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    "# Intra-annual variability of precipitation\n",
    "> A comparison between the seasonality of Tel Aviv and London\n",
    "\n",
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    "![](hydrology_figures/monthly_tel_aviv_london_bars.png)\n",
    "\n",
    "Let's shift the months according the the hydrological year:  \n",
    "![](hydrology_figures/monthly_tel_aviv_london_bars_hydrological_year.png)\n",
    "\n",
    "![](hydrology_figures/radar_chart_tel_aviv_london.png)"
   ]
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   "cell_type": "markdown",
   "id": "polar-raise",
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   "source": [
    "## Seasonality Index, Walsh and Lawler (1981)\n",
    "http://leddris.aegean.gr/ses-parameters/293-rainfall-seasonality.html#:~:text=Rainfall%20seasonality%20index%20is%20a,in%20relation%20to%20water%20availability\n",
    "\n",
    "$R=$ mean annual precipitation  \n",
    "$m_i$ precipitation mean for month $i$  \n",
    "\n",
    "$$ SI = \\displaystyle \\frac{1}{R} \\sum_{n=1}^{n=12} \\left| m_i - \\frac{R}{12} \\right| $$\n",
    "\n",
    "| $SI$ | Precipitation Regime |\n",
    "| --- | --- |\n",
    "| <0.19 | Precipitation spread throughout the year |\n",
    "| 0.20-0.39\t | Precipitation spread throughout the year, but with a definite wetter season |\n",
    "| 0.40-0.59\t | Rather seasonal with a short dry season |\n",
    "| 0.60-0.79\t | Seasonal |\n",
    "| 0.80-0.99\t | Marked seasonal with a long dry season |\n",
    "| 1.00-1.19\t\t | Most precipitation in <3 months |\n"
   ]
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     "text": [
      "Seasonality index (Walsh and Lawler, 1981)\n",
      "London: 0.13\n",
      "Tel Aviv: 1.00\n"
     ]
    }
   ],
   "source": [
    "#collapse-hide\n",
    "\n",
    "# import packages\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "from calendar import month_abbr\n",
    "\n",
    "# load data\n",
    "month_numbers = np.arange(1,13)\n",
    "month_names = [month_abbr[i] for i in month_numbers]\n",
    "def monthly_mean(station_name, freq):\n",
    "    # import daily data\n",
    "    df = pd.read_csv(station_name + '_' + freq + '.csv', sep=\",\")\n",
    "    # make 'DATE' the dataframe index\n",
    "    df['DATE'] = pd.to_datetime(df['DATE'])\n",
    "    df = df.set_index('DATE')\n",
    "    # print(df.index[0], df.index[-1])\n",
    "    if freq == 'daily':\n",
    "        # resample data by month\n",
    "        df_month = df['PRCP'].resample('M').sum()  # sum is labeled at the last day of the month \n",
    "        df_month = df_month/10                     # PRCP is given in tens of mm (see readme)\n",
    "    if freq == 'monthly':\n",
    "        df_month = df['PRCP']\n",
    "    # calculate monthly mean\n",
    "    monthly_mean = np.array([])  # empty array\n",
    "    for m in month_numbers:      # cycle over months (1, 2, 3, etc)\n",
    "        this_month_all_indices = (df_month.index.month == m)       # indices in df_month belonging to month m\n",
    "        this_month_mean = df_month[this_month_all_indices].mean()  # this is the monthly mean\n",
    "        monthly_mean = np.append(monthly_mean, this_month_mean)    # append\n",
    "    # make new df and return it\n",
    "    df_return = pd.DataFrame({'monthly rainfall (mm)':monthly_mean,\n",
    "                              'month names':month_names,\n",
    "                              'month number':month_numbers\n",
    "                            })\n",
    "    return df_return\n",
    "\n",
    "# load monthly mean\n",
    "df_london = monthly_mean(\"LONDON HEATHROW\", 'monthly')\n",
    "df_telaviv = monthly_mean(\"TEL AVIV READING\", 'monthly')\n",
    "\n",
    "#collapse-hide\n",
    "\n",
    "def walsh_index(df):\n",
    "    m = df[\"monthly rainfall (mm)\"]\n",
    "    R = df[\"monthly rainfall (mm)\"].sum()\n",
    "    SI = np.sum(np.abs(m-R/12)) / R\n",
    "    return SI\n",
    "\n",
    "london_index = walsh_index(df_london)\n",
    "telaviv_index = walsh_index(df_telaviv)\n",
    "print(\"Seasonality index (Walsh and Lawler, 1981)\")\n",
    "print(f\"London: {london_index:.2f}\")\n",
    "print(f\"Tel Aviv: {telaviv_index:.2f}\")"
   ]
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   "cell_type": "markdown",
   "id": "contained-lucas",
   "metadata": {},
   "source": [
    "![](hydrology_figures/si_walsh_telaviv.png)\n",
    "![](hydrology_figures/si_walsh_london.png)"
   ]
  },
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   "execution_count": null,
   "id": "designed-database",
   "metadata": {},
   "outputs": [],
   "source": []
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