# Modeling the Joint Distribution of Wind Speed and Direction using Gaussain Mixture Models¶

OEN Method: Harris, Cook The parent wind speed distribution: Why Weibull? http://www.sciencedirect.com/science/article/pii/S0167610514001056

Gaussian Mixture Models, http://scikit-learn.org/stable/modules/mixture.html

# 1. Set up¶

## 1.1 Environment¶

In [1]:
%matplotlib inline

from import_file import *
from helpers.parallel_helper import *

plt.rcParams['axes.autolimit_mode'] = 'round_numbers'
plt.rcParams['axes.xmargin'] = 0.
plt.rcParams['axes.ymargin'] = 0.
mpl.rcParams['patch.force_edgecolor'] = True


In [2]:
# file_path, bandwidth= './data/NCDC/europe/uk/marham/dat.txt', 1.7
# file_path, bandwidth, NUMBER_OF_GAUSSIAN= './data/NCDC/europe/uk/tiree/dat.txt', 1.9, 4
# file_path, bandwidth, NUMBER_OF_GAUSSIAN = './data/NCDC/europe/uk/boscombe_down/dat.txt', 1.5, 4
# file_path, bandwidth= './data/NCDC/europe/uk/middle_wallop/dat.txt', 1.3
# file_path, bandwidth= './data/NCDC/europe/uk/bournemouth/dat.txt',1.3 # 4?
# file_path= "./data/NCDC/europe/uk/weybourne/dat.txt"
# file_path= "./data/NCDC/europe/uk/skye_lusa/dat.txt" #
# file_path= "./data/NCDC/europe/uk/wattisham/dat.txt"
# file_path= "./data/NCDC/europe/uk/south_uist_range/dat.txt" # inpropoer direction R square measure
# file_path= "./data/NCDC/europe/uk/holbeach/dat.txt" # inpropoer direction R square measure
# file_path= "./data/NCDC/europe/uk/cambridge/dat.txt" # inpropoer direction R square measure
# file_path= "./data/NCDC/europe/us/baltimore/dat.txt" # time too short
# file_path= "./data/NCDC/europe/uk/bealach_na_ba/dat.txt" # time too short
# file_path= "./data/NCDC/europe/uk/benbecula/dat.txt" # truncate (untruncate in m/s), 4?
# file_path= './data/NCDC/europe/uk/southhamption/dat.txt' # high 0, trend

# file_path, bandwidth, NUMBER_OF_GAUSSIAN = "./data/NCDC/europe/germany/landsberg_lech/dat.txt", 0.9, 4
# file_path, bandwidth= "./data/NCDC/europe/germany/neuburg/dat.txt", 0.7
# file_path, bandwidth= "./data/NCDC/europe/germany/laupheim/dat.txt", 0.7 # double peak, 4?, trend
# file_path, bandwidth= './data/NCDC/europe/germany/niederstetten/dat.txt', 0.9 # get the peak
# file_path, bandwidth= "./data/NCDC/europe/germany/holzdorf/dat.txt", 0.9 # 2008 year
# file_path, bandwidth, NUMBER_OF_GAUSSIAN= './data/NCDC/europe/france/nantes/dat.txt', 0.9, 4 # unit shift, one direction deviate big
# file_path= './data/NCDC/europe/france/pau_pyrenees/dat.txt' # unit shift, 2; force using knot
# file_path= "./data/NCDC/europe/france/avord/dat.txt" # try 4, initial speed (should be good with m/s), incompete dataset
# file_path= "./data/NCDC/europe/france/vatry/dat.txt"  # double peak, initial speed, incompete dataset
# file_path, bandwidth, NUMBER_OF_GAUSSIAN= "./data/NCDC/europe/spain/valladolid/dat.txt", 1.1, 4
# file_path= './data/NCDC/europe/spain/jerez/dat.txt' # high 0
# file_path, bandwidth= "./data/NCDC/europe/spain/barayas/dat.txt", 0.7 # not good fit
# file_path, bandwidth= './data/NCDC/europe/spain/malaga/dat.txt', 0.7 # directions blocked?
# file_path, bandwidth= './data/NCDC/europe/spain/tenerife_sur/dat.txt', 0.7 # directions blocked?
# file_path, bandwidth= './data/NCDC/europe/spain/almeria/dat.txt', 0.7 # negative dimensions?
# file_path, bandwidth= './data/NCDC/europe/greece/eleftherios_intl/dat.txt',0.7 # some direction might be blocked
# file_path= './data/NCDC/europe/ciampino/dat.txt' # try 4, bandwidth?
# file_path= "./data/NCDC/europe/huspel_aws/dat.txt"  # integer, 4?
# file_path= './data/NCDC/gibraltar/dat.txt' # bad fit

# MidEast
# file_path, bandwidth= './data/NCDC/mideast/uae/al_maktoum/dat.txt', 1.1
# file_path= './data/NCDC/mideast/uae/sharjah_intl/dat.txt'
# file_path= './data/NCDC/mideast/uae/dubai_intl/dat.txt'
# file_path= './data/NCDC/mideast/uae/abu_dhabi_intl/dat.txt' # Time shift
# file_path= './data/NCDC/mideast/uae/bateen/dat.txt' # Time shift
# file_path= './data/NCDC/mideast/buraimi/dat.txt' # not good dataset
# file_path= './data/NCDC/mideast/turkey/konya/dat.txt'
# file_path= './data/NCDC/mideast/turkey/sivas/dat.txt' # bad dataset
# file_path= './data/NCDC/mideast/turkey/balikesir/dat.txt' # bad dataset
# file_path= './data/NCDC/mideast/turkey/bartin/dat.txt' # bad dataset
# file_path= './data/NCDC/mideast/iran/chahbahar/dat.txt'
# file_path= './data/NCDC/mideast/iran/zabol/dat.txt' # Problematic data
# file_path= './data/NCDC/mideast/iran/torbat_heydarieh/dat.txt' # Unusable

# file_path, bandwidth = "./data/NCDC/cn/shanghai/hongqiao_intl/dat.txt", 0.6
# file_path, bandwidth= "./data/NCDC/cn/shanghai/pudong/dat.txt", 0.8
# file_path, bandwidth= "./data/NCDC/cn/hefei_luogang/dat.txt", 0.6 # few 0, trend, try 2
# file_path, bandwidth= "./data/NCDC/cn/nanjing_lukou/dat.txt", 0.5
# file_path= "./data/NCDC/cn/zhengzhou_xinzheng/dat.txt"
# file_path= "./data/NCDC/cn/tianjin/binhai/dat.txt" # few 0, trend, stationary speed, unstationary direction
# file_path= "./data/NCDC/cn/tianjin/tianjing/dat.txt" # 16 sectors
# file_path= "./data/NCDC/cn/shijiazhuang_zhengding/dat.txt"
# file_path= "./data/NCDC/cn/henan_gushi/dat.txt" # 16 sectors, fit not very good
# file_path= "./data/NCDC/cn/nanning_wuxu/dat.txt" # numpy priblem, unstationary speed
# file_path= './data/NCDC/cn/macau/dat.txt'
# file_path= "./data/NCDC/cn/hk_intl/dat.txt" # few 0
# file_path= './data/NCDC/cn/gaoqi/dat.txt'

# file_path= './data/NCDC/southeast_asia/malaysia/mersing/dat.txt' # 2 mode, paper comparison
# file_path= './data/NCDC/southeast_asia/malaysia/penang/dat.txt'
# file_path= './data/NCDC/southeast_asia/malaysia/butterworth/dat.txt' # 2 mode
# file_path= "./data/NCDC/southeast_asia/malaysia/bsultan_mahmud/dat.txt" # stable
# file_path= "./data/NCDC/southeast_asia/malaysia/bsultan_ismail/dat.txt" #
# file_path= "./data/NCDC/southeast_asia/singapore/changi/dat.txt" # trend, no 0, questionary data
# file_path= "./data/NCDC/southeast_asia/singapore/paya_lebar/dat.txt" # questionary data
# file_path= "./data/NCDC/southeast_asia/singapore/seletar/dat.txt"
# file_path= "./data/NCDC/east_asia/cheongju_intl/dat.txt" # 2005-2009  may have problem, fit is good; numpy problem
# file_path= "./data/NCDC/east_asia/daegu_ab/dat.txt" # recent 5 year may have problem, but fit is generally good; numpy problem

# file_path, bandwidth= "./data/NCDC/oceania/auckland_intl/dat.txt", 0.9  # Good data, double mode
# file_path= "./data/NCDC/oceania/brisbane_archerfield/dat.txt" # high 0, few data
# file_path= "./data/NCDC/oceania/narrandera/dat.txt" # high 0, few data
# file_path, bandwidth= "./data/NCDC/oceania/canberra/dat.txt", 0.7 # high 0, bad fit
# file_path, bandwidth, NUMBER_OF_GAUSSIAN= './data/NCDC/oceania/horsham/dat.txt', 0.9, 4 # get the peak

# file_path, bandwidth= './data/NCDC/us/boston_16nm/dat.txt', 0.9 # Offshore, mixed type

# file_path, bandwidth= './data/asos/olympia/hr_avg.csv', 0.5 # might block
# file_path, bandwidth, NUMBER_OF_GAUSSIAN  = './data/asos/bismarck_ND/hr_avg.csv', 1.1, 4
# file_path, bandwidth, NUMBER_OF_GAUSSIAN = './data/asos/aberdeen_SD/hr_avg.csv', 1.7, 2 # only to 2012
file_path, bandwidth, NUMBER_OF_GAUSSIAN = './data/asos/minneapolis/hr_avg.csv', 1.1, 4
# file_path, bandwidth = './data/asos/lincoln_NE/hr_avg.csv', 0.9
# file_path, bandwidth = './data/asos/des_moines_IA/hr_avg.csv', 1.3
# file_path, bandwidth = './data/asos/springfield_IL/hr_avg.csv', 1.1
# file_path, bandwidth = './data/asos/topeka/hr_avg.csv', 0.7 # High 0
# file_path, bandwidth = './data/asos/denver/hr_avg.csv', 1.3

# file_path, bandwidth, NUMBER_OF_GAUSSIAN = './data/NDAWN/baker/hr_avg.csv', 0.7, 4
# file_path, bandwidth = './data/NDAWN/dickinson/hr_avg.csv', 0.6
# file_path = './data/NDAWN/rugby/hr_avg.csv'
# file_path = './data/NDAWN/bowman/hr_avg.csv'
# file_path = './data/NDAWN/grand_forks/hr_avg.csv'
# file_path = './data/NDAWN/williston/hr_avg.csv'
# file_path = './data/NDAWN/jamestown/hr_avg.csv'

# file_path, bandwidth, NUMBER_OF_GAUSSIAN = 'data/ECMWF/usa/47N123W/dat.csv', 0.7, 4 #good
# file_path, bandwidth = 'data/ECMWF/venezuela/8N67W/dat.csv', 0.7 # good, but the data might be problematic.
# file_path, bandwidth = 'data/ECMWF/chile/52S75W/dat.csv', 1.9 # good
# file_path, bandwidth= 'data/ECMWF/iceland/65N17W/dat.csv', 1.9 # good
# file_path, bandwidth, NUMBER_OF_GAUSSIAN  = 'data/ECMWF/germany/49N9E/dat.csv', 1.1, 4 # miss peak
# file_path, bandwdith = 'data/ECMWF/sudan/18N32E/dat.csv', 1.1 # good
# file_path, bandwidth = 'data/ECMWF/china/24N121E/dat.csv', 0.9 # good
# file_path, bandwidth, NUMBER_OF_GAUSSIAN = 'data/ECMWF/australia/37S142E/dat.csv', 0.7, 4 # miss the peak, force bandwidth 0.7

In [3]:
if "cn_database" in file_path:
elif 'NCDC' in file_path:
df.rename(columns={'Date':'date','Dir':'dir','Spd':'speed','Type':'type','I.1':'wind_type'}, inplace=True)
df = df[['date','HrMn','type','dir','speed','wind_type' ]]
df.dropna(subset=['dir','speed'], inplace=True)
integer_data = True
elif 'NDAWN' in file_path:
df['type']='default'
df['wind_type']='default'
df = df.dropna()
convert_to_knot = False
integer_data = False
elif 'asos' in file_path:
# ASOS
df['type']='default'
df['wind_type']='default'
df = df.dropna()
convert_to_knot = False
integer_data = False
knot_unit = True
else:
df.rename(columns={'U':'x','V':'y'}, inplace=True)
df.x=-df.x
df.y=-df.y
df['speed']=np.sqrt(df.x**2+df.y**2)
df['dir']=np.degrees(np.arctan2(df.y, df.x))%360
df['time']=pd.to_datetime('1979-01-01T00:00:00Z')+pd.to_timedelta(df['time'], unit='h')
df['date']=df['time'].dt.strftime('%Y%m%d')
df['date']=df['date'].astype(int)
df['HrMn']=df['time'].dt.strftime('%H00')
df['type']='default'
df['wind_type']='default'
convert_to_knot = True
integer_data = False
cartesian = True

In [4]:
df

Out[4]:
date speed_max speed dir HrMn type wind_type
0 20000101 10.0 7.25 265.54 0000 default default
1 20000101 11.0 7.54 282.57 0100 default default
2 20000101 9.0 5.99 300.36 0200 default default
3 20000101 13.0 7.57 316.85 0300 default default
4 20000101 11.0 7.55 326.70 0400 default default
5 20000101 10.0 5.72 333.54 0500 default default
6 20000101 13.0 7.84 359.81 0600 default default
7 20000101 17.0 7.66 9.60 0700 default default
8 20000101 15.0 9.01 10.83 0800 default default
9 20000101 15.0 8.97 22.07 0900 default default
10 20000101 17.0 11.09 43.60 1000 default default
11 20000101 15.0 8.08 59.34 1100 default default
12 20000101 16.0 9.98 64.34 1200 default default
13 20000101 13.0 8.63 73.64 1300 default default
14 20000101 14.0 9.11 73.27 1400 default default
15 20000101 16.0 9.43 76.12 1500 default default
16 20000101 15.0 8.78 68.38 1600 default default
17 20000101 14.0 9.30 63.63 1700 default default
18 20000101 15.0 9.25 68.60 1800 default default
19 20000101 17.0 9.10 68.59 1900 default default
20 20000101 15.0 9.75 61.73 2000 default default
21 20000101 15.0 9.66 65.37 2100 default default
22 20000101 12.0 7.53 48.52 2200 default default
23 20000101 12.0 7.94 45.52 2300 default default
24 20000102 9.0 6.92 31.84 0000 default default
25 20000102 13.0 8.38 38.74 0100 default default
26 20000102 12.0 9.04 41.45 0200 default default
27 20000102 13.0 8.53 46.76 0300 default default
28 20000102 13.0 8.94 49.42 0400 default default
29 20000102 17.0 10.15 47.74 0500 default default
... ... ... ... ... ... ... ...
140860 20161230 12.0 8.29 148.22 1500 default default
140861 20161230 18.0 10.55 163.86 1600 default default
140862 20161230 17.0 11.02 171.45 1700 default default
140863 20161230 18.0 11.54 176.00 1800 default default
140864 20161230 19.0 10.65 173.49 1900 default default
140865 20161230 8.0 3.75 196.33 2000 default default
140866 20161230 10.0 2.98 240.04 2100 default default
140867 20161230 16.0 8.37 271.96 2200 default default
140868 20161230 21.0 11.02 291.91 2300 default default
140869 20161231 21.0 11.02 278.03 0000 default default
140870 20161231 22.0 12.44 285.56 0100 default default
140871 20161231 22.0 12.03 290.84 0200 default default
140872 20161231 21.0 12.82 300.28 0300 default default
140873 20161231 20.0 11.11 300.06 0400 default default
140874 20161231 22.0 13.55 333.92 0500 default default
140875 20161231 21.0 12.67 327.34 0600 default default
140876 20161231 24.0 13.80 322.47 0700 default default
140877 20161231 24.0 15.98 324.02 0800 default default
140878 20161231 22.0 13.95 318.25 0900 default default
140879 20161231 15.0 9.97 313.95 1000 default default
140880 20161231 16.0 10.38 308.63 1100 default default
140881 20161231 15.0 9.10 288.69 1200 default default
140882 20161231 14.0 9.22 274.42 1300 default default
140883 20161231 12.0 7.33 263.12 1400 default default
140884 20161231 14.0 8.47 239.63 1500 default default
140885 20161231 14.0 8.32 234.34 1600 default default
140886 20161231 13.0 7.68 225.05 1700 default default
140887 20161231 13.0 5.99 205.11 1800 default default
140888 20161231 13.0 7.02 204.43 1900 default default
140889 20161231 13.0 7.69 206.57 2000 default default

140890 rows Ã— 7 columns

In [5]:
if 'NCDC' in file_path:
lat, long = get_lat_long(file_path)
print(lat,long)
map_osm = folium.Map(location=[lat, long], zoom_start=4)
display(map_osm)

In [6]:
df['time']=pd.to_datetime(df["date"].astype(str).map(str) + df["HrMn"], format='%Y%m%d%H%M')
df.set_index(['time'], inplace=True)
df['HrMn']=df['HrMn'].astype(int)
df = df.query("(dir <= 999) & (speed < 100) ")['1970':'2016']

In [7]:
plot_speed_and_angle_distribution(df.speed, df.dir)

D:\ProgramData\Anaconda3\lib\site-packages\matplotlib\__init__.py:938: UserWarning: axes.color_cycle is deprecated and replaced with axes.prop_cycle; please use the latter.
warnings.warn(self.msg_depr % (key, alt_key))

In [8]:
# Dir [10,360]=> [0,350]
df['dir'] = df['dir'].apply(lambda x: x%360 if x < 999 else x)
# Convert Windrose coordianates to Polar Cooridinates
if 'cartesian' in globals():
df['dir_windrose'] = df['dir'].apply(lambda x: (90 - x)%360 if x < 999 else x)
else:
df['dir_windrose'] = df['dir']
df['dir'] = df['dir'].apply(lambda x: (90 - x)%360 if x < 999 else x)
display(df.describe())
df.plot(y='speed',legend=True,figsize=(20,5))

date speed_max speed dir HrMn dir_windrose
count 1.408900e+05 140890.000000 140890.000000 140890.000000 140890.000000 140890.000000
mean 2.008173e+07 13.783746 7.817171 195.383235 1150.363404 196.856811
std 4.882175e+04 6.476898 4.134382 96.638849 692.392299 99.056700
min 2.000010e+07 0.000000 0.000000 0.000000 0.000000 0.000000
25% 2.004052e+07 9.000000 4.700000 123.570000 500.000000 126.100000
50% 2.008091e+07 13.000000 7.340000 192.690000 1200.000000 196.990000
75% 2.012111e+07 18.000000 10.450000 285.880000 1800.000000 288.680000
max 2.016123e+07 76.000000 31.900000 359.980000 2300.000000 359.990000
Out[8]:
<matplotlib.axes._subplots.AxesSubplot at 0xc19e048>

## 1.3 General Data Info¶

### 1.3.1 Unit Detection¶

In [9]:
df['decimal'] = df.speed % 1
df.decimal.hist(alpha=0.5, label='m/s', figsize=(4, 3))

if 'convert_to_knot' not in globals():
convert_to_knot = True if len(df.query('decimal >= 0.2')) / len(df) > 0.3 else False

if convert_to_knot:
knot_unit = True
df['speed'] = df['speed'] * 1.943845
df['decimal'] = df.speed % 1
df.decimal.hist(alpha=0.5, label='knot')
# need more elaboration, some is not near an integer
if integer_data:
df['speed'] = df['speed'].apply(lambda x: int(round(x)))
plt_configure(xlabel='Decimal', ylabel='Frequency', legend={'loc': 'best'}, title='Decimal Distribution')
else:
if 'knot_unit' not in globals():
knot_unit = False

df.drop(['decimal'], 1,inplace=True)
print(knot_unit)

True

In [10]:
dir_unit_text = ' (degree)'
if knot_unit == True:
speed_unit_text = ' (knot)'
else:
speed_unit_text = ' (m/s)'


### 1.3.2 Sampling Type Selection¶

In [11]:
sample_type = df.query('date > 20000000')['type']
sample_type.value_counts().plot(
kind = 'bar', title = 'Report Types Comprisement', figsize=(4,3))

report_type_most_used = sample_type.value_counts().argmax()
df = df.query("type==@report_type_most_used")


### 1.3.3 Sampling Time Selection¶

In [12]:
MID_YEAR = int(np.average(df.index.year))

df['HrMn'].value_counts().sort_index().plot(kind='bar', alpha=0.5,label='Overall')
df[str(MID_YEAR):]['HrMn'].value_counts().sort_index().plot(
kind='bar', alpha=0.5, label='>= %s' %  MID_YEAR )

plt_configure(xlabel='Sampling Time', ylabel='Frequency', legend={'loc':'best'}, figsize=(8, 4),
title = 'Sampling Time Distribution, Overall and > %s ' %  MID_YEAR)

In [13]:
df['sample_time'] = df.HrMn % 100
sample_time = df['2000':]['sample_time']
sample_times = sample_time.value_counts()[sample_time.value_counts() > 2000]
sample_times = sample_times.index.tolist()
# df = df.query("sample_time in @sample_times")
df = df.query("sample_time == @sample_times[0]")
df.drop(['sample_time'], 1,inplace=True)
print(sample_times)

df['HrMn'].value_counts().sort_index().plot(kind='bar', alpha=0.5, figsize=(10, 4))

[0]

Out[13]:
<matplotlib.axes._subplots.AxesSubplot at 0xc184cf8>

## 1.4 Error Data handling and Adjustment¶

### 1.4.1 Artefacts¶

wrong direction record

In [14]:
if integer_data:
display(df.query("(dir % 10 >= 0.1) & (dir != 999)"))
df = df.query('(dir % 10 <= 0.1) | (dir == 999)')


sudden increase in speed

In [15]:
# sudden increse
df['incre'] = df.speed.diff(1)
df['incre'].fillna(0, inplace=True)
df['incre_reverse'] = df.speed.diff(-1)
df['incre_reverse'].fillna(0, inplace=True)

df['incre'].plot(kind='hist', bins=arange(-15, 15), legend=True, figsize=(8, 3))

date speed_max speed dir HrMn type wind_type dir_windrose incre incre_reverse
time
2014-06-14 12:00:00 20140614 56.0 31.90 293.63 1200 default default 156.37 8.04 7.09
2001-04-07 09:00:00 20010407 45.0 29.69 253.22 900 default default 196.78 4.57 1.22
2000-04-05 20:00:00 20000405 51.0 29.36 165.55 2000 default default 284.45 3.80 0.82
2016-11-18 15:00:00 20161118 51.0 28.81 118.13 1500 default default 331.87 4.33 5.72
2000-04-05 21:00:00 20000405 43.0 28.54 155.62 2100 default default 294.38 -0.82 6.01
2001-04-07 10:00:00 20010407 43.0 28.47 246.85 1000 default default 203.15 -1.22 0.18
2001-04-07 11:00:00 20010407 42.0 28.29 236.30 1100 default default 213.70 -0.18 0.46
2001-04-07 12:00:00 20010407 40.0 27.83 228.62 1200 default default 221.38 -0.46 0.08
2001-04-07 13:00:00 20010407 42.0 27.75 224.03 1300 default default 225.97 -0.08 2.55
2010-10-26 19:00:00 20101026 52.0 27.29 209.15 1900 default default 240.85 0.45 0.92
Out[15]:
<matplotlib.axes._subplots.AxesSubplot at 0xd2203c8>
In [16]:
incre_threshold = 20 if knot_unit else 10
print('sudden increase number', len(df.query('(incre > @incre_threshold )&(incre_reverse > @incre_threshold )')))
df = df.query('(incre < @incre_threshold )|(incre_reverse < @incre_threshold )')

# Check the max speed
df.drop(['incre', 'incre_reverse'], 1, inplace=True)

sudden increase number 0

date speed_max speed dir HrMn type wind_type dir_windrose incre incre_reverse
time
2014-06-14 12:00:00 20140614 56.0 31.90 293.63 1200 default default 156.37 8.04 7.09
2001-04-07 09:00:00 20010407 45.0 29.69 253.22 900 default default 196.78 4.57 1.22
2000-04-05 20:00:00 20000405 51.0 29.36 165.55 2000 default default 284.45 3.80 0.82
2016-11-18 15:00:00 20161118 51.0 28.81 118.13 1500 default default 331.87 4.33 5.72
2000-04-05 21:00:00 20000405 43.0 28.54 155.62 2100 default default 294.38 -0.82 6.01
2001-04-07 10:00:00 20010407 43.0 28.47 246.85 1000 default default 203.15 -1.22 0.18
2001-04-07 11:00:00 20010407 42.0 28.29 236.30 1100 default default 213.70 -0.18 0.46
2001-04-07 12:00:00 20010407 40.0 27.83 228.62 1200 default default 221.38 -0.46 0.08
2001-04-07 13:00:00 20010407 42.0 27.75 224.03 1300 default default 225.97 -0.08 2.55
2010-10-26 19:00:00 20101026 52.0 27.29 209.15 1900 default default 240.85 0.45 0.92

### 1.4.2 Direction re-aligment¶

For some dataset, the 16 sectors are not record properly,

e.g. the sectors are [0,20,50 ...], need to redistribute the angle into 22.5, e.g. [0, 22.5, 45...]

In [17]:
display(df['dir'].value_counts().sort_index())
effective_column = df.query('dir < 999')['dir'].value_counts()[df['dir'].value_counts() > 30].sort_index()
if integer_data:
SECTOR_LENGTH = 360/len(effective_column)
else:
SECTOR_LENGTH = 10
print(len(effective_column), SECTOR_LENGTH)

0.00      4
0.01      1
0.02      1
0.03      1
0.05      3
0.06      1
0.07      4
0.08      1
0.09      1
0.10      1
0.11      3
0.12      1
0.13      2
0.14      1
0.15      1
0.16      1
0.17      2
0.19      1
0.20      2
0.21      5
0.22      1
0.23      1
0.24      1
0.25      6
0.26      4
0.27      2
0.28      1
0.29      3
0.31      2
0.32      3
..
359.66    1
359.69    3
359.70    1
359.71    3
359.72    1
359.73    1
359.74    3
359.75    2
359.76    2
359.77    1
359.78    1
359.79    3
359.80    2
359.81    4
359.82    3
359.84    4
359.85    3
359.86    4
359.87    2
359.88    4
359.89    1
359.90    3
359.91    3
359.92    1
359.93    1
359.94    2
359.95    3
359.96    3
359.97    5
359.98    1
Name: dir, dtype: int64
1 10

In [18]:
df=realign_direction(df, effective_column)


### 1.4.3 0 Speed¶

In [19]:
with_too_many_zero, null_wind_frequency = is_with_too_many_zero(df['2005':])
delete_zero = with_too_many_zero
if delete_zero:
df = df.query('(speed > 0)')
print(delete_zero, null_wind_frequency)

False 0.0160740718664

In [20]:
print(df.query('dir == 999')['speed'].value_counts())
df=fill_direction_999(df, SECTOR_LENGTH)

Series([], Name: speed, dtype: int64)


## 1.5 Time Shift Comparison¶

In [21]:
DIR_REDISTRIBUTE = 'even'
if DIR_REDISTRIBUTE == 'even':
DIR_BIN = arange(-5, 360, 10)
elif DIR_REDISTRIBUTE == 'round_up':
DIR_BIN = arange(0, 360+10, 10)

# Comparison between mid_year, looking for:
# 1. Odd Even Bias
# 2. Time Shift of Wind Speed Distribution
bins = arange(0, df.speed.max() + 1)
df[:str(MID_YEAR)]['speed'].plot(
kind='hist', alpha=0.5,bins=bins, label='< %s' % MID_YEAR)

df[str(MID_YEAR+1):]['speed'].plot(
kind='hist', alpha=0.5,bins=bins, label='> %s' % MID_YEAR)

plt.suptitle('Speed Comparison between year < %s, > %s ' % (MID_YEAR, MID_YEAR), fontsize = 14)
plt_configure(xlabel='Speed', ylabel='Frequency', legend=True, figsize=(8, 3))

In [22]:
df[:str(MID_YEAR)]['dir'].plot(
kind='hist', alpha=0.5,bins=DIR_BIN, label='< %s' % MID_YEAR)

df[str(MID_YEAR+1):]['dir'].plot(
kind='hist', alpha=0.5,bins=DIR_BIN, label='> %s' % MID_YEAR)

plt.suptitle('Dir Comparison between year < %s, and > %s ' % (MID_YEAR, MID_YEAR), fontsize = 14)
plt_configure(xlabel='Dir', ylabel='Frequency', legend={'loc':'best'}, figsize=(8, 3), tight='x')

In [23]:
display(df[df['dir'].isnull()])
df.dropna(subset=['dir'], inplace=True)

date speed_max speed dir HrMn type wind_type dir_windrose
time
In [24]:
# Inspect the time shift of speed and degree distribution, and odd-even bias
check_time_shift(df, speed_unit_text=speed_unit_text, dir_unit_text=dir_unit_text)

2001 - 2005

D:\ProgramData\Anaconda3\lib\site-packages\matplotlib\__init__.py:938: UserWarning: axes.color_cycle is deprecated and replaced with axes.prop_cycle; please use the latter.
warnings.warn(self.msg_depr % (key, alt_key))

2006 - 2010

2011 - 2015

In [25]:
df.resample('A').mean().plot(y='speed')
plt.gca().set_ylim(bottom=0)
df.resample('M').mean().plot(y='speed', figsize=(20,4))
plt.gca().set_ylim(bottom=0)

Out[25]:
(0, 11.0)
In [26]:
%%time
for column in ['speed', 'dir']:
if column == 'speed':
bins = arange(0, df[column].max()+1, 1)
else:
bins = arange(0, 361, 10)
den, _ = np.histogram(df[column], bins=bins, density=True)
y_top=max(den)*1.2
for year in arange(1980, 2016):
end_year = year
sub_df = df[str(year):str(end_year)]
if len(sub_df) > 1000:
plt.figure()
df[column].hist(bins=bins, alpha=0.3, normed=True)
sub_df[column].hist(bins=bins, alpha=0.5, figsize=(3,1.5), normed=True)
plt.gca().set_ylim(top=y_top)
plt_configure(title=str(year))
align_figures()

Wall time: 10.3 s

In [27]:
for column in ['speed', 'dir']:
if column == 'speed':
bins = arange(0, df[column].max()+1, 1)
else:
bins = arange(0, 361, 10)
density_all, _ = np.histogram(df[column], bins=bins, density=True)
df[column].hist(bins=bins, figsize=(5,3))

R_squares = []
years = []
for year in arange(1980, 2016):
start_year, end_year = year-1, year+1
sub_df = df[str(start_year):str(end_year)]
if len(sub_df) > 1000:
density, _ = np.histogram(sub_df[column], bins=bins, density=True)
y_mean = np.mean(density_all)
SS_tot = np.sum(np.power(density_all - y_mean, 2))
SS_res = np.sum(np.power(density_all - density, 2))

R_square = 1 - SS_res / SS_tot
R_squares.append(R_square)
years.append(year)

plt.figure()
plot(years, R_squares)
ylim = max(min(plt.gca().get_ylim()[0],0.85),0)
plt.gca().set_ylim(bottom=ylim, top=1)
plt_configure(figsize=(5,3))
align_figures()


## 1.6 Re-distribute Direction and Speed (Optional)¶

e.g. Dir 50 -> -45 ~ 55, to make KDE result better

In [28]:
if integer_data:
df = randomize_angle(df, DIR_REDISTRIBUTE, SECTOR_LENGTH)

In [29]:
if integer_data:
if delete_zero:
redistribute_method = 'down'
else:
redistribute_method = 'up'

df, speed_redistribution_info = randomize_speed(df, redistribute_method)


## 1.7 Generate (x,y) from (speed,dir)¶

In [30]:
# Cook orientation
# df['dir']= (df['dir'] + 180)%360

In [31]:
# There might be a small dot in the centre, which is due to too many zero (more than 1 speed) in center
# Scatter plot in matplot has performance issue, the speed is very slow
df['x'] = df['speed'] * cos(df['dir'] * pi / 180.0)
df['y'] = df['speed'] * sin(df['dir'] * pi / 180.0)


# 2. Re-select Data and Overview¶

## 2.1 Data Overview¶

In [32]:
## Summery of the data selection
print('Knot unit?', knot_unit)
print('Report type used:', report_type_most_used)
print('Sampling time used:', sample_times)
if 'speed_redistribution_info' in globals():
print('Speed redistribution info:', speed_redistribution_info )

df_all_years = df # for later across-year comparison
df = df_all_years['2011':'2015']
# df = df.query('(HrMn == 0) and (speed >= 0.5) and (date%10000 > 900) and (date%10000 < 1000)' )
df.describe()

Knot unit? True
Report type used: default
Sampling time used: [0]

Out[32]:
date speed_max speed dir HrMn dir_windrose x y
count 4.253800e+04 42538.000000 42538.000000 42538.000000 42538.000000 42538.000000 42538.000000 42538.000000
mean 2.013078e+07 14.087522 7.755293 197.030299 1150.303258 195.962790 -0.716125 -0.125169
std 1.410164e+04 6.613855 4.157751 97.192196 691.598382 99.198001 6.240054 6.161663
min 2.011010e+07 1.000000 0.000000 0.020000 0.000000 0.000000 -25.695173 -29.225280
25% 2.012040e+07 9.000000 4.600000 124.220000 600.000000 125.120000 -4.660698 -4.296425
50% 2.013071e+07 13.000000 7.190000 194.155000 1200.000000 193.390000 -0.470672 -0.637495
75% 2.014100e+07 18.000000 10.430000 288.790000 1700.000000 288.630000 3.539646 4.221872
max 2.015123e+07 59.000000 31.900000 359.970000 2300.000000 359.990000 25.003446 21.725100
In [33]:
df.plot(y='speed',legend=True,figsize=(20,5))

Out[33]:
<matplotlib.axes._subplots.AxesSubplot at 0x11f8c0b8>
In [34]:
# Accumulation by month
df.resample('M').count().plot(y='date', kind='bar',figsize=(20,4))

Out[34]:
<matplotlib.axes._subplots.AxesSubplot at 0x16d92320>
In [35]:
# 90 degree is east
ax = WindroseAxes.from_ax()
viridis = plt.get_cmap('viridis')
ax.bar(df.dir_windrose, df.speed, normed=True, opening=0.8, edgecolor='white', nsector=36, cmap=viridis)
ax.set_legend()

D:\ProgramData\Anaconda3\lib\site-packages\matplotlib\cbook.py:136: MatplotlibDeprecationWarning: The axisbg attribute was deprecated in version 2.0. Use facecolor instead.
warnings.warn(message, mplDeprecation, stacklevel=1)