the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 21 Jul 2026
Quantifying parametric uncertainty in future food demand in GCAM
Abstract. Projecting food demand is important for understanding the future of land, water, and energy in the integrated human-Earth system and also has implications for health and human well-being. Uncertainty in demand has many drivers, including model structure, technological change, socio-economic development, trade, and policies. An under-studied driver is the uncertainty in model parameters estimated on historical data. We use the Global Change Analysis Model (GCAM), an integrated model of land, water, energy, and economy interactions, to investigate the parametric uncertainty in projected food demand. We modify GCAM’s demand functions to better represent regional variation in consumption patterns, disaggregate consumption within regions across income deciles, and re-estimate uncertain parameters. To more efficiently characterize uncertainty, we use the demand functions as an emulator of the full food system in the more complex model and project a large ensemble of demand for staples and non-staples in a GCAM reference scenario. We find that parametric uncertainty in demand, as well as in the response of demand to price changes, is a substantial source of uncertainty in future outcomes and is especially large in low-income deciles. Using scenario discovery techniques, we identify five sets of parameters that effectively span the range of uncertainty across regions and deciles in both demand and its response to price changes. These parameter sets allow GCAM users to capture parametric uncertainty in a small number of scenarios. This uncertainty in demand can substantially affect uncertainty in cropland, water withdrawals, and biomass production in some regions.
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Status: final response (author comments only)
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RC1: 'Comment on egusphere-2026-3848', Anonymous Referee #1, 18 Aug 2026
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AC1: 'Reply on RC1', Brian O'Neill, 16 Sep 2026
Many thanks to the reviewer for very helpful comments. We have copied the full review here and respond to each comment in turn below, with our responses in bold text.
This study modifies the food demand function in GCAM by incorporating regional fixed effects for staples and minimum demand thresholds. In addition, the study quantified parametric uncertainty in food demand projections and developed ambrosia, an independent reduced-form model, to project future food demand. Overall, this work represents a valuable improvement to the food demand module in GCAM. However, several issues that need to be addressed before the manuscript can be considered for publication:
- The food demand changes in this study are primarily driven by income. However, urbanization can also significantly influence food consumption patterns. How do the authors view this effect, and to what extent might the omission of urbanization as a driver affect the results?
We agree that there is evidence that urbanization can affect food consumption independently of income, although it likely impacts composition of consumption more than its level, and its effect is secondary to income. We choose to exclude urbanization as an independent variable in the demand model since GCAM, the modeling framework in which the demand function operates, does not account for urbanization. Our income effects may therefore be partly confounded with urbanization effects (given that urbanization and income are correlated to some extent). Our projections will fail to differentiate scenarios with similar income growth pathways but differences in urbanization.
We will add discussion of urbanization and other variables that could influence consumption to the Conclusions section. This general limitation of the demand model is currently missing from that section.
- Due to the lack of consumption data at the decile level, the study initializes decile consumption using the demand functions and applies a uniform additive bias term. If food consumption patterns vary substantially across income groups and regions, could this simplified treatment introduce significant uncertainty? Would it be possible to validate this approach using household survey data from a subset of countries where such data are available?
The bias term is added in order to ensure that total regional food demand is consistent with observations in the base year. Regarding its implications for uncertainty, this approach treats total base year regional demand as certain, but base year demand at the decile level varies over different parameter sets (since the bias term depends on demand function parameters). We account for base year uncertainty at the decile level in this way (note the uncertainty intervals in decile-level demand in Figure 5, for example).
Nonetheless, it would be valuable to draw on household survey data to supplement (and validate) the approach taken here, which uses national-level consumption data. However, as we note in the Conclusions section, obtaining nationally representative surveys that contain consumption data (quantities, not just expenditures), income, and prices is a large task; we consider it beyond the scope of work here. We will plan to expand the discussion of the benefits of future work with survey data to improve on the approach taken here.
We would also point out that the choice to apply an additive bias term that is uniform across income groups is based on the desire to have all income groups within a given region follow the same demand function as income rises (given prices). This avoids having the consumption of currently low income groups, when their income has grown, differ from currently high income groups.
- The study imposes a minimum demand threshold of 600 cal/person/day for staples. What is the basis for this specific threshold, and how sensitive are the results to alternative threshold values?
The minimum demand threshold is a mathematical device to avoid potentially unrealistic demand at very low incomes, rather than an empirically-based constraint. It was selected to be low enough to allow us to model demand that falls below Minimum Daily Energy Requirements (MDER), an important food security indicator, but not so low as to allow anomalous demand behavior. We briefly mention this on lines 128-132 of the main text and 462-464 of the appendix.
We will edit the text to make sure the rationale for the threshold is clearer, and we will add a sensitivity analysis to the appendix. The starting point will be to quantify the number of cases (demand in a particular region, income decile, and time step) that are affected when the minimum demand is changed. If this is a small number, as we expect, then sensitivity is low. If it is large, then we could extend the analysis by, for example, re-running the GCAM scenarios with an alternative threshold and examining how much the outcomes change.
- In Figure 5, the uncertainty range appears to shrink to near zero around 2050 for certain deciles. Could the authors provide a more detailed explanation of the mechanisms driving this behavior?
The reason for this feature of uncertainty in some regions and deciles is explained briefly in lines 250-254 of the main text, but we will expand this explanation. It is a consequence of the nature of the demand functions and their dependence on parameter values. In low income settings, parameter sets that produce high staples demand (for example) over most time periods (which is a criterion for parameter selection) have low initial demand that increases monotonically over time. In contrast, parameter sets that produce low demand over most time periods begin with high and sometimes increasing demand until it reaches a peak and then declines as consumers substitute away from staples toward non-staples. These alternative patterns reflect historical experience in the data. As a result, an ensemble of demand trajectories across parameter sets produces a crossover point where initially high demand trajectories are trending to lower demand, and initially low demand trajectories are trending to higher demand. This crossover point shrinks uncertainty to a very low level.
- In lines 303–307, the authors note that in a very small number of cases, demand for both staples and non-staples increases simultaneously in response to higher prices—a counterintuitive outcome. Could the authors elaborate further on the underlying causes? Is this a realistic outcome that could occur in practice, or does it reflect a limitation or artifact of the model structure?
This possible but very unlikely behavior of the demand functions is an artefact of their structure. There is nothing in the structure that forbids the combination of parameters that produces simultaneous increases in both staples and non-staples demand in response to increased prices. In addition, the available historical data does not rule out parameter values producing such behavior, although only a very small number of cases are identified in the MCMC estimation. In practice, given that our goal is to identify a small number of parameter sets for further use in GCAM, none of which exhibit this behavior, we do not believe it is a significant issue.
- The authors may wish to add a brief section in the Conclusions that discusses policy implications, particularly regarding how the four alternative parameter sets could be used to inform decision-making under uncertainty in food security or agricultural planning contexts.
We will add text that describes in more detail how other modeling teams could use the parameter sets we produce to generate scenarios that can inform decision-making. As one specific example, the specialized parameters offer an improved way to produce scenarios more likely to be consistent with caloric targets such as those associated with the EAT-LANCET diet.
Citation: https://doi.org/10.5194/egusphere-2026-3848-AC1
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AC1: 'Reply on RC1', Brian O'Neill, 16 Sep 2026
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RC2: 'Comment on egusphere-2026-3848', Anonymous Referee #2, 19 Aug 2026
This manuscript provides a thorough assessment of parametric uncertainty in GCAM food demand projections using Bayesian parameter estimation, large ensemble simulations with the ambrosia emulator, and a scenario-discovery approach to identify representative parameter sets. The study extends the GCAM food demand framework by introducing regional fixed effects and income-decile representation, and demonstrates how uncertainty in food demand propagates to downstream land-use and biomass outcomes. The overall methodological framework is well motivated and generally clearly presented, and the emulator validation is convincing at the aggregate level. Several methodological details and internal inconsistencies, however, should be clarified to improve interpretability and reproducibility.
1) Lines 303-304: The manuscript notes that, in a very small number of cases, demand for both staples and non-staples increases under higher prices due to strong cross-price effects. It would be helpful to briefly indicate whether these rare outcomes materially affect the upper tails of the demand-response distributions shown in Fig. 8, or whether their influence on the reported uncertainty ranges is negligible.
2) Lines 395-396: While overall emulator performance is very good, Table C6 indicates a few cases with weak or negative correlations for price-response outcomes at the decile level. The manuscript briefly acknowledges this issue, but a more detailed explanation of the underlying mechanisms and the practical implications for using ambrosia as a surrogate for GCAM would strengthen the validation discussion.
3) Figure 13: Several inconsistencies appear between the figure, caption, main text, and abstract. The displayed panels show cropland, pasture, and biomass production, whereas the caption refers to cropland, water withdrawals, and biomass production. The displayed regions are the USA, Brazil, and Western Africa, whereas the caption refers to the USA, India, and Western Africa. In addition, the discussion immediately preceding the figure refers to Eastern Africa, while the figure is labeled Western Africa. The abstract also refers to effects on water withdrawals. Please verify these variables and regions throughout and revise the figure, caption, text, and abstract consistently.
4) Lines 430-431： The statement that parametric uncertainty “could be substantial relative to other sources of uncertainty” would benefit from either a supporting comparison from the literature or clarification that this is a qualitative assessment.
5) “5. Code and data availability” The code archive appears to contain the relevant functionality for parameter estimation, but it was not immediately clear which files reproduce the MCMC estimation described in Section 2.2. Consider expanding the README or the Code Availability section with a short guide to the parameter estimation workflow and the scripts used to generate the posterior distributions and ensemble simulations.
Citation: https://doi.org/10.5194/egusphere-2026-3848-RC2 -
AC2: 'Reply on RC2', Brian O'Neill, 16 Sep 2026
Many thanks to the reviewer for very helpful comments. We have copied the full review here and respond to each comment in turn below, with our responses in bold text.
This manuscript provides a thorough assessment of parametric uncertainty in GCAM food demand projections using Bayesian parameter estimation, large ensemble simulations with the ambrosia emulator, and a scenario-discovery approach to identify representative parameter sets. The study extends the GCAM food demand framework by introducing regional fixed effects and income-decile representation, and demonstrates how uncertainty in food demand propagates to downstream land-use and biomass outcomes. The overall methodological framework is well motivated and generally clearly presented, and the emulator validation is convincing at the aggregate level. Several methodological details and internal inconsistencies, however, should be clarified to improve interpretability and reproducibility.
p1) Lines 303-304: The manuscript notes that, in a very small number of cases, demand for both staples and non-staples increases under higher prices due to strong cross-price effects. It would be helpful to briefly indicate whether these rare outcomes materially affect the upper tails of the demand-response distributions shown in Fig. 8, or whether their influence on the reported uncertainty ranges is negligible.
These cases do not have a noticeable effect on the uncertainty distributions. In the main text (lines 301-303) we try to point out that the upper end of the range in total food demand is determined by cases in which one food type dominates, but we will clarify that the case of increases in demand for both types does not affect the ranges in the figure. Also see response to reviewer 1 (comment 5) for further explanation of this behavior.
2) Lines 395-396: While overall emulator performance is very good, Table C6 indicates a few cases with weak or negative correlations for price-response outcomes at the decile level. The manuscript briefly acknowledges this issue, but a more detailed explanation of the underlying mechanisms and the practical implications for using ambrosia as a surrogate for GCAM would strengthen the validation discussion.
We will add explanation of the exceptions in the emulation performance table. Generally these occur when the GCAM scenarios themselves have anomalous behavior, for example GDP growth rates that change significantly from year to year in the Northern South America region (dominated by Venezuela) or in Argentina. In these cases the emulator would not be expected to work as well, and do not necessarily signal a problem for the use of the emulator in other scenarios.
3) Figure 13: Several inconsistencies appear between the figure, caption, main text, and abstract. The displayed panels show cropland, pasture, and biomass production, whereas the caption refers to cropland, water withdrawals, and biomass production. The displayed regions are the USA, Brazil, and Western Africa, whereas the caption refers to the USA, India, and Western Africa. In addition, the discussion immediately preceding the figure refers to Eastern Africa, while the figure is labeled Western Africa. The abstract also refers to effects on water withdrawals. Please verify these variables and regions throughout and revise the figure, caption, text, and abstract consistently.
Thank you for pointing out this mistake. Figure 12 is correct, but the caption and text were not correctly updated relative to a previous version of the figure that was being used. The revised manuscript will fix the caption and text.
4) Lines 430-431： The statement that parametric uncertainty “could be substantial relative to other sources of uncertainty” would benefit from either a supporting comparison from the literature or clarification that this is a qualitative assessment.
We will add comparison to the literature and make this a more clearly quantitative comparison. The parametric uncertainty is comparable to, for example, uncertainty in the climate impacts on consumption in some studies.
5) “5. Code and data availability” The code archive appears to contain the relevant functionality for parameter estimation, but it was not immediately clear which files reproduce the MCMC estimation described in Section 2.2. Consider expanding the README or the Code Availability section with a short guide to the parameter estimation workflow and the scripts used to generate the posterior distributions and ensemble simulations.
We will add a readme file that explains the MCMC code and its use to produce the parameter estimations.
Citation: https://doi.org/10.5194/egusphere-2026-3848-AC2
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AC2: 'Reply on RC2', Brian O'Neill, 16 Sep 2026
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This study modifies the food demand function in GCAM by incorporating regional fixed effects for staples and minimum demand thresholds. In addition, the study quantified parametric uncertainty in food demand projections and developed ambrosia, an independent reduced-form model, to project future food demand. Overall, this work represents a valuable improvement to the food demand module in GCAM. However, several issues that need to be addressed before the manuscript can be considered for publication: