Westward shift of western North Paci c tropical cyclogenesis · Westward shift of western North Paci c tropical cyclogenesis Wu et al. (2015 ... Introduction Results Discussion

Original paperData preparation

Data processing and visualization

Westward shift of western North Pacifictropical cyclogenesis

Wu et al. (2015), Geophys. Res. Lett.doi:10.1002/2015GL063450

Jonathon S. Wright

[email protected]

21 March, 2017

http://dx.doi.org/10.1002/2015GL063450



Original paperIntroductionResultsDiscussion

Data preparationThe netCDF4 moduleThe datetime modulePre-processing

Data processing and visualizationMapping: the cartopy moduleLinear regression and correlationsMore contour plots and masked arrays



IntroductionResults

Motivation

I Tropical cyclones in Western North Pacific account for aboutone third of all TCs

I Changes in TC genesis location could affect billions of people

Previous studies indicate that TC genesis location may change

I Poleward movement of mean TC max intensity

I Large-scale changes in vertical wind shear and potentialintensity

I Changes in the distribution of mid-tropospheric RH

I More synoptic-scale disturbances in central Pacific



IntroductionResults

The tropical upper tropospheric trough

I Extends from 15◦N in the WNP to 35◦N in the ENP

I Apparent in 200 hPa wind field during boreal summer

I Strong vertical wind shear along the eastern flank limitseastward extension of TC activity in WNP

Data and methodology

I Tropical cyclone best track data: JTWC and ADT-HURSAT

I Reanalysis data: 20CR, NCEP-NCAR, ERA-Interim, JRA-25,MERRA, NCEP-DOE, CFSR

I Linear trends and correlations, with significance testing



IntroductionResults

from Wu et al., 2015

Figure 1. Monthly mean 200hPa wind field (vectors, m s−1) and vertical shear

of zonal wind between 850 hPa and 200 hPa (shaded, m s−1) during

June–November. Blue dots indicate TC genesis locations and thick green lines

show the TUTT trough line.

http://dx.doi.org/10.1002/2015GL063450



IntroductionResults


Figure 2. Time series of (a) annual mean TC genesis longitude (blue) from the

JTWC dataset and annual mean TUTT longitude (red), and (b) annual mean

TC longitude from the ADT-HURSAT data set with (blue) and without (red)

the ENSO effect.

http://dx.doi.org/10.1002/2015GL063450



IntroductionResults


Figure 3. Annual means of (a) TC formation frequency in the western and

eastern portions of the WNP basin, and (b) the difference of the tropospheric

temperature (red, K) between the tropics and the subtropics and the vertical

shear of the zonal wind (m s−1) in the TUTT region.

http://dx.doi.org/10.1002/2015GL063450



IntroductionResults


Figure 4. (a) July–November mean zonal wind speed (contour, m s−1) and the

associated trends (shaded, m s−1 decade−1) averaged over 5◦N–25◦N during

1979–2012 and (b) July–November mean temperature (contour, K) and the

associated trend (shaded, K decade−1) averaged over 145◦E–170◦W.

http://dx.doi.org/10.1002/2015GL063450



The netCDF4 moduleThe datetime modulePre-processing

Much of the data we use is in NetCDF format, which we can read(and write) using the netCDF4 module:� �

1 from netCDF4 import Dataset

23 # read in IBTraCS tropical cyclone best track data4 ncdf = Dataset(’../ data/Basin.WP.ibtracs_all.v03r08.nc’)� �

The variables are a dictionary attribute of the file variable:

In[10]: ncdf.variables.keys()

Out[10]:

[u’storm_sn’,

u’name’,

u’numObs’,

u’season’,

u’track_type’,

u’genesis_basin’,

u’num_basins’,

...]

http://netcdf4-python.googlecode.com/svn/trunk/docs/netCDF4-module.html




We need to read in several variables from the IBTraCS dataset:� �1 from netCDF4 import Dataset

23 # read in IBTraCS tropical cyclone best track data4 ncdf = Dataset(’../ data/Basin.WP.ibtracs_all.v03r08.nc’)

5 year = ncdf.variables[’season ’][:] # year6 genb = ncdf.variables[’genesis_basin ’][:] # 2 = Western North Pacific7 tc_v = ncdf.variables[’source_wind ’][:,:,10] # wind speed, in knots8 tc_y = ncdf.variables[’source_lat ’][:,:,10] # latitude of storm center9 tc_x = ncdf.variables[’source_lon ’][:,:,10] # longitude of storm center

10 tc_t = ncdf.variables[’source_time ’][:,:] # modified Julian day11 ttyp = ncdf.variables[’track_type ’][:] # 0,1 include cyclogenesis12 ncdf.close()� �

The index 10 refers to data from the Joint Typhoon WarningCenter (JTWC) in the Western Pacific, as we can see from

In[11]: ’’.join(ncdf.variables[’source’][10])

Out[11]: ’jtwc_wp’




IBTraCS stores dates as modified Julian days (number of dayssince 17 November 1858). We want storms during specific months(June–November). We can check this using datetime:� �

1 import datetime

23 # function to return month given modified Julian day4 def mjd2month(mjd ,y0=1858,m0=11,d0=17):

5 """6 A function for finding the month of a date expressed in7 days relative to some baseline date89 Variables:

10 mjd :: relative date (scalar)11 (note: arrays will not work for mjd under this approach)1213 Parameters:14 y0 :: year of baseline date15 m0 :: month of baseline date16 d0 :: day of baseline date1718 Note:19 The default date used in this function corresponds to20 the modified Julian date used by the IBTrACS data set.21 """22 date0 = datetime.datetime(year=y0, month=m0 , day=d0)

23 date1 = date0 + datetime.timedelta(days=mjd)

24 r e t u r n date1.month� �

https://docs.python.org/3/library/datetime.html




This example function is easy to use:

In[12]: print mjd2month(56628.75)

Out[12]: 12

but it is also somewhat limited. In particular, it cannot handlearrays of dates (we will learn about methods for dealing with arraysof dates later). However, the datetime module is often usefulwhen dealing with relative times like modified Julian days orsituations when we need to output dates in a particular format (seethe datetime.strftime() function).

https://docs.python.org/3/library/datetime.html#strftime-strptime-behavior




We then need to find the genesis locations, which in this case aredefined as the first time that the maximum windspeed exceeded 25knots (∼13 m s−1):� �

1 import numpy as np

23 # loop through storms and find genesis locations4 cgx = []; cgy = []; cgm = []

5 # start with all tracks that include cyclogenesis in the WP6 sdx = np.where ((( ttyp == 0) | (ttyp == 1)) & (genb == 2))[0]

7 # note that loop is over indices, not over a range!8 f o r ss i n sdx:

9 #−− check to see if the wind ever exceeds 25 knots10 i f np.any(tc_v[ss ,:] >= 25):

11 cg = np.where(tc_v[ss ,:] >= 25) [0][0]

12 #−−−−−− append lat/lon/month of cyclogenesis13 cgy.append(tc_y[ss,cg])

14 cgx.append(tc_x[ss,cg])

15 cgm.append(mjd2month(tc_t[ss,cg]))

16 # convert to arrays17 cgy = np.array(cgy)

18 cgx = np.array(cgx)

19 cgm = np.array(cgm)

20 # longitude in IBTraCS is (−180,180); convert to (0,360)21 cgx[cgx < 0] += 360� �




We also need some reanalysis data for the winds and temperatures.Here, we will use the JRA-55 reanalysis, which was not used in theoriginal paper. The data files are quite large, and it is thereforeconvenient to preprocess the files to make them manageable. Todo this, I use the Climate Data Operators (CDO) utilitiesdeveloped at the Max-Planck Institut fur Meteorologie. First, Iselect the temperature and wind data for June through Novemberusing the selmon (select month) command:

cdo selmon,6,7,8,9,10,11 jra55nl_tmp_monthly_1958-2015.nc4 tmp_jjason.nc4

cdo selmon,6,7,8,9,10,11 jra55nl_ugrd_monthly_1958-2015.nc4 uwd_jjason.nc4

cdo selmon,6,7,8,9,10,11 jra55nl_vgrd_monthly_1958-2015.nc4 vwd_jjason.nc4

CDO can be installed by downloading and installing the sourcefrom the project website, but on Mac OSX it is easier to useMacPorts or Homebrew. CDO has excellent documentation.

http://jra.kishou.go.jp/JRA-55/index_en.html

https://code.zmaw.de/projects/cdo

https://code.zmaw.de/projects/cdo

https://www.macports.org/

http://brew.sh/




To produce a JRA-55 version of Fig. 1 from the paper, we need todo a bit more preprocessing using CDO. Specifically, we need tocalculate monthly climatologies of zonal and meridional winds over1958–2015 using the ymonmean command, which calculatesmonthly means spanning multiple years (i.e., an annual cycle):

cdo ymonmean uwd_jjason.nc4 uwd_jjason_mm.nc4

cdo ymonmean vwd_jjason.nc4 vwd_jjason_mm.nc4

and then select the 200 and 850 hPa levels, removing the rest ofthe vertical profile (recall that we only need 850 hPa zonal wind tocalculate vertical shear, and do not need 850 hPa meridional wind):

cdo sellevel,85000,20000 uwd_jjason_mm.nc4 fig1_uwd.nc4

cdo sellevel,20000 vwd_jjason_mm.nc4 fig1_vwd.nc4




We can then read in the data and calculate the zonal wind shear:� �1 from netCDF4 import Dataset

23 # read in JRA−55 wind data4 ncdf = Dataset(ddir+’fig1_uwd.nc4’)

5 jlon = ncdf.variables[’lon’][:]

6 jlat = ncdf.variables[’lat’][:]

7 u850 = ncdf.variables[’ugrd’][:,0,:,:]

8 u200 = ncdf.variables[’ugrd’][:,1,:,:]

9 ncdf.close()

10 ncdf = Dataset(ddir+’fig1_vwd.nc4’)

11 v200 = ncdf.variables[’vgrd’][:,0,:,:]

12 ncdf.close()

13 # calculate vertical wind shear14 ushr = u850 -u200� �



Mapping: the cartopy moduleLinear regression and correlationsMore contour plots and masked arrays

We can plot a map using cartopy:� �1 import cartopy.crs as ccrs

2 import cartopy.feature as cfeat

3 from cartopy.mpl.ticker import LongitudeFormatter , LatitudeFormatter

45 # formatting for tick marks6 xfr = LongitudeFormatter(zero_direction_label=True)

7 yfr = LatitudeFormatter ()

89 fig = plt.figure(figsize =(13, 4))

10 axs = fig.add_subplot (111, projection=ccrs.PlateCarree(central_longitude

=180))

11 prj = ccrs.PlateCarree(central_longitude =0)

12 # zonal wind shear13 cs0 = axs.contourf(jlon , jlat , ushr[0,:,:], clv , cmap=plt.cm.PuOr , extend=

’both’, transform=prj)

14 # streamplot to show winds15 axs.streamplot(jlon , jlat , u200[0,:,:], v200[0,:,:], color=’k’, density=

dns , transform=prj)

16 # scatter plot of TC genesis locations for June17 idx = np.where(cgm ==6)

18 axs.scatter(cgx[idx], cgy[idx], marker=’o’, c=’#377 eb8’, s=50, zorder =10,

transform=prj)

19 axs.set_extent ([100, 240, 0, 40], prj)

20 axs.set_xticks( range (100, 241, 20), crs=prj)

21 axs.set_yticks( range (0, 41, 10), crs=prj)

22 axs.xaxis.set_major_formatter(xfr)

23 axs.yaxis.set_major_formatter(yfr)

24 axs.add_feature(cfeat.COASTLINE , edgecolor=’#333333 ’)� �

http://scitools.org.uk/cartopy/




The result is effectively the same as what is shown in the paper,although our version is missing the location of the TUTT. Thecartopy module has been developed by the UK Met Office.

100°E 120°E 140°E 160°E 180° 160°W 140°W 120°W0°

10°N

20°N

30°N

40°NJune

The cartopy interface can sometimes be confusing, but it hassome nice features that make it (in most cases) preferable to thealternative basemap toolkit. We have also used the streamplot

function from matplotlib to represent the 200 hPa wind speedsand directions, and the contourf function from matplotlib toshow the wind shear.

http://matplotlib.org/basemap/

http://matplotlib.org/examples/images_contours_and_fields/streamplot_demo_features.html

http://matplotlib.org/examples/pylab_examples/contourf_demo.html




Adding the location of the TUTT is more challenging, as the paperdoes not describe this procedure clearly. The authors mention thatthe TUTT is defined as the location where easterly windstransition to westerly; here, I have extrapolated from the idea thatthe transition from easterly to westerly indicates mass divergenceto define the TUTT location at each latitude as the longitude ofthe maximum (positive) zonal gradient in zonal wind.� �

1 import numpy as np

2 # for smoothing the visualization of the TUTT3 from statsmodels.nonparametric.smoothers_lowess import lowess

45 # TUTT6 ttt = np.empty (20)

7 f o r yy i n range (45 ,65):8 dux = np.gradient(np.squeeze(u200[5,yy,xdx]))

9 ttt[yy -45] = jlon[xdx[dux.argmax ()]]

10 tut = lowess(ttt , jlat [45:65] , frac =0.75 , return_sorted=False)

11 axs.plot(tut , jlat [45:65] , color=’#999999 ’, linewidth=3, transform=prj)� �I have also used a local regression (lowess) filter from thestatsmodels module to smooth the curve.

https://en.wikipedia.org/wiki/Local_regression

http://statsmodels.sourceforge.net/




100°E 120°E 140°E 160°E 180° 160°W 140°W 120°W0°

10°N

20°N

30°N

40°NJune

100°E 120°E 140°E 160°E 180° 160°W 140°W 120°W0°

10°N

20°N

30°N

40°NJuly

100°E 120°E 140°E 160°E 180° 160°W 140°W 120°W0°

10°N

20°N

30°N

40°NAugust

100°E 120°E 140°E 160°E 180° 160°W 140°W 120°W0°

10°N

20°N

30°N

40°NSeptember

100°E 120°E 140°E 160°E 180° 160°W 140°W 120°W0°

10°N

20°N

30°N

40°NOctober

100°E 120°E 140°E 160°E 180° 160°W 140°W 120°W0°

10°N

20°N

30°N

40°NNovember




We need to do a bit more data processing to get the meanlongitude of cyclogenesis and the location of the TUTT between5◦N and 25◦N for each year:� �

1 # get mean longitude of cyclogenesis for each year2 yrs = np.arange (1958 ,2015)

3 mln = np.empty(yrs.shape)

4 f o r ii i n range ( l e n (yrs)):5 idx = np.where ((cgt == yrs[ii]) & (cgm >= 6) & (cgm <= 11))[0]

6 i f idx.any():7 mln[ii] = cgx[idx].mean()

89 # get location of TUTT (transition from easterlies to westerlies)

10 xdx = np.where((jlon >= 120) & (jlon <= 240))[0]

11 tutt = np.empty(yrs.shape)

12 f o r ii i n range ( l e n (yrs)):13 u = u200[ii,xdx]

14 x = jlon[xdx]

15 tutt[ii] = x[np.where(u > 0) [0][0]]� �




Once we have these variables, we have multiple options for trendanalysis. For example, we could use the scipy.stats module towork directly with the numpy arrays:� �

1 # linear regressions2 from scipy import stats

34 # linear regression over full time series5 a0,b0,r0 ,p0,s0 = stats.linregress(yrs ,mln)

6 #linear regression from 1979−20137 a1,b1,r1 ,p1,s1 = stats.linregress(yrs[21:],mln [21:])

89 # linear regression over full time series

10 a2,b2,r2 ,p2,s2 = stats.linregress(yrs ,tutt)

11 #linear regression from 1979−201312 a3,b3,r3 ,p3,s3 = stats.linregress(yrs[21:], tutt [21:])

1314 # linear correlation15 r,p = stats.pearsonr(mln ,tutt)� �stats.linregress returns the slope, intercept, correlationcoefficient R, 2-tailed p-value (that the slope is non-zero), and thestandard error of the slope estimate; stats.pearsonr returns thePearson correlation coefficient and the associated 2-tailed p-value.

http://docs.scipy.org/doc/scipy/reference/stats.html

http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.linregress.html#scipy.stats.linregress

http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.pearsonr.html#scipy.stats.pearsonr




A convenient alternative in many cases is to construct a pandas

DataFrame and use seaborn.regplot(), especially if we onlyneed to see the trend:� �

1 # −∗− coding: utf−8 −∗−2 import pandas as pd

3 import matplotlib.pyplot as plt

4 import seaborn as sns

56 # plot parameters7 sns.set_style(’darkgrid ’)

89 # make a pandas dataframe

10 df = pd.DataFrame ({’jtwc’:mln , ’tutt’:tutt}, index=yrs)

1112 # plot time series of mean longitude of cyclogenesis, with trends13 fig = plt.figure(figsize =(12 ,6))

14 axa = fig.add_subplot (211)

15 axa.plot(df.index , df[’jtwc’], ’-’, color=’#377 eb8’)

16 sns.regplot(df.index , df[’jtwc’], color=’#377 eb8’, ax=axa , truncate=True)

17 sns.regplot(df.ix [1979:]. index , df.ix [1979:][ ’jtwc’], color=’#377 eb8’,

18 line_kws ={’linestyle ’:’--’}, truncate=True , ci=None , ax=axa)

19 axa.set_xlabel(’’)

20 axa.set_xlim (1955 ,2015)

21 axa.set_xticks( range (1960, 2011, 10))

22 axa.set_ylabel(u’TC mean genesis longitude [\ u00b0E]’, color=’#377 eb8’)

23 axa.set_ylim (125 ,150)

24 axa.set_yticks( range (125 ,151 ,5))25 axa.set_yticklabels( range (125 ,151 ,5), color=’#377 eb8’)� �

http://pandas.pydata.org/pandas-docs/stable/generated/pandas.DataFrame.html

http://pandas.pydata.org/pandas-docs/stable/generated/pandas.DataFrame.html

http://stanford.edu/~mwaskom/software/seaborn/generated/seaborn.regplot.html




� �1 sns.regplot(df.index , df[’jtwc’], color=’#377 eb8’, ax=axa , truncate=True)

2 sns.regplot(df.ix [1979:]. index , df.ix [1979:][ ’jtwc’], color=’#377 eb8’,

3 line_kws ={’linestyle ’:’--’}, truncate=True , ci=None , ax=axa)� �

1960 1970 1980 1990 2000 2010125

130

135

140

145

150

TC m

ean

gene

sis

long

itude

[°E

]

R = 0.64

140

150

160

170

180

190

TUTT

long

itude

[°E

]




A more sophisticated alternative to scipy.stats.linregress()

is offered by statsmodels.OLS():� �1 import statsmodels.api as sm

2 # add_constant prepares the x values3 xvl = sm.add_constant(df[’year’])

4 # use standard−type OLS to generate slope and intercept5 trd = sm.OLS(df[’tutt’], xvl).fit()

67 import statsmodels.formula.api as smf

8 # use formula−type ols to generate slope and intercept9 trd = smf.ols(’tutt ~ year’, data=df).fit()

10 # for 1979 − 201411 trd = smf.ols(’tutt ~ year’, data=df.ix [21:]).fit()� �

Here we focus only on the 1979–2014 trend in TUTT longitude forcomparison with the results in the paper. The use of the functionsm.add constant() adds a column of ones to the independent(x) variable array. This ensures that the regression model willcontain an intercept. We also subtract the initial year from theindependent variable, ensuring that that intercept is appropriate forthe year 1979 rather than the year 0.




We can print a detailed summary of the regression model:

In[13]: print trd.summary()

Out[13]:

OLS Regression Results

==============================================================================

Dep. Variable: tutt R-squared: 0.187

Model: OLS Adj. R-squared: 0.163

Method: Least Squares F-statistic: 7.809

Date: Tue, 22 Mar 2016 Prob (F-statistic): 0.00848

Time: 08:50:25 Log-Likelihood: -114.38

No. Observations: 36 AIC: 232.8

Df Residuals: 34 BIC: 235.9

Df Model: 1

Covariance Type: nonrobust

==============================================================================

coef std err t P>|t| [95.0% Conf. Int.]

------------------------------------------------------------------------------

const 163.4347 1.950 83.830 0.000 159.473 167.397

x1 -0.2677 0.096 -2.794 0.008 -0.462 -0.073

==============================================================================

Omnibus: 3.578 Durbin-Watson: 1.963

Prob(Omnibus): 0.167 Jarque-Bera (JB): 1.571

Skew: 0.004 Prob(JB): 0.456

Kurtosis: 1.977 Cond. No. 39.9

==============================================================================

which tells us that the trend in TUTT is −0.27◦ longitude yr−1,and that this trend is significant at the 99% level.




ENSO can also cause interannual variability in the locations ofcyclogenesis and the TUTT, so we should remove it from the timeseries. Here we use statsmodels.OLS() to calculate the ordinaryleast squares linear regression of mean cyclogenesis longitudeagainst the Nino3.4 index and then subtract it from the originaltime series:� �

1 import pandas as pd

2 import statsmodels.formula.api as smf

34 # make a pandas dataframe5 df = pd.DataFrame ({’jtwc’:mln , ’tutt’:tutt , ’nino’:nino}, index=yrs)

6 # regress JTWC mean longitude of cyclogenesis against Nino 3.47 rgr = smf.ols(’jtwc ~ nino’, data=df).fit()

8 # remove ENSO component of variability9 df[’estm’] = df[’jtwc’].mean() + (df[’jtwc’]-rgr.predict(df[’nino’]))� �




1960 1970 1980 1990 2000 2010Year

120

130

140

150

160

TC m

ean

gene

sis

long

itude

[°E

]

JTWC (original)JTWC (ENSO influence removed)

Although ENSO affects the year-to-year variability, the trend withENSO removed (−0.11◦ longitude yr−1) is within the 95%confidence interval around the original trend (−0.14± 0.14◦

longitude yr−1), so we can neglect ENSO effects.




The next step is to count the annual number of TCs generated inwestern (λ < 145◦E) and eastern (λ > 145◦E) parts of WNP:� �

1 # get number of TCs forming in the eastern/western WNP for each year2 yrs = np.arange (1958 ,2015)

3 w_n = np.empty(yrs.shape)

4 e_n = np.empty(yrs.shape)

5 f o r ii i n range ( l e n (yrs)):6 idx = np.where ((cgt == yrs[ii]) & (cgm >= 6) & (cgm <= 11))[0]

7 i f idx.any():8 w_n[ii] = (cgx[idx] < 145).sum()

9 e_n[ii] = (cgx[idx] >= 145).sum()� �

1960 1970 1980 1990 2000 20100

5

10

15

20

25

30

TC c

ount

R = −0.27

Western WNPEastern WNP




To get the mean tropical–subtropical temperature gradient wereturn to cdo, first selecting levels between 850 and 200 hPa andthen calculating the vertical and annual averages:

cdo vertmean tmp_jjason_ts.nc4 tmp_jjason_tsmean.nc4

cdo yearmean tmp_jjason_tsmean.nc4 tmp_yr_tsmean.nc4

cdo sellonlatbox,145,180,-10,5 tmp_yr_tsmean.nc4 tmp_yr_tsmean_tropics.nc4

cdo sellonlatbox,145,180,15,30 tmp_yr_tsmean.nc4 tmp_yr_tsmean_subtrop.nc4

cdo fldmean tmp_yr_tsmean_tropics.nc4 fig3_tmp_tropics.nc4

cdo fldmean tmp_yr_tsmean_subtrop.nc4 fig3_tmp_subtrop.nc4

where sellonlatbox selects a region and fldmean takes thearea-weighted spatial average. The processing for calculating themean zonal wind shear in the TUTT region is similar:

cdo sellevel,85000,20000 uwd_jjason.nc4 uwd_jjason_vs.nc4

cdo sellonlatbox,145,180,5,25 uwd_jjason_vs.nc4 uwd_jjason_subtrop.nc4

cdo fldmean uwd_jjason_subtrop.nc4 uwd_jjason_subtropmean.nc4

cdo yearmean uwd_jjason_subtropmean.nc4 fig3_uwd.nc4

The actual subtraction of 850 hPa u from 200 hPa u is left for thepython code.




1960 1970 1980 1990 2000 2010Year

0.0

0.3

0.6

0.9

1.2

1.5

1.8

2.1

Tem

pera

ture

gra

dien

t [K

]

R = 0.97

0

2

4

6

8

10

12

14

Zona

l win

d sh

ear [

m s−

1 ]

The strong relationship between these two time series is consistentwith the hypothesis that interannual variability and trends in windshear (and hence the preferred location of cyclogenesis) in thisregion are driven by the thermal wind relationship.




To calculate vertical cross-sections of zonal wind and temperaturetrends, we first calculate the appropriate vertical cross-sections ofzonal wind and temperature using cdo. For temperature:

cdo sellonlatbox,145,190,-50,50 tmp_jason.nc4 tmp_jason_pac.nc4

cdo yearmean tmp_jason_pac.nc4 tmp_annual_pac.nc4

cdo zonmean tmp_annual_pac.nc4 fig4_tmp_paczm.nc4

and for zonal wind:

cdo sellonlatbox,90,210,5,25 uwd_jason.nc4 uwd_jason_pac.nc4

cdo yearmean uwd_jason_pac.nc4 uwd_annual_pac.nc4

cdo mermean uwd_annual_pac.nc4 fig4_uwd_pacmm.nc4

Note that we calculate the zonal mean (zonmean) of temperatureacross the selected region, but the meridional mean (mermean) ofzonal wind.




To calculate trends in a time series effectively, we can define afunction that uses statsmodels.OLS():� �

1 import statsmodels.api as sm

23 # function to calculate trend and significance from a pandas time series4 def pdtrend(x,ci =0.95):

5 """6 A basic function for calculating trends given a pandas time7 series.89 Variables:

10 x :: the series1112 Parameters:13 ci :: confidence interval for significance testing14 """15 # statsmodels regression require us to add a constant16 xvl = sm.add_constant(np.array(x.index))

17 # ordinary least squares linear regression18 rgr = sm.OLS(x.values ,xvl).fit()

19 # trend slope (per year in this case)20 trnd = rgr.params [1]

21 # simple representation of statistical significance (True/False)22 tsig = (rgr.pvalues [1] < (1-ci))

23 r e t u r n (trnd , tsig)� �




An important note at this point: the example paper we are workingfrom uses a non-parametric Mann-Kendall test, and accounts forauto-correlation in the time series in significance testing. Thefunction on the previous page uses Student’s t test, which is (a)parametric and (b) assumes that the underlying data are normallydistributed. We have also not adjusted the effective sample size toaccount for auto-correlation. Our approach is acceptable forexploratory analysis, but would be unsuitable for publication-qualitywork. The reason that we have used a function in this case is thatthis makes it easier to later add or modify the criteria for statisticalsignificance to make them more sophisticated or data-aware. Formore details, see Chapter 17 of Statistical Analysis in ClimateResearch by Hans von Storch and Francis W. Zwiers.

http://www.amazon.com/Statistical-Analysis-Climate-Research-Storch/dp/0521012309

http://www.amazon.com/Statistical-Analysis-Climate-Research-Storch/dp/0521012309




Our function returns both the slope of the trend and a boolean(True or False) value indicating whether it is significant or not,which we can use in tandem with numpy masked arrays:� �

1 import pandas as pd

23 tru = np.ma.masked_all(mm_u.shape [1:])

4 trt = np.ma.masked_all(zm_t.shape [1:])

5 f o r zz i n range (tru.shape [0]):6 f o r xx i n range (tru.shape [1]):7 ser = pd.Series(mm_u[:,zz,xx])

8 m,s = pdtrend(ser)

9 tru.data[zz,xx] = m*10 # convert trend to per decade10 tru.mask[zz,xx] = ~s

11 f o r yy i n range (trt.shape [1]):12 ser = pd.Series(zm_t[:,zz,yy])

13 m,s = pdtrend(ser)

14 trt.data[zz,yy] = m*10 # convert trend to per decade15 trt.mask[zz,yy] = ~s� �

Masked arrays make it convenient to emphasize significant trendsor hide insignificant trends in the contour plots.




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� �1 cs1 = ax.contour(jlon , jlev , mm_u.mean(axis =0), np.arange (-50,50,2),

2 colors=’k’)

3 cs2 = ax.contourf(jlon , jlev , tru.data , np.linspace (-1,1,11),

4 cmap=plt.cm.RdBu_r , extend=’both’)

5 ax.contourf(jlon , jlev , tru.mask.astype(’int’), [-0.5,0.5],

6 hatches =[’xx’,’none’], colors=’none’, edgecolor=’#666666 ’,

7 zorder =10)

8 cb = plt.colorbar(cs2 , orientation=’vertical ’, extend=’both’, aspect =50)

9 cb.set_ticks ([-1,-0.5,0,0.5,1])

10 cb.set_label(’Trend in zonal wind [m s$^{-1}$ dec$ ^{-1}$]’)� �




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We can also limit our trend analysis to only the period after 1979,in which case our results are more similar to those in the paper.� �

1 ncdf = Dataset(ddir+’fig4_uwd_pacmm.nc4’)

2 jlev = ncdf.variables[’lev’][:27]*0.01

3 jlon = ncdf.variables[’lon’][:]

4 mm_u = np.squeeze(ncdf.variables[’ugrd’][21: ,:27 ,: ,:])

5 ncdf.close()� �

Documents

Westward shift of western North Paci c tropical cyclogenesis · Westward shift of western North Paci c tropical cyclogenesis Wu et al. (2015 ... Introduction Results Discussion