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In my previous post, I discussed nitrous oxide (N₂O) emissions in crop fields. Today, I’ll explain how to convert nitrous Oxide (N₂O) emissions from ppm to kg ha^-1.

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□ Investigating Patterns of Nitrous Oxide Emissions in Corn Agriculture

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If you measure N₂O (ppm) using a ‘Gasmet,’ a portable gas analyzer (https://www.gasmet.com/products/category/portable-gas-analyzers/), you’ll ultimately obtain CO₂ and N₂O data like the one shown below (Of course, we can also obtain data for CH₄ and NH₃ using the Gasmet, but in this post, I’ll focus solely on N₂O data).

Time	Carbon dioxide (CO2) [ppm]	Nitrous oxide (N2O) [ppm]
12:11:11	926.7	0.3672
12:11:32	1205.21	0.3645
12:11:53	1265.57	0.3589
12:12:14	1279.95	0.3577
12:12:35	1286.73	0.3552
12:12:56	1293.44	0.3595
12:13:17	1298.49	0.3607
12:13:39	1300.81	0.3622
12:14:01	1306.12	0.3628
12:14:23	1311.14	0.3678
12:14:44	1317.64	0.3668

For 4 minutes, Gasmet recorded the emissions of carbon dioxide (CO₂) and nitrous oxide (N₂O) in ppm. Let’s use these data to upscale to different units.

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Step 1) to calculate R² and the slope of CO₂ and N₂O over time

Second	Carbon dioxide (CO2) [ppm]	Nitrous oxide (N2O) [ppm]
0	926.7	0.3672
20	1205.21	0.3645
40	1265.57	0.3589
60	1279.95	0.3577
80	1286.73	0.3552
100	1293.44	0.3595
120	1298.49	0.3607
140	1300.81	0.3622
160	1306.12	0.3628
180	1311.14	0.3678
200	1317.64	0.3668

When measuring a single spot for 4 minutes, it’s important to first discard the initial three data points, as they might be influenced by the previous recording. Following this, we can calculate R² and the slope of CO₂ and N₂O over time, respectively.

Simply, you can obtain R² and the slope using =RSQ() and =SLOPE() in Excel.

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Step 2) to calculate the volume and later surface of the cylinder

First, we need to calculate the volume of the cylinder installed in the soil and the chamber attached to the Gasmet. We know the volume of the chamber in the Gasmet is 3L. Thus, we only need to calculate the volume of the cylinder installed in the soil. We have already measured the height and diameter of the cylinder, which were 5.3 cm and 20.5 cm respectively. Diameter will not be changed in the ground, but the height would be altered according to how deep we insert the cylinder into the soil. It could be more than 5.3 cm or less than 5.3 cm. Therefore, it is important to measure each cylinder’s height at every spot.

The volume of the cylinder is calculated using the formula:

cylinder volume (cubic centimeters, cm3) = π × cylinder radius² × cylinder height 

where
π = 3.14
cylinder radius = 10.25 cm
cylinder height = 5.3 cm

cylinder volume (cm3) = 3.14 * 10.25 * 10.25 *  5.3 ≈ 1748.450125

∴ Cylinder volume (L) ≈ 1.75 L  (∵ 1cm3 = 0.001L)

Therefore, the total volume will be 3 + 1.75 ≈ 4.75 L

Next, we need to calculate the lateral surface of the cylinder installed in the soil.

The volume of the cylinder is calculated using the formula:

Later surface of a cylinder = (2π × cylinder radius) × cylinder height

where
π = 3.14
cylinder radius = 10.25 cm
cylinder height = 5.3 cm

Later surface of a cylinder (m2) = 2 * 3.14 * 0.1025 * 0.053 ≈ 0.034

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Step 3) to set up the temperature in Kelvin

The Celsius and Kelvin scales are two of the most commonly used temperature scales in science, and they have a simple, linear relationship. The Kelvin scale is an absolute temperature scale, meaning it starts at absolute zero, the theoretically lowest possible temperature where all molecular motion ceases. Absolute zero is equivalent to -273.15 degrees Celsius.

The relationship between the Celsius and Kelvin scales can be expressed with the following formula:

K = °C + 273.15
where K is the temperature in Kelvin and °C is the temperature in Celsius.

We set up K as 302.5

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Step 4) to calculate volume and surface of the cylinder

I created a simple calculation cell to compute the volume and lateral surface area of the cylinder, using the height and radius of the cylinder.

For volume (L), the formula in excel is 
=3+((3.14*10.25*10.25*D2))/1000

For lateral surface (m2) the formula in excel is 
=(2*3.14*0.1025*(D2/100))

Since the cylinder’s radius is a fixed value of 10.25 cm, I used this constant value. However, since the height of the cylinder can vary for each spot, I made a cell (D2) where you can input the individual height value. Then, I created additional cells for inputting the slopes of CO₂ and N₂O.

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Step 5) to calculate the number of moles of a gas, using a form of the Ideal Gas Law.

The equation below is used to calculate the number of moles of CO₂ and N₂O gas.

CO2
=((990/1013.25) * 0.000001 * cylinder volume * slope of CO2)/(0.0821* K)

N2O
=((990/1013.25) * 0.000001 * cylinder volume * slope of N2O)/(0.0821* K)

where K is the temperature in Kelvin

The Ideal Gas Law is usually stated as PV = nRT, where:

• P is the pressure of the gas,
• V is the volume,
• n is the number of moles of the gas,
• R is the Ideal Gas Constant,
• T is the temperature (in Kelvin).

In the above equation,

• 990/1013.25 is likely a correction factor for atmospheric pressure. Standard atmospheric pressure is defined as 1013.25 hPa (hectopascal), but in the actual field situation, it might be 990 hPa. So, the fraction 990/1013.25 is used to correct for the actual pressure.
• 0.000001 is a conversion factor to go from ppm (parts per million) to a ratio (since 1 ppm = 1/1,000,000).
• The volume of the cylinder is V, as in the Ideal Gas Law.
• The slope of carbon dioxide is presumably related to the concentration of the gas.
• 0.0821 is the value of the Ideal Gas Constant R, when pressure is in atmospheres and volume is in liters. This value is often used when dealing with gases under conditions close to standard temperature and pressure (STP).
• The Kelvin temperature is T, as in the Ideal Gas Law.

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Step 6) to upscale CO₂ and N₂O from ppm to flux (mg/m² h) respectively

The equation below is used to calculate the Flux (mg/m² h) of CO₂ and N₂O

CO2
=((the number of moles of CO2 * 44) / later surface of a cylinder) * 1000000

N2O
=((the number of moles of N2O * 44) / later surface of a cylinder) * 1000000

The number 44 is the molar mass of carbon dioxide (CO₂) and nitrous Oxide (N₂O). In chemistry, the molar mass is the mass of 1 mole of a substance. For example, CO₂, this is about 44 g/mol (or equivalently, 44,000,000 µg/mol). So multiplying the number of moles of CO₂ by 44 changes your units from moles to µg, which are more commonly used in the context of environmental studies.

The lateral surface of a cylinder is used because flux is typically measured per unit area. If you are measuring the emission of a gas from a soil surface, you would place a cylinder on the surface and measure the amount of gas coming out of that cylinder. The lateral surface area of the cylinder is the relevant surface area for this measurement.

The multiplication by 1,000,000 is a conversion factor to go from grams to µg since 1 gram is equivalent to 1,000,000 µg. Therefore, in this equation, you are essentially converting the amount of CO₂ from moles to µg, and then dividing by the area to obtain a flux.

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Next, I’ll convert the flux (µg/m² s) to flux (mg/m² h).

The equation below is used to convert the Flux (µg/m² s) to Flux (mg/m² h).

Flux (mg/m2 h) = (Flux (µg/m2 s) / 1000) * 3600

CO2 Flux (mg/m2 h) = (61.13 /1000)*3600 ≈ 220.06
N2O Flux (mg/m2 h) = (0.02 /1000)*3600 ≈ 0.07

For N₂O, the Flux (mg/m² h) is too low to see the value, so I’ll convert to the Flux (µg/m² h). Simply we can multiply 1,000 (∵ 1mg = 1,000µg), and the value will be 71.30 (µg/m² h).

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Step 7) to upscale CO₂ and N₂O from flux (g m^-2 day^-1) respectively.

Flux (mg m-2 day-1) = (Flux (mg m-2 h-1) / 1,000) * 24

CO2 Flux (mg/m2 h) = (220.06 / 1000) * 24 ≈ 5.28144 g m-2 day-1
N2O Flux (mg/m2 h) = (0.07 /1000)* 24 ≈ 0.00168 g m-2 day-1

Finally, I calculated CO₂ Flux (mg m^-2 day^-1) and N₂O Flux (mg m^-2 day^-1) from the ppm results.

Second	Carbon dioxide (CO2) [ppm]	CO2 Flux (mg m-2 day-1)	Nitrous oxide (N2O) [ppm]	N2O Flux (mg m-2 day-1)
0	926.7	5.28144	0.3672	0.00168
20	1205.21		0.3645
40	1265.57		0.3589
60	1279.95		0.3577
80	1286.73		0.3552
100	1293.44		0.3595
120	1298.49		0.3607
140	1300.81		0.3622
160	1306.12		0.3628
180	1311.14		0.3678
200	1317.64		0.3668

If you take gas samples 10 times, you will obtain cumulative CO₂ Flux (mg m^-2 day^-1) and N₂O Flux (mg m^-2 day^-1) over time.

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