Sensitivity and error analysis

E. Nemitz et al. Agricultural and Forest Meteorology 105 2000 405–425 419 Table 3 Sensitivity analysis for the 3-layer model: a single parameter is changed within the bounds specified in brackets, while all other parameters are kept constant a Modified value Γ sq constant 2270 Γ sq fitted for F t model = F t measured R F measured vs. F model Mean F t ng m − 2 s − 1 F sq F t daytime Best fit Γ sq R F measured vs. F model F sq F t daytime Unmodified model 0.62 15.7 = F t measured 1.07 2270 0.62 1.07 F t measured ∓25 0.620.62 15.715.7 1.071.07 17852755 0.610.63 1.041.09 χ a measured ∓25 0.650.59 18.612.9 0.991.17 19202619 0.650.60 0.961.17 Γ sf ∓25 0.620.63 15.216.2 1.101.04 23302209 0.620.63 1.101.03 Γ sq ∓25 0.610.63 11.120.3 1.031.09 NA NA NA Γ l,max ∓25 0.600.64 14.117.4 1.160.99 24762063 0.610.64 1.160.97 R ac + R b1 ∓ 50 0.660.61 21.314.0 0.861.16 15532482 0.630.61 0.731.15 R sf ∓ 50 0.610.63 14.916.2 1.121.04 23702212 0.610.63 1.131.03 R sq ∓ 50 0.620.63 29.912.4 1.121.04 14743065 0.600.63 1.081.06 T z ′ ∓ 25 0.560.62 7.130.4 1.101.05 41121221 0.630.61 1.140.96 a The sensitivity to each parameter is assessed a by applying the model with a constant value of the silique [NH 4 + ][H + ] ratio Γ sq = 2270, and b by choosing a new value of Γ sq to fit the predicted net exchange flux to the measured average. The correlation coefficient R and the net flux F t provide a means to test the sensitivity of the model performance, while the ratio of silique flux to total flux F sq F t is indicative of the partitioning of the exchange between plant parts. T z ′ is the temperature of the mean canopy height in ◦ C, all other parameters are defined in Fig. 5b. Although Figs. 11 and 12 show the comparison of the measurements with the foliage–litter model, these could equally be shown for the foliage–litter–silique model. While the latter model is considered to be a more realistic mechanistic representation of the ex- change process, the comparison shows that the simpler foliage–litter model is adequate to predict the main features of net fluxes. A comparison of the overall performance of the two models is shown in Table 2. This shows the mean component fluxes through dif- ferent plant parts as predicted by a the foliage–litter model and b the foliage–litter–silique model with h -dependent Γ l . The measured net-flux F t is slightly underestimated by both models. However, the aver- ages do not cover exactly the same periods: short gaps of up to 2 h in the χ a data were interpolated and still used as model input, although measured fluxes could not be calculated. By contrast, for a few periods the flux could be measured, but there are parameters miss- ing, which are essential for the model application. Whereas the foliage–litter model predicts deposi- tion to the leaf stomata F s of −9.1 ng m − 2 s − 1 for daytime, the inclusion of a silique-layer into the model suggests that the deposition to the leaf stomata of − 4.4 ng m − 2 s − 1 is more than balanced by the emis- sion from the silique stomata of 23.3 ng m − 2 s − 1 . At night-time stomata are, as expected, inactive, with small fluxes being induced by some duskdawn ef- fects. Surprisingly, the suppression of Γ l during dry daytime conditions as a consequence of Eq. 15 leads to the litter emission flux F l being on an average the same during day and night about 10 ng m − 2 s − 1 ; the increased turbulence at daytime, favouring the ground level emission coming through the canopy, and in- creased T are exactly compensated for by the smaller daytime value of Γ l . If Γ l is kept constant over the day, as in the foliage–litter model, the night-time emission is only 40 of its daytime value. Both models sug- gest that the night-time leaf litter emission is roughly balanced by deposition to leaf water-layers F w , with the ratio of the deposition to siliques F wq and leaves F wf in the foliage–litter–silique model being 2:1. The leaf litter emission is mainly captured by the lower leaves, whereas atmospheric deposition takes place to the aerodynamically more exposed siliques.

6. Sensitivity and error analysis

The development of the single-layer χ s –R w -model into a 3-layer model with h-dependent Γ l has resulted in an increased numbers of parameters, each of which is associated with some uncertainty. A sensitivity analysis was therefore carried out to establish the 420 E. Nemitz et al. Agricultural and Forest Meteorology 105 2000 405–425 impact of the uncertainty in the main parameters on i the stability of the prediction of the net exchange flux F t and ii the partitioning of the net flux into com- ponent fluxes. Of interest are here the effects of errors in the emission potentials Γ sf , Γ sq and Γ l and the resistances R sf , R sq and total in-canopy resistance, R ac + R b1 , and in particular in the parameters that have been derived from measurements χ a , F t and T z ′ . Sutton et al. 2000b estimated errors for the individual 10 min values of χ a and F t as 25 and 50, respectively, while the error of the average should be much smaller. Parameters were varied over a range of typically ∓25 of their original values, and the results were calculated i for a constant Γ sq = 2270 and ii by adjusting Γ sq for each modification to re- produce the measured net flux Table 3. Apart from the response to changes in T z ′ , relative effects on F t and the ratio F sq F t were always much smaller than the relative change in the parameter investigated, in- dicating that the model is very robust in predicting net emissions and partitioning the flux. Major uncertain- ties in T z ′ can be ruled out as heatfluxes were mea- sured simultaneously with several instruments Sutton et al., 2000b. The contribution of the litter emis- sion to the net emission increased most sensitively with increasing Γ l as well as with decreasing χ a and R ac + R b1 , but variations were within 20. The mod- ification of a single parameter never led to a marked change with implications for the mechanistic interpre- tation of the results, although it is evident that a 50 uncertainty is associated with the emission potentials Γ l, max and Γ sq that were derived through fit to the measurements.

7. Discussion