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 20th 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 21st 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
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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
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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
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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.
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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 5th 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
China
BCC-CSM1-1
128×64 L26
Meteorological Administration
b
Beijing Normal University
China
BNU-ESM
128×64 L26
c
Canadian Centre for Climate
Canada
CanESM2
128×64 L35
China
FGOALS-s2
128×108 L26
USA
GFDL-ESM2G
144×90 L24
USA
GFDL-ESM2M
144×90 L24
Modelling and Analysis
d
Institute of Atmospheric Physics,
Chinese Academy of Sciences
e
Geophysical Fluid Dynamics
Laboratory
f
Geophysical Fluid Dynamics
Laboratory
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
Germany
MPI-ESM-LR
192×96 L47
Germany
MPI-ESM-MR
192×96 L95
Meteorology
j
Max Planck Institute for
Meteorology
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/m2 (~550 ppm CO2 concentration) by 2100 while RCP8.5
(~1000ppm CO2 concentration) has a rising pathway leading to 8.5 W/m2 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)
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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)
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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
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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.
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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, IPSLCM5A-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 MPIESM-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 BNUESM (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
general, the multi-model mean change of excess kurtosis for RCP4.5 and RCP8.5 are
positive with significantly greater than zero at 5% level which are 0.19 and 0.11,
respectively. Again, they are consistent with the CMIP3 models by Hannachi et al.
(2013). It means the jet latitude becomes less flat and more peaked by adding the
external forcing. This can be linked to a decrease of the possibility of multimodality as
discussed in section 5.3.1. However, the individual results show the same as the
skewness that the response of each model is different. There are 7 out of 20 simulations
with an increase excess kurtosis, while 3 simulations give the opposite response. These
10 simulations are significantly different from zero at 5% level. Interestingly, an
increase of excess kurtosis is mainly dominated by the last three models which are
IPSL-CA5M-MR (model h) and two MPI models (model i and j). The excess kurtosis
is increased significantly by both RCP4.5 and RCP8.5 scenarios. It can be said that the
external forcing affects the pdfs to be unimodal structure quite strongly in these
particular models.
Fig. 24 The (a) skewness and (b) kurtosis difference between the forced scenarios (RCP4.5 - open circles,
RCP8.5 - filled circles) and control run. The shading represents the 5% significance level.
30
6.2 Jet latitude
In this sub-section, the mean jet latitude is further examined by testing the relation with
other moments such as standard deviation, skewness and excess kurtosis. Four model
simulations (20C3M, control, RCP4.5 and RCP8.5) in winter months (DJFM) are used.
The mean jet latitude, standard deviation, skewness and excess kurtosis are calculated
for each month. Accordingly, there are 160 points and a point of ERA-40 in each test.
6.2.1 Jet latitude versus standard deviation
Figure 25 shows a scatter plot of the mean jet latitude versus standard deviation in
winter months. There is only a weak negative correlation (-0.1) between them and the
slope of the regression line is also without the statistically significance. This result
seems not fully agree with the finding from Hannachi et al. (2013). They found a
statistically significant negative correlation (-0.42) in CMIP3 models which is more
robust than in here. In order to test the contribution of each model to that negative
correlation in CMIP5 models, the models are then examined individually. Surprisingly,
there are only three models showing the negative correlation such as CANESM2,
FGOALS-G2 and IPSL-CM5A-MR. Coincidentally, these models can also be found in
the CMIP3 models selected by Hannachi et al. (2013). On the other hand, the other
CMIP5 models have either positive or zero correlation. As a result, the above weak
negative correlation might be caused by individual performance or characteristic of
each model.
Barnes and Hartmann (2011) also found similar negative correlation in a
barotropic model. They observed that the narrowing of pdfs histograms (smaller spread)
can be found for moving the jet to the pole. The jet variability is transited from a
meridional shift to a more change of jet speed. However, for the CMIP5 models selected
in this paper, the more narrowing pdfs are found in the twentieth century simulations,
compared to ERA-40. At the same time, the mean jet latitudes are also equatorward
shifted. These contradict to the negative correlation between the mean jet latitude and
standard deviation. To conclude, the mechanism behind the relationship seems not to
be straight forward, a further analysis for this topic should be done.
31
Fig. 25 Mean jet latitude versus standard deviation. (20C3M- triangle, control – circle, RCP4.5 – square
and RCP8.5 – pentagram, filled circle – ERA40 reanalyses).
6.2.2 Jet latitude versus skewness
The relationship between the mean jet latitude and the skewness is plotted in figure 26.
The ERA-40 value in winter can be found within the cluster that the mean jet latitude
is around 47°N and skewness equals to 0.1. Most simulations show a positively skewed
and equatorward results. Notably, a strong negative correlation (-0.69) can be found.
The R-squared value is also relatively large which is about 0.47. The slope of the
regression line is statistically significant different with zero at 5% level. It means the
equatorward jet has more positively skewed jet latitude and the pdfs become more
symmetric as the jet moves toward high latitude. This result is consistent with the
previous finding from Barnes and Hartmann (2010a). They suggested that the negative
skewness can be limited by the reduction of wave breaking near the pole and the eddyfeedback. In fact, there are only 6 out of 160 simulations give the negative skewness.
On the other hand, the mid-latitude jets also have less probability distribution to
subtropics because of the existence of subtropical jets. As a result, the pdfs become
more symmetric when the mean jets move poleward.
32
Fig. 26 Mean jet latitude versus skewness. (20C3M- triangle, control – circle, RCP4.5 – square and
RCP8.5 – pentagram, filled circle – ERA40 reanalyses).
6.2.3 Jet latitude versus excess kurtosis
Figure 27 shows the correlation between the mean jet latitude and excess kurtosis in
winter. The ERA-40 value in winter is also located within the cluster that the mean jet
latitude is around 47°N and excess kurtosis equals to -0.5. Most data from the four
model runs are more peaked and more equatorward with respect to ERA-40.
Importantly, a negative correlation (-0.44) with small R-squared value (0.19) between
the mean jet latitude and excess kurtosis is presented. The slope of the regression line
is significantly different from zero at the 5% significance level. Despite it means the
pdfs are less peaked (smaller value) when the jet move to poleward. In fact, the excess
kurtosis even turns to a negative value when the jet latitude is higher than around 45°N.
It is because the blocking events can occur frequently in the northern part of north
Atlantic which is called ‘high-latitude blocking’ (Woollings and Hoskins, 2008).
Consequently, the jets are then diverted to the southern position or/and the northern
position. Thus, the occurrence at central position become less and the distribution
becomes broader and less peaked than the normal distribution (a more negative value).
33
Fig. 27 Mean jet latitude versus excess kurtosis. (20C3M- triangle, control – circle, RCP4.5 – square and
RCP8.5 – pentagram, filled circle – ERA40 reanalyses).
6.3 Persistence
From the previous studies such as Barnes and Hartmann (2010b), Hannachi et al. (2013)
and Kidston and Vallis (2010), they reported that the jet persistence is correlated to the
jet latitude in CMIP3 models, as well as the parameters in last section such as standard
deviation, skewness and excess kurtosis. Generally, in the selected 10 CMIP5 models,
these features are less significant or even opposite to the above studies. Nevertheless,
they are still briefly discussed and documented in this section. As same as the method
used in last section, all simulations (20C3M, control, RCP4.5 and RCP8.5) in winter
days (DJFM) are used to provide the monthly persistence, mean jet latitude, standard
deviation, skewness and kurtosis. In other words, there are 16 points for each model
and 10 models in total. The correlation from the ERA-40 is also presented which is with
a filled circle.
At first, the correlation between the jet persistence and mean jet latitude is shown
in figure 28(a). Only a small negative correlation (-0.01) between the persistence and
34
jet latitude is presented. The R-squared value (0.0001) and the slope (-0.004) which is
without statistically significance. These values are also very small in this case. There is
no strong agreement with Barnes and Hartmann (2010b) and Kidston and Vallis (2010)
that the persistence decreases as the jet moves to pole because of the weaker eddies
feedback. In fact, this mechanism is true for the ERA-40 data, as discussed in section
5.1. However, it become less robust if all model simulations are included. Thus, the
four types of model run are investigated individually. Surprisingly, the mixture of 20th
century and control runs show a relatively large negative correlation (-0.17) compared
to -0.01 from above. However, in the mixture of both RCP4.5 and RCP8.5, a positive
correlation (0.14) can be found. The climate change seems to shift the correlation
between the persistence and mean latitude in winter months. However, such result are
not representative because of the small R-squared value and without statistically
significance. In order to examine the warming effect on the correlation between the
persistence and latitude, it should be further analyzed by a barotropic model.
For the relationship between persistence and skewness, a positive correlation (0.14)
can be found in CMIP5 models, see figure 28(b). The slope of the regression is 0.29
which is significantly greater than zero at 5% level and the R-squared value is 0.02. For
the individual response of each run, all four integrations also show a positive correlation
between the persistence and skewness. The negative skewness is presented if the jet
persistence is small. This shows a strong agreement with the previous findings that both
skewness and persistence decrease with the mean jet latitude, as discussed in section
6.2.2 and the above paragraph. In other words, the poleward shifted jets tend to have
negative skewness and therefore the persistence is shorter. To sum up, the relationship
between the jet latitude, skewness and persistence is consistent in these CMIP5 models.
As same as the skewness, both standard deviation and excess kurtosis also
decrease with the latitude, see section 6.2.1 and 6.2.3. Thereby, a positive correlation
between these two parameters and the persistence is expected because of the
relationship between the persistence and latitude. In fact, Hannachi et al. (2013) also
presented that the persistence are positively correlated with the standard deviation.
However, for the CMIP5 models used in this study, the positively correlation is no
longer exist for both standard deviation and excess kurtosis, as illustrated in figure 28(c)
and 28(d), respectively. Both of them show a slightly negatively or nearly zero
correlation to the persistence which are -0.06 and -0.04, respectively. The slope of
regression lines are not statistical significantly different from zero. This is also true for
four individual runs. As a result, the relationships between the persistence and these
two parameters still remain unknown. More models should be included to increase the
sample size and then find a representative conclusion.
35
Fig. 28 The jet persistence versus (a) jet latitude, (b) standard deviation, (c) skewness and (d) excess
kurtosis. (20C3M- triangle, control – circle, RCP4.5 – square and RCP8.5 – pentagram, filled circle –
ERA40 reanalyses).
6.4 Comparison between CMIP3 and CMIP5 models
As presented in section 5.2, the performance of CMIP5 models in the 20th century
simulation seems to be comparable to ERA-40 historical data. In order to find the
improvement by the upgraded models, some are selected to directly compare with the
CMIP3 models presented in Hannachi et al. (2013). However, according to the limited
model provision, there are only three centres providing both CMIP3 and CMIP5 models.
They are the centres from Canada, USA and France, see details in table 2. For the
France models, one additional model is provided in CMIP5 models. As a result, there
are four CMIP3 models but five CMIP5 models in total. Similar to section 5.2, the
seasonality of jet latitude, the seasonality of wind speed and the jet latitude pdfs are
studied in the following sub-sections, by indicating the difference between the 20th
century simulations and ERA-40 with centre by centre basis.
36
Table.2 The three selected centres for comparison
Canada
USA
France
CMIP3
CMIP5
CGCM3.1
GFDL-CM2.0 and
GFDL-CM2.1
IPSL-CM4
CanESM2
GFDL-ESM2G and
GFDL-ESM2M
IPSL-CM5A-LR and
IPSL-CM5A-MR
6.4.1 Seasonality – jet latitude
Figure 29 show the seasonal cycle of anomalies jet latitude bias with respect to ERA40 in CMIP3 and CMIP5 models, respectively. They are obtained by subtracting the
annual mean. Overall speaking, as discussed in 5.2.1, the performances of seasonality
in CMIP5 models are slightly better than that in CMIP3 models. However, there is no
huge improvement by the selected CMIP5 models in this part. The latitude bias is still
around -2° to 2° which is comparable to the CMIP3 models. In these selected 3 centres’
models, the equatorward shifted jet in winter (November to March) and poleward
shifted jet in summer (July to September) can be found in the Canadian CMIP3 model.
This feature is less robust in the CMIP5 models. In addition, in the USA’s models, the
poleward shifted jets in late summer (August and September) and the equatorward
shifted jets in early winter (November and December) are also presented for CMIP3
and CMIP5 models.
6.4.2 Seasonality – wind speed
The differences between the old and new models are greater in the seasonality of wind
speed, see figure 30. They are the seasonal cycle of mean wind speed bias compared to
ERA-40. Basically, all the patterns of seasonal cycle are maintained in CMIP5 models
compared to CMIP3 models. For instances, the overestimated wind speed for all
Canadian and USA’s models. Also, the underestimated wind speed in summer only in
the French models. These overestimated and underestimated wind speed are with
respected to ERA-40. Besides the preserved patterns, no improvement can be found for
all models. Interestingly, the biases become even larger in CMIP5 models. It is quite
difficult to understand the mechanism behind this increasing trend of wind speed. In
order to have a more definite explanation, one of the suggestions is to further analyze
the height of tropopause in CMIP5 models and check if it is more overestimated than
that in previous phase. In addition, the meridional temperature gradient can be also
examined, as the secondary role in jet strength. Actually, both Canadian and French
37
centres have increased the vertical resolution in their new models. Thus, it could be
reasonable to study the connection between the increasing vertical resolution and the
overestimation of tropopause height.
Fig. 29 The seasonal cycle of mean anomaly jet latitude bias from 20C3M with respect to ERA40 in (left)
CMIP3 and (right) CMIP5.
38
Fig. 30 The seasonal cycle of mean wind speed bias from 20C3M with respect to ERA40 in (left) CMIP3
and (right) CMIP5.
39
6.4.3 Probability distribution – jet latitude
Further analysis on the jet latitude is done by comparing the probability distribution of
jet latitude in winter, see figure 31. The frequency differences in both CMIP3 and
CMIP5 models with respect to ERA-40 are similar in overall which are between -0.02
and 0.04. There is a slightly improvement for the accuracy of jet distribution in the
USA’s models only. The difference is lower in both USA’s new models. Obviously,
the higher resolution in CMIP5 models can be one of possible reasons for the
improvement. As suggested by Scaife and Knight (2008) that the vertical resolution has
a great contribution in the model bias. However, both horizontal and vertical resolution
are the same in USA’s CMIP3 and CMIP5 models. The only enhancement between
these two phases’ models is that the more advanced land model is utilized in CMIP5
models. In fact, Berckmans et al. (2012) showed that more detailed in orography can
improve the blocking prediction which is one of the important constraint to the jet
distribution.
In addition, the shapes are also slightly different. For example, the peak in
Canadian CMIP3 model is shifted to poleward in CMIP5 model. In other words, the
distribution is less positive skewed. Similar result can be noted in USA’s models as
well. In fact, there is also a less frequency difference between these models (Canadian
and USA) and the reanalyses at northern position. These results seem to agree that the
European blocking frequency increases with the model resolution as well as the more
detailed orography in CMIP5 models. In French models, the patterns seem to be more
peaked at central position and also amplified in the new models. The jets tend to stay
around the central region of North Atlantic when the blocking frequency is low.
According to these complicated changes, the comparison in the blocking frequency
between the models in two phases should be made to further account for the above
explanation.
40
Fig. 31 The frequency difference of pdfs between 20C3M and ERA40 in (left) CMIP3 and (right)
CMIP5.
41
7 Conclusion
The performance of 10 selected CMIP5 models have been well documented by comparing
the jet latitude and wind speed to those obtained from ERA-40. Generally speaking, the
seasonal cycles of jet latitude and wind speed are comparable to the reanalyse. However,
an overestimation of wind speed for each month is presented in all models. In addition,
most of the models cannot simulate the trimodal structure of probability distribution of jet
latitude. The pdfs are in fact too narrow and peaked. This might be related to the overall
underestimation of blocking event in CMIP5 models.
Regarding the climate change scenarios, the effects from the RCP4.5 forcing are
merely observed. For the higher forcing simulations, there is no different for the seasonal
cycle of jet latitude and that of wind speed. The jet latitude distribution is slightly poleward
shifted and peaked. This feature is further agreed by finding the difference of skewness
and excess kurtosis between the forcing scenarios and control run. Beside the poleward
shifting effect, the jet is also strengthened. However, noticed that not every model shows
the same to this argument.
The correlation between the mean jet latitude and the other moments is also
performed. The other moments are the standard deviation, skewness and excess kurtosis
of the jet. Basically, these moments have a negative correlation to the mean jet latitude.
Additionally, the jet persistence shows no significant correlation to the mean jet latitude,
standard deviation and excess kurtosis while indicates a small positive correlation to the
skewness only.
A few models from 3 centres are also chosen for briefly comparing the performance
between the CMIP3 and CMIP5 phases. There is no significant difference in the
seasonality of jet latitude. However, surprisingly, the monthly bias of wind speed in the
new models is even larger than that in CMIP3. The pdfs of jet latitude in CMIP5 models
is also more poleward and peaked compared to that in the previous models.
As mentioned at the beginning that the surface weather patterns are closely related to
the jet stream at upper troposphere. From this study, the global warming effect on the jet
stream is well discussed. Undoubtedly, our ordinary life can be affected by the climate
change though the jet stream. In recent years, the frequency of severe weather events are
in fact raised because of the changes of jet stream. Besides that, the changes can also
affected our life via the aviation field, for example, the clear-air turbulence (Williams and
Joshi, 2013). Actually, the current North Atlantic flight corridor might be affected (Irvine
et al., 2013), as well as the carbon emission by aircrafts. Thus, the feedback systems could
be produced because the aircrafts are the main source of greenhouse gas. This study is
recommend to further extend in future in order to get a comprehensive view on this issue.
42
Acknowledgments
I would like to express my deepest gratitude to Prof. Abdel Hannachi for his
guidance, support and valuable comments throughout this interesting research study.
I would like to also thank Prof. Caroline Leck for her inspirational and helpful
presentation showing the practical guides and skills of the master project.
Special thanks go to Prof. Elizabeth A. Barnes for providing all the CMIP5 dataset
used in this study.
43
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