def plotAdvectionOnMap(targetStation, variable, date, \
width_fac = 16, height_fac = 12):
from mpl_toolkits.basemap import Basemap
import matplotlib.pyplot as plt
import wUAdvection as Adv
import wUUtils as Util
# setup Lambert Conformal basemap.
m = Basemap(width=width_fac*100000,height=height_fac*100000, \
projection='lcc', resolution='i', \
lat_1=45.,lat_0=43.6,lon_0=-82.)
# draw coastlines.
m.drawcoastlines()
m.drawcountries()
m.drawstates()
# draw a boundary around the map, fill the background.
# this background will end up being the ocean color, since
# the continents will be drawn on top.
m.drawmapboundary(fill_color='aqua')
# fill continents, set lake color same as ocean color.
m.fillcontinents(color='wheat',lake_color='aqua')
# get station locations (Toronto, Montreal, Detroit)
stations = Util.getStationList()
lon, lat = Util.getStationLonLat(stations)
# convert to map projection coords.
# Note that lon,lat can be scalars, lists or numpy arrays.
xpt,ypt = m(lon,lat)
m.plot(xpt,ypt,'bo') # plot a blue dot there
# compute advection arrows between all other cities
# and the target station
for istation in range(len(stations)):
if stations[istation] != targetStation:
# print(targetStation, stations[istation], variable, date, date)
dD, uVec = Adv.dDeriv(targetStation, stations[istation], variable, \
date, nextDay(date))
stretch = 2500
dD = stretch*dD[0]
dx, dy = dD*uVec
plt.arrow(xpt[istation],ypt[istation],dx,dy,color='r',width=12000,head_length=40000,head_width=40000)
for istation in range(len(stations)):
plt.text(xpt[istation]+30000,ypt[istation]+20000,stations[istation])
plt.show()
def advectionTaylorPredict(model_params, startDate, endDate, actual=True):
# predict targetVar for a single station using
# previously generated regression model
import numpy as np
import wUUtils as Util
import wUAdvection as Adv
# extract city and feature data
stations = model_params['stations']
targetVar = model_params['targetVar']
features = model_params['features']
regr = model_params['regr']
lag = model_params['lag']
order = model_params['order']
# build list of dates in datetime format
date_list = Util.dateList(startDate, endDate)
date_list = date_list[(lag+order):]
# if actual data available
if actual:
# load target variable data
target = Util.loadDailyVariableRange(stations[0], startDate, endDate, \
targetVar, castFloat=True)
# "baseline" model is predicted target same as value on prediction day
baseline = target[order:(-lag)]
baseline = np.array(baseline)
# shift vector by lag
target = target[lag:]
target = np.array(target)
else:
target = None
# load feature data
featureData = []
# add data for target station
for feature in features:
fd = Util.loadDailyVariableRange(stations[0], startDate, endDate, \
feature, castFloat=True)
# shorten vector by lag
fd = fd[:(-lag)]
featureData.append(fd)
# for other stations, add the advection of each feature in the
# direction of the target station
for station in stations[1:]:
for feature in features:
# print("Adding " + feature + " from " + station)
fd, uVec = Adv.dDeriv(stations[0], station, \
feature, startDate, endDate)
# shorten vector by lag
fd = fd[:(-lag)]
featureData.append(fd)
# add in "derivative" terms
for ideriv in range(1,order+1):
ncols = len(stations)*len(features)
for ii in range(ncols):
# print("Adding " + str(ideriv) + " derivative of " + feature[jfeat])
fd = np.diff(featureData[ii],n=ideriv)
featureData.append(fd)
# shorten vectors to length of highest order derivative
nrows = len(featureData[-1])
for column in range(len(featureData)):
featureData[column] = featureData[column][-nrows:]
if actual:
target = target[-nrows:]
# convert features to np arrays
featureData = (np.array(featureData)).T
pred = regr.predict(featureData)
if actual:
print("R^2_mean:" + "\t" + str(regr.score(featureData,target)))
sse = ((pred-target)**2).sum()
ssm = ((baseline-target)**2).sum()
print("R^2_base:" + "\t" + str(1 - sse/ssm))
rmse = np.sqrt(((pred - target)**2).mean())
print("RMSE:\t" + "\t" + str(rmse))
model_perf = {
'R2_mean': regr.score(featureData,target), \
'R2_base': 1 - sse/ssm, \
'RMSE': rmse}
else:
model_perf = None
return date_list, pred, target, model_perf
def advectionTaylorModel(stations, startDate, endDate, \
features, targetVar='TempMax', \
lag=1, order=0, verbose=False):
# build regression model to predict "variable" for a single
# station using training data from multiple stations
# between startdate and enddate. Uses a "Taylor expansion"
# by combining information from several days (higher order
# time derivatives)
#
# for each variable, at target station, use value, and
# at other stations, only the projection of its gradient
# in the direction of the target station
#
# stations: a list of station codes, the first entry is
# the target station (for which forecast is generated)
# features: a list of variables to use as predictors
# lag: the number of days in the future to forecast
# order: the number of days in the past to include
# (also maximum order of time derivative)
import numpy as np
import wUUtils as Util
import wUAdvection as Adv
reload(Adv)
from sklearn import linear_model
# load target variable data
target = Util.loadDailyVariableRange(stations[0], startDate, endDate, \
targetVar, castFloat=True)
# shift vector by lag
target = target[lag:]
# load feature data
featureData = []
# add data for target station
for feature in features:
fd = Util.loadDailyVariableRange(stations[0], startDate, endDate, \
feature, castFloat=True)
# shorten vector by lag
fd = fd[:(-lag)]
featureData.append(fd)
# for other stations, add the advection of each feature in the
# direction of the target station
for station in stations[1:]:
for feature in features:
# print("Adding " + feature + " from " + station)
fd, uVec = Adv.dDeriv(stations[0], station, \
feature, startDate, endDate)
# shorten vector by lag
fd = fd[:(-lag)]
featureData.append(fd)
# add in "derivative" terms
for ideriv in range(1,order+1):
ncols = len(stations)*len(features)
for ii in range(ncols):
# print("Adding " + str(ideriv) + " derivative of " + feature[jfeat])
fd = np.diff(featureData[ii],n=ideriv)
featureData.append(fd)
# shorten vectors to length of highest order derivative
nrows = len(featureData[-1])
for column in range(len(featureData)):
featureData[column] = featureData[column][-nrows:]
target = target[-nrows:]
# convert target and features to np arrays
target = np.array(target)
featureData = (np.array(featureData)).T
regr = linear_model.LinearRegression()
regr.fit(featureData, target)
model_params = {
'stations': stations, \
'startDate': startDate, \
'endDate': endDate, \
'targetVar': targetVar, \
'features': features, \
'regr': regr, \
'lag': lag, \
'order': order}
# report regression results:
print("R^2: " + str(regr.score(featureData,target)))
if verbose:
print("Regression coefficients:")
print(" intercept" + ":\t" + str(regr.intercept_))
column = 0
for ideriv in range(order+1):
print(" " + str(ideriv) + "th derivative:")
for jj, station in enumerate(stations):
if jj > 0:
print(" Station (Adv): " + station)
else:
print(" Station: " + station)
for ii, feature in enumerate(features):
print(" " + feature + ":\t" + str(regr.coef_[column]))
column += 1
return featureData, target, model_params