The influence of global warming on precipitation extremes in West-Central Europe

(1)

The influence of global warming

on precipitation extremes in

West-Central Europe

University of Amsterdam

Bachelor project: Iris Balk

Primary supervisor: dr. ir. J.H. van Boxel

11-07-2020, Amsterdam

Second corrector: dr. ir. E.E. van Loon

(2)

2

Abstract

Global warming, induced by the anthropogenic emissions of greenhouse gases, has caused a change in the intensity and frequency of extreme precipitation events globally. Extreme precipitation has impact on an environmental as well as a social level, it can lead to floods, loss of life, crop losses and infrastructural damage. The aim of the research was to quantify the changes in the intensity and frequency of extreme precipitation for a west-east transect across Europe at about 52°N. Daily precipitation data for 1951-2019 were collected from the Europe Climate Assessment & Dataset. Trend analysis was used to establish trends in the precipitation in the annual values of the 90th, 95th, 98th, and 99th percentile. Also a trend analysis was done for the frequency at which the percentiles of the first 30 years were exceeded. The change of these trends from west to east was evaluated. Some sporadically significant trends were found for the change in the intensity and frequency of extreme precipitation in the beginning of the transect and towards the end of the transect. Despite of most of the trends not being statistically significant, a clear pattern was found with positive trends near the west coast, decreasing to near slightly negative trends between 9°E to 18°E and again positive trends more to the east, forming a quadratic trend over the distance. The pattern for can be explained by the influences of the higher sea surface temperatures and atmospheric circulation near the west coast. On the eastern side of the transect the pattern can be influenced by the atmospheric circulation and the elevation of the region. The results of this research can be used to provide a better insight in the changes of extreme precipitation events and to examine the hazards of vulnerable regions, such as flooding, crop lost, erosion, life lost and infrastructural damage.

(3)

3

Table of content

Abstract ... 2

Table of content ... 3

Introduction ... 4

Methods ... 5

Study area ... 5

Scientific literature review ... 5

Extreme precipitation ... 5

Results ... 8

Intensity ... 9

Frequency ... 10

Spatial differences ... 12

Discussion ... 14

Results ... 14

Previous studies ... 15

Limitations and improvements ... 16

Conclusion ... 17

Acknowledgements ... 17

References ... 18

Appendices ... 20

Appendix 1: overview weather stations ... 20

Appendix 2: MATLAB script for intensity ... 21

Appendix 3: MATLAB script frequency ... 22

(4)

4

Introduction

Over the century global temperatures have rising considerably (IPCC, 2014). According to the IPCC (2014) this warming has both natural and anthropogenic causes, however since the mid-20th century the warming is largely driven by the anthropogenic emissions of greenhouse gases. When the global warming continues, the tropospheric temperatures will further increase, causing the sea surface temperatures (SST’s) to rise slowly as the oceans absorb the most of the excess heat (Yang et al., 2003; Trenberth et al., 2007). Additionally as the tropospheric temperatures and SST’s are rising the water-holding capacity of the air over the oceans will increase, causing higher amounts of water vapor in the atmosphere (Trenberth et al., 2003). Since water vapor has a residence time of only 8-10 days in the atmosphere, the higher amounts of water vapor will lead to more precipitation and cause an increase in extreme precipitation (Kuchment, 2004; Trenberth, 1999). The increase of extreme precipitation will mainly occur in the wet tropics and mid-latitude regions (Van Boxel, 2001; Frei et al., 2006; Kundezewicz et al., 2006; Beniston et al., 2007; IPCC, 2014; Attema et al., 2014).

An increase in the extreme precipitation events can have large impacts on society and the environment. The events can lead to flooding, life loss, erosion, landslides, infrastructural damage, damages to crop and therefore lower crop yields. A better understanding of the change in extreme precipitation is needed to provide an insight in the effects of the change on society and the environment. Previous research has been done on the patterns of extreme precipitation in West and Central Europe. For example, on a more regional scale for the Netherlands, Germany, Poland and Belarus. These studies illustrate an increase of extreme precipitation in the Netherlands and in Central-Eastern Germany (Daniels et al., 2014; Łupikasza et al., 2011). Danilovich (2020) found an increase in the extreme precipitation for the central and southern regions of Belarus. Furthermore, IPCC models show that in many regions precipitation events become more frequent and intense, especially in the mid-latitudes regions (IPCC, 2014). On the contrary in Southern Poland the extreme precipitation events overall decreased (Łupikasza et al., 2011). According to a study of Lenderink et al. (2009) a higher increase in extreme precipitation seems to be present in Dutch coastal areas compared to land inwards. This could be linked to the distance from the sea and atmospheric circulation (Kyselý, 2009; Lenderink et al., 2009; Attema et al. 2014; Daniels, 2016).

However, a wider transect for analyzing changes in extreme precipitation events from the Dutch coast towards Belarus, has not been analyzed before. The aim of this research was to quantify the changes in the intensity and frequency of extreme precipitation for a west-east transect across Europe. In this research, statistical data analysis was used to analyze the data of 13 weather stations in a transect from the Netherlands to Belarus on changes in extreme precipitation over a period of 1951-2019. Through primary and secondary data analysis the following main research question was answered: To what extent does global warming influence extreme precipitation for a west-east transect across Europe?

In order to answer the main question, the following sub-questions were defined: 1. To what extent is the hydrological cycle influenced by global warming? 2. Does the intensity of extreme precipitation events show significant trends? 3. Does the frequency of extreme precipitation events show significant trends? 4. Does the changes in extreme precipitation events show a spatial pattern?

(5)

5

Methods

Study area

The study area of the research is a west-east transect of 1868 km from the Netherlands to Belarus between a latitude of 51°N and 53°N and a longitude of 04°E and 30°E. On this transect 13 weather stations were selected with a in between distance of approximately 2 degrees, as shown in figure 1. The stations were selected based on location, years of available data, elevation and their in between distance. From these stations the daily precipitation data over a time period of 1951-2019 was collected through the European Climate Assessment & Dataset (Klein Tank et al., 2002). An overview of all the weather stations, abbreviations, station numbers and distance can be found in appendix 1.

Figure 1: Selected stations on the west-east transect: Scheveningen, Vonkel, Altenberge, Hannover, Magdeburg, Lindenberg, Wrocław, Poznań, Warszawa-Okęcie, Brest, Pinsk, Zitkovici and Vasilevici (adapted from KNMI Climate Explorer, 2020).

Scientific literature review

To provide insight on the hydrological cycle and the influences of global warming on the cycle a literature review was carried out. The influences of global warming on different components of the hydrological cycle and the result of the change in the cycle has been researched. In addition, previous research and future predictions on extreme precipitation events in the research area were compared.

Extreme precipitation

In order to answer the sub-questions several statistical tests had to be performed. With these statistical tests the change in intensity and frequency of extreme precipitation has been measured. In the hydrological science and heavy rainfall event studies common used measures for extreme precipitation are the 90th, 95th, 98th, and 99th percentile of the annual precipitation (Oliveira et al., 2017). In this research the extreme precipitation is therefore defined as the 90th, 95th, 98th, and 99th percentile of the annual precipitation.

Preparing data

Before performing the statistical tests, the data had to be prepared.

The precipitation rates in the datasets of the European Climate Assessment & Dataset were given in 0.1 mm, therefore the precipitation rates were corrected to precipitation rates of 1 mm. The datasets also included several missing values coded as -9999. When preparing the data in Excel an additional row was created with a code to replace the -9999 values with an empty cell, hereby the cell with missing data was not included in further calculations. The years with more than 10 missing values were removed from the dataset, in this way the data was representative for precipitation rates throughout the entire year.

Preparing intensity

For the change in intensity of extreme precipitation over time the change over the percentiles were measured in order to analyze whether if a (significant) trend was present. In Excel the 90th, 95th, 98th, and 99th percentile over the row with daily precipitation rates have been calculated per year. To be able to measure whether the intensity of extreme precipitation is increasing, the values of the 90th,

(6)

6

95th, 98th, and 99th percentile were calculated in Excel and visualized in a graph. The values were loaded into a separated Excel file for a period of 1951-2019.

Preparing frequency

For the change in frequency of extreme precipitation the level of the 90th, 95th, 98th, and 99th percentile were determined per station over 1951-1980. Over the time period of 1951-2019 the times of exceedance per year were counted and plotted in a graph. The values were loaded into a separated Excel file.

Statistical testing

Concluding from the literature a positive linear trend was expected in the intensity and frequency of extreme precipitation over time. Therefore a test that indicates a continuous increasing or decreasing trend is needed. In the hydrometeorology different statistical methods are used to identify trends in timeseries. For trends in hydrologic time series the Mann-Kendall test is commonly used (Niedźwiedź et al., 2009; Karagiannidis et al., 2012; Madsen et al., 2014). This method is often used to replace the linear regression and is based on the association between two samples. The Mann-Kendall test is a non-parametric test and therefore not dependent upon assumptions of distribution, the magnitude of data or outliers (ITRC, 2013). The limitations of the model are however, that the data input should not be influenced by seasonal trends and therefore be annual or seasonal (Fatichi, 2009). In this research the focus lays on the extreme precipitation rates per year. Extreme precipitation is most likely not normally distributed, therefore in this research the Mann-Kendall method was applied. In addition, a Theil-Sen test was performed. This test returned the magnitude of the slope of the plausible trend. The Theil-Sen is insensitive to outliers (ITRC, 2013).

The tests were performed in MATLAB with a pre-made function which both returned the test statistics for the Mann-Kendall test as for the Theil-Sen test. The pre-made function, named ktaub, was provided by Burkey (2006) and specified as follow:

[taub tau h sig Z S sigma sen n senplot CIlower CIupper] = ktaub(datain, alpha)

The ktaub function returns several variables. The Mann-Kendall correlation coefficient tau assess the nonparametric correlation between two datasets (ITRC, 2013). Tau ranges from -1 to 1 and a statistical trend exists when tau is significantly different from zero. Taub returns the Mann-Kendall coefficient adjusted for ties, if a duplicate of a value is present in both samples the function has corrected the tie (Burkey, 2006). The H indicates if the null-hypothesis is rejected or not. The outcome H=1 will indicate that the null hypothesis is rejected at the alpha significance level. H=0 indicates that the rejection of the null hypothesis at the significance level has failed. The sig will give the p-value of the statistical test at the specified alpha level. The value of Z indicates the presence of a statistically significant trend, where Z>0 indicates an upward trend, Z<0 a downward trend . The test statistic S returns the variance of the data. An upward trend is indicated when S>0, a downward trend when S<0 and no trend when S=0. The variable sen will return the slope of the trend, it indicates how the precipitation changes linearly with time.

The Mann-Kendall test and Theil-Sen tests were performed over the time series created for the intensity and frequency (appendix 2 and appendix 3). The following hypotheses were tested for these timeseries on a 95% confidence level:

Intensity:

• H0 No monotonic trend is present in the intensity of the extreme precipitation events. • Ha A monotonic trend is present in the intensity of the extreme precipitation events. Frequency:

• H0 No monotonic trend is present in the frequency of the extreme precipitation events. • Ha A monotonic trend is present in the frequency of the extreme precipitation events.

(7)

7 Spatial differences

In order to examine if a spatial pattern in the changes of extreme precipitation is present, the change in the Sen’s slope along the transect was analyzed. First the distance between each station was calculated by applying the grand circle method. These calculations can be found in appendix 4. A linear regression was performed in Excel over the distance and the Sen’s slope , since a negative linear trend was expected according to the literature.

If no linear trend was present a quadratic regression was performed in Excel. The linear regression has returned the variable A and intercept B and the quadratic regression has returned the variable A, B and intercept C for the following functions:

Linear function: TS = A*d + B

Quadratic function TS = A*d2_{+ B*d + C}

TS is the Theil-Sen estimator, for intensity in [mm/year] and for frequency in [year-2_{], the distance d is}

in [km].

Both function were tested for significance on a 95% confidence for the following hypothesis:

Linear:

• H0 No trend is present in the spatial difference of the extreme precipitation events. • Ha A linear trend is present in the spatial difference of the extreme precipitation events. Quadratic

• H0 No trend is present in the spatial difference of the extreme precipitation events.

(8)

8

Results

In this section an overview is given of precipitation and extreme precipitation for an individual station and within the transect. That section is followed by a visualization of the results per variable i.e., intensity, frequency and distance.

In this research the change in extreme precipitation in a west-east transect over a time period of 1951-2019 was analyzed. To give an indication how the precipitation has changed over the research period for a station, the total precipitation in Scheveningen is visualized in figure 2. Over the precipitation a linear trendline was fitted to give an indication of the general change in total precipitation over time. The linear function is as following: y = 2.8412x + 774.97. The linear function fitted has a slope of 2.8412 this is corresponding to the obtained Sen’s slope of the total precipitation in Scheveningen. The Sen’s slope results will be further discussed per variable i.e., intensity, frequency and distance in the second part of the results.

Figure 2: The total precipitation in Scheveningen over 1951-2019 with a fitted linear trendline of y = 2.8412x + 774.97

Extreme precipitation is in this research is defined as the 90th, 95th, 98th and 99th percentile of the precipitation rate. To give a representation of the precipitation rate at different percentiles levels the different precipitation rates were calculated for Scheveningen over 1951-2019 (Figure 3). For the 10th, 20th, 30th and 40th percentile the precipitation rate is equal to zero. From the 50th percentile precipitation rates are showing. For the extreme precipitation the precipitation rates lay between 7.6 and 22.1 mm/day. An overview of the precipitation rate of extreme precipitation and total precipitation for the entire transect is visualized in figure 4. The 90th, 95th, 98th and 99th percentiles are illustrated on the primary y-axis. Over the transect the percentiles are approximately the same. A small decline is shown in the percentiles from Scheveningen towards Magdeburg and from Magdeburg on eastwards it slowly increases. However, at Wrocław the percentiles

y = 2,8412x + 774,97 500 600 700 800 900 1000 1100 1200 1300 1951 1954 1957 1960 1963 1966 1969 1972 1975 1978 1981 1984 1987 1990 1993 1996 1999 2002 2005 2008 2011 2014 2017 Prec ip ita tio n [m m ]

Total precipitation in Scheveningen over

1951-2019

Figure 3: The corresponding precipitation rates of the different percentile levels for the station Scheveningen over 1951-2019 00 05 10 15 20 40% 50% 60% 70% 80% 90% 95% 98% 99% Pre ci p itati o n rat e [mm]

Precipitation rate at different percentile levels for Scheveningen

(9)

9

Figure 4: An overview of the total precipitation and percentiles per station in a time period from 1951-2019. The percentiles are illustrated on the primary y-axis in [mm/day], with continuous gridlines. The total precipitation is illustrated on the secondary y-axis in [mm/year], with dotted gridlines.

have a small peak in the 98th and 99th percentile in comparison to the surrounding stations. The total precipitation is illustrated on the secondary y-axis. Over the transect the total precipitation from Scheveningen towards Magdeburg is declining. From Magdeburg it follows an in general flat line and from Warszawa-Okęcie the total precipitation is slowly increasing. The peak that was visible at Wrocław in the 98th and 99th percentile is not clearly recurring in the total precipitation apart from that the total precipitation level is slightly higher at Lindenberg and Wrocław then the other stations at the considerable flat line in the middle of the transect.

Before moving on to the second part of the results it should be noted that with preparing the data the years 1965, 1972 and 1975 for Pinsk, 1956 and 1957 for Vasilevici and 1957, 1959, 1971, 1972, 1973, 1975, 1981, 1985 and 1986 for Zitkovici are removed from the dataset due to a high level of missing data.

Intensity

The null hypothesis of ‘no monotonic trend is present for change in the intensity of extreme precipitation’ was tested by performing a Mann-Kendall and Theil-Sen test over the 90th, 95th, 98th, and 99th percentile. The Mann-Kendall test returned the p-value for the 13 weather stations (Table 1). The null hypothesis of the Mann-Kendall test was rejected for all the percentiles and total precipitation for the weather station of Scheveningen. Furthermore, the null hypotheses was rejected for the total precipitation and 90th percentile for the stations Warszawa-Okęcie, Pinsk, Zitkovici and Vasilevici. For Zitkovici and Vasilevici the null hypothesis was also rejected for the 95th and 98th percentile.

Table 1: P-values of the Mann-Kendall test of the intensity of extreme precipitation. The significant tested trends are visualized in bold.

Station SCH VON ALT HAN MAG LIN WRO POZ WAR BRE PIN ZIT VAS Distance [km] 0 109 239 395 531 706 933 1105 1262 1448 1615 1736 1868 PrSum 0.00 0.81 0.63 0.19 0.32 0.81 0.44 0.29 0.05 0.46 0.01 0.00 0.01 P90 0.00 0.34 0.80 0.17 0.36 0.92 0.29 0.21 0.00 0.16 0.02 0.00 0.00 P95 0.00 0.11 0.70 0.34 0.77 0.76 0.08 0.77 0.05 0.13 0.11 0.01 0.00 P98 0.00 0.08 0.06 0.87 0.60 0.71 0.84 0.08 0.07 0.47 0.22 0.02 0.00 P99 0.00 0.12 0.07 0.27 0.33 0.62 0.96 0.16 0.36 0.84 0.37 0.19 0.06 0 100 200 300 400 500 600 700 800 900 0 5 10 15 20 25 PrSu m [mm/ ye ar ] [mm/ d ay ]

Overview of the total precipitation and percentiles per

station (1951-2019)

P90 P95 P98 P99 PrSum

(10)

10

Figure 5: The Sen’s slope of intensity in [mm/year]. The percentiles are illustrated on the primary y-axis, with continuous gridlines. The total precipitation is illustrated on the secondary y-axis, with dotted gridlines.

The Theil-Sen test returned the Sen’s slope of the total precipitation and percentiles for the 13 weather stations (Figure 5). The percentiles are illustrated on the primary y-axis. The total precipitation is of a different magnitude and therefore illustrated on the secondary y-axis. In the beginning of the transect a positive trend was denoted for both the total precipitation and percentiles. From station Hannover to Wrocław the trend is mostly negative, except for the 99th percentile at Hannover and the 98th percentile at Wrocław. Furthermore this applies also for all the values at the Lindenberg stations, except for the 95th percentile. From Poznań on eastwards the trend becomes positive again.

Frequency

The null hypothesis of ‘no monotonic trend is present for change in the frequency of extreme precipitation’ was tested by determining the level of the 90th, 95th, 98th, and 99th percentile per station over 1951-1980 (Figure 6). The times of exceedance of these levels for 1951-2019 were counted and over the times of exceedance a Kendall and Theil-Sen test were performed. The Mann-Kendall test returned the p-value for the 13 weather stations, as can be seen in table 2. The null hypothesis of the Mann-Kendall test was rejected for all variables of Scheveningen. Furthermore the null hypotheses was rejected for the total precipitation for Pinsk and Zitkovici, as well for the 90th and 95th percentile for Warszawa-Okęcie, Pinsk and Vasilevici. Aditionally the null hypothesis was rejected for the 90th percentile of Zitkovici and for the 98th percentile of Altenberge.

Table 2: P-values of the Mann-Kendall test of the frequency of the exceedance of extreme precipitation levels from 1951-1980. The significant tested trends are visualized in bold.

Station SCH VON ALT HAN MAG LIN WRO POZ WAR BRE PIN ZIT VAS Distance [km] 0 109 239 395 531 706 933 1105 1262 1448 1615 1736 1868 P90 0.00 0.49 0.56 0.11 0.47 0.98 0.35 0.18 0.02 0.11 0.04 0.02 0.00 P95 0.00 0.16 0.23 0.20 0.44 0.75 0.34 0.63 0.02 0.28 0.05 0.26 0.02 P98 0.00 0.15 0.03 0.94 0.26 0.76 0.53 0.15 0.06 0.62 0.08 0.39 0.05 P99 0.00 0.11 0.25 0.54 0.13 0.48 0.97 0.25 0.08 0.70 0.74 0.93 0.18 -1,5 -1 -0,5 0 0,5 1 1,5 2 2,5 3 3,5 -0,03 -0,02 -0,01 0 0,01 0,02 0,03 0,04 0,05 0,06 0,07 0,08 Se n 's s lop e o f P rSu m

Sen's slope of intensity [mm/year]

P90 P95 P98 P99 PrSum

(11)

11

Figure 6: An overview of the percentiles per station in a time period from 1951-1980.

Figure 7: The Sen’s slope per percentile for the frequency in [year-2_]

The Theil-Sen returned the Sen’s slope of for the 13 weather stations (Figure 7). An overall trend is denoted where in the beginning of the transect a positive trend is visible. From station Hannover to Wrocław the trend is mostly negative. From Poznań on eastwards the trend becomes overall positive again. However, there are a few exceptions to this overall trend. For the 99th percentile, the Sen’s slope is equal to zero, except for the positive values at Scheveningen, Warszawa-Okęcie and Vasilevici. Furthermore the Sen’s slope is equal to zero for all percentiles of Lindenberg and for the 98th percentile at Hannover, Wrocław and Brest. The magnitude of the lines in figure 5 are corresponding to the size scale of the variable. This is shown in a vastly small magnitude of the 99th percentile and large magnitude for the 90th percentile. The largest magnitude of the Sen’s slope at every station is mainly the slope of the 90th percentile. The 95th percentile at Vonkel and the 95th and 98th at Altenberge have a larger magnitude then the 90th percentile.

0 5 10 15 20 25 [m m /d ay ]

Overview of the percentiles per station (1951-1980)

P90 P95 P98 P99 -0,1 -0,05 0 0,05 0,1 0,15 0,2

Sen's slope of frequency [year

-2

_]

P90 P95 P98 P99

(12)

12

Spatial differences

First, they hypotheses ‘no trend is present in the spatial difference of the extreme precipitation events’ is tested for a linear trend. The linear regressions were performed over the distance in kilometer and the Sen’s slope of the total precipitation or percentiles as given in figure 5 and figure 7. The linear regression test returned the variable A, intercept B and the p-value for the regression (Table 3). The values of variable A and intercept B can be used in the linear function:

TS = A*d + B

in [km]. For the vast majority of the linear function’s the null hypothesis was not rejected. The null hypothesis was only rejected for the 90th percentile of frequency.

Table 3: The coefficients and the p-values of the linear regression over the Sen’s slope and distance for the intensity and frequency.

PrSum P90 P95 P98 P99

Intensity A [mm year-1_km-1_] _7.37E-04 _7.56E-06 _8.60E-06 _6.01E-06 _1.12E-06

B [mm year-1] 1.26E-01 1.14E-03 2.64E-03 1.66E-02 2.25E-02

p-value 0.18 0.15 0.23 0.55 0.92

Frequency A [mm year-1_km-1_] _7.58E-05 _1.97E-05 _3.68E-06 _2.25E-07

B [mm year-1] -1.10E-02 1.39E-02 1.38E-02 4.28E-03

p-value 0.03 0.35 0.70 0.96

When plotting the Mann-Kendall correlation coefficient and Sen’s slope over the distance, a quadratic structure is found. This is illustrated in figure 8. The quadratic function fitted over the total precipitation gives a quadratic function of y = 0.066x2_{– 0.8113x + 2.3254. However, the coefficients}

given in this quadratic function are based on a distance of 1 till 13, instead of the real distance of every station which is illustrated on the x-axis. Yet when performing a quadratic regression with x = 1:13 and x2_{= (1:13)}2_{, the same formula is obtained: y = 0.0660x}2_{– 0.8113x + 2.3254.}

Figure 8: The Sen’s slope of the total precipitation of intensity plotted against the distance of every station within the transect. The quadratic function given by the fitted trendline gives a quadratic function based on a distance of 1 till 13, instead of the real distance which is illustrated on the x-axis.

The second hypotheses ‘no trend is present in the spatial difference of the extreme precipitation events’ is tested for a quadratic trend. The quadratic regressions were performed over the distance in

y = 0,066x2_{- 0,8113x + 2,3254} -1,5 -1 -0,5 0 0,5 1 1,5 2 2,5 3 3,5 0 109 239 395 531 706 933 1105 1262 1448 1615 1736 1868 [mm/ ye ar ] distance [km]

Sen's slope of the total precipitation of intensity

PrSum

Poly. (PrSum)

(13)

13

kilometer and the Sen’s slope of the total precipitation or percentiles as given in figure 5 and figure 7. The quadratic regression returned the p-value, variable A, B and the intercept C for the regression (Table 4). The values of variable A, B and intercept C can be used in the quadratic function:

TS = A*d2_{+ B*d + C}

in [km]. For the vast majority of the linear function’s the null hypothesis was rejected. The null hypothesis was not rejected for the 99th percentile of frequency.

Table 4: The coefficients and the p-values of the linear regression over the Sen’s slope and distance for the intensity and frequency.

PrSum P90 P95 P98 P99

Intensity A [mm year-1_km-2_] _2.59E-06 _2.45E-08 _3.92E-08 _5.44E-08 _5.41E-08

B [mm year-1 km-1] -4.07E-03 -3.79E-05 -6.42E-05 -9.51E-05 -9.93E-05 C [mm year-1] 1.38E+00 1.30E-02 2.16E-02 4.30E-02 4.87E-02

p-value 0.01 0.01 0.00 0.00 0.02

Frequency A [mm year-1_km-2_] _1.45E-07 _1.01E-07 _4.39E-08 _1.29E-08

B [mm year-1 km-1] -1.94E-04 -1.68E-04 -7.78E-05 -2.37E-05 C[mm year-1] 5.93E-02 6.29E-02 3.51E-02 1.05E-02

(14)

14

Discussion

Results

Intensity

Sporadically significance trends were found for the change in the intensity of extreme precipitation events. These monotonic significant trends are all positive trends and found in the very beginning of the transect, for Scheveningen, and more towards the end of the transect, for Warszawa-Okęcie, Pinsk, Zitkovici and Vasilevici. The vast majority of the trends were not significant at the 95% confidence level. Positive trends were found near the west coast till 9°E and from 18°E till the end of the transect. The positive trends suggest an increase in the intensity of extreme precipitation. The highest positive trends are present at stations with significant or close to significant trends. For the most part of the 9°E to 18°E of the transect negative trends were found, indicating a decrease in the intensity of extreme precipitation. The found negative trends are not significant however, due to the small magnitude of the trend. This cause also applies to the positive trends that were not significant. The magnitude of the trend is not large enough to have proven to be significant over time, a slope that is close to zero can not reject the null hypothesis. The not significant trends represent a weak trend to almost no trend and the significant trends indicate the strong trends.

The Sen’s slope shows that the total precipitation has a large magnitude, caused by the larger values since these are based on annual values. Notable is that the magnitude of the increase of the total precipitation is considerably more than the magnitude of the decrease of total precipitation. This suggests that overall the total precipitation in the transect is increasing. For extreme precipitation the largest magnitudes belong to the 98th and the 99th percentile. This could indicate that these percentiles increase more in intensity then the 90th and 95th percentile, however it should be taken in consideration that the values of the higher percentiles are larger and that this could (partly) cause the larger magnitude.

Frequency

The change in the frequency of extreme precipitation events was also sporadically significant. Significant trends were all positive trends and found for Scheveningen, Altenberge, Warszawa-Okęcie, Pinsk, Zitkovici and Vasilevici. Nevertheless, the vast majority of the trends was not significant at the 95% confidence level, due to the small magnitude of the trend. When analyzing the Sen’s slope positive trends were found near the west coast till 9°E and from 18°E till the end of the transect. The positive trends suggest an increase in the frequency of extreme precipitation. The highest positive trends are corresponding with the significant found trends. From 9°E and from 18°E negative and several non-trends were found, the negative non-trends suggest a decrease in the frequency of extreme precipitation and the non-trends suggest that no trend is present. These trends are not significant, due to the small magnitude of the slope, for a longer time series the negative trends could be proven to be significant.

The largest magnitude of the Sen’s slope is overall the slope of the 90th percentile, indicating that over time the times of exceedance of the 90th percentile will increase the most. The 90th percentile will logically be exceeded more times then the 99th percentile, which also explains why the 90th percentile has the largest increase or decrease in the exceedance level. At the stations Vonkel and Altenberge the largest magnitude is assigned to the 95th percentile. This could be caused by a slight increase of the precipitation rates that already exceeded the 90th percentile, so that the rate will also exceed the 95th percentile, while at the same time the increase of the precipitation rates did not have the magnitude to exceed the 90th percentile. The Sen’s slope is equal to zero for the 99th percentile for the majority of the stations, suggesting that the frequency of the 99th percentile is not increasing nor decreasing. The 99th percentile only slightly increases at the west coast and in the eastern part of the transect.

(15)

15 Spatial difference

The difference in change in the Sen’s slope of the intensity and frequency of extreme precipitation over the transect is variable. Despite that the expected linear trend is not found, the change in intensity and frequency of extreme precipitation showcases a clear pattern, with positive trends near the west coast, decreasing to near slightly negative trends between 9°E to 18°E and again positive trends more to the east. The pattern forms a quadratic function over the distance of the transect. The quadratic function is found to be significant on a 95% confidence level for all the percentiles and the total precipitation for both the intensity and frequency, except for the 99th percentile of frequency. It makes sense that the 99th percentile of frequency has not been found significant, because figure 7 clearly illustrates an almost flat line for the 99th percentile. What should be considered is that although the quadratic function over the transect is mostly found to be significant, the trend whereof the quadratic function is fitted is for the largest part not significant at the 95% confidence level. The tables 1 and 2 showcase that the p-values are extremely variable throughout the whole transect. If the stations would be grouped for overall positive trends, namely Schevenigen, Vonkel, Altenberge, Poznań, Warszawa-Okęcie, Brest, Pinsk, Zitkovici and Vasilevici, and for overall the negative trends, Hannover, Magdeburg, Lindenberg and Wrocław, a distinction could be made between these groups. The stations with positive trends generally have lower p-values and the stations with negative trends have considerably high p-values. High p-values for the negative trends suggest any other trend, besides a continuous negative trend could be present. Considering the fact that the stations with negative trends define the quadratic pattern, the quadratic pattern should be queried.

The positive trends that slowly decrease from the west coast land inwards are most likely caused under influence of the sea surface temperatures and atmospheric circulation (Kyselý, 2009; Lenderink et al., 2009; Attema et al. 2014; Daniels, 2016). The increase of the intensity of frequency of the extreme precipitation towards the eastern part could be induced by the atmospheric circulation and the slightly higher elevation of these areas (Kyselý, 2009). Allowing the clouds and so the precipitation to accumulate and release higher levels of precipitation. In addition the increase for the intensity and frequency at station Pinsk, Zitkovici and Vasilevici could be influenced by the manner in how the data was prepared, since these stations had several years with more than 10 missing data, wherefore these years have been removed.

Previous studies

The results are partly corresponding with research that has been done previously in this field. Studies of Boxel (2001), Keijzer & Boxel (2003) and Daniels et al. (2014) mentioned an increase of extreme precipitation in the Netherlands, corresponding with the present research. For Germany increasing trends of extreme precipitation were observed for central-eastern Germany by Łupikasza et al. (2011) and for entire Germany by Zolina et al. (2008). In the results of the present study a decrease of extreme precipitation in Germany is suggested however, these trends are not proven to be significant. In addition, Zolina et al. (2008) found that the frequency of extreme precipitation has decreased. Corresponding to the overall decrease of frequency of extreme precipitation in this research, it should be noted that also these trends were not significant. A decrease of extreme precipitation over 1951-2006 was found for entire Poland by Łupikasza (2010). Opposed to the mostly positive trends found in the present research for Poland over 1951-2019. For Wrocław, the most south-west Polish station, negative trends were found in the present study. Corresponding with the studies of Łupikasza (2010) and Łupikasza et al. (2011) where a decrease was found for Southern Poland. Furthermore, Pińskwar et al. (2019) found a decrease in the extreme precipitation in the south-west part of Poland and increasing trends for the more eastern part of the country. Corresponding with the trends found in the present study. In Belarus positive trends for the increase of extreme precipitation were found in the carried out study. In agreement with a study of Danilovich (2020) who found an increase in the extreme precipitation for the central and southern regions of Belarus. Furthermore, Zolina (2012) found significant positive trends for extreme precipitation in Belarus. The IPCC (2014) models show an overall increase of intensity and frequency of precipitation events, this is in agreement with results found in

(16)

16

the research, except for the middle part from 9°E to 18°E where slightly negative trends where found. Research on the spatial pattern of precipitation has been done by Lendrink et al. (2011) and Daniels (2016) in both researches a higher increase in extreme precipitation in Dutch coastal areas was present compared to land inwards. In the western part of the transect a similar pattern is visible. These results are similar the results obtained for the western part of the transect. Degirmendžić et al. (2004) found that the total precipitation in Poland depends on components of the atmospheric circulation, which could be an explanation for the increase in precipitation in the eastern part of the transect. Another explanation could be the slightly higher elevation within the eastern region, this was also found for the elevation in the Netherlands in a study of Boxel & Cammeraat (1999). It should be noted that the results presented in various articles may not be directly comparable due to the various methods used for analyzing trends of extreme precipitation and differences in the definition of extreme precipitation.

Limitations and improvements

Limitations of the research

Precipitation has an extremely large spatial and temporal variability, which can lead to difficulties while searching for significant trends in timeseries. Therefore when analyzing precipitation timeseries, long timeseries are needed, within this research the timeseries were quite short. Furthermore, the measuring methods could be changed over time, this could have influenced the measured precipitation rates. Another influence could be the movement of the weather stations or the change in the surroundings of the weather station which could both influence the measured precipitation rates, due to the high spatial and temporal variability of precipitation (Boxel, 2001). To test if inhomogeneities occurred due to change in measurement methods, surroundings or station movement the data should be tested for homogeneity. Unfortunately due to time restrictions the data used in this research was not tested for homogeneity.

In this research significant testing was performed on a 95% confidence level however, since precipitation is extremely variable it is hard to proof significant trends. Some researches have therefore used different confidence levels to prove strong and weak trends in precipitation (Łupikasza et al., 2011).

Improvements

Improvements that could be made in researching the change in intensity, frequency and the spatial pattern of extreme precipitation is to include more stations into the transect. This can result in a better and more detailed insight in the change over time and distance. For the current research area it is not possible to include more stations with an equal mutual distance between the stations, therefore the research area should be shortened. A shorter research area (ending in Germany) would also eliminate the small influence of elevation and would allow for a longer study period, which could increase the significance of several trends.

(17)

17

Conclusion

Some sporadically significant trends were found for the change in the intensity and frequency of extreme precipitation in the beginning of the transect and towards the end of the transect. Despite of most of the trends not being statistically significant, a clear pattern was found with positive trends near the west coast, decreasing to near slightly negative trends between 9°E to 18°E and again positive trends to the east, forming a consistent pattern. The consistent pattern is considered to be quadratic and a quadratic function was fitted. The quadratic function over the transect is mostly found to be significant however, whereof the quadratic function is fitted is for the largest part not found significant. The quadratic pattern should be queried, since the section that defines this quadratic pattern could have any shape of trend or no trend at all, due to the high p-values. Under assumption for the quadratic function being true, there are a few explanations that could be considered. The pattern can be explained by the influences of the higher sea surface temperatures and atmospheric circulation near the west coast. On the eastern side of the transect the pattern can be influenced by the atmospheric circulation and the elevation of the region.

It can be concluded that the intensity and frequency of extreme precipitation within the western part of the transect is partly influenced by global warming. The warming is causing an increase in the sea surface temperatures, inducing the water-holding capacity. The increased water-holding capacity will lead to an increase in extreme precipitation. However, multiple factors have an influence on the change in intensity and frequency of extreme precipitation over the entire west-east transect. Other influences could be the elevation or the change in atmospheric circulation.

The results can be used to provide a better insight in the changes of extreme precipitation events and to examine the hazards of vulnerable regions, such as flooding, crop lost, erosion, life lost and infrastructural damage.

Acknowledgements

I would like to express my gratitude to my research supervisor, dr. ir. J.H. van Boxel, for providing guidance and support throughout this research. He shared several valuable literature and even went out his way to provide calculations and an elevation map of my transect which I was able to use for selecting my weather stations. In addition, I would like to thank dr. ir. E.E. van Loon, besides for fulfilling the task of second corrector, for advising me in significance testing and helping me in finding the right direction.

(18)

18

References

Attema, J. J., Loriaux, J. M., & Lenderink, G. (2014). Extreme precipitation response to climate perturbations in an atmospheric mesoscale model. Environmental Research Letters, 9(1), 014003.

Beniston, M., Stephenson, D. B., Christensen, O. B., Ferro, C. A., Frei, C., Goyette, S., ... & Palutikof, J. (2007). Future extreme events in European climate: an exploration of regional climate model projections. Climatic Change, 81(1), 71-95.

Burkey, J. (2006). A non-parametric monotonic trend test computing Mann-Kendall Tau, Tau-b, and Sen Slope written in Mathworks-MATLAB implemented using matrix rotations. King County, Department of Natural Resources and Parks, Science and Technical Services section. Seattle, Washington. USA. http://www.mathworks.com/matlabcentral/fileexchange/authors/23983

Daniels, E. E., Lenderink, G., Hutjes, R. W. A., & Holtslag, A. A. M. (2014). Spatial precipitation patterns and trends in The Netherlands during 1951–2009. International Journal of Climatology, 34(6), 1773- 1784.

Daniels, E. E. (2016). Land surface impacts on precipitation in the Netherlands (Doctoral dissertation, Wageningen University).

Danilovich, I. (2020). The peculiarities of the moistening regime in the accordance to the climate change at the eastern part of the Baltic Sea Basin with a focus on Belarus. 3rd Baltic Earth Conference - Earth system changes and Baltic Sea coasts. pp 115-116. Retrieved from:

https://www.researchgate.net/profile/Zuzanna_Borawska/publication/341827458_Benthic_fauna_infl uence_on_the_marine_silicon_cycle_in_the_coastal_zones_of_the_southern_Baltic_Sea/links/5ed64

44a92851c9c5e726d40/Benthic-fauna-influence-on-the-marine-silicon-cycle-in-the-coastal-zones-of-the-southern-Baltic-Sea.pdf#page=145

Degirmendžić, J., Kożuchowski, K., & Żmudzka, E. (2004). Changes of air temperature and precipitation in Poland in the period 1951–2000 and their relationship to atmospheric circulation. International Journal of Climatology: A Journal of the Royal Meteorological Society, 24(3), 291-310.

de Keijzer, S., & van Boxel, J. (2003). De vernatting van Nederland: het gevolg van een toename van de extreme neerslag?. Weerspiegel, 30.

DPA (2017). A cyclist tries to ride through the flooded streets of Cologne on Wednesday. Retrieved from:

https://www.thelocal.de/20170720/heavy-storms-flood-streets-kill-one-in-west-germany-weather-cologne

Fatichi, S. (2009). Mann-Kendall Test. MATLAB Central File Exchange. Retrieved on 24 April 2020, from:

https://www.mathworks.com/matlabcentral/fileexchange/25531-mann-kendall-test

Frei, C., Schöll, R., Fukutome, S., Schmidli, J., & Vidale, P. L. (2006). Future change of precipitation extremes in Europe: Intercomparison of scenarios from regional climate models. Journal of Geophysical Research: Atmospheres, 111(D6).

IPCC (2014). Climate Change 2014: Synthesis Report. Contribution of Working Groups I, II and III to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change [Core Writing Team, R.K. Pachauri and L.A. Meyer (eds.)]. IPCC, Geneva, Switzerland, 151 pp.

ITRC (Interstate Technology & Regulatory Council). 2013. Groundwater Statistics and Monitoring Compliance, Statistical Tools for the Project Life Cycle. GSMC-1. Washington, D.C.: Interstate Technology & Regulatory Council, Groundwater Statistics and Monitoring Compliance Team. http://www.itrcweb.org/gsmc-1/.

Karagiannidis, A. F., Karacostas, T., Maheras, P., & Makrogiannis, T. (2012). Climatological aspects of extreme precipitation in Europe, related to mid-latitude cyclonic systems. Theoretical and Applied Climatology, 107(1-2), 165-174.

Klein Tank, A.M.G. and Co-authors, 2002. Daily dataset of 20th-century surface air temperature and precipitation series for the European Climate Assessment. International Journal of Climatology, 22, 1441-1453. KNMI (2020). KNMI Climate Explorer. Retrieved on 29 April 2020, from: https://climexp.knmi.nl/start.cgi

(19)

19

Kuchment, L. S. (2004). The hydrological cycle and human impact on it. Encyclopedia of Life Support Systems, 1-40.

Kundzewicz, Z. W., Radziejewski, M., & Pinskwar, I. (2006). Precipitation extremes in the changing climate of Europe. Climate Research, 31(1), 51-58.

Kyselý, J. (2009). Trends in heavy precipitation in the Czech Republic over 1961–2005. International Journal of Climatology: A Journal of the Royal Meteorological Society, 29(12), 1745-1758.

Lenderink, G., Van Meijgaard, E., & Selten, F. (2009). Intense coastal rainfall in the Netherlands in response to high sea surface temperatures: analysis of the event of August 2006 from the perspective of a changing climate. Climate Dynamics, 32(1), 19-33.

Lupikasza, E. (2010). Spatial and temporal variability of extreme precipitation in Poland in the period 1951–2006. International Journal of Climatology: A Journal of the Royal Meteorological Society, 30(7), 991-1007. Łupikasza, E. B., Hänsel, S., & Matschullat, J. (2011). Regional and seasonal variability of extreme precipitation

trends in southern Poland and central‐eastern Germany 1951–2006. International Journal of Climatology, 31(15), 2249-2271.

Madsen, H., Lawrence, D., Lang, M., Martinkova, M., & Kjeldsen, T. R. (2014). Review of trend analysis and climate change projections of extreme precipitation and floods in Europe. Journal of Hydrology, 519, 3634-3650. Niedźwiedź, T., Twardosz, R., & Walanus, A. (2009). Long-term variability of precipitation series in east central

Europe in relation to circulation patterns. Theoretical and Applied Climatology, 98(3-4), 337-350. Oliveira, P. T., e Silva, C. S., & Lima, K. C. (2017). Climatology and trend analysis of extreme precipitation in

subregions of Northeast Brazil. Theoretical and Applied Climatology, 130(1-2), 77-90.

Peel, M.C., Finlayson, B.L. & McMahon, (2007). Updated world map of the Köppen-Geiger climate classification. Hydrology and Earth System Sciences, 11, 1633-1644.

Pińskwar, I., Choryński, A., Graczyk, D., & Kundzewicz, Z. W. (2019). Observed changes in extreme precipitation in Poland: 1991–2015 versus 1961–1990. Theoretical and Applied Climatology, 135(1-2), 773-787. Trenberth, K. E. (1999). Conceptual framework for changes of extremes of the hydrological cycle with climate

change. Climatic Change, 42, 327-339.

Trenberth, K. E., Dai, A., Rasmussen, R. M., & Parsons, D. B. (2003). The changing character of precipitation. Bulletin of the American Meteorological Society, 84(9), 1205-1218.

Trenberth, K. E., Smith, L., Qian, T., Dai, A., & Fasullo, J. (2007). Estimates of the global water budget and its annual cycle using observational and model data. Journal of Hydrometeorology, 8(4), 758-769.

van Boxel, J. H. (2001). Climate change and precipitation: detecting changes. Meteorología colombiana, 3, 21-31. van Boxel, J. H., & Cammeraat, E. (1999). Wordt Nederland steeds natter? Een analyse van de neerslag in deze

eeuw. Meteorologica, 8(1), 11-15.

Yang, F., Kumar, A., Schlesinger, M. E., & Wang, W. (2003). Intensity of hydrological cycles in warmer climates. Journal of Climate, 16(14), 2419-2423.

Zolina, O., Simmer, C., Kapala, A., Bachner, S., Gulev, S., & Maechel, H. (2008). Seasonally dependent changes of precipitation extremes over Germany since 1950 from a very dense observational network. Journal of Geophysical Research: Atmospheres, 113(D6).

(20)

20

Appendices

Appendix 1: overview weather stations

Table A1: overview of weather stations

Station Abbreviation Country Station number Distance [km]

Scheveningen SCHE NL 541 0 Vonkel VON NL 442 109 Altenberge ALT DE 11875 239 Hannover HAN DE 476 395 Magdeburg MAG DE 477 531 Lindenberg LIN DE 324 706 Wrocław WRO PL 210 933 Poznań POZ PL 206 1105 Warszawa-Okęcie WAR PL 209 1262 Brest BRE BY 653 1448 Pinsk PIN BY 655 1615 Zitkovici ZIT BY 656 1736 Vasilevici VAS BY 410 1868

(21)

21

Appendix 2: MATLAB script for intensity

%%% BACHELOR PROJECT 2020 %%% %%% STUDENT: IRIS BALK

%%% STUDENTNUMBER: 11906537

% Testing for Mann Kendall Tau'b with Sen's Method % Intensity of extreme precipitation events

clear all close all clc % SCHEVENINGEN_NL % station number: 541

Scheveningen541 = xlsread('541_SCHEVENINGEN_NLm1951.xlsx');

Scheveningen_541 = array2table(Scheveningen541);

Scheveningen_541.Properties.VariableNames = {'Year''PrSum''Average''P90''P95''P98''P99'};

Pr_541 = [Scheveningen_541.Year Scheveningen_541.PrSum];

Average_541 = [Scheveningen_541.Year Scheveningen_541.Average]; P90_541 = [Scheveningen_541.Year Scheveningen_541.P90];

P95_541 = [Scheveningen_541.Year Scheveningen_541.P95]; P98_541 = [Scheveningen_541.Year Scheveningen_541.P98]; P99_541 = [Scheveningen_541.Year Scheveningen_541.P99];

[Pr_541taub Pr_541tau Pr_541h Pr_541sig Pr_541Z Pr_541S Pr_541sigma Pr_541sen Pr_541n Pr_541senplot Pr_541CIlower Pr_541CIupper] = ktaub(Pr_541, 0.05);

[A_541taub A_541tau A_541h A_541sig A_541Z A_541S A_541sigma A_541sen A_541n A_541senplot A_541CIlower A_541CIupper] = ktaub(Average_541, 0.05);

[P90_541taub P90_541tau P90_541h P90_541sig P90_541Z P90_541S P90_541sigma P90_541sen P90_541n P90_541senplot P90_541CIlower P90_541CIupper] = ktaub(P90_541, 0.05);

% Making a table of the results

Table_541 = [Pr_541taub Pr_541tau Pr_541h Pr_541sig Pr_541Z Pr_541S Pr_541sigma Pr_541sen Pr_541n Pr_541senplot Pr_541CIlower Pr_541CIupper;

A_541taub A_541tau A_541h A_541sig A_541Z A_541S A_541sigma A_541sen A_541n A_541senplot A_541CIlower A_541CIupper;

P90_541taub P90_541tau P90_541h P90_541sig P90_541Z P90_541S P90_541sigma P90_541sen P90_541n P90_541senplot P90_541CIlower P90_541CIupper;

P99_541taub P99_541tau P99_541h P99_541sig P99_541Z P99_541S P99_541sigma P99_541sen P99_541n P99_541senplot P99_541CIlower P99_541CIupper];

The script used for Scheveningen is repeated for every following weather station. For every new station the station name, Excel file name and station numbers where replaced.

(22)

22

Appendix 3: MATLAB script frequency

% Testing for Mann Kendall Tau'b with Sen's Method % Frequency exceedance clear all close all clc % SCHEVENINGEN_NL % station number: 541

Scheveningen541 = xlsread('541_SCHEVENINGEN_NLmtimesf1951.xlsx');

Scheveningen_541 = array2table(Scheveningen541);

Scheveningen_541.Properties.VariableNames = {'Year''Average''P90''P95''P98''P99'};

Average_541 = [Scheveningen_541.Year Scheveningen_541.Average]; P90_541 = [Scheveningen_541.Year Scheveningen_541.P90];

P95_541 = [Scheveningen_541.Year Scheveningen_541.P95]; P98_541 = [Scheveningen_541.Year Scheveningen_541.P98]; P99_541 = [Scheveningen_541.Year Scheveningen_541.P99];

[A_541taub A_541tau A_541h A_541sig A_541Z A_541S A_541sigma A_541sen A_541n A_541senplot A_541CIlower A_541CIupper]= ktaub(Average_541, 0.05);

[P90_541taub P90_541tau P90_541h P90_541sig P90_541Z P90_541S P90_541sigma P90_541sen P90_541n P90_541senplot P90_541CIlower P90_541CIupper]= ktaub(P90_541, 0.05);

% Making a table of the results

Table_541 = [A_541taub A_541tau A_541h A_541sig A_541Z A_541S A_541sigma A_541sen A_541n A_541senplot A_541CIlower A_541CIupper;

P99_541taub P99_541tau P99_541h P99_541sig P99_541Z P99_541S P99_541sigma P99_541sen P99_541n P99_541senplot P99_541CIlower P99_541CIupper];

The script used for Scheveningen is repeated for every following weather station. For every new station the station name, Excel file name and station numbers where replaced.

(23)

23

Appendix 4: MATLAB script grand circle

% Calculating for distance between stations % Source for calculating the grand circle

% https://www.aa.quae.nl/nl/reken/grootcirkel.html

clear clc close all

% Radius of the earth = 6371 km

% The distance per degree is equal to the 2*pi*radius/360

degreekm = (2*pi*6371)/360 % = 111.1949

%% Setting the coordinates as vectors

b = [52.12; 51.66; 52.05; 52.47; 52.10; 52.21; 51.1; 52.2; 52.16; 52.12; 52.12; 52.2; 52.25] l = [4.30; 5.71; 7.49; 9.68; 11.58; 14.14; 16.9; 18.66; 20.96; 23.68; 26.13; 27.90; 29.83] %% Calculating manually % 1. SCHEVENINGEN 541 - VONKEL 442 i = 1; j = 1; m = 2; n = 2; valueI = b(i,1); valueJ = l(j,1); valueM = b(m,1); valueN = l(n,1); x1 = cosd(valueJ) * cosd(valueI); y1 = sind(valueJ) * cosd(valueI); z1 = sind(valueI); x2 = cosd(valueN) * cosd(valueM); y2 = sind(valueN) * cosd(valueM); z2 = sind(valueM);

PSI1 = acosd(x1*x2 + y1*y2 + z1*z2);

Distance1 = PSI1*degreekm;

The script used for Scheveningen and Vonkel is repeated for every following distance in between two stations. For every new station the station names, the number of PSIx and Distancex and the values for i, j, m, and n were changed.

% Making a table of the distance

DistanceAll = [Distance1; Distance2; Distance3; Distance4; Distance5; ...