Until next week, work through the material provided in Unit 4 and solve the following exercise in a notebook.
In the following exercise, you will work with synthetically created precipitation data. Let me set this ‘data set’ up for you:
import numpy as npimport matplotlib.pyplot as plt# create a "time" vector of hourly counts over 7 dayst = np.arange(24*7)# create random "outage" time and noiset_outage = np.random.randint(140, 160, 1)precip_noise = np.random.normal(1.5, 1, t.size)# create a precipitation pattern with a sine wave and superposed noiseprecip =3*np.sin(t/(6*np.pi)) + precip_noise# set all negative precip to zero and create "precipitation gauge outage"precip[precip <0] =0precip[(t > t_outage-5) & (t < t_outage+5)] =0
The previous code cell generated what I refer to as the “time” vector t for now. It symbolizes time by counting the hours of one week (=24*7 hours). It also generates a synthetic precipitation measurement from a rain gauge by combining a sine wave with random noise. Unfortunately, our rain gauge experienced a problem, which caused the measurement to be unrealiable for a short time.
Make sure you understand what the previous code cells do, before you jump to the actual exercises.
Rewrite my vectorized statement precip[(t > 150) & (t < 160)] = 0 in a for loop
Calculate the total precipitation at each day (i.e., Day 1 goes from 0–23) and store it in a vector precip_total. Then, plot each daily precipitation sum at noon each day with the time vector t_noon = np.arange(12, 8*24, 24). You can add your result to the plot we already have by adding the line plt.plot(t_noon, precip_total, marker = 'o', color = "black").
Tip for Question 2
In my approach, I create yet another time vector t_midnight analogously to t_noon. Then I iterate over the indices and element of t_midnight to compute the relevant element of precip_total from the relevant elements of precip.
Calculate the moving average of precip using a 3h time window. Implement the moving average with a for loop. Basically, at each iteration i the moving average equals the sum of precip elements precip[i-1], precip[i], precip[i+1]. Do not compute moving averages for the first and last elements of precip. When you’re done, add the moving average to the plot.
Code a function that computes the start times of storms based on hourly precipitation data. Your algorithm should be based on the following assumptions:
We define the start time of a storm as the last hour with zero precip, one hour prior should also be precip-free, and one hour later should have non-zero precip. The first and last hours of our data set can therefore not be start times of a storm.
Implement one function that solves the challenge with a for loop, and then a second function that solves the challenges with a vectorized solution
Tips: use np.isclose() to check whether your floats are 0. For the vectorized approach, apply array slicing to create three slighty shifted arrays. Once you have these, you can come up with a logical expression that satisfies our defined rules.
How long did you take for each of the implementations? You get what I meant when I said vectorization can take up a bit of coding time..
Analogously, code a function that detects the start and end times of rain gauge outages based on the following assumptions:
We assume a rain gauge outage, when the precip is zero for more than three hours and when the precip drops and increases rapidly at the start/end times of the outage, i.e., with an absolute difference of more than twice the precip standard deviation.
Tip for Question 5
In my approach, I start out by computing the difference between precip elements using np.diff(). Then, I test where this array of differences exceeds 2 standard deviations of precip using np.where(). Then I iterate over the time intervals between the abrupt changes and test whether all precip elements during these time intervals are zero. If so, I add the relevant start and end times to the lists outage_start and outage_end, which are the return variables of the function.
When you’re done with steps 4 and 5, edit the following code cell to adjust the plot, so that the red vertical line and red shading match the correct times based on the calculations of your functions. If you re-run the first code cell where precip is generated, you will get slightly different times. If you then run the following code cell again, you will see whether your functions pick up on the changed data set and still return the correct result. If they don’t return the correct result, try to assess whether our underlying rules and assumptions are too crude or whether there is a bug in your function.
