Causes of variation among rice models in yield response to CO2 examined with Free-Air CO2 Enrichment and growth chamber experiments

The CO2 fertilization effect is a major source of uncertainty in crop models for future yield forecasts, but coordinated efforts to determine the mechanisms of this uncertainty have been lacking. Here, we studied causes of uncertainty among 16 crop models in predicting rice yield in response to elevated [CO2] (E-[CO2]) by comparison to free-air CO2 enrichment (FACE) and chamber experiments. The model ensemble reproduced the experimental results well. However, yield prediction in response to E-[CO2] varied significantly among the rice models. The variation was not random: models that overestimated at one experiment simulated greater yield enhancements at the others. The variation was not associated with model structure or magnitude of photosynthetic response to E-[CO2] but was significantly associated with the predictions of leaf area. This suggests that modelled secondary effects of E-[CO2] on morphological development, primarily leaf area, are the sources of model uncertainty. Rice morphological development is conservative to carbon acquisition. Uncertainty will be reduced by incorporating this conservative nature of the morphological response to E-[CO2] into the models. Nitrogen levels, particularly under limited situations, make the prediction more uncertain. Improving models to account for [CO2] × N interactions is necessary to better evaluate management practices under climate change.

. Summary of the experimental conditions for the Japanese and Chinese FACE experiments 63 Japan (1998Japan ( -2000 China ( Bulk density 1.2 g cm -3 Plow layer 12.3 cm Plow layer 13.0 cm Total C 82.5 g kg -1 ; Total N 18 g kg -1 Total C 15.0 g kg -1 ; Total N 1.59 g kg -1 Simulations of growth and yield include two sources of uncertainty. One is the uncertainty 66 caused by the difference between measured and simulated yield (Ubias) and the other is due to 67 the variation among crop models (Umodel). In this study, we quantified both uncertainties by 68 the following two methods: 69 1. To determine overall Ubias, a pairwise comparison between observed and simulated was 70 made for datasets excluding those used for the model calibration. This was followed by 71 further analysis on the deviations between simulations and observations to quantify the 72 source of Ubias. 73 2. To determine sources of Umodel, the sum of squares (SS) from different sources was 74 calculated for all simulation results. 75 76 FACE study 77 Simulations vs. observations 78 In step 1, we compared the measured and simulated yield and biomass under ambient [CO2].

79
The bias for grain yield in Shizukuishi was significantly different from 0 (P<0.05), but only 80 about 3.6 % of the measured yield. In Wuxi, simulated and measured yield did not differ 81 significantly, but biomass was underestimated by 1.2 t/ha in Wuxi (P < 0.001), but about 6.7 % 82 of the measured mean of 17.3 t/ha. The bias was consistent over the N treatments (Table S3, 83 Figure S2). The mean bias in biomass of 0.4 t/ha in Shizukuishi was not significant. 84 The mean enhancement of grain yield in response to elevated [CO2] was slightly but 85 significantly overestimated in Shizukuishi, by 3 percentage point (P<0.05, Table S3, Figure  86 S3). The bias was greater under low or high N conditions. In Wuxi, there was virtually no bias 87 observed when averaged, but was slightly overestimated in medium N but underestimated in 88 high N (Table S3, Figure S3). Overall, however, the mean biases were mostly not greater than 89 the range of experimental errors (Table S3), suggesting that the mean of models was close to the 90 measurements. We further analysed the sources of variation in the biases by means of analysis 91 of variance, using differences between measured and simulated as a dependent variable and N 92 and models as independent variables (Table S4). In general, more than half of the variation was 93 due to models. These results suggest that Ubias is not large for the model ensemble means, but 94 that for individual models is not negligible.

96
Variation among models (Umodel) 97 The simulated yield and biomass were further analysed for their sources of variation in a similar 98 manner to the previous variance components (Table S5). Here we used all datasets including 99 those used for calibration because the analyses targeted variation only among the simulated 100 data. Variation in the experimental data is also shown in the table for reference, however. 101 For simulated yield and biomass, models are a large source of variation, but variation due to 102 year and nitrogen levels were also large sources. The modelled variation follows that in 103 observed yields and biomass. Model by N interactions were relatively small, suggesting that the 104 models tend to behave similarly to different levels of N. The results were similar in both sites. 105 For yield and biomass enhancements to elevated [CO2], 60% or more of the variation 106 was due to the models. The main effect of year or N did not account for the variation (7 % or 107 less). 108 109

SPAR chamber study 110
A pairwise comparison between the simulated and observed was first made on the yield and 111 biomass under ambient (330 µmol mol -1 ) conditions, using Experiment 1, 2 and 3 under 112 sufficient N conditions (Table S6). For the SPAR study, models were not calibrated except for 113 phenology so all the data were used for this comparison. On average, grain yield was slightly 114 but consistently overestimated by the models but no significant difference was observed for 115 biomass. Models account for 65 % and 55 % of the total variation in the model bias for grain 116 yield and biomass respectively. 117 Grain yield enhancement was significantly underestimated by the models (P < 0.05) by 4.5 118 percentage points and biomass was overestimated by 3.8%, but these differences were less than 119 the standard error for the experiments (Table S6). The major source of the variation in the 120 model simulations was models, accounting for more than 60 % of the total variations (Table  121 S7). The model by CO2 interaction was relatively small ranging from 4 to 6 %, suggesting that 122 relative model performance was similar under two [CO2] conditions. 123 These analyse highlight the importance of reducing uncertainties among the models. 124 125 1) Standard error for the measurements was obtained from the residual mean square of the analysis of variance using year and N as main factors (see Table S3).
2) The same alphabetic letters followed by the values for each N treatment are not significantly different between the treatments. 1) Sum of squares (SS) for the differences between measured and simulated values were calculated by the general liner model procedures (Type I sum of squares).

126
2) % of SS of the total (corrected by the overall mean). Analysis of variance testing the difference among model types showed no significant differences.

Figure S2. Simulated and observed yield (a) and biomass (b) under ambient [CO2]
Box-whiskers represent the variation among simulated values by 14 rice models and red dots and bars represent the measured mean ±80% confidence intervals. The 80 % confidence intervals are to compare the whiskers of the simulated values ranging from 10 to 90 percentiles. Datasets not used for the calibration are shown. Measurements for biomass in LN at Shizukuishi in 1998 and for yield and biomass in HN in 2001were not available.

Figure S3. Simulated and observed yield (a) and biomass (b) enhancement by elevated [CO2]
Box-whiskers represent the range of simulated values by 14 rice models and red dots and bars represent the measured mean ±80% confidence intervals.