\documentclass[11pt]{exam} %For printing lab %\documentclass[10pt, answers]{exam} %For printing answer key \usepackage{mathpazo} %Palatino \usepackage{graphicx} %For figures \usepackage[obeyspaces]{url} %Typeset pathnames \usepackage{color} %For shaded solutions %\usepackage{multicol} %For multiple columns %\usepackage{wrapfig} %For figures floated left or right %\usepackage{subfig} %For figures with subfigures \usepackage{floatflt} %For figures floated left or right %\usepackage{fancybox} \usepackage{upgreek} \usepackage{booktabs} \usepackage{rotating} \usepackage[margin=10pt,font=small,textfont=it,labelfont=bf]{caption} %labelsep=endash %Change this each term: \newcommand{\thislab}{Lab 6} \newcommand{\thisterm}{Fall 2011} % Fine-tuning \renewcommand{\solutiontitle}{\noindent} \newcommand{\blank}{\underline{\hspace{2in}}} \newcommand{\exercise}[1]{\fbox{\parbox{0.95\textwidth}{\textbf{Exercise:} #1}}} \setlength{\parindent}{0.0in} \setlength{\parskip}{0.1in} \setlength{\fboxrule}{0.5mm} %thickness of line in boxes \setlength{\fboxsep}{0.8em} %separation between box and text \shadedsolutions \firstpageheader{\textbf{GEOL-301, Hydrology\\ Bader, \thisterm}}% {\textbf{Name:}}{} \runningheader{GEOL-301}{}{\thislab, \thisterm} \firstpagefooter{}{}{} \runningfooter{}{---\thepage---}{} \headrule \begin{document} \begin{center} {\large \textbf{\thislab:}} \\ {\Large \textbf{Working with discharge data}} \\ \vspace{0.2in} \fbox{\parbox{0.9\textwidth}{ \textbf{Goals:} \begin{itemize} \item Gain proficiency in finding and using USGS discharge data. \item Understand how long-term flood frequency is calculated. \item See how a simple flood map can be drawn using discharge data. \end{itemize} \textbf{You will hand in:} This lab packet, an Excel spreadsheet, and a flood map. }} \end{center} \textbf{Overview:} \textit{In this lab you will get up-to-date gaging station data for Walla Walla rivers and apply the data to answering questions about flooding and discharge variability.} \vspace{1em}\hrule%\vspace{1em} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Introduction to USGS discharge data} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% The USGS maintains a website that allows you to view real-time discharge data from a subset of the USGS gaging stations. (At some stations this data must still be collected manually.) This is an amazingly powerful tool. \begin{itemize} \item Open a browser and navigate to the USGS real-time water data website at \path{http://waterdata.usgs.gov/nwis/rt} \item Go to the Washington State data. Notice the colored dots, depicting real-time conditions at stream gages statewide. The dots are colored to show you if the streamflow is unusually high or low for this time of year. Note that ``unusual'' is a matter of degree; while the 25-74th percentile category is certainly not unusual, the next higher and lower categories (between the 10th and 90th percentiles) are perhaps mildly unusual. Discharges greater than 90th or less than 10th are occur about 20\% of the time, on average. \end{itemize} \subsection{Hydrographs} %%%%%%%%%%%%%%%%%%%%%%%% Click on the stream gage dot on Mill Creek at Rooks Park (``Mill Creek at Walla Walla'' will appear when your cursor hovers over the correct dot on the map). You will see a real-time \emph{hydrograph} incorporating discharge data from the past week. A hydrograph is a plot of river discharge vs. time. \exercise{ \begin{questions} \question Describe the shape of the hydrograph. Does the shape make sense given what you remember about the precipitation we've felt over the past few days?\vspace*{1in} \question What was the \emph{peak discharge} (maximum discharge) over the past week, and when did it occur? \question What was the peak discharge for the next station downstream (Walla Walla River near Touchet) over the same time period, and when did it occur? \end{questions}} %%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Monthly summaries} %%%%%%%%%%%%%%%%%%%%%%%%%%% We can also look at summaries of the stream data. \begin{itemize} \item Still at the ``Walla Walla River near Touchet'' gaging station, use the drop-down menu to select ``Monthly statistics.'' \item Click on the checkbox to select the Discharge parameter, and click the ``Submit'' button. \item You can scroll to the bottom of the resulting table to see the mean discharge for each month. \end{itemize} \exercise{ \begin{enumerate} \item What months had the lowest discharge? \begin{solution} Late summer \end{solution} \item What months had the highest? \begin{solution} Winter-spring \end{solution} \item What do you think is providing much of the water during the highest-discharge months? \begin{solution} Snowmelt \end{solution} \end{enumerate}} %%%%%%%%%%%%%%%%%%%% \section{Daily data} %%%%%%%%%%%%%%%%%%%% Let's look a little further into the data available for this gaging station. \begin{itemize} \item Still in the ``Walla Walla River near Touchet'' page, select "Daily data" from the dropdown menu. \item Request all available daily data for the ten-year period 1996-01-01 to 2006-01-01 in tab-separated format. Click anywhere in the resulting document, then type \path{Ctrl-a} to select all and then \path{Ctrl-c} to copy the text to the clipboard. \item Open Excel. Click on the top left cell of your worksheet and then find the Paste button on the far left side of your Home tab. Click the drop-down arrow and choose Paste Special, selecting ``Text.'' Hopefully the data will be properly arranged in cells in the worksheet (you need to scroll down to see where the data starts). At the bottom of the window, name this worksheet ``Daily data''. \textbf{Note:} If a column is filled with hash signs (\path{#}) instead of numbers, then the column is not wide enough to display the data. Make the column wider by clicking on the line separating this column's letter from the next, then dragging it to the right. \item Immediately save the resulting Excel file in your personal folder. \end{itemize} \subsection{Making a rating curve} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% A \emph{rating curve} shows the relationship between discharge and gage height. \begin{itemize} \item First, let's clean up the spreadsheet. All you need to do this exercise is discharge, but you should also keep the columns containing gage height and the date of the measurement. \begin{itemize} \item Delete unnecessary columns. \item Give your remaining data columns understandable column names, like\\ \path{discharge(cfs)}. \item Delete the header rows above the table. \end{itemize} \item For this exercise, we need to delete two outliers. During two days during the flood of 1996, the gage/discharge relationship was different from the others. We need to remove these points in order to have a readable graph. Delete the two rows from 2/10/1996 and 2/11/1996. \item Change the order of the columns using copy and paste so that gage height comes before discharge. \item Select the data in these two columns, including the column labels, by clicking on the top left cell and shift-clicking on the lower right cell. \item Find Charts in the Insert tab. Select an X-Y scatterplot with no lines connecting the points. You should see a plot of discharge (on the Y axis) as a function of gage height (on the X axis). \item You can move the chart to a new worksheet by right-clicking it and selecting Move Chart. Call the new worksheet ``Rating Curve.'' \end{itemize} \exercise{ \begin{questions} \question Describe the relationship between gage height and discharge.\vspace*{1in} \begin{solution} Steepening at higher discharges \end{solution} \question Given this relationship, do you think the precision of the discharge data is better at relatively low discharge or high discharge? Why? (Hint: think about how a 100 cfs increase in discharge would look when the river is high and when it is low.)\vspace*{1in} \begin{solution} Better at medium discharges, because an increase in discharge changes the gage height more. \end{solution} \question What is the gage height at the lowest discharge measured? \begin{solution} 2 feet \end{solution} \question \begin{parts} \part Going back to the data table, approximately how much water in cubic feet flowed past the gaging station per year on average? (Hint: remember discharge is in volume per second. You can add another column showing daily volume.)\vspace*{0.5in} \begin{solution} 6.74 $\times 10^{12}$ cfs \end{solution} \part In cubic meters? \end{parts} \end{questions}} %%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Frequency analysis} %%%%%%%%%%%%%%%%%%%%%%%%%%%% We can use the peak data provided by the USGS to ask questions about the likelihood of flood events. \begin{itemize} \item Add a new worksheet to your Excel spreadsheet, and rename it ``Peak data''. \item Back at the USGS website, select ``Peak Streamflow'' from the dropdown menu. \item Select ``Tab-separated file.'' As before, copy the text and then use ``Paste special'' as text to get the data into your new Excel worksheet. \end{itemize} \exercise{Examine the data. \begin{questions} \question What years are covered by this dataset? \begin{solution} 1949--2008 \end{solution} \question Find the maximum discharge on record during this time. \begin{parts} \part When did it occur? \begin{solution} 22 Dec 1964 \end{solution} \part What was the discharge in cfs? \begin{solution} 33,400 cfs \end{solution} \part What was the gage height during this discharge? \begin{solution} 18.9 feet \end{solution} \end{parts} \end{questions}} \begin{itemize} \item Clean up the spreadsheet as you did with the daily data. You should keep the date, gage height, and discharge columns. \item Using the Excel functions \path{AVERAGE()} and \path{STDEV()}, calculate the mean and standard deviation of discharge for this dataset. \end{itemize} Remember that to enter a formula, you must first type `=' and that you can refer to cell contents by their position. An example formula to calculate the mean of some numbers in column B between rows 3 and 7 might therefore be: \path{=AVERAGE(B3:B7)} \exercise{ \begin{questions} \question What is the mean peak discharge across all of the years (always include units)?\vspace*{0.25in} \begin{solution} 7572 cfs \end{solution} \question What is the standard deviation of peak discharge?\vspace*{0.25in} \begin{solution} 6389 cfs \end{solution} \question Approximately how many standard deviations above the mean was the highest peak discharge?\vspace*{0.25in} \begin{solution} 5--6 \end{solution} \end{questions}} \subsection{Ranked discharge} %%%%%%%%%%%%%%%%%%%%%%%%%%%%% We can use peak data such as this to calculate the probability of floods of a particular size. This is how we figure out that a particular discharge is e.g. ``a 100-year flood'' for a given stream. \begin{description} \item[Discharge probability] is the probability of experiencing a flood of this large \emph{or larger} in any year. \item[Long-term recurrence interval] is a misleading term. It is equal to $1/p$ where $p$ is the discharge probability. A flood frequency of 100, for example, means that a discharge this high or higher is a ``100-year flood,'' which means that over a very long period you can expect to see about one flood of this size per 100 years of record. \end{description} \exercise{Given the way flood frequency is calculated, if there was a 100-year flood two years ago, how long would you have to wait for the next 100-year flood? (Careful, this is a trick question!)\vspace*{0.25in} \begin{solution} Unknown, flooding has the same probability every year. \end{solution}} \begin{itemize} \item Copy the all of the Peak Discharge data to a new worksheet. Name the worksheet ``Flood.'' \item Now use the ``Sort Z to A'' function to sort the data from the highest discharge at the top to the lowest at the bottom. \item Add a new column, named \path{Rank}. In the top row, with the largest flood discharge on record, put a ``1'' in the Rank column. Then rank the remaining peak discharges: \begin{itemize} \item In the Rank column, in the cell just below the ``1,'' type a formula adding one to the cell above it, and hit return. There should now be a ``2'' in the cell. \item Select the cell with the formula, and shift-click on the last cell in the Rank column to select the rest of the column. \item Type \path{Ctrl - d} to fill the formula into the remaining cells. \end{itemize} \item Now start a new column, called \path{Probability}. For this column, we can calculate the probability of a discharge this large or larger, based on the data. We will calculate this as the total number of peak events this high or higher divided by the total number of events on record, or $P = R / (n+1)$ where $R$ is the rank and $n$ is the total number of events on record. Note: we adjust the denominator by one to correct a systematic bias and reflect our uncertainty. You can see that if we only had one discharge on record, it would be more sensible to make assign a probability of 50\% rather than 100\%. %Calculate the long-term recurrence interval = 1/p \item Use a formula to calculate the discharge probability for each discharge. \item Make a new column, and calculate the long-term recurrence interval, or $1/P$. \item Plot your results. Make a new X-Y scatterplot with Recurrence Interval on the X-axis and Discharge on the Y axis. Make both axes logarithmic. \item To improve readability, right-click on the numbers along an axis and select ``add minor gridlines.'' \end{itemize} \exercise{ \begin{questions} \question \begin{parts} \part Based on your graph, what discharge is a 50-year flood for this basin? \vspace*{0.25in} \begin{solution} ??? \end{solution} \part How about a 100-year flood?\vspace*{0.25in} \begin{solution} ??? \end{solution} \end{parts} \end{questions} } \subsection{Flood stage} %%%%%%%%%%%%%%%%%%%%%%%% \emph{Flood stage} refers to an arbitrary gage height at which there is ``significant'' inundation and flooding --- that is, flooding that threatens lives, properties, or commerce. This definition only makes sense in populated areas; elsewhere it is undefined. \exercise{ \begin{questions} \question From the USGS website, what is flood stage for the Walla Walla near Touchet? \begin{solution} 13 feet \end{solution} \question From the rating curve you made, approximately how much discharge is occurring when the gage is at flood stage? \begin{solution} ?? \end{solution} \question From your flood frequency analysis, what is the long-term recurrence interval of discharge events at least this large? \begin{solution} ?? \end{solution} \question From the USGS website, what is the elevation of the gage above sea level in feet? \begin{solution} ?? \end{solution} \question If the Walla Walla River has just reached flood stage, what is the elevation of the top of the floodwaters in this area, in feet and in meters? \begin{solution} Gage elevation plus gage height (minus gage base) = ?? \end{solution} \end{questions}} \subsection{Modeling flood inundation area with ArcGIS} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% If we know the flood stage near a particular gaging station, then we can use ArcGIS to quickly generate a map of the potentially-flooded area. \begin{itemize} \item Copy the folder located at \path{M:\geol301\lab5_discharge} to your personal folder on the \path{D:} drive. \item Fire up ArcMap and drum your fingers impatiently while it loads. Open a new empty map. \item Use the ``Add data'' button to add the datasets in the \path{lab5_discharge} folder. \begin{description} \item[\path{topo24k}] is a scanned USGS 7.5-minute quadrangle map. \item[\path{elevation}] is a digital elevation model. This is a rectangular grid of cells, in which each cell contains a number representing elevation in meters above sea level. \end{description} \item Notice that you can only see one of these datasets at a time. Check the boxes next to each layer in the Table of Contents (the pane on the left) to toggle visibility of each layer. % XX NEW DATA? ARRANGE IF NECESSARY \item Make sure the Spatial Analyst Toolbar is visible: if you don't see a button on one of your toolbars that says ``Spatial Analyst,'' then go into View $\to$ Toolbars and select it. \item In the Spatial Analyst Toolbar, make sure that the Layer window shows your elevation data (not the topo map). \item Click ``Spatial Analyst'' and choose ``Raster Calculator'' from the drop-down menu. \end{itemize} You will use a \emph{conditional expression} to locate the cells in your digital elevation model that are below flood stage. A conditional expression generates a new grid of cells based on your criteria. The syntax is: \path{con(} \{condition to test for each cell\}, \{value to assign if the condition is true\}, \{value to assign if the condition is false\} \path{)} We will test the condition that the elevation in each DEM cell is less than or equal to the elevation of the top of the water at flood stage. \textbf{Note:} You have to type ``con'' and the commas --- for everything else you should use the keypad, because it will add the correct number of spaces for you. You can input the name of the elevation data by double-clicking it in the list above. \begin{itemize} \item In the Raster Calculator window, type \path{con([elevation] <= }$E_f$\path{, 1, 0)}, where $E_f$ is the elevation, in meters, that you determined for the top of the water at flood stage. Click ``OK.'' \item A new layer called ``Calculation'' should appear in the Table of Contents. Each cell in the raster contains a ``1'' if it would be flooded and ``0'' if it would not. \item Right-click on the Calculation layer and select ``Properties.'' Click the Symbology tab. \begin{itemize} \item First, click on the row showing the color of the zero values. Click the ``Remove'' button to stop drawing those cells. \item Double-click on the colored rectangle next to the ``1.'' Change the color to something appropriately watery. \end{itemize} \item Click on the Display tab and set the transparency to 50\%. Click ``OK.'' \item Make sure that the topo map is visible underneath the flood zone. Zoom in to take a closer look at the flood boundaries. \end{itemize} \exercise{\begin{questions} \question Does your map look reasonable? \question Describe the flooded area. What are its extents on the map? \question Why does this type of analysis only work for small geographic areas? \begin{solution} Fills the floodplain \end{solution} \question Go to a location of your choice on the map. Take a screenshot using the Print Screen button on your keyboard. \end{questions}} You're finished! Be sure to upload your Excel spreadsheet and your map screenshot to your CLEo dropbox. \end{document}