## Nonsense, facts that aren't facts, and turf in 3 dimensions

##### 20 January 2015

I received this inquiry about nutrient application and soil nutrient concentration:

I have in mind that somebody wrote that one rise any element by 6.7 ppm when it is applied by 1g/m². Is that true or is it different for any element so that i have to change the factor in my calculation?

This 6.7 ppm factor is correct when thinking of the turf system in 3 dimensions. How does this work out? It is like this. Assuming a rootzone depth of 10 cm, and a soil bulk density of 1.5 g/cm^{3}, then the mass of the rootzone in 1 m^{2} is 150 kg. An application of 1 g/m^{2} of an element to the surface, assuming distribution throughout the rootzone, is going to cause an increase of 6.7 ppm (1000 mg/150 kg). Likewise, nutrient harvest can be estimated in the same way.

If you like to use other units, or a different rootzone depth, or have a soil with a different bulk density, the calculations are elementary.

I've written before about the ease of such calculations using metric units. The calculations can be made in other units, but I find it especially easy to visualize these in 2-dimensional and 3-dimensional space using metric units.

Being familiar with 2-dimensional and 3-dimensional thinking can help to pick out nonsense pretty quickly. Here are two examples.

I saw this tweet about a cubic mile of fog being made up of less than a gallon of water. That just didn't sound right at all. This is a 3-dimensional space we are thinking of, and I remembered that in non-foggy conditions, I'd read one can get up to half a liter of dew in 1 m^{2} with the amount of water in a column of air something like 10 to 50 meters high. I'd read this in Nobel's Physicochemical and Environmental Plant Physiology, and looked it up again, and it turns out that at an air temperature of 10°C, the column of air would need to be 53 m high to provide that much water. My memory wasn't exactly right, but now I had the basic information I needed.

Now obviously, 53 m^{3} is a hell of a lot less than a cubic mile. One cubic mile is about 4,165,509,529 m^{3}. Roughly estimating that a half liter of water is slightly more than an eighth of a gallon, one can calculate that there are 78,594,519 units of 53 m^{3} in a cubic mile, each with potentially an eighth of a gallon of water, so in a cubic mile of fog there may be something like 9,824,315 gallons. This is easier if one just keeps it all in metric units, but the point is, being aware of what the volume is, one can think in 3-dimensional terms and get a rough estimate of just how outrageous such a statement of less than one gallon of water in a cubic mile of fog is.

One can find other estimates, such as 56,000 gallons of condensed water in a cubic mile of fog. I prefer to consider the total amount of water, and that obviously is way way more than a gallon.

There was also the estimate of how the length of roots in a lawn was supposedly extending to a distance equivalent to 15 round trips between the sun and the earth.

That just sounds outrageous from the start, for anyone who has seen turfgrass roots, an average lawn, and has some idea of how far the sun is from the earth. Even with generous estimates of root length, and including root hairs, the cumulative root distance falls well short of even a one way trip to the sun. Thinking in 2-dimensional and 3-dimensional terms makes these estimates easy.

So whether one wants to know a simple conversion between nutrient uptake and depletion from the soil, fertilizer addition and increase in the soil, water application and increase in soil moisture, plant water use and decrease in soil moisture content, or expand this to consider whether nonsense "facts" can possibly be true, thinking about turf in 2 and 3 dimensions can be useful.

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