IF-depth Model

The relationship between inundation frequency (IF) and bathymetry is modelled using a boat survey conducted by a team of researchers at one of the lakes within the middle-lower Amazon reach – Curuai (Barbosa et al., 2006). The more frequently inundated parts of the lake are generally observed to be deeper, hence the depth of Curuai measured from the bathymetry survey is plotted against how often that part of Curuai is flooded.

Code

import numpy as np
import matplotlib.pyplot as plt
import rasterio as rio

# Import Curuai IF
IF_CR = rio.open("../data/IF_CR.tif")

# Read into a NumPy array (only 1 band)
IF_CR_np = IF_CR.read(1)

# Plot
fig, ax = plt.subplots(figsize=(10, 4))
img = ax.imshow(IF_CR_np)

# Set background to beige
fig.patch.set_facecolor("#F9F8F2")
ax.set_facecolor("#F9F8F2")

# Create an inset axes for the colorbar in the bottom right
cax = ax.inset_axes([0.75, 0.8, 0.15, 0.03])  # [x, y, width, height]

# Colorbar
cbar = fig.colorbar(img, cax=cax, orientation='horizontal', shrink=0.3)
cbar.ax.set_title("IF (%)", fontsize=10, pad=4, color='white') # title
cbar.outline.set_linewidth(0)                                  # remove black outline
cbar.ax.tick_params(size=0)                                    # remove ticks
cbar.ax.xaxis.set_tick_params(pad=4, colors='white')           # tick labels

# Remove axes for clean aesthetics
ax.axis("off")

Figure 1: Inundation frequency at Curuai

Code

import numpy as np
import matplotlib.pyplot as plt
import matplotlib.colors as mcolors
import rasterio as rio

# Import curuai reprojected
curuai_proj = rio.open("../data/Barbosa_bathy/Barbosa_bathy2.tif")

# Read into a NumPy array (only 1 band)
curuai_proj_np = curuai_proj.read(1)

# Change <0 to NaN
curuai_over0 = curuai_proj_np
curuai_over0[curuai_over0<0]=np.nan

# Define breaks
breaks = [0,1,2,3,4,5,6,7,9.999783]

# Define discrete colormap
cmap = plt.get_cmap('BuPu', len(breaks) - 1)
norm = mcolors.BoundaryNorm(breaks, cmap.N)

# Plot
fig, ax = plt.subplots(figsize=(9,14))
img = ax.imshow(curuai_over0, cmap=cmap, norm=norm)

# Set background to beige
fig.patch.set_facecolor("#F9F8F2")
ax.set_facecolor("#F9F8F2")

# Create an inset axes for the colorbar in the bottom right
cax = ax.inset_axes([0.7, 0.8, 0.15, 0.03])  # [x, y, width, height]

# Colorbar
cbar = fig.colorbar(img, cax=cax, orientation='horizontal', shrink=0.3)
cbar.ax.set_title("Surveyed depth (m)", fontsize=10, pad=4) # title
cbar.outline.set_linewidth(0) # Remove the black outline
cbar.ax.tick_params(size=0) # Remove ticks

# Custom tick labels
cbar.set_ticklabels(['0','','','','','','','','10'])
cbar.ax.xaxis.set_tick_params(pad=4) # tick labels

# Remove axes for clean aesthetics
ax.axis("off")

Data points with IF below 50% are found at peripheral lake boundaries, which are elevated and mostly remain dry even during the wet season, or in small lakes (under 1 km²) disconnected from the river (Park et al., 2020). These points are excluded from the IF-depth model, to focus on the large and interconnected round lakes that are more sensitive to the model. Even with the exclusion of such points, 70.8% to 93.8% of the floodplain areas are retained for bathymetric calculations.

Code

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt

# Load data on model
model = pd.read_csv("../data/model.csv")

def exponential_regression(x, y):
    """Calculates the exponential regression line for given x and y values."""

    # Transform the data into a linear relationship
    log_y = np.log(y)

    # Perform linear regression on the transformed data
    coeffs = np.polyfit(x, log_y, 1)

    # Extract the coefficients
    a = np.exp(coeffs[1])
    b = coeffs[0]

    # Return the exponential function
    return lambda x: a * np.exp(b * x)

regression_func = exponential_regression(model['IF'],model['Depth'])

# Trendline
trendline = regression_func(range(50, 100))

fig, ax = plt.subplots(figsize=(10, 6))

ax.scatter(
    model['IF'],
    model['Depth'],
    marker="o",
    alpha=0.75,
    zorder=10
)

# Plot the regression line on top of the scatter plot
ax.plot(
    range(50, 100),
    trendline,
    color = "grey",
    linewidth=3,
    zorder=15
)

# Annotate equation
plt.text(53, 7.2, r'$y = 0.0008x^{1.9679}$', fontsize=12)

# Format graph
ax.set_xlabel("Inundation Frequency (%)") # x-axis label
ax.set_ylabel("Depth (m)") # y-axis label
ax.set_facecolor('#F9F8F2') # background colour
fig.patch.set_facecolor('#F9F8F2')
ax.spines['top'].set_visible(False) # turn off 2 lines
ax.spines['right'].set_visible(False)