STOCKHOLM UNIVERSITY DEPARTMENT OF METEOROLOGY

STOCKHOLM UNIVERSITY DEPARTMENT OF METEOROLOGY MASTER OF SCIENCE IN ATMOSPHERIC SCIENCE, OCEANOGRAPHY AND CLIMATE MASTER PROJECT (30HP) Analysis of North Atlantic jet stream variability from CMIP5 simulations by LEUNG WAI NANG September 2013 Project Supervisor : Abdel Hannachi

ABSTRACT The North Atlantic eddy-driven jet is an intensified westerly wind occurring at upper troposphere. It is well-known that the European weather system is closely linked to the North Atlantic jet associated with the frontogenesis. In order to have a better understanding on the surface weather patterns, it is beneficial to make a comprehensive analysis on the jet variability. Some new climate models from the coupled model intercomparison project phase 5 are available in recent years which can be used to examine the jet variability in terms of the seasonality, probability distribution and persistence. Two parameters, the defined jet latitude and wind speed, are chosen to review the jet variability in seasonal and also particular in cold season. A series of systematic analysis is performed by using four scenarios - historical, control, RCP4.5 and RCP8.5. The historical and control runs are basically used to examine the performances of the latest models compared to the reanalyses. The latter two scenarios are for studying the effect on jet variability by the anthropogenic forcing in future. The jet variability is further studied by testing the correlation among the mathematical moments. The performances between these updated models and the old models are also investigated. For the performance of those climate models, the seasonal cycles of the jet latitude and wind speed are well captured, the patterns are generally comparable to the observations. However, most of the models cannot simulate the trimodal structure of jet latitude distribution. In addition, all models show an overestimation in wind speed. If the external forcing is introduced, there is no consistent response among all the models. There is only a weak agreement with the well-established responses which are the poleward shifted and strengthen jets. These responses can be found in some models only. Additionally, the analysis also indicates a negative correlation between the mean jet latitude and the other moments like standard deviation, skewness and excess kurtosis. Finally, regarding the improvement in the updated models, no major improvement can be found for the jet latitude and wind speed compared to the models in the previous phase.

Contents 1 Introduction... 1 2 Theory... 1 2.1 Jet stream... 1 2.2 Teleconnection patterns... 3 2.2.1 North Atlantic Oscillation and East Atlantic pattern... 3 2.2.2 Jet stream and teleconnection... 4 2.3 Global circulation model... 6 3 Data and model description... 8 4 Methodology... 9 4.1 Definition of the jet latitude and speed... 9 4.2 Seasonality of jet latitude and wind speed... 10 4.3 Probability density function... 11 4.4 Skewness and excess kurtosis... 12 4.5 Jet persistence... 13 5 Results... 13 5.1 ERA-40 jet latitude and wind speed... 13 5.2 CMIP5 integrations on 20 th century (20C3M)... 15 5.2.1 Seasonality Jet latitude... 15 5.2.2 Seasonality Wind speed... 18 5.2.3 Probability distribution Jet latitude... 20 5.3 Climate change scenarios RCP4.5 and RCP8.5... 22 5.3.1 Jet latitude... 22 5.3.2 Wind speed... 26

6 Discussion... 29 6.1 Climate change on skewness and excess kurtosis... 29 6.1.1 Skewness... 29 6.1.2 Excess kurtosis... 29 6.2 Jet latitude... 31 6.2.1 Jet latitude versus standard variation... 31 6.2.2 jet latitude versus skewness... 32 6.2.3 Jet latitude versus excess kurtosis... 33 6.3 Persistence... 34 6.4 Comparison between CMIP3 and CMIP5 models... 36 6.4.1 Seasonality Jet latitude... 37 6.4.2 Seasonality Wind speed... 37 6.4.3 Probability distribution Jet latitude... 40 7 Conclusion... 42 Acknowledgments... 43 References... 44

1 Introduction Certainly, the mid-latitude weather system is strongly linked to the eddy-driven jet stream. The changes in jet stream determine which region is affected by the severe weather like storms and heavy precipitation. Many studies have examined the jet variability in terms of the preferred jet positions, jet persistence and also the responses to external forcing. Recently, the accuracy of climate model has been advanced owing to the improvement in model resolution, physics as well as data assimilation. In order to check whether the previous findings are consistent in the new models, the jet variability in updated models is examined by the following analyses. The understanding of the jet variability can be enhanced by evaluating the models. The main objective of this study is to provide the evaluation of the latest climate models by simulating the North Atlantic eddy-driven jet variability. The jet latitude and wind speed are chosen to examine the jet variability in seasonal. In particular, for the probability distribution of jet latitude, the cold season (DJFM) is mainly concerned. Generally, this project is divided into four parts. The first part is to examine their performances in present day by comparing with the reanalyses. The second part is to predict the effect of climate change on the jets in the late 21 st century. Next, some properties of the jet variability are further analyzed such as the correlation among the jet latitude, skewness, excess kurtosis and jet persistence. Finally, in order to check whether the models are improved, the performances between some old and updated models are individually compared. In the next section, a brief theory on jet stream, teleconnection weather pattern and climate model are given. In section 3, the dataset and model description are introduced. Section 4 describes the methodology used in this study. Main results and further discussions are presented in section 5 and 6, respectively. Finally, section 7 gives the conclusion including a summary of major findings. 2 Theory 2.1 Jet stream Jet streams are defined as the relatively high speed westerly winds located at upper troposphere. They often associate with the north-south shifting. In general, there are 1

two types of jet stream, namely subtropical thermally-driven jet and polar eddy-driven jet, as demonstrated in figure 1. The latter one is more important as linked to the surface weather systems while the first one is mainly confined at the high altitude with relatively smaller jet speed. Fig. 1 The vertical structure of general circulation in the atmosphere. (Adopted from the website: NOAA NWS Jet Stream - The Jet Stream) Subtropical jet streams which are baroclinic and mainly located at 30 N, close to the divergent zone of Hadley cell. They are caused by the angular momentum transport in the thermally direct Hadley cell (Held and Hou, 1980). The thermal wind in the cell increases the velocity with height. The westerly winds are then intensified up until the tropopause. On the other hand, polar jet streams are linked to the frontogenesis (baroclinic eddies) at mid-latitude, as known as polar front. It is the boundary between higher latitude cold air and low latitude warm air. The polar jets are formed because of the temperature gradient and the eddy momentum flux convergence by eddies disturbances. The jet strength is enhanced by greater temperature different across the front. Therefore, a stronger polar jet can be found in winter which means a greater wind speed and equatorward shifted jet. In fact, the position and strength of subtropical jet stream have also an effect on the polar jet, as suggested by Lee and Kim (2003). As shown in figure 2, an annual mean zonal wind at 300hPa from ERA-40, it can merely notice that there are two jets over the north Atlantic and Pacific, respectively. The Atlantic one is mainly the eddy-driven jet while the pacific one is a mixture of both thermally-driven and eddy-driven jets, as the jets are shown over Eastern Africa and Asia (Li and Wettstein, 2011). Interestingly, the stronger jets can be found over the Eastern side of the continents (located next to Japan and USA). These features is caused by the Tibetan plateau and Rocky Mountains. They lead to the weakening of the jets over the western sides of the continents but favour the formation of baroclinic zones over the eastern sides (Brayshaw et al., 2009). These stronger winds can be further 2

strengthened by the sea surface temperature (SST) associated with the Gulf Stream and the Kuroshio Current (Sampe et al., 2010). Certainly, this figure is just the climatological average. Both jet latitude and strength are in fact changing with a few days of persistence. This jet persistence means that the jet tends to remain the same state from the previous. Fig. 2 The annual zonal wind with isotachs at 300hPa wind from ERA-40. (Adopted from the website: CEOS climate diagnostics) 2.2 Teleconnection patterns Teleconnection patterns refer to the temporal correlation between the climate anomalies that are located far apart. They are also with long time scale variability (months to years). In fact, they always reflect the large scale changes in atmospheric wave and weather pattern. In the following sub-sections, the connection between the teleconnection patterns in North Atlantic jet stream is discussed. 2.2.1 North Atlantic Oscillation and East Atlantic pattern The North Atlantic Oscillation (NAO) is one of the most dominated weather patterns over the North Atlantic Ocean (Hurrell et al., 2003). It can be measured by the NAO index which is the normalized sea level pressure between the subtropical high (Azores) and the mid-latitude low pressure system (Icelandic low) (Walker and Bliss, 1932). The positive phase of the NAO (NAO+) means a larger difference of these two permanent pressure systems can be found. During the NAO+, the eddy-driven and subtropical jet stream are separated, as illustrated in figure 3. Therefore, it brings the warmer and wetter air to northern Europe while the cold and dry air might blow over the 3

Mediterranean area. In contrast, the North Atlantic jet shifts equatorward and merge with the subtropical jet during the NAO-. It yields moist and warm air into the Mediterranean area while the dry and cold air move to northern Europe. The East Atlantic (EA) is another type of teleconnection patterns. It is structurally similar to NAO which means a north-south dipole of anomaly pressure existing over the North Atlantic. However, the anomaly centres are positioned southeastward to the approximate nodal lines of NAO pattern, as shown in figure 4 (Barnston and Livezey, 1987). Thus, the weather patterns are slightly different to NAO. The positive phase of the EA implies warmer in Europe. It is also associated with more precipitation across northern Europe while with less precipitation over southern Europe. Fig. 3 The wintertime positive and negative phase of the NAO as seen from the 300hPa wind field. Positive and negative phases are defined using a one standard deviation threshold. (Adopted from Woollings et al., 2010a) Fig. 4 The wintertime positive phase of NAO and EA patterns. The contours represent positive and negative geopotential height anomalies at 250hPa. (Adopted from Irvine et al., 2013) 2.2.2 Jet stream and teleconnection Recently, many studies have suggested that the phase of NAO is strongly connected to the variability of North Atlantic eddy-driven jet stream (Hannachi et al., 2012; Woollings et al., 2010b; Woollings and Blackburn, 2012). They also found that the jets have three preferred positions which are the southern (~ 37 N), central (~ 47 N) and northern (~ 58 N) positions. Clearly, the negative phase of NAO is highly linked with 4

the presence of blocking over Greenland. Thereby, the jets shift equatorward which can explain the southern jet preferred position (Woollings et al., 2008). However, the NAO alone cannot explain all the variations of the eddy-driven stream. Fyfe and Lorenz (2005) and Sparrow et al. (2009) presented that more than one pattern is required to describe a jet of constant speed shifting in latitude. Woollings et al. (2010b) showed that the EA pattern is the second prominent mode for the jet variability. The EA pattern is also used to describe the jet preferred position associated with NAO. Specifically, the southern, central and northern positions correspond to NAO-, EA+ and EA-, respectively. For instances, as summarized in figure 5, the southern position is associated with the negative NAO phase only. The central position can be explained by both positive NAO and EA patterns. The northern position is mainly associated with a shift to more negative EA and positive NAO. These positions can also easily linked to the atmospheric blocking systems, as shown in figure 6. The southern jet position is closely linked to the Greenland blocking while the northern position is more favour when a strong blocking over central Western Europe and weak Greenland blocking are presented. The central position is rather act as the non-disturbed state where the low pressure is located at the centre of North Atlantic. The above description of the jet variability is further strengthened by Hannachi et al. (2012) using the Gaussian mixture model. They also analyze the lifecycles of those preferred positions by applying the extended empirical orthogonal function. The lifecycles of northern and central jets, about 10 days, are less than that of southern jet, about 15 days. Apparently, they are consistent with the idea that reduced persistence can be found for poleward shifted jet. Fig. 5 Three component mixture model estimate of the NAO/EA pdfs. (Blue southern jets, green central jets and yellow northern jets) (Adopted from Woollings et al., 2010b) 5

Fig. 6 Z500 anomaly composites for the 300 days closest to each of the three maxima of the PDF denoted the southern, central and northern jet locations from left to right in the PDF. Contours are drawn every 20m with the zero contour omitted. (Adopted from Woollings et al., 2010b) 2.3 Global circulation model Global circulation model (GCM) is a numerical model to simulate the circulation of the atmosphere. The earth is divided into many grid cells both horizontally and vertically in GCM. Basically, the model performance is related to the horizontal and vertical resolution. In each grid cell, the atmosphere is based on a set of mathematical equations with the observed meteorological state as initial conditions. However, these initial conditions are mostly important for the numerical weather predict which has shorter forecast range and higher resolution. The GCM rather concerns more about the relevance of ocean dynamics, land surface and ice surface. Using the numerical equations for weather/climate prediction is first proposed by Bjerknes (1904) who stated that air is a heat conducting fluid and obeys the fundamental physical laws (primitive equations). After that, Richardson (1922) carried out a calculation of the change in pressure over central Europe, using continuity equation. The result was unrealistic that the surface pressure is reduced 145hPa in 6 hours due to an imbalance of initial data. However, his efforts were a foundation for the future of modern weather forecasting. In fact, the first model was not attempted until the 1950 s by Charney et al. (1950) with the help of numerically solving the non-divergent barotropic voricity equation on the electronic computer. In a typical GCM model, the three-dimensional atmosphere is discretized and the primitive equations are solved numerically. The behaviour of the atmosphere is 6

governed by a set of physical laws. They dictate how metrological elements will change from their initial values. They can be converted into a series of mathematical equations that make up the core of GCM. The following are the basic equations for the models (James, 1994): - Newton s second law (the momentum equation), describing the rate of change of momentum of an air parcel due to the pressure gradient and the Coriolis force; - The 1st law of thermodynamics (the thermodynamic energy equation), requiring that the change of the internal energy equals the amount of heat added to plus the work done on the system; - Conservation of water vapour mixing ratio, requiring that the rate of change of water vapour following an air parcel equals to the source (evaporation) minus sink (condensation); - Equation of continuity, which is statement of the conservation of mass; - Ideal gas law; - Hydrostatic equation (for hydrostatic models only), describing the (approximate) balance between the vertical pressure gradient force and the gravitational force. Apart from that, parameterization is also required to account for physical processes that are either not explicitly resolved on the grid scale or because they are too complex. Examples include condensational heating, orographic processes, radiative forcing and ozone chemical reactions. In recent years, the GCMs are widely used for the future climate change projections. The global warming is a well-known established effect by the human impact to the climate system. In order to the responses, some scenarios are designed in the GCMs to examine the climate change under different external forcing. However, there are some limitations to cause the GCMs that might not give the accurate projections, called model bias. These uncertainty can be easily found by comparing with the observations. The effects of clouds are one of the major uncertainties in GCMs. Actually, the clouds have double roles on the climate whereas they are competing to each other. The first role is the cooling effect that they reflect the incoming solar radiation back into space. At the same time, they also increase the amount of longwave radiation emitted from the atmosphere to surface. Besides that, the GCMs also have large bias on the atmospheric blocking which is one of the constraints for jet stream. Many studies have shown an underestimated blocking over the north Atlantic in GCMs (Scaife et al., 2010; Woollings et al., 2010b). Nevertheless, the GCMs still provide certain insights for the general climate prospects. 7

3 Data and model description In general, there are two types of dataset used in this study. They are the observations and model simulations. The first dataset is ERA-40 which is a reanalysis of meteorological observations from 1957 to 2002 (Uppala et al., 2005). Only the daily jet latitude and wind speed are estimated from the reanalyses, see details in section 4.1. The same latitude and speed are also deviated from 40 global circulation models simulations performed for the 5 th phase of the Coupled Model Intercomparison Project (CMIP5). The model outputs are widely from 7 centres whereas 10 models are selected in total, see details in table 1. Table. 1 CMIP5 climate models. Label Institution Country Model Resolution a Beijing Climate Center, China Meteorological Administration China BCC-CSM1-1 128 64 L26 b Beijing Normal University China BNU-ESM 128 64 L26 c Canadian Centre for Climate Modelling and Analysis Canada CanESM2 128 64 L35 d Institute of Atmospheric Physics, Chinese Academy of Sciences China FGOALS-s2 128 108 L26 e Geophysical Fluid Dynamics Laboratory USA GFDL-ESM2G 144 90 L24 f Geophysical Fluid Dynamics Laboratory USA GFDL-ESM2M 144 90 L24 g Institut Pierre-Simon Laplace France IPSL-CM5A-LR 96 96 L39 h Institut Pierre-Simon Laplace France IPSL-CM5A-MR 144 143 L39 i Max Planck Institute for Meteorology Germany MPI-ESM-LR 192 96 L47 j Max Planck Institute for Meteorology Germany MPI-ESM-MR 192 96 L95 8

There are four different scenarios for each model: Historical (20C3M) (1980-2004, 25 years), Pre-industrial (picontrol, 25 years), RCP4.5 (2076-2099, 25 years) and RCP8.5 (2076-2099, 25 years). The latter two scenarios (Representative Concentration Pathways, RCP4.5 and RCP8.5) correspond to the total radiative forcing due to anthropogenic emissions in future. Specifically, RCP4.5 has a stabilized radiation forcing pathway to 4.5 W/m 2 (~550 ppm CO2 concentration) by 2100 while RCP8.5 (~1000ppm CO2 concentration) has a rising pathway leading to 8.5 W/m 2 by 2100 (Meinshausen et al., 2011), as displayed in figure 7. Fig. 7 Total radiative forcing (anthropogenic plus natural) for RCPs. (Adopted from Meinshausen et al., 2011) 4 Methodology 4.1 Definition of the jet latitude and speed In this study, the jet streams are based on the eddy-driven jet component at low levels (Woollings et al., 2010b). They suggested that the variability reflects changes in the eddy-driven component because of the interaction between the eddy forcing and wind variations. Actually, the eddy-driven jet extends to the whole troposphere while the subtropical jet is restricted to the upper troposphere, as illustrated in figure 8. As a result, it is suitable to diagnose the jet stream from the low level wind fields. The imaginary 9

jet stream is constructed by vertically averaging the daily mean zonal wind over the 925hPa 700hPa. The wind field is then zonally averaged over the North Atlantic sector (0 60 W, 15 75 N) for ERA-40. However, for the CMIP5 models, only 850hPa 700hPa is selected because of the present of subtropical westerlies aloft (Barnes and Polvani, 2013). Meanwhile, the North Atlantic sector (0 60 W, 0 90 N) is used in the model simulations. After that, a 10-day Lanczos filter is applied to low-pass filter out the noise associated with individual synoptic systems. Finally, the maximum wind speed can be found in the wind profile which is defined as the jet speed. The latitude for this maximum wind speed is defined as the jet latitude. Fig. 8 Composites of the zonal wind averaged over 0-60 W for the three jet stream locations. (Adopted from Woollings et al., 2010b) 4.2 Seasonality of jet latitude and wind speed The jet variability is strongly linked to different seasons. Both jet latitude and wind speed are clearly altering over a year. The daily mean latitude and smoothed cycle are used to examine the seasonality of jet latitude. The smoothed cycle (as known as the 10

climatology jet latitude) is calculated by averaging over all years and then filtering with Fourier transforms, followed by retaining only the mean and the lowest two frequencies (Woollings et al., 2010b). In addition, the jet latitude anomalies reported in this study are also estimated by subtracting this smoothed jet latitude. These anomalies are then used to find the monthly mean biases with respect to the historical data. On the other hand, the boxplot and the monthly mean bias are the tools to examine the seasonality of wind speed. In the boxplot, the central line in the box is the median. The top and bottom of the box are the upper and lower quartiles, respectively. The difference between them is called the Inter-Quartiles Range (IQR) which states the spread of the data. The whiskers mean the nearest value is still within 1.5 IQR of the both upper and lower quartiles. While the points are beyond the whiskers, they will be drawn individually (Hannachi et al., 2013). 4.3 Probability density function Apart from the seasonality, the jet latitude distribution is another way to study the jet variability. The analysis mainly concerns on the winter season which is defined by four months (December March, DJFM), because the polar jet is stronger and is not merge with subtropical jets. As stated from above section, the jets shift to poleward or equatorward accordingly rather than steady at certain latitude. Figure 9 illustrates the jet latitude time series in winter. The jet roughly moves between 30 and 60 N. In order to study this time series, the probability density functions (pdfs) are used associate with a kernel density estimation (Silverma, 1981). The standing smoothing parameter h = 1.06σn 1/5 has been applied, with σ and n representing the standard deviation and the sample size of the time series, respectively. Fig. 9 The 10-day low-pass filtered winds averaged over 925-700hPa and 0-60 W for the winter of 2001/02. (Adopted from Woollings et al., 2010b) 11

4.4 Skewness and excess kurtosis Besides the raw and central mathematical moments (mean and variance), the third and fourth standardized moments (skewness and excess kurtosis) are also used in particular to analyze the probability density functions of jet latitude. Skewness is a measure of symmetry. There are two types of skewness which are positive skewness and negative skewness. As illustrated in figure 10(top), the positive skewness reflects the peak towards the left and the right tail is longer, and vice versa. If the skewness is zero, the distribution can be act as normal or symmetrical. Apart from skewness, the height and sharpness of the peak is measured by a number called kurtosis. The normal distribution has a kurtosis of 3. As shown in figure 10(bottom), the positive excess kurtosis means the kurtosis of the distribution is larger than 3 and the peak is higher and sharper. The negative excess kurtosis is flipped around. The shape of the jet distribution are finally customized to a number for further analysis. In other words, the difference between two pdfs can be numerically measured by the skewness and excess kurtosis. Given that the standard deviations of skewness and excess kurtosis are 6/n and 2 6/n, the statistical test can be performed to check the significance. Fig. 10 The distribution for (top) skewness and (bottom) excess kurtosis. (Adopted from the website: Financial Planning Body of Knowledge skewness and excess kurtosis) 12

4.5 Jet persistence There are various methods to measure the jet persistence, as demonstrated by Barnes and Hartmann (2010a, 2010b) and Hannachi et al. (2013). The latter one method is employed in this study. The persistence is measured by the area under the autocorrelation curve of jet latitude between 0 and 10 days. The autocorrelation is a correlation coefficient. However, it is a time series of the correlation between the past and present values of the same variables rather than the correlation between two variables. If the correlation is larger, the area under the curve is thus bigger, as well as the persistence. 5 Results 5.1 ERA-40 jet latitude and wind speed Before showing the CMIP5 model simulations, the general properties of jet stream from the historical data ERA-40 are provided at first. Those properties such as the seasonal cycle, the daily jet latitude and the pdfs of jet latitude in winter are shown in figure 11. Figure 11(a) shows the seasonal cycle of jet latitude based on the daily average over the years. Besides that, the smoothed cycle is also plotted in the same figure. Generally, the seasonal cycle presents the poleward shifted jets in summer and equatorward shifted jets in winter by around 4 variation, although there is a small poleward shift due to an extreme case in February. This North-South variation is consistent with the changes of meridional temperature gradients over a year. The cycle also shows a lag response to the insolation. For instance, the poleward shifted states are reached after the summer solstice, mainly during July to October. The same response can be found during cold months. The seasonal cycle of jet speed is illustrated in figure 11(b). It is a boxplot of the wind speed which is plotted by averaging the daily zonal wind speed over the years then dividing into 12 month boxes. The detail of the boxplot has been discussed in section 4.2.1. Normally, the wind speed is weaker in summer and stronger in winter, which can be clearly pointed out by the central median line. The amplitude of the cycle over a year is around 5 ms -1. Such seasonal variation is as expected with the effect of meridional temperature gradients. Regarding the spread of wind speed in each month, the minimum variation can be found in July when the jet is around the weakest. In other 13

words, the wind speed is nearly at minimum and the jet latitude is at maximum. Interestingly, the cycle seems to be asymmetric which is alike to the latitude seasonal cycle. The wind speed rapidly decreases from its maximum in January to its minimum in May, but the strengthening rate is relatively slower. The physical mechanism is still unknown which is also stated by Woollings et al. (2013). Apart from the seasonal cycle, the persistence is another feature of jet variability. Figure 11(c) presents the jet latitude during the first 500 winter days which can give a brief view about the persistence. The jets always locate around the preferred latitudes (30 to 60 ) in winter. The same result can be found by plotting the last 500 winter days (not shown). In addition, the jets tend to remain at similar latitude for a while but not fluctuating from day to day. This feature can be easily observed at lower latitude. As demonstrated by Barnes and Hartmann (2010b) and Barnes et al. (2010), the turning latitude caused by the sphericity of Earth can prevent Rossby wave from breaking because of the effects of Rossby parameter (β). Thus, the positive feedback between eddies and mean flow is decreased, therefore the eddy reinforcement is less because eddies are likely to turn before breaking. The jet is then less self-sustained and the variability also changes from a shift to a pulse. As a result, the poleward shifted jet is always less persistent than the equatorward shifted jet. The persistence is further examined by using the kernel pdf estimation (Silverman, 1981). Figure 11(d) shows the histogram, the kernel pdf estimate (solid line) and the normal density function (dashed line) fitted to the total jet latitude in winter. The result agrees with the figure 11(c) that most occurrences are located within the preferred latitude. In fact, a trimodal structure can be noticed which means the preferred southern, central and northern positions of the jet, as illustrated in figure 6 and figure 8. A similar shape can be found for the jet latitude anomalies with removing the seasonal cycle as provided by Woollings et al. (2010b). They suggest that those three robust modes are associated with the mid-atlantic flow regimes (NAO and EA), as discussed in section 2.2.2. For instances, the southern jet position closely related to the Greenland blocking. The central peak could be seen where the low pressure is located at the centre of North Atlantic. The northern mode is favoured when there is a strong blocking over central Western Europe and also reduced Greenland blocking, thereby the jet stream is diverted to the North. 14

Fig. 11 ERA-40 North Atlantic jet latitude and wind speed characteristics (a) the daily mean jet latitude and smoothed seasonal cycle, (b) the boxplot of daily mean wind speed, (c) excerpt the jet latitude of the first 500 winter days and (d) the histogram and the kernel estimated pdf of the imaginary jet latitude in DJFM. 5.2 CMIP5 integrations on twentieth century (20C3M) 5.2.1 Seasonality Jet latitude As same as the ERA-40 reanalyses, the seasonal cycle of jet latitude and wind speed using the twentieth century CMIP5 model simulations (20C3M) are investigated. Figure 12 illustrates the mean and smoothed seasonal cycle of jet latitude from the 10 models used in this project. In order to examine the performances of those models, the cycle of the ERA-40 as presented in figure 11(a) is also plotted along with the simulations (bottom right corner). The general shapes are shown while there are some differences from the reanalyses. For example, the amplitude of seasonal cycle is larger than that of the reanalyses. The majority of models present more than 5 latitude change over a year, except MPI-ESM-LR (fig. 12i) that simulates the cycle nicely. Some 15

extreme cases are BCC-CSM1-1 (fig. 12a) and BNU-ESM (fig. 12b) which is around 10 compared to 4 for the reanalyses. In fact, this large amplitude might be caused by the over prediction of both maximum and minimum jet latitude. In other words, the peak and trough become sharpening. From the historical cycle, there are two flat regions/states in the first and second half of a year. The maximum and minimum points could be barely found in mid-april and July, respectively. Specifically, the jet latitude increases gradually from May. The high phase is reached in July, it remains stable until November. Then, it returns to the low phase until May. In contrast, many models have a robust peak and trough instead, particularly for the peak. The minimum latitude is shifted equatorward by up to 5 whereas the maximum is also shifted poleward about 5. The similar feature is also found by Hannachi et al. (2013) in CMIP3 models. However, in general, this overestimation of CMIP5 is relatively lower than that of CMIP3. Interestingly, there are several models demonstrate a double peak such as two GFDL models (fig. 12 e,f). Apart from the major peak latitude in mid-summer, there is also a minor peak around mid-winter which contradicts to the strong jet or the high temperature gradient during that period. Besides the shifted latitudes, the time of the peak/ trough occurrence is also shifted. For instances, the peak is shifted from July to August and the trough is shifted from mid-april to March compared to the reanalyses. These changes can be found for almost every models, especially in FGOALS-G2 (fig. 12d) and IPSL-CM5A-MR (fig. 12h). The equatorward and poleward shift of seasonality in CMIP3 models are also observed by Kidson and Gerber (2010) and Woollings and Blackburn (2012). In order to further investigate the seasonal errors in CMIP5 models, the biases between the seasonal anomalies of the model simulations and that of the ERA-40 are presented in figure 13. The seasonal anomalies are computed by subtracting the annual mean, because the average bias of each model, with respect to ERA-40, is not an important element for investigating the seasonal response. Clearly, all models have negative bias of latitude anomalies in November and December. The jets lie more equatorward at the beginning of winter. A positive bias in August and September indicates that the latitudes place more poleward at the end of summer. In the other months, there is no integrated response from the models. The individual response is diverted differently for each model. Overall speaking, the seasonal error is about 1-2 for the majority of models, except BCC-CSM1-1(fig.13a) and BNU-ESM (fig.13b). It is smaller than that of CMIP3 which is about 5, as indicated by Hannachi et al. (2013). Thus, the models have fairly good performance compared to CMIP3, particularly for MPI-ESM-LR (fig. 13i). 16

Fig. 12 The seasonal cycle of mean and smoothed jet latitude from 20C3M in CMIP5 and ERA40. Fig. 13 The seasonal cycle of mean anomaly jet latitude bias from 20C3M in CMIP5 with respect to ERA40. The anomaly is computed by subtracting the annual mean. 17

5.2.2 Seasonality Wind speed The seasonal cycles of wind speed from CMIP5 models are performed in figure 14, along with the ERA-40 reanalyses. In general, the phase of seasonal cycle from simulations is quite similar to the historical data, especially for CANESM2 (fig.14c), MPI-ESM-LR (fig. 14i) and MP-ESM-MR (fig.14j). It is not surprising that the minimum speed can be found in summer whereas the maximum is located in winter. However, some models illustrate a doubled amplitude of seasonal variation such as IPSL-CM5A-LR (fig. 14g) and IPSL-CM5A-MR (fig. 14h) which is about 10 ms -1. For the other models, it is around 6 to 8 ms -1 which is relatively small compared to the old CMIP3 models, as stated by Hannachi et al. (2013). They also suggest that both maximum and minimum values become more extreme. A sharp dip minimum in July can be easily found in the majority models. This feature is maintained in CMIP5 models. In order to form a concrete comparison between the models and reanalyses, the bias between the monthly mean wind speed of CMIP5 and that of ERA-40 is demonstrated in figure 15. All models have a positive bias over a year. Only two exceptional models from IPSL (fig. 15g and 15h) show an under estimation in summer. Thus, despite the phase between the models and ERA-40 is similar, the monthly mean of the wind speed is actually overestimated by the models together with the spread of wind speed in each month. The bias of monthly standard deviation of wind speed also have similar positive bias with the mean plot (not shown). 18

Fig. 14 The boxplot of the daily mean wind speed from 20C3M in CMIP5 and ERA40. Fig. 15 The seasonal cycle of mean wind speed bias from 20C3M in CMIP5 with respect to ERA40 19

5.2.3 Probability distribution jet latitude The kernel estimates of absolute jet latitude pdfs in winter (DJFM) are presented in figure 16. The similar results can be found for the anomaly jet latitude pdfs (not shown). Basically, the significant trimodal feature of ERA-40 s pdf (bottom right corner) is no longer exist in all CMIP5 models. Some pdfs have slightly signature of multimodality such as MPI-ESM-LR (fig. 16i) and MPI-ESM-MR (fig. 16j). On the contrary, IPSL- CM5A-LR (fig. 16g) and IPSL-CM5A-MR (fig. 16h) just simulate the pdfs with unimodal structure. Generally, most models are peaked round the central position (47 N). A positive kurtosis is presented with respect to the normal distribution. While a negative kurtosis is found in the ERA-40 because of the relatively broad probability distribution. To sum up, the occurrence at central position is overestimated whereas the pdfs at southern and northern positions are reduced. The reason might be caused by the under estimation of the blocking systems in Northern Atlantic. However, compared to the CMIP3 models which are used in Hannachi et al. (2013), the CMIP5 models are less positive skewed in overall. This feature is supported by the improvement of European blocking frequency in higher resolution models (Berckmans et al., 2012). In addition, similar to CMIP3 models, the new models roughly also show a narrow pdfs compared to ERA-40, except IPSL-CM5A-LR (fig. 16g). It means the spread of jet latitude is underestimated because the width is based on the standard deviation (h = 1.06 σn 1/5 ). The probability distribution of jet latitude is further examined by calculating the pdf difference between the models and the ERA-40 which is illustrated in figure 17. Most of them are with an overestimated central jet, meanwhile, both southern and northern jet are reduced. Most models even show a greater underestimation at northern jet than at southern jet such as two IPSL models (fig. 17g, h) and two MPI models (fig. 17i, j). Thus, the European blocking should be too far under predicted. This feature agrees the suggestion by Dunn-Sigouin and Son (2012) that the Euro-Atlantic blocking frequency in CMIP5 simulations is underestimated during the cold season. However, there is an exceptional case like FGOALS-G2 (fig. 16d). The pdf at southern position are higher and have a positive skewness compared to the reanalyses. The mode of central jet is also missing. The overestimated southern jet and underestimated northern jet is shown in figure 17d. Thus, the Greenland blocking might be over predicted in this model. Obviously, the performance of the jet distribution is increased with the higher resolution, because the MPI and GDFL models have the least difference with respect to reanalyses. In fact, they have the highest and second highest resolution among all the CMIP5 models. However, in terms of the seasonality, the higher resolution models seem not to have a significant advantage, as shown in section 5.2.1 and 5.2.2. 20

Fig. 16 The histogram and kernel-estimate pdfs of the DJFM jet stream latitude time series from 20C3M in CMIP5 models and ERA-40. Fig. 17 The frequency difference between the 20C3M simulations and ERA-40. 21

5.3 Climate change scenarios - RCP 4.5 and RCP 8.5 In this section, the effects of climate change on the North Atlantic jet are discussed. The effects of two climate change scenarios, namely RCP4.5 and RCP8.5, on both jet latitude and wind speed are presented. The responses are computed by comparing these two scenarios with the pre-industrial control run which shows a fairly good similarity to the historical data (not shown). 5.3.1 Jet latitude In general, the effects of both scenarios on the jet latitude seasonal cycle are not significant. The seasonality of jet latitude in all models tends to remain unchanged (not shown), for instances, an equatorward jet in winter and a poleward jet in summer. The amplitude variation is also similar to that in control run. Consequently, the effects are discussed mainly on the probability distribution of jet latitude in the following. The pdfs of the RCP4.5 scenario in winter are shown in figure 18. The additional forcing seems to be no effect on the jet variability (unimodal shape). Most features in control runs also exhibit in RCP4.5 runs, for examples, the positive skewness in FOALS-G2 (fig. 18d) and sharply peak in both IPSL models (fig. 18g, h). Regarding the response of central peak, some signatures of sharpening the peak can be seen in both IPSL models. In fact, it is not easy to draw a concrete conclusion from here. Hence, the differences between the pdfs of control runs and forcing runs are plotted in figure 19. A more distinctive effect of RCP4.5 forcing on the pdfs can be noticed in the figure, especially in these five models: BNU-ESM, two IPSL models and two MPI models. However, the responses are not consistent among these models. For instances, the first model gives the response with a weakening frequency at mid-latitudes but strengthening around 33 N and 53 N. On the contrary, the latter four models (IPSL and MPI) have the opposite responses that are the sharpening central peak and reduced southern and northern jet frequency. Surprisingly, none of these responses show a fairly strong agreement with the well-established response that a poleward shifted jet is induced by the anthropogenic forcing (Kushner et al., 2001; Lorenz and Deweaver, 2007; Woollings and Blackburn, 2012). As a results, the external forcing is then increased to 8.5 for further investigation. 22

Fig. 18 The histogram and kernel-estimate pdfs of the DJFM jet stream latitude time series from RCP4.5 in CMIP5 models. Fig. 19 The frequency difference between the RCP4.5 simulations and control run. 23

Basically, the responses of RCP8.5 on the latitude pdfs are nearly the same with the responses of RCP4.5 and control runs which is presented in figure 20. A similar unimodal probability distribution is found for all models again. For the pdfs differences between the RCP8.5 and control runs in figure 21, two significant features of external forcing are clearly displayed. Firstly, more than half models (fig. 21b to 21g) present the poleward shifted effect from the anthropogenic forcing which is a well-known response. This poleward shifted jet can be simply linked to the NAO and EA patterns, as suggested by Woollings and Blackburn (2012) that both NAO and EA indices are increased in response to the external forcing. In fact, an increase in the NAO corresponds to a poleward shifted jet whereas an increased EA has more contribution to a strengthening of the jet. The response of forcing on the wind speed is discussed in section 5.3.2. In addition, a dynamical interpretation for this poleward shifted jet is further demonstrated by Riviere (2011) using a simple dry atmospheric global climate model. The global warming can enhance the upper-tropospheric baroclinicity which tends to favour the anti-cyclonic breaking because of the longer waves amplitude. Thus, the averaged poleward momentum fluxes increase and move the jets more poleward. Apart from the poleward shifted effect, however, the last three CMIP5 models in the figure such as IPSL-CA5M-MR and two MPI models have a slightly different effect. Their responses are not purely dominated by poleward shifted jet. The occurrence of the jets which are located above 50 N is also decreased. The peak of those pdfs remain robust in central position which is still consistent with the responses of RCP4.5 runs. The mechanism for this complicated response is still unknown. However, these models seem to agree with the reduction of multimodality. It might be related to the reduced blocking frequency over the north Atlantic in RCP8.5 runs, especially in fall and winter (Dunn-Sigouin and Son, 2012). Accordingly, the jets are then less disturbed by the blocking systems and keep staying around at central position, it is also associated with an increase of the NAO. A positive NAO means less favour to blocking event. Overall speaking, it is still reasonable to have different responses from the models, because the North Atlantic jet is influenced by many factors which can be produced from the ocean to the stratosphere (Woollings, 2010). 24

Fig. 20 The histogram and kernel-estimate pdfs of the DJFM jet stream latitude time series from RCP8.5 in CMIP5 models. Fig. 21 The frequency difference between the RCP8.5 simulations and control run. 25

5.3.2 Wind speed Generally, the effects of external forcing on the seasonal cycle of wind speed are similar to the jet latitude responses from above. There is no significant response of the seasonal cycle for both RCP4.5 and RCP8.5 runs which means similar to seasonal cycle of the control run. The minimum wind speed is presented in summer and the maximum speed can be found during the wintertime (not shown). The mean difference and standard deviation difference of wind speed between both scenarios and control runs are then analyzed in this sub-section. However, as demonstrated from the last section, the effects of RCP4.5 can merely be noted. Consequently, the results of RCP8.5 are then selected to discuss in this part. In figure 22, the mean speed differences between control run and RCP8.5 in winter are plotted. There is no strong agreement can be drawn for the seasonal changes, because the models show their response individually. However, for the overall changes (sum up all the monthly difference), there are 50% of total models performing an increase of wind speed over a year (e.g. two GFDL models, two IPSL models and MPI- ESM-MR). Meanwhile, the other models show rather a large spread of projections. In fact, Woollings and Blackburn (2012) stated that there is no consistent response among the CMIP3 models on the north Atlantic jet wind speed, especially in winter. Barnes and Polvani (2013) also reported that the north Atlantic jet speed remains nearly constant for the external forcing (RCP8.5) in CMIP5 models. Nevertheless, at least half of the models are consistent with the well-established effect that wind speed is strengthened by the global warming (Lorenz and Deweaver, 2007; Raisanen, 2003; Woollings and Blackburn, 2012). However, an increase of wind speed seems to contradict the fundamental knowledge of the jet mechanism. It is straight forward to think that the wind speed should be decreased by global warming. According to the Arctic amplification, the polar region has stronger effect by the climate change. Then, the temperature increases greater than that at equator. As a result, the wind speed might be decreased by the weaker low-level temperature gradient between the equator and the pole. Francis and Vavrus (2012) introduced the similar mechanism for jet response to the anthropogenic forcing. In the reality, Archer and Caldeira (2008) also found that the jet strength has a small decrease in northern hemisphere but a relatively high increase in southern hemisphere in winter during 1979 2001. In fact, jet stream has a complex nature, the above mechanism might not be the only reason to explain the response of jet strength. Some studies suggested rather the opposite response that is an increase of wind speed for the climate change. 26

Lorenz and DeWeaver (2007) and Raisanen (2003) found that a raise in the tropopause height actually has a dominate effect to the wind speed, while the low-level meridional temperature gradient plays a secondary role only. The external forcing cause cooling in the stratosphere and warming in the troposphere and such changes decrease the static stability nearly the tropopause. In other words, a higher tropopause is induced by the forcing. It is more favourable to the synoptic eddy activity, thus an increase in kinetic energy and wind speed may also occur. Remarkably, the correlation between tropopause height and wind speed is smaller at Northern Hemisphere than that at Southern Hemisphere. This may explain why not all the models are with an increase of wind speed in North Atlantic. At last, for the effect on the variation of seasonal wind speed, Barnes and Polvani (2013) suggested that the jet variability in north Atlantic becomes more change in jet speed and less wobble of a meridional jet. However, there is no consistent result from the monthly standard deviation differences of wind speed which are shown in figure 23. There is no clear effect on the wind speed variation for both seasonally and over a year. The responses from each month and each model are varied differently. As a result, a further analysis should be made for explaining the mechanism of more changing in wind speed. 27

Fig. 22 The seasonal cycle of mean wind speed bias in RCP8.5 with respect to the control run. Fig. 23 The seasonal cycle of wind speed standard deviation bias in RCP8.5 with respect to the control run. 28

6 Discussion 6.1 Climate change on skewness and excess kurtosis In the above section, the effects of climate change on the jet latitude have been discussed. As suggested by Hannachi et al. (2013), the effects can be further examined by finding the differences of skewness and excess kurtosis between the forcing scenarios and control run. The following analyses may provide an extra agreement or disagreement to the previous findings. 6.1.1 Skewness It is well-known that the jet latitude tends to move poleward under the global warming. This feature can be easily proved by testing the skewness difference. The positive skewness means the pdfs shifted to equatorward, and vice versa. Recently, Barnes and Polvani (2013) demonstrated that a decrease of skewness is found for poleward shifted jet in CMIP5 models with RCP8.5 forcing. However, for the CMIP5 models used in this study, the differences between two forcing scenarios and control run in winter are quite small which are presented in figure 24(a). The 5% significant level is shown by the shaded area. In general, there are 4 out of 20 simulations with the increase of skewness while 5 simulations are with significantly reduced skewness. There is only one model has a negative change in skewness for both forcing scenarios which is BNU- ESM (model b). The warming effects on the skewness are not robust. In order to have an ensemble effect, the multi-model mean changes of skewness for RCP4.5 and RCP8.5 are estimated which are -0.04 and -0.03, respectively. These changes are both significantly different from zero at 5% level. Clearly, the skewness just slightly decrease for both forcing scenarios. In other words, the jet latitudes shift slightly to the pole under the global warming. Nevertheless, this results seem to agree the section 5.3.1 findings that the poleward shifted jets are discovered in some models of RCP8.5 case (see figure 21). They are also consistent and comparable with the CMIP3 results from Hannachi et al. (2013) using the same approach. 6.1.2 Excess kurtosis Apart from the skewness, the alternative approach of testing the pdf changes can be also applied to the change of excess kurtosis which is also evaluated in figure 24(b). In 29