5  Results

This chapter presents the results of the process rate estimator run over all the available dates, depths and columns. Once the process rate estimator is run as instructed in the previous chapter, the results can be found in the sub-directory scripts/run-process-rate-estimator/output, or in the corresponding sub-directory of the GitHub repository.

5.1 Looking at the process rates over time

Figure 5.1 show all results, from column 1 to 12 and depths 7.5 cm, 30 cm, 60 cm, 90 cm and 120 cm. Note that while the measurements are certainly correlated over time and among depth layers, the process rate estimates are performed independently – the estimates of one day do not influence the estimates of another day per se.

Figure 5.1: Estimated process rates over time for all columns and depths. Note: You may click on the column or depth buttons on the top of the tab set to navigate between the visualizations.

Notably, looking though all the results, we can observe quite a few cases where the estimations for the process rates are negative – which we know to be impossible. An overview of the processes, columns and depth layers affected by negative process rate estimates is provided in table 5.1.

Table 5.1: Percentage of negative process rate estimates (number of days with negative rates divided by total number of days) for each column, depth and process. Instances of 0% are left blank in this table.
Nitrification
7.5 cm 30 cm 60 cm 90 cm 120 cm
1 13% 26% 18% 67% 73%
2 74% 100%
3 7% 15% 17%
4 2% 73%
5 56% 100%
6 21%
7 23% 25%
8 16% 24% 37% 82%
9 2% 42% 65%
10 27% 2% 44% 28%
11 6% 83% 100% 100%
12 17% 22% 19% 100%
Denitrification
7.5 cm 30 cm 60 cm 90 cm 120 cm
1
2
3
4 22%
5
6
7
8
9 6% 43% 25%
10
11 1%
12 47% 5% 42%
Reduction
7.5 cm 30 cm 60 cm 90 cm 120 cm
1
2
3 9%
4 35% 27%
5
6 1%
7 17%
8 11%
9 1% 84% 30%
10 17%
11
12 83% 47% 37% 54%

Table 5.1 shows that nitrification rates are particularly affected by this phenomenon – especially at lower depths – with five cases where negative estimates were made for every single day. Denitrification and reduction rates are much less affected.

5.2 Results of the mean process rates

Figure 5.2 depicts the values of all mean process rates. Notably, column 12 stands out with its markedly negative denitrification and reduction rates, contrasted by extremely high nitrification rates. This observation aligns with the inherent correlation among the three process rate estimates.

Figure 5.2: Combinations of scatterplots of the mean estimated process rates for nitrification, denitrification and reduction. Each point represents one mean process rate for a given depth and column. For some estimates, the column is indicated on the top. The grey area represents the physically impossible space.

Although physically impossible, the uncorrected values of mean nitrification, denitrification, and reduction are used for further analyses in the interest of intellectual honesty.

The results presented in table 5.2 also show the mean nitrous oxide nitrification (\(\ce{N2O}_{\text{nit}}\)), denitrification (\(\ce{N2O}_{\text{den}}\)), consumption (\(\ce{N2O}_{\text{consumed}}\)), and production (\(\ce{N2O}_{\text{produced}}\)). The N2O production is hereby defined as:

\[\ce{N2O}_{\text{production}} = \ce{N2O}_{\text{nit}} + \ce{N2O}_{\text{den}} \tag{5.1}\]

Meanwhile, the consumption is simply the mean N2O reduction.

Table 5.2: Overall results of the mean estimated process rates (μ ± σ) by depth layer and variety. N2Onit is the mean nitrification rate over the entire estimated period, while N2Oden is the mean denitrification rate. For reference, this table also displays N2Oproduced, which is simply N2Onit + N2Oden, as well as N2Oconsumed, which is the mean reduction rate.
Variety Depth [cm] N2Onit N2Oden N2Oproduced N2Oconsumed
CH Claro 7.5 7.2 ± 2.1 16 ± 0.99 23 ± 2.9 30 ± 5
30.0 5.3 ± 1.2 16 ± 1.7 22 ± 2.8 32 ± 1.4
60.0 2.3 ± 0.3 18 ± 2.5 20 ± 2.8 33 ± 2.6
90.0 1.9 ± 1.7 16 ± 1.4 18 ± 1.1 32 ± 3.2
120.0 1.1 ± 1.7 15 ± 1.8 17 ± 2.2 32 ± 3.1
Monte Calme 268 7.5 36 ± 52 7.7 ± 13 44 ± 39 14 ± 33
30.0 13 ± 8.7 24 ± 3.6 37 ± 12 21 ± 22
60.0 6.4 ± 2.7 13 ± 2.7 20 ± 3.2 11 ± 8.2
90.0 2.5 ± 0.52 7 ± 5.4 9.5 ± 4.9 10 ± 18
120.0 -0.35 ± 1.7 11 ± 1.1 11 ± 2.8 25 ± 3.7
Probus 7.5 11 ± 8.8 13 ± 3.1 24 ± 5.8 31 ± 3.7
30.0 12 ± 4.6 27 ± 16 39 ± 21 31 ± 1.2
60.0 3.4 ± 3.1 24 ± 16 28 ± 19 31 ± 10
90.0 2.5 ± 4.7 10 ± 7.4 13 ± 3.4 11 ± 34
120.0 -0.72 ± 0.32 12 ± 4.5 11 ± 4.3 24 ± 12
Zinal 7.5 11 ± 7.4 14 ± 4.9 25 ± 2.7 30 ± 1.7
30.0 5.2 ± 2.2 19 ± 3.6 24 ± 4.8 29 ± 6.9
60.0 0.71 ± 2.5 14 ± 1.5 15 ± 1.4 24 ± 3.2
90.0 -0.89 ± 1.8 14 ± 1.1 13 ± 2.9 28 ± 5.1
120.0 -0.4 ± 2 13 ± 2.7 12 ± 4.7 28 ± 8

5.3 Testing for variety effects

Owing to all processes’ significant divergence of the linear model’s residuals from a normal distribution, as determined by the Shapiro-Wilk normality test, the Kruskal-Wallis rank sum test was employed to examine group variation among the varieties. These respective tests were performed utilizing the relevant functions – shapiro.test and kruskal.test, from the stats package, as referred to in (R Core Team 2023).

Table 5.3: Results of the Kruskal-Wallis rank sum test inspecting the effects of variety on the mean estimated process rates.
Process Kruskal-Wallis χ² degrees of freedom p-value
Nitrification 2.85 3 0.42
Denitrification 5.34 3 0.15
Reduction 10.57 3 0.01 *

Among the different varieties, there were no significant group differences detected for neither N2Onit nor N2Oden, and hence also not for N2Oproduced (Table 5.4). However, significant differences among the varieties for N2Oconsumed were detected (p = 0.01098). The group means and standard deviations for each variety are showcased in table 5.4.

Table 5.4: Values from table 5.2 aggregated by variety. The superscript compact letter display indicates significant differences among groups based on Dunn’s Kruskal-Wallis multiple comparison (α = 0.05).
Variety N2Onit N2Oden N2Oproduced N2Oconsumed
CH Claro 3.5 ± 2.7 16 ± 1.8 20 ± 3.2 32 ± 2.9 a
Monte Calme 268 11 ± 24 13 ± 8.5 24 ± 21 16 ± 18 b
Probus 5.7 ± 6.8 17 ± 12 23 ± 15 26 ± 17 ab
Zinal 3.1 ± 5.6 15 ± 3.4 18 ± 6.4 28 ± 5.1 ab

5.4 Testing for depth effects

Conversely, N2Oconsumed did not show any significant group differences with respect to the depth layers. However, all other processes did: N2Onit (p = 1.005e-07) nor N2Oden (p = 0.001029), and hence also for N2Oproduced (p = 3.883e-08).

Table 5.5: Results of the Kruskal-Wallis rank sum test inspecting the effects of depth layer on the mean process rates over all days.
Process Kruskal-Wallis χ² degrees of freedom p-value
Nitrification 36.46 4 p < 0.001 ***
Denitrification 18.16 4 0.0011 **
Reduction 2.85 4 0.58
Table 5.6: Values in Table 5.2 aggregated by depth layer. The superscript compact letter display indicates significant differences among groups based on Dunn’s Kruskal-Wallis multiple comparison (α = 0.05).
Depth [cm] N2Onit N2Oden N2Oproduced N2Oconsumed
7.5 16 ± 26 b 13 ± 6.9 a 29 ± 19 b 27 ± 16
30 8.9 ± 5.8 b 22 ± 8.5 b 30 ± 13 b 28 ± 11
60 3.2 ± 3 ab 17 ± 8.4 ab 21 ± 9.6 ab 25 ± 11
90 1.5 ± 2.7 a 12 ± 5.3 a 13 ± 4.2 a 20 ± 20
120 -0.092 ± 1.5 a 13 ± 2.9 a 13 ± 3.8 a 27 ± 7.4