Correlation between rainfall and overflow

import context
import pandas as pd
import seaborn as sns
from matplotlib import pyplot as plt

sns.set()
sns.set_context("paper", rc={"font.size":8.0,
                             'lines.linewidth':1,
                             'patch.linewidth':0.5,
                             "axes.titlesize":8,
                             "axes.labelsize":8,
                             'xtick.labelsize':8,
                             'ytick.labelsize':8,
                             'legend.fontsize':8 ,
                             'pgf.rcfonts' : False})

result_data = 'data_results/overflow_130616_130617_2.pkl'
results = pd.read_pickle(result_data)
max_overflow = pd.DataFrame(results.max(axis=1))\
        .rename({0:'max_overflow'},axis=1)
#max_overflow.head()

rain_data = 'data_pmm/20130616-S000000-E002959-20130617-S233000-E235959.pkl'
rain_dataf = pd.read_pickle(rain_data).set_index('Reach_ID')
area = rain_dataf[['area_sk']]
rain = rain_dataf.drop('area_sk',axis=1)

rain_flow = pd.DataFrame(rain\
            .sum(axis=1))\
            .rename({0:'total_rain_mmh'},axis=1)\
            .join(max_overflow)
rain_flow['total_rain_mm'] = rain_flow['total_rain_mmh'] / 2
rain_flow.head()

	total_rain_mmh	max_overflow	total_rain_mm
Reach_ID
40763397	126.416490	745.046714	63.208245
40894470	23.594527	12.946060	11.797264
40894471	45.016647	16.197745	22.508323
40763399	91.566055	308.959039	45.783027
40763402	181.004435	3655.129534	90.502218

fig = plt.figure(figsize=(3.5,3),dpi=150)
fig.patch.set_alpha(0)
ax = fig.add_subplot(111)
ax = sns.scatterplot(data=rain_flow,x='total_rain_mm',y='max_overflow',s = 10,edgecolor='white')
plt.ylabel('Overflow m$^3$/s');
plt.xlabel('Total rain [mm]');
#plt.savefig('../../thesis/report/figs/scatter.pdf', bbox_inches = 'tight')

We can obtain a measure for locality of effect by plotting rainfall versus overflow for each reach. This is done in the figure. If rainfall causes a local overflow, we would expect an correlation between increasing rainfall and overflow in that reach. If that is not the case, rainfall causes overflows downstream than there is no clear correlation between the two. The figure shows that there is no clear correlation between rainfall and overflow within the same reach. This figure shows that the effect of rainfall is not local, but downstream. This is an indication of the cascading effect.

Another observation from the plot are the dots that form horizontal patterns, for example just above 8000 m\(^3\)/s. These patters exist because of subsequent connected reaches. If a reach is flooded, the neighbouring reaches are likely to be flooded by the same amount. These dots at the same overflow level, with slightly different rainfall appear as ‘lines’ in the graph.