Imports¶

First cell in notebook should always contain all necessary imports

Load the dataset and take a look at the contents¶

The dataset contains a single variable called 'tmax' with time coordinate 'time'.

The 'tmax' variable is ERA5 daily-maximum surface temperature from the Pacific Northwest area of the USA for the period 1950-2021.

Extract the tmax data array and plot it¶

Clearly, the summer 2021 of was an extreme event, you can read about it here

The properties of time¶

The 'time' coordinate is a datetime64 object, which provides lots of powerful functionality in xarray, see here

In particular, the .dt method gives access to a lot of information: “year”, “month”, “day”, “hour”, “minute”, “second”, “dayofyear”, “week”, “dayofweek”, “weekday”, “quarter” and "season".

Exercises¶

Compute the mean, median and 99th percentile temperature¶

Use the xarray .mean and .quantile functions

Compute the mean summer (May-Sep) temperature for the years 2011-2020¶

Use .sel to select the years 2011-2020

Use .where to filter out non-summer days

Use .coarsen to take means over each the summer of each year

Compute a smoothed seasonal cycle¶

Use .groupby to group data by day of year and average over all years -- this gives a "raw" seasonal cycle

Apply .rolling to the raw seasonal cycle to compute a 31-day running-mean smoothed seasonal cycle; you will need to use .pad with mode='wrap' to extend the raw seasonal cycle periodically, so the running mean window doesn't run out of data at the beginning and end

Extract annual block maxima (i.e. the maximum temperature for each year in the dataset)¶

Use .groupby to group data by year and extract the maximum value for each year

Compute the linear time trend in the annual maxima¶

A linear time trend is just a linear regression of the data onto time.

Compute the trend in the annual block maxima calculated above using stats.linregress

Estimating the probability density function (PDF)¶

The PDF is interpreted as "in a given year, a the temperature will have a value $\ell$ contined in a bin ($\ell$,$\ell+d\ell$) with probability $p \, d\ell$", where $p$ is the PDF.

The PDF for a given dataset can be estimated 2 ways:

1. parametrically: assume the data follows a given distribution function, and fit the parameters
2. non-parametrically: compute a histogram

Exercise:

Apply both these approaches to the annual block maxima:

1. Use stats.genextreme.fit to fit a generalized extreme value (GEV) distribution to the block maxima, leaving out the extreme data point for 2021
2. Generate a "frozen" random variate object by calling stats.genextreme with the fitted parameters: rv = stats.genextreme(params)
3. Compute the PDF using rv.pdf
4. Compare to histogram, computed using the xarray .plot.hist function