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hydrograph.py
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hydrograph.py
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import numpy as np
from matplotlib import pyplot as plt
from ipywidgets import (interact, fixed, interactive_output,
HBox, Button, VBox, Output, IntSlider, Checkbox, FloatSlider,
FloatLogSlider, Dropdown, FloatText, Label, Layout)
from matplotlib.patches import Rectangle,Polygon
from scipy.special import expi, k0
from scipy.integrate import quad
from scipy.optimize import root
from functools import partial
_FS = [4,4]
ER = np.array([2.69, 4.9, 4.6])
DD = np.array([12,54,150,259,301,222,111,52,40,24,9])
ER = np.pad(ER, [0,len(DD)-len(ER)])
_COLOR = ['r','b','g','m','y','c',[0.5,0.5,1],[1,0.5,0.5],[0.5,1,0.5],[0.5,0.5,0.5],]
def check(yest, ytrue):
return bool(abs(yest - ytrue)/abs(ytrue) < 2.e-2)
class Hydrograph(object):
def __init__(self, er, dd, dt=1):
self.er = er
self.dd = dd
self.n = len(dd)
self.dt = dt
self.t = np.arange(1, self.n+1)*self.dt
self.c = _COLOR[:self.n]
self.solve_hydrograph()
def solve_hydrograph(self):
# set up matrix problem
self.A = np.array([np.pad(self.er,[i,0])[:self.n] for i in range(self.n)]).T
self.uh = np.linalg.solve(self.A, self.dd)
def get_correct(self, kwargs):
n = 0
for i in range(len(kwargs.values())):
if check(kwargs['item{:02d}'.format(i)], self.uh[i]):
n+=1
return n
def rainfall(self, **kwargs):
dd = kwargs.pop('dd')
hint = kwargs.pop('hint')
f = plt.figure(figsize=_FS)
ax = plt.axes([0.1, 0.1, 0.85,0.85])
ax.set_xlabel('time [hr]')
ax.set_ylabel('excess rainfall [cm]')
ax.bar(self.t,self.er,self.dt, alpha=0.5, color=[1,1,1], edgecolor='k')
n = self.get_correct(kwargs)
i = np.min([int(np.sum(np.sign(self.er)))-1,n])
for j,ti, eri in zip(range(len(self.t)), self.t, self.er):
c = 'k'
if dd == 1 and hint and i == j:
c = 'r'
ax.text(ti,eri,'{:2.1f}'.format(eri), size=8, ha='center', va='bottom', color = c)
if dd == 1:
ax.bar(self.t,self.er,self.dt,alpha=0.5,color=self.c)
plt.show()
def unit_hydrograph(self,**kwargs):
dd = kwargs.pop('dd')
hint = kwargs.pop('hint')
f = plt.figure(figsize=_FS)
ax = plt.axes([0.1, 0.1, 0.85,0.85])
ax.set_xlabel('time')
ax.set_ylabel('discharge per unit rainfall [m$^3$/s/cm]')
vs = np.array([kwargs['item{:02d}'.format(i)] for i in range(self.n-2)])
ax.set_ylim([0, 1.3*np.max(self.uh)])
ax.bar(self.t[:self.n-2],vs,self.dt, alpha=0.5, color=[1,1,1], edgecolor='k')
n = self.get_correct(kwargs)
if n == 0 and hint:
ax.text(self.t[0], vs[0], '{:d}$\div${:2.1f}\n$\downarrow$\n '.format(self.dd[0], self.er[0]),
ha='center', va='bottom', color='r')
if dd == 2:
ax.bar(self.t[:self.n-2],vs,self.dt, alpha=0.5, color=self.c[:self.n-2])
i = np.min([int(np.sum(np.sign(self.er)))-1,n])
for j, ti, eri in zip(range(len(self.t)), self.t, vs):
c = 'k'
if dd == 1 and hint and n>0 and (n-i) == j:
c = 'r'
ax.text(ti,eri,'{:2.1f}'.format(eri), size=8, ha='center', va='bottom', color=c)
plt.show()
def streamflow(self,**kwargs):
dd = kwargs.pop('dd')
hint = kwargs.pop('hint')
f = plt.figure(figsize=_FS)
ax = plt.axes([0.1, 0.1, 0.85,0.85])
ax.bar(self.t,self.dd,self.dt, alpha=0.5, color=[1,1,1], edgecolor='k')
ax.set_xlabel('time [hr]')
ax.set_ylabel('discharge [m$^3$/s]')
n = self.get_correct(kwargs)
if dd == 1:
vs = np.array([kwargs['item{:02d}'.format(i)] for i in range(self.n-2)])
bottom = 0.*vs
bin = 0
for er,c in zip(self.er,self.c):
i = self.c.index(c)
v = np.pad(er*vs, [i,0])[:self.n-2]
if n < len(v):
vn = v[n]
v = v*np.sign(vs)
if n < len(v):
v[n] = vn
if hint and n < len(v):
ax.bar(self.t[n], v[n], self.dt, alpha=0.25,
color=self.c[i], bottom=bin)
bin += v[n]
if i == np.min([int(np.sum(np.sign(self.er)))-1,n]) and n>0:
ax.text(self.t[n]+self.dt/2., bin-v[n]/2.,
'$\leftarrow=${:2.1f}'.format(self.er[i])+r'$\times$'+'{:2.1f} '.format(vs[n-i]),
ha='left', va='center', color='r')
if n < len(v):
v[n] = 0.
ax.bar(self.t[:self.n-2], v, self.dt, alpha=0.5,
color=self.c[i], bottom= bottom)
bottom += v
elif dd == 2:
if n>0:
bottom = 0.*self.t
for i in range(n):
v = self.uh[i]*self.A[:,i].T
ax.bar(self.t, v, self.dt, alpha=0.5, color=self.c[i], bottom= bottom)
bottom += v
for ti, eri in zip(self.t, self.dd):
ax.text(ti,eri,'{:d}'.format(int(eri)), size=8, ha='center', va='bottom')
plt.show()
def hintbox(self, **kwargs):
dd = kwargs.pop('dd')
hint = kwargs.pop('hint')
n = self.get_correct(kwargs)
f = plt.figure(figsize=(18,1))
ax = plt.axes([0,0,1,1])
ax.axis('off')
ax.set_xlim([0,1])
ax.set_ylim([0,1])
if hint:
if n == 0:
text = 'Compute the ratio of rainfall to discharge in the first time step.'
if n > 0:
text = 'In the current discharge step, subtract the runoff due to all rainfall time steps except the first.\n'
text += 'What remains is the delayed runoff due to rainfall in the first time step.\n'
text += 'Compute the ratio of initial rain fall with this remainder discharge.'
ax.text(0.5, 1, text, color='r', ha='center', va = 'top', size=18)
plt.show()
def linked_widgets(self):
items = []
N = self.n-2
hint = Checkbox(value=False, description='show hint')
for i in range(N):
ft = FloatText(value = 0., description='$U_'+'{:d}'.format(i+1)+'$', disabled=True)
items.append(ft)
items[0].disabled=False
def box_change(i, change):
items[i+1].disabled = not check(change.new, self.uh[i])
if check(change.new, self.uh[i]):
hint.value=False
def box_disabled(i, change):
if change.new:
for item in items[i+1:]:
item.disabled = True
else:
for item, item0, uhi in zip(items[i+1:], items[i:], self.uh[i:]):
item.disabled = (not check(item0.value, uhi))
for i in range(N-1):
items[i].observe(partial(box_change, i), names = 'value')
items[i].observe(partial(box_disabled, i), names = 'disabled')
itemsd = dict(('item{:02d}'.format(i),item) for i,item in enumerate(items))
itemsd.update({'hint':hint})
return itemsd
def isiterable(a):
try:
[_ for _ in a]
return True
except TypeError:
return False
def hydrograph_exercise():
h = Hydrograph(ER,DD,dt=0.5)
dd = Dropdown(options = {'rainfall':1, 'unit hydrograph':2},
value = 1, description='highlight')
items = h.linked_widgets()
hint = items.pop('hint')
its = list(items.values())
N = int(np.ceil(len(its)/3.))
items_list = [VBox(its[:N]), VBox(its[N:2*N]), VBox(its[2*N:]), VBox([dd,hint])]
items.update({'dd':dd,'hint':hint})
io1 = interactive_output(h.rainfall, items)
io2 = interactive_output(h.unit_hydrograph, items)
io3 = interactive_output(h.streamflow, items)
io4 = interactive_output(h.hintbox, items)
return VBox([HBox([io1,io2,io3]),io4,HBox(items_list)])
if __name__ == "__main__":
hydrograph_exercise()