1 The Science and Mathematics of Natural Disasters Tides and Surge Mathematics: Day Nine

2 Day Nine of the 2006 South Mississippi Science and Mathematics Partnership Program [ (SMP) 2 ] 8:30 am to 10:15 am: VCS math, QKS sci 10:15 am to 10:30 am: break 10:30 am to 12:30 pm: VCS math, QKS sci 12:30 pm to 1:00 pm: Lunch 1:00 pm to 3:00 pm: QKS math, VCS sci 3:00pm to 3:15 pm: break 3:15 pm to 5:00 pm: QKS math, VCS sci

3 (SMP) 2 Institute Staff 2006 July 10 – July 14 July 24 – July 28 Dr. Sherry Herron, Dr. Shelia Brown, Dr. Sharon Walker, Dr. David Beckett Science Dr. Myron Henry *, Mrs. Lida McDowell *, Mrs. Mary Peters Mathematics * Responsible for Katrina Mathematics Materials

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5 Day Nine Mathematics Topics latitude and longitude interpreting graphs spreadsheets, cellsheets function tables bar and line graphs positive and negative decimal numbers applied to real life situations decimal numbers addition and subtraction transformations (translations)

6 Day Nine Partial Objectives from the 2007 Mississippi Mathematics Objectives (Revised) 6 th grade 2b (Complete a function table based on a given rule), 3a [Compare, classify, and construct transformations (translations)] 5a (Construct, interpret, and explain line graphs and bar graphs) 7 th grade 1b (Solve problems involving addition and subtraction of positive and negative rational numbers), 1h (Solve contextual problems requiring application of positive and negative rational numbers), 3d [Perform transformations (rigid translations) on two-dimensional figures using the coordinate plane.], 5c (Construct and interpret line graphs and scatter plots to generalize trends from given data) Pre-Algebra 1b (Formulate and solve standard and real-life problems using operations of rational numbers), 5d (Construct and interpret scatter plots to generalize trends from given data sets) Algebra 1a (Apply properties of real numbers to simplify algebraic expressions), 5a (Draw conclusions and make predictions from scatter plots)

7 Storm Surge + Normal Tide = Storm Tide

8 Richelieu Apartments before and after Hurricane Camille. A seven meter storm surge devastated all in its path (Pass Christian, Mississippi, August 1969) Katrina Surge near Pass Christian, August 2005

9 As one moves north or south of the equator, the distance between the lines of longitude gets shorter until they actually meet at the poles. At 45 degrees N or S of the equator, one degree of longitude is about 49 miles. On a two dimensional map, the lines of latitude and longitude are often used as horizontal and vertical lines thereby creating a Cartesian coordinate system. What would the x and y axes be? Latitude and Longitude as a Rectangular Grid

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11 Hurricane Categories zero [ mph ] one [ mph ] two [ mph ] three [ mph ] four [ mph ] five [ > 155 mph ]

mph (111 mph) (96 mph)

mph (111 mph) (96 mph)

mph (111 mph) (96 mph)

mph (111 mph) (96 mph)

mph (111 mph) (96 mph)

mph (111 mph) (96 mph)

mph (111 mph) (96 mph)

mph (111 mph) (96 mph)

20 Katrina Wind and Surge at Eight MS Coastal Communities Mississippi Gulf Coast City Longitude Degrees Lattitude Degrees Approx. Time Max Wind Speed Approx. Max Wind Speed (mph) Approx.Time Max Surge Height Approx. Max Surge in feet above MSL Waveland City Hall A 7 am10029 A 10 am24 Bay St. Louis City Hall A 7 am10229 A 10 am26 Bay St. Louis Bridge A 7 am10129 A 11 am25.1 Pass Christian City Hall A 9 am10129 A 10 am25 Long Beach Harbor A 8:30 am11029 A 10 am26 Gulfport City Hall A 9 am11529 A 11 am27 Biloxi City Hall A 8 am11929 A 12 noon27 Ocean Springs City Hall A 9 am11529 A 11 am27.5

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23 Tides are measured and recorded at water- level stations. Most stations are operated and maintained by the National Ocean Service (NOS) which is part of the National Oceanic and Atmospheric Administration (NOAA). The rise and fall of tides are measured relative to a reference plane known as a datum. The reference plane depends on- a geodetic datum. Scattered across the states are stations with precisely measured elevations called benchmarks. Each water-level station is associated with one or more benchmarks. a tidal datum. The most commonly used tidal datum is that of mean lower low water (MLLW) - the mean (average) of the lower of the two low tides over the span of a 19-year period. This measurement of a datum is specific to a certain station. The MLLW is also measured relative to the geodetic datum described above. Today's tidal measuring stations send an audio signal down a half-inch-wide sounding tube and measure the time it takes for the reflected signal to travel back from the water's surface. Data is collected every six minutes. Timing for collection is controlled by a Geostationary Operations Environmental Satellites (GOES) which transmit data to NOAA headquarters. All raw and processed data are available over the Internet.

24 Note: MLLW is the Mean Lower Low Water, the average (mean) height of the lowest of low waters over a 19 year period specified by the National Ocean Service. The predicted tides reported in the newspapers are relative to MLLW. All tidal data reported from NOS-operated stations are given relative to the MLLW for that station.

25 input time (hrs.) output height (ft.) The previous graph shows the relation between the input values of the independent variable on the horizontal axis and the output values of the dependent variable on the vertical axis. Often the variable x is used to represent the input values and the output variable y is used to represent the output values. In this graph, time (in hours) is the independent variable and height (in feet) of the tide level above MLLW is the dependent variable. table of values (0-24 hours)

26 QUESTIONS: 1.Find the highest (maximum) water level (in feet) given in the table, the lowest (minimum) water level (in feet) given in the table. 2. Find the difference between these two heights. This difference is called the range of tides.

27 1. The highest (maximum) water level (in feet) given in the table is a height of 1.4 ft. The lowest (minimum) water level (in feet) given in the table is a height of ft. 2. RECALL: For real numbers a and b, a ─ b = a + (- b).

28 QUESTION: 3. Find the mean of the high (maximum) water height and the low (minimum) water height. This value is called the mean tide level or the half-tide level feet is the mean tide level.

29 Construct the spreadsheet to the right using Excel and also the scatter plot and line graph on the next slide. Observed Dauphin Island Water Levels to Time in hoursHt from MLLWTrans Ht. (0.585)

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31 Construct the Cellsheet and Accompanying graphs using the TI-84

32 If we subtract feet from each output height, the mean tide level would be equivalent to an output of 0. In other words, the horizontal axis on the graph would be translated vertically to feet using the current vertical scale.

33 Use an appropriate formula to create another column in the previous spreadsheet to include the translated height. Then construct the line graph on the next slide for all data.

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35 Use the observed water levels for Gulfport Harbor, MS (June 27-28, 2006) and Pascagoula NOAA Lab, MS (July 8-9, 2006) to answer the following questions. Tasks: 1.Identify the independent and dependent variables. 2. Find the highest (maximum) water level (in feet) given in the table, the lowest (minimum) water level (in feet) given in the table. 3. Find the difference between these two heights. This difference is called the range of tides. 4. Find the mean of the high (maximum) water height and the low (minimum) water height. This value is called the mean tide level or the half-tide level. 5.Draw in the horizontal axis that would result from translating the graph so the mean tide level value is the horizontal axis 6.Create a spreadsheet, CelSheet, and appropriate charts for tide data.

36 Input time (hrs) Output height (ft.) table of values (0–24 hours)

37 Input time (hrs) Output height (ft.) table of values (0–24 hours)