Interface B 2017 a River Runs Through Math and Science

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Interface B – 2017 – A River Runs Through Math and Science

A River Runs Through Math and Science

Missouri River Background

Historically the Missouri River experienced a spring rise around March caused by local snowmelt and breakup of ice jams on the river. A second rise around June was caused by snowmelt from the eastern Rocky Mountains and summer rains.

The spring rise triggered spawning in native fish, which swam into flooded streams and wetlands to deposit eggs. The hatchlings lived, fed and grew in shallow and productive backwaters until carried back into the main channel by later floods.

The channel itself varied along its length from swift gravel bottomed streams in the mountains to slow, meandering braided channels in the prairies.

In 1838, snags were removed to encourage commercial navigation. By 1902 there wasa 5.5 foot deep navigation channel. In 1944 Congress adopted the Pick-Sloan plan to manage the river for irrigation, navigation, hydropower, flood control, water quality, water supply, fish and wildlife, and recreation. This plan resulted in the construction of five more dams (Fort Peck already had a dam) on the main stem of the Missouri. The 1945 Rivers and Harbors act established a navigation channel 9 feet deep and 300 feet wide all the way up to Sioux City Iowa. This is the situation that exists today.

The dams and their associated reservoirs reduced the March and June rises, and increased the flow in the summer. Along with straightening and deepening the channel, this cut the river off from its wetlands.

“Together with the removal of snags, the loss of good habitat has caused an estimated loss of more than 80 percent of the fish in the river. Changes in habitat and increased water clarity due to the trapping of sediments in the main stem reservoirs has caused an increase in the numbers of species such as skipjack herring, gizzard shad, white bass, bluegill, white crappie and the emerald, river and red shiners. In Missouri, two large river species, the pallid sturgeon and the flathead chub, are in serious decline.

Water Protection Program Fact Sheet -

The flood control provided by upstream reservoirs and dams, and levees along the channelized river led to a 4300% increase in cultivated lands, and more recently in some areas, buildings in areas that used to be wetlands. The levees also limited the amount of sediment flowing into the river. Since this sediment used to recharge the Louisiana shoreline where the Mississippi flows into the Gulf, the shoreline is slowly but steadily retreating. At the same time the fertilizers applied to grain crops in the Missouri watershed, when not taken up by crop plants, end up flowing into the Gulf and causing a dead zone, where there is not enough oxygen in the water for living organisms.

The Missouri River is a large and complex system whose historic patterns of flow and structure have been altered to meet multiple human needs. While management has provided significant benefits to humans, the costs to river species and connected ecosystem are not sustainable. The challenge is to figure out how to benefit people without harming the river.

Effects of Reservoirs on Flood Discharges in the Kansas and Missouri River Basins

Inspring and summer 1993, thunderstorms released torrential rains somewhere over the North-Central states every day. Some rainfall totals were over 5 inches. Because the soil was alreadysaturated, this lead to local flash floods in small streams and persistent flooding in the Missouri River Basin. When snowmelt from the Rockies was added in summer, the result was record flooding inundating much of the lower Missouri.

Property losses alone exceeded $10 billion. Damaged highways and submerged roads disrupted transportation throughout the flooded region. The Mississippi and Missouri Rivers were closed to navigation before, during and after the flooding. The banks and channels of many rivers were severely eroded, and sediment was deposited over large areas of the basin’s flood plain. Levees failed, flooding cities and factories, as well as farmland, andraised concerns about industrial chemicals, sewage and agricultural chemicals being spread over the basin.

Although the flooding was extensive, reservoirs upstream in the basin reduced flooding compared to historic floods. The computer program BENEFITS was used to estimate what the uncontrolled peak flowwould have been in the absence of reservoirs. Results of modeling suggest that flood waters from the Kansas River and the Missouri would have over-topped the Kansas City levees if there were no reservoirs.

• interpret data on peak flow with and without reservoirs to predict future floods
• how would increases in human population and consumption rates in Missouri affect the need for dams and levees to control the flow of water, what other ways could flood damage in populated areas be reduced
• what impact is climate change likely to have on the frequency and severity of floods

• (7th) compute ratios of observed flow to area and modeled flow to area and compare them

• (7th) use a number line to determine the differences between observed and modeled flow

• (8th) use scientific notation to perform operations, and/or convert metric to English units
• (8th) graph the relationship between area and flows, choose line of best fit, derive linear equations, compare them and make predictions

• (7th) make a scale drawing that shows the difference between the observed and modeled flow

• (8th) construct a scatter plot of observed and modeled flow vs area

Table 1. Observed and Modeled Peak River Flow from Gage Stations on the Missouri River

Observed flow is with reservoirs, modeled flow is based on historic flood data and measured river volume

Sources and Transport of Nitrogen in the Mississippi River Basin

Hypoxia is an environmental phenomenon where the concentration of dissolved oxygen (DO) in the water column decreases so much it can’t support life. Hypoxic areas, or "Dead Zones," have increased in duration and frequency across our planet's oceans since first being noted in the 1970s.The largest hypoxic zone currently affecting the United States, and the second largest worldwide, is the northern Gulf of Mexico by the Mississippi River outflow.

The Mississippi and Atchafalaya Rivers are the primary river sources of fresh water and nutrients for the Gulf of Mexico. Their combined annual mean streamflow (21,800 cubic meters per second) represents about 80% of the estimated freshwater discharge to the Gulf. They also account for an estimated 90% of total nitrogen load and 87% of the total phosphorus load discharged annually to the Gulf.

The reduction in DO occurs each year during late spring and summer following high inflows of fresh water and nutrients to the Gulf. From1985-1992, the hypoxia zone (DO less than 2 parts per million) averaged about 10,000 square kilometers.After the 1993 flood, the hypoxia zone covered nearly 17,000 square kilometers. In 1994, 1995, and 1996 the hypoxia zone was about 18,000 square kilometers.

The increased use of nitrogen and phosphorus fertilizers in the entire Mississippi basinis the most likely cause of hypoxia in the Gulf of Mexico. Fertilizer use has increased significantly over the past 25 years and has similar patterns to increasing nitrate concentrations in the Mississippi River. However, there are other sources of nitrogen in the basin including animal manure, legumes (soybeans and alfalfa), domestic effluents, and atmospheric deposition and soil nitrogen.

• how are the chemical formulas of N the same and different?
• what are the chemical reactions in plants that require N?
• how are chemical fertilizers manufactured (Haber-Bosch process)? Life Sciences

• describe how is N used by living organisms, include chlorophyll

• develop a model to describe the cycling of N among living and non-living parts of an ecosystem
• evaluate benefits and limitations of differing design solutions for limiting N in the Gulf of Mexico, would it be different for different basins

• how does human activity change the distribution of N in the ecosystem, what are the different human activities in each basin that contribute to changing the distribution of N

• (7th)compute the total volume of water leaving the Missouri basin (m3/s * 60 * 60 * 24 *365) and then the unit rate for any form of N
• (7th) find the ratio of any 2 forms of N across all 3 basins

• (7th) plot forms of N for the Missouri basin on a number line

• (8th) convert values in the table to scientific notation and perform computations
• (7th) write a linear equation for the form of N across all three basins
• (8th) graph proportional relationships, interpret unit rate as slope, compare different proportional relationships
• (8th) apply concepts of slope and y-intercept to graphs, equations and proportional relationships
• (8th) solve linear equations in one variable

• (7th) make a scale drawing representing the amount of the top three forms of N contributed by each watershed

• (7th) use data from multiple samples to draw inferences about a population and investigate variability in estimates of the characteristic of interest
• (8th) make a scatter plot of a type of N and the area of the basin; find the linear equation for the line of best fit; repeat using the flow of the Missouri basin
• (8th) generate and use a trend line for the type of N and area or flow of the Missouri, find the line of best fit
• (8th) use relative frequencies calculated for forms of N or basin to describe possible associations
• (7th) compare measures of center, frequency, and variability from 2 different forms of N across all three basins

• (8th) determine if the relation between a basin’s flow and the amount of a form of N is a function, if so, graph the function, find the line of best fit and use the linear equation to make a prediction

Table 1. Sources of Nitrogen in the Mississippi and Atchafalaya* watershed by inputs in metric tons

• commercial fertilizer as anydrous ammoninum

• commercial fertilizer as urea

• commercial fertilizer as nitrogen solutions

• commercial fertilizer as miscellaneous forms of N

• commercial fertilizer as ammonium nitrate

* The Atchafalaya is a 137 mile long distributary west of the Mississippi river that branches off at Simmesport LA. It carries the water from the Red River and about 30% of the flow of the Mississippi into the Gulf. It serves as a significant industrial shipping channel for the state of Louisiana.

Larval Fish Use of Lower Missouri River Scour Basins in Relation to Connectivity

Many fishes in large, low-gradient rivers like the Missouri use floodplain water bodies (sloughs, side channels, backwaters) for reproduction or early development. These slow, shallowhabitats provide conditions of temperature, turbidity and substrate, as well as access to food, that are critical for larval fish. But they have to be connected to the river at least part of the time so adults can spawn and larval fish can travel back to the main channel. Therefore they depend on a predictable “flood pulse” to connect these habitats with the main river channel during their spawning period.

Anthropogenic changes in the lower Missouri River from Sioux City, Iowa to its mouth near St. Louis, Missouri, have disrupted the natural dynamics of this river-floodplain linkage. The formerly shallow, braided channel of the Missouri has been converted to a single, deep, swift navigation channel resulting in a 50% reduction in river-floodplain water surface area and a 39% decrease in area of floodplain wetlands. The historic flood pulses of April and June are regulated by upstream dams to provide a constant flow from April to the fall, and high agricultural levees confine the river to a width of 183-335 m.

The historic flood of 1993 connected the lower Missouri to its ancestral floodplain for the first time in over 20 years. Floods overtopped and breached over 500 flood-control levees between Kanas City and St. Louis. The water pressure and flow through levee breaks caused intense erosion that produced over 450 new, steep-sided water bodies or “scour basins”.

This study sampled larval fish populations in three categories of scour basins – continuously connected, periodically connected and isolated, to see how they functioned as replacements for ancestral spawning habitat for Missouri river fish.

• describe how environmental conditions affect reproduction and early in a species of fish

• construct an explanation that predicts the patterns of interactions among and between the biotic and abiotic factors in a given ecosystem

• construct an argument supported by empirical evidence that explains how differences among the scours affects reproduction of a species of fish
• construct an explanation based on evidence that describes how variation can affect probability of surviving and reproducing in a specific environment (use probability statements and proportional reasoning on species’ variation)

• construct an explanation for how geoscience processes have changed the Earth’s surface.
• design a method for monitoring and minimizing human impact on the environment
• treating the scours as “natural experiments” determine which “design” might be most effective habitat for promoting reproduction in native fish species

• (7th) find the proportion of the larva for all the species of fish in a scour

• (7th) plot numbers of each species of fish in a scour on a number line
• (8th) convert decimals to fractions and vice versa for a species of fish Expressions, Equations and Inequalities

• (7th) write a linear equation relating the number of larval fish species in a scour to the scour’s distance from the river
• (8th) graph the duration of exchange as distance from the river increases, estimate the slope of the line and interpret it as a rate of change
• (8th) graph the number fish species as distance from the river increases, estimate the slope of the line and interpret is as a rate of change

• (7th) make a scale drawing of scours that shows their river km, distance from the river, and area, and show the measurements in metric and English units using appropriate units and number of significant digits

• (8th) make a scatter plot of any scour characteristic (area, depth, distance, etc.) and at least one fish species; fit a trend line and then find the linear equation for the line of best fit
• (8th) use the linear equation to predict the behavior of the dependent variable as the independent variable changes
• (8th) calculate the relative frequencies of any of the variables in the data set to see if there is a possible association
• (7th) compare measures of center, frequency, and variability for any variable for all three sets of scours
• (7th) for a fish species, determine the probability of catching that species in each kind of scour (C, P, I)
• (7th) for two fish species, determine the probability of catching both species in each kind of scour

• (8th) for any pair of variables in the data set, determine if it is a function
• (8th) graph the relationship between any pair of variables in the data set
• (8th) determine the parameters of the relationship between any pair of variables in the data set
• (8th) describe the functional relationship between any pair of variables in the data set

Table 1. Characteristics of the scours sampled for this study, and number of larval fishand fish density

• Site - C-continuous connection, P-periodic connection, I-isolated; numbers are km upstream from confluence of Missouri and Mississippi Rivers
• Mean exchange - mean level of scour connection over all dates, ranging from 0 (no connection) to 7 (fullyconnected)
• Duration - days scour was connected to river
• Temperature - difference between river and scour (positive temp means scour is warmer than river)
• Secchi depth - difference between river and scour (positive Sd means scour is clearer than river)
• Larval Fish Density –number of fish/100 cubic m over all sampling periods

Table 2. The three most common larval fish species in each category (C, P, I) of scour basins