The Effects of Climate Change on the Upper Air Circulation over Temperate Latitudes

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The Effects of Climate Change on the

Upper Air Circulation over Temperate

Latitudes

Master Thesis

MSc Earth Sciences University of Amsterdam Supervisor: J.H. van Boxel

E. Birgitt Brandts (6070353)

July 14, 2015

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Abstract

After several years of reoccurring extreme weather around the world the question has been raised whether this has to do with climate change. It is believed that the arctic amplification is causing a weakening of the polar jet stream and strengthening of the Rossby waves, which in turn can cause blocking events and persisting weather patterns. This research uses existing climate models to establish whether climate change has an effect on the upper air circulation, and therefore on the weather patterns in the mid-latitudes. Two climate models, ESM2M and GFDL-ESM2G, of the 5th_{Coupled Models Intercomparison Project are used to}

determine the behaviour of the meridional and zonal wind components, as an indicator for the activity of the Rossby waves, in four different scenarios of atmospheric composition. This is done by using forward analysis data ranging from the year 2006 to 2100. It appears that the trends of the zonal wind component are positive, whereas the trends of the meridional wind component are positive in the least extreme scenarios but become negative in the more extreme scenarios, which are contrary results to what is generally assumed. The behaviour of the components leads to believe that there will be less extreme weather patterns in a scenario where little effort is made to reduce greenhouse gas emissions. This is assumed to be either related to forced climate variability or a loss of efficiency of the arctic amplification.

Keywords: climate change, emission scenarios, zonal and meridional wind, extreme weather

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1 Introduction

The climate is changing, and it is now clear that humans are significantly affecting the climate system (IPCC, 2013). Extreme events, such as longer periods of heat waves, cold spells, droughts, floods and so forth are increasingly common. Some examples of recent extreme events are the heat waves in Europe in the summer of 2003, which resulted in roughly 70.000 deaths (Robine et al., 2008) and in Russia in the summer of 2010, which resulted in 56.000 deaths (Munich, 2011). The east coast of the US has endured extreme low temperatures and heavy blizzards the last few winters (NOAA, 2011), whereas the west coast is dealing with its fourth consecutive year of severe drought (Venton, 2015). Continuous heavy rainfall caused major flooding in Central Europe in 2002 (NOAA, 2002) and this year in Texas (NOAA, 2015), just to name a few. It is crucial to understand the processes causing these events because it gives decision makers the opportunity to take the necessary measures to slow down global warming and climate change (WMO, 2013).

The earth has been in a cooling trend for the past 2,000 years, but this trend reversed during the twentieth century, with 4 out of the 5 warmest decades occurring between 1950 and 2000 (Kaufman et al., 2009). The reversal of the trend has occurred before, and is in itself not a very strong indicator for anthropogenic global warming (IPCC, 2013), but has nevertheless sparked interest and questions among many scientists.

The observed trend is linked to an increase in greenhouse gas (GHG) emis-sions (IPCC, 2013). The warming effects of the increased GHG concentrations are stronger in the Arctic due to arctic amplification (AA) (Francis and Vavrus, 2012). The poles warm up faster than the other latitudes primarily due to a positive feed-back of melting sea ice, and ice and snow on land (Overland and Wang, 2010; Spielhagen et al., 2011). Instead of reflecting solar radiation, the darker ocean wa-ter and land absorb more heat than snow and ice resulting in the warming of both the ocean and the air, which then melts more ice and snow (Screen and Simmonds, 2013). The effect of AA is greatest in the winter, when stored heat in the upper layer of the ocean from the summer is being released into the atmosphere (Francis and Vavrus, 2012).

A decreasing temperature gradient from the poles to the tropics leads to a weak-ening of the polar vortex. The polar vortex is a planetary-scale circumpolar zonal thermal wind, located in the middle and upper troposphere and the stratosphere (Simmons et al., 2005). The Coriolis effect causes the rotation of the polar vor-tex in the Northern Hemisphere, which flows from west to east. The weakening of this zonal wind allows the development of more meridional winds/waves, which flow from north to south (Francis and Vavrus, 2012). These meridional winds at an approximate geopotential height of 500 hPa (mid-level of the troposphere) con-tain giant meanders called Rossby waves. Rossby waves are more pronounced in the Arctic than in the Antarctic due to the distribution of land masses. They are thought to be initiated by large barriers such as the Rocky Mountains and changes in vorticity, and contribute to the weakening of the polar vortex (Bryant, 1997). The more prominent the Rossby wave amplitudes are, the more heat exchange oc-curs between the different latitudes, further decreasing the temperature gradient

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and weakening the zonal circulation patterns (Francis and Vavrus, 2012). The heat of the lower latitudes that flows northwards in the Northern Hemisphere causes ridges at the 500 hPa level, and the cold of the polar latitudes that flows south-wards causes troughs in the mid-latitudes (Walsh, 2014). When these waves are not well developed and almost straight, there is a constant flow of the zonal wind with eastward propagation, which is known to generate random weather patterns. On the other hand, when these waves are very prominent and cover a wide range of latitudes, they tend to propagate eastward more slowly. This causes ‘blocking’, which enforces long-lasting (i.e. extreme) weather patterns such as heat waves, cold spells, droughts and floods (Francis and Vavrus, 2012; Walsh, 2014).

A decent amount of research has been done on this topic, but as of yet there is no generally accepted conclusion on the matter. For example, Francis and Vavrus (2012) and Screen and Simmonds (2013) investigated the AA and the meridional amplitude, relating it to extreme weather patterns based on reanalysis data from the 1970’s onwards. Many other studies, e.g. Gillett et al. (2000), Kuzmina et al. (2005) and Watanabe et al. (2013), related the changing meridional circulation to forced variability of the climate, instead of linking it to climate change, due to insufficient statistical significance. This lack of statistical significance may be due to insufficient data collected over a short period of time. The data used in this research extends over the entire 21st _{century by applying forward analysis on data}

from climate models.

The aim of this research is to show how climate change affects the upper air circu-lation and weather patterns in the temperate latitudes. This is done by focusing on the following research questions:

1. Do the climate models predict a more meridional circulation over the temper-ate latitudes in a warmer climtemper-ate?

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2 Data and Methods

This research focuses on the meridional (north-south) and zonal (west-east) com-ponents of the middle troposphere wind in the mid-latitudes. This chapter explains what type of climate models is used and how data for the future is extracted from these models, using different scenarios of atmospheric composition. This chapter also explains the different types of calculations that are used for interpretation of the data.

2.1 Data and Models

The data and models used for this research come from the 5th _{Coupled Model}

Inter-comparison Project (CMIP5), which is a standard experimental protocol used in the latest IPCC Assessment Report (AR5) (Meinshausen et al., 2011). These CMIP5 climate simulation models incorporate scenarios for the evolution of atmospheric composition to give insights into predictions of the future, called Representative Concentration Pathways (RCP). These scenarios are designed to allow researchers to explore the long-term consequences of decisions made today. The RCPs repre-sent radiative forcing levels that can potentially occur in the year 2100, relative to pre-industrial values (Weyant et al., 2009; IPCC, 2013; Collins et al., 2013).

This research uses forward analysis, whereby properties of the output of the pro-gram are determined by the properties of the inputs. Therefore, it is important that the selected scenarios contain future projections of the atmospheric composition. The selected scenarios from Collins et al. (2013) are:

• RCP2.6: The ”peak” scenario; the radiative forcing level reaches around 3.1 W/m2 _{mid-century, returning to 2.6 W/m}2 _{by the end of the century}

(2100). To reach such radiative forcing levels, GHG emissions must be re-duced strongly over time (van Vuuren et al., 2011).

• RCP4.5: The stabilization scenario; the total radiative forcing is stabilized at 4.5 W/m2 _{before the end of the century (2100) by implementing different}

technologies and strategies to reduce GHG emissions (Thomson et al., 2011). • RPC6.0: The stabilization scenario; the total radiative forcing is stabilized at 6 W/m2 after the end of the century (2100) without excessive implementation of different technologies and strategies to reduce GHG emissions (Masui et al., 2011).

• RCP8.5: The continuing increase scenario; the total radiative forcing will exceed 8.5 W/m2 _{at the end of the century (2100) due to lack of technology}

implementation and high population, leading to it being scenario with the highest GHG emissions (Riahi et al., 2011) (Figure 1).

The CMIP5 models used in this thesis are the Geophysical Fluid Dynamics Laboratory-Earth System Models GFDL-ESM2G and GFDL-ESM2M. These models are made to better understand the interactions between the ecosystem and the climate sys-tem, including human actions. These models simulate climate predictions similar to the previous GFDL versions described in the 4th _{IPCC report, but now}

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Figure 1 –Total radiative forcing for RCP2.6 (also called RCP3-PD), RCP4.5, RCP6.0 and RCP8.5. The tinted section of the graph represents the radiative forcing for the scenarios in the 21st _{century. The ECPs (Extended Concentration Pathways) describe the extensions}

beyond 2100 (Meinshausen et al., 2011).

latitude resolution. The only differences between these two models lie in the phys-ical ocean component, such as the thermocline depth being relatively deep in the ESM2M model and relatively shallow in the ESM2G model (Dunne et al., 2012), and the presence of geothermal heating in the ESM2M model, but missing in the ESM2G model (Hallberg et al., 2011). The other available models provided by the CMIP5 are not suitable for this research because data for the wanted scenarios are not available.

The data sets represent the Earth’s atmosphere in the form of grid cells between 40◦ and 50◦ north, ‘halfway’ the temperate latitudes. The data is extracted for the 500 hPa geopotential height, at the mid-level of the troposphere, where the Rossby waves approximately occur (Francis and Vavrus, 2012). The collected data ranges from the year 2006 to the year 2100 (95 years).

2.1.1 Network Common Data Form

The climate data is available in NetCDF (.nc) format. A NetCDF file is a machine-independent interface in Unidata software, generally used by atmosphere and ocean scientists and software tool developers to create, access and share scientific informa-tion in a network-transparent manner. The NetCDF files contain multidimensional variables including their coordinate systems and the representation of inherent rela-tions between the elements of those multidimensional arrays (attributes). NetCDF is being used to gather broadcast-weather data at point locations and to obtain

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ing limits;

• Time (in days, 365x95=34675) Limits: 2006 - 2100

• Longitude (in grids of 2.5 degrees 360/2.5=144) Limits: 0 - 360 degrees east

• Latitude (in grids of approximately 2 degrees) Limits: 40 - 50 degrees north

• Pressure level (in Pa, contains 6 different pressure levels) and 2 variables;

• Va or meridional, northward wind (in m·s−1₎

• Ua or zonal, eastward wind (in m·s−1_).

The attributes in this file contain information about the data with text-string or numerical values, e.g. the units of a variable. The size of the downloaded data is approximately 220 GBytes. A new NetCDF file containing only the data needed for the research is created by extracting all daily mean values, all longitude values, the latitude values between approximately 40◦ and 50◦ north, the pressure level at 500 hPa, all bounds, all values for Va and Ua, and all attributes (Appendix A). One year’s worth of data contains 365 days, leap days are left out in these files.

2.2 Calculations

The downloaded data is worked on in the programming language MATLAB.

2.2.1 MATLAB scripts

The new NetCDF file is read into MATLAB, and several scripts are made to analyse, animate and execute experiments with the data (Appendix A to C).

Because the model resolution is of great importance for representative results (Kinter et al., 2013), calculations for the daily meridional (Va) and zonal (Ua) components are done between roughly 40◦ and 50◦ north in aggregations of (Figure 2); • 2.5◦_x10◦ _{(144 grid cells)} • 10◦_x10◦ _{(36 grid cells)} • 360◦_x10◦ _{(1 grid cell)} • Europe (0◦ - 60◦ east) • Asia (60◦ - 140◦ east)

• Pacific Ocean (140◦ - 240◦ east) • United States (240◦ - 300◦ east) • Atlantic Ocean (300◦ - 360◦ east)

Wind speeds during winter are higher than during summer, leading to substan-tial variability within a year. To cancel out the noise of this variability it is decided to cluster the daily mean values into yearly mean values, to render 95 means.

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Figure 2 –Division of the oceanic and continental aggregations between 40◦and 50◦ north.

2.2.2 Zonal and Meridional Components of the Wind

Separate analyses are done on the mean absolute values of the meridional compo-nent and the regular mean values of the zonal compocompo-nent to detect any trends (Ap-pendix B). For the meridional component absolute values must be used, since both the northward and southward winds indicate a meridional circulation, or waves, re-gardless of the direction. The zonal component on the other hand is characterized by eastward winds. A westward wind rarely occurs at this latitude, but when it does it is relatively weak and will therefore have little effect. Next, the ratios of the two components are analysed.

2.2.3 Ratio

To gain insight on the variations of the meridional and zonal components, the ratio is calculated of the absolute values of Va and the regular values of Ua throughout the century (Appendix C):

R = |Va| Ua

Trend probability tables are generated using the ANOVA F-test. It is designed to test for significant differences between means of multiple samples. This is done by comparing the ratio of the means of these samples, where the sum of squares is partitioned into the components due to differences between means (SSregression) and the component due to random error within the variable (SSresiduals), each divided by their respective degrees of freedom (Johnson and Wichern, 2007). This function assumes a normal distribution of the data and independently sampled variables:

F = (SSregression/df ) (SSresiduals/df )

The ANOVA function returns an analysis of variance table containing the Sum of Squares, Degrees of Freedom and Mean Square of the regression and residuals, an F-value and a P-value. With the F-test the F-values are compared using a

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distribu-result in low F-values, so that only few trends would be significant. A P-value lower than 0.05 would conclude a significant trend. However, the F-values do not give information about the direction and magnitude for these differences. This informa-tion is attained by applying MATLAB’s multiple linear regression funcinforma-tion to the data. The slope values and their significances will then be used for interpretation and comparison between the results of each grid cell size, region, scenario and model. To determine whether the trends of the ratio are mainly caused by the trends of the meridional component or by the trends of the zonal component we have formulated an approximation equation. This equation rewrites the trends of the ratios as a linear relationship between the trends of the two components:

Rt= (Vt∗ U − Ut∗ |V |)/U 2

where Vt is the trend value of |V a|, Ut is the trend value of Ua, |V | and U are

the mean values of |V a| and Ua respectively, and Rt is the trend value of the ratio.

To establish which component exerts the most influence on the trend of the ratio the two elements need to be compared, (+Vt∗ U /U

2

) for |V a| and (−Ut∗ V /U2)

for Ua. The element related to Vt or Ut with the largest deviation from 0 has the

greatest influence on the trend of the ratio. This is done for each of the 36 cells of the 10◦x10◦ aggregations and for all 7 combinations of models and scenarios. Further explanation on the derivation of the equation can be found in Appendix D.

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3 Results

This research studies the projections by two climate models combined with four different scenarios of atmospheric composition for the period 2006-2100. Each of these eight runs contains 95 years worth of daily mean wind speed data, whereby two runs are incomplete. The obtained results mainly consist of information about the statistical significance of the ANOVA F-test and their trend values using a 95% confidence interval. Figure 3 displays a basic plot of the daily averages of the absolute values of the meridional and zonal components plotted against time. Noticeable occurrences are the high and the low peaks in each graph. The high peaks represent the daily mean wind speeds in winter, while the low peaks represent the daily mean wind speeds in summer. As can be seen in Figure 3, the data set of the zonal component of model ESM2G(scenario 2.6) is missing 394 days, a bit over a year worth of data, and the data set of the meridional component of model ESM2M(scenario 2.6) is missing 6424 days, a bit over 17.5 years in total.

Year 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100 m/s 0 5 10 15 20 25 30 Ua absolute for G 2.6 m/s 2 4 6 8 10 12 14 Va absolute for M 2.6

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This research investigates future prospects of the GHG emissions and their effect on the upper air circulation through the mentioned scenarios. Since ‘M2.6’ misses over 18% of its data it is decided to dismiss all results from this combination. However, ‘G2.6’ misses just over 1% of its data and will therefore still be used for interpretation.

It is also decided that even though the research has been performed on the 2.5◦x10◦ aggregations, the focus is put on the 10◦x10◦ aggregations because of the influence of outliers; they have the tendency to skew the results. The influence of outliers is more prevalent when a fine resolution is used, while at a more course resolution the averaging causes the outliers to become less prevalent. As can be seen in Figure 3, there is a large annual course in wind speeds. The effect of this variability is reduced by applying the ANOVA trend analysis on annual averages.

3.1 Zonal and Meridional Components of the Wind

Table 1 shows trend values and their statistical significances for the zonal wind component, Ua, for the grids above Europe, Asia, the Pacific Ocean, the Unites States, the Atlantic Ocean and around the world overall.

Ua G-Model M-Model Location 2.6 4.5 6.0 8.5 2.6 4.5 6.0 8.5 360◦ 0.110 -0.076 0.185 0.072 - 0.369 0.236 0.326 Europe 0.514 -0.142 0.151 0.798 - 0.672 0.475 0.114 Asia -0.007 -0.077 -0.331 -0.161 - 0.180 0.002 -0.016 Pacific 0.381 -0.096 0.778 -0.147 - 0.477 0.150 0.130 U.S. -0.331 -0.425 0.041 -0.036 - 0.597 0.544 0.958 Atlantic -0.148 0.376 0.063 0.130 - -0.093 0.146 0.747

Table 1 –Trend values of the Ua component expressed in m.s−1.century−1, for the period 2006-2100 and for all 7 combinations of models and scenarios. The blue values symbolize a positive significant change (increase) and red values symbolize a negative significant change (decrease) of the component over the century, using a 95% confidence interval.

There is some similarity between the results of the two models of the zonal component, since the only trend values that are significant are positive (Table 1). But when looking closer, half of the trends of the zonal component in the ‘G’ model are negative (though not significant), whereas the majority of the trend values of the ‘M’ model are positive. These are indications that the differences between the models do affect the outcomes. This will further be elaborated in the discussion.

The annual wind speed averages from which the trends for the zonal component are calculated are illustrated in the graphs in Appendix E. The highest zonal wind speeds are found over the Atlantic and Pacific Ocean, approximately 17 m.s−1 (Figure 4). The zonal wind speeds over Europe are in the order of 9-10 m.s−1, which is considerably lower than in the other regions. Asia and the US are in between. Remarkable is also that for most runs the trend line for the US is close to that of the world average, especially in the ‘G’ model. The distinct peak near the year 2070 in ‘G2.6’ is caused by the missing days around that time.

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year 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100 annual average [m/s] 6.0 8.0 10.0 12.0 14.0 16.0 18.0 20.0 Ua for G2.6 Europe Asia Pacific US Atlantic 360°

Figure 4 –Trend graph in [m/s] on annual averages of Ua for the period 2006-2100 for the ‘G’ model under the RCP2.6 scenario. The continental aggregations are indicated with circles, the oceanic aggregations are indicated with squares and the world as a whole is indicated with a solid line. See Appendix E for the other combinations of models and scenarios.

The ANOVA F-test results and trend values for the 10◦x10◦aggregations of the zonal component, Ua, are listed in Appendix H to get an impression of the signifi-cances on a smaller scale. These tables also show few significant trend values, where most of which are positive. Again nearly half of all trend values of the ‘G’ model are negative (though not significant), whereas the majority of the trend values of the ‘M’ model are positive. However, it should be pointed out that nearly all trend values that are not significant are highly insignificant and are therefore negligible. Comparison between the results of the two models for the meridional wind compo-nent, |V a|, shows that for both models the significant trend values are positive in the least extreme scenarios and negative in the more extreme scenarios (Table 2). The trend values in both models are predominantly negative (though not all signif-icant). Especially trends of the ‘G’ model seem to become more negative with each ascending scenario. Once more, the slight differences between the models resulted in different outcomes.

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Va abs G-Model M-Model Location 2.6 4.5 6.0 8.5 2.6 4.5 6.0 8.5 360◦ 0.073 -0.107 -0.211 -0.483 - 0.066 -0.232 -0.231 Europe 0.219 -0.049 -0.069 -0.202 - 0.180 0.039 -0.030 Asia 0.037 0.062 -0.021 -0.192 - 0.093 -0.043 -0.161 Pacific 0.088 -0.281 -0.480 -0.798 - 0.041 -0.452 -0.437 U.S. 0.038 -0.242 -0.151 -0.604 - -0.051 -0.337 -0.150 Atlantic -0.017 0.033 -0.219 -0.510 - 0.075 -0.280 -0.263

Table 2 –Trend values of the |V a| component expressed in m.s−1.century−1, for the period 2006-2100 and for all 7 combinations of models and scenarios. Values in blue indicate a positive significant trend and values in red indicate a negative significant trend, using a 95% confidence interval. year 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100 annual average [m/s] 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 Va(abs) for G2.6 Europe Asia Pacific US Atlantic 360°

Figure 5 –Trend graph in [m/s] on annual averages of |V a| for the period 2006-2100 for the ‘G’ model under the RCP2.6 scenario. The continental aggregations are indicated with circles, the oceanic aggregations are indicated with squares and the world as a whole is indicated with a solid line. See Appendix F for the other combinations of models and scenarios.

The annual wind speed averages from which the trends for the meridional compo-nent are calculated are displayed in the graphs in Appendix F. The annual averages of the aggregations for the meridional component have a smaller distribution. The graphs again illustrate the similarities between the annual averages of the US and the world as a whole and that the oceanic aggregations have the highest annual av-erage wind speeds at approximately 8.5 m.s−1 (Figure 5). In contrast to the zonal component, Asia has the lowest average meridional wind speeds compared to the other continental aggregations.

The ANOVA F-test results and trend values for the 10◦x10◦aggregations of the meridional component are listed in Appendix I to get an impression of the signif-icances on a smaller scale. These tables show more significant values than for the

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zonal component. Most significant values of the ‘G’ model are highly significant (P < 1%). However, nearly all trend values that are not significant are highly insignif-icant and are therefore negligible. The above-mentioned initial positive signifinsignif-icant trend values followed by negative significant trend values throughout the scenar-ios can be observed through both models. Still, it seems as though this transition occurs in a ‘lower’ scenario for the ‘G’ model (RCP4.5), than for the ‘M’ model (RCP6.0).

3.2 Ratio

In order to better express the waviness we calculated the ratio of the meridional wind speed to the zonal wind speed (|V a|/Ua) and did a regression analysis on these (Table 3). All significant trend values of the ratio are negative. With little exception, all remaining trend values for both models (though not significant) are also negative. This could either mean that the zonal component gets stronger over time relative to the meridional component, or that the meridional component gets weaker over time relative to the zonal component. Also, the trend values in both models are overall negative with each ascending scenario. This is the exact opposite of what we originally expected.

Ratio G-Model M-Model

Location 2.6 4.5 6.0 8.5 2.6 4.5 6.0 8.5 360◦ 0.003 0.001 -0.022 -0.045 - -0.018 -0.029 -0.032 Europe -0.018 0.008 -0.021 -0.083 - -0.035 -0.024 -0.014 Asia 0.002 0.012 0.011 -0.012 - -0.002 -0.003 -0.007 Pacific -0.009 -0.010 -0.055 -0.046 - -0.024 -0.038 -0.041 U.S. 0.014 0.002 -0.014 -0.049 - -0.037 -0.058 -0.062 Atlantic 0.001 -0.011 -0.016 -0.044 - 0.008 -0.023 -0.039

Table 3 –Trend values of the |V a|/Ua ratio for the period 2006-2100 and for all 7 combinations of models and scenarios. Values in blue indicate a positive significant trend and values in red indicate a negative significant trend, using a 95% confidence interval.

The annual wind speed averages from which the trends for the |V a|/Ua ratio are calculated are displayed in the graphs in Appendix G. Europe’s trends stick out far from the trends of the other aggregations in both models and all scenarios (Figure 6). Also, Europe’s annual average ratios are far more dispersed compared to the dispersion of the other aggregations. In addition, just as in the instances of the zonal and meridional components, the graphs show the similarities between the annual averages of the US and the world as a whole. The distinct peak near the year 2070 in ‘G2.6’ is caused by the missing days around that time.

The ANOVA F-test results and trend values for the 10◦x10◦aggregations of the ratio are listed in Appendix J to get an impression of the significances on a smaller scale. Contrary to the above-mentioned overall negative trends, there are also some positive trends in the ‘lower’ scenarios. However, only two of these are significant.

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year

2010 2020 2030 2040 2050 2060 2070 2080 2090 2100

annual average |Va| / Ua

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 Ratio for G2.6 Europe Asia Pacific US Atlantic 360°

Figure 6 –Trend graphs on annual averages of the |V a|/Ua ratio for the period 2006-2100 and for all 7 projections. The continental aggregations are indicated with circles, the oceanic aggregations are indicated with squares and the world as a whole is indicated with a solid line.

To check whether the approximation equation is applicable to the ratios we plotted the values of the ratios from the regression against the values of the ratios calculated with the approximation equation. From the summary graph with all scenarios it appears that they are practically 1:1 linear with each other with a margin of error of about 1-2% (Figure 7).

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Table 4 lists the number of times either the trend of the zonal or that of the meridional component had the most effect on the trend in the ratio. There is no large difference between the influences of the trends of the components on the trends of the ratios; the trends of the meridional component exert about 4% more influence on the trends of the ratio than trends of the zonal component. However, the differences in number of times a component has the most effect on the trend in the ratio seem to be larger when the trends of the meridional component are the main influence. Ut |Vt| G2.6 Rt 22 14 G4.5 Rt 20 16 G6.0 Rt 19 17 G8.5 Rt 10 26 M4.5 Rt 20 16 M6.0 Rt 11 25 M8.0 Rt 19 17 Total 121 131

Table 4 –Number of times a component exerts more influence than the other in the ratio, using the approximation equation for all 36 10◦x10◦aggregations, for all 7 used combinations of models and scenarios.

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4 Discussion

This research uses the results of two climate models to establish whether climate change has an effect on the modelled upper air circulation in the mid-latitudes. The climate models are combined with four different future projections of atmospheric compositions for the period 2006-2100, in order to examine the behaviour of the meridional and zonal wind components. This section discusses the results and com-pares them to published literature on the topic.

Significant trends of the zonal component generally were positive, which is the opposite of what we anticipated. As expected, significant trends for the merid-ional component were positive in the lower scenarios, but as the radiative forcing increases in the more extreme scenarios, these trends tend to become negative.

In the trend graphs of the zonal component it is apparent that the wind speeds above the Pacific and Atlantic Ocean are greater than of the other aggregations. This can be explained by looking at a geopotential height map of the 500 hPa plane with reanalysis data. This map illustrates the geopotential heights in January and in June, for the period 1979-1998 (Figure 8). It is particularly visible in the January map that the contour lines of the 500 hPa plane are closer together above the oceans compared to above the continents. This indicates a steep gradient, and thus high zonal wind speeds. The contour lines above Asia and the US are also overall close together, whereas those above Europe are farther apart. This clarifies why the trend graphs above Asia and the US indicate greater mean annual wind speeds than above Europe.

Figure 8 –Geopotential heights of the 500 hPa plane in January and June, for the period 1979-1998 (Kistler et al., 2001).

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The distributions of the wind speeds of the meridional component are harder to explain using these maps, since meridional winds are associated with propagating waves. Over the oceans where zonal winds speeds are high, any waves in the flow also cause relatively high meridional wind speeds. Friction has a negligibly small effect on wind speeds above the atmospheric boundary layer of roughly 1-2 km (Cushman-Roisin, 2014), so it will not affect the 500 hPa flow, which is at about 5-6 km elevation. The only obstructions affecting the 500 hPa flow would be the high mountain ranges in the area. In the case of the used aggregations these would be the Rocky Mountains in the United States and the Alpes in Europe, which could explain their relatively high meridional wind speeds. Asia has no major mountain ranges in the proximity of the study area, resulting in a less meridional flow pat-tern. Nonetheless, the meridional component generates far more significant trends than the zonal component. This means that meridional component will change more over time, when considering that the components are independent, whereas the zonal component will remain more constant. As for the high extent of simi-larities between the trends of the ratio of the US and those of the world, it seems as though the patterns of the US could be an approximation for the patterns that occur around the world as a whole. However, no logical explanation could be made for this occurrence, other than it being a coincidence.

The unexpected behaviour of the two components, especially in the more extreme scenarios, leads to the results of the ratios being the opposite of what we initially anticipated. As influenced by the meridional component, only the trends of the ra-tios in the ‘G2.6’ scenario were positive whereas they became negative in the more extreme scenarios. This is also found in a recent study done by Hassanzadeh et al. (2014), which shows a robust decrease in the meridional amplitude of waves caused by a decrease in the temperature gradient. Since the Earth’s warming causes AA, it would in turn slow down the Rossby waves giving it a larger amplitude (Francis and Vavrus, 2012). However, this does not seem to happen in the more extreme scenar-ios. It could be that the AA becomes less efficient at more extreme scenarios, since most of the snow and ice has already melted. The strong positive feedback would then disappear, whereby other factors would take over (Reichler, 2009). A possible consequence for this could be a general slowdown of the circulation because of the decreased temperature gradient, which also means that there would likely be less extreme weather patterns when considering the more extreme scenarios (Hassan-zadeh et al., 2014). The unexpected results could perhaps also be linked to forced random variability of the climate, as suggested by Gillett et al. (2000), Kuzmina et al. (2005), Watanabe et al. (2013) and others.

These results are conflicting with studies done by Sillmann et al. (2013), among others, who found that weather patterns generally indicate an intensification in the more extreme scenarios. Different factors could possibly account for the contrasting results. One of those factors could be the fact that most other studies, including that of Sillmann et al. (2013), perform their calculations on temperature and

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pre-while most studies base their results on calculations made at surface level.

Aside from the meridional component having far more significant trends as an individual component, the approximation equation suggested that the ratios are more or less equally determined by either component. This indicates that both components are continuously changing, considering that there are several combina-tions within a ratio that could determine the influence of the components. This raises the question whether the simple calculation of a ratio could indeed explain the complex relationship between the two components in the weather system, or that something critical is being overlooked.

When looking at the distribution of significant trend values throughout the sce-narios it appears that the two more extreme scesce-narios generated more significance than the less extreme scenarios. A likely explanation for this occurrence could be linked to the GHG emissions. As can be seen in the description of the scenarios, a large effort is made in the first two scenarios to reduce GHG emissions while little effort is made in the last two scenarios to reduce GHG emissions.

When comparing the outcomes of the two models used in this research it is dif-ficult to establish which one provides better results. The difference between the outcomes of the two models can partly be explained by the chaos theory, first de-scribed by Lorenz (1963), where there is a fundamental limit to what we can know about the smallest scales of nature. The best you can do is make an approximation of reality, but the slightest change in starting conditions can cause major differ-ences in the final outcome (Lorenz, 1963). The more precise we want a model to simulate certain aspects, the less precise the complimentary variables can become. Thus subtle differences between the two models lead to considerable differences in outcome. Understanding why the models arrive at different answers and adjusting the differences would considerably help in understanding the underlying causes and mechanisms, and lead to more reliable simulations of future predictions (Reichler, 2009). In this case the differences in starting conditions lie in the used oceanic ther-mocline depths, the presence of geothermal heating in the ESM2M model and the absence of this in the ESM2G model. Houghton (2015) explained that the improve-ment of the oceanic component, especially through introducing higher resolutions, lead to adequate descriptions of the climate without artificially adjusting the fluxes. This highlights the importance of the oceanic component, and that small variations within can be of importance. The differences in outcome between the two models are an additional indication that in weather, everything is in some way connected. When revisiting the methods used in this research we came across certain things that could have been approached differently. For instance, in this study the research area is ‘halfway’ the temperate latitude, between 40◦ and 50◦, but after examining the results we realized that a larger area closer to the polar front would possibly render better and more statistically significant results. For example, expanding the research area up to 60◦ NH would likely improve the results, since the Rossby waves are more pronounced between 40◦ and 60◦ and because that region is more related to the exchange between the temperate latitudes and the polar regions (Holton, 2012). For further research we also suggest examining the behavioural patterns of

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the components in seasonal changes, similar to that done for Figure 8. Wind speeds generally reach higher velocities in the winter than in the summer, but the contrast is cancelled out by taking annual averages. Also, using a model that generates data with smaller grid sizes could improve the quality of the results (Matsueda et al., 2009). Recent developments in grid cell sizes has had a major impact on weather forecasting, whereby the forecasting period and accuracy has improved drastically. Nowadays, the forecast for three days ahead are just as good as the forecast was for one day in 1985 (Houghton, 2015). Considering the grid size in this research being 2.5◦ (approximately 275 km), the small scale factors that might influence the atmospheric circulation cannot be observed at this resolution (Scaife et al., 2011). Unfortunately, due to time constraints we were unable to implement these changes.

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5 Conclusion

This study set out to explore the effect of climate change on the upper air circulation, and therefore on the weather patterns, in the temperate latitudes using two different climate models and four different scenarios of future atmospheric composition. The focus lies on the behaviour of the zonal and meridional wind components in the 500 hPa flow. We hypothesized that that the models would predict a more meridional circulation over time, indicating more pronounced waves and hence more extreme weather patterns. When analysing the zonal and meridional components of the flow we found that the significant trends of the zonal wind component are mostly positive. The meridional wind component behaves the opposite of what we initially expected. The significant trends are positive in the least extreme scenarios and negative in the more extreme scenarios. The ratio of the meridional component to the zonal component of the flow was used as an indication for the meridionality of the flow. The significant trend values of the ratio are negative for the most part and tend to become more negative with each ascending scenario, which is the opposite of what we hypothesized. From the approximation equation it becomes apparent that the trends in the zonal component and the trends in the meridional component exert roughly an equal amount of influence on the trends of the ratio. These conflicting results lead us to believe that the change in frequency and intensity of extreme weather patterns could either be related to forced random variability of the climate, or a loss of efficiency of the AA in the more extreme scenarios. Constant improvement of the climate models and minimizing the grid cell sizes are some steps towards better weather predictions. All in all, climate change is a given fact and cannot be completely avoided, but it ultimately depends on human behaviour to what extent the climate will change.

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A MATLAB script; Data Extractor

This simplified MATLAB script extracts all the needed information from the orig-inal large NetCDF file. By changing the letter of the model type and the scenario number in lines 3 and 4, all data from each of the 7 projections can be easily extracted. clc; clear; modType = 'G'; scenarioNum = '26';

%% Open NETcdf file filename =

strcat('_2',modType,'_rcp',scenarioNum,'_2006_2100_File.nc'); ncid1 = netcdf.open(strcat('va',filename),'NOWRITE');

ncid2 = netcdf.open(strcat('ua',filename),'NOWRITE'); %% Explore the Contents

[numdims,nvars,natts] = netcdf.inq(ncid1); %% Get Global attributes Information for ii = 0:natts-1

fieldname = netcdf.inqAttName(ncid1, netcdf.getConstant('NC_GLOBAL'), ii); fileinfo.(fieldname) =

netcdf.getAtt(ncid1,netcdf.getConstant('NC_GLOBAL'), fieldname ); end

% Allocate structure

dimension = repmat(struct('name', '', 'length', 0), numdims, 1); for ii = 1:numdims

[dimension(ii).name, dimension(ii).length] = netcdf.inqDim(ncid1,ii-1);

% Padding name for table layout

padlength = min(0, length(dimension(ii).name));

name_padded = [dimension(ii).name repmat(' ', padlength+1)]; fprintf('%s\t\t%d\n', name_padded, dimension(ii).length); end

%% Get the Data for ii = 1:nvars

[name, ~, ~, natts] = netcdf.inqVar(ncid1,ii-1); % Get Variable Attributes

tmpstruct = struct(); for jj = 1:natts

fieldname = netcdf.inqAttName(ncid1, ii-1, jj-1); if(strcmpi(fieldname,'_FillValue'))

continue; else

tmpstruct.(fieldname) = netcdf.getAtt(ncid1, ii-1, fieldname );

end end

% Get raw data

data = netcdf.getVar(ncid1,ii-1);

% Replace missing numbers

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data( data == tmpstruct.missing_value ) = NaN; end

% Scale data

if( isfield(tmpstruct, 'scale_factor') )

data = double(data) * tmpstruct.scale_factor; end

% Apply offset

if( isfield(tmpstruct, 'add_offset') ) data = data + tmpstruct.add_offset; end

% Store attribute and data with appropriate name varinfoname = [name '_info'];

assignin('caller', varinfoname, tmpstruct); assignin('caller', name, data);

end

netcdf.close(ncid1); netcdf.close(ncid2);

ua = ncread(strcat('ua',filename),'ua'); %% Clean up temporary variables

clear ndims nvars natts ii jj tmpstruct idx ncid filename

clear fieldname name vartype dimids varinfoname data date_offset

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B MATLAB script; Experiment on the Zonal and

Meridional Components

This simplified MATLAB script performs the analyses on the independent compo-nents |V a| and Ua and can be used on each of the 7 combinations of models and scenarios, together with the data extractor from Appendix A.

function [data_grid] = DataGenerationForResolution(names,lon_analysis_span, lon_width, lon_res,data) %% Initialiazation of variables data_grid = cell(size(names,1),2); index = 1:(360/lon_res); for i = 1:size(names,1) data_grid{i,1} = names(i); evaluationregion = ceil(lon_analysis_span(i,1)/lon_res):ceil(lon_analysis_span(i,2)/lon_re s); for j=evaluationregion index(j) = j; end

analysis_span = lon_analysis_span(i,2) - lon_analysis_span(i,1) + 1;

number_areas = analysis_span / lon_width(i); res = lon_width(i) / lon_res;

analysis_area = ceil(lon_analysis_span(i,1)/lon_width(i)) - 1:lon_analysis_span(i,2)/lon_width(i) - 1;

tmp = zeros(size(analysis_area,2),size(data,3));

for j=analysis_area

index_log = (index > (j*res) & index <= ((j+1)*res)); k = find(analysis_area == j); tmp(k,:) = squeeze(nanmean(nanmean(data(index_log,:,:),2),1))'; end data_grid{i,2} = tmp; end

function [Regress_Ua,Regress_Va] = experiment_Absolute(ua,va,time_bnds) %% Initialiazation of variables

ua = squeeze(ua)); va = abs(squeeze(va)); ua((ua == 0)) = nan; va((va == 0)) = nan;

%% Reduce lon and lat to match wanted resolution (NORMAL) names_ua =

{'ua_25_100';'ua_100_100';'ua_600_100';'ua_3600_100';'ua_europe';'ua_as ia';'ua_pacific';'ua_america';'ua_atlantic'};

names_va =

{'va_25_100';'va_100_100';'va_600_100';'va_3600_100';'va_europe';'va_as ia';'va_pacific';'va_america';'va_atlantic'};

lon_span = [1 360;1 360;1 360;1 360; 1 60; 61 140; 141 240; 241 300; 301 360];

lon_width = [2.5; 10 ; 60; 360 ; 60; 80; 100; 60; 60]; lon_res = 2.5;

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[ua_data] = DataGenerationForResolution(names_ua,lon_span, lon_width, lon_res,ua);

[va_data] = DataGenerationForResolution(names_va,lon_span, lon_width, lon_res,va);

function[Result] = Regression(x,y) %% Regression analyses Result = zeros(size(x,1),4); for i = 1:size(x,1) yearlyData = nanmean(vec2mat(x(i,:), 365)'); yearlyData(isinf(yearlyData))=NaN; [b,bint,~,~,~] = regress(yearlyData',y); Result(i,1) = b(2); Result(i,2:3) = bint(2,1:2);

Result(i,4) = ((bint(2,1)<0) & (bint(2,2)<0)) | ((bint(2,1)>0) & (bint(2,2)>0));

end

function[Result,Stats,Tbl] = Anova(x) %% ANOVA F-test Result = zeros(size(x,1),3); Stats = cell(size(x,1),1); Tbl = {}; for i = 1:size(x,1) yearlyData = vec2mat(x(i,:), 365)'; yearlyData(isinf(yearlyData))=NaN;

[p,tbl,stats] = anova1(yearlyData, [],'off'); Result(i,1) = tbl{2,5}; Result(i,2) = p; Result(i,3) = p < 0.05; Stats{i} = stats; Tbl = [Tbl tbl ]; end

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C MATLAB script; Experiment on the Ratio

This simplified MATLAB script performs the analyses on the |V a|/Ua ratio and can be used on each of the 7 projections, together with the data extractor from Appendix A. function [data_grid] = DataGenerationForResolution(names,lon_analysis_span, lon_width, lon_res,data) %% Initialiazation of variables data_grid = cell(size(names,1),2); index = 1:(360/lon_res); for i = 1:size(names,1) data_grid{i,1} = names(i); evaluationregion = ceil(lon_analysis_span(i,1)/lon_res):ceil(lon_analysis_span(i,2)/lon_re s); for j=evaluationregion index(j) = j; end

analysis_span = lon_analysis_span(i,2) - lon_analysis_span(i,1) + 1;

number_areas = analysis_span / lon_width(i); res = lon_width(i) / lon_res;

analysis_area = ceil(lon_analysis_span(i,1)/lon_width(i)) - 1:lon_analysis_span(i,2)/lon_width(i) - 1;

tmp = zeros(size(analysis_area,2),size(data,3));

for j=analysis_area

index_log = (index > (j*res) & index <= ((j+1)*res)); k = find(analysis_area == j); tmp(k,:) = squeeze(nanmean(nanmean(data(index_log,:,:),2),1))'; end data_grid{i,2} = tmp; end

function [Regress_Ratio_Abs] = experiment_ratio_abs(ua,va,time_bnds) %% Initialiazation of variables ua = squeeze(ua); va = abs(squeeze(va)) ua((ua == 0)) = nan; va((va == 0)) = nan; Ratio = va./ua; %% names_Ratio =

{'Ratio_25_100';'Ratio_100_100';'Ratio_600_100';'Ratio_3600_100';'Ratio _europe';'Ratio_asia';'Ratio_pacific';'Ratio_america';'Ratio_atlantic'} ;

lon_span = [1 360;1 360;1 360;1 360; 1 60; 61 140; 141 240; 241 300; 301 360];

lon_width = [2.5; 10 ; 60; 360 ; 60; 80; 100; 60; 60]; lon_res = 2.5;

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[Ratio_data] = DataGenerationForResolution(names_Ratio,lon_span, lon_width, lon_res,Ratio); [ua_data] = DataGenerationForResolution(names_Ratio,lon_span, lon_width, lon_res,ua); [va_data] = DataGenerationForResolution(names_Ratio,lon_span, lon_width, lon_res,va); Regress_Ratio_Abs = cell(size(Ratio_data,1)+1 , 4 ); Regress_Ratio_Abs{1,1} = 'name'; Regress_Ratio_Abs{1,2} = 'resolution';

Regress_Ratio_Abs{1,3} = 'longitudinal span'; Regress_Ratio_Abs{1,4} = 'Result Table';

function[Result] = Regression(x,y) %% Regression analyses Result = zeros(size(x,1),4); for i = 1:size(x,1) yearlyData = nanmean(vec2mat(x(i,:), 365)'); yearlyData(isinf(yearlyData))=NaN; [b,bint,~,~,~] = regress(yearlyData',y); Result(i,1) = b(2); Result(i,2:3) = bint(2,1:2);

Result(i,4) = ((bint(2,1)<0) & (bint(2,2)<0)) | ((bint(2,1)>0) & (bint(2,2)>0));

end

function[Result,Stats,Tbl] = Anova(x) %% ANOVA F-test Result = zeros(size(x,1),3); Stats = cell(size(x,1),1); Tbl = {}; for i = 1:size(x,1) yearlyData = vec2mat(x(i,:), 365)'; yearlyData(isinf(yearlyData))=NaN;

[p,tbl,stats] = anova1(yearlyData, [],'off'); Result(i,1) = tbl{2,5}; Result(i,2) = p; Result(i,3) = p < 0.05; Stats{i} = stats; Tbl = [Tbl tbl ]; end

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D Approximation Equation

Sequence of derivations of the approximation equation from the ratio. Further ex-planation on next page.

1 R =

|Va|

Ua

Original equation of the ratio. The influence of the trends of the

components on the ratios is estimated on the basis of the following

steps. The time unit of the approximation is the length of the

mea-surement, in this case from R

0

to R

1

.

t

= U

1

− U

0

= (U + 0.5U

t

) − (U − 0.5U

t

)

R

t

= R

1

_{U −0.5U}V −0.5Vt t

R

0

= (V − 0.5V

t

)(

_U1

+ 0.5

Ut U2

R

1

=

V_U

− V ∗ 0.5

Ut U2

+ 0.5

Vt U

− 0.25

Vt∗Ut U2

Additional derivation of R

0

and R

1

.

4 R

t

= (

V_U

−V ∗0.5

Ut U2

+0.5

Vt U

−0.25

Vt∗Ut U2

)−(

V U

−V ∗0.5

Ut U2

+0.5

Vt U

−0.25

Vt∗Ut U2

1

,

(36)

E Graphs of annually averaged values of Ua and

trend lines

year 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100 annual average [m/s] 6.0 8.0 10.0 12.0 14.0 16.0 18.0 20.0 Ua for G2.6 Europe Asia Pacific US Atlantic 360° year 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100 annual average [m/s] 6.0 8.0 10.0 12.0 14.0 16.0 18.0 20.0 Ua for G4.5 Europe Asia Pacific US Atlantic 360°

(37)

l

annual average [m/s] 6.0 8.0 10.0 12.0 14.0 16.0 18.0 20.0 Ua for M4.5 Europe Asia Pacific US Atlantic 360°

(38)

l

year 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100 annual average [m/s] 6.0 8.0 10.0 12.0 14.0 16.0 18.0 20.0 Ua for G6.0 Europe Asia Pacific US Atlantic 360° year 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100 annual average [m/s] 6.0 8.0 10.0 12.0 14.0 16.0 18.0 20.0 Ua for G8.5 Europe Asia Pacific US Atlantic 360°

(39)

l

year 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100 annual average [m/s] 6.0 8.0 10.0 12.0 14.0 16.0 18.0 20.0 Ua for M6.0 Europe Asia Pacific US Atlantic 360° annual average [m/s] 6.0 8.0 10.0 12.0 14.0 16.0 18.0 20.0 Ua for M8.5 Europe Asia Pacific US Atlantic 360°

(40)

F Graphs of annually averaged values of |V a| and

trend lines

year 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100 annual average [m/s] 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 Va(abs) for G2.6 Europe Asia Pacific US Atlantic 360° year 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100 annual average [m/s] 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 Va(abs) for G4.5 Europe Asia Pacific US Atlantic 360°

(41)

l

annual average [m/s] 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 Va(abs) for M4.5 Europe Asia Pacific US Atlantic 360°

(42)

l

year 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100 annual average [m/s] 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 Va(abs) for G6.0 Europe Asia Pacific US Atlantic 360° year 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100 annual average [m/s] 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 Va(abs) for G8.5 Europe Asia Pacific US Atlantic 360°

(43)

l

year 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100 annual average [m/s] 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 Va(abs) for M6.0 Europe Asia Pacific US Atlantic 360° annual average [m/s] 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 Va(abs) for M8.5 Europe Asia Pacific US Atlantic 360°

(44)

G Trend graphs of the Ratio

year

2010 2020 2030 2040 2050 2060 2070 2080 2090 2100

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 Ratio for G2.6 Europe Asia Pacific US Atlantic 360° year 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100

(45)

l

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 Ratio for M4.5 Europe Asia Pacific US Atlantic 360°

(46)

l

year

2010 2020 2030 2040 2050 2060 2070 2080 2090 2100

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 Ratio for G6.0 Europe Asia Pacific US Atlantic 360° year 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100

(47)

l

year

2010 2020 2030 2040 2050 2060 2070 2080 2090 2100

(48)

H ANOVA F-test results of Ua

ANOVA F-test for Ua G2.6

Long. F Trend P(F) 5 3.126 0.846 8.0% 15 2.545 0.795 11.4% 25 1.995 0.691 16.1% 35 1.308 0.507 25.6% 45 0.360 0.242 55.0% 55 0.000 0.004 99.1% 65 0.006 -0.028 93.7% 75 0.081 0.092 77.7% 85 0.127 0.108 72.2% 95 0.014 0.037 90.7% 105 0.035 -0.059 85.2% 115 0.093 -0.098 76.1% 125 0.071 -0.090 79.0% 135 0.003 -0.020 95.8% 145 0.002 0.019 96.3% 155 0.037 0.086 84.8% 165 0.091 0.146 76.3% 175 0.264 0.279 60.8% 185 0.753 0.500 38.8% 195 2.003 0.778 16.0% 205 2.723 0.804 10.2% 215 1.919 0.636 16.9% 225 0.667 0.388 41.6% 235 0.136 0.176 71.3% 245 0.019 0.062 89.1% 255 0.008 -0.035 92.9% 265 0.257 -0.193 61.3% 275 0.773 -0.357 38.2% 285 1.917 -0.602 16.9% 295 3.701 -0.861 5.7% 305 4.746 -0.989 3.2% 315 2.787 -0.827 9.8% 325 0.619 -0.438 43.3% 335 0.029 0.096 86.6% 345 0.937 0.510 33.5% 355 2.437 0.756 12.2%

ANOVA F-test for Ua G4.5 ANOVA F-test for Ua M4.5

Long. F Trend P(F) F Trend P(F)

5 1.082 0.443 30.1% 1.197 0.449 27.7% 15 0.256 0.206 61.4% 1.957 0.586 16.5% 25 0.006 -0.032 93.9% 2.096 0.604 15.1% 35 0.537 -0.281 46.6% 3.919 0.773 5.1% 45 2.065 -0.545 15.4% 5.635 0.880 2.0% 55 2.707 -0.643 10.3% 3.789 0.740 5.5% 65 2.521 -0.581 11.6% 1.746 0.513 19.0% 75 1.837 -0.426 17.9% 1.015 0.340 31.6% 85 0.818 -0.261 36.8% 0.149 0.107 70.1% 95 0.154 -0.116 69.5% 0.001 -0.010 96.9% 105 0.003 0.017 95.5% 0.017 -0.035 89.5% 115 0.309 0.167 57.9% 0.039 0.058 84.4% 125 0.768 0.286 38.3% 0.413 0.204 52.2% 135 0.570 0.300 45.2% 0.574 0.263 45.1% 145 0.346 0.279 55.8% 0.124 0.138 72.6% 155 0.624 0.421 43.2% 0.011 -0.045 91.8% 165 1.167 0.609 28.3% 0.093 -0.145 76.1% 175 1.088 0.606 30.0% 0.016 -0.064 89.9% 185 0.210 0.269 64.8% 0.115 0.176 73.6% 195 0.324 -0.311 57.0% 0.829 0.470 36.5% 205 1.993 -0.691 16.1% 2.742 0.838 10.1% 215 2.736 -0.786 10.1% 3.981 1.043 4.9% 225 2.072 -0.735 15.3% 4.572 1.165 3.5% 235 1.332 -0.624 25.1% 4.843 1.198 3.0% 245 0.864 -0.494 35.5% 3.875 1.118 5.2% 255 0.848 -0.443 36.0% 2.513 0.878 11.6% 265 0.852 -0.414 35.8% 1.823 0.680 18.0% 275 1.680 -0.538 19.8% 1.194 0.479 27.7% 285 1.467 -0.472 22.9% 0.712 0.345 40.1% 295 0.230 -0.185 63.3% 0.042 0.083 83.8% 305 0.011 -0.042 91.5% 0.180 -0.181 67.3% 315 0.013 0.047 91.1% 0.241 -0.223 62.4% 325 0.411 0.281 52.3% 0.079 -0.131 77.9% 335 1.298 0.531 25.7% 0.062 -0.110 80.4% 345 2.277 0.744 13.5% 0.035 -0.079 85.2% 355 2.122 0.697 14.9% 0.167 0.167 68.4%

(49)

5 1.406 0.559 23.9% 0.575 0.313 45.0% 15 0.812 0.396 37.0% 1.359 0.456 24.7% 25 0.120 0.154 73.0% 2.306 0.559 13.2% 35 0.008 -0.040 92.9% 2.423 0.556 12.3% 45 0.026 -0.068 87.2% 2.088 0.508 15.2% 55 0.052 -0.092 82.0% 1.520 0.460 22.1% 65 0.196 -0.169 65.9% 1.169 0.405 28.2% 75 0.853 -0.310 35.8% 0.334 0.190 56.5% 85 2.527 -0.475 11.5% 0.168 -0.115 68.3% 95 3.023 -0.483 8.5% 0.431 -0.180 51.3% 105 2.651 -0.457 10.7% 0.259 -0.138 61.2% 115 1.926 -0.455 16.9% 0.265 -0.150 60.8% 125 0.626 -0.289 43.1% 0.144 -0.115 70.5% 135 0.000 -0.006 98.7% 0.127 0.121 72.2% 145 0.148 0.157 70.2% 0.067 0.102 79.6% 155 0.504 0.316 48.0% 0.000 0.003 99.5% 165 1.509 0.598 22.2% 0.007 0.041 93.5% 175 2.543 0.875 11.4% 0.012 0.058 91.2% 185 3.936 1.186 5.0% 0.020 0.073 88.8% 195 5.184 1.380 2.5% 0.095 0.155 75.8% 205 4.615 1.255 3.4% 0.163 0.194 68.7% 215 2.899 0.926 9.2% 0.083 0.135 77.5% 225 1.206 0.549 27.5% 0.190 0.221 66.4% 235 1.437 0.534 23.4% 0.881 0.523 35.0% 245 0.975 0.397 32.6% 1.810 0.771 18.2% 255 0.001 0.012 97.5% 2.597 0.874 11.0% 265 0.017 -0.047 89.7% 1.754 0.684 18.9% 275 0.048 -0.084 82.7% 0.890 0.459 34.8% 285 0.016 -0.050 90.0% 0.436 0.309 51.1% 295 0.002 0.018 96.4% 0.119 0.167 73.1% 305 0.000 -0.009 98.3% 0.015 0.062 90.4% 315 0.114 -0.156 73.7% 0.002 0.021 96.9% 325 0.113 -0.173 73.7% 0.066 0.130 79.7% 335 0.000 -0.008 98.8% 0.305 0.259 58.2% 345 0.148 0.211 70.1% 0.282 0.237 59.7% 355 0.972 0.513 32.7% 0.149 0.166 70.0%

5 5.943 1.095 1.7% 0.766 0.403 38.4% 15 5.606 1.070 2.0% 0.420 0.281 51.8% 25 3.527 0.830 6.4% 0.146 0.159 70.4% 35 2.679 0.669 10.5% 0.026 0.064 87.1% 45 2.369 0.589 12.7% 0.000 0.002 99.7% 55 1.997 0.538 16.1% 0.388 -0.224 53.5% 65 0.948 0.367 33.3% 2.104 -0.529 15.0% 75 0.079 0.093 77.9% 1.349 -0.401 24.8% 85 0.846 -0.271 36.0% 0.798 -0.277 37.4% 95 2.228 -0.439 13.9% 0.664 -0.245 41.7% 105 3.418 -0.530 6.8% 0.129 -0.107 72.0% 115 3.356 -0.521 7.0% 0.113 0.106 73.7% 125 0.409 -0.200 52.4% 1.587 0.414 21.1% 135 0.377 0.216 54.1% 2.200 0.548 14.1% 145 0.500 0.291 48.1% 1.039 0.431 31.1% 155 0.012 0.055 91.3% 0.029 0.083 86.5% 165 0.118 -0.208 73.2% 0.216 -0.245 64.3% 175 0.262 -0.348 61.0% 0.643 -0.440 42.5% 185 0.235 -0.337 62.9% 0.709 -0.478 40.2% 195 0.189 -0.284 66.5% 0.295 -0.312 58.8% 205 0.449 -0.378 50.5% 0.000 0.004 99.4% 215 0.631 -0.384 42.9% 0.404 0.354 52.7% 225 0.053 -0.105 81.9% 1.943 0.759 16.7% 235 0.261 0.230 61.1% 4.813 1.145 3.1% 245 0.693 0.377 40.7% 5.989 1.244 1.6% 255 0.478 0.278 49.1% 5.587 1.198 2.0% 265 0.020 0.053 88.7% 4.148 1.039 4.5% 275 0.244 -0.181 62.3% 3.539 0.882 6.3% 285 0.642 -0.318 42.5% 3.398 0.754 6.8% 295 0.913 -0.426 34.2% 2.535 0.630 11.5% 305 0.826 -0.453 36.6% 1.505 0.532 22.3% 315 0.383 -0.334 53.7% 1.625 0.598 20.6% 325 0.009 -0.052 92.4% 2.953 0.844 8.9% 335 0.262 0.270 61.0% 4.331 1.017 4.0%