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ATMS 391: Geophysical Data Analysis

Homework 12


(1) Recreate Figure 1 from Horel and Wallace (1981) using the NCEP reanalysis data.

In [47]:
import pandas as pd import numpy as np from numpy import ma from matplotlib import pyplot as plt from mpl_toolkits.basemap import Basemap as bm import xray %matplotlib inline #%config InlineBackend.figure_format = 'svg'
In [48]:
sstdata=xray.open_dataset('sst_seas_ncep.nc') sstdata
<xray.Dataset> Dimensions: (lat: 94, lon: 192, time: 272) Coordinates: * lat (lat) float32 88.542 86.6531 84.7532 82.8508 80.9473 79.0435 ... * lon (lon) float32 0.0 1.875 3.75 5.625 7.5 9.375 11.25 13.125 15.0 ... * time (time) datetime64[ns] 1948-02-29 1948-05-31 1948-08-31 ... Data variables: skt (time, lat, lon) float32 -38.5333 -38.5388 -38.5811 -38.6714 ...
In [49]:
#find time series at point nearest to 10N and 95W tser=sstdata.sel(lat=[10.],lon=[360.-95.],method='nearest') tser plt.figure() plt.plot(tser['time'].values,tser['skt'].values.ravel()) #sst_resample
[<matplotlib.lines.Line2D at 0x7f26d23d4710>]
In [50]:
ls=xray.open_dataset('lsmask.19294.nc',decode_times=False) ls['lsmask']
<xray.DataArray 'lsmask' (time: 1, lat: 94, lon: 192)> array([[[ 0., 0., 0., ..., 0., 0., 0.], [ 0., 0., 0., ..., 0., 0., 0.], [ 0., 0., 0., ..., 0., 0., 0.], ..., [-1., -1., -1., ..., -1., -1., -1.], [-1., -1., -1., ..., -1., -1., -1.], [-1., -1., -1., ..., -1., -1., -1.]]]) Coordinates: * lat (lat) float32 88.542 86.6531 84.7532 82.8508 80.9473 79.0435 ... * lon (lon) float32 0.0 1.875 3.75 5.625 7.5 9.375 11.25 13.125 15.0 ... * time (time) float64 -1.577e+07 Attributes: long_name: Surface land/sea mask valid_range: [-1. 1.] actual_range: [-1. 0.] units: none precision: 2 var_desc: Land/Sea Mask level_desc: Surface statistic: Individual Obs parent_stat: Other dataset: NCEP Reanalysis Derived Products
In [51]:
plt.figure() plt.imshow(ls['lsmask'].values[0,:,:]) plt.colorbar()
<matplotlib.colorbar.Colorbar instance at 0x7f26de2f3200>
In [52]:
mask3d=ls['lsmask'].values.repeat(272,0) np.shape(mask3d)
(272, 94, 192)
In [53]:
sstdata
<xray.Dataset> Dimensions: (lat: 94, lon: 192, time: 272) Coordinates: * lat (lat) float32 88.542 86.6531 84.7532 82.8508 80.9473 79.0435 ... * lon (lon) float32 0.0 1.875 3.75 5.625 7.5 9.375 11.25 13.125 15.0 ... * time (time) datetime64[ns] 1948-02-29 1948-05-31 1948-08-31 ... Data variables: skt (time, lat, lon) float32 -38.5333 -38.5388 -38.5811 -38.6714 ...
In [54]:
sstdata['skt'].values=np.ma.masked_where(mask3d == -1, sstdata['skt'].values) plt.figure() plt.pcolormesh(sstdata['lon'].values,sstdata['lat'].values,sstdata['skt'].values[0,:,:]) plt.clim([-20,40]) plt.colorbar()
<matplotlib.colorbar.Colorbar instance at 0x7f26de08af80>
In [55]:
#calculate seasonal climatology .resample('Q-NOV', 'time',how='mean') sstseas=sstdata.groupby('time.season').mean(dim='time') for i in np.arange(4): plt.figure() plt.pcolormesh(sstdata['lon'].values,sstdata['lat'].values,sstseas['skt'].values[i,:,:]) plt.clim([-20,40]) plt.title(sstseas['season'].values[i]) plt.colorbar()
In [56]:
fixed_sstseas=xray.concat([sstseas.sel(season='DJF'),sstseas.sel(season='MAM'),\ sstseas.sel(season='JJA'),sstseas.sel(season='SON')], 'season')
In [57]:
#resize to be the same shape as the data meansstseas=np.tile(fixed_sstseas['skt'].values,(68,1,1)) np.shape(meansstseas) anomsst = sstdata['skt'].values-meansstseas plt.pcolormesh(sstdata['lon'].values,sstdata['lat'].values,anomsst[269,:,:]) plt.clim([-10,10]) plt.colorbar()
<matplotlib.colorbar.Colorbar instance at 0x7f26dd6a22d8>
In [58]:
def seas_departure(inputarr,field): seas=inputarr.groupby('time.season').mean(dim='time') fixed_seas=xray.concat([seas.sel(season='DJF'),seas.sel(season='MAM'),\ seas.sel(season='JJA'),seas.sel(season='SON')], 'season') #calculates the seasonal climatology but np.tile gives you back a numpy array mean_seas=np.tile(fixed_seas[field].values,(68,1,1)) #put it back into an xray dataset #foo = xray.DataArray(data, coords=[times, locs], dims=['time', 'space']) mean_seas=xray.DataArray(mean_seas,coords=[inputarr['time'].values,inputarr['lat'].values,\ inputarr['lon'].values],dims=['time','lat','lon']) anom = inputarr[field].values-mean_seas return anom anomsst=seas_departure(sstdata,'skt') anomsst
<xray.DataArray (time: 272, lat: 94, lon: 192)> array([[[-4.44317245, -4.42129898, -4.42863083, ..., -4.36367035, -4.38543701, -4.41463852], [-3.66640091, -3.62452698, -3.5991745 , ..., -3.80857468, -3.74745941, -3.69694901], [-2.69404984, -2.68140411, -2.68823242, ..., -2.91536331, -2.82406235, -2.74878693], ..., [ nan, nan, nan, ..., nan, nan, nan], [ nan, nan, nan, ..., nan, nan, nan], [ nan, nan, nan, ..., nan, nan, nan]], [[ 0.24821091, 0.236166 , 0.22953606, ..., 0.2504406 , 0.23942375, 0.23883057], [-0.18886185, -0.17407227, -0.17473221, ..., -0.18044281, -0.18090248, -0.18618202], [-0.53155708, -0.53410149, -0.55817604, ..., -0.47854424, -0.48344994, -0.49978828], ..., [ nan, nan, nan, ..., nan, nan, nan], [ nan, nan, nan, ..., nan, nan, nan], [ nan, nan, nan, ..., nan, nan, nan]], [[ 0.1597655 , 0.1592178 , 0.15766378, ..., 0.15960911, 0.16175385, 0.16141357], [ 0.08877152, 0.08609134, 0.08308157, ..., 0.09800881, 0.09455049, 0.0925636 ], [ 0.08442968, 0.07982728, 0.07721651, ..., 0.07750982, 0.07400101, 0.07632336], ..., [ nan, nan, nan, ..., nan, nan, nan], [ nan, nan, nan, ..., nan, nan, nan], [ nan, nan, nan, ..., nan, nan, nan]], ..., [[ 2.27892876, 2.31128883, 2.3406601 , ..., 2.24229813, 2.25616646, 2.26855087], [ 1.16251183, 1.19216156, 1.21855164, ..., 1.09598541, 1.11626434, 1.14008904], [ 0.4730587 , 0.49069405, 0.51582336, ..., 0.38220024, 0.4081707 , 0.43649483], ..., [ nan, nan, nan, ..., nan, nan, nan], [ nan, nan, nan, ..., nan, nan, nan], [ nan, nan, nan, ..., nan, nan, nan]], [[-0.06331694, -0.06201929, -0.06022108, ..., -0.06985188, -0.06650722, -0.0647417 ], [-0.09672892, -0.09461612, -0.09230238, ..., -0.0998579 , -0.10013518, -0.09952298], [-0.14694038, -0.14691013, -0.14581865, ..., -0.15556499, -0.15461025, -0.15049592], ..., [ nan, nan, nan, ..., nan, nan, nan], [ nan, nan, nan, ..., nan, nan, nan], [ nan, nan, nan, ..., nan, nan, nan]], [[ 7.78704834, 7.74666405, 7.72187042, ..., 7.8416481 , 7.81916046, 7.79504013], [ 8.52528572, 8.4527874 , 8.36215687, ..., 8.60693169, 8.59012032, 8.56120872], [ 8.34811211, 8.25792885, 8.17016029, ..., 8.36702538, 8.37867928, 8.35907364], ..., [ nan, nan, nan, ..., nan, nan, nan], [ nan, nan, nan, ..., nan, nan, nan], [ nan, nan, nan, ..., nan, nan, nan]]], dtype=float32) Coordinates: * time (time) datetime64[ns] 1948-02-29 1948-05-31 1948-08-31 ... * lat (lat) float32 88.542 86.6531 84.7532 82.8508 80.9473 79.0435 ... * lon (lon) float32 0.0 1.875 3.75 5.625 7.5 9.375 11.25 13.125 15.0 ...
In [59]:
dsub = sstdata.sel(lat=slice(40,-40), lon=slice(120,290)) lat = dsub['lat'].values lon = dsub['lon'].values #calculate sst climatology meansst=dsub['skt'].mean(axis=0) plt.figure() plt.pcolormesh(meansst.values) plt.clim([-20,40]) plt.colorbar() #resize to be the same shape as the data meansst=np.tile(meansst.values.reshape(1,np.shape(meansst)[0],np.shape(meansst)[1]),(272,1,1)) #calculate anomalies anomsst = dsub['skt'].values-meansst lons, lats = np.meshgrid(lon, lat) plt.figure() plt.pcolormesh(anomsst[2,:,:]) plt.clim([-5,5]) plt.colorbar()
<matplotlib.colorbar.Colorbar instance at 0x7f26dd406b48>
In [60]:
X = np.reshape(anomsst, (anomsst.shape[0], len(lat) * len(lon)), order='F') X.shape
(272, 3822)
In [61]:
X = ma.masked_array(X, np.isnan(X)) land = X.sum(0).mask ocean = -land X = X[:,ocean] X.shape
(272, 3356)
In [62]:
from sklearn import preprocessing scaler = preprocessing.StandardScaler() scaler_sst = scaler.fit(X) X = scaler_sst.transform(X) from sklearn.decomposition import pca skpca = pca.PCA() skpca.fit(X)
PCA(copy=True, n_components=None, whiten=False)
In [63]:
f, ax = plt.subplots(figsize=(5,5)) ax.plot(skpca.explained_variance_ratio_[0:10]*100) ax.plot(skpca.explained_variance_ratio_[0:10]*100,'ro') ax.set_title("% of variance explained", fontsize=14) ax.grid()
In [64]:
#get PCs PCs = skpca.transform(X) np.shape(PCs) EOFs = skpca.components_ np.shape(EOFs) ipc=272 EOF_recons = np.ones((ipc, len(lat) * len(lon))) * -999. for i in range(ipc): EOF_recons[i,ocean] = EOFs[i,:] EOF_recons = ma.masked_values(np.reshape(EOF_recons, (ipc, len(lat), len(lon)), order='F'), -999.) EOF_recons.shape
(272, 42, 91)
In [65]:
def plot_field(m, X, lats, lons, vmin, vmax, step, cmap=plt.get_cmap('jet'), \ ax=False, title=False, grid=False): if not ax: f, ax = plt.subplots(figsize=(8, (X.shape[0] / float(X.shape[1])) * 8)) m.ax = ax im = m.contourf(lons, lats, X, np.arange(vmin, vmax+step, step), \ latlon=True, cmap=cmap, extend='both', ax=ax) m.drawcoastlines() if grid: m.drawmeridians(np.arange(0, 360, 30), labels=[0,0,0,1]) m.drawparallels(np.arange(-80, 80, 20), labels=[1,0,0,0]) m.colorbar(im) if title: ax.set_title(title) m = bm(projection='cyl',llcrnrlat=lat.min(),urcrnrlat=lat.max(),\ llcrnrlon=lon.min(),urcrnrlon=lon.max(),\ lat_ts=0,resolution='c') plot_field(m, EOF_recons[1,:,:], lats, lons, -.1, .1, .01, grid=True, cmap=plt.get_cmap('RdBu_r'))
In [66]:
from sklearn.preprocessing import StandardScaler scaler_PCs = StandardScaler() scaler_PCs.fit(PCs) PCs_std = scaler_PCs.transform(PCs) PCdf = pd.DataFrame(PCs_std, index = dsub['time'], \ columns = ["EOF%s" % (x) for x in range(1, PCs_std.shape[1] +1)]) from scipy.signal import detrend f, ax = plt.subplots(figsize=(10,4)) PCdf.ix[:,1].plot(ax=ax, color='r', label='PC2') ax.axhline(0, c='0.8') #ax.set_xlabel('period', fontsize=18) #ax.plot(PCdf.index, detrend(PCdf.ix[:,1].values), 'r', label='PC2 (trend removed)',linewidth=13) plt.title('NCEP Reanalysis Pacific Basin EOF2 ') ax.grid('off') ax.legend(loc=2); plt.savefig('EOF2.svg')

(2) Create normalized index values (mean=0, sd=1) of Sea Level Pressure between Tahiti and Darwin similar to Fig. 4. Invert the index (multiply by -1, as in the paper). Plot the time series.

In [67]:
slp=xray.open_dataset('slp_seas_ncep.nc') slp tahitimslp = slp.sel(lat=-15., lon=360-149.,method='nearest') tahitimslp darwinmslp = slp.sel(lat=-12., lon=131.,method='nearest') darwinmslp plt.figure() plt.plot(tahitimslp['time'].values,-1*(tahitimslp['slp'].values-darwinmslp['slp'].values)) plt.title('-1*Tahiti-Darwin mslp') plt.ylabel('MSLP (hPa)') plt.xlabel('Time (years)') #calculate normalized index, with mean=0 and std=1 diff=-1*(tahitimslp['slp']-darwinmslp['slp']) diff=(diff-np.mean(diff)) diff=diff/np.std(diff) diff plt.figure() plt.plot(diff['time'].values,diff) plt.title('normalized Tahiti-Darwin mslp index') plt.ylabel('index') plt.xlabel('Time (years)')
<matplotlib.text.Text at 0x7f26dd89ce10>

(3) Create normalized index values of 200 hPa height at the stations listed in Fig 6. Plot the time series.

In [68]:
h200=xray.open_dataset('h200_seas_ncep.nc') sites= ['NAI','DAR','NAN','HIL','SAJ'] lat=np.array([-1.2,-12.4,-17.5, 19.7, 18.0]) lon=np.array([36.8,130.0,177.0,-155.0,-66.0]) def grab_h200(h200,lat,lon): return h200.sel(lat=lat, lon=360-lon,method='nearest') all_h200={} for i in np.arange(len(lat)): all_h200[sites[i]]=grab_h200(h200,lat[i],lon[i]) z200index=0.2*all_h200['NAI']+0.23*all_h200['DAR']+0.23*all_h200['NAN']+0.25*all_h200['HIL']+0.27*all_h200['SAJ'] plt.plot(z200index['time'].values,z200index['hgt'].values) def standardize(var): var=var-np.mean(var) return var/np.std(var) z200index_std=standardize(z200index) z200index_std plt.figure() plt.plot(z200index_std['time'].values,z200index_std['hgt'].values)
[<matplotlib.lines.Line2D at 0x7f26dd330e90>]

(4) Compute the PNA and WP indices as on p. 823 of the paper. Plot the time series.

In [69]:
h700=xray.open_dataset('h700_seas_ncep.nc') sites= ['S1','S2','S3','S4','S5'] lat=np.array([55.,45.,30., 30., 60.]) lon=np.array([-115.,-165.,-85.,155.0,155.0]) def grab_h700(h700,lat,lon): return h700.sel(lat=lat, lon=360-lon,method='nearest') def standardize(var): var=var-np.mean(var) return var/np.std(var) all_h700={} for i in np.arange(len(lat)): all_h700[sites[i]]=grab_h700(h700,lat[i],lon[i]) all_h700[sites[i]]=all_h700[sites[i]].isel(time=np.arange(0,len(h700['time'].values),4)) all_h700[sites[i]]=standardize(all_h700[sites[i]]) pnaindex=all_h700['S1']-0.5*(all_h700['S2']+all_h700['S3']) wpindex=0.5*(all_h700['S4']+all_h700['S5']) plt.figure() plt.plot(h700['time'].values[::4],pnaindex['hgt'].values,'-r') plt.plot(h700['time'].values[::4],wpindex['hgt'].values,'-b')
[<matplotlib.lines.Line2D at 0x7f26dd181110>]

(5) Compute standardized rainfall values at the locations in Fig. 3. Plot the time series.

In [76]:
precip = xray.open_dataset('precip_seas_ncep.nc') precip = seas_departure(precip,'prate') tarawamslp = precip.sel(lat=1.4167,lon=173.0333,method='nearest') tarawamslp = standardize(tarawamslp) cantonmslp = precip.sel(lat=-2.8106,lon=360.-171.6756,method='nearest') cantonmslp = standardize(cantonmslp) christmasmslp = precip.sel(lat=-10.4833,lon=105.6333,method='nearest') christmasmslp = standardize(christmasmslp) fanningmslp = precip.sel(lat=3.86,lon=360.-159.3644,method='nearest') fanningmslp = standardize(fanningmslp) plt.figure(figsize=[8,12]) plt.subplot(4,1,1) plt.plot(tarawamslp['time'],tarawamslp) plt.title('Standardized Precipitation Rate at Tarawa') plt.subplot(4,1,2) plt.plot(cantonmslp['time'],cantonmslp) plt.title('Standardized Precipitation Rate at Canton') plt.subplot(4,1,3) plt.plot(christmasmslp['time'],christmasmslp) plt.title('Standardized Precipitation Rate at Christmas') plt.subplot(4,1,4) plt.plot(fanningmslp['time'],fanningmslp) plt.title('Standardized Precipitation Rate at Fanning')
<matplotlib.text.Text at 0x7f26dd789910>

(6) Reproduce Fig 8 with the top 4 and bottom 4 values of PNA index (that you find in part 4), except contour the values you have rather than plot points as in the paper.

In [77]:
slp=xray.open_dataset('h700_seas_ncep.nc'); slp2=xray.open_dataset('h700_seas_ncep.nc'); PNAsort = np.sort(PNA) Topvals =[PNAsort[-1],PNAsort[-2],PNAsort[-3],PNAsort[-4]] max_time = []; for i in range(len(Topvals)): k = np.where(PNA==Topvals[i])[0][0] max_time.append(slp['time'].values[k]); istime = (max_time[0]==slp2['time']) set1 = slp2['hgt'][istime,:,:] istime = (max_time[1]==slp2['time']) set2 = slp2['hgt'][istime,:,:] istime = (max_time[2]==slp2['time']) set3 = slp2['hgt'][istime,:,:] istime = (max_time[3]==slp2['time']) set4 = slp2['hgt'][istime,:,:] max_set = (set1.values+set2.values+set3.values+set4.values)/4 plt.figure() plt.contour(np.reshape((max_set),[73,144])); plt.title('200 mb height max', fontsize=20) plt.colorbar()
<matplotlib.colorbar.Colorbar instance at 0x7f26dd390320>

(7) Recreate Figure 9 using your data.

In [70]:
#200 hPa - 700 hPa correlation map z200index_std['hgt'] h700=xray.open_dataset('h700_seas_ncep.nc') print(np.shape(h700['hgt'].values)) def spatial_corr(index,mapvals): sz=np.shape(mapvals) outmap=np.zeros([sz[1],sz[2]]) for i in np.arange(sz[1]): for j in np.arange(sz[2]): maptser=np.squeeze(mapvals[:,i,j]) #print(np.shape(maptser)) #print(np.shape(index)) df_bis = pd.DataFrame({'maptser': maptser, 'index': np.squeeze(index)}) outmap[i,j]=df_bis.corr().values[1,0] return outmap
(272, 73, 144)
In [71]:
h700['time']
<xray.DataArray 'time' (time: 272)> array(['1948-02-29T00:00:00.000000000Z', '1948-05-31T00:00:00.000000000Z', '1948-08-31T00:00:00.000000000Z', '1948-11-30T00:00:00.000000000Z', '1949-02-28T00:00:00.000000000Z', '1949-05-31T00:00:00.000000000Z', '1949-08-31T00:00:00.000000000Z', '1949-11-30T00:00:00.000000000Z', '1950-02-28T00:00:00.000000000Z', '1950-05-31T00:00:00.000000000Z', '1950-08-31T00:00:00.000000000Z', '1950-11-30T00:00:00.000000000Z', '1951-02-28T00:00:00.000000000Z', '1951-05-31T00:00:00.000000000Z', '1951-08-31T00:00:00.000000000Z', '1951-11-30T00:00:00.000000000Z', '1952-02-29T00:00:00.000000000Z', '1952-05-31T00:00:00.000000000Z', '1952-08-31T00:00:00.000000000Z', '1952-11-30T00:00:00.000000000Z', '1953-02-28T00:00:00.000000000Z', '1953-05-31T00:00:00.000000000Z', '1953-08-31T00:00:00.000000000Z', '1953-11-30T00:00:00.000000000Z', '1954-02-28T00:00:00.000000000Z', '1954-05-31T00:00:00.000000000Z', '1954-08-31T00:00:00.000000000Z', '1954-11-30T00:00:00.000000000Z', 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In [78]:
outmap=spatial_corr(z200index_std['hgt'].values,h700['hgt'].values)
In [79]:
from mpl_toolkits.basemap import Basemap import numpy as np import matplotlib.pyplot as plt # setup north polar stereographic basemap. # The longitude lon_0 is at 6-o'clock, and the # latitude circle boundinglat is tangent to the edge # of the map at lon_0. Default value of lat_ts # (latitude of true scale) is pole. m = Basemap(lon_0=180) m.pcolormesh(h700['lon'].values,h700['lat'].values,outmap) m.drawcoastlines() plt.colorbar()
<matplotlib.colorbar.Colorbar instance at 0x7f26dbae60e0>
In [ ]: