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Rainfall Lab

January 29, 2018

Rain Measurement, Rainfall Time Series, Rainfall Return Period

Overview

This lab has three objectives:

1)  Discussion of rainfall measurement instrumentation

2)  Time series analysis of rainfall

3)  Design storm return period, peak flow prediction and culvert sizing

The assignment is broken into 3 parts (rainfall histogram, storm return time, culvert sizing) – you will be provided with data; guidelines for the analyses are provided in this document.

Introduction

Measuring the rain is the most fundamental part of the water budget. This lab will first take a look at the different methods that we use to measure rainfall, and then look at some actual rainfall data to examine patterns and distribution. Finally, we will use information for the rainfall time series to design a culvert.

Rainfall arrives in patterns that vary from time-to-time and place-to-place. Consider the following two graphs of annual rainfall and frequency distributions between Gainesville (Florida) and Seattle (Washington) for the same period of record (1948-2006).

Our first deliverable will be to describe the rainfall pattern from a new data set (Gainesville Florida between 1900 and 2006). Usually, what we want to know the total rainfall for a year, the degree to which that annual rainfall is reliable (how variable is it), when the rainfall arrives. In particular, what we’ll infer from actual data is:

1)  How complete is the data record? How many days/months/years do we have actual data for?

2)  What are the annual totals for the period of record; what is the mean annual rainfall; what is the standard deviation?

3)  What are the average monthly rainfall totals for the period of record; what are the standard deviations?

4)  What is the frequency distribution of rainfall events (in % of total days) for the period of record?

Our second deliverable is to determine the rainfall associated with engineering design requirements for flow control/conveyance structures. Engineering projects for dealing with stormwater are designed based on rainfall intensity. While it is actually flow from the rain that structures must withstand, flow data sufficient for statistical calculations are rarely available. Instead, we use rainfall data which are available for many areas, and frequently have long records. The obvious problems are 1) that not all rainfall becomes runoff, and 2) it takes time for that rainfall which does become runoff to get to the location where we are dealing with flow. A variety of rainfall-runoff relationships (e.g., the “Rational Method”, the NRCS Curve Number, finite element process-modeling) are used with “design” storms to statistically compute expected flows for structures like bridges and culverts. For example, the design storm for a temporary logging culvert might be a 10 year/1 hour storm (Q10); a design storm for a permanent logging road might be a 25year/1 hour (Q25) storm; and a design storm for a permanent public access road might be a 100 year/1 hour (Q100) storm. That is, as our risk tolerance gets smaller, we design for increasingly rare events (this is a general theme of any kind of risk analysis).

It’s probably obvious that the probability of a small rainfall event occurring is much higher than the probability of much larger events. By way of example, consider the probability that a 2”/24-hour storm will occur in 2007 vs. the probability that a 10” storm will occur. In fact, if we have a long record of rainfall for a particular location, we can quantify the probability of a given storm event statistically; this statistical description is called the annual maximum series and it is fitted to a theoretical log-normal recurrence curve by plotting on log-linear axes (linear for the Y-axis [rainfall amount] and log for the X-axis [return time]). From the plot you can estimate the recurrence interval, which is the predicted average interval (in years) between rainfall events of a given size (or greater), and the probability that a rainfall event of a particular size will occur in any given year.

Ok…so now we have a rainfall recurrence that we can use to meet the design requirements of some flow structure. This might be a culvert (for permitting flow under a road), a stormwater pond (to store a certain amount of flow and let it out slowly), or a pump house for moving water from somewhere we don’t want it to somewhere that we do. For this exercise we will be designing a culvert.

Our third deliverable is to compute the necessary culvert diameter to convey water of a particular design storm. The Division of Forestry Forest BMP manual makes selecting a culvert size easy. However, each step of the underlying engineering involves decisions and assumptions that will affect the outcome, but are hidden to the BMP manual user. In this lab you will examine a real rainfall time series (daily rainfall at Gainesville, Florida, between 1899 and 2006), construct a storm return probability graph and estimate peak flow from a watershed during a “design storm” using the Rational Method.

Design storms are useful but there are two things to keep in mind in their application:

1)  Many “permanent” structures and flood pain delineations have design storms with 100-year recurrence intervals. However, you’re lucky to find 100 years of data, much less several hundreds of years of data to base your calculations on. Extrapolation to time periods beyond the data set can be risky.

2)  Design storm methodology only calculates a probability. A misconception is that after the 50-year storm occurs that it will be 50 more years before the next 50-year storm can occur. In reality, big storms are often clumped together, for example during a bad hurricane season or El Nino events.

Predicting runoff from rainfall involves another level of assumptions and subjective decision making. For example rarely does rainfall occur uniformly across the watershed, and it makes a huge difference if the watershed is wet or dry when the intense rainfall occurs. Also the method doesn’t distinguish between a short period of intense rainfall that’s part of a small storm or a more prolonged rainfall event associated with a large storm. There are numerous different tables and equations for deriving the variables of the Rational Equation and different users will frequently get different results.

Lab Report Analyses

1.0  Description of Gainesville Rainfall Data Record

There are three worksheets within the file “Gainesville_rainfall.xlsx”. The first is labeled Gainesville_Rainfall. Open that file and look at the data set that you’ve been provided. Whoa! That’s a lot of data – in fact it is a relatively continuous record of daily rainfall totals between January 1900 and December 2012.

1)  Your first task will be to examine the completeness of the data. To do this, you will need to look at the worksheet labeled “Data_Pivot”.

  1. Read the help files about pivot-tables if you’ve never used them – they are very helpful (that is, pivot tables…the help files may not be so helpful).
  2. The pivot table is empty (you should see a “Pivot Table Field List” to the right of your screen). To add data, simply pick a Field from the Pivot Table Field List and drop it in the appropriate location. For example, if you wanted to look at the rainfall totals by year, you would drag the “Prcp” field into the main body of the table (that is, the data you want to examine). You should get a number that is the total rainfall (“Sum of Prcp” written in the upper left cell) over the entire period of record. If you don’t get a sum (for example, you might get “Count of Prcp”), simply right-click over the cell that says “Count of Prcp” and go to field settings; there you should change the setting to “Sum”…you could change it to any of the other settings like average, standard deviation, which will come in handy later). Next, drag-and-drop the “Year” field to the left column (the “Row Field”). Now, you should see each year for which there are data and the total precipitation recorded. Look at 1927. What’s weird? The dataset may be incomplete
  3. To check data completeness, change the field settings (see above) to count. What do you see? It appears that our rainfall gage had issues during the 1920’s, then shut-off completely during the Great Depression and World War II. Be cognizant of this later. How many years have complete data (365 or 366 observations)?

2)  Your next task is to plot the annual rainfall totals. Use the pivot table to set up the annual Sum of Prcp, and plot Year (X-axis) vs. Total Rainfall (Y-axis). What do you see?

3)  Next compute the average annual rainfall. You could take the average of all the year data that you just plotted, but we know that some of the years aren’t complete. So the first step will be to exclude those years that have less than a full data set (365 or 366 daily observations). Then, compute the average and standard deviation of annual rainfall. How does that compare with Seattle (average = 38.2”; SD = 6.5”)? How does the value compare when we DON’T exclude years that have an incomplete record?

4)  Next, we want to understand when rainfall occurs within the year, and the variability of that delivery between years. So, we want a plot with average monthly rainfall (in inches) and the standard deviation of that monthly average. To do this, we go back to the pivot table. We should still have “Year” in the rows, and Sum of Prcp in the cells. All we need to do is add month to the columns (again, drag and drop) and we now have a matrix of total rainfall for each month of each year (years as rows, months as columns). There will, as before, be some missing months – this is ok. Now, we want to compute the average of each month’s total rainfall across all the years and the standard deviation. That is, we want to average the columns across all the rows. So we scroll down to the bottom of the table and compute the average of each month and the standard deviation. Now plot the average that you computed (do the numbers make sense?) vs. month using a bar chart. By double clicking on the bars, you can add Y-error bars, which, for this work, should be the + and – the computed standard deviations. Your work should look something like the figure below (for Seattle). How is Gainesville different? Consider both the timing and size of the error bars (both within a site over time, and between sites).

Monthly Rainfall Averages and Standard Deviations for Seattle Washington (1948-2006)

5)  The next task is to plot a frequency distribution of the rainfall events for Gainesville. To do this, we need to add some functionality to Excel. In Office2007, go to “Office Button” in the upper left of the Excel screen, click “Excel Options”, “Add-Ins” and make sure the “Analysis Tool Pack” is active. This may take a minute or two.

  1. Go to Tools – Data Analysis. A window will pop-up and you should select a histogram. The input range is all of the daily rainfall observations (all of them) and the bin range is on the worksheet titled “Bins”. Don’t forget to check the “labels” button if you’ve selected the labels. Set the output range to the “Bins” worksheet…don’t click any of the output options.
  2. You’ll get a table with the bins on the left and the number of observations on the right. The bins represent the upper bound of categories (for example, the Bin labeled will collect all the rainfall events that are less or equal to 0.6”, but greater than 0.4” (the bin below). So we have tabulated the frequency of occurrence for rainfall events of different sizes (a graph of the data will look something like the Figure on Page 2 of this document). What fraction of the observations are 0”? What fraction are greater than 2”? What is the maximum rainfall?

2.0 Gainesville Rainfall Recurrence

Our next step is to use the Gainesville data to determine the probability that a rainfall event of given size will occur in any given year. To do this, we need a list of the maximum observed rainfall in each year. To get this, use the following steps:

1)  Return to the pivot table and remove the months (columns) so it’s just the years.

2)  Change the field settings so that instead of the sum of rainfall over each year, report the “Max”…this is the largest observation for that given row field (year).

3)  You should now have a table that is years in the row, and a number (maximum rainfall in inches) in the cells. This annual maximum rainfall series is the basis of the remaining analyses. Save this somewhere and present it graphically in your lab report. Make sure the numbers make sense (go back to the data if you’re not sure).

4)  Now using the annual maximum rainfall series between 1900 and 1980 plot a recurrence interval line.

  1. Rank (m) all the storms with biggest storm = 1.
  2. For each year calculate the Recurrence interval (T) for the plot:

T= (number of years of data + 1) / m

  1. Plot T (x axis) vs. rainfall (y axis) using a scatter plot (NO LINES). Now, click on the x-axis, go to scale tab and change to a logarithmic scale.
  2. Add a trendline (chart menu) and add a “Logarithmic” type fit.
  3. In chart options (chart menu) display major and minor gridlines in X and Y.
  4. Be sure to attach the graph to your report – it will look something like this…