Model error quantification

General assessment of errors

To provide some context to the implications of the model results, the effect of two different growth regimes on the error over the seasonal cycle is presented. An idealised boreal [P OC] seasonal cycle for each of the growth regimes, single-bloom and double-bloom, are shown alongside the temporal variation in adsorption rate error resulting from the equilibrium assumption (Figure 3.4). The single-bloom scenario generally results in lower errors in the diagnosed adsorption rates, with maximum errors around 15% compared with 35% for the double-bloom scenario. This difference is due to the greater rate of change of [P OC] during the double-bloom scenario, as revealed by the slope in Figure 3.4. When the[P OC]is changing quickly the disequilibrium between the adsorption, desorption and fallout is greatest. The times of largest ∂[P OC_∂t ] coincide with the largest errors for both of the scenarios; at the end of March for the single-bloom scenario and the end of February for the double-bloom scenario. This effect is modified by the prior history of the system, as seen most clearly in the difference in the errors between the double-bloom February and November absolute maxima in ∂[P OC_∂t ]. The February maximum produces errors of 35%, whereas the November maximum produces errors of 20%.

This initial analysis shows that the gradient in [P OC] affects the magnitude of the error. This is modified by the prior history of the system, meaning the increase in [P OC] during Spring of the seasonal cycle produces the largest error. Periods following the Spring bloom are less affected by errors resulting from the equilibrium assumption.

Rate error assessments for cruise data

For relevant errors to be applied to each pair of diagnosed data-derived rates, the seasonal variation in the errors needs to be put into the context of the time at which the data was sampled. The D350 cruise took place in early May 2010 (Julian day 122 to 129) and the D354 cruise took place in July-August 2010 (Julian day 197 to 221). The errors associated with the respective cruises were taken from days 110 to 140 for D350 and 185 to 235 for D354. When extracting errors for the data points these time periods are used to determine the appropriate choice, including a temporal mismatch in the seasonal cycles of approximately two weeks.

These errors are extracted from the model ensembles by taking the maximum absolute error that is found within the time period defined above and denoted by the dotted lines on the plots. The minimum and maximum errors in adsorption and fallout rates diagnosed from the suite of model ensembles run for each dataset are presented here as an example of the results found with this method.

The minimum error for adsorption rates during D350 was 18% (Figure 3.5a) and the maximum adsorption rate error was 50% (Figure 3.5b). These minimum and maximum adsorption rate errors emerge from different adsorption-fallout rate pairings calculated at a specific station from the cruise. These errors are then applied to the diagnosed adsorption rates to give minimum and maximum errors for D350 data as 0.068±18%d−1 and 0.0018

±58%d−1 _{respectively. Similarly, minimum and maximum errors in the fallout}

and fallout rate results are presented more completely in the following section, but to avoid repetition the error quantification results are presented first, even though their calculation relies on the calculated adsorption and fallout rates.

(a) Minimum adsorption errors

J F M A M J J A S O N D −40 −20 0 20 40 60 80 100 120 Error,%

Time of year, month

(b) Maximum adsorption errors

J F M A M J J A S O N D −40 −20 0 20 40 60 80 100 120 Error,%

Time of year, month

Figure 3.5: Plots of normalised adsorption error over the seasonal cycle for D350, dotted line shows timing of in situ measurements±10 days.

(c) Minimum fallout rate errors

J F M A M J J A S O N D −200 −150 −100 −50 0 50 Error,%

Time of year, month

(d) Maximum fallout rate errors

J F M A M J J A S O N D −200 −150 −100 −50 0 50 Error,%

Time of year, month

Figure 3.6: Plots of normalised fallout rate error over the seasonal cycle for D350, dotted line shows timing of in situ measurements±10 days.

The D354 dataset was gathered in the summer of 2010 a few months following the spring bloom and later in the year than D350. Consistent with the model inferences the errors in the adsorption and fallout rates are much lower in this later dataset than for D350. The minimum and maximum errors in adsorption rates (Figure 3.7) were 0.095 ± 8% d−1 and 0.0055 ± 19% d−1 respectively, whereas the minimum and maximum errors in fallout rates (Figure 3.8) were

0.40±1%d−1 and 0.03±20%d−1 respectively.

(a) Minimum adsorption errors

J F M A M J J A S O N D −40 −20 0 20 40 60 80 100 120 Error,%

Time of year, month

(b) Maximum adsorption errors

J F M A M J J A S O N D −40 −20 0 20 40 60 80 100 120 Error,%

Time of year, month

Figure 3.7: Plots of normalised adsorption error over the seasonal cycle for D354, dotted line shows timing of in situ measurements±10 days.

(c) Minimum fallout rate errors

J F M A M J J A S O N D −200 −150 −100 −50 0 50 Error,%

Time of year, month

(d) Maximum fallout rate errors

J F M A M J J A S O N D −200 −150 −100 −50 0 50 Error,%

Time of year, month

Figure 3.8: Plots of normalised fallout rate error over the seasonal cycle for D354, dotted line shows timing of in situ measurements±10 days.