## LA Rainfall Time Plot

In a previous post, we had an elementary look at the seasonal rainfall data in Los Angeles, California, using graphs (histograms) and numerical summaries to describe the data. The rainfall data were collected over time (total rainfall in inches over 132 fiscal years). So it is a good idea to plot the data according to time (the histograms in the previous post ignored the time order). In this post, we present a time plot of the LA rainfall data. The advantage of such a plot is that it can display changes in rainfall pattern over time, revealing trends in rainfall (or the lack of).

The data are obtained in Los Angeles Almanac and are displayed in the previous post and at the end of this post. The rain seasons are on a fiscal year basis (July 1 to June 30). Thus the season 2008-2009 refers to the period July 1, 2008 to June 30, 2009.

A time plot of a data distribution is a graph that plots each data value against the time at which the data value was measured. The time is always put on the horizontal axis and the variable being measured is on the vertical axis. In order to make the changes over time easier to see, a time plot usually connects the data points by line.

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The Time Plots

The following are two time plots of the LA rainfall data, one without lines connecting the data and one with lines connecting the points. The two time plots are created in Excel. The time in the horizontal axis is the fiscal year (July 1 to June 30). The first point lies above 1877 on the fiscal year scale at height 21.26 inches. The last point lies above the year 2008 at height 9.08 inches.

The point in the upper right corner lies above the fiscal year 2004 at height 37.96 inches and is the second wettest season in the plot. The dryest season is the point above the year 2006 at height 3.21 inches.

For comparison, we also present the histogram shown in the previous post.

$\displaystyle . \ \begin{bmatrix} \text{Class}&\text{ }&\text{ } \\\text{(in inches)}&\text{ }&\text{Frequency} \\\text{ }&\text{ }&\text{ } \\\text{0 to 4.99}&\text{ }&3 \\\text{5 to 9.99}&\text{ }&32 \\\text{10 to 14.99}&\text{ }&45 \\\text{15 to 19.99}&\text{ }&27 \\\text{20 to 24.99}&\text{ }&13 \\\text{25 to 29.99}&\text{ }&5 \\\text{30 to 34.99}&\text{ }&5 \\\text{35 to 39.99}&\text{ }&2 \\\text{ }&\text{ }&\text{ } \\\text{Total}&\text{ }&132 \end{bmatrix}$

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Observations

The time plots confirm the right-skewedness in the histogram. For example, most of the seasons are under 20 inches. There are progressively fewer and fewer data points in the time plots as we move up the vertical scale. There are ony seven season above 30 inches in rainfall and only two seasons above 35 inches in rainfall (both of these observations can be seen in the frequency distribution and in the time plots).

Another observation is that there is a great deal of year-to-year variation in the time plots. The data points oscillate up and down over the time period in the plots. Extremely high rainfall seasons tend to be followed by more moderate rainfall seasons and extremely low seasons tend to be followed by more moderate seasons. The time plots seem to be saying that the extreme rainfall seasons tend to revert to the mean. The mean rainfall amount in the study period of 1877-2008 is about 15 inches (14.98 inches).

Another observation is that there seem to be no trend effect over time. For example, there is no clear increasing trend over time (nor a decreasing trend). The data points in the time plots are falling and rising, but there are no clear upward (or downward) trendlines that can be drawn to describe the seemingly random pattern of points. The time plots indicate that the seasonal rainfall amounts in Los Angeles deviate from the mean in a random pattern. Overall, the time plots exhibit a highly stable pattern of seasonal rainfall rainfall data.

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Source Data – Los Angeles Rainfall

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