 ## 3.1 hydrological year

A time period of 12 months for which precipitation totals are measured. The hydrological year is designated by the calendar year in which it ends.
Let’s define the hydrological year for Tel Aviv from 1 October to 30 September.

האם אקלים הגשם שלנו משתנה  ## 3.2 coefficient of variation

$$\langle{P}\rangle=$$ average precipitation
$$\sigma=$$ standard deviation

$CV = \frac{\sigma}{\langle{P}\rangle}$

Assuming that the inter-annual distribution is a gaussian: 67% of the time, rainfall will vary +/- 30% from its long term average in Tel Aviv.

Precipitation averages are usually calculated for time intervals of 30 years.  Show/hide the code
import altair as alt
import pandas as pd

# make 'DATE' the dataframe index
df['DATE'] = pd.to_datetime(df['DATE'])
df = df.set_index('DATE')

df_year_all = df['PRCP'].resample('A-SEP').sum().to_frame()  # annual frequency, anchored end of September
df_year_all.columns = ['rain (mm)'] # rename 'PRCP' column to 'rain (mm)'
df_year = df_year_all.iloc[:-1]  # exclude last row

# Altair only recognizes column data; it ignores index values.
# You can plot the index data by first resetting the index
# I know that I've just made 'DATE' the index, but I want to have this here nonetheless so I can refer to this in the future
source = df_year.reset_index()
brush = alt.selection(type='interval', encodings=['x'])

# T: temporal, a time or date value
# Q: quantitative, a continuous real-valued quantity
# https://altair-viz.github.io/user_guide/encoding.html#encoding-data-types
bars = alt.Chart().mark_bar().encode(
x=alt.X('DATE:T', axis=alt.Axis(title='date')),
y=alt.Y('rain (mm):Q',  axis=alt.Axis(title='annual precipitation (mm) and average')),
opacity=alt.condition(brush, alt.OpacityValue(1), alt.OpacityValue(0.2)),
brush
).properties(
title='Select year range and drag for rolling average of annual precipitation in Tel Aviv'
).properties(
width=600,
height=400
)

line = alt.Chart().mark_rule(color='orange').encode(
y='mean(rain (mm)):Q',
size=alt.SizeValue(3)
).transform_filter(
brush
)

alt.layer(bars, line, data=source)