

In [1]:

    
# Load Biospytial modules and etc.
%matplotlib inline
import sys
sys.path.append('/apps')
import django
django.setup()
import pandas as pd
import matplotlib.pyplot as plt
## Use the ggplot style
plt.style.use('ggplot')



In [2]:

    
# My mac
#data = pd.read_csv("/RawDataCSV/plotsClimateData_11092017.csv")
# My Linux desktop
data = pd.read_csv("/RawDataCSV/idiv_share/plotsClimateData_11092017.csv")









    



/opt/conda/envs/biospytial/lib/python2.7/site-packages/IPython/core/interactiveshell.py:2717: DtypeWarning: Columns (24) have mixed types. Specify dtype option on import or set low_memory=False.
  interactivity=interactivity, compiler=compiler, result=result)



In [3]:

    
data.SppN.mean()









    Out[3]:





5.1824128104220382



In [4]:

    
import geopandas as gpd



In [5]:

    
from django.contrib.gis import geos
from shapely.geometry import Point



In [6]:

    
data['geometry'] = data.apply(lambda z: Point(z.LON, z.LAT), axis=1)
new_data = gpd.GeoDataFrame(data)

Let´s reproject to Alberts or something with distance



In [7]:

    
new_data.crs = {'init':'epsg:4326'}

Uncomment to reproject

proj string taken from: http://spatialreference.org/



In [8]:

    
#new_data =  new_data.to_crs("+proj=aea +lat_1=29.5 +lat_2=45.5 +lat_0=37.5 +lon_0=-96 +x_0=0 +y_0=0 +ellps=GRS80 +datum=NAD83 +units=m +no_defs ")

Model Fitting Using a GLM

The general model will have the form: $$ Biomass(x,y) = \beta_1 AET + \beta_2 Age + Z(x,y) + \epsilon $$ Where: $\beta_1$ and $\beta_2$ are model parameters, $Z(x,y)$ is the Spatial Autocorrelation process and $\epsilon \sim N(0,\sigma^2)$



In [9]:

    
##### OLD #######
len(data.lon)
#X = data[['AET','StandAge','lon','lat']]
#X = data[['SppN','lon','lat']]
X = data[['lon','lat']]
#Y = data['plotBiomass']
Y = data[['SppN']]
## First step in spatial autocorrelation
#Y = pd.DataFrame(np.zeros(len(Y)))
## Let´s take a small sample only for the spatial autocorrelation
#import numpy as np
#sample_size = 2000
#randindx = np.random.randint(0,X.shape[0],sample_size)
#nX = X.loc[randindx]
#nY = Y.loc[randindx]
nX = X
nY = Y



In [10]:

    
## Small function for systematically selecting the k-th element of the data.
#### Sughgestion use for now a small k i.e. 10
systematic_selection = lambda k : filter(lambda i : not(i % k) ,range(len(data)))



In [12]:

    
idx = systematic_selection(50)
print(len(idx))
nX = X.loc[idx]
nY = Y.loc[idx]
new_data = data.loc[idx]



In [13]:

    
len(new_data)









    Out[13]:





737



In [22]:

    
# Import GPFlow
import GPflow as gf
k = gf.kernels.Matern12(2,ARD=False,active_dims = [0,1]) + gf.kernels.Bias(1)
#k = gf.kernels.Matern12(2, lengthscales=1, active_dims = [0,1] ) + gf.kernels.Bias(1)
l = gf.likelihoods.Poisson()
model = gf.gpmc.GPMC(nX.as_matrix(), nY.as_matrix().reshape(len(nY),1).astype(float), k, l)



In [24]:

    
#model = gf.gpr.GPR(nX.as_matrix(),nY.as_matrix().reshape(len(nY),1).astype(float),k)
## If priors
#model.kern.matern12.lengthscales.prior = gf.priors.Gaussian(25.0,3.0)
#model.kern.matern32.variance.prior = GPflow.priors.Gamma(1.,1.)
#model.kern.bias.variance.prior = gf.priors.Gamma(1.,1.)
## Optimize

%time model.optimize(maxiter=100) # start near MAP









    



CPU times: user 35.9 s, sys: 3.04 s, total: 39 s
Wall time: 14.9 s






    Out[24]:





      fun: array([ 1913.86902295])
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  message: 'STOP: TOTAL NO. of ITERATIONS EXCEEDS LIMIT'
     nfev: 114
      nit: 101
   status: 1
  success: False
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         4.19618309e-02,   9.62864421e-02,   8.74883480e-04,
         8.37360432e-03,   1.09728009e-01,   4.20469869e-02,
         1.45126598e-01,  -1.83762312e-02,   3.86635153e-02,
         8.69823451e-02,   3.58537924e-04,  -1.04487183e-01,
        -2.45852537e-01,   5.14327089e-02,   1.19603458e-01,
         2.85768887e-02,   1.08473534e-01,   1.05474765e-01,
         2.20459676e-01,   1.46270680e-01,   7.50594352e-02,
         1.97907230e-01,   1.48012811e-01,   1.65757473e-02,
        -5.87251654e-02,   1.53539234e-01,   6.69509268e-02,
         1.21907588e-01,   1.51393475e-01,  -2.63809742e-04,
         2.41674922e-02,  -2.22419706e-01,   4.45444038e-02,
         3.27989364e-02,  -2.89163527e-01,  -1.55113408e-01,
        -1.00844963e-01,   1.23985422e-01,  -2.28174605e-01,
         2.28146346e-01,   1.39339786e-01,   1.70601181e-02,
        -7.11815963e-03,   4.01522057e-02,  -5.07584481e-02,
         2.16524993e-01,   5.50088078e-02,   4.98188647e-02,
        -4.70365645e-02,  -7.54697494e-02,  -4.79838494e-02,
        -1.09040227e-01,  -1.09500533e-01,  -1.00045826e-01,
         4.41687730e-02,  -1.08207002e-01,  -1.07927252e-01,
        -8.82630267e-02,  -9.09400376e-02,  -2.13603337e-01,
        -9.60832841e-02,   3.10071648e-02,  -9.68290681e-02,
        -1.21319957e-02,   3.20076769e-02,   7.74974606e-02,
         1.74561184e-02,   9.43795242e-02,   6.86565025e-02,
         1.34606927e-01,   8.82879786e-02,   1.27684525e-01,
         3.01693189e-02,   1.57034996e-01,   1.36229575e-01,
         1.38071561e-01,  -2.53134826e-01,   7.76376490e-02,
         1.27002004e-01,   2.83792913e-02,  -8.70124444e-02,
         4.78445033e-02,   7.22063874e-02,   1.12118901e-01,
         7.64935537e-02,   1.19837796e-01,  -4.55258084e-02,
         2.14174065e-01,   9.84080974e-02,   9.06559766e-02,
        -7.30136498e-02,   8.69776513e-02,   1.27742318e-01,
         4.39258793e-02,  -2.73302888e-02,   6.58541634e-02,
         8.52276073e-02,  -6.05889766e-02,  -4.64643463e-02,
        -2.30426846e-01,   8.40224833e-03,   4.34120037e-03,
        -4.43145900e-02,   2.70375518e-02,  -1.03619488e-01,
        -1.38906925e-01,   2.26609165e-02,  -1.01974856e-01,
         7.92645558e-02,  -2.49703331e-01,   6.85769022e-03,
        -5.75569664e-02,  -1.16740931e-01,   6.45636538e-03,
         1.01311024e-02,   5.46279469e-02,  -2.10341031e-01,
         1.59814515e-02,   1.26607666e-01,  -1.17623882e-01,
         1.47459515e-01,  -1.54374667e-01,  -4.94605430e-02,
         6.10530255e-02,   3.71143418e-04,  -1.25649938e-02,
         1.27805037e-01,   2.07061127e-01,   1.60948010e-01,
         3.46812797e-03,  -6.03664894e-03,   9.07043501e-02,
        -7.77421549e-03,   4.23033378e-02,   6.99738133e-02,
        -1.12243048e-02,  -1.16454029e-02,   1.05765734e-01,
         1.01957068e-01,  -1.13298270e-01,   7.20562393e-02,
        -2.75689751e-03,   2.62257125e-02,   3.92531799e-02,
         6.00809695e-02,   1.36869803e-01,   2.28936019e-02,
         1.06593523e-01,  -1.25092432e-01,  -1.39701259e-01,
         1.43435852e-01,   1.56955351e-01,  -6.81471080e-02,
        -2.51083108e-01,   7.91610824e-02,   8.88977367e-02,
        -1.17000255e-01,   1.72084722e-01,   1.72922943e-02,
         1.59501748e-01,  -2.54246262e-02,   1.46573579e-01,
         1.49634062e-01,  -7.85896896e-02,   1.00551817e-01,
        -3.05451100e-02,   9.56232340e-02,   1.62702525e-01,
         3.19564617e-02,  -1.94911485e-02,  -1.87556197e-02,
        -1.14175211e-01,  -8.95948669e-02,   4.19087800e-02,
         1.12978735e-01,   3.66152636e-01,  -4.06523847e-02,
         5.87593566e-02,  -3.47792191e-01,  -2.07739205e-01,
        -1.75074220e-02,  -3.25719715e-01,  -1.46003667e-02,
        -8.80783038e-02,   7.43829388e-02,   2.56135095e+00,
        -6.91135597e-01,   2.81189070e+01])



In [25]:

    
model.kern









    Out[25]:




Name values prior constraint
kern.bias.variance [ 2.63571738] None +ve
kern.matern12.lengthscales [ 0.40613709] None +ve
kern.matern12.variance [ 28.11890802] None +ve



In [26]:

    
samples = model.sample(50, verbose=True, epsilon=1, Lmax=100)









    



warning: numerical instability.                  Rejecting this proposal prematurely
warning: numerical instability.                  Rejecting this proposal prematurely
warning: numerical instability.                  Rejecting this proposal prematurely
warning: numerical instability.                  Rejecting this proposal prematurely
warning: numerical instability.                  Rejecting this proposal prematurely
warning: numerical instability.                  Rejecting this proposal prematurely
warning: numerical instability.                  Rejecting this proposal prematurely
warning: numerical instability.                  Rejecting this proposal prematurely
warning: numerical instability.                  Rejecting this proposal prematurely
warning: numerical instability.                  Rejecting this proposal prematurely
warning: numerical instability.                  Rejecting this proposal prematurely
warning: numerical instability.                  Rejecting this proposal prematurely
warning: numerical instability.                  Rejecting this proposal prematurely
warning: numerical instability.                  Rejecting this proposal prematurely
warning: numerical instability.                  Rejecting this proposal prematurely
warning: numerical instability.                  Rejecting this proposal prematurely
warning: numerical instability.                  Rejecting this proposal prematurely
warning: numerical instability.                  Rejecting this proposal prematurely
warning: numerical instability.                  Rejecting this proposal prematurely
warning: numerical instability.                  Rejecting this proposal prematurely
warning: numerical instability.                  Rejecting this proposal prematurely
warning: numerical instability.                  Rejecting this proposal prematurely
warning: numerical instability.                  Rejecting this proposal prematurely
warning: numerical instability.                  Rejecting this proposal prematurely
warning: numerical instability.                  Rejecting this proposal prematurely
warning: numerical instability.                  Rejecting this proposal prematurely
warning: numerical instability.                  Rejecting this proposal prematurely
warning: numerical instability.                  Rejecting this proposal prematurely
warning: numerical instability.                  Rejecting this proposal prematurely
warning: numerical instability.                  Rejecting this proposal prematurely

Fitted parameters (From HEC)



In [ ]:

    
model.kern.lengthscales = 25.4846122373
model.kern.variance = 10.9742076021
model.likelihood.variance = 4.33463026664



In [ ]:

    
%time mm = k.compute_K_symm(X.as_matrix())



In [ ]:

    
import numpy as np
Nn = 500
dsc = data
predicted_x = np.linspace(min(dsc.lon),max(dsc.lon),Nn)
predicted_y = np.linspace(min(dsc.lat),max(dsc.lat),Nn)
Xx, Yy = np.meshgrid(predicted_x,predicted_y)
## Fake richness
fake_sp_rich = np.ones(len(Xx.ravel()))
predicted_coordinates = np.vstack([ Xx.ravel(), Yy.ravel()]).transpose()
#predicted_coordinates = np.vstack([section.SppN, section.newLon,section.newLat]).transpose()



In [ ]:

    
len(predicted_coordinates)



In [ ]:

    
#We will calculate everything with the new model and parameters
#model = gf.gpr.GPR(X.as_matrix(),Y.as_matrix().reshape(len(Y),1).astype(float),k)



In [ ]:

    
%time means,variances = model.predict_y(predicted_coordinates)

#USING k-partition = 10 import cartopy plt.figure(figsize=(17,11)) proj = cartopy.crs.PlateCarree() ax = plt.subplot(111, projection=proj) ax = plt.axes(projection=proj) #algo = new_data.plot(column='SppN',ax=ax,cmap=colormap,edgecolors='') #ax.set_extent([-93, -70, 30, 50]) ax.set_extent([-125, -60, 20, 50]) #ax.set_extent([-95, -70, 25, 45]) #ax.add_feature(cartopy.feature.LAND) ax.add_feature(cartopy.feature.OCEAN) ax.add_feature(cartopy.feature.COASTLINE) ax.add_feature(cartopy.feature.BORDERS, linestyle=':') ax.add_feature(cartopy.feature.LAKES, alpha=0.9) ax.stock_img() #ax.add_geometries(new_data.geometry,crs=cartopy.crs.PlateCarree()) #ax.add_feature(cartopy.feature.RIVERS) mm = ax.pcolormesh(Xx,Yy,means.reshape(Nn,Nn),transform=proj ) #cs = plt.contour(Xx,Yy,np.sqrt(variances).reshape(Nn,Nn),linewidths=2,cmap=plt.cm.Greys_r,linestyles='dotted') cs = plt.contour(Xx,Yy,means.reshape(Nn,Nn),linewidths=2,colors='k',linestyles='dotted',levels=[4.0,5.0,6.0,7.0,8.0]) plt.clabel(cs, fontsize=16,inline=True,fmt='%1.1f') #ax.scatter(new_data.lon,new_data.lat,edgecolors='',cmap=plt.cm.Accent,alpha=0.6) plt.colorbar(mm) plt.title("Predicted Species Richness") #(x.LON > -90) & (x.LON < -80) & (x.LAT > 40) & (x.LAT < 50)



In [ ]:

    
-

Predictions with +2std.Dev



In [ ]:

    
#Using k-partition = 7
import cartopy
plt.figure(figsize=(17,11))

proj = cartopy.crs.PlateCarree()
ax = plt.subplot(111, projection=proj)


ax = plt.axes(projection=proj)
#algo = new_data.plot(column='SppN',ax=ax,cmap=colormap,edgecolors='')


#ax.set_extent([-93, -70, 30, 50])
ax.set_extent([-125, -60, 20, 50])
#ax.set_extent([-95, -70, 25, 45])

#ax.add_feature(cartopy.feature.LAND)
ax.add_feature(cartopy.feature.OCEAN)
ax.add_feature(cartopy.feature.COASTLINE)
ax.add_feature(cartopy.feature.BORDERS, linestyle=':')
ax.add_feature(cartopy.feature.LAKES, alpha=0.9)
ax.stock_img()
#ax.add_geometries(new_data.geometry,crs=cartopy.crs.PlateCarree())
#ax.add_feature(cartopy.feature.RIVERS)
mm = ax.pcolormesh(Xx,Yy,means.reshape(Nn,Nn) + (2* np.sqrt(variances).reshape(Nn,Nn)),transform=proj )
#cs = plt.contour(Xx,Yy,np.sqrt(variances).reshape(Nn,Nn),linewidths=2,cmap=plt.cm.Greys_r,linestyles='dotted')
cs = plt.contour(Xx,Yy,means.reshape(Nn,Nn) + (2 * np.sqrt(variances).reshape(Nn,Nn)),linewidths=2,colors='k',linestyles='dotted',levels=range(1,20))
plt.clabel(cs, fontsize=16,inline=True,fmt='%1.1f')
#ax.scatter(new_data.lon,new_data.lat,edgecolors='',color='white',alpha=0.6)
plt.colorbar(mm)
plt.title("Predicted Species Richness + 2stdev")

Predicted means



In [ ]:

    
#Using k-partition = 7
import cartopy
plt.figure(figsize=(17,11))

proj = cartopy.crs.PlateCarree()
ax = plt.subplot(111, projection=proj)


ax = plt.axes(projection=proj)
#algo = new_data.plot(column='SppN',ax=ax,cmap=colormap,edgecolors='')


#ax.set_extent([-93, -70, 30, 50])
ax.set_extent([-125, -60, 20, 50])
#ax.set_extent([-95, -70, 25, 45])

#ax.add_feature(cartopy.feature.LAND)
ax.add_feature(cartopy.feature.OCEAN)
ax.add_feature(cartopy.feature.COASTLINE)
ax.add_feature(cartopy.feature.BORDERS, linestyle=':')
ax.add_feature(cartopy.feature.LAKES, alpha=0.9)
ax.stock_img()
#ax.add_geometries(new_data.geometry,crs=cartopy.crs.PlateCarree())
#ax.add_feature(cartopy.feature.RIVERS)
mm = ax.pcolormesh(Xx,Yy,means.reshape(Nn,Nn),transform=proj )
#cs = plt.contour(Xx,Yy,np.sqrt(variances).reshape(Nn,Nn),linewidths=2,cmap=plt.cm.Greys_r,linestyles='dotted')
cs = plt.contour(Xx,Yy,means.reshape(Nn,Nn),linewidths=2,colors='k',linestyles='dotted',levels=range(1,20))
plt.clabel(cs, fontsize=16,inline=True,fmt='%1.1f')
#ax.scatter(new_data.lon,new_data.lat,edgecolors='',color='white',alpha=0.6)
plt.colorbar(mm)
plt.title("Predicted Species Richness")



In [ ]:

    
#Using k-partition = 7
import cartopy
plt.figure(figsize=(17,11))

proj = cartopy.crs.PlateCarree()
ax = plt.subplot(111, projection=proj)


ax = plt.axes(projection=proj)
#algo = new_data.plot(column='SppN',ax=ax,cmap=colormap,edgecolors='')


#ax.set_extent([-93, -70, 30, 50])
ax.set_extent([-125, -60, 20, 50])
#ax.set_extent([-95, -70, 25, 45])

#ax.add_feature(cartopy.feature.LAND)
ax.add_feature(cartopy.feature.OCEAN)
ax.add_feature(cartopy.feature.COASTLINE)
ax.add_feature(cartopy.feature.BORDERS, linestyle=':')
ax.add_feature(cartopy.feature.LAKES, alpha=0.9)
ax.stock_img()
#ax.add_geometries(new_data.geometry,crs=cartopy.crs.PlateCarree())
#ax.add_feature(cartopy.feature.RIVERS)
mm = ax.pcolormesh(Xx,Yy,means.reshape(Nn,Nn) - (2* np.sqrt(variances).reshape(Nn,Nn)),transform=proj )
#cs = plt.contour(Xx,Yy,np.sqrt(variances).reshape(Nn,Nn),linewidths=2,cmap=plt.cm.Greys_r,linestyles='dotted')
cs = plt.contour(Xx,Yy,means.reshape(Nn,Nn) - (2 * np.sqrt(variances).reshape(Nn,Nn)),linewidths=2,colors='k',linestyles='dotted',levels=[4.0,5.0,6.0,7.0,8.0])
plt.clabel(cs, fontsize=16,inline=True,fmt='%1.1f')
#ax.scatter(new_data.lon,new_data.lat,edgecolors='',color='white',alpha=0.6)
plt.colorbar(mm)
plt.title("Predicted Species Richness - 2stdev")

Model Analysis



In [ ]:

    
model.get_parameter_dict()

Let's calculate the residuals



In [ ]:

    
X_ = data[['LON','LAT']]
%time Y_hat = model.predict_y(X_)



In [ ]:

    
pred_y = pd.DataFrame(Y_hat[0])
var_y = pd.DataFrame(Y_hat[1])



In [ ]:

    
new_data['pred_y'] = pred_y
new_data['var_y'] = var_y



In [ ]:

    
new_data= new_data.assign(error=lambda y : (y.SppN - y.pred_y)**2 )



In [ ]:

    
new_data.error.hist(bins=50)



In [ ]:

    
print(new_data.error.mean())
print(new_data.error.std())

Experiment

In this section we will bring a Raster Data from the US, using Biospytial Raster API.

First select a polygon, then get A Raster FRom there, say Mean Temperature.



In [ ]:

    
import raster_api.tools as rt
from raster_api.models import MeanTemperature,ETOPO1,Precipitation,SolarRadiation
from sketches.models import Country



In [ ]:

    
## Select US
us_border = Country.objects.filter(name__contains='United States')[1]



In [ ]:

    
from django.db import close_old_connections



In [ ]:

    
close_old_connections()



In [ ]:

    
#Get Raster API
us_meantemp = rt.RasterData(Precipitation,us_border.geom)
us_meantemp.getRaster()



In [ ]:

    
us_meantemp.display_field()



In [ ]:

    
%time coords = us_meantemp.getCoordinates()



In [ ]:



In [ ]:

Name	values	prior	constraint
kern.bias.variance	[ 2.63571738]	None	+ve
kern.matern12.lengthscales	[ 0.40613709]	None	+ve
kern.matern12.variance	[ 28.11890802]	None	+ve