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\begin{Large}
\section{\bf Surface Water Flow Features on Mars}
\end{Large}

\subsection{Introduction}

In this lab you will be making measurements of some valleys and channels on 
Mars.  The main goal of this lab is to be able to distinguish the different 
surface features left by small, slow flowing streams and large, rapid 
outflows.  You will calculate the volumes of water required to carve these 
features, and consider how this volume compares with other bodies of water.  
Be sure to write down and turn in all of your measurements and work.\\

\subsection{Warrego Valles}

{\it The first three questions refer to the two images of Warrego Valles. 
One image is a close-up, the other a wider view.  First, look
at the close-up view and find the valley system.  Look at the impact craters 
and determine which direction the sunlight is coming from.  Warrego Valles is located in Mars' southern hemisphere; its location is identified on the Mars globe and map we have available for you to look at.}

\begin{enumerate}

\item  By looking at the morphology, or shape, of the valley,
geologists can tell how the valley was formed. Does this valley
system have a dendritic pattern (like the veins in a leaf) or an anastomosing pattern (like an intertwined rope)?  ({\bf 2 points})
\vspace{1in}

\item Overlay a transparency film onto the {\it \bf close-up} image. Trace 
the valley pattern onto the transparency. Does the shape of this valley point 
to slow formation over time or to fast formation from a localized water 
source?  Why do you say this? ({\bf 3 points})
\vspace{2in}

\item  Now, trace the boundary between the uplands and plains on your 
close-up overlay (the transparency sheet) and label the UPLANDS and the 
PLAINS. Is Warrego located in the uplands or on the plains?  ({\bf 2 points}) 
\vspace{1.0in}

\item Which terrain is older?  Recall that we can use crater counting to help 
determine the age of a surface, so let's do some crater counting. {\it Overlay 
the transparency sheet on the wide-view image.}  Pick out 
two square regions on the wide view image, each 3~cm $\times$ 3~cm.
One region should cover the smooth plains and the other should cover the cratered region.  Draw these two squares on the transparency sheet. Count all the 
impact craters greater than 1 millimeter in diameter within each of the two 
squares you have outlined.  Write these numbers below, with identification.  
Which region is older?  What does this exercise tell you about approximately 
(or relatively) when Warrego formed?  ({\bf 5 points})
\vspace{2in}

\item  To figure out how much water was required to form this valley, we first 
need to estimate its volume.  The volume of a rectangular solid (like a 
shoebox) is equal to $\ell \times w \times h$, where $\ell$ is the length of 
the box, $h$ is the height of the box, and $w$ is the width.  We will 
approximate the shape of the valley as one long shoebox and focus only on the 
main valley system.  {\it Use the close-up image for this purpose.}

First, we need to add up the total length of all the branches of the valley.  
Measure the length, in millimeters, of each branch and the main trunk.  Be 
careful not to count the same length twice.  Sometimes it is hard to tell 
where each branch ends.  You need to use your own judgment and be consistent 
in the way you measure each branch.  Now add up all your measurements and 
convert the sum to kilometers.  In this image 1~mm = 2~km. What is the 
total length $\ell$ of the valley system in kilometers?  \underline{ 
Show your work.}  ({\bf 3 points})
\vspace{1.5in}

Second, we need to find the average width of the valley.  Carefully measure
the width of the valley (in millimeters) in several places.  What is the 
average width?  Convert this to kilometers.  \underline{Show your 
work.} ({\bf 3 points})
\vspace{1.5in}

\item Finally, we need to know the depth.  It is hard to measure depths from
photographs, so we will just guess.  From other evidence that we will not
discuss here, the depth of typical Martian valleys is about 200 meters.  
Convert this to kilometers.  ({\bf 2 points})
\vspace{0.8in}

\item Now find the total valley volume in $\rm km^3$, using the relation 
$V = \ell \times w \times h$. This is the amount of sediment and rocks that 
was removed by water erosion to form this valley.  We do not know for sure how 
much water was required to remove each cubic kilometer, but we can guess.  
Let's assume that $100\,\rm km^3$ of water was required to erode $1\,\rm km^3$ 
of Mars.  How much water was required to form Warrego Valles? 
\underline{Show your work.} ({\bf 5 points})
\vspace{2in}

{\bf Clean-off transparency for the next section!}\\

\subsection{Ares and Tiu Valles}

{\it 
The remaining questions refer to Ares and Tiu Valles.  On the wide scale image, Ares is on the right and Tiu is on the left (your instructor will show you which way to hold the images).  The {\rm Mars Pathfinder} spacecraft landed in the top left region of this image in 1997.  Can you guess why that particular spot was chosen? Again, look at the impact craters to get an idea of where the Sun is.}

\item  First, which way did the water flow that carved these channels?  The 
way to tell is to look at streamlined islands, like those on the second print.
When flowing water erodes an island, it leaves a shape that has the smallest 
amount of drag possible.  This same shape is used in things like cars and 
airplane wings.  Think about these every-day shapes. In the close-up photo, 
did water flow south-to-north or north-to-south?  ({\bf 2 points})
\vspace{1in}

Find these same two islands in the large scale print (they are close to the 
top, left of center).  Find other islands with the same shape elsewhere
in the channel.  {\it Lay the transparency 0n your photo and make a 
sketch of the pattern of these channels.} {\bf Now add arrows to show the path 
and direction the flowing water took.}  Look at pattern of these channels. 
Are they dendritic or anastomosing?  ({\bf 5 points} )
\vspace{1in}

Can you identify locations where the ground seems to have collapsed and the 
ground water poured out? These are called ``chaos" regions because the ground 
surface appears to be a chaotic jumble.  Label these regions on your 
sketch and show it to your TA.  ({\bf 5 points})
\vspace{0.5in}

\item  Now we want to get an idea of the volume of water required to form Ares (the right hand) Valles.  Measure the length of the channel from near the Pathfinder landing site to the bottom right corner of the image.  Also,
measure the length of any tributaries that you see.  In this image, 1~mm = 
10~km.  How long is the channel in km? \underline{Show your work}
 ({\bf 5 points})
\vspace{1.75in}

\item Measure the channel width in several places and find the average width.
On average, how wide is the channel in km? \underline{Show your work} ({\bf 5 points})
\vspace{1.75in}

\item The average depth is about 700 m. How much is that in km?  ({\bf 5 points})
\vspace{0.75in}

\item Now multiply your answers (in units of km) to {\bf find the volume of 
the channel in km$^3$.} Use the same ratio of water volume to
channel volume that we used in Question 3 to find the volume
of water required to form the channel.  \underline{\bf Show your work}
({\bf 5 points})
\vspace{1.5in}

\item  You have now studied Warrego and Ares Valles up close.  {\bf Compare
and contrast the two different varieties of fluvial (water-carved) landforms 
in as many ways as you can think of (at least three!).} Do you think they 
formed the same way?  How does the volume of water required to form Ares 
Valles compare to the volume of water required to form Warrego Valles?  
({\bf 8 points})
\end{enumerate}
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\hspace*{3.0in}Name:{\hrulefill} \\
\hspace*{3.25in}Date:{\hrulefill}\\

\subsection{Take Home Exercise (35 points total)}

Answer the following question on a separate sheet of paper, and turn it in with the rest of your lab.\\

\begin{enumerate}
\item  What happened to all of the water that carved these valley systems?  We 
do not see any water on the surface of Mars when we look at present-day images 
of the planet, but if our interpretation of these features is correct, and 
your calculated water volumes are correct (which they probably are), then 
where has all of the water gone?  Discuss two possible (probable?) fates that 
the water might have experienced.  Think about discussions we have had in 
class about planets' atmospheres and what their fates have been.  Also think 
about how Earth compares to Mars and how the water abundances on the two 
planets now differ. {\bf If you have questions, please ask!}\\
\end{enumerate}

\subsection{Possible Quiz Questions}
\begin{enumerate}

\item Is water an important erosion process?

\item What does ``dendritic'' mean?

\item What does ``anastomosing'' mean?

\end{enumerate}

\subsection{Extra Credit (ask your TA for permission before attempting, 5 points)}

In this lab you have found that dendritic and anastomosing ``river''
patterns are found on Mars, suggesting there was free flowing water at some
time in Mars' history. Use web-based resources to investigate our current
ideas about the history of water on Mars. Then find images of both 
dendritic and anastomosing features on the Earth (include them in your
report). Describe where on our planet those particular patterns were found, 
and what type of climate exists in that part of the world. What does this 
suggest about the formation of similar features on Mars?
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