Temperature and Rainfall partial trends in Oxford, 1870-2019

In this study, the trends and stabilities of temperature and precipitation hydro-meteorology time series recorded since 1870 in Oxford city of England were analyzed in detail. The Innovative Triangular Trend Analysis (ITTA) method has been inspired to identify and analyze the trends and stabilities of the selected time series. To compare the results obtained by the above-mentioned method, the Classical Mann Kendall (MK) method has been applied to each series determined for ITTA design. Thanks to the innovative design of ITTA which is preferred by the Classic MK and Sen slope methods, the trends of time series could be analyzed in detail. In this study, the first draft structure has been improved with the help of ±5-±10 % percentage change levels which were added to the ITTA method, and thus more objective evaluations about the trend magnitudes in time series is possible. For the same draft, the monotonic trend slopes which were found by the classical MK were also calculated through the Sen slope method. The data trends could explain in more detail with the help of the draft used in this study, compared to the studies in the literature. Climate change, which has been the most important factor in trend formation in recent years, has been taken into consideration while determining the design series. The thirty-year period up to 2019, a year in which the climate change was felt much more, constitutes the most important reference years for the analysis beginning from 1990, a year in which the climate change effects started to emerge. When the data trends of one hundred fifty years are examined for the different sub-time series, it is seen that the temperature increase in during1990-2019 period is much higher than the past hundred and twenty years, according to the analysis results. The highest average precipitation occurred in the 1990-2019 and 1900-1929 periods, and their amounts and patterns are nearly similar.


Introduction
As a result of climate change, it requires to review engineering designs that affect our lives seriously from agriculture to health, from insurance to energy (Nelson et al., 2009;Watts et l., 2015;Thistlethwaite, J., & Wood, M. O. (2018) ;Şen 2008;Wang et al., 2010). However, this phenomenon, its positive and negative consequences should be considered in future planning.
For this reason, the researchers, designers, practitioners, and users should analyze the available data, changes, and/or trends in data in the best manner for all areas in which the change effects to be seen, especially the adaptation studies on climate change. It is highly important to analyze in detail the meteorological, hydrological, and hydro-meteorological data. Thus, the quality and quantity of studies on this subject are bound to continue to increase day by day.
In the original studies on trend analysis, the Mann-Kendall (MK) (Mann 1945;Kendall 1975) and Sen's slope (1968) methods, and linear regression trend test (Haan, 1977) suggestion methodologies are in favorable use. These methods analyze holistically the monotonic trends in data based on various assumptions. The literature review shows that there are many important studies in which these methods have been also preferred after 2000. For instance; Kalra et al., (2008) investigated the trends in six-hundred thirty-nine streamflow stations in the U.S.A. through Spearman's rho, Mann-Kendall, and linear regression methods using the data collected over a fifty-two-year period between 1951 and 2002, inclusive. According to this study, there is an increasing trend in data in the Mississippi and Missouri regions data, while there is a decrease in the Pacific Northwest and South Atlantic-Gulf regions. In another study conducted by Ahmad et. Al. (2014), the data trends were investigated through non-parametric MK and Spearman's rho (SR) tests using annual, seasonal, and monthly precipitation data collected over a fifty-one-year period from 1961 to 2011 in Swat River basin in Pakistan. In this study, the annual, seasonal, and monthly increasing and decreasing precipitation trends were identified in detail for each station. The spatial and temporal trends of annual and daily mean and extreme rainfall and temperature were analyzed by Pingale et. al (2014) using the Mann-Kendall test and Sen's slope estimators in arid and sub arid state of Rajasthan at 33 urban centers, where certain predominant changes were observed. The spatial changes of annual and daily mean and extreme rainfall and temperature data trends were estimated by using the inverse-distanceweighted interpolation technique. Amirataee et al. (2015) analyzed the annual and monthly evapotranspiration (ET0) data trend changes and slopes through MK and, Modified Mann Kendall (MKK) methodologies (Hamed andRao 1998), Theil (1950), and Sen (1968) applied methods in synoptic stations in Urmia Lake basin located in the northwest of Iran. According to the study results, a trend increase has been seen in the ET0 data of all stations. On the other hand, the trend increase values obtained by the classical MK test have decreased significantly after the MKK test use.
Although these studies, the restrictive assumptions of classical methods such as independent serial structure, and the compliance of given time series with the normal distribution constitute directly a significant obstacle for the use of data trend analysis methods. If the selected data are checked before the trend analysis, it is possible to see that the current series may be statistically have serial correlations and may not follow the normal distribution. Therefore, some actions should be taken to make the trend series methods suitable for use. However, there are many studies in the literature in which the trend methodologies are used without any testing or data processing. Using inappropriate series and trend methods directly will cause misleading results.
For this reason, Von Storch (1995) stated that the trend-setting probability increases by the MK test application for the data with positive serial correlation and without a trend. The abovementioned researcher suggested the pre-whitening (PW) method to separate the serial correlation component from the time series before the MK test application. Even though there is more powerful over-whitening (OW) procedure by Şen (2017a), it has not been taken into consideration for alleviation of restrictive serial correlation structure into independent character. Some researchers apply the PW method to reduce the serial correlation effect before the MK test (Douglas et al. 2000, Zhang et al. 2001and Beyazit and Önöz 2007. In a study conducted a while later, it was seen that the pre-whitening method has various advantages and disadvantages, so Yue et al. proposed a modified PW procedure (Yue et al. 2002(Yue et al. , 2003. In a conclusion, it is understood that there are significant issues and processes which are taken into consideration while using the above-listed methods.
Determining the trends, partial trends, and stability of trends, interpreting their results, and moving directly from the raw data to the verbal information are difficult by classical methods.
The used assumptions cause losses during the verbal conversion of information in numerical data. The innovative trend analysis (ITA) method developed by Şen (2012) is the first study without any assumptions in trend research. This method has frequently been preferred because of its simple structure, it is used easily without any assumptions, and the trends and scatterings are identified through the charts. In the ITA methodology, the trend determination over different subgroups such as visually low, medium, and high rather than holistically and the development flexibility of methods and outputs attract the attention of many researchers (Sonali and Kumar 2013;Dabanlı et al. 2016;Alashan 2018;Morbidelli et al.2018;Ahmad et al. 2018;Güçlü et al. 2019;Şişman 2019;2021;Wang et al. 2020;Malik et al. 2020;Oruc 2020;Arslan et al. 2020 and others).
The classical and innovative methods have been used recently to determine the partial data trends. Researching, evaluating, and interpreting the partial trends have become crucial, especially due to the increasing data number. It is also clear that this one will increase in importance. There are many studies conducted to analyze the partial trends which are caused by climate change, urbanization, or similar causes in accordance with different times or periods, the scope of trend analysis is enlarging. Öztopal and Şen (2017) determined the trends through the ITA methodology by dividing sixty year-precipitation data into three consecutive equal subseries of twenty years according to the first series. In another study, Mohorji et al. (2017) analyzed the partial trends in global temperature data by dividing the time series into ten, twenty, thirty, forty, and fifty years sub-durations. In a study conducted by Güçlü (2018) to analyze the partial trends, the double ITA and triple ITA methodologies were proposed as alternative ITA versions. In this study, the different data trends have been analyzed for the first time by the suggested partial MK test. Finally, a new template design was proposed by using the ITA method to analyze in detail and systematically the partial trends and theirs changes in a given time series, and this one was designated as innovative triangular trend analysis (ITTA) (Güçlü et al., 2020). The trend stabilities can also be analyzed through this design.
This study aims to analyze and evaluate in detail the precipitation and temperature data partial trends in Oxford station of England through the ITTA method, according to the researches and methods used on partial trends in recent years. In this study, it was tried to analyze the percentage increase and decrease without a subjective approach by adding ±5-10 % straights to the ITTA draft. In addition, the classical Mann-Kendall method was used by referencing the triangular design draft of ITTA. Thus, a comparison of innovative and classical methods was made through the classical MK method, a method showing the monotonic partial trends and stabilities in the most detailed way.

Study area and data
England has a temperate oceanic climate with rains every season. The western part of the country has more rainfall than the eastern part. In addition, the rainfall totals are higher in highland areas. In this study, Oxford city, was selected as the study area, which is located in the south of England with a surface area of 45.59 km² (Fig. 1).

Fig. 1 Study area
The general climatic conditions of Oxford are very similar to England. The coldest month is January with an average minimum temperature of 6.26C. The lowest temperature ever recorded was 5.80C in January 1963. When the temperature records between 1870 and 2019 are analyzed, it is seen that the coldest winter on record was 1963, with a temperature of 2.96C and the warmest summer on record was 1922 with 9.93C. According to the minimum temperature values of the above-mentioned one hundred-fifty-year period, seventy years were below the average while eighty years were above. In general, the hottest month is July, with an annual mean temperature of 13.97C. The highest mean monthly temperature on record was in

Methodology
The parametric and non-parametric methods are frequently used to determine the trends of long- In this study, the classical Mann-Kendall (MK) test was used to determine the time series trends and the Sen slope estimator in addition to innovative triangular trend analysis (ITTA) method were used with percentage increase and decrease indicators to predict possible trend magnitudes.

Innovative trend analysis (ITA)
In this method developed by Şen (2012), any time series is divided firstly into two noncoincident sub-series with equal time. Thereafter, two trend series are formed by sorting increasingly each value of the sub-series. The ordered pairs which are equal to the number of terms of trend sequences, are formed by matching the two smallest values, and the two biggest values of each trend sequence, separately. For each of these ordered pairs, scatter plots (see Fig   2) are obtained on the two-dimensional coordinate system such that the first term and the second term correspond to the x and y-axis, respectively. A 1:1 straight line is drawn to determine the trend direction in order to decide whether there is a trend component or not. If the points are on the line, there is no trend, which implies neutral trend. If the point scatters of trend sequences are above (below) the 1:1 straight line, there is an increasing (decreasing) trend. Various trend slope lines such as ±5-±10% parallel to the 1:1 straight line are added in later ITA applications to analyze the trend magnitude. With these straight lines, it is much easier to analyze and describe the increasing and decreasing trends visually. The average trend slope value of data can be calculated using the following mathematical expression. The ±5-±10 % slope lines on the chart can be drawn in parallel with the 1:1 straight line using similar calculations.
Herein, s is the average trend slope, ℎ ̅̅̅̅̅̅ is the average of the first-half series, ℎ ̅̅̅̅̅̅ is the average of the second-half series, and n is the total data number.

Innovative triangular trend analysis (ITTA)
This method inspired by the ITA methodology and developed by Güçlü et al., (2020) is used to determine the trends of the selected sub-series given in Table 2. In this method, the time series are split into consecutive and non-coincident sub-series in the t time interval. After determining the sub-series, the basic principle of trend determination is exactly the same as the ITA method. The data of each sub-series are arranged in increasing order as the ITA method.
The sub-series are compared with each other by considering the procedures determined in the ITA methodology into account from past to present. This comparison is made by triangular matrix for the sub-series given in Table 2. The partial trends in time series are determined after the comparison of sub-series. Sub series 1 st 2 nd 3 rd (n/t) th 1 st 1 1 st -2 nd 1 st -3 rd 1 st (n/t) th 2 nd 1 2 nd -3 rd 2 nd (n/t) nd 3 rd 1 3 rd (n/t) rd no meaning (n/t) th 1 The suggested calculation steps of the ITTA method are as follows: 1) A time series in the form of 1 , 2 , … … … is split into consecutive and non-coincident sub-series in the t time interval. These sub-series are given below through equations 2-5.
2) The comparison series is obtained by arranging the values of each sub-series in increasing order.
3) The ITA charts of each pair of sub-series are drawn as given in Table 2.
4) In this study, the 5% and 10% trend slope lines were added to the ITTA draft chart for the first time, so it is easier for experts and readers to understand and evaluate the data trends.

Mann-Kendall Test
Mann-Kendall is a significant statistical and non-parametric test that is widely used in meteorology, hydrology, and climatology domains for determining the monotonic trends of time series. In this method, any conformity to the normal distribution as in parametric tests is not necessary. It is accepted that there is no trend in the series assuming that the data are independently distributed and come from the same population, according to the MK test null hypothesis (H0). However, it is accepted in an alternative hypothesis (H1) that there are monotonic trends in the series.
In the MK test, each data in the time series is compared with the next one. When the MK test started, the statistic value is accepted as zero. If the data value in any period of the series is less than the next data value, is increased by 1, otherwise decreased. The net increase or decrease is obtained by the final value of .
In any { 1 , 2 , 3 , … . . } time series, represents the total data number, represents the data points in i. and . time series. The MK test statistic, , is expressed by the following In this equation, High positive values of S statistics show an increasing trend while low negative values indicate a decreasing trend. The mean and variance of S statistic are given by Kendall (1975) in Equations 8 and 9 below on the assumption that the data are distributed independently and similarly. ( Where, indicate respectively the number of dependent groups in the series and the number of dependent observations in the series of length.  (Table 3). The trend directions are determined for each trend series by calculating the sstatistics and p-values through the classical MK method and the trend evaluation is made for each series given in Table 3.  1-Any time series is given as { 1 , 2 , 3 , … … … } with n data number. This time series is split into pieces of consecutive non-coincident sub-series in the t time interval. These subseries are listed above similarly (2-5).
2-The trend analysis series are formed by combining each sub-series according to the combinations given in Table 3.

3-The classical Mann-Kendall test is applied by calculating the s-statistics and p-values for
each series to decide the trend direction and whether the trend is available.

Sen' Slope Estimator
The trend magnitudes identified by the MK method are calculated by the Sen slope (SS) method. The trend line slope (magnitude) median is calculated through Equations 11 and 12 below.
where, is the trend line magnitude, and are the consecutive time series. The positive and negative values of indicate the increasing and decreasing magnitudes of the trend.

Application
The annual maximum temperature data and mean annual maximum temperature, and trends and slopes in annual total rainfall data with one hundred-fifty-year record in Oxford station were determined in detail through the TTA, TMK, and Sen slope methods considering the formed draft series. The time series of one hundred-fifty years was divided into five consecutive non-coincident sub-series with an equal length of thirty years. The first thirty-year series was composed of data between 1870 and 1899. The others were composed of data between 1990-1929, 1930-1959, 1960-1989, and 1990-2019. The trends in time series were revealed through the TTA, TMK, and Sen slope methods under the triangular matrix structure described in the method section, according to the determined periods. The trends hidden in time series can be revealed through the design periods. Thus, the researchers get a chance to calculate the hidden trends through the formed design, compared to the classical methods. In this article, the decision whether there was a trend is achieved by taking the 5-10-20% significance levels as a reference for the MK tests. Also, the trend slopes of each series were calculated through the Sen slope method. The trend slopes were evaluated according to the 5-10% increasing and decreasing levels which were added to the TTA method in this study, the other method was selected to determine the trends.
In the first step, the analysis results of MK and Sen's slope methods about the annual maximum temperature, mean annual maximum temperature, and annual total rainfall data were given in Tables 4, 5, and 6. Each of them provides information on whether trends are available or not, according to the p-value, s-statistic value, calculated Z, Sen slope method, and 5-10-20% significant levels. If the one hundred-fifty-year data between 1870 and 2019 are designed as five different series of thirty years, it is possible to make ten different trend evaluations (as in Tables 4-6) over the trend series formed according to the TMK analysis. The period 1990-2019 which is found in the last column of Table 4 draws attention right from the start. In this period, a significant trend increase is observed in terms of mean annual maximum temperature, compared to the other periods. On the other hand, certain significant trends are observed in the period 1930-1959 which is found in the second column in another period. According to the structure in question and Sen slope calculations, the mean annual maximum temperature increase, for the sixty-year period in which the years 1990-2019 are taken as reference, is 2,34C, 2,4C, 1,62C, and 2,22C in the periods 1870-1899, 1900-1929, 1930-1959 and 1960-1989, respectively. In addition, when the first and third columns in Table 4  In conclusion, a significant trend increase was observed besides an average increase of 1,5 C/150 years, according to the Sen slope calculations.  1900-1929 1930-1959 1960-1989 1990- The partial trends, test statistics, and trend slopes of the annual maximum temperatures (1870-2019) are given in Table 5 1900-1929 1930-1959 1960-1989 1990- Finally, the analysis results obtained from the partial trends of precipitation data for the same meteorological locations are given in Table 6 by consideration of the similar design structure.
According to the MK and Sen slope indicators and the 5-10-20% significance level, there are no significant trends in the five different precipitation periods and ten different combinations.
When the table is analyzed in detail, it is seen that the Sen slope values change between -1.015 mm/year and 0,768 mm/year depending on design years in the table. When the trends are analyzed in terms of annual total rainfall data between 1870 and 2019, it is clear that there is no trend according to the classical MK test and the -10 % and 20% significance levels. As a result of the one hundred-fifty-year rainfall data analysis with Sen's slope method, an average increase trend of 8,85 mm/150 years was calculated in total.  Years 1900Years -1929Years 1930Years -1959Years 1960Years -1989Years 1990 As an alternative solution, the TTA structure and ITA method are used to compare the partial trends obtained for the trend sequences. The charts of mean annual maximum temperatures, annual maximum temperatures, and annual total rainfall data are given in Figures 3, 4, and 5.
The ITA method charts on the one hundred-fifty-year data were given as a large chart in the lower-left corner of the figures. In this study, the 5-10% trend percentage change lines in parallel with the 1:1 straight trendless line are added to the ITTA charts, as can be seen in the trend evaluation figures. The trends are evaluated much more easily and objectively by taking the five lines in the charts into consideration. Also, the average trends are obtained with the small red circle in the figures.
Firstly, it is seen that the data are above the 1:1 trendless straight line (0%) when examined the one hundred-fifty-year trend change of average maximum temperature (Figure 3). This shows that there is a trend increase in data. The trend increase percentage is very close to the 5% line, according to the figures. If the data are grouped as high and low mean maximum temperature, the trend increase rates are in the range of 5-10% in the data above average, while the trends are under 5% below average. According to the trends above average, there is an increase up to 15.15-14.05 = 1.10C, whereas the lowest increase is 13.53-12.88=0.65C below average. As for the partial trends, there is a trend increase, except for the 1930-1989 periods, according to the ten figures in draft structure. When the 1930-1989 period is analyzed, it occurs that there is a trend decrease at the level of -2,83% on average. According to the TTA charts (Figure 3   The trends of total annual rainfall records which are kept for one hundred-fifty years were also determined through the TTA analyzes ( Figure 5) in Oxford station. When analyzed in detail, we can see that the non-monotonic increases and decreases in data come to the forefront especially, differently from the trend temperature data charts. Although there is no obvious or significant trend according to the charts on partial trends and stabilities, the trends differ in the case of different rainfall data subgroups such as low, medium, and high. On the other hand, it has not been possible to identify and evaluate this situation through the classical methods and used applications until now. When the trend charts given below are examined in terms of averages, it is seen that there is no significant trend in general, except for certain periods. If we group the data as small and large in accordance with their averages beginning from the 1960-  1930-1959/1990-2019 and 1960-1989/1990-2019 with certain small differences and limit value differences in the pattern.
The non-monotonic increase trend limits are between -5% and +10%. The trend decrease was calculated as -2.55% on average for the years 1900-1929/1960-1989. According to the last sixty-year time series in the 1960-2019 periods, there is a trend increase of +3.32% in total annual rainfall depth. The researchers can examine all charts one by one and interpret them similarly. Finally, the method results used for determining trends and their magnitudes were given in Table 7. The partial trends were revealed through the TTA, TMK, and Sen's slope analyzes for thirty-year consecutive periods, and the data trends were evaluated through the MK, ITA, and Sen's slope analyzes. When the method results summarized in tables are evaluated in detail, it is observed that the trend directions and magnitudes are compatible for all data sets. Only two of the eleven analyzes made for annual total rainfall data have minor differences. The trend series are the combinations of the years 1870-1899/1930-1959 and 1900-1929/1930-1959. According to the MK method, there is no significant monotonic trend, but there is an increasing and decreasing trend in the ITA method. This is due to the fundamental difference between the ITA and MK methods. While inferences can only be made about the monotonic trends with the MK method, it is also possible to analyze the non-monotonic trends with the ITA method.
According to the partial trend charts on rainfall data, the trends are not only monotonic.
Therefore, while the MK method is taking the monotonic trend situations into account, the ITA method analyzes the monotonic and non-monotonic trends. As a conclusion, the method results differ depending on the available data series. Table 7. Comparison of TMK, Sen's slope, ITA, and ITTA data results Years 1900Years -1929Years 1930Years -1959Years 1960Years -1989Years 1990

Conclusion
In recent years, there have been studies on partial trends besides the classical approaches, and new methodologies have been included in these studies. For example; in this study, the ITA and MK methodologies were used together with the TTA design to determine the partial trends.
When the analysis results are examined, it is observed that there are significant similarities between the method results for the series with monotonic trend changes. According to this study, if the evaluations on trend series whose data numbers and record lengths have increased over the years are made by the expert opinions in accordance with the determined line or design periods such as twenty, thirty, forty years, etc., this contributes significantly to the detailed evaluations of trend directions, magnitudes, and stabilities. An extensive evaluation has been made for Oxford city in the application section, according to the trend analyses made by taking the temperature and precipitation data of the past hundred and fifty years into account for the thirty-year period after 1990, an important period for climate change studies.
The MK and SS analysis results show that there is a mean temperature increase of 1,5C, according to the mean maximum temperature data of one hundred and fifty years. For the periods of 1990-1929 and 1990-2019, a trend increase of 2,4C has been calculated considering the thirty-year design periods. When a similar evaluation is made for annual maximum temperature, a trend increase of 1,35C on average is observed for one hundred and fifty years of data, on the other hand, the monotonic increase of annual maximum temperature data is2,76C on average for the period 1960-2019. According to the results of the analysis made through the MK and SS methods, there is no significant monotonic trend totally and partially in annual total rainfall data.
The trend analyzes have been made once more again through the TTA method for all design series and interpreted in detail in the application section by taking into consideration the increase and decrease trends of the ±5-10 % levels as a reference. The TTA, MK, and SS methods have similar results in terms of the mean annual maximum temperature and annual maximum temperature data. On the other hand, it is seen in the resultant charts that the monotonic trend changes can be evaluated together with the non-monotonic trend changes. In this context, the interpretation of the patterns in non-monotonic trends has been made in detail in the application section for the rainfall data with no significant trend change, according to the MK and SS test results. The special trends of climate change in the 1990-2019 period have been identified through the analysis results on meteorology data of Oxford city.