<jupyter_start><jupyter_text>Examples of hillslope plotting using the hillslope toy, steady state For all of these examples, we need to first import the hillslope toy package, along with matplotlib for plotting<jupyter_code>import hillslopetoy as ht
import matplotlib.pyplot as plt<jupyter_output><empty_output><jupyter_text>Steady state hillslopes Here are some examples of steady state hillslopes. First we plot linear hillslopes.In these plots `C_0` is the uplift rate (using the symobols from early Roering et al. papers)The default values are:-    `C_0` = 0.001   uplift in m/yr-   `D` = 0.001 the transport coefficient in m^2/yr-   `rho_ratio` = 2 the ratio of soil and rock density (dimensionless)-   `c` = 20 a constant that sets the elevation of the divide. We use another function to set the edge to zero after the profile is calculated.<jupyter_code>x = ht.set_profile_locations_half_length(half_length = 30,spacing = 1)

z1 = ht.ss_linear_elevation(x,C_0=0.0001)
z1 = ht.set_channel_to_zero(z1)

z2 = ht.ss_linear_elevation(x,C_0=0.0002)
z2 = ht.set_channel_to_zero(z2)

z3 = ht.ss_linear_elevation(x,C_0=0.0004)
z3 = ht.set_channel_to_zero(z3)
%matplotlib inline
plt.rcParams['figure.figsize'] = [10, 5]

# Create two subplots and unpack the output array immediately
plt.clf()
f, (ax1) = plt.subplots(1, 1)
ax1.fill_between(x, 0,z1, label="U = 0.1 mm/yr",alpha = 0.8,facecolor="r")
ax1.fill_between(x, z1,z2, label="U = 0.2 mm/yr",alpha = 0.5,facecolor="r")
ax1.fill_between(x, z2,z3, label="U = 0.4 mm/yr",alpha = 0.2,facecolor="r")

# These are just the labels for the figure
ax1.set_xlabel("Distance from divide (m)",fontsize=24)
ax1.set_ylabel("Elevation (m)",fontsize=20)

for tick in ax1.xaxis.get_major_ticks():
    tick.label.set_fontsize(14)
for tick in ax1.yaxis.get_major_ticks():
    tick.label.set_fontsize(14)    

plt.legend(fontsize = 14)
plt.tight_layout()<jupyter_output><empty_output><jupyter_text>Now lets plot some nonlinear hilltops.The default values are:-    `C_0` = 0.001   uplift in m/yr-   `D` = 0.001 the transport coefficient in m^2/yr-   `S_c` = 1 The critical slope value-   `rho_ratio` = 2 the ratio of soil and rock density (dimensionless)-   `c` = 20 a constant that sets the elevation of the divide. We use another function to set the edge to zero after the profile is calculated.<jupyter_code>z1 = ht.ss_nonlinear_elevation(x,C_0=0.0001)
z1 = ht.set_channel_to_zero(z1)

z2 = ht.ss_nonlinear_elevation(x,C_0=0.0002)
z2 = ht.set_channel_to_zero(z2)

z3 = ht.ss_nonlinear_elevation(x,C_0=0.0004)
z3 = ht.set_channel_to_zero(z3)

# Create two subplots and unpack the output array immediately
plt.clf()
f, (ax1) = plt.subplots(1, 1)
ax1.fill_between(x, 0,z1, label="U = 0.1 mm/yr",alpha = 0.8,facecolor="r")
ax1.fill_between(x, z1,z2, label="U = 0.2 mm/yr",alpha = 0.5,facecolor="r")
ax1.fill_between(x, z2,z3, label="U = 0.4 mm/yr",alpha = 0.2,facecolor="r")

# These are just the labels for the figure
ax1.set_xlabel("Distance from divide (m)",fontsize=24)
ax1.set_ylabel("Elevation (m)",fontsize=20)

for tick in ax1.xaxis.get_major_ticks():
    tick.label.set_fontsize(14)
for tick in ax1.yaxis.get_major_ticks():
    tick.label.set_fontsize(14)    

plt.legend(fontsize = 14)
plt.tight_layout()<jupyter_output><empty_output><jupyter_text>Compare linear and nonlinear slopes<jupyter_code>z1 = ht.ss_linear_elevation(x,C_0=0.0004)
z1 = ht.set_channel_to_zero(z1)

z2 = ht.ss_nonlinear_elevation(x,C_0=0.0004)
z2 = ht.set_channel_to_zero(z2)

# Create two subplots and unpack the output array immediately
plt.clf()
f, (ax1) = plt.subplots(1, 1)
ax1.fill_between(x, 0,z1, label="linear",alpha = 0.8,facecolor="r")
ax1.fill_between(x, z1,z2, label="nonlinear",alpha = 0.5,facecolor="g")

# These are just the labels for the figure
ax1.set_xlabel("Distance from divide (m)",fontsize=24)
ax1.set_ylabel("Elevation (m)",fontsize=20)

for tick in ax1.xaxis.get_major_ticks():
    tick.label.set_fontsize(14)
for tick in ax1.yaxis.get_major_ticks():
    tick.label.set_fontsize(14)    

plt.legend(fontsize = 14)
plt.tight_layout()
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