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<!DOCTYPE html>
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<title>Chapter 11 Flow Duration Curves | Hydroinformatics at VT</title>
<meta name="description" content="This bookdown contains notes and exercises for a course in hydroinformatics at Virginia Tech." />
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<meta property="og:title" content="Chapter 11 Flow Duration Curves | Hydroinformatics at VT" />
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<meta name="twitter:title" content="Chapter 11 Flow Duration Curves | Hydroinformatics at VT" />
<meta name="twitter:description" content="This bookdown contains notes and exercises for a course in hydroinformatics at Virginia Tech." />
<meta name="author" content="JP Gannon" />
<meta name="date" content="2021-02-23" />
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<li><a href="./">Hydroinformatics</a></li>
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<li class="chapter" data-level="1" data-path="index.html"><a href="index.html"><i class="fa fa-check"></i><b>1</b> Introduction</a>
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<li class="chapter" data-level="1.0.1" data-path="index.html"><a href="index.html#table-of-contents"><i class="fa fa-check"></i><b>1.0.1</b> Table of contents:</a></li>
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<li class="chapter" data-level="2.1" data-path="Plotting.html"><a href="Plotting.html#download-and-install-tidyverse-library"><i class="fa fa-check"></i><b>2.1</b> Download and install tidyverse library</a></li>
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<li class="chapter" data-level="2.4" data-path="Plotting.html"><a href="Plotting.html#change-point-type"><i class="fa fa-check"></i><b>2.4</b> Change point type</a></li>
<li class="chapter" data-level="2.5" data-path="Plotting.html"><a href="Plotting.html#set-colors"><i class="fa fa-check"></i><b>2.5</b> Set colors</a></li>
<li class="chapter" data-level="2.6" data-path="Plotting.html"><a href="Plotting.html#controlling-color-with-a-third-variable-and-other-functions"><i class="fa fa-check"></i><b>2.6</b> Controlling color with a third variable and other functions</a></li>
<li class="chapter" data-level="2.7" data-path="Plotting.html"><a href="Plotting.html#plotting-multiple-groups"><i class="fa fa-check"></i><b>2.7</b> Plotting multiple groups</a></li>
<li class="chapter" data-level="2.8" data-path="Plotting.html"><a href="Plotting.html#facets"><i class="fa fa-check"></i><b>2.8</b> Facets</a></li>
<li class="chapter" data-level="2.9" data-path="Plotting.html"><a href="Plotting.html#two-variable-faceting"><i class="fa fa-check"></i><b>2.9</b> Two variable faceting</a></li>
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<li class="chapter" data-level="3.1" data-path="Programming.html"><a href="Programming.html#introduction-1"><i class="fa fa-check"></i><b>3.1</b> Introduction</a></li>
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<li class="chapter" data-level="3.3" data-path="Programming.html"><a href="Programming.html#you-can-create-new-objects-using--"><i class="fa fa-check"></i><b>3.3</b> You can create new objects using <-</a></li>
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<li class="chapter" data-level="3.5" data-path="Programming.html"><a href="Programming.html#read-in-some-data."><i class="fa fa-check"></i><b>3.5</b> Read in some data.</a></li>
<li class="chapter" data-level="3.6" data-path="Programming.html"><a href="Programming.html#wait-hold-up.-what-is-a-tibble"><i class="fa fa-check"></i><b>3.6</b> Wait, hold up. What is a tibble?</a></li>
<li class="chapter" data-level="3.7" data-path="Programming.html"><a href="Programming.html#data-wrangling-in-dplyr"><i class="fa fa-check"></i><b>3.7</b> Data wrangling in dplyr</a>
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<li class="chapter" data-level="3.7.1" data-path="Programming.html"><a href="Programming.html#filter---returns-rows-that-meet-specified-conditions"><i class="fa fa-check"></i><b>3.7.1</b> filter() - returns rows that meet specified conditions</a></li>
<li class="chapter" data-level="3.7.2" data-path="Programming.html"><a href="Programming.html#arrange---reorders-rows"><i class="fa fa-check"></i><b>3.7.2</b> arrange() - reorders rows</a></li>
<li class="chapter" data-level="3.7.3" data-path="Programming.html"><a href="Programming.html#select---pull-out-variables-columns"><i class="fa fa-check"></i><b>3.7.3</b> select() - pull out variables (columns)</a></li>
<li class="chapter" data-level="3.7.4" data-path="Programming.html"><a href="Programming.html#mutate---create-new-variables-columns-or-reformat-existing-ones"><i class="fa fa-check"></i><b>3.7.4</b> mutate() - create new variables (columns) or reformat existing ones</a></li>
<li class="chapter" data-level="3.7.5" data-path="Programming.html"><a href="Programming.html#summarize---collapse-groups-of-values-into-summary-stats"><i class="fa fa-check"></i><b>3.7.5</b> summarize() - collapse groups of values into summary stats</a></li>
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<li class="chapter" data-level="3.8" data-path="Programming.html"><a href="Programming.html#filter"><i class="fa fa-check"></i><b>3.8</b> Filter</a>
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<li class="chapter" data-level="3.8.1" data-path="Programming.html"><a href="Programming.html#multiple-conditions"><i class="fa fa-check"></i><b>3.8.1</b> Multiple conditions</a></li>
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<li class="chapter" data-level="3.9" data-path="Programming.html"><a href="Programming.html#arrange"><i class="fa fa-check"></i><b>3.9</b> Arrange</a></li>
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<li class="chapter" data-level="3.11" data-path="Programming.html"><a href="Programming.html#mutate"><i class="fa fa-check"></i><b>3.11</b> Mutate</a></li>
<li class="chapter" data-level="3.12" data-path="Programming.html"><a href="Programming.html#summarize"><i class="fa fa-check"></i><b>3.12</b> Summarize</a></li>
<li class="chapter" data-level="3.13" data-path="Programming.html"><a href="Programming.html#multiple-operations-with-pipes"><i class="fa fa-check"></i><b>3.13</b> Multiple operations with pipes</a>
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<li class="chapter" data-level="3.13.1" data-path="Programming.html"><a href="Programming.html#lets-say-we-want-to-tell-r-to-make-a-pbj-sandwich-by-using-the-pbbread-jbread-and-joinslices-functions-and-the-data-ingredients.-if-we-do-this-saving-each-step-if-would-look-like-this"><i class="fa fa-check"></i><b>3.13.1</b> Let’s say we want to tell R to make a PB&J sandwich by using the pbbread(), jbread(), and joinslices() functions and the data “ingredients.” If we do this saving each step if would look like this:</a></li>
<li class="chapter" data-level="3.13.2" data-path="Programming.html"><a href="Programming.html#if-we-nest-the-functions-together-we-get-this"><i class="fa fa-check"></i><b>3.13.2</b> If we nest the functions together we get this</a></li>
<li class="chapter" data-level="3.13.3" data-path="Programming.html"><a href="Programming.html#using-the-pipe-it-would-look-like-this"><i class="fa fa-check"></i><b>3.13.3</b> Using the pipe it would look like this</a></li>
<li class="chapter" data-level="3.13.4" data-path="Programming.html"><a href="Programming.html#when-you-use-the-pipe-it-basically-takes-whatever-came-out-of-the-first-function-and-puts-it-into-the-data-argument-for-the-next-one"><i class="fa fa-check"></i><b>3.13.4</b> When you use the pipe, it basically takes whatever came out of the first function and puts it into the data argument for the next one</a></li>
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<li class="chapter" data-level="3.14" data-path="Programming.html"><a href="Programming.html#save-your-results-to-a-new-tibble"><i class="fa fa-check"></i><b>3.14</b> Save your results to a new tibble</a></li>
<li class="chapter" data-level="3.15" data-path="Programming.html"><a href="Programming.html#what-about-nas"><i class="fa fa-check"></i><b>3.15</b> What about NAs?</a></li>
<li class="chapter" data-level="3.16" data-path="Programming.html"><a href="Programming.html#what-are-some-things-you-think-ill-ask-you-to-do-for-the-activity-next-class"><i class="fa fa-check"></i><b>3.16</b> What are some things you think I’ll ask you to do for the activity next class?</a></li>
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<li class="chapter" data-level="4" data-path="introactivity.html"><a href="introactivity.html"><i class="fa fa-check"></i><b>4</b> Intro Skills Activity</a>
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<li class="chapter" data-level="4.1" data-path="introactivity.html"><a href="introactivity.html#problem-1"><i class="fa fa-check"></i><b>4.1</b> Problem 1</a></li>
<li class="chapter" data-level="4.2" data-path="introactivity.html"><a href="introactivity.html#problem-2"><i class="fa fa-check"></i><b>4.2</b> Problem 2</a></li>
<li class="chapter" data-level="4.3" data-path="introactivity.html"><a href="introactivity.html#problem-3"><i class="fa fa-check"></i><b>4.3</b> Problem 3</a></li>
<li class="chapter" data-level="4.4" data-path="introactivity.html"><a href="introactivity.html#problem-4"><i class="fa fa-check"></i><b>4.4</b> Problem 4</a></li>
<li class="chapter" data-level="4.5" data-path="introactivity.html"><a href="introactivity.html#problem-5"><i class="fa fa-check"></i><b>4.5</b> Problem 5</a></li>
<li class="chapter" data-level="4.6" data-path="introactivity.html"><a href="introactivity.html#problem-6"><i class="fa fa-check"></i><b>4.6</b> Problem 6</a></li>
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<li class="chapter" data-level="5" data-path="stats.html"><a href="stats.html"><i class="fa fa-check"></i><b>5</b> Introduction to Basic Statistics</a>
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<li class="chapter" data-level="5.1" data-path="stats.html"><a href="stats.html#reading-for-this-section-statistical-methods-in-water-resources-chapter-1"><i class="fa fa-check"></i><b>5.1</b> Reading for this section: Statistical Methods in Water Resources: Chapter 1</a></li>
<li class="chapter" data-level="5.2" data-path="stats.html"><a href="stats.html#questions-for-today"><i class="fa fa-check"></i><b>5.2</b> Questions for today:</a>
<ul>
<li class="chapter" data-level="5.2.1" data-path="stats.html"><a href="stats.html#what-is-the-difference-between-a-sample-and-a-population"><i class="fa fa-check"></i><b>5.2.1</b> What is the difference between a sample and a population?</a></li>
<li class="chapter" data-level="5.2.2" data-path="stats.html"><a href="stats.html#how-do-we-look-at-the-distribution-of-data-in-a-sample"><i class="fa fa-check"></i><b>5.2.2</b> How do we look at the distribution of data in a sample?</a></li>
<li class="chapter" data-level="5.2.3" data-path="stats.html"><a href="stats.html#how-do-we-measure-aspects-of-a-distribution"><i class="fa fa-check"></i><b>5.2.3</b> How do we measure aspects of a distribution?</a></li>
<li class="chapter" data-level="5.2.4" data-path="stats.html"><a href="stats.html#what-is-a-normal-distribution"><i class="fa fa-check"></i><b>5.2.4</b> What is a normal distribution?</a></li>
<li class="chapter" data-level="5.2.5" data-path="stats.html"><a href="stats.html#stack-plots-to-compare-histogram-and-pdf"><i class="fa fa-check"></i><b>5.2.5</b> Stack plots to compare histogram and pdf</a></li>
</ul></li>
<li class="chapter" data-level="5.3" data-path="stats.html"><a href="stats.html#what-is-the-difference-between-a-sample-and-a-population."><i class="fa fa-check"></i><b>5.3</b> What is the difference between a sample and a population.</a></li>
<li class="chapter" data-level="5.4" data-path="stats.html"><a href="stats.html#measuring-our-sample-distribution-central-tendency."><i class="fa fa-check"></i><b>5.4</b> Measuring our sample distribution: central tendency.</a>
<ul>
<li class="chapter" data-level="5.4.1" data-path="stats.html"><a href="stats.html#so-whats-a-weighted-average"><i class="fa fa-check"></i><b>5.4.1</b> So what’s a weighted average?</a></li>
</ul></li>
<li class="chapter" data-level="5.5" data-path="stats.html"><a href="stats.html#measures-of-variability"><i class="fa fa-check"></i><b>5.5</b> Measures of variability</a></li>
<li class="chapter" data-level="5.6" data-path="stats.html"><a href="stats.html#what-is-a-normal-distribution-and-how-can-we-determine-if-we-have-one"><i class="fa fa-check"></i><b>5.6</b> What is a normal distribution and how can we determine if we have one?</a></li>
</ul></li>
<li class="chapter" data-level="6" data-path="statsactivity.html"><a href="statsactivity.html"><i class="fa fa-check"></i><b>6</b> Intro Stats Activity</a>
<ul>
<li class="chapter" data-level="6.1" data-path="statsactivity.html"><a href="statsactivity.html#load-the-tidyverse-and-patchwork-libraries-and-read-in-the-flashy-and-pine-datasets."><i class="fa fa-check"></i><b>6.1</b> 1. Load the tidyverse and patchwork libraries and read in the Flashy and Pine datasets.</a></li>
<li class="chapter" data-level="6.2" data-path="statsactivity.html"><a href="statsactivity.html#using-the-flashy-dataset-make-a-pdf-of-the-average-basin-rainfall-pptavg_basin-for-the-northeast-aggecoregion.-on-that-pdf-add-vertical-lines-showing-the-mean-median-standard-deviation-and-iqr.-make-each-a-different-color-and-note-which-is-which-in-a-typed-answer-below-this-question.-or-if-you-want-an-extra-challenged-make-a-custom-legend-that-shows-this"><i class="fa fa-check"></i><b>6.2</b> 2. Using the flashy dataset, make a pdf of the average basin rainfall (PPTAVG_BASIN) for the NorthEast AGGECOREGION. On that pdf, add vertical lines showing the mean, median, standard deviation, and IQR. Make each a different color and note which is which in a typed answer below this question. (or if you want an extra challenged, make a custom legend that shows this)</a></li>
<li class="chapter" data-level="6.3" data-path="statsactivity.html"><a href="statsactivity.html#perform-a-shapiro-wilk-test-for-normality-on-the-data-from-question-2.-using-the-results-from-that-test-and-the-plot-and-stats-from-question-2-discuss-whether-or-not-the-distribution-is-normal."><i class="fa fa-check"></i><b>6.3</b> 3. Perform a Shapiro-Wilk test for normality on the data from question 2. Using the results from that test and the plot and stats from question 2, discuss whether or not the distribution is normal.</a></li>
<li class="chapter" data-level="6.4" data-path="statsactivity.html"><a href="statsactivity.html#make-a-plot-that-shows-the-distribution-of-the-data-from-the-pine-watershed-and-the-nfdr-watershed-two-pdfs-on-the-same-plot.-log-the-x-axis."><i class="fa fa-check"></i><b>6.4</b> 4. Make a plot that shows the distribution of the data from the PINE watershed and the NFDR watershed (two pdfs on the same plot). Log the x axis.</a></li>
<li class="chapter" data-level="6.5" data-path="statsactivity.html"><a href="statsactivity.html#you-want-to-compare-how-variable-the-discharge-is-in-each-of-the-watersheds-in-question-4.-which-measure-of-spread-would-you-use-and-why-if-you-wanted-to-measure-the-central-tendency-which-measure-would-you-use-and-why"><i class="fa fa-check"></i><b>6.5</b> 5. You want to compare how variable the discharge is in each of the watersheds in question 4. Which measure of spread would you use and why? If you wanted to measure the central tendency which measure would you use and why?</a></li>
<li class="chapter" data-level="6.6" data-path="statsactivity.html"><a href="statsactivity.html#compute-3-measures-of-spread-and-2-measures-of-central-tendency-for-the-pine-and-nfdr-watershed.-hint-use-group_by-and-summarize-be-sure-your-code-outputs-the-result.-which-watershed-has-higher-flow-which-one-has-more-variable-flow-how-do-you-know"><i class="fa fa-check"></i><b>6.6</b> 6. Compute 3 measures of spread and 2 measures of central tendency for the PINE and NFDR watershed. (hint: use group_by() and summarize()) Be sure your code outputs the result. Which watershed has higher flow? Which one has more variable flow? How do you know?</a></li>
</ul></li>
<li class="chapter" data-level="7" data-path="getdata.html"><a href="getdata.html"><i class="fa fa-check"></i><b>7</b> Joins, Pivots, and USGS dataRetrieval</a>
<ul>
<li class="chapter" data-level="7.1" data-path="getdata.html"><a href="getdata.html#goals-for-today"><i class="fa fa-check"></i><b>7.1</b> Goals for today</a>
<ul>
<li class="chapter" data-level="7.1.1" data-path="getdata.html"><a href="getdata.html#get-familiar-with-the-dataretrieval-package"><i class="fa fa-check"></i><b>7.1.1</b> 1. Get familiar with the dataRetrieval package</a></li>
<li class="chapter" data-level="7.1.2" data-path="getdata.html"><a href="getdata.html#learn-about-long-vs.-wide-data-and-how-to-change-between-them"><i class="fa fa-check"></i><b>7.1.2</b> 2. Learn about long vs. wide data and how to change between them</a></li>
<li class="chapter" data-level="7.1.3" data-path="getdata.html"><a href="getdata.html#brief-intro-to-joins"><i class="fa fa-check"></i><b>7.1.3</b> 3. Brief intro to joins</a></li>
<li class="chapter" data-level="7.1.4" data-path="getdata.html"><a href="getdata.html#prep-question-how-would-you-get-data-from-the-usgs-non-r"><i class="fa fa-check"></i><b>7.1.4</b> Prep question: How would you get data from the USGS (non-R)?</a></li>
</ul></li>
<li class="chapter" data-level="7.2" data-path="getdata.html"><a href="getdata.html#install-the-dataretrieval-package.-load-it-and-the-tidyverse."><i class="fa fa-check"></i><b>7.2</b> Install the dataRetrieval package. Load it and the tidyverse.</a></li>
<li class="chapter" data-level="7.3" data-path="getdata.html"><a href="getdata.html#exploring-what-dataretrieval-can-do."><i class="fa fa-check"></i><b>7.3</b> Exploring what dataRetrieval can do.</a></li>
<li class="chapter" data-level="7.4" data-path="getdata.html"><a href="getdata.html#so-how-do-you-find-the-site-ids-for-downloading-data"><i class="fa fa-check"></i><b>7.4</b> So how do you find the site ids for downloading data?</a></li>
<li class="chapter" data-level="7.5" data-path="getdata.html"><a href="getdata.html#ok-lets-download-some-data"><i class="fa fa-check"></i><b>7.5</b> OK let’s download some data!</a></li>
<li class="chapter" data-level="7.6" data-path="getdata.html"><a href="getdata.html#pivoting-wide-and-long-data"><i class="fa fa-check"></i><b>7.6</b> Pivoting: wide and long data</a>
<ul>
<li class="chapter" data-level="7.6.1" data-path="getdata.html"><a href="getdata.html#long"><i class="fa fa-check"></i><b>7.6.1</b> LONG</a></li>
<li class="chapter" data-level="7.6.2" data-path="getdata.html"><a href="getdata.html#wide"><i class="fa fa-check"></i><b>7.6.2</b> WIDE</a></li>
<li class="chapter" data-level="7.6.3" data-path="getdata.html"><a href="getdata.html#why"><i class="fa fa-check"></i><b>7.6.3</b> Why?</a></li>
</ul></li>
</ul></li>
<li class="chapter" data-level="8" data-path="joinpivotDR.html"><a href="joinpivotDR.html"><i class="fa fa-check"></i><b>8</b> Joins Pivots dataRetrieval Activity</a>
<ul>
<li class="chapter" data-level="8.0.1" data-path="joinpivotDR.html"><a href="joinpivotDR.html#load-the-tidyverse-dataretrieval-and-patchwork-packages."><i class="fa fa-check"></i><b>8.0.1</b> Load the tidyverse, dataRetrieval, and patchwork packages.</a></li>
<li class="chapter" data-level="8.0.2" data-path="joinpivotDR.html"><a href="joinpivotDR.html#using-readnwisqw-read-all-the-chloride-00940-data-for-the-new-river-at-radford-03171000."><i class="fa fa-check"></i><b>8.0.2</b> 1. Using readNWISqw(), read all the chloride (00940) data for the New River at Radford (03171000).</a></li>
<li class="chapter" data-level="8.0.3" data-path="joinpivotDR.html"><a href="joinpivotDR.html#use-the-head-function-to-print-the-beginning-of-the-output-from-readnwisqw."><i class="fa fa-check"></i><b>8.0.3</b> Use the head() function to print the beginning of the output from readNWISqw.</a></li>
<li class="chapter" data-level="8.0.4" data-path="joinpivotDR.html"><a href="joinpivotDR.html#using-the-readnwisdv-daily-values-function-download-discharge-00060-temperature-00003-and-specific-conductivity-00095-for-the-new-river-at-radford-from-2007-to-2009-regular-year."><i class="fa fa-check"></i><b>8.0.4</b> 2. Using the readNWISdv (daily values) function, download discharge (00060), temperature (00003), and specific conductivity (00095) for the New River at Radford from 2007 to 2009 (regular year).</a></li>
<li class="chapter" data-level="8.0.5" data-path="joinpivotDR.html"><a href="joinpivotDR.html#use-renamenwiscolumns-to-rename-the-output-of-the-download."><i class="fa fa-check"></i><b>8.0.5</b> Use renameNWIScolumns() to rename the output of the download.</a></li>
<li class="chapter" data-level="8.0.6" data-path="joinpivotDR.html"><a href="joinpivotDR.html#use-head-to-show-the-beginning-of-the-results-of-your-download."><i class="fa fa-check"></i><b>8.0.6</b> Use head() to show the beginning of the results of your download.</a></li>
<li class="chapter" data-level="8.0.7" data-path="joinpivotDR.html"><a href="joinpivotDR.html#do-a-left-join-on-newphys-and-newriver-to-add-the-chloride-data-to-the-daily-discharge-temp-and-conductivity-data.-hint-you-will-join-on-the-date."><i class="fa fa-check"></i><b>8.0.7</b> 3. Do a left join on newphys and newriver to add the chloride data to the daily discharge, temp, and conductivity data. hint: you will join on the date.</a></li>
<li class="chapter" data-level="8.0.8" data-path="joinpivotDR.html"><a href="joinpivotDR.html#preview-your-data-below-the-chunk-using-head"><i class="fa fa-check"></i><b>8.0.8</b> Preview your data below the chunk using head()</a></li>
<li class="chapter" data-level="8.0.9" data-path="joinpivotDR.html"><a href="joinpivotDR.html#create-a-line-plot-of-date-x-and-flow-y.-create-a-scatter-plot-of-date-x-and-chloride-concentration-y.-put-the-graphs-on-top-of-each-other-using-the-patchwork-library."><i class="fa fa-check"></i><b>8.0.9</b> 4. Create a line plot of Date (x) and Flow (y). Create a scatter plot of Date (x) and chloride concentration (y). Put the graphs on top of each other using the patchwork library.</a></li>
<li class="chapter" data-level="8.0.10" data-path="joinpivotDR.html"><a href="joinpivotDR.html#create-a-scatter-plot-of-specific-conductivity-y-and-chloride-x.-challenge-what-could-you-do-to-get-rid-of-the-warning-this-plot-generates-about-nas."><i class="fa fa-check"></i><b>8.0.10</b> 5. Create a scatter plot of Specific Conductivity (y) and Chloride (x). Challenge: what could you do to get rid of the warning this plot generates about NAs.</a></li>
<li class="chapter" data-level="8.0.11" data-path="joinpivotDR.html"><a href="joinpivotDR.html#read-in-the-gg-chem-subset-data-and-plot-mg_e1-x-vs-ca_e1-y-as-points."><i class="fa fa-check"></i><b>8.0.11</b> 6. Read in the GG chem subset data and plot Mg_E1 (x) vs Ca_E1 (y) as points.</a></li>
<li class="chapter" data-level="8.0.12" data-path="joinpivotDR.html"><a href="joinpivotDR.html#we-want-to-look-at-concentrations-of-each-element-in-the-6-dataset-along-the-stream-distance-which-is-difficult-in-the-current-format.-pivot-the-data-into-a-long-format-the-data-from-ca-mg-and-na-_e1-columns-should-be-pivoted."><i class="fa fa-check"></i><b>8.0.12</b> 7. We want to look at concentrations of each element in the #6 dataset along the stream (Distance), which is difficult in the current format. Pivot the data into a long format, the data from Ca, Mg, and Na _E1 columns should be pivoted.</a></li>
<li class="chapter" data-level="8.0.13" data-path="joinpivotDR.html"><a href="joinpivotDR.html#make-line-plots-of-each-element-where-y-is-the-concentration-and-x-is-distance.-use-facet_wrap-to-create-a-separate-plot-for-each-element-and-use-the-scales-argument-of-facet_wrap-to-allow-each-plot-to-have-different-y-limits."><i class="fa fa-check"></i><b>8.0.13</b> Make line plots of each element where y is the concentration and x is distance. Use facet_wrap() to create a separate plot for each element and use the “scales” argument of facet_wrap to allow each plot to have different y limits.</a></li>
</ul></li>
<li class="chapter" data-level="9" data-path="Summative1.html"><a href="Summative1.html"><i class="fa fa-check"></i><b>9</b> Summative Activity 1</a>
<ul>
<li class="chapter" data-level="9.0.1" data-path="Summative1.html"><a href="Summative1.html#instructions"><i class="fa fa-check"></i><b>9.0.1</b> Instructions</a></li>
<li class="chapter" data-level="9.1" data-path="Summative1.html"><a href="Summative1.html#load-the-tidyverse-lubridate-and-dataretrieval-packages."><i class="fa fa-check"></i><b>9.1</b> 1. Load the tidyverse, lubridate, and dataRetrieval packages.</a></li>
<li class="chapter" data-level="9.2" data-path="Summative1.html"><a href="Summative1.html#read-in-the-mcdonald-hollow-dataset-in-the-project-folder."><i class="fa fa-check"></i><b>9.2</b> 2. Read in the McDonald Hollow dataset in the project folder.</a>
<ul>
<li class="chapter" data-level="9.2.1" data-path="Summative1.html"><a href="Summative1.html#what-are-the-data-types-of-the-first-three-columns"><i class="fa fa-check"></i><b>9.2.1</b> What are the data types of the first three columns?</a></li>
<li class="chapter" data-level="9.2.2" data-path="Summative1.html"><a href="Summative1.html#how-long-is-the-data-number-of-rows"><i class="fa fa-check"></i><b>9.2.2</b> How long is the data (number of rows)?</a></li>
<li class="chapter" data-level="9.2.3" data-path="Summative1.html"><a href="Summative1.html#what-is-the-name-of-the-last-column"><i class="fa fa-check"></i><b>9.2.3</b> What is the name of the last column?</a></li>
</ul></li>
<li class="chapter" data-level="9.3" data-path="Summative1.html"><a href="Summative1.html#plot-the-stage-of-the-stream-stage_m_pt-on-the-y-axis-as-a-line-and-the-date-on-the-x.-these-stage-data-are-in-meters-convert-them-to-centimeters-for-the-plot."><i class="fa fa-check"></i><b>9.3</b> 3. Plot the stage of the stream (Stage_m_pt) on the y axis as a line and the date on the x. These stage data are in meters, convert them to centimeters for the plot.</a>
<ul>
<li class="chapter" data-level="9.3.1" data-path="Summative1.html"><a href="Summative1.html#for-all-plots-in-this-test-label-axes-properly-and-use-a-theme-other-than-the-default."><i class="fa fa-check"></i><b>9.3.1</b> For all plots in this test, label axes properly and use a theme other than the default.</a></li>
</ul></li>
<li class="chapter" data-level="9.4" data-path="Summative1.html"><a href="Summative1.html#we-want-to-look-at-the-big-event-that-happens-from-november-11-2020-to-november-27-2020.-filter-the-dataset-down-to-this-time-frame-and-save-it-separately.-make-a-plot-with-the-same-setup-as-in-3-with-these-newly-saved-data."><i class="fa fa-check"></i><b>9.4</b> 4. We want to look at the big event that happens from November 11, 2020 to November 27, 2020. Filter the dataset down to this time frame and save it separately. Make a plot with the same setup as in #3 with these newly saved data.</a></li>
<li class="chapter" data-level="9.5" data-path="Summative1.html"><a href="Summative1.html#for-this-storm-we-are-curious-about-how-conductivity-changes-with-the-stream-level.-to-do-this-make-a-scatter-plot-that-shows-stage-on-the-x-axis-and-specific-conductivity-spc_mscm-on-the-y.-units-mscm-color-the-points-on-the-plot-using-the-datetime-column.-use-the-plot-to-describe-how-specific-conductivity-changes-with-stream-stage-throughout-the-storm.-not-functionally-just-how-the-values-change"><i class="fa fa-check"></i><b>9.5</b> 5. For this storm, we are curious about how conductivity changes with the stream level. To do this, make a scatter plot that shows Stage on the x axis and specific conductivity (SpC_mScm) on the y. (units: mScm) Color the points on the plot using the datetime column. Use the plot to describe how specific conductivity changes with stream stage throughout the storm. (not functionally, just how the values change)</a></li>
<li class="chapter" data-level="9.6" data-path="Summative1.html"><a href="Summative1.html#continuing-to-look-at-the-storm-as-an-exploratory-data-analysis-we-want-to-create-a-plot-that-shows-all-the-parameters-measured.-to-do-this-pivot-the-storm-event-data-so-there-is-a-column-that-has-the-values-for-all-the-parameters-measured-as-individual-rows-along-with-another-column-that-identifies-the-type-of-measurement.-then-use-facet_wrap-with-the-name-column-or-whatever-you-call-it-as-the-facet.-be-sure-to-set-the-parameters-of-facet_wrap-such-that-the-y-axes-are-all-allowed-to-be-different-ranges."><i class="fa fa-check"></i><b>9.6</b> 6. Continuing to look at the storm, as an exploratory data analysis, we want to create a plot that shows all the parameters measured. To do this, pivot the STORM EVENT data so there is a column that has the values for all the parameters measured as individual rows, along with another column that identifies the type of measurement. Then use facet_wrap with the “name” column (or whatever you call it) as the facet. Be sure to set the parameters of facet_wrap such that the y axes are all allowed to be different ranges.</a></li>
<li class="chapter" data-level="9.7" data-path="Summative1.html"><a href="Summative1.html#we-want-to-create-a-table-that-clearly-shows-the-differences-in-water-temperature-for-the-three-months-at-the-two-locations-flow-and-pool-in-the-full-data-set-not-the-storm-subset.-to-do-this-create-a-new-column-in-the-full-dataset-called-month-and-set-it-equal-to-the-month-of-the-datetime-column-using-the-month-function.-then-group-your-dataset-by-month-and-summarize-temperature-at-each-location-by-mean.-save-these-results-to-a-new-object-and-output-it-so-it-appears-below-your-chunk-when-you-knit.-be-sure-the-object-has-descriptive-column-names."><i class="fa fa-check"></i><b>9.7</b> 7. We want to create a table that clearly shows the differences in water temperature for the three months at the two locations (flow and pool) in the FULL data set (not the storm subset). To do this: Create a new column in the full dataset called “month” and set it equal to the month of the datetime column using the month() function. Then group your dataset by month and summarize temperature at each location by mean. Save these results to a new object and output it so it appears below your chunk when you knit. Be sure the object has descriptive column names.</a></li>
<li class="chapter" data-level="9.8" data-path="Summative1.html"><a href="Summative1.html#plot-the-distribution-of-the-flow-temperature-and-show-as-vertical-lines-on-the-plot-the-mean-median-and-iqr.-be-careful-about-how-you-show-iqr.-look-at-the-definition-and-then-think-about-how-you-would-put-it-on-the-plot.-describe-in-the-text-above-the-chunk-what-color-is-what-statistic-in-the-plot.-using-the-shape-of-the-distribution-and-the-measures-you-plotted-explain-why-you-think-the-distribution-is-normal-or-not.-what-statistical-test-could-you-perform-to-see-if-it-is-normal"><i class="fa fa-check"></i><b>9.8</b> 8. Plot the distribution of the flow temperature and show as vertical lines on the plot the mean, median, and IQR. Be careful about how you show IQR. Look at the definition and then think about how you would put it on the plot. Describe in the text above the chunk what color is what statistic in the plot. Using the shape of the distribution and the measures you plotted, explain why you think the distribution is normal or not. What statistical test could you perform to see if it is normal?</a></li>
<li class="chapter" data-level="9.9" data-path="Summative1.html"><a href="Summative1.html#in-this-question-we-will-get-and-format-data-for-three-usgs-gages."><i class="fa fa-check"></i><b>9.9</b> 9. In this question we will get and format data for three USGS gages.</a>
<ul>
<li class="chapter" data-level="9.9.1" data-path="Summative1.html"><a href="Summative1.html#a.-read-and-save-the-gage-information-for-the-three-gages-using-readnwissite."><i class="fa fa-check"></i><b>9.9.1</b> a. Read and save the gage information for the three gages using readNWISsite().</a></li>
<li class="chapter" data-level="9.9.2" data-path="Summative1.html"><a href="Summative1.html#b.-use-the-readnwisdv-function-to-read-and-save-the-daily-discharge-values-for-the-following-three-gages-for-the-2020-water-year-10-01-2019-to-9-30-2020.-and-then-use-the-renamenwiscolumns-function-to-make-the-names-human-friendly."><i class="fa fa-check"></i><b>9.9.2</b> b. Use the readNWISdv() function to read and save the daily discharge values for the following three gages for the 2020 water year (10-01-2019 to 9-30-2020). And then use the renameNWIScolumns() function to make the names human-friendly.</a></li>
<li class="chapter" data-level="9.9.3" data-path="Summative1.html"><a href="Summative1.html#c.-join-the-gage-site-information-from-a-to-the-data-from-b-so-you-can-reference-the-gages-by-their-names."><i class="fa fa-check"></i><b>9.9.3</b> c. Join the gage site information from (a) to the data from (b) so you can reference the gages by their names.</a></li>
</ul></li>
<li class="chapter" data-level="9.10" data-path="Summative1.html"><a href="Summative1.html#using-the-data-from-9-plot-flow-on-the-y-axis-and-date-on-the-x-axis-showing-the-data-as-a-line-and-coloring-by-gage-name."><i class="fa fa-check"></i><b>9.10</b> 10. Using the data from #9, Plot flow on the y axis and date on the x axis, showing the data as a line, and coloring by gage name.</a></li>
</ul></li>
<li class="chapter" data-level="10" data-path="fdcs.html"><a href="fdcs.html"><i class="fa fa-check"></i><b>10</b> Flow Duration Curves</a></li>
<li class="chapter" data-level="11" data-path="flow-duration-curves.html"><a href="flow-duration-curves.html"><i class="fa fa-check"></i><b>11</b> Flow Duration Curves</a>
<ul>
<li class="chapter" data-level="11.1" data-path="flow-duration-curves.html"><a href="flow-duration-curves.html#get-data"><i class="fa fa-check"></i><b>11.1</b> Get data</a></li>
<li class="chapter" data-level="11.2" data-path="flow-duration-curves.html"><a href="flow-duration-curves.html#review-describe-the-distribution"><i class="fa fa-check"></i><b>11.2</b> Review: describe the distribution</a></li>
<li class="chapter" data-level="11.3" data-path="flow-duration-curves.html"><a href="flow-duration-curves.html#ecdfs"><i class="fa fa-check"></i><b>11.3</b> ECDFs</a></li>
<li class="chapter" data-level="11.4" data-path="flow-duration-curves.html"><a href="flow-duration-curves.html#calculate-flow-exceedence-probabilities"><i class="fa fa-check"></i><b>11.4</b> Calculate flow exceedence probabilities</a></li>
<li class="chapter" data-level="11.5" data-path="flow-duration-curves.html"><a href="flow-duration-curves.html#plot-a-flow-duration-curve-using-the-probabilities"><i class="fa fa-check"></i><b>11.5</b> Plot a Flow Duration Curve using the probabilities</a></li>
<li class="chapter" data-level="11.6" data-path="flow-duration-curves.html"><a href="flow-duration-curves.html#make-an-almost-fdc-with-stat_ecdf"><i class="fa fa-check"></i><b>11.6</b> Make an almost FDC with stat_ecdf</a></li>
<li class="chapter" data-level="11.7" data-path="flow-duration-curves.html"><a href="flow-duration-curves.html#example-use-of-an-fdc"><i class="fa fa-check"></i><b>11.7</b> Example use of an FDC</a></li>
<li class="chapter" data-level="11.8" data-path="flow-duration-curves.html"><a href="flow-duration-curves.html#compare-to-a-boxplot-of-the-same-data"><i class="fa fa-check"></i><b>11.8</b> Compare to a boxplot of the same data</a></li>
<li class="chapter" data-level="11.9" data-path="flow-duration-curves.html"><a href="flow-duration-curves.html#challenge-examining-flow-regime-change-at-the-grand-canyon"><i class="fa fa-check"></i><b>11.9</b> Challenge: Examining flow regime change at the Grand Canyon</a></li>
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<li class="chapter" data-level="12" data-path="lfas.html"><a href="lfas.html"><i class="fa fa-check"></i><b>12</b> Low Flow Analysis</a></li>
<li class="chapter" data-level="13" data-path="low-flow-analyses.html"><a href="low-flow-analyses.html"><i class="fa fa-check"></i><b>13</b> Low Flow Analyses</a>
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<li class="chapter" data-level="13.1" data-path="low-flow-analyses.html"><a href="low-flow-analyses.html#what-is-a-xqy-flow"><i class="fa fa-check"></i><b>13.1</b> What is a xQy flow?</a></li>
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<li class="chapter" data-level="14" data-path="floods.html"><a href="floods.html"><i class="fa fa-check"></i><b>14</b> Flood Frequency Analysis</a>
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<li class="chapter" data-level="14.1" data-path="floods.html"><a href="floods.html#challenge-create-a-function"><i class="fa fa-check"></i><b>14.1</b> Challenge: Create a function</a></li>
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<li class="chapter" data-level="15" data-path="intro.html"><a href="intro.html"><i class="fa fa-check"></i><b>15</b> Introduction</a></li>
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<div id="flow-duration-curves" class="section level1" number="11">
<h1><span class="header-section-number">Chapter 11</span> Flow Duration Curves</h1>
<p>Alright team. So far we have learned to wrangle data, make plots, and look at data distributions. Now it is time to put all that knowledge to use.</p>
<p>We are on our way to doing analyses of extreme discharge events: low flow statistics and flood. But in order to do that, we need to understand a common way to look at data distributions in hydrology: the flow duration curve. As you’ll see below, this is basically just a different way of looking at a pdf, and it can take some getting used to. But it is also a very useful tool!</p>
<div id="get-data" class="section level2" number="11.1">
<h2><span class="header-section-number">11.1</span> Get data</h2>
<p>To start, let’s grab the USGS discharge data for the gage in Linville NC from 1960 to 2020.</p>
<p>We will download the data using USGS dataRetrieval and look at a line plot.</p>
<div class="sourceCode" id="cb160"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb160-1"><a href="flow-duration-curves.html#cb160-1" aria-hidden="true" tabindex="-1"></a>siteno <span class="ot"><-</span> <span class="st">"02138500"</span> <span class="co">#Linville NC</span></span>
<span id="cb160-2"><a href="flow-duration-curves.html#cb160-2" aria-hidden="true" tabindex="-1"></a>startDate <span class="ot"><-</span> <span class="st">"1960-01-01"</span></span>
<span id="cb160-3"><a href="flow-duration-curves.html#cb160-3" aria-hidden="true" tabindex="-1"></a>endDate <span class="ot"><-</span> <span class="st">"2020-01-01"</span></span>
<span id="cb160-4"><a href="flow-duration-curves.html#cb160-4" aria-hidden="true" tabindex="-1"></a>parameter <span class="ot"><-</span> <span class="st">"00060"</span></span>
<span id="cb160-5"><a href="flow-duration-curves.html#cb160-5" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb160-6"><a href="flow-duration-curves.html#cb160-6" aria-hidden="true" tabindex="-1"></a>Qdat <span class="ot"><-</span> <span class="fu">readNWISdv</span>(siteno, parameter, startDate, endDate) <span class="sc">%>%</span> </span>
<span id="cb160-7"><a href="flow-duration-curves.html#cb160-7" aria-hidden="true" tabindex="-1"></a> <span class="fu">renameNWISColumns</span>()</span>
<span id="cb160-8"><a href="flow-duration-curves.html#cb160-8" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb160-9"><a href="flow-duration-curves.html#cb160-9" aria-hidden="true" tabindex="-1"></a><span class="co">#Look at the data</span></span>
<span id="cb160-10"><a href="flow-duration-curves.html#cb160-10" aria-hidden="true" tabindex="-1"></a>Qdat <span class="sc">%>%</span> <span class="fu">ggplot</span>(<span class="fu">aes</span>(<span class="at">x =</span> Date, <span class="at">y =</span> Flow))<span class="sc">+</span></span>
<span id="cb160-11"><a href="flow-duration-curves.html#cb160-11" aria-hidden="true" tabindex="-1"></a> <span class="fu">geom_line</span>()</span></code></pre></div>
<p><img src="Hydroinformatics_Bookdown_files/figure-html/unnamed-chunk-86-1.png" width="672" /></p>
</div>
<div id="review-describe-the-distribution" class="section level2" number="11.2">
<h2><span class="header-section-number">11.2</span> Review: describe the distribution</h2>
<p>Make a plot to view the distribution of the discharge data.</p>
<p>What is the median flow value? What does this tell us about flow at that river? How often is the river at or below that value? Could you pick that number off the plot? What about the flow the river is at or above only 5% of the time?</p>
<div class="sourceCode" id="cb161"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb161-1"><a href="flow-duration-curves.html#cb161-1" aria-hidden="true" tabindex="-1"></a>Qdat <span class="sc">%>%</span> <span class="fu">ggplot</span>(<span class="fu">aes</span>(Flow))<span class="sc">+</span></span>
<span id="cb161-2"><a href="flow-duration-curves.html#cb161-2" aria-hidden="true" tabindex="-1"></a> <span class="fu">stat_density</span>()<span class="sc">+</span></span>
<span id="cb161-3"><a href="flow-duration-curves.html#cb161-3" aria-hidden="true" tabindex="-1"></a> <span class="fu">scale_x_log10</span>()<span class="sc">+</span></span>
<span id="cb161-4"><a href="flow-duration-curves.html#cb161-4" aria-hidden="true" tabindex="-1"></a> <span class="fu">geom_vline</span>(<span class="at">xintercept =</span> <span class="fu">median</span>(Qdat<span class="sc">$</span>Flow), <span class="at">color =</span> <span class="st">"red"</span>)</span></code></pre></div>
<p><img src="Hydroinformatics_Bookdown_files/figure-html/unnamed-chunk-87-1.png" width="672" /></p>
</div>
<div id="ecdfs" class="section level2" number="11.3">
<h2><span class="header-section-number">11.3</span> ECDFs</h2>
<p>Let’s look at an Empirical Cumulative Density Function (ECDF) of the data.</p>
<p>Look at this carefully, what does it show? How is it different from the pdf of the data?</p>
<p>Plot the median again. Without the line on the plot, how would you tell where the median is?</p>
<p>Given your answer to the question above, can you determine the flow the river is at or above only 25% of the time? Think carefully about what the y axis of the ECDF means.</p>
<div class="sourceCode" id="cb162"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb162-1"><a href="flow-duration-curves.html#cb162-1" aria-hidden="true" tabindex="-1"></a>Qdat <span class="sc">%>%</span> <span class="fu">ggplot</span>(<span class="fu">aes</span>(Flow))<span class="sc">+</span></span>
<span id="cb162-2"><a href="flow-duration-curves.html#cb162-2" aria-hidden="true" tabindex="-1"></a> <span class="fu">stat_ecdf</span>()<span class="sc">+</span></span>
<span id="cb162-3"><a href="flow-duration-curves.html#cb162-3" aria-hidden="true" tabindex="-1"></a> <span class="fu">scale_x_log10</span>()<span class="sc">+</span></span>
<span id="cb162-4"><a href="flow-duration-curves.html#cb162-4" aria-hidden="true" tabindex="-1"></a> <span class="fu">geom_vline</span>(<span class="at">xintercept =</span> <span class="fu">median</span>(Qdat<span class="sc">$</span>Flow), <span class="at">color =</span> <span class="st">"red"</span>)<span class="sc">+</span></span>
<span id="cb162-5"><a href="flow-duration-curves.html#cb162-5" aria-hidden="true" tabindex="-1"></a> <span class="fu">geom_vline</span>(<span class="at">xintercept =</span> <span class="fu">quantile</span>(Qdat<span class="sc">$</span>Flow)[<span class="dv">4</span>], <span class="at">color =</span> <span class="st">"blue"</span>)</span></code></pre></div>
<p><img src="Hydroinformatics_Bookdown_files/figure-html/unnamed-chunk-88-1.png" width="672" /></p>
</div>
<div id="calculate-flow-exceedence-probabilities" class="section level2" number="11.4">
<h2><span class="header-section-number">11.4</span> Calculate flow exceedence probabilities</h2>
<p>It is common to look at a similar representation of flow distributions in hydrology, but with flow on the Y axis and “% time flow is equaled or exceeded” on the X axis. There are a number of ways we could make this plot: for example we could transform the axes of the plot above or we could use the function that results from the ECDF function in R to calculate exceedence probabilities at flow throughout our range of flows. But for our purposes, we are just going to calculate it manually.</p>
<p>We are going to calculate our own exceedence probabilities because knowing how to do this will hopefully help us understand what a flow duration curve is AND we will need to do similar things in our high and low flow analyses.</p>
<p>The formula for exceedence probability (P) is below. What do we need to calculate this?</p>
<p>Exceedence probability (P), Probability a flow is equaled or exceeded P = 100 * [M / (n + 1)] M = Ranked position of the flow n = total number of observations in data record</p>
<p>Here’s a description of what we will do: Pass our Qdat data to mutate and create a new column that is equal to the ranks of the discharge column. Then pass that result to mutate again and create another column equal to the 100 times the rank of each discharge divided by the length of the record (use length()) + 1.</p>
<div class="sourceCode" id="cb163"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb163-1"><a href="flow-duration-curves.html#cb163-1" aria-hidden="true" tabindex="-1"></a>Qdat <span class="ot"><-</span> Qdat <span class="sc">%>%</span></span>
<span id="cb163-2"><a href="flow-duration-curves.html#cb163-2" aria-hidden="true" tabindex="-1"></a> <span class="fu">mutate</span>(<span class="at">rank =</span> <span class="fu">rank</span>(<span class="sc">-</span>Flow)) <span class="sc">%>%</span> <span class="co">#Flow is negative to make high flows ranked low (#1)</span></span>
<span id="cb163-3"><a href="flow-duration-curves.html#cb163-3" aria-hidden="true" tabindex="-1"></a> <span class="fu">mutate</span>(<span class="at">P =</span> <span class="dv">100</span> <span class="sc">*</span> (rank <span class="sc">/</span> (<span class="fu">length</span>(Flow) <span class="sc">+</span> <span class="dv">1</span>)))</span></code></pre></div>
</div>
<div id="plot-a-flow-duration-curve-using-the-probabilities" class="section level2" number="11.5">
<h2><span class="header-section-number">11.5</span> Plot a Flow Duration Curve using the probabilities</h2>
<p>Now construct the following plot: A line with P on the x axis and flow on the y axis. Name the x axis “% Time flow equaled or exceeded” and log the y axis.</p>
<p>That’s a flow duration curve!</p>
<p>Questions about the flow duration curve: How often is a flow of 100 cfs exceeded at this gage? Is flow more variable for flows exceeded 0-25% or of the time or 75-100% of the time? How can you tell? These data are daily observations. Given that, what is a more accurate name for the x axis? What would the X axis be called if we were using maximum yearly data?</p>
<div class="sourceCode" id="cb164"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb164-1"><a href="flow-duration-curves.html#cb164-1" aria-hidden="true" tabindex="-1"></a>Qdat <span class="sc">%>%</span> <span class="fu">ggplot</span>(<span class="fu">aes</span>(<span class="at">x =</span> P, <span class="at">y =</span> Flow))<span class="sc">+</span></span>
<span id="cb164-2"><a href="flow-duration-curves.html#cb164-2" aria-hidden="true" tabindex="-1"></a> <span class="fu">geom_line</span>()<span class="sc">+</span></span>
<span id="cb164-3"><a href="flow-duration-curves.html#cb164-3" aria-hidden="true" tabindex="-1"></a> <span class="fu">scale_y_log10</span>()<span class="sc">+</span></span>
<span id="cb164-4"><a href="flow-duration-curves.html#cb164-4" aria-hidden="true" tabindex="-1"></a> <span class="fu">xlab</span>(<span class="st">"% Time flow equalled or exceeded"</span>)<span class="sc">+</span></span>
<span id="cb164-5"><a href="flow-duration-curves.html#cb164-5" aria-hidden="true" tabindex="-1"></a> <span class="fu">ylab</span>(<span class="st">"Q (cfs)"</span>)</span></code></pre></div>
<p><img src="Hydroinformatics_Bookdown_files/figure-html/unnamed-chunk-90-1.png" width="672" /></p>
</div>
<div id="make-an-almost-fdc-with-stat_ecdf" class="section level2" number="11.6">
<h2><span class="header-section-number">11.6</span> Make an almost FDC with stat_ecdf</h2>
<p>Below is an example of making a very similar plot with the stat_ecdf() geometry in ggplot. Notice how similar the result is to the one we calculated manually.</p>
<div class="sourceCode" id="cb165"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb165-1"><a href="flow-duration-curves.html#cb165-1" aria-hidden="true" tabindex="-1"></a>Qdat <span class="sc">%>%</span> <span class="fu">ggplot</span>(<span class="fu">aes</span>(Flow))<span class="sc">+</span></span>
<span id="cb165-2"><a href="flow-duration-curves.html#cb165-2" aria-hidden="true" tabindex="-1"></a> <span class="fu">stat_ecdf</span>()<span class="sc">+</span></span>
<span id="cb165-3"><a href="flow-duration-curves.html#cb165-3" aria-hidden="true" tabindex="-1"></a> <span class="fu">scale_x_log10</span>()<span class="sc">+</span></span>
<span id="cb165-4"><a href="flow-duration-curves.html#cb165-4" aria-hidden="true" tabindex="-1"></a> <span class="fu">scale_y_reverse</span>()<span class="sc">+</span></span>
<span id="cb165-5"><a href="flow-duration-curves.html#cb165-5" aria-hidden="true" tabindex="-1"></a> <span class="fu">coord_flip</span>()<span class="sc">+</span></span>
<span id="cb165-6"><a href="flow-duration-curves.html#cb165-6" aria-hidden="true" tabindex="-1"></a> <span class="fu">xlab</span>(<span class="st">"Q (cfs)"</span>)<span class="sc">+</span></span>
<span id="cb165-7"><a href="flow-duration-curves.html#cb165-7" aria-hidden="true" tabindex="-1"></a> <span class="fu">ylab</span>(<span class="st">"Probability flow is not exceeded"</span>)</span></code></pre></div>
<p><img src="Hydroinformatics_Bookdown_files/figure-html/unnamed-chunk-91-1.png" width="672" /></p>
</div>
<div id="example-use-of-an-fdc" class="section level2" number="11.7">
<h2><span class="header-section-number">11.7</span> Example use of an FDC</h2>
<p>Let’s explore one potential use of flow duration curves: examining the differences between two sets of flow data.</p>
<p>From the line plot of the discharge, it looked like the flow regime may have shifted a bit in the data between the early years and newer data. Let’s use flow duration curves to examine potential differences. We can come up with groups and then use group_by to run the analysis by groups instead of the whole dataset.</p>
<p>We are introducing a new function here called case_when(). This allows you to assign values to a new column based on values in another column. In our case, we are going to name different time period in our data.</p>
<p>We will then group the data by these periods and calculate exceedence probabilities for each. The procedure works the same, except we add a group_by statement before we create the rank and P columns. Then, when we plot, we can just tell ggplot to create different colored lines based on the time period names and it will plot a separate flow duration curve for each. Tidyverse FOR THE WIN!</p>
<p>Describe the differences in flow regime you see between the three periods.</p>
<div class="sourceCode" id="cb166"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb166-1"><a href="flow-duration-curves.html#cb166-1" aria-hidden="true" tabindex="-1"></a>Qdat <span class="ot"><-</span> Qdat <span class="sc">%>%</span></span>
<span id="cb166-2"><a href="flow-duration-curves.html#cb166-2" aria-hidden="true" tabindex="-1"></a> <span class="fu">mutate</span>(<span class="at">year =</span> <span class="fu">year</span>(Date)) <span class="sc">%>%</span></span>
<span id="cb166-3"><a href="flow-duration-curves.html#cb166-3" aria-hidden="true" tabindex="-1"></a> <span class="fu">mutate</span>(<span class="at">period =</span> <span class="fu">case_when</span>( year <span class="sc"><=</span> <span class="dv">1980</span> <span class="sc">~</span> <span class="st">"1960-1980"</span>,</span>
<span id="cb166-4"><a href="flow-duration-curves.html#cb166-4" aria-hidden="true" tabindex="-1"></a> year <span class="sc">></span> <span class="dv">1980</span> <span class="sc">&</span> year <span class="sc"><=</span> <span class="dv">2000</span> <span class="sc">~</span> <span class="st">"1980-2000"</span>,</span>
<span id="cb166-5"><a href="flow-duration-curves.html#cb166-5" aria-hidden="true" tabindex="-1"></a> year <span class="sc">></span> <span class="dv">2000</span> <span class="sc">~</span> <span class="st">"2000-2020"</span>))</span>
<span id="cb166-6"><a href="flow-duration-curves.html#cb166-6" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb166-7"><a href="flow-duration-curves.html#cb166-7" aria-hidden="true" tabindex="-1"></a>Qdat <span class="ot"><-</span> Qdat <span class="sc">%>%</span></span>
<span id="cb166-8"><a href="flow-duration-curves.html#cb166-8" aria-hidden="true" tabindex="-1"></a> <span class="fu">group_by</span>(period) <span class="sc">%>%</span></span>
<span id="cb166-9"><a href="flow-duration-curves.html#cb166-9" aria-hidden="true" tabindex="-1"></a> <span class="fu">mutate</span>(<span class="at">rank =</span> <span class="fu">rank</span>(<span class="sc">-</span>Flow)) <span class="sc">%>%</span> </span>
<span id="cb166-10"><a href="flow-duration-curves.html#cb166-10" aria-hidden="true" tabindex="-1"></a> <span class="fu">mutate</span>(<span class="at">P =</span> <span class="dv">100</span> <span class="sc">*</span> (rank <span class="sc">/</span> (<span class="fu">length</span>(Flow) <span class="sc">+</span> <span class="dv">1</span>)))</span>
<span id="cb166-11"><a href="flow-duration-curves.html#cb166-11" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb166-12"><a href="flow-duration-curves.html#cb166-12" aria-hidden="true" tabindex="-1"></a>Qdat <span class="sc">%>%</span> <span class="fu">ggplot</span>(<span class="fu">aes</span>(<span class="at">x =</span> P, <span class="at">y =</span> Flow, <span class="at">color =</span> period))<span class="sc">+</span></span>
<span id="cb166-13"><a href="flow-duration-curves.html#cb166-13" aria-hidden="true" tabindex="-1"></a> <span class="fu">geom_line</span>()<span class="sc">+</span></span>
<span id="cb166-14"><a href="flow-duration-curves.html#cb166-14" aria-hidden="true" tabindex="-1"></a> <span class="fu">scale_y_log10</span>()<span class="sc">+</span></span>
<span id="cb166-15"><a href="flow-duration-curves.html#cb166-15" aria-hidden="true" tabindex="-1"></a> <span class="fu">xlab</span>(<span class="st">"% Time flow equalled or exceeded"</span>)<span class="sc">+</span></span>
<span id="cb166-16"><a href="flow-duration-curves.html#cb166-16" aria-hidden="true" tabindex="-1"></a> <span class="fu">ylab</span>(<span class="st">"Q (cfs)"</span>)</span></code></pre></div>
<p><img src="Hydroinformatics_Bookdown_files/figure-html/unnamed-chunk-92-1.png" width="672" /></p>
</div>
<div id="compare-to-a-boxplot-of-the-same-data" class="section level2" number="11.8">
<h2><span class="header-section-number">11.8</span> Compare to a boxplot of the same data</h2>
<p>We are really just looking at the data distribution here. Remember another good way to compare distributions is a boxplot. Let’s create a boxplot showing flows from these time periods. (we will also mess with the dimensions of the plot so the boxes aren’t so wide, using fig.width and fig.height in the ``` header above the code chunk)</p>
<p>What are the advantages/disadvantages of the flow duration curves vs. boxplots?</p>
<div class="sourceCode" id="cb167"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb167-1"><a href="flow-duration-curves.html#cb167-1" aria-hidden="true" tabindex="-1"></a>Qdat <span class="sc">%>%</span> <span class="fu">ggplot</span>(<span class="fu">aes</span>(<span class="at">x =</span> period, <span class="at">y =</span> Flow)) <span class="sc">+</span></span>
<span id="cb167-2"><a href="flow-duration-curves.html#cb167-2" aria-hidden="true" tabindex="-1"></a> <span class="fu">geom_boxplot</span>()<span class="sc">+</span></span>
<span id="cb167-3"><a href="flow-duration-curves.html#cb167-3" aria-hidden="true" tabindex="-1"></a> <span class="fu">scale_y_log10</span>()</span></code></pre></div>
<p><img src="Hydroinformatics_Bookdown_files/figure-html/unnamed-chunk-93-1.png" width="480" /></p>
</div>
<div id="challenge-examining-flow-regime-change-at-the-grand-canyon" class="section level2" number="11.9">
<h2><span class="header-section-number">11.9</span> Challenge: Examining flow regime change at the Grand Canyon</h2>
<p>The USGS Gage “Colorado River at Yuma, AZ” is below the Hoover dam. The Hoover Dam closed in 1936, changing the flow of the Colorado River. Load average daily discharge data from 10-01-1905 to 10-01-1965. Use a line plot of discharge and flow duration curves to examine the differences in discharge for the periods: 1905 - 1936, 1937 - 1965.</p>
<div class="sourceCode" id="cb168"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb168-1"><a href="flow-duration-curves.html#cb168-1" aria-hidden="true" tabindex="-1"></a>siteid <span class="ot"><-</span> <span class="st">"09521000"</span></span>
<span id="cb168-2"><a href="flow-duration-curves.html#cb168-2" aria-hidden="true" tabindex="-1"></a>startDate <span class="ot"><-</span> <span class="st">"1905-10-01"</span></span>
<span id="cb168-3"><a href="flow-duration-curves.html#cb168-3" aria-hidden="true" tabindex="-1"></a>endDate <span class="ot"><-</span> <span class="st">"1965-10-01"</span></span>
<span id="cb168-4"><a href="flow-duration-curves.html#cb168-4" aria-hidden="true" tabindex="-1"></a>parameter <span class="ot"><-</span> <span class="st">"00060"</span></span>
<span id="cb168-5"><a href="flow-duration-curves.html#cb168-5" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb168-6"><a href="flow-duration-curves.html#cb168-6" aria-hidden="true" tabindex="-1"></a>WS <span class="ot"><-</span> <span class="fu">readNWISdv</span>(siteid, parameter, startDate, endDate) <span class="sc">%>%</span> </span>
<span id="cb168-7"><a href="flow-duration-curves.html#cb168-7" aria-hidden="true" tabindex="-1"></a> <span class="fu">renameNWISColumns</span>() <span class="sc">%>%</span></span>
<span id="cb168-8"><a href="flow-duration-curves.html#cb168-8" aria-hidden="true" tabindex="-1"></a> <span class="fu">mutate</span>(<span class="at">year =</span> <span class="fu">year</span>(Date)) <span class="sc">%>%</span></span>
<span id="cb168-9"><a href="flow-duration-curves.html#cb168-9" aria-hidden="true" tabindex="-1"></a> <span class="fu">mutate</span>(<span class="at">period =</span> <span class="fu">case_when</span>( year <span class="sc"><=</span> <span class="dv">1936</span> <span class="sc">~</span> <span class="st">"Pre Dam"</span>,</span>
<span id="cb168-10"><a href="flow-duration-curves.html#cb168-10" aria-hidden="true" tabindex="-1"></a> year <span class="sc">></span> <span class="dv">1936</span> <span class="sc">~</span> <span class="st">"Post Dam"</span>)) <span class="sc">%>%</span></span>
<span id="cb168-11"><a href="flow-duration-curves.html#cb168-11" aria-hidden="true" tabindex="-1"></a> <span class="fu">group_by</span>(period) <span class="sc">%>%</span></span>
<span id="cb168-12"><a href="flow-duration-curves.html#cb168-12" aria-hidden="true" tabindex="-1"></a> <span class="fu">mutate</span>(<span class="at">rank =</span> <span class="fu">rank</span>(<span class="sc">-</span>Flow)) <span class="sc">%>%</span> </span>
<span id="cb168-13"><a href="flow-duration-curves.html#cb168-13" aria-hidden="true" tabindex="-1"></a> <span class="fu">mutate</span>(<span class="at">P =</span> <span class="dv">100</span> <span class="sc">*</span> (rank <span class="sc">/</span> (<span class="fu">length</span>(Flow) <span class="sc">+</span> <span class="dv">1</span>)))</span>
<span id="cb168-14"><a href="flow-duration-curves.html#cb168-14" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb168-15"><a href="flow-duration-curves.html#cb168-15" aria-hidden="true" tabindex="-1"></a>flow <span class="ot"><-</span> <span class="fu">ggplot</span>(WS, <span class="fu">aes</span>(Date, Flow))<span class="sc">+</span><span class="co">#, color = period))+</span></span>
<span id="cb168-16"><a href="flow-duration-curves.html#cb168-16" aria-hidden="true" tabindex="-1"></a> <span class="fu">geom_line</span>()<span class="sc">+</span></span>
<span id="cb168-17"><a href="flow-duration-curves.html#cb168-17" aria-hidden="true" tabindex="-1"></a> <span class="fu">ylab</span>(<span class="st">"Q (cfs)"</span>)</span>
<span id="cb168-18"><a href="flow-duration-curves.html#cb168-18" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb168-19"><a href="flow-duration-curves.html#cb168-19" aria-hidden="true" tabindex="-1"></a>fdc <span class="ot"><-</span> WS <span class="sc">%>%</span> <span class="fu">ggplot</span>(<span class="fu">aes</span>(<span class="at">x =</span> P, <span class="at">y =</span> Flow, <span class="at">color =</span> period))<span class="sc">+</span></span>
<span id="cb168-20"><a href="flow-duration-curves.html#cb168-20" aria-hidden="true" tabindex="-1"></a> <span class="fu">geom_line</span>()<span class="sc">+</span></span>
<span id="cb168-21"><a href="flow-duration-curves.html#cb168-21" aria-hidden="true" tabindex="-1"></a> <span class="co">#scale_y_log10()+</span></span>
<span id="cb168-22"><a href="flow-duration-curves.html#cb168-22" aria-hidden="true" tabindex="-1"></a> <span class="fu">xlab</span>(<span class="st">"% Time flow equalled or exceeded"</span>)<span class="sc">+</span></span>
<span id="cb168-23"><a href="flow-duration-curves.html#cb168-23" aria-hidden="true" tabindex="-1"></a> <span class="fu">ylab</span>(<span class="st">"Q (cfs)"</span>)</span>
<span id="cb168-24"><a href="flow-duration-curves.html#cb168-24" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb168-25"><a href="flow-duration-curves.html#cb168-25" aria-hidden="true" tabindex="-1"></a>flow <span class="sc">/</span> (fdc <span class="sc">+</span> <span class="fu">plot_spacer</span>())</span></code></pre></div>
<p><img src="Hydroinformatics_Bookdown_files/figure-html/unnamed-chunk-94-1.png" width="672" /></p>
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