Study of correlation between average yearly sunspots and Guaíba river maximum heights

guaiba.py

import matplotlib
import pandas as pd
from scipy.stats import pearsonr
from sklearn.preprocessing import MinMaxScaler

matplotlib.use('Qt5Agg')  # Or another interactive backend such as 'Qt5Agg', 'GTK3Agg', etc.

import matplotlib.pyplot as plt

# Create a time index
time_index = pd.date_range(start='1899-01-01', periods=116, freq='YE')

# Define the data
ts1 = {
    'Year': [
        1899, 1900, 1901, 1902, 1903, 1904, 1905, 1906, 1907, 1908, 1909,
        1910, 1911, 1912, 1913, 1914, 1915, 1916, 1917, 1918, 1919, 1920,
        1921, 1922, 1923, 1924, 1925, 1926, 1927, 1928, 1929, 1930, 1931,
        1932, 1933, 1934, 1935, 1936, 1937, 1938, 1939, 1940, 1941, 1942,
        1943, 1944, 1945, 1946, 1947, 1948, 1949, 1950, 1951, 1952, 1953,
        1954, 1955, 1956, 1957, 1958, 1959, 1960, 1961, 1962, 1963, 1964,
        1965, 1966, 1967, 1968, 1969, 1970, 1971, 1972, 1973, 1974, 1975,
        1976, 1977, 1978, 1979, 1980, 1981, 1982, 1983, 1984, 1985, 1986,
        1987, 1988, 1989, 1990, 1991, 1992, 1993, 1994, 1995, 1996, 1997,
        1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008,
        2009, 2010, 2011, 2012, 2013, 2014, 2015
    ],
    'Height': [
        2.60, 1.48, 0.98, 1.99, 1.45, 1.51, 2.50, 1.53, 2.00, 1.69, 1.52,
        1.34, 2.05, 2.13, 1.19, 2.60, 1.91, 1.78, 0.98, 1.49, 2.21, 1.60,
        1.58, 1.68, 1.75, 1.61, 1.31, 2.60, 1.56, 3.20, 2.05, 2.35, 1.70,
        1.84, 1.34, 1.70, 1.64, 3.24, 2.51, 1.43, 1.60, 2.24, 4.75, 2.33,
        1.60, 1.90, 1.26, 1.55, 1.67, 1.68, 1.71, 1.91, 2.10, 2.06, 2.52,
        2.91, 1.80, 2.32, 2.08, 2.00, 1.99, 1.77, 2.16, 1.25, 2.67, 1.73,
        2.72, 2.61, 3.13, 1.18, 1.36, 1.71, 1.72, 2.21, 1.93, 1.48, 1.64,
        1.84, 2.13, 1.19, 1.66, 1.58, 1.54, 1.97, 2.32, 2.56, 1.96, 1.73,
        2.36, 1.98, 2.00, 2.22, 1.45, 1.94, 2.07, 1.86, 1.96, 1.62, 1.96,
        1.97, 1.46, 1.86, 2.40, 2.46, 1.74, 1.56, 2.10, 1.38, 2.44, 1.82,
        2.23, 1.62, 2.04, 1.66, 2.24, 2.11, 2.94
    ]
}

ts2 = {
    'Year': [
        1899, 1900, 1901, 1902, 1903, 1904, 1905, 1906, 1907, 1908, 1909,
        1910, 1911, 1912, 1913, 1914, 1915, 1916, 1917, 1918, 1919, 1920,
        1921, 1922, 1923, 1924, 1925, 1926, 1927, 1928, 1929, 1930, 1931,
        1932, 1933, 1934, 1935, 1936, 1937, 1938, 1939, 1940, 1941, 1942,
        1943, 1944, 1945, 1946, 1947, 1948, 1949, 1950, 1951, 1952, 1953,
        1954, 1955, 1956, 1957, 1958, 1959, 1960, 1961, 1962, 1963, 1964,
        1965, 1966, 1967, 1968, 1969, 1970, 1971, 1972, 1973, 1974, 1975,
        1976, 1977, 1978, 1979, 1980, 1981, 1982, 1983, 1984, 1985, 1986,
        1987, 1988, 1989, 1990, 1991, 1992, 1993, 1994, 1995, 1996, 1997,
        1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008,
        2009, 2010, 2011, 2012, 2013, 2014, 2015
    ],
    'Sunspot Number': [
        12.1, 9.5, 2.7, 5.0, 24.4, 42.0, 63.5, 53.8, 62.0, 48.5, 43.9, 18.6, 5.7, 3.6,
        1.4, 9.6, 47.4, 57.1, 103.9, 80.6, 63.6, 37.6, 26.1, 14.2, 5.8, 16.7, 44.3, 63.9,
        69.0, 77.8, 64.9, 35.7, 21.2, 11.1, 5.7, 8.7, 36.1, 79.7, 114.4, 109.6, 88.8, 67.8,
        47.5, 30.6, 16.3, 9.6, 33.2, 92.6, 151.6, 136.3, 134.7, 83.9, 69.4, 31.5, 13.9, 4.4,
        38.0, 141.7, 190.2, 184.8, 159.0, 112.3, 53.9, 37.6, 27.9, 10.2, 15.1, 47.0, 93.8, 105.9,
        105.5, 104.5, 66.6, 68.9, 38.0, 34.5, 15.5, 12.6, 27.5, 92.5, 155.4, 154.6, 140.4, 115.9,
        66.6, 45.9, 17.9, 13.4, 29.4, 100.2, 157.6, 142.6, 145.7, 94.3, 54.6, 29.9, 17.5, 8.6,
        21.5, 64.3, 93.3, 119.6, 111.0, 104.0, 63.7, 40.4, 29.8, 15.4, 7.9, 2.4, 2.8, 15.6, 50.1,
        52.8, 60.7, 74.7, 46.1
    ]
}

# Create DataFrame
df1 = pd.DataFrame(ts1)
df1['Year'] = pd.to_datetime(df1['Year'], format='%Y')
df1.set_index('Year', inplace=True)

df2 = pd.DataFrame(ts2)
df2['Year'] = pd.to_datetime(df2['Year'], format='%Y')
df2.set_index('Year', inplace=True)

# Plotting
plt.figure(figsize=(10, 5))
plt.plot(df1.index, df1['Height'], label='Time Series 1')
plt.plot(df2.index, df2['Sunspot Number'], label='Time Series 2')
plt.title('Comparison of Two Time Series')
plt.xlabel('Time')
plt.ylabel('Value')
plt.legend()
plt.show()

# Create a scaler object
min_max_scaler = MinMaxScaler()

# Fit and transform the data
df1['Height_min_max_scaled'] = min_max_scaler.fit_transform(df1[['Height']])
df2['Sunspot_min_max_scaled'] = min_max_scaler.fit_transform(df2[['Sunspot Number']])

# Plotting
plt.figure(figsize=(10, 5))
plt.plot(df1.index, df1['Height_min_max_scaled'], label='Min-Max Normalized Height Time Series')
plt.plot(df2.index, df2['Sunspot_min_max_scaled'], label='Min-Max Normalized Sunspot Time Series')
plt.title('Comparison of Min-Max Normalized Time Series')
plt.xlabel('Time')
plt.ylabel('Normalized Value (0 to 1)')
plt.legend()
plt.savefig('min_max_normalized_time_series.png')  # Saves the figure as an image file
plt.show()

combined_df = pd.merge(df1, df2, left_index=True, right_index=True, how='inner')
plt.figure(figsize=(10, 6))
plt.scatter(combined_df['Height'], combined_df['Sunspot Number'], color='b', alpha=0.5)
plt.title('Relationship Between Heights and Sunspot Numbers')
plt.xlabel('Height (m)')
plt.ylabel('Sunspot Number')
plt.grid(True)
plt.show()


# Correlation calculation
correlation, _ = pearsonr(df1['Height'], df2['Sunspot Number'])
print(f'Pearson correlation coefficient: {correlation:.3f}')