View Full Table | Close Full ViewTable 1.

Descriptions of flux calculation procedures used.

 
Method no. Method description† Application description
1 Linear regression (LR) use all 100,000 calculated fluxes
2 Quadratic method (Quad) use all 100,000 calculated fluxes
3 Hutchinson and Mosier (H/M) use only noncomputational-failure fluxes (∼40,000 fluxes for each Monte Carlo sampling)
4 Pedersen HMR (HMR) use only fluxes that the software indicated were calculated by the HMR model (∼2800 fluxes for each Monte Carlo sampling scenario)
5 restricted quadratic (rQuad) use only Quad-calculated fluxes when data did not meet the rejection criteria (∼50,000 fluxes for each Monte Carlo sampling scenario)
6 restricted Hutchinson and Mosier (rH/M) use H/M-calculated fluxes when data did not meet the rejection criteria (∼17,500 fluxes for each Monte Carlo sampling scenario)
For the LR, Quad, H/M, rQuad, and rH/M methods, 100,000 Monte Carlo samplings were performed for each sampling intensity (three or four time points), deployment time, and analytical precision level. For the HMR method, 10,000 Monte Carlo samplings were performed at all deployment times and analytical precisions using only four-time-point data sets.



View Full Table | Close Full ViewTable 2.

Means, standard deviations, and normality test of populations of N2O fluxes generated by Monte Carlo simulation. Data are presented for fluxes calculated with six different methods using four time points and a 0.75-h chamber deployment time over a range of analytical precisions.

 
Precision (CV) LR† Quad H/M rQuad rH/M HMR
nL L−1 h−1
0.02 −0.010 (11.5) ‡ 0.011 (40.0) 0.294 (37.5)* −0.230 (47.7)* 0.456 (49.4)* −40,499 (1,874,000)*
0.04 −0.024 (22.9) 0.460 (80.3) −0.219 (74.3)* 0.102 (95.6)* −1.53 (96.2)* −120,910 (4,176,000)*
0.06 −0.002 (34.4) 0.550 (121) −0.294 (112)* −1.34 (143.4)* −0.150 (145.7)* −275,639 (9,846,000)*
0.08 0.122 (45.9) −0.401 (161) 0.325 (148)* 0.782 (191.2)* −0.229 (198.8)* −19,540 (8,979,000)*
0.10 −0.074 (57.2) 0.670 (201) −1.46 (188)* 0.644 (239.2)* 0.728 (246.5)* 115,816 (11,120,000)*
0.12 0.231 (68.9) 1.055 (241) 0.957 (221)* 0.657 (286.9)* 0.127 (294.4)* −238,600 (14,090,000)*
*Distributions of the fluxes are significantly different from a normal distribution at P < 0.001.
H/M, Hutchinson/Mosier; HMR, revised Hutchinson/Mosier; LR, linear regression; rH/M, restricted Hutchinson/Mosier; rQuad, restricted quadratic.
Standard deviations are shown in parentheses.



View Full Table | Close Full ViewTable 3.

Factors (slopes) relating precision to N2O flux detection limit for different flux calculation methods using three time points at different deployment times. Factors are slopes of the regression lines shown in Fig. 7. The y-intercepts of the regressions were not significantly different from zero.†

 
Deployment time Negative limit of detection slope
Positive limit of detection slope
LR‡ Quad H/M rQuad rH/M LR Quad H/M rQuad rH/M
h nL L−1 h−1 CV−1
0.1 −7,506 −26,851 −22,659 −29,878 −31,758 7,465 26,863 22,163 29,914 31,167
0.25 −2,977 −10,698 −8,942 −11,913 −12,742 2,966 10,694 9,066 11,885 12,834
0.5 −1,490 −5,375 −4,518 −5,963 −6,349 1,488 5,383 4,540 5,967 6,346
0.75 −992 −3,594 −3,031 −3,995 −4,268 993 3,578 3,037 3,972 4,276
1.0 744 −2,679 −2,275 −2,966 −3,187 743 2,689 2,240 2,988 3,158
2.0 −371 −1,338 −1,139 −1,484 −1,603 374 1,349 1,140 1,506 1,601
In all cases, r2 values exceeded 0.9996.
H/M, Hutchinson/Mosier; HMR, revised Hutchinson/Mosier; LR, linear regression; Quad, quadratic; rH/M, restricted Hutchinson/Mosier; rQuad, restricted quadratic.



View Full Table | Close Full ViewTable 4.

Factors relating precision to detection limit of fluxes determined with four flux calculation methods using four time points for different deployment times. Factors are slopes of the regression lines shown in Fig. 7. The y-intercepts of the regressions were not significantly different from zero.†

 
Deployment time Negative limit of detection slope
Positive limit of detection slope
LR‡ Quad H/M rQuad rH/M HMR LR Quad H/M rQuad rH/M HMR
h nL L−1 h−1 CV−1
0.1 −7,033 −24,620 −21,165 −28,153 −28,493 −41,370 7,036 24,570 20,725 28,002 28,112 42,547
0.25 −2,819 −9,846 −2,529 −11,261 −11,711 −16,746 2,824 9,862 8,543 11,278 11,650 17,091
0.5 −1,414 −4,935 −4,312 −5,653 −5,831 −8,380 1,411 4,943 4,290 5,649 5,768 8,400
0.75 −944 −3,289 −2,863 −3,757 −3,816 −5,573 939 3,305 2,858 3,776 3,875 5,835
1.0 −708 −2,471 −2,114 −2,829 −2,883 −4,120 707 2,479 2,143 2,835 2,881 4,216
2.0 −353 −1,238 −1,069 −1,410 −1,429 −1,990 352 1,230 1,066 1,400 1,447 2,163
In all cases, r2 values exceeded 0.9996.
H/M, Hutchinson/Mosier; HMR, revised Hutchinson/Mosier; LR, linear regression; Quad, quadratic; rH/M, restricted Hutchinson/Mosier; rQuad, restricted quadratic.



View Full Table | Close Full ViewTable 5.

Scaled slope factors relating precision to detection limit of fluxes determined with calculation procedures using three time points for different deployment times. Scaled slopes were calculated by dividing the corresponding slopes in Table 3 by the ambient mean N2O concentration (320 ppb) used in the Monte Carlo simulations.

 
Deployment time Negative limit of detection factor
Positive limit of detection factor
LR† Quad H/M rQuad rH/M LR Quad H/M rQuad rH/M
h h−1 CV−1
0.1 −23.5 −83.9 −70.8 −93.4 −99.2 23.3 83.9 69.3 93.5 97.4
0.25 −9.30 −33.4 −27.9 −37.2 −39.8 9.27 33.4 28.3 37.0 40.1
0.5 −4.66 −16.8 −14.1 −18.6 −19.8 4.65 16.8 14.2 18.6 19.8
0.75 −3.10 −11.2 −9.47 −12.5 −13.3 3.10 11.2 9.49 12.4 13.4
1.0 −2.33 −8.37 −7.11 −9.27 −9.96 2.32 8.40 7.00 9.34 9.87
2.0 −1.16 −4.18 −3.56 −4.64 −5.01 1.17 4.22 3.56 4.71 5.00
H/M, Hutchinson/Mosier; HMR, revised Hutchinson/Mosier; LR, linear regression; Quad, quadratic; rH/M, restricted Hutchinson/Mosier; rQuad, restricted quadratic.



View Full Table | Close Full ViewTable 6.

Scaled slope factors relating precision to detection limit of fluxes determined with calculation procedures using four time points for different deployment times. Scaled slopes were calculated by dividing the corresponding slopes in Table 4 by the ambient mean N2O concentration (320 ppb) used in the Monte Carlo simulations.

 
Deployment time Negative limit of detection scaled factor
Positive limit of detection scaled factor
LR† Quad H/M rQuad rH/M HMR LR Quad H/M rQuad rH/M HMR
h h−1 CV−1
0.1 −22.0 −76.9 −66.1 −88.0 −89.0 −129.3 22.0 76.8 64.8 87.5 87.9 133.0
0.25 −8.81 −30.8 −7.90 −35.2 −36.6 −52.33 8.83 30.8 26.7 35.2 36.4 53.4
0.5 −4.42 −15.4 −13.5 −17.7 −18.2 −26.2 4.41 15.4 13.4 17.7 18.0 26.3
0.75 −2.95 −10.3 −8.95 −11.4 −11.9 −17.0 2.93 10.3 8.93 11.8 12.1 18.1
1.0 −2.21 −7.72 −6.6 −8.84 −9.00 −12.9 2.21 7.75 6.70 8.86 9.00 13.2
2.0 −1.10 −3.87 −3.34 −4.41 −4.47 −6.22 1.10 3.84 3.33 4.38 4.52 6.76
H/M, Hutchinson/Mosier; HMR, revised Hutchinson/Mosier; LR, linear regression; Quad, quadratic; rH/M, restricted Hutchinson/Mosier; rQuad, restricted quadratic.



View Full Table | Close Full ViewTable 7.

Regression coefficients and coefficient of determination for regression model relating deployment time to the scaled slope factors shown in Tables 5 and 6.†

 
Flux calculation procedure‡ Regression coefficients
r2
a b
Three sampling points
Linear regression 2.314 1.005 ≥0.9999
Quad 10.06 0.9904 0.9998
H/M 9.290 1.002 ≥0.9999
rQuad 7.095 0.9944 0.9998
rH/M 8.369 1.001 ≥0.9999
Four sampling points
Linear regression 2.211 0.9975 ≥0.9999
Quad 7.617 1.004 0.9998
H/M 6.058 1.035 0.9870
rQuad 8.844 0.9966 ≥0.9999
rH/M 9.231 0.9820 0.9998
HMR 13.20 0.9973 0.9996
The exponential model used was θ = a DT−b (see Fig. 8).
H/M, Hutchinson/Mosier; HMR, revised Hutchinson/Mosier; Quad, quadratic; rH/M, restricted Hutchinson/Mosier.



View Full Table | Close Full ViewTable 8.

Examples of how the equation for the rQuad flux calculation method is used to calculate flux detection limits for N2O, CH4, and CO2 when the ambient concentrations and analytical precisions are known (shown in Fig. 3) with three time points of data and a deployment time of 0.667 h. Exponential model regression coefficients (shown in Table 7) that relate chamber deployment time to the rQuad slope factor were used.

 
Parameter N2O CH4 CO2
Mean ambient concentration, ηL−1 (N2O); mL L−1 (CH4 and CO2) 323 1.79 385.5
Precision, CV 0.044 0.071 0.0014
Deployment time, h 0.667 0.667 0.667
θ (calculated from Table 7, rQuad method, three time points, 0.667 h deployment time) 10.61 10.61 10.61
Slope factor (θ × mean concentration) 3428 18.99 4091
Positive flux detection limit, ppb h−1 or ppm h−1 (slope factor × CV) 150.8 1.349 5.728
Negative flux detection limit, ppb h−1 or ppm h−1 (−1 × slope factor × CV) −150.8 −1.349 −5.728