Variations in submarine channel sinuosity as a function of latitude and slope¶
The purpose of this notebook is to provide the data and the plotting / analysis scripts that were used in the paper: Sylvester, Z., Pirmez, C., Cantelli, A., & Jobe, Z. R. (2013). Global (latitudinal) variation in submarine channel sinuosity: COMMENT. Geology, 41(5), e287–e287. doi:10.1130/G33548C.1. If you have comments or questions, please send them to zoltan_dot_sylvester_at_gmail_dot_com.
The original article that is discussed in the comment and the reply are as follows:
Peakall, J., Kane, I. A., Masson, D. G., Keevil, G., McCaffrey, W., & Corney, R. (2011). Global (latitudinal) variation in submarine channel sinuosity. Geology, 40(1), 11–14. doi:10.1130/G32295.1.
Peakall, J., Wells, M. G., Cossu, R., Kane, I. A., Masson, D. G., Keevil, G. M., et al. (2013). Global (latitudinal) variation in submarine channel sinuosity: REPLY. Geology, 41(5), e288–e288. doi:10.1130/G34319Y.1.
Read and plot data¶
import pandas as pd
from scipy import stats
pd.set_option('display.mpl_style', 'default') # nicer plots than the default matplotlib style
fileurl = 'https://dl.dropboxusercontent.com/u/25694950/channel_sinuosities.csv'
data = pd.read_csv(fileurl)
The majority of the data comes from the book by Clark and Pickering (1996), which also forms the basis of the analysis by Peakall et al. (2011); graphs in the book were digitized using Graphclick. Data for the Amazon Channel comes from Pirmez and Flood (1995) (provided by Carlos Pirmez); and Popescu et al. (2001) (centerline digitized from map in paper and half-wavelength sinuosities calculated from centerline). See full references in paper.
Let's have a look at the first 20 lines of the data table:
data[:20]
figure(figsize=(10,8))
data['Name'].value_counts().plot(kind='bar');
figure(figsize=(10,8))
groups = data.groupby('Large_river')
labels = ('no large river','large river')
colors = (plt.rcParams['axes.color_cycle'][4],plt.rcParams['axes.color_cycle'][0])
for name, group in groups:
plot(group.Slope, group.Sinuosity, marker='o', linestyle='', ms=8, label=labels[name], color=colors[name])
legend(loc='best')
xlabel('valley slope', fontsize=18)
ylabel('sinuosity', fontsize=18)
axis([0.0,0.03,1.0,3.0]);
figure(figsize=(10,8))
groups = data.groupby('Large_river')
labels = ('no large river','large river')
colors = (plt.rcParams['axes.color_cycle'][4],plt.rcParams['axes.color_cycle'][0])
for name, group in groups:
plot(group.Latitude, group.Sinuosity, marker='o', linestyle='', ms=8, label=labels[name], color=colors[name])
legend(loc='best')
xlabel('latitude', fontsize=18)
ylabel('sinuosity', fontsize=18)
axis([0.0,70,1.0,3.0]);
Analysis of correlations¶
def bootstrap_regression(x,y,nit):
slope, intercept, r_value, p_value, std_err = stats.linregress(x, y)
r = np.zeros(nit)
n = len(x)
for i in range(1,nit):
x1 = x[np.random.randint(n, size=n)]
y1 = y[np.random.randint(n, size=n)]
slope, intercept, r_value2, p_value2, std_err = stats.linregress(x1,y1)
r[i] = r_value2
if r_value>0:
p_value_boot = len(r[r >= r_value])/float(len(r))
else:
p_value_boot = len(r[r <= r_value])/float(len(r))
return r_value, p_value, p_value_boot
r_values = np.zeros([3,1])
p_values = np.zeros([3,1])
p_values_boot = np.zeros([3,1])
r_values[0], p_values[0], p_values_boot[0] = bootstrap_regression(data.Latitude,data.Sinuosity,1000)
# for variable pairs that involve slope, we can only use those data points that have slope measurements:
r_values[1], p_values[1], p_values_boot[1] = bootstrap_regression(data.Slope[isnan(data.Slope)==0],data.Sinuosity[isnan(data.Slope)==0],1000)
r_values[2], p_values[2], p_values_boot[2] = bootstrap_regression(data.Latitude[isnan(data.Slope)==0],data.Slope[isnan(data.Slope)==0],1000)
Create a dataframe that contains the result of the regression:
df = pd.DataFrame(np.hstack(([[292],[268],[268]],r_values,r_values**2,
p_values,p_values_boot)),columns=['n','Pearson R','R squared','p-value',
'p-value bootstrap'],index=('latitude and sinuosity','slope and sinuosity','latitude and slope'))
df