Python气象数据处理与绘图(5)：气候突变检验(年代际突变检验)

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参考技术A 长时间尺度的气候研究中通常涉及到年际变化和年代际变化。文献中也经常出现所谓年代际突变这类的描述，这次便介绍两个用来检验年代际变化的方法， 其一是滑动t检验(sliding t-test)，另一个则是曼肯德尔检验(Man-Kendall test)。

滑动t检验是考察两组样本平均值的差异是否显著来检验突变。
滑动t检验的基本思想是：把一气候序列中两段子序列均值有无显著差异看为来自两个总体均值有无显著差异的问题来检验。如果两段子序列的均值差异超过了一定的显著性水平，可以认为均值发生了质变，有突变发生。

原文也提到了该方法的局限性，需要人为设置滑动步长，具有一定主观性，需反复设置不同步长最终确定合适的突变点。

自由度n1+n2-2，根据置信度检验表查找对应显著性阈值。

曼肯检验是一种非参检验方法，避免了滑动t检验的局限性，在年代际变化研究中受到广泛应用。

以下是计算步骤：

对于同一组数据：

分别使用两种方法进行检验，首先是滑动t检验：

存在多个突变点，这时便需要调整滑动补偿，选取合适的步长。
而利用MK检验：

对于该组数据，相比之下，MK检验的效果要优于滑动t检验。
两种检验的分析方法如下：
滑动t检验:

M-K检验：

python数据分析实战-第9章-数据分析实例气象数据

第9章　数据分析实例——气象数据　　230
9.1　待检验的假设：靠海对气候的影响　　230
9.2　数据源　　233
9.3　用IPython Notebook做数据分析　　234
9.4　风向频率玫瑰图　　246
9.5　小结　　251

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import numpy as np
import pandas as pd
import datetime
 
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ferrara = pd.read_json(‘http://api.openweathermap.org/data/2.5/history/city?q=Ferrara,IT‘)
 
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torino = pd.read_json(‘http://api.openweathermap.org/data/2.5/history/city?q=Torino,IT‘)
 
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mantova = pd.read_json(‘http://api.openweathermap.org/data/2.5/history/city?q=Mantova,IT‘)
 
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milano = pd.read_json(‘http://api.openweathermap.org/data/2.5/history/city?q=Milano,IT‘)
 
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ravenna = pd.read_json(‘http://api.openweathermap.org/data/2.5/history/city?q=Ravenna,IT‘)
 
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asti = pd.read_json(‘http://api.openweathermap.org/data/2.5/history/city?q=Asti,IT‘)
 
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bologna = pd.read_json(‘http://api.openweathermap.org/data/2.5/history/city?q=Bologna,IT‘)
 
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piacenza = pd.read_json(‘http://api.openweathermap.org/data/2.5/history/city?q=Piacenza,IT‘)
 
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cesena = pd.read_json(‘http://api.openweathermap.org/data/2.5/history/city?q=Cesena,IT‘)
 
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faenza = pd.read_json(‘http://api.openweathermap.org/data/2.5/history/city?q=Faenza,IT‘)
 
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def prepare(city_list,city_name):
    temp = [ ]
    humidity = [ ]
    pressure = [ ]
    description = [ ]
    dt = [ ]
    wind_speed = [ ]
    wind_deg = [ ]
    for row in city_list:
       temp.append(row[‘main‘][‘temp‘]-273.15)
       humidity.append(row[‘main‘][‘humidity‘])
       pressure.append(row[‘main‘][‘pressure‘])
       description.append(row[‘weather‘][0][‘description‘])
       dt.append(row[‘dt‘])
       wind_speed.append(row[‘wind‘][‘speed‘])
       wind_deg.append(row[‘wind‘][‘deg‘])
    headings = [‘temp‘,‘humidity‘,‘pressure‘,‘description‘,‘dt‘,‘wind_speed‘,‘wind_deg‘]
    data = [temp,humidity,pressure,description,dt,wind_speed,wind_deg]
    df = pd.DataFrame(data,index=headings)
    city = df.T
    city[‘city‘] = city_name
    city[‘day‘] = city[‘dt‘].apply(datetime.datetime.fromtimestamp)
    return city
 
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df_ferrara = prepare(ferrara.list,‘Ferrara‘)
df_milano = prepare(milano.list,‘Milano‘)
df_mantova = prepare(mantova.list,‘Mantova‘)
df_ravenna = prepare(ravenna.list,‘Ravenna‘)
df_torino = prepare(torino.list,‘Torino‘)
#df_alessandria = prepare(alessandria.list,‘Alessandria‘)
df_asti = prepare(asti.list,‘Asti‘)
df_bologna = prepare(bologna.list,‘Bologna‘)
df_piacenza = prepare(piacenza.list,‘Piacenza‘)
df_cesena = prepare(cesena.list,‘Cesena‘)
df_faenza = prepare(faenza.list,‘Faenza‘)
 
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print df_ferrara.shape
print df_milano.shape
print df_mantova.shape
print df_ravenna.shape
print df_torino.shape
print df_asti.shape
print df_bologna.shape
print df_piacenza.shape
print df_cesena.shape
print df_faenza.shape
 
(24, 9)
(24, 9)
(24, 9)
(24, 9)
(24, 9)
(24, 9)
(24, 9)
(24, 9)
(24, 9)
(24, 9)

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#http://it.thetimenow.com/distance-calculator.php
#(Comacchio)
df_ravenna[‘dist‘] = 8
df_cesena[‘dist‘] = 14
df_faenza[‘dist‘] = 37
df_ferrara[‘dist‘] = 47
df_bologna[‘dist‘] = 71
df_mantova[‘dist‘] = 121 
df_piacenza[‘dist‘] = 200
df_milano[‘dist‘] = 250
df_asti[‘dist‘] = 315
df_torino[‘dist‘] = 357
 
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import pandas as pd
#df_ferrara.to_csv(‘ferrara_270615.csv‘)
#df_milano.to_csv(‘milano_270615.csv‘)
#df_mantova.to_csv(‘mantova_270615.csv‘)
#df_ravenna.to_csv(‘ravenna_270615.csv‘)
#df_torino.to_csv(‘torino_270615.csv‘)
#df_asti.to_csv(‘asti_270615.csv‘)
#df_bologna.to_csv(‘bologna_270615.csv‘)
#df_piacenza.to_csv(‘piacenza_270615.csv‘)
#df_cesena.to_csv(‘cesena_270615.csv‘)
#df_faenza.to_csv(‘faenza_270615.csv‘)
df_ferrara = pd.read_csv(‘ferrara_270615.csv‘)
df_milano = pd.read_csv(‘milano_270615.csv‘)
df_mantova = pd.read_csv(‘mantova_270615.csv‘)
df_ravenna = pd.read_csv(‘ravenna_270615.csv‘)
df_torino = pd.read_csv(‘torino_270615.csv‘)
df_asti = pd.read_csv(‘asti_270615.csv‘)
df_bologna = pd.read_csv(‘bologna_270615.csv‘)
df_piacenza = pd.read_csv(‘piacenza_270615.csv‘)
df_cesena = pd.read_csv(‘cesena_270615.csv‘)
df_faenza = pd.read_csv(‘faenza_270615.csv‘)
 
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df_cesena.columns
 
Index([‘Unnamed: 0‘, ‘temp‘, ‘humidity‘, ‘pressure‘, ‘description‘, ‘dt‘,
       ‘wind_speed‘, ‘wind_deg‘, ‘city‘, ‘day‘, ‘dist‘],
      dtype=‘object‘)

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dist = [df_ravenna[‘dist‘][0],
     df_cesena[‘dist‘][0],
     df_faenza[‘dist‘][0],
     df_ferrara[‘dist‘][0],
     df_bologna[‘dist‘][0],
     df_mantova[‘dist‘][0],
     df_piacenza[‘dist‘][0],
     df_milano[‘dist‘][0],
     df_asti[‘dist‘][0],
     df_torino[‘dist‘][0]
]
temp_max = [df_ravenna[‘temp‘].max(),
     df_cesena[‘temp‘].max(),
     df_faenza[‘temp‘].max(),
     df_ferrara[‘temp‘].max(),
     df_bologna[‘temp‘].max(),
     df_mantova[‘temp‘].max(),
     df_piacenza[‘temp‘].max(),
     df_milano[‘temp‘].max(),
     df_asti[‘temp‘].max(),
     df_torino[‘temp‘].max()
]
temp_min = [df_ravenna[‘temp‘].min(),
     df_cesena[‘temp‘].min(),
     df_faenza[‘temp‘].min(),
     df_ferrara[‘temp‘].min(),
     df_bologna[‘temp‘].min(),
     df_mantova[‘temp‘].min(),
     df_piacenza[‘temp‘].min(),
     df_milano[‘temp‘].min(),
     df_asti[‘temp‘].min(),
     df_torino[‘temp‘].min()
]
hum_min = [df_ravenna[‘humidity‘].min(),
     df_cesena[‘humidity‘].min(),
     df_faenza[‘humidity‘].min(),
     df_ferrara[‘humidity‘].min(),
     df_bologna[‘humidity‘].min(),
     df_mantova[‘humidity‘].min(),
     df_piacenza[‘humidity‘].min(),
     df_milano[‘humidity‘].min(),
     df_asti[‘humidity‘].min(),
     df_torino[‘humidity‘].min()
]
hum_max = [df_ravenna[‘humidity‘].max(),
     df_cesena[‘humidity‘].max(),
     df_faenza[‘humidity‘].max(),
     df_ferrara[‘humidity‘].max(),
     df_bologna[‘humidity‘].max(),
     df_mantova[‘humidity‘].max(),
     df_piacenza[‘humidity‘].max(),
     df_milano[‘humidity‘].max(),
     df_asti[‘humidity‘].max(),
     df_torino[‘humidity‘].max()
]
 
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%matplotlib inline
import matplotlib.pyplot as plt
import matplotlib.dates as mdates
 
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#temperatura massima
plt.plot(dist,temp_max,‘ro‘)
 
[<matplotlib.lines.Line2D at 0xd697650>]

技术分享图片

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x = np.array(dist)
y = np.array(temp_max)
x1 = x[x<100]
x1 = x1.reshape((x1.size,1))
y1 = y[x<100]
x2 = x[x>50]
x2 = x2.reshape((x2.size,1))
y2 = y[x>50]
 
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from sklearn.svm import SVR
svr_lin1 = SVR(kernel=‘linear‘, C=1e3)
svr_lin2 = SVR(kernel=‘linear‘, C=1e3)
svr_lin1.fit(x1, y1)
svr_lin2.fit(x2, y2)
xp1 = np.arange(10,100,10).reshape((9,1))
xp2 = np.arange(50,400,50).reshape((7,1))
yp1 = svr_lin1.predict(xp1)
yp2 = svr_lin2.predict(xp2)
 
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plt.plot(xp1, yp1, c=‘r‘, label=‘Strong sea effect‘)
plt.plot(xp2, yp2, c=‘b‘, label=‘Light sea effect‘)
plt.axis((0,400,20,40))
plt.scatter(x, y, c=‘k‘, label=‘data‘)
 
<matplotlib.collections.PathCollection at 0x18627cf8>

技术分享图片

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from scipy.optimize import fsolve

def line1(x):
    a1 = svr_lin1.coef_[0][0]
    b1 = svr_lin1.intercept_[0]
    return -a1*x + b1
def line2(x):
    a2 = svr_lin2.coef_[0][0]
    b2 = svr_lin2.intercept_[0]
    return -a2*x + b2
def findIntersection(fun1,fun2,x0):
 return fsolve(lambda x : fun1(x) - fun2(x),x0)

result = findIntersection(line1,line2,0.0)
print "[x,y] = [ %d , %d ]" % (result,line1(result))
x = numpy.linspace(0,300,31)
plt.plot(x,line1(x),x,line2(x),result,line1(result),‘ro‘)
 
[x,y] = [ 101 , 34 ]



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

NameError                                 Traceback (most recent call last)

<ipython-input-25-389f5c694cae> in <module>()
     14 result = findIntersection(line1,line2,0.0)
     15 print "[x,y] = [ %d , %d ]" % (result,line1(result))
---> 16 x = numpy.linspace(0,300,31)
     17 plt.plot(x,line1(x),x,line2(x),result,line1(result),‘ro‘)


NameError: name ‘numpy‘ is not defined

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#temperatures min
plt.axis((0,400,15,25))
plt.plot(dist,temp_min,‘bo‘)
 
[<matplotlib.lines.Line2D at 0x18716320>]

技术分享图片

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#min humidity
plt.plot(dist,hum_min,‘bo‘)
 
[<matplotlib.lines.Line2D at 0x18b3de80>]

技术分享图片

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#max humidity
plt.plot(dist,hum_max,‘bo‘)
 
[<matplotlib.lines.Line2D at 0x18bc8080>]

技术分享图片

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#temperature
y1 = df_milano[‘temp‘]
x1 = df_milano[‘day‘]
fig, ax = plt.subplots()
plt.xticks(rotation=70)
hours = mdates.DateFormatter(‘%H:%M‘)
ax.xaxis.set_major_formatter(hours)
ax.plot(x1,y1,‘r‘)
 
[<matplotlib.lines.Line2D at 0x1a109f28>]

技术分享图片

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#humidity
y1 = df_milano[‘humidity‘]
x1 = df_milano[‘day‘]
fig, ax = plt.subplots()
plt.xticks(rotation=70)
hours = mdates.DateFormatter(‘%H:%M‘)
ax.xaxis.set_major_formatter(hours)
ax.plot(x1,y1,‘r‘)
 
[<matplotlib.lines.Line2D at 0x1a2f47f0>]

技术分享图片

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y1 = df_ravenna[‘temp‘]
x1 = df_ravenna[‘day‘]
y2 = df_ferrara[‘temp‘]
x2 = df_ferrara[‘day‘]
y3 = df_milano[‘temp‘]
x3 = df_milano[‘day‘]
fig, ax = plt.subplots()
plt.xticks(rotation=70)
hours = mdates.DateFormatter(‘%H:%M‘)
ax.xaxis.set_major_formatter(hours)
plt.plot(x1,y1,‘r‘,x2,y2,‘b‘,x3,y3,‘g‘)
 
[<matplotlib.lines.Line2D at 0x1a432e10>,
 <matplotlib.lines.Line2D at 0x1a586748>,
 <matplotlib.lines.Line2D at 0x1a586b38>]

技术分享图片

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y1 = df_ravenna[‘humidity‘]
x1 = df_ravenna[‘day‘]
y2 = df_ferrara[‘humidity‘]
x2 = df_ferrara[‘day‘]
y3 = df_milano[‘humidity‘]
x3 = df_milano[‘day‘]
fig, ax = plt.subplots()
plt.xticks(rotation=70)
hours = mdates.DateFormatter(‘%H:%M‘)
ax.xaxis.set_major_formatter(hours)
plt.plot(x1,y1,‘r‘,x2,y2,‘b‘,x3,y3,‘g‘)
 
[<matplotlib.lines.Line2D at 0x1a5d6f60>,
 <matplotlib.lines.Line2D at 0x1a7fb9b0>,
 <matplotlib.lines.Line2D at 0x1a7fbda0>]

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y1 = df_ravenna[‘humidity‘]
x1 = df_ravenna[‘day‘]
y2 = df_faenza[‘humidity‘]
x2 = df_faenza[‘day‘]
y3 = df_cesena[‘humidity‘]
x3 = df_cesena[‘day‘]
y4 = df_milano[‘humidity‘]
x4 = df_milano[‘day‘]
y5 = df_asti[‘humidity‘]
x5 = df_asti[‘day‘]
y6 = df_torino[‘humidity‘]
x6 = df_torino[‘day‘]
fig, ax = plt.subplots()
plt.xticks(rotation=70)
hours = mdates.DateFormatter(‘%H:%M‘)
ax.xaxis.set_major_formatter(hours)
plt.plot(x1,y1,‘r‘,x2,y2,‘r‘,x3,y3,‘r‘)
plt.plot(x4,y4,‘g‘,x5,y5,‘g‘,x6,y6,‘g‘)
 
[<matplotlib.lines.Line2D at 0x18606668>,
 <matplotlib.lines.Line2D at 0x1a86ec18>,
 <matplotlib.lines.Line2D at 0x1a861470>]

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y1 = df_ravenna[‘temp‘]
x1 = df_ravenna[‘day‘]
y2 = df_faenza[‘temp‘]
x2 = df_faenza[‘day‘]
y3 = df_cesena[‘temp‘]
x3 = df_cesena[‘day‘]
y4 = df_milano[‘temp‘]
x4 = df_milano[‘day‘]
y5 = df_asti[‘temp‘]
x5 = df_asti[‘day‘]
y6 = df_torino[‘temp‘]
x6 = df_torino[‘day‘]
fig, ax = plt.subplots()
plt.xticks(rotation=70)
hours = mdates.DateFormatter(‘%H:%M‘)
ax.xaxis.set_major_formatter(hours)
plt.plot(x1,y1,‘r‘,x2,y2,‘r‘,x3,y3,‘r‘)
plt.plot(x4,y4,‘g‘,x5,y5,‘g‘,x6,y6,‘g‘)
 
[<matplotlib.lines.Line2D at 0x1aa22a90>,
 <matplotlib.lines.Line2D at 0x1ac54ba8>,
 <matplotlib.lines.Line2D at 0x1ac49518>]

技术分享图片

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hum_mean = [df_ravenna[‘humidity‘].mean(),
     df_cesena[‘humidity‘].mean(),
     df_faenza[‘humidity‘].mean(),
     df_ferrara[‘humidity‘].mean(),
     df_bologna[‘humidity‘].mean(),
     df_mantova[‘humidity‘].mean(),
     df_piacenza[‘humidity‘].mean(),
     df_milano[‘humidity‘].mean(),
     df_asti[‘humidity‘].mean(),
     df_torino[‘humidity‘].mean()
]
plt.plot(dist,hum_mean,‘bo‘)
 
[<matplotlib.lines.Line2D at 0x1acbfb70>]

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y1 = df_ravenna[‘wind_speed‘]*20
y2 = df_ravenna[‘humidity‘]
x = df_ravenna[‘day‘]
fig, ax = plt.subplots()
plt.xticks(rotation=70)
hours = mdates.DateFormatter(‘%H:%M‘)
ax.xaxis.set_major_formatter(hours)
plt.plot(x,y1,‘r‘,x,y2,‘b‘)
 
[<matplotlib.lines.Line2D at 0x1ab2ee80>,
 <matplotlib.lines.Line2D at 0x1b0a0668>]

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plt.plot(df_ravenna[‘wind_deg‘],df_ravenna[‘wind_speed‘],‘ro‘)
 
[<matplotlib.lines.Line2D at 0x1b11c4e0>]

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plt.subplot(211)
plt.plot(df_cesena[‘wind_deg‘],df_cesena[‘humidity‘],‘bo‘)
plt.subplot(212)
plt.plot(df_cesena[‘wind_deg‘],df_cesena[‘wind_speed‘],‘bo‘)
 
[<matplotlib.lines.Line2D at 0x1b4db6d8>]

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hist, bins = np.histogram(df_ravenna[‘wind_deg‘],8,[0,360])
print hist
print bins
 
[3 4 9 6 1 1 0 0]
[   0.   45.   90.  135.  180.  225.  270.  315.  360.]

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def showRoseWind(values,city_name,max_value):
   N = 8
   theta = np.arange(0.,2 * np.pi, 2 * np.pi / N)
   radii = np.array(values)
   plt.axes([0.025, 0.025, 0.95, 0.95], polar=True)
   colors = [(1-x/max_value, 1-x/max_value, 0.75) for x in radii]
   plt.bar(theta, radii, width=(2*np.pi/N), bottom=0.0, color=colors)
   plt.title(city_name,x=0.2, fontsize=20)
 
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hist, bin = np.histogram(df_ravenna[‘wind_deg‘],8,[0,360])
print hist
showRoseWind(hist,‘Ravenna‘, 15.0)
 
[3 4 9 6 1 1 0 0]

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hist, bin = np.histogram(df_piacenza[‘wind_deg‘],8,[0,360])
print hist
showRoseWind(hist,‘Piacenza‘, 15.0)
 
[8 3 4 2 4 1 1 1]

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print df_milano[df_milano[‘wind_deg‘]<45][‘wind_speed‘]
print df_milano[df_milano[‘wind_deg‘]<45][‘wind_speed‘].mean()
 
1     2.6
3     2.1
5     2.1
13    0.5
14      1
18      1
21      1
Name: wind_speed, dtype: object
1.47142857143

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print df_milano[df_milano[‘wind_deg‘]<45][‘wind_speed‘].mean()
#print df_milano[(df_milano[‘wind_deg‘]>0) & (df_milano[‘wind_deg‘]<45)][‘wind_speed‘].mean()
print df_milano[(df_milano[‘wind_deg‘]>44) & (df_milano[‘wind_deg‘]<90)][‘wind_speed‘].mean()
print df_milano[(df_milano[‘wind_deg‘]>89) & (df_milano[‘wind_deg‘]<135)][‘wind_speed‘].mean()
print df_milano[(df_milano[‘wind_deg‘]>134) & (df_milano[‘wind_deg‘]<180)][‘wind_speed‘].mean()
print df_milano[(df_milano[‘wind_deg‘]>179) & (df_milano[‘wind_deg‘]<225)][‘wind_speed‘].mean()
print df_milano[(df_milano[‘wind_deg‘]>224) & (df_milano[‘wind_deg‘]<270)][‘wind_speed‘].mean()
print df_milano[(df_milano[‘wind_deg‘]>269) & (df_milano[‘wind_deg‘]<315)][‘wind_speed‘].mean()
#print df_milano[(df_milano[‘wind_deg‘]>314) & (df_milano[‘wind_deg‘]<360)][‘wind_speed‘].mean()
print df_milano[df_milano[‘wind_deg‘]>314][‘wind_speed‘].mean()
 
1.47142857143
2.04
2.06666666667
2.05
2.68333333333
2.1
nan
nan

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degs = np.arange(45,361,45)
print degs
 
[ 45  90 135 180 225 270 315 360]

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tmp =  []
for deg in degs:
    #print df_milano[(df_milano[‘wind_deg‘]>(deg-46)) & (df_milano[‘wind_deg‘]<deg)][‘wind_speed‘].mean()
    tmp.append(df_milano[(df_milano[‘wind_deg‘]>(deg-46)) & (df_milano[‘wind_deg‘]<deg)][‘wind_speed‘].mean())
speeds = np.array(tmp)
print speeds
 
[ 1.675              nan         nan         nan  2.93333333  3.13636364
  2.58               nan]

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N = 8
theta = np.arange(0.,2 * np.pi, 2 * np.pi / N)
radii = np.array(speeds)
plt.axes([0.025, 0.025, 0.95, 0.95], polar=True)
colors = [(1-x/10.0, 1-x/10.0, 0.75) for x in radii]
bars = plt.bar(theta, radii, width=(2*np.pi/N), bottom=0.0, color=colors)
plt.title(‘Milano‘,x=0.2, fontsize=20)
 
<matplotlib.text.Text at 0x1be13ef0>

技术分享图片

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def RoseWind_Speed(df_city):
   degs = np.arange(45,361,45)
   tmp =  []
   for deg in degs:
      tmp.append(df_city[(df_city[‘wind_deg‘]>(deg-46)) & (df_city[‘wind_deg‘]<deg)][‘wind_speed‘].mean())
   return np.array(tmp)
 
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def showRoseWind_Speed(speeds,city_name):
   N = 8
   theta = np.arange(0.,2 * np.pi, 2 * np.pi / N)
   radii = np.array(speeds)
   plt.axes([0.025, 0.025, 0.95, 0.95], polar=True)
   colors = [(1-x/10.0, 1-x/10.0, 0.75) for x in radii]
   bars = plt.bar(theta, radii, width=(2*np.pi/N), bottom=0.0, color=colors)
   plt.title(city_name,x=0.2, fontsize=20)
 
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showRoseWind(RoseWind_Speed(df_milano),‘Milano‘,10)

技术分享图片

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showRoseWind_Speed(RoseWind_Speed(df_ravenna),‘Ravenna‘)

技术分享图片

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showRoseWind_Speed(RoseWind_Speed(df_faenza),‘Faenza‘)

技术分享图片

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showRoseWind_Speed(RoseWind_Speed(df_cesena),‘Cesena‘)

技术分享图片

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showRoseWind_Speed(RoseWind_Speed(df_ferrara),‘Ferrara‘)

技术分享图片

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showRoseWind_Speed(RoseWind_Speed(df_torino),‘Torino‘)

技术分享图片

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showRoseWind_Speed(RoseWind_Speed(df_mantova),‘Mantova‘)

技术分享图片

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ferrara = pd.read_json(‘http://api.openweathermap.org/data/2.5/history/city?q=Ferrara,IT‘)
 
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df_ferrara.to_csv(‘ferrara.csv‘)
df_milano.to_csv(‘milano.csv‘)
df_mantova.to_csv(‘mantova.csv‘)
df_ravenna.to_csv(‘ravenna.csv‘)
df_torino.to_csv(‘torino.csv‘)
df_asti.to_csv(‘asti.csv‘)
df_bologna.to_csv(‘bologna.csv‘)
df_piacenza.to_csv(‘piacenza.csv‘)
df_cesena.to_csv(‘cesena.csv‘)
df_faenza.to_csv(‘faenza.csv‘)











































































































































































































































































































































































































































































































































































































































































































































































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