Tag Archives: agriculture

Nitrates never end

Nitrates, nitrates…

Well, the semester is coming to a close again. Two more weeks of class and then finals. My corn has grown pretty tall and survived a squirrel attack, and next weekend I should be able to plant it outside: April 30 is our average last frost date in my area. It's been a nice week weather-wise, though, and so the plants are outside in my thrown-together "cold frame." I'm using soil with built-in compost for the young plants since corn is a heavy feeder, and once I move them to the ground I'll put them into areas where I've pulled up the hairy vetch (which is supposed to fix nitrogen) and added more compost. We will consider manure, but for the moment it seems like we might make it with the contents of our own compost pile this summer. The benefit of working without commercial fertilizer is that we don't have to think very hard about whether we're contributing to the nitrates in the Mississippi river -- even considering that urban areas contribute less than 10% of Minnesota's nitrate runoff.

The Star Tribune (the Minneapolis paper) had an article this weekend about nitrates in well water in the rest of Minnesota. It's costing taxpayers a lot of money -- up to $3,300 per household in some areas to install nitrate-removal equipment and ensure that people can drink the water safely! In fact, nitrates made the news because in Randall, MN, people can't drink the water safely. Nitrate levels are too high and dangerous to human health, especially babies and the elderly. The majority of nitrates in Minnesota water come from agricultural fertilizer runoff, and dealing with the runoff has become a hot local political topic. It's not just a problem in the Gulf of Mexico when it's affecting our local drinking water and lakes.

Nitrates in drinking water would be a great topic for a social studies debate. Farmers need nitrates to grow their corn at a level that provides enough for food products, corn syrup, compostable cups, and ethanol. As taxpayers we subsidize some of these uses, and as taxpayers we pay for the removal of nitrates from the water. Paying for removal of nitrates is hugely expensive: besides the initial up-front cost of the equipment, it looks like it costs 15 to 35 cents per 1000 gallons of water to do the processing and maintenance, while low-nitrate water costs only 5 to 10 cents per 1000 gallons TOTAL. That's a huge percentage increase in water costs! (The figures are from the linked Minnesota Department of Agriculture file.)

Interestingly, I couldn't find nice data online about nitrates in water in Minnesota, so I returned to the tried and true USGS data from the Raccoon River near Des Moines, Iowa. The past month's data provides enough for a numerical integration and estimation worksheet:

Numerical Integration: Nitrates

It is a pretty basic worksheet -- provides enough information for a social-studies debate starting point, but not much more. It would be very cool to make some more sophisticated optimization problems for nitrate use, to help students (and perhaps the public) think about the tradeoffs involved in agriculture and environment.

Spring fling: hairy vetch

It's spring in Minnesota, which found me flinging hairy vetch seeds from a flowerpot into the back yard.

Dirt where hopefully hairy vetch will fixate. Strawberries already started....

Dirt where hopefully hairy vetch will fixate. Strawberries already started....

Let's back up a moment. My garden fever has been ramping up; those of you who live in the great frozen north might understand the hunger to see green things. It's why all the undergrads were in shorts last week (that and we set a record of 84 degrees!). For the past few years my husband & I have tried to start seeds in egg containers, and every year something terrible happens: they blow off the porch, or they all drown in a big rainstorm, or squirrels eat them. No more. This year I marched into Eggplant Urban Farm Supply a few blocks away and made a stand. I spent what felt like an exorbitant amount of money, but it'll be less than a dollar a plant even if we have a few failures. I got a seed-starting tray and a seed heater for our cold house and some hairy vetch and inoculant for nitrogen fixation!

Nitrogen what?

Continue reading

A first draft of a monarch matrix worksheet

Well, let's get a first pass at a monarch worksheet posted. It's definitely about matrix models and graphs, and there are a few things you need to talk about with students prior to putting it to work:

South and north: Monarchs overwintering Mexico have hit pause on their reproductive lives. Really, it's called reproductive diapause! They get to live 6-9 months down in the highlands of central Mexico, living on the oyamel fir trees in the mountains.

MountainsOfMexicoThis is not a beach vacation: the monarchs cover the trees high up in the forest. I had the good fortune to visit Cerro Pelon butterfly reserve last January with Joel Moreno of Joel's Butterfly B&B, and these are pictures I took from that trip.

Monarchs in the trees at Cerro Pelon

Monarchs in the trees at Cerro Pelon

Continue reading

Amazon version of book! and revisiting the Raccoon River

The EarthCalc book is now on Amazon, too! Amazon is a touch inconvenient because I couldn't include the worksheets and solutions as an automatic download, but it's a big platform that reaches a lot of people. At Leanpub you get the worksheets and solutions as well as epub/pdf/mobi formats for the book...

Raccoon River: A while ago I wrote some posts about the Raccoon River in Iowa, and the flow of nitrates into the river. The posts talked about how fertilizing our big corn and soybean fields can lead to problems with nitrate runoff, especially in spring when the snow melts and washes leftover fertilizer into rivers and lakes. The associated worksheets were about increasing/decreasing functions, average rate of change, interpretation of graphs, etc.

It's spring again! Nitrates are a topic with continuing relevance even though the worksheet data is from 2013. Recently, the city of Des Moines voted to sue three Iowa counties for not managing nitrate and nitrite runoff: according to the linked National Public Radio report, removing the nitrates in 2013 cost the city $900,000! The New York Times (coincidentally?) recently featured an article about no-till farming, which reduces fertilizer runoff.

So, how much agriculture is practiced in your state? How big an impact does fertilizer runoff have on your ecosystem? Consider asking your students to report on whether their families fertilize their lawns, and find out what your community is doing to deal with runoff into lakes and streams!

Average change: nitrates again

Spring still keeps happening slowly in Minnesota, and snow is still melting up north. Iowa and other big agricultural states to our south have experienced all their snow melt, though, and are beginning the farming season.

Here's a worksheet that's pretty well inappropriate to the academic year -- no one is doing rate of change right now in calculus or precalculus! But it's written, so I may as well share. Again, it's about nitrate and nitrite runoff into the Raccoon River in Iowa. Spring is a good time to fertilize soil, but the runoff that's happening during the first snow melt is actually all from fertilizer applied last summer.

Average Change: Nitrates in the Raccoon River

The semester is coming to a close. Just a few more weeks of class and it's over. I'm working, as slowly as the spring, on some new worksheets about White Bear Lake water levels and about bee ecology. I learned today that Michelle Obama keeps bees near the White House garden. They're fascinating creatures!

More later... just a few final exams to go 🙂

Runoff in the Raccoon River

Did you know that raccoons wash their food when near a body of water? I love the image. I don't even know if raccoons live near the Raccoon River in Iowa anymore. But I do know where to find real-time nitrate and nitrite monitoring data for the Raccoon River.

Nitrate is NO3 and nitrite is NO2. They both occur naturally in soil and are also vitally important components of fertilizer. Fertilizer, of course, is necessary for the high-yield agriculture practiced in US states like Iowa. The difficulty is that nitrate and nitrite are highly water soluble. They're only useful to a plant if they're available to the plant at the right time in its growth cycle. If the soil is too dry for it to sink in and get to the roots of the plants or the plant doesn't grow due to bad weather, then excess fertilizer is left on the ground and runs off in the rain.

An interesting time to look at nitrate/nitrite runoff is as the snow is melting in the fields of Iowa. Fertilizer hasn't been applied for a season, so all that is left is the runoff from last year's application. It's often not raining yet, so the only water for runoff comes from snowmelt. Daily temperature fluctuations rule the amount of runoff each day for a few days.

So here's a graph-reading worksheet: it's not calculus, and is perhaps more focused on high-school or junior-high skills, but these are always worth a reminder....

Precalc: Nitrates in the Raccoon River


It's been a while. First set of midterms written, given, and graded. Spring may (?) be coming to Minnesota. Ski trips taken. Spring break coming.

I've been working on this nitrate run-off project for a while. Learning about the problem of nitrite and nitrate runoff from agriculture -- mostly from fertilizers -- has been a non-linear process! I've heard reports on the radio about the problems nitrate runoff causes, not only for drinking water in towns in Minnesota and Iowa, but in the dead zone it is causing in the Gulf of Mexico. I read some papers as well, looking for data and ideas tractable for calculus worksheets. Finally I found some real-time data tracking nitrate levels in Iowa rivers, including the Racoon River. Since Iowa is so heavily agricultural, nitrate levels are a significant problem for drinking water treatment plants.

This is the perfect time of year to look at nitrate levels because the spring thaw is either here now or coming soon. Over the winter, farmers did not fertilize -- that would be silly! -- but the spring thaw means a lot of water from snowmelt and precipitation washing over fields and into rivers and streams, bringing with it the leftover nitrate from last year's fertilization. There are some interesting things to see in the data: when temperatures are hovering around freezing, the daily freeze-thaw cycle can often be seen in the nitrate levels measured by the monitors.

It's not easy to model daily nitrate runoff because it depends so much on daily temperature, precipitation, level of snowmelt, and other factors that can change quickly. On the other hand, we can look at data over a period of time and use calculus to understand some of the factors involved. Now that I've wrestled the time and date formatting of the real-time data into compliance using the R programming language, I can make you some beautiful graphs and present some numerical integration worksheets estimating nitrate runoff as well as some graph interpretation worksheets asking students to come up with physical explanations for the data they see presented.

Coming soon....

Give me some optimal sugar... calculus-style

I was on a math trip this week, so have been a bit delayed in posting. After four days of intensive pure math thought, I've returned to my little farm in the city, the minuscule plot that is my back yard. Today was spent doing math and picking cherries. The beans and peas are doing well, too; we've got peas planted where we used to grow tomatoes in an effort to increase the nitrogen content of the soil without applying fertilizer.

I have the luxury of not depending on my little garden for my primary food source. Instead, I buy food from farmers either at the farmer's market or at the grocery store. It is nice to live in the city and be able to take the bus to the opera, but it means I depend on others for agriculture. They use fertilizer and irrigate their land because farmers must do everything they can to control growing conditions for their crops.

Today is about sugar beet production. (I also looked into optimization of conditions for composting, but there are no equations I can find!) Sugar beets are a major crop across the US, particularly in North Dakota, Minnesota, and Idaho. We love sugar and want it in many foods (until we find it's killing us) and of course farmers want to optimize their yields. Sugar beets are interesting because simply adding more nutrients to the soil can be counterproductive: you don't want the biggest sugar beets, you want the sweetest ones! Too little nitrogen means yellow leaves and poor growth. Too much nitrogen means impurities in your beets and reduced sucrose, or at worst killing your seedlings (source). It's the Goldilocks question.

An older report on how nitrogen levels affect recoverable sugar yields has some very nice equations. G.L. Malzer and Greg Buzicky looked at many variables and came up with several equations that predicted recoverable sugar yield pretty well, all in terms of the soil's nitrate-nitrogen content. And they're quadratic! This is a nice way to do a pretty easy optimization exercise with applications to something... sweet!

The first page is all about finding the optimum recoverable sugar yields given different levels of nitrate-nitrogen in the soil. The second page mixes in some experimentation and treats a two-variable function, foreshadowing multivariable calculus techniques. Including discussion of multivariable functions in a first-semester calculus course is a really cool idea that deserves more attention -- it does not disturb students, but only people who have a set idea of what one "should" learn in first-semester calculus. The third page asks students to use the first and second derivative tests to prove the results they've already produced, and asks them to think about the applicability of the Extreme Value Theorem. As in many situation, physical constraints could lead to a closed-interval phrasing of the problem, although it's not necessary mathematically. Provoke an argument!

Optimization: Sugar Beets

Agriculture is often ignored in calculus and STEM classes, as it's not so sexy these days. Universities like the University of Minnesota and Cornell have big ag programs, though, and they're hugely important. You sure can't be a vegan or vegetarian in the north without the products of modern agriculture!

I've learned a lot from my ag students and they need to deal with optimization often: they need to optimize nutrient composition in animal feed, optimize nutrient composition of fertilizers for soybean growth, optimize temperature for dry-matter intake of chickens, and of course look at the economics of all the above. Their decisions impact the diets, waterways, air quality, climate, and fuel prices of city-dwellers. Don't forget the ag, even if you live in LA.