{Map of the area surrounding Frankfurt, including the 25 locations
examined in this study indicated by dots (refer to Table 1 for precise
identification of these locations). ~
{\label{827917}}%
}}
\end{center}
\end{figure}

The R software (version 4.1.2) and the packages ``devtools'' and GitHub
(``ProcessMiner/nlcor'') were used for the analyses in this study. The R
package ggplot2 was utilised to generate the diagrams in the study. The
following section of the report contains all scriptable R codes for the
analyses performed in this investigation. We began by importing NetCDF
as an NC file and converted it to CSV format. This is to improve the
compatibility and ease in opening and manipulating CSV files in RStudio
using the R programming language.

\subsection*{~~~~2.5 Statistical Method and Data
Analysis}

{\label{941270}}

A statistical summary, including the minimum value, maximum value,
quartiles, median and mean, was performed, allowing for trend comparison
across all locations. The inter quartile range (IQR) was also
calculated, providing a confidence interval for 50\% of distributed
data. Annual temperature follows a normal distribution. A Shapiro Wilk
test was used to test the null hypothesis that temperature data is also
normally distributed in our sample data for September. Contrary to
expectation, the p-value was not insignificant, and so it was accepted
that the data was more likely not to be normally distributed.

As the data did not follow a confident normal distribution, future
consideration must be applied. Hence the `rnorm()' function commonly
used in R to simulate normally distributed values, cannot be applied in
this instance. Therefore an alternative method to simulate our data is
required in the determination of false coordinate values. A location was
chosen at random to test possible alternate methods.\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/location-trends/location-trends}
\caption{{Original data distributions per location. Note the degree of similarity
between individual graphs prior to subsequent analysis~
{\label{780120}}%
}}
\end{center}
\end{figure}

Location 7 showed to have the highest correlation with location 8 and
then 6, and the lowest correlation with location 25. If a confidence
threshold is produced, it may be possible to statistically determine
when a value from location 7 is truly from location 8, and not just
highly correlated. Therefore various methods were assessed in their
confidence to accurately reproduce the distribution of data from
location 7.

\section*{}

{\label{244674}}

\section*{3. Results}

{\label{244674}}

The function `descdist()' was performed to estimate kurtosis and skew in
location 7. Kurtosis indicates the length of a skew tail, whereas the
resulting skew output indicates the skew bias. The function showed a
positive skew and a kurtosis not far from three. Therefore three common
right-skewed distributions could be considered for fit: Weibull, gamma
and lognormal distributions. As the skew is very short tailed, a
possible normal distribution could be accepted upon rejection of the
other distributions, even with the previously rejected Shapiro-Wilks
test.

The function `fitdistr()' was used to assess each chosen possible
distribution (Weibull, gamma, lognormal and normal). The resulting value
provides a mean as the maximum likelihood parameter. Therefore whichever
distribution is closest in result to the true mean is selected. The
distribution which provided the most promising value was normal
distribution.

Transformation of location 7 to a true normal distribution was
considered, but given the above results the data was assumed to be
nearest in distribution to a normal distribution. Sample data was then
generated using the aforementioned normal distribution simulation
function and was applied to the distribution of location 7. The
resulting sample spread ,however, showed to have a very low correlation
with the data, showing that reproducing sample data for location 7 with
a normal distribution was still inappropriate.

An alternative idea was then produced: generating sample data under the
same distribution curve of location 7. With values fitted to a graphical
distribution, what amount of adjustment is required for correlation to
no longer occur? To assess this, it must first~be possible to regenerate
the sample data to have a correlation of near 1 to the original observed
values. First the density from the observed values was evaluated and
used to create the model of observed distribution. The `adjust' function
was applied to shift data values in order to create our sample values.
Correlation, with minimal adjustment, appeared to be close to zero,
showing this method to be equally unusable as the previous.

It was then realised that the function `cor()' was being used to measure
the correlation, however this measures linear correlation, with our data
being non-linear. Therefore `nlcor()' was introduced and previous
correlation calculations were reassessed non-linearly. The correlation
values improved slightly, but not significantly enough to be accepted.
The need for a probability matrix for each temperature was then
considered, however deemed to introduce unwanted bias.

As the previous methods had provided little progression, an entirely
different approach was deliberated. Rather than creating sample data
through the generation of individual values, the existing values could
themselves shift slightly, therefore, overtime, the data will eventually
deviate in correlation from observed location values. The R function
used to achieve this is the base function `jitter()'. If 0.1\% of change
can be added to each value in progression, at what amount of change in
jitter (or in this case `noise') can we say that the value no longer
belongs to, or correlated with the original dataset? If correlation
occurs with surrounding data, at what stage or amount of noise does this
occur? The default amount of jitter created is the factor by one fifth
of the smallest difference between observed values. Therefore a minimal
amount of noise (within realistic values) is applied. However
temperature values recorded can be greater than 5 significant figures,
so the noise applied would be too insignificant. Therefore our chosen
noise value is set to amount and not factor within the function. This
resulted in extremely high correlation, near 1 (0.99999998) with
p\textless{}0.05, so the resulting sample dataset is accepted. This was
then applied to location 7 in varying degrees of noise, from 0.01 to
4.00 in increments of 0.01, and repeated five times so as to gain more
accurate value estimates. Further trials would be carried out, however,
this test was extensive and required an extended duration. This was also
carried out on the additional 24 locations.

Once 5 trials were run for every location, the max correlation for each
row within a trial was calculated. This indicated the amount of noise
added where the sample data no longer had the highest correlation with
observed data for the location, and instead had a higher correlation
with a nearby location. The degree of noise and correlation were
extracted for these threshold points.\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Fig3/Fig3}
\caption{{R elative correlation values between locations. Darkest coloured dots
equate to greater correlation frequency.
{\label{667798}}%
}}
\end{center}
\end{figure}

\textbf{}Each location was then plotted by highest correlation
frequency, allowing for visualisation in the spread of locational
correlations for each location. It was hence decided that locations that
did not have all neighbouring locations present were excluded, as this
lack in data could cause a potential skew in our results, as potential
correlations could not occur. Therefore locations 7, 8, 9, 12, 13, 14,
17, 18, 19 were chosen to continue with analysis.

Sample data for the spread of values in correlations and degree of noise
were created to generate larger datasets, ensuing confidence in our
resulting data. These were validated using a t-test. A Shapiro-Wilks
test was performed to assess distribution. Both variables indicated
normal distribution, however original correlation values, when plotted,
showed to have a slight skew to the left, and so the degree of noise was
accepted as our variable for analysis, due to its visual confidence and
clear statistical normal distribution.\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Fig4/Fig4}
\caption{{Histogram of original locational noise values. Threshold value
indicating correlation deviance shown in blue
{\label{375880}}%
}}
\end{center}
\end{figure}

A confidence interval was then created within two standard deviations of
the mean. This was to ensure that our lowest threshold value () was
confidently within expected or possible threshold values. 1.481252
\textless{}1.53 \textgreater{}2.427654 \textbf{}\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Fig5/Fig5}
\caption{{Sampled noise with threshold value and confidence interval included
{\label{484729}}%
}}
\end{center}
\end{figure}

To assess the likelihood of the threshold correlation occurring at our
confirmed noise threshold, the correlation values occurring at 1.53 for
each locational trial were extracted. Our threshold correlation was
assessed to see if it occurred within a likely range of correlations
occurring at 1.53 degrees of noise.~ 0.9744052 \textless{} 0.9744667
\textgreater{} 0.9781093\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Fig6-I-guess/Fig6-I-guess}
\caption{{Precise frequency of correlation values between all 25 locations given a
value of simulated noise of 1.53 degrees
{\label{223746}}%
}}
\end{center}
\end{figure}

\par\null

\section*{4. Discussion}

{\label{217130}}

\subsection*{~~~~4.1 Location Errors in the ERA5
datasets}

{\label{126304}}

The distribution of temperature based on satellite measurements, on a
given time and date, can be seen for the 25 stations in Fig. 3. From
this graph, it is clear that in the surrounding areas of Frankfurt, the
temperature values are spread evenly. The even spread of temperatures
shows that the temperature data produced by ERA5 is potentially
reliable, as opposed to a dataset with large fluctuations between data
points. The high spatial resolution of ERA5 means that temperatures can
potentially be mapped out accurately over relatively small geographical
areas. This would make it a valuable dataset, which has been noted in
Figure 4. It is clear that for each year, the temperature difference
varies in a cyclic pattern. This can be observed when following the
median of each location as the maximum likelihood parameter. Location 7
, 8, 9, 12, 13, 14, 17, 18, 19 were chosen to continue further analysis
of true mean with promising value for a normal~distribution with the
result shown in Figure 5.~

The accuracy \textbf{} of results reflected within ERA5 datasets has
been shown to be significantly dependent on the location of the area
being studied, with some areas known for having less reanalysis
potential in comparison to others. Antarctica is a notable example of
this, owing its lack of study potential to a lack of long-term direct
observations, most of which are largely constrained to coastal areas~
(Tetzner \emph{et al.}, 2019). Therefore, reanalysis is often used as
the sole means to obtain reliable estimates of atmospheric structure
through time by constraining a physical atmospheric model by use of what
few observational records exist (Bracegirdle, 2013). Though we do not
anticipate a lack of observations to be a significant \textbf{} issue in
this study, there still remains some potential sources for significant
biases and errors in our measurements, such as land use cover and
change, which can have notable implications for factors such as albedo
and rates of radiative surface temperature change (Li \emph{et al.},
2023). From this observation, it stands to reason that heavily urbanised
areas would frequently display higher temperature measurements due to
the presence of the urban island heating effect, creating a potential
positive skew of measurements unrepresentative of true temperature
values. Furthermore, as explained previously,~ there were a significant
number of cases in which certain locations displayed particularly strong
correlations with others. Given the lack of geological complexity within
the study area, it stands to reason that there was noticeable error in
the data, and that it was likely influenced by potential misreporting of
station location.

Errors in station location can arise due to several factors, including
inaccuracies in GPS signals, interference caused by multipath or
atmospheric conditions, poor satellite geometry, errors with receiver
clocks, or even deliberate interference. These variables can result in
inaccuracies when calculating the precise position of a GPS receiver.

For location coordinates, noise can contribute to inaccuracies, causing
slight variations or shifts in the reported location as shown in Figure
7. In the case of 2-meter surface temperature data, noise can introduce
errors or biases into temperature readings, making it difficult to
identify accurate temperature patterns and trends. This can impact the
reliability of weather forecasts, climate studies, and other
applications that rely on precise temperature data.

\subsection*{~~~~4.2 Data Reliability and ERA
Datasets}

{\label{386646}}

Owing to the relatively flat gradient of the locations of study
surrounding Frankfurt and the high number of available weather stations
there, we managed to obtain surface temperature measurements of
relatively high accuracy within the city.~This network of numerous,
interconnected weather monitoring stations operate in a manner that
optimises economic and social benefit that stands as a testament to the
careful consideration given to their establishment (Amorim \emph{et
al.}, 2012). In anticipation of the inherently random nature of
temperature variations, the simulated noise levels were deemed necessary
in accounting for this unpredictability, and indeed we were able to
generate correlation values for each location at a given level of noise.
However, as we extracted our chosen data solely from the ERA5 dataset,
the accuracy of our analysis may have had the opportunity to improve in
significant degrees if the dataset's land-based counterpart, ERA5-Land
(Gleixner \emph{et al.}, 2020), was used in conjunction with the data
obtained in this study. This would have allowed for the potential
identification of any non-surface variables, such as cloud cover, for
any potential influence on surface temperature. This also may have
potentially mitigated any significant lack of clarity in the data
resulting from the coarse resolution of the ERA5 dataset (Gleixner
\emph{et al.}, 2020).

We assess the synthetic dataset's precision, dependability, and general
robustness to improve the data quality assessment. A range of factors
were considered to evaluate the degree to which the data quality can be
enhanced and maintained, including station movements, errors, and noise.
The analysis in Figure 3 helps us pinpoint which locations were most
sensitive or responsive to the introduction of noise, providing insights
into how noise affects the correlation between temperature data and
location coordinates for different weather stations. Noise, in this
sense, refers to the unpredictable variations in the temperature data.
For example, if location 1 has a correlation of 0.9633642, it means
there is a strong positive variable (temperature) being measured at
location 1 with low noise or random variability in the data.~~

\subsection*{~~4.3 Meteorological data
loss}

Weather radars often suffer from data loss issues, which limits their
data quality and applications. The traditional weather radar missing
data completion method based on radar physics and statistics has defects
in various aspects (Gong, \emph{et al.}, 2023).Modern weather radars are
powerful tools in today's real-time weather monitoring. Thanks to their
high spatial resolution and short scanning interval, radars can usually
obtain more comprehensive and finer-grained observations in regions than
rain gauges and satellites. Despite the advantages of radars, they
suffer from the data-missing problem that limits their data quality. A
significant cause of radar missing data is beam blockage, which occurs
when radar beams are obstructed by terrain objects like mountains and
buildings, resulting in wedge-shaped blind zones behind the objects.
Some data is missing. This may also cause abnormal temperature data
(Gong, \emph{et al.}, 2023). [?]Besides beam blockage, other equally
significant factors include the phenomenon of attenuation, whereby radar
signals are weakened as they pass through intense rainfall, which leads
to underestimations of rainfall and linked temperature data (Fabry,
1996). [?][?]These restrictions in radar technology can cause gaps in
meteorological data, which could lead to inaccurate temperature results.
[?]

\subsection*{4.4 Local factors~}

Due to the largely spherical shape of the Earth, it stands to reason
that it receives unequal amounts of heat energy from the Sun across such
a large spatial scale. However, the global-scale temperature regime is
made even more nonlinear and inconsistent across several regions due to
the influence of local meteorological and climatological controls over
smaller-scale areas.

Local variations in topography are well known to exert significant
control over, and bring about distortions in,~small-scale temperature
regimes over given locations (Zhu~\emph{et al.}, 2021), which presents
an obstacle in calculating the true values for surface air temperature.
This observational gap in data may be evidently shown by separate
stations as far apart as 3km given sufficient altitudinal differences
(Zhu~\emph{et al.}, 2021). The potential for trees to influence air flow
and precipitation patterns brings to attention the land-use cover and
change (LUCC) regime of the specified area. Research conducted by
Li~\emph{et al.} (2023) demonstrates the cooling effect of reforestation
efforts, with areas of grassland-to-forest conversion displaying lower
daily maximum surface temperatures in summer and autumn over reforested
areas of southern China. The degree of continentality (distance from the
sea or ocean) of a given area must also be considered. Locations at a
closer proximity to the coast are shown to experience variations in
temperature in lesser magnitude than locations found in inland
environments, due to the faster rate of temperature change observed in
continental rock in comparison to the ocean, resulting in general
decrease in land-surface temperature in areas closer to the ocean
(Ning~\emph{et al.}, 2018). This factor can result in temperature
regimes that are inconsistent with the latitudinal location of a given
region: for example,~ the cities of Glasgow and Moscow are located at
similar latitudes, but the location of the former city closer to the
coast results in milder, warmer winters than that of the latter (BBC,
n.d.).

\textbf{~~~~4.5 Future Consideration}

ERA5 reanalysis studies are often hindered by a similar set of
obstacles, such as complex terrain and a lack of in situ observations
(Gleixner \emph{et al.}, 2020). And in the case of the ERA5 model
itself, its resolution value of 0.25 degrees is considered too coarse
for small-scale regional modelling and impact models (Gleixner \emph{et
al.}, 2020) (though its land-only counterpart, ERA5-Land, is often used
instead to counteract this limitation (Gleixner \emph{et al.}, 2020)).
Nevertheless, ERA5 is widely agreed to be a vast improvement upon its
predecessor, the ERA-interim dataset, on the grounds of precipitation
measurements, as well as those of temperature (Gleixner \emph{et al.},
2020). This will ultimately prove essential when observational values
are needed in conjunction with multiple climate variables in order to,
for example, model the natural variability of coupled systems (Trenberth
\emph{et al.}, 2008). Whether or not any improvements in ERA5 will prove
significant will depend on the outcome of future studies, which often
test such newfound capabilities in regions whose climate is difficult to
analyse, e.g. East Africa (Gleixner \emph{et al.}, 2020), which features
complex terrain and frequently heavy cloud cover (Holmes \emph{et al.},
2016) in addition to a sparsity of in situ measurements (Gleixner
\emph{et al.}, 2020). A wealth of advantages obtained in any reanalysis
study therefore allows for additional statistical experimentation to be
performed, as is the case with our study, in which sufficient data was
made available for the assimilation of random variation of surface
temperature in our calculations. Due to this, we can state with more
confidence that shifts in station location remain one of the most likely
sources of error or bias in the data. Though another method to consider
is one suggested by Almeida and Coelho (2023), involving the simulation
of different climatic conditions in a study area to eliminate further
uncertainties. In the case of this study, it may have proved useful in
identifying further potential sources of skew in location correlation
data.~

\par\null

\section*{5. Conclusion}

The~study~yielded valuable insights into the strengths and limitations
of the ERA5 temperature dataset, especially in data quality assessment.
The findings are significant in advancing the methodologies used to
evaluate reanalysis products and underscore the need to consider the
dataset's limitations when interpreting climate research outcomes.~

ERA5 reanalysis data is highly reliable and provides detailed
information on global atmospheric conditions at high spatial (up to 0.25
degrees) and temporal (hourly) resolutions. It is possible to conduct
comprehensive climate studies by considering various atmospheric
variables, such as wind, humidity, precipitation, and temperature. ERA5
employs advanced data assimilation techniques, combining observational
data with model outputs to represent atmospheric conditions more
accurately.

Biases, also known as systematic errors, are commonly found in
data-assimilation systems. All system components, including the forecast
model, boundary conditions, observations, observation operators, and
covariance models, can introduce, extrapolate, or amplify biases. To
detect biases, differences between observations and their
model-predicted equivalents can be monitored on the input side. At the
same time, systematic features of the analysis increments can be
examined on the output side. Identifying different sources of bias
requires additional information, such as independent observations,
knowledge of underlying causes, or hypotheses about the error
characteristics of possible sources.

Most data assimilation systems do not correct biases during the analysis
step, although developing bias-aware assimilation methods is
conceptually straightforward. The main challenge is correctly
attributing detected biases to their sources and developing applicable
models for them. Assimilation may correct the wrong source when multiple
sources produce similar biases. This risk increases when more degrees of
freedom are added to the system. For example, in a
weak-constraint~variational~analysis, parameters for radiance bias
correction support the model-error correction. It is still being
determined whether constraints on the correction terms can be
designed~to ensure that model and observation biases can always be
correctly and simultaneously identified in the analysis.

A bias-aware analysis scheme designed to correct bias in either the
background or the observations will reduce mean analysis increments by
construction, but not necessarily for the correct reason. It is
necessary to test whether the analysis has improved by verifying that
the bias attribution is accurate. Figure 7 illustrates how a successful
bias correction of the background during assimilation should lead to
better analysis and reduced forecast errors. However, reducing the bias
in the initial conditions may only improve the forecast in practice if
the model itself is changed.

Model bias correction is particularly challenging because it is
difficult to develop valuable representations for the biases or the
mechanisms that cause them. Intermittent bias correction of background
estimates in a sequential estimation scheme does not prevent the
generation of bias during the integration of the model. Incremental bias
correction schemes, which use bias estimates to correct model
tendencies, may be more effective in guiding the model to an unbiased
forecast, provided the corrections are physically meaningful.

\par\null

\section*{6. Bibliography}

{\label{783845}}

Almeida, M. and Coelho, P. (2023). A first assessment of ERA5 and
ERA5-Land reanalysis air temperature in Portugal. International Journal
of Climatology, 43(14), pp.6643-6663.

Amorim, A.M., Gon\selectlanguage{ngerman}çalves, A.B., Nunes, L.M. and Sousa, A.J. (2012).
Optimizing the location of weather monitoring stations using estimation
uncertainty. International Journal of Climatology, 32(6), pp.941-952.

Anon, (2019). How Atmospheric Sounding Transformed Weather Prediction -
NASA. {[}online{]} Available at:
\url{https://www.nasa.gov/history/how-atmospheric-sounding-transformed-weather-prediction-jdzlx/}
{[}Accessed 5 Feb. 2024{]}.

Auffhammer, M., Hsiang, S.M., Schlenker, W. and Sobel, A., 2013. Using
weather data and climate model output in economic analyses of climate
change. Review of Environmental Economics and Policy.

Baker, Z. (2017). Climate state: Science-state struggles and the
formation of climate science in the US from the 1930s to 1960s. Social
Studies of Science, 47(6), 861--887.

Baker, N. and Phillips, K. (2022). `Mares' tails and mackerel scales':
The many bizarre ways humans have tried to predict the weather. (2022).
ABC News. {[}online{]} 6 Jul. Available at:
\url{https://www.abc.net.au/news/2022-07-07/the-history-of-weather-forecasting/101181492}.

Barry, R.G. and Chorley, R.J., 2009. Atmosphere, weather and climate.
Routledge.

BBC (n.d.). Factors Affecting Climate - Factors Affecting Climate - CCEA
- GCSE Geography Revision - CCEA. {[}online{]} BBC Bitesize. Available
at: \url{https://www.bbc.co.uk/bitesize/guides/zgyw4qt/revision/2}.

Bengtsson, L. and Shukla, J., 1988. Integration of space and in situ
observations to study global climate change. Bulletin of the American
Meteorological Society, 69(10), pp.1130-1143.

Bengtsson, L., Arkin, P., Berrisford, P., Bougeault, P., Folland, C.K.,
Gordon, C., Haines, K., Hodges, K.I., Jones, P., Kallberg, P. and
Rayner, N., 2007. The need for a dynamical climate reanalysis. Bulletin
of the American Meteorological Society, 88(4), pp.495-501.

Bowman, D.M.J.S., Balch, J.K., Artaxo, P., et al. (2009). Fire in the
Earth system. Science, 324(5926), 481-484

Bouktif, S., Fiaz, A., Ouni, A. and Serhani, M.A., 2018. Optimal deep
learning lstm model for electric load forecasting using feature
selection and genetic algorithm: Comparison with machine learning
approaches. Energies, 11(7), p.1636.

Bracegirdle, T.J. (2013). Climatology and recent increase of westerly
winds over the Amundsen Sea derived from six reanalyses. International
Journal of~ Climatology, 33, pp. 843-851

Che-Castaldo C, Crisafulli CM. Long-term monitoring of Mount St. Helens
micrometeorology. Ecology. 2023 Mar;104(3):e3950. doi: 10.1002/ecy.3950.
Epub 2023 Jan 6. PMID: 36484720.

Chen, G., Shi, Y., Wang, R., Ren, C., Ng, E., Fang, X. and Ren, Z.,
2022. Integrating weather observations and local-climate-zone-based
landscape patterns for regional hourly air temperature mapping using
machine learning. Science of The Total Environment, 841, p.156737.

Cucchi, M., Weedon, G.P., Amici, A., Bellouin, N., Lange, S., Müller
Schmied, H., Hersbach, H. and Buontempo, C., 2020. WFDE5: bias-adjusted
ERA5 reanalysis data for impact studies. Earth System Science Data,
12(3), pp.2097-2120.

Dee, D.P., Balmaseda, M., Balsamo, G., Engelen, R., Simmons, A.J. and
Thépaut, J.N., 2014. Toward a consistent reanalysis of the climate
system. Bulletin of the American Meteorological Society, 95(8),
pp.1235-1248.

Doddy Clarke, E.; Griffin, S.; McDermott, F.; Monteiro Correia, J.;
Sweeney, C. Which Reanalysis Dataset Should We Use for Renewable Energy
Analysis in Ireland? Atmosphere 2021, 12, 624.

Edwards P.N (2010).~ A VAST MACHINE: Computer models, climate data, and
the politics of global warming. The MIT Press Cambridge, Massachusetts
London, England.

Essa, Y.H., Cagnazzo, C., Madonna, F., Cristofanelli, P., Yang, C.,
Serva, F., Caporaso, L. and Santoleri, R., 2022. Intercomparison of
Atmospheric Upper-Air Temperature From Recent Global Reanalysis
Datasets. Frontiers in Earth Science, 10, p.935139.

Fabry, F. (1996). Radar Meteorology: Principles and Practice. Cambridge
University Press.

Ghajarnia, N., Akbari, M., Saemian, P., Ehsani, M.R., Hosseini\selectlanguage{english}-Moghari,
S.M., Azizian, A., Kalantari, Z., Behrangi, A., Tourian, M.J., Klove, B.
and Haghighi, A.T., 2022. Evaluating the evolution of ECMWF
precipitation products using observational data for Iran: From ERA40 to
ERA5. Earth and Space Science, 9(10), p.e2022EA002352.

Gleixner, S., Demissie, T. and Diro, G.T., 2020. Did ERA5 improve
temperature and precipitation reanalysis over East Africa?. Atmosphere,
11(9), p.996.

Gong, A.; Chen, H.; Ni, G. Improving the Completion of Weather Radar
Missing Data with Deep Learning. Remote Sens. 2023, 15, 4568.

Hersbach, H., Bell, B., Berrisford, P., Hirahara, S., Horanyi, A.,
Munoz\selectlanguage{english}-Sabater, J., Nicolas, J., Peubey, C., Radu, R., Schepers, D. and
Simmons, A., 2020. The ERA5 global reanalysis. Quarterly Journal of the
Royal Meteorological Society, 146(730), pp.1999-2049.

Hoffmann, L., Gunther, G., Li, D., Stein, O., Wu, X., Griessbach, S.,
Heng, Y., Konopka, P., Muller, R., Vogel, B. and Wright, J.S., 2019.
From ERA-Interim to ERA5: the considerable impact of ECMWF's
next-generation reanalysis on Lagrangian transport simulations.
Atmospheric Chemistry and Physics, 19(5), pp.3097-3124.

Holmes, T.R., Hain, C.R., Anderson, M.C. and Crow, W.T. (2016). Cloud
tolerance of remote-sensing technologies to measure land surface
temperature. Hydrology and Earth System Sciences, 20(8), pp.3263-3275.

Houghton, J., 2005. Global warming. Reports on progress in physics,
68(6), p.1343.

Hu, Q., Li, Z., Wang, L., Huang, Y., Wang, Y. and Li, L., 2019. Rainfall
spatial estimations: A review from spatial interpolation to multi-source
data merging. Water, 11(3), p.579

Huang, X., Han, S. and Shi, C., 2021. Multiscale assessments of three
reanalysis temperature data systems over China. Agriculture, 11(12),
p.1292.

Jiao, D., Xu, N., Yang, F. and Xu, K., 2021. Evaluation of
spatial-temporal variation performance of ERA5 precipitation data in
China. Scientific Reports, 11(1), p.17956.

Jones, P.G. and Thornton, P.K., 2013. Generating downscaled weather data
from a suite of climate models for agricultural modelling applications.
Agricultural Systems, 114, pp.1-5.

Kalnay, E., 2003. Atmospheric modeling, data assimilation, and
predictability. Cambridge University Press.

Karl, T.R., Tarpley, J.D., Quayle, R.G., Diaz, H.F., Robinson, D.A. and
Bradley, R.S., 1989. The recent climate record: What it can and cannot
tell us. Reviews of Geophysics, 27(3), pp.405-430.

Kirsanov, A.; Rozinkina, I.; Rivin, G.; Zakharchenko, D.; Olchev, A.
Effect of Natural Forest Fires on Regional Weather Conditions in
Siberia. Atmosphere 2020, 11, 1133.

Li, Z., Gong, X., Liu, M., Tang, H., Yao, Y., Liu, M. and Yang, F.,
2022. A Temperature Refinement Method Using the ERA5 Reanalysis Data.
Atmosphere, 13(10), p.1622.

Li, X., Chen, H., Hua, W., Ma, H., Li, X., Sun, S., Lu, Y., Pang, X.,
Zhang, X. and Zhang, Q. (2023). Modeling the effects of realistic land
cover changes on land surface temperatures over China. Climate Dynamics,
61(3), pp.1451-1474.

Maraun, D. and Widmann, M., 2018. Statistical downscaling and bias
correction for climate research. Cambridge University Press.

Mauelshagen, F. (2014). Redefining historical climatology in the
Anthropocene. The Anthropocene Review, 1(2), 171-204.

McNicholl, B., Lee, Y.H., Campbell, A.G. and Dev, S., 2021. Evaluating
the reliability of air temperature from ERA5 reanalysis data. IEEE
Geoscience and Remote Sensing Letters, 19, pp.1-5.

Munoz-Sabater, J., Dutra, E., Agusti-Panareda, A., Albergel, C.,
Arduini, G., Balsamo, G., Boussetta, S., Choulga, M., Harrigan, S.,
Hersbach, H. and Martens, B. (2021). ERA5-Land: A state-of-the-art
global reanalysis dataset for land applications. Earth system science
data, 13(9), pp.4349-4383.

Ning, J., Gao, Z., Meng, R., Xu, F. and Gao, M. (2018). Analysis of
relationships between land surface temperature and land use changes in
the Yellow River Delta. Frontiers of earth science, 12, pp.444-456.

Oke, T.R. (1982). The energetic basis of the urban heat island.
Quarterly Journal of the Royal Meteorological Society, 108(455), 1-24.

Parker, W.S., 2016. Reanalyses and observations: What's the difference?.
Bulletin of the American Meteorological Society, 97(9), pp.1565-1572.

Pitman, A.J., 2003. The evolution of, and revolution in, land surface
schemes designed for climate models. International Journal of
Climatology: A Journal of the Royal Meteorological Society, 23(5),
pp.479-510.

Ramirez-Villegas, J. and Challinor, A., 2012. Assessing relevant climate
data for agricultural applications. Agricultural and forest meteorology,
161, pp.26-45

Robock, A., 2000. Volcanic eruptions and climate. Reviews of geophysics,
38(2), pp.191-219.

Rummukainen, M., 2012. Changes in climate and weather extremes in the
21st century. Wiley Interdisciplinary Reviews: Climate Change, 3(2),
pp.115-129.

Schauberger, B., Jagermeyr, J. and Gornott, C., 2020. A systematic
review of local to regional yield forecasting approaches and frequently
used data resources. European Journal of Agronomy, 120, p.126153.

Salcedo-Sanz, S., Ghamisi, P., Piles, M., Werner, M., Cuadra, L.,
Moreno-Martinez, A., Izquierdo-Verdiguier, E., Munoz-Mari, J., Mosavi,
A. and Camps-Valls, G., 2020. Machine learning information fusion in
Earth observation: A comprehensive review of methods, applications and
data sources. Information Fusion, 63, pp.256-272.

Shi, H., Cao, X., Li, Q., Li, D., Sun, J., You, Z. and Sun, Q., 2021.
Evaluating the accuracy of ERA5 wave reanalysis in the water around
China. Journal of Ocean University of China, 20, pp.1-9.

Tetzner, D., Thomas, E. and Allen, C. (2019). A validation of ERA5
reanalysis data in the Southern Antarctic Peninsula---Ellsworth land
region, and its implications for ice core studies. Geosciences, 9(7),
p.289.

Trenberth, K.E. and Olson, J.G., 1988. An evaluation and intercomparison
of global analyses from the National Meteorological Center and the
European Centre for Medium Range Weather Forecasts. Bulletin of the
American Meteorological Society, 69(9), pp.1047-1057.

Trenberth, K.E., Koike, T. and Onogi, K. (2008). Progress and prospects
for reanalysis for weather and climate. Eos, Transactions American
Geophysical Union, 89(26), pp.234-235.

Velikou, K., Lazoglou, G., Tolika, K. and Anagnostopoulou, C., 2022.
Reliability of the ERA5 in replicating mean and extreme temperatures
across Europe. Water, 14(4), p.543.

Wolfe, J., Mar 5,2000.
\href{http://www.earthdata.nasa.gov}{www.earthdata.nasa.gov}.
{[}online{]}

{[}date of visit: 24 01 2024{]}.

Yilmaz, M., 2023. Accuracy assessment of temperature trends from ERA5
and ERA5-Land. Science of The Total Environment, 856, p.159182.

Yu, Y., Xiao, W., Zhang, Z., Cheng, X., Hui, F. and Zhao, J., 2021.
Evaluation of 2-m air temperature and surface temperature from ERA5 and
ERA-I using buoy observations in the Arctic during 2010--2020. Remote
Sensing, 13(14), p.2813.

Zhu, J., Xie, A., Qin, X., Wang, Y., Xu, B. and Wang, Y. (2021). An
assessment of ERA5 reanalysis for Antarctic near-surface air
temperature. Atmosphere, 12(2), p.217.

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