In [1]:
import matplotlib.pyplot as plt
import matplotlib.patches as pat
import cartopy.crs as ccrs
import cartopy.feature as cfeature
from cartopy.mpl.ticker import LongitudeFormatter, LatitudeFormatter
fig = plt.figure(figsize=(12, 5))
ax = plt.axes(projection=ccrs.PlateCarree(central_longitude=180))
ax.add_feature(cfeature.LAND)
ax.add_feature(cfeature.OCEAN)
ax.coastlines()
ax.set_extent([30, 300, -30, 30], ccrs.PlateCarree())
xticks = [30, 60, 90, 120, 150, 180, 210, 240, 270, 300]
yticks = [-30, -5, 5, 30]
ax.set_xticks(xticks, crs=ccrs.PlateCarree())
ax.set_yticks(yticks, crs=ccrs.PlateCarree())
ax.xaxis.set_major_formatter(LongitudeFormatter())
ax.yaxis.set_major_formatter(LatitudeFormatter())
ax.gridlines(xlocs=xticks, ylocs=yticks, color='white')
ax.add_patch(pat.Rectangle(xy = [210, -5], width=60, height=10, facecolor='red',
alpha=0.2, transform=ccrs.PlateCarree(), zorder=10))
plt.text(240, 0, 'NINO.3', horizontalalignment='center', verticalalignment='center',
transform=ccrs.Geodetic(), size=18)
plt.show()
/opt/local/Library/Frameworks/Python.framework/Versions/3.6/lib/python3.6/site-packages/matplotlib/ticker.py:1685: UserWarning: Steps argument should be a sequence of numbers
increasing from 1 to 10, inclusive. Behavior with
values outside this range is undefined, and will
raise a ValueError in future versions of mpl.
warnings.warn('Steps argument should be a sequence of numbers\n'
/opt/local/Library/Frameworks/Python.framework/Versions/3.6/lib/python3.6/site-packages/cartopy/io/__init__.py:264: DownloadWarning: Downloading: http://naciscdn.org/naturalearth/110m/physical/ne_110m_land.zip
warnings.warn('Downloading: {}'.format(url), DownloadWarning)
/opt/local/Library/Frameworks/Python.framework/Versions/3.6/lib/python3.6/site-packages/cartopy/io/__init__.py:264: DownloadWarning: Downloading: http://naciscdn.org/naturalearth/110m/physical/ne_110m_ocean.zip
warnings.warn('Downloading: {}'.format(url), DownloadWarning)
海面水温変動¶
ファイルの読み込みや統計をする方法を学び，海面水温変動を見てみよう。NetCDF形式で保存しておいた海面水温データを開く。
In [2]:
import netCDF4 as nc4
nc = nc4.Dataset('HadISST1_SST_1961-1990.nc')
NINO.3で平均を求める。
In [3]:
import numpy as np
sst_nino3 = np.zeros(12 * 30)
for i in range(12*30):
sst_nino3[i] = nc.variables['sst'][i, 85:95, 30:90].mean()
図示して変動の様子を確認しよう。さらにこのデータ内の最大値，最小値，平均値，標準偏差を計算する。
In [4]:
plt.plot(sst_nino3)
plt.show()
In [5]:
sst_nino3.max()
Out[5]:
29.21263313293457
In [6]:
sst_nino3.min()
Out[6]:
23.031665802001953
In [7]:
sst_nino3.mean()
Out[7]:
25.7389995098114
In [8]:
sst_nino3.std()
Out[8]:
1.2339356425648902
x軸に日付を入れるために日付要素とする配列を作る。日付の作成には，datetimeモジュールを用いる。
In [9]:
from datetime import date
dates = np.array([date(y, m+1, 15) for y in range(1961, 1991) for m in range(12)])
In [10]:
plt.plot(dates, sst_nino3)
plt.show()
海面水温偏差¶
海面水温の平年からのずれ（偏差）を描こう。描くなら一番偏差が大きい月がいいだろう。最大値は何年何月だろうか。
In [11]:
sst_nino3.argmax()
Out[11]:
267
In [12]:
dates[sst_nino3.argmax()]
Out[12]:
datetime.date(1983, 4, 15)
1983年4月の海面水温と4月の気候値を読み，差をとって海面水温偏差を描いてみよう。
In [13]:
sst_elnino = nc.variables['sst'][sst_nino3.argmax(),:,:]
lon = nc.variables['lon'][:]
lat = nc.variables['lat'][:]
In [14]:
ncc = nc4.Dataset('HadISST1_SST_1961-1990_clim.nc')
m = dates[sst_nino3.argmax()].month
sst_clim = ncc.variables['sst'][m-1,:,:]
In [15]:
ax = plt.axes(projection=ccrs.Orthographic(central_longitude=210))
plt.contourf(lon, lat, sst_elnino-sst_clim, 60, transform=ccrs.PlateCarree(), vmin = -4, vmax = 4)
plt.colorbar()
ax.coastlines()
plt.show()
5度を超える高温偏差が東太平洋赤道域にみられる。日付変更線付近が白く抜けてしまった。これを解消するために，東西に周期的に点を追加する。
In [16]:
from cartopy.util import add_cyclic_point
dsst, lonc = add_cyclic_point(sst_elnino-sst_clim, coord=lon)
In [17]:
dsst.shape
Out[17]:
(180, 361)
In [18]:
lonc
Out[18]:
masked_array(data = [-179.5 -178.5 -177.5 -176.5 -175.5 -174.5 -173.5 -172.5 -171.5 -170.5
-169.5 -168.5 -167.5 -166.5 -165.5 -164.5 -163.5 -162.5 -161.5 -160.5
-159.5 -158.5 -157.5 -156.5 -155.5 -154.5 -153.5 -152.5 -151.5 -150.5
-149.5 -148.5 -147.5 -146.5 -145.5 -144.5 -143.5 -142.5 -141.5 -140.5
-139.5 -138.5 -137.5 -136.5 -135.5 -134.5 -133.5 -132.5 -131.5 -130.5
-129.5 -128.5 -127.5 -126.5 -125.5 -124.5 -123.5 -122.5 -121.5 -120.5
-119.5 -118.5 -117.5 -116.5 -115.5 -114.5 -113.5 -112.5 -111.5 -110.5
-109.5 -108.5 -107.5 -106.5 -105.5 -104.5 -103.5 -102.5 -101.5 -100.5
-99.5 -98.5 -97.5 -96.5 -95.5 -94.5 -93.5 -92.5 -91.5 -90.5
-89.5 -88.5 -87.5 -86.5 -85.5 -84.5 -83.5 -82.5 -81.5 -80.5
-79.5 -78.5 -77.5 -76.5 -75.5 -74.5 -73.5 -72.5 -71.5 -70.5
-69.5 -68.5 -67.5 -66.5 -65.5 -64.5 -63.5 -62.5 -61.5 -60.5
-59.5 -58.5 -57.5 -56.5 -55.5 -54.5 -53.5 -52.5 -51.5 -50.5
-49.5 -48.5 -47.5 -46.5 -45.5 -44.5 -43.5 -42.5 -41.5 -40.5
-39.5 -38.5 -37.5 -36.5 -35.5 -34.5 -33.5 -32.5 -31.5 -30.5
-29.5 -28.5 -27.5 -26.5 -25.5 -24.5 -23.5 -22.5 -21.5 -20.5
-19.5 -18.5 -17.5 -16.5 -15.5 -14.5 -13.5 -12.5 -11.5 -10.5
-9.5 -8.5 -7.5 -6.5 -5.5 -4.5 -3.5 -2.5 -1.5 -0.5
0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5
10.5 11.5 12.5 13.5 14.5 15.5 16.5 17.5 18.5 19.5
20.5 21.5 22.5 23.5 24.5 25.5 26.5 27.5 28.5 29.5
30.5 31.5 32.5 33.5 34.5 35.5 36.5 37.5 38.5 39.5
40.5 41.5 42.5 43.5 44.5 45.5 46.5 47.5 48.5 49.5
50.5 51.5 52.5 53.5 54.5 55.5 56.5 57.5 58.5 59.5
60.5 61.5 62.5 63.5 64.5 65.5 66.5 67.5 68.5 69.5
70.5 71.5 72.5 73.5 74.5 75.5 76.5 77.5 78.5 79.5
80.5 81.5 82.5 83.5 84.5 85.5 86.5 87.5 88.5 89.5
90.5 91.5 92.5 93.5 94.5 95.5 96.5 97.5 98.5 99.5
100.5 101.5 102.5 103.5 104.5 105.5 106.5 107.5 108.5 109.5
110.5 111.5 112.5 113.5 114.5 115.5 116.5 117.5 118.5 119.5
120.5 121.5 122.5 123.5 124.5 125.5 126.5 127.5 128.5 129.5
130.5 131.5 132.5 133.5 134.5 135.5 136.5 137.5 138.5 139.5
140.5 141.5 142.5 143.5 144.5 145.5 146.5 147.5 148.5 149.5
150.5 151.5 152.5 153.5 154.5 155.5 156.5 157.5 158.5 159.5
160.5 161.5 162.5 163.5 164.5 165.5 166.5 167.5 168.5 169.5
170.5 171.5 172.5 173.5 174.5 175.5 176.5 177.5 178.5 179.5
180.5],
mask = False,
fill_value = 1e+20)
In [19]:
ax = plt.axes(projection=ccrs.Orthographic(central_longitude=210))
plt.contourf(lonc, lat, dsst, 60, transform=ccrs.PlateCarree(), vmin = -4, vmax = 4)
plt.colorbar()
ax.coastlines()
plt.show()
In [20]:
n = sst_nino3.size
sst_nino3_smooth = np.zeros(n - 4)
sst_nino3_smooth[2] = sst_nino3_smooth[0:5].mean()
for i in range(3,n-4):
sst_nino3_smooth[i] = sst_nino3_smooth[i-1] - sst_nino3[i-3]/5 + sst_nino3[i+2]/5
In [21]:
dates_smooth = dates[2:-2]
plt.plot(dates_smooth, sst_nino3_smooth - sst_nino3_smooth.mean())
plt.show()
畳み込みを使うと，移動平均値を簡単に計算することができる。Numpyで畳み込みを行う関数はnumpy.convolve()である。
In [22]:
kernel = np.ones(5)/5
sst_nino3_smooth = np.convolve(sst_nino3, kernel, mode='valid')
In [23]:
plt.plot(dates_smooth, sst_nino3_smooth - sst_nino3_smooth.mean())
plt.show()
NINO.3の海面水温偏差が0.5度より高いときをTrue，そうでないときをFalseとする配列を作る。
In [24]:
condition = sst_nino3_smooth - sst_nino3_smooth.mean() > 0.5
In [25]:
condition
Out[25]:
array([ True, True, True, False, False, False, False, False, False,
False, False, False, False, True, False, False, False, False,
False, False, False, False, False, False, True, True, True,
True, True, False, False, False, False, False, False, True,
False, False, False, False, False, False, False, False, False,
False, False, False, True, True, True, True, True, True,
True, True, True, True, True, True, True, True, True,
False, False, False, False, False, False, False, False, False,
False, True, True, False, False, False, False, False, False,
False, False, False, False, False, False, False, False, False,
False, False, False, False, False, True, True, True, True,
True, True, False, False, False, False, False, True, True,
True, True, False, False, False, False, False, False, False,
False, False, False, False, False, False, False, False, False,
False, False, False, False, False, False, True, True, True,
True, True, True, True, True, True, True, True, True,
True, True, False, False, False, False, False, False, False,
False, False, False, False, False, True, False, False, False,
False, False, False, False, False, False, False, False, False,
False, False, False, False, False, False, False, False, False,
False, True, True, True, True, True, False, False, False,
True, True, True, True, True, True, False, False, False,
False, False, False, False, False, True, True, True, False,
False, False, False, False, False, False, False, False, True,
True, True, True, True, False, False, False, False, False,
False, False, True, True, True, True, True, False, False,
False, False, False, False, False, False, True, True, True,
False, False, False, False, False, False, False, False, True,
True, True, True, True, True, True, True, True, True,
True, True, True, True, True, True, True, True, False,
False, False, False, False, False, False, False, True, False,
False, False, False, False, False, False, False, False, False,
False, False, False, False, False, False, False, False, False,
False, False, False, False, True, True, False, False, False,
False, False, False, True, True, True, True, True, True,
True, True, True, True, True, False, False, True, True,
True, False, False, False, False, False, False, False, False,
False, False, False, False, False, False, False, False, False,
False, False, False, False, False, False, True, True, True,
True, False, False, False, False], dtype=bool)
5つ以上Trueが続く期間を見つけるのは人力でもできるが，面倒なことはPythonにやってもらおう。拡張モジュールitertoolsに登場願う。
In [26]:
from itertools import groupby
groupbyはキーが変わるごとに値をひとまとまりにする。listにして長さを調べてみる。
In [27]:
for key, group in groupby(condition):
print(key)
print(list(group))
True [True, True, True] False [False, False, False, False, False, False, False, False, False, False] True [True] False [False, False, False, False, False, False, False, False, False, False] True [True, True, True, True, True] False [False, False, False, False, False, False] True [True] False [False, False, False, False, False, False, False, False, False, False, False, False] True [True, True, True, True, True, True, True, True, True, True, True, True, True, True, True] False [False, False, False, False, False, False, False, False, False, False] True [True, True] False [False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False] True [True, True, True, True, True, True] False [False, False, False, False, False] True [True, True, True, True] False [False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False] True [True, True, True, True, True, True, True, True, True, True, True, True, True, True] False [False, False, False, False, False, False, False, False, False, False, False, False] True [True] False [False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False] True [True, True, True, True, True] False [False, False, False] True [True, True, True, True, True, True] False [False, False, False, False, False, False, False, False] True [True, True, True] False [False, False, False, False, False, False, False, False, False] True [True, True, True, True, True] False [False, False, False, False, False, False, False] True [True, True, True, True, True] False [False, False, False, False, False, False, False, False] True [True, True, True] False [False, False, False, False, False, False, False, False] True [True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True] False [False, False, False, False, False, False, False, False] True [True] False [False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False] True [True, True] False [False, False, False, False, False, False] True [True, True, True, True, True, True, True, True, True, True, True] False [False, False] True [True, True, True] False [False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False] True [True, True, True, True] False [False, False, False, False]
知りたいのは期間なので配列の添え字をまとめるように変更する。キーをconditionの要素にするため無名関数lambdaを使った。
In [28]:
for key, group in groupby(range(condition.size), lambda i: condition[i]):
print(key)
print(list(group))
True [0, 1, 2] False [3, 4, 5, 6, 7, 8, 9, 10, 11, 12] True [13] False [14, 15, 16, 17, 18, 19, 20, 21, 22, 23] True [24, 25, 26, 27, 28] False [29, 30, 31, 32, 33, 34] True [35] False [36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47] True [48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62] False [63, 64, 65, 66, 67, 68, 69, 70, 71, 72] True [73, 74] False [75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94] True [95, 96, 97, 98, 99, 100] False [101, 102, 103, 104, 105] True [106, 107, 108, 109] False [110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131] True [132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145] False [146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157] True [158] False [159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180] True [181, 182, 183, 184, 185] False [186, 187, 188] True [189, 190, 191, 192, 193, 194] False [195, 196, 197, 198, 199, 200, 201, 202] True [203, 204, 205] False [206, 207, 208, 209, 210, 211, 212, 213, 214] True [215, 216, 217, 218, 219] False [220, 221, 222, 223, 224, 225, 226] True [227, 228, 229, 230, 231] False [232, 233, 234, 235, 236, 237, 238, 239] True [240, 241, 242] False [243, 244, 245, 246, 247, 248, 249, 250] True [251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268] False [269, 270, 271, 272, 273, 274, 275, 276] True [277] False [278, 279, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 300] True [301, 302] False [303, 304, 305, 306, 307, 308] True [309, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319] False [320, 321] True [322, 323, 324] False [325, 326, 327, 328, 329, 330, 331, 332, 333, 334, 335, 336, 337, 338, 339, 340, 341, 342, 343, 344, 345, 346, 347] True [348, 349, 350, 351] False [352, 353, 354, 355]
In [29]:
for key, group in groupby(range(condition.size), lambda i: condition[i]):
if (key):
l = list(group)
if len(l) >= 6:
print([l[0], l[-1]])
[48, 62] [95, 100] [132, 145] [189, 194] [251, 268] [309, 319]
関数にまとめて，NINO.3の月平均海面水温を与えればエルニーニョの期間が得られるようにする。
In [30]:
from itertools import groupby
def detect_elnino(sst):
sst_smooth = np.convolve(sst_nino3, np.ones(5)/5, mode='valid')
condition = sst_smooth - sst_smooth.mean() >= 0.5
elnino_period = []
for key, group in groupby(range(condition.size), lambda i: condition[i]):
if (key):
l = list(group)
if len(l) >= 6:
elnino_period.append([l[0], l[-1]])
return elnino_period
In [31]:
elnino = detect_elnino(sst_nino3)
エルニーニョの期間が特定できた。
In [32]:
for i in elnino:
print(dates_smooth[i])
[datetime.date(1965, 3, 15) datetime.date(1966, 5, 15)] [datetime.date(1969, 2, 15) datetime.date(1969, 7, 15)] [datetime.date(1972, 3, 15) datetime.date(1973, 4, 15)] [datetime.date(1976, 12, 15) datetime.date(1977, 5, 15)] [datetime.date(1982, 2, 15) datetime.date(1983, 7, 15)] [datetime.date(1986, 12, 15) datetime.date(1987, 10, 15)]
最後にエルニーニョの期間に影をつけたグラフを描く。
In [33]:
plt.plot(dates_smooth, sst_nino3_smooth - sst_nino3_smooth.mean(), color='black')
plt.plot(dates_smooth, 0.5 * np.ones(sst_nino3_smooth.size), color='red')
for i in elnino:
plt.axvspan(dates_smooth[i[0]], dates_smooth[i[1]], color='red', alpha=0.3)
plt.show()
In [ ]: