Climate Change, Crop Yields, and Undernutrition: Development of a Model to Quantify the Impact of Climate Scenarios on Child Undernutrition

Background: Global climate change is anticipated to reduce future cereal yields and threaten food security, thus potentially increasing the risk of undernutrition. The causation of undernutrition is complex, and there is a need to develop models that better quantify the potential impacts of climate change on population health. Objectives: We developed a model for estimating future undernutrition that accounts for food and nonfood (socioeconomic) causes and can be linked to available regional scenario data. We estimated child stunting attributable to climate change in five regions in South Asia and sub-Saharan Africa (SSA) in 2050. Methods: We used current national food availability and undernutrition data to parameterize and validate a global model, using a process-driven approach based on estimations of the physiological relationship between a lack of food and stunting. We estimated stunting in 2050 using published modeled national calorie availability under two climate scenarios and a reference scenario (no climate change). Results: We estimated that climate change will lead to a relative increase in moderate stunting of 1–29% in 2050 compared with a future without climate change. Climate change will have a greater impact on rates of severe stunting, which we estimated will increase by 23% (central SSA) to 62% (South Asia). Conclusions: Climate change is likely to impair future efforts to reduce child malnutrition in South Asia and SSA, even when economic growth is taken into account. Our model suggests that to reduce and prevent future undernutrition, it is necessary to both increase food access and improve socioeconomic conditions, as well as reduce greenhouse gas emissions.

Hunger and under nutrition are pervasive, thought to be worsening in absolute terms, and are major contributors to global ill health [Black et al. 2008; Food and Agricultural Organization of the United Nations (FAO) 2009]. More than one billion people are under nourished (FAO 2009), and about a third of the burden of disease in children < 5 years of age is attributable to under nutrition (Black et al. 2008). Economic growth is anticipated by many to reduce future under nutrition (Smith and Haddad 2002), although recent observations do not support this assumption (Subramanyam et al. 2011).
Global food security depends on a range of factors (Schmidhuber and Tubiello 2007), with cereal production playing a major role (Parry et al. 2009). Data suggest that global per capita cereal production plateaued during the 1980s and has since declined (Magdoff and Tokar 2010), despite production increases in some regions (FAO 2011). Further, with eco nomic growth, dietary preferences tend toward greater meat consumption, placing greater demands on cereal production to provide ani mal feed (Msangi and Rosegrant 2011).
Concern is growing that efforts to reduce under nutrition in the coming decades may be threatened by global climate change (Nelson et al. 2010;Parry et al. 2009;Schmidhuber and Tubiello 2007). Scientific assessments indicate that warming will have an overall negative impact on major cereal yields in lowlatitude areas, although yields may increase in some highlatitude areas (Easterling et al. 2007). Climate change could place an additional 5-170 million people "at risk of hunger" by the 2080s (Parry et al. 1999(Parry et al. , 2004Rosenzweig and Parry 1994). Food security is now one of the leading concerns associated with anthropo genic climate change (Parry et al. 2009).
A number of terms are used to describe hun ger and under nutrition. "Undernourishment" is not a health outcome per se; it is a theoreti cal modelbased estimate of access to calories developed by the FAO and is defined as the proportion of people "whose dietary energy consumption is continuously below a minimum dietary energy requirement for maintaining a healthy life and carrying out light physical activ ity with an acceptable minimum bodyweight for attainedheight" (FAO 2010). That is, it has one final cause: a lack of food. "At risk of hun ger" is synonymous with under nourishment.
"Undernutrition" refers to a physical state and is measured using (among other things) anthropometric indices such as stunting (heightforage) and underweight (weightfor age) [World Health Organization (WHO) 2010]. A lack of food-that is, under nourishment-is one of the many causes of under nutrition, which also include poor water and sanitation provision, low levels of women's education, repeated episodes of infec tious diseases, and low birth weight [United Nations Children's Fund (UNICEF 1990); for more details on causes, see Black et al. 2008;UNICEF 1990]. Checkley et al. (2008), for example, estimated that 25% [95% confidence interval (CI): 8, 38%] of irreversible stunting at 24 months of age could be attributed to having had five or more episodes of diarrhea. Although it can be argued that under nutrition itself is not a health outcome, under nutrition can be directly linked to increased risk of death and poor health (Black et al. 2008). Additionally, child under nutrition has long term consequences for the health and earning potential of adults (Victora et al. 2008).
To quantify future health burdens, it is preferable to model under nutrition (which refers to a physical state and accounts for com plex causation) rather than under nourishment (which is a theoretical concept). They are often poorly correlated (Klasen 2006;Svedberg 2002) and this suggests that under nourishment is a poor proxy for under nutrition. The WHO concluded that (using a number of simplify ing assumptions) under nutrition represented a significant proportion of the total burden of disease estimated to be attributable to cli mate change in (McMichael et al. 2004). Only one group has provided more recent quantitative estimates of future under nutrition attributable to climate change. Nelson et al. (2009) Smith and Haddad (2000), which is driven by per capita calorie availability and socioeconomic indica tors: the ratio of female to male life expectancy, female enrollment in secondary education, and access to improved water supply. Future per capita calorie availability was estimated by modeling crop yield and global food trade. All other non climate factors were assumed to stay constant over time (i.e., unchanged from baseline values). These assumptions are likely to have led to an overestimate of the future burden attributable to climate change because this approach assumes that living conditions in countries will improve little over the next 40 years. This is not consistent with historical trends; between 1970 and 1995, 43% of the reduction in child underweight has been attrib uted to improved female education, compared with 26% for increased food availability and 19% from improved water access (Smith and Haddad 2000).
More recently, the same group produced updated estimates for a broader range of sce narios using a similar strategy (Nelson et al. 2010). Based on expert opinion, the socioeco nomic variables driving the underweight model were varied with time but were considered constant across three socioeconomic scenarios broadly representing pessimistic, businessas usual, and optimistic economic growth.
Despite the importance of socioeconomic influences on health, the data currently avail able for climate impact studies are largely lim ited to population and gross domestic product (GDP) projections that were created for esti mating future greenhouse gas emission concen trations. At present, any modeling efforts must work within these constraints. However, atten tion is now being focused on creating a wider range of plausible socioeconomic scenarios for climate impact assessments (Moss et al. 2010).
We developed a parsimonious model for estimating future under nutrition attributable to global climate change, specifically due to its impacts on crop productivity. We then esti mated the future impact of climate scenarios on under nutrition in children for five world regions in Africa and Asia in 2050 using previ ously published estimates of climate changeattributable changes in calorie availability from Nelson et al. (2009). [The more recent esti mates (Nelson et al. 2010) are not included in our assessment because they were released after the completion of our project.]

Materials and Methods
We first describe the development and fit ting of a model for estimating the prevalence of stunting. Second, we outline the process of estimating the proportion under nourished (PoU) using per capita calorie availability esti mates from Nelson et al. (2009). Finally, we discuss the simulation process for estimating future under nutrition attributable to global climate change.
Model development. Our outcome of interest is stunting in children < 5 years of age, because this best captures the impact of condi tions over the long term (Black et al. 2008). Children are considered moderately stunted if they are > 2 SDs below the mean expected heightforage and severely stunted if > 3 SDs below the mean (de Onis and Blossner 2003).
Scenario data are limited essentially to future food availability and per capita GDP, and many causes of stunting cannot be explic itly modeled. We considered stunting to have two main causes, which we refer to as "food causes" and "non food causes." Food causes are represented as PoU, which accounts for climate change effects on calorie availability (via changes in crop productivity) and food access. [Stunting has food causes other than calories, e.g., micronutrient deficiencies (Black et al. 2008), but these are not represented in PoU, nor are they modeled in climatecrop models.] Non food causes are represented as a "black box cluster" of socioeconomic fac tors acting at various levels and represent the wide range of social and demographic causes of stunting, such as low female literacy and poor health care access (Frongillo et al. 1997). Non food causes are modeled using per capita GDP and the Gini coefficient for income dis tribution to generate a "development score," as described below.
The conceptual model is represented by two general equations: [1] for every i, j; k = 2, 3, [2] for every i, j; k = 1, where y ijk is the proportion of children < 5 years of age stunted in country i, in region j, at level k, where k is 1 if no/mild stunting, 2 if moderate stunting, or 3 if severe stunting; x ij is food causes of stunting, represented by the PoU in country i, in region j; and w ij is non food causes of stunting, represented by the "development score" (defined below) in coun try i, in region j. The parameters α k , β k , γ k , and θ k are to be determined: β k is the physi ological relation between under nourishment and stunting (details given below), γ k relates the development score to stunting, θ k relates the interaction between under nourishment and the development score to stunting, and α k is the regression constant.
Equation 1 is a bilinear model because it is a linear function of the independent vari ables (x ij and w ij ) and their product (x ij w ij ). After estimating moderate (y ij2 ) and severe (y ij3 ) stunting, we estimated the proportion not or mildly stunted (y ij1 ) as described in Equation 2.
The "development score" is an indicator of the non food causes of stunting. It is driven by countrylevel projections of future per capita GDP and the baseline (i.e., most recent esti mate available) Gini coefficient (because no projections were available). The development score is scaled from 0 to 1; it equals 0 when socioeconomic conditions are optimal (in terms of avoiding under nutrition) and all under nutrition is attributable to food causes, and it equals 1 when non food causes are at their cur rent (baseline) global maximum [for additional information on development score calculations, see Supplemental Material, Annex 1 (http:// dx.doi.org/10.1289/ehp.1003311)].
To parameterize the equations, we assem bled a global data set obtaining countrylevel under nourishment estimates from the FAO (FAO 2010), per capita GDP and Gini data from the World Bank Development Indicators (WBDI) database (World Bank 2010), and stunting data from the WHO's Global Database on Child Growth and Malnutrition (WHO 2010).
Stunting data were matched to under nourishment data to within a 1year period. Per capita GDP and Gini coefficient estimates were matched as closely as possible to the stunting data year. The data set covered the period 1988-2008 and contained 186 records with complete data. Countries were included in the data set more than once if they had data for multiple years.
Fitting the model. We decided, a priori, to use a processdriven (theorybased) rather than a standard datadriven (statistical) approach to develop and parameterize the model equations. The purpose of the model is to describe plausible futures, so we designed it to be driven as much as possible by relation ships that will be stable over time.
Of the two model variables, we assumed that food causes have a more stable relation ship with stunting than do non food causes because food causes are physiologically related to stunting, and it is reasonable to assume that this relationship will hold over the next 50 years. In contrast, we assumed that non food causes-which we modeled using per capita GDP and the Gini coefficient-do not necessarily have a stable relationship with stunting because the relationship is mediated, at least partly, by social and political factors that may change over time. Therefore, when fitting our model, we first quantified the rela tionship between stunting and food causes and then considered socioeconomic factors.
We assumed that if someone had insuffi cient food, and non food causes of stunting were absent (i.e., socioeconomic conditions were optimal in terms of avoiding under nutrition), there would be a predictable risk of stunting; that is, we assumed the relationship between food intake and stunting is physiologically determined and holds globally. This assumption is supported by ample evidence that, at least until 6 years of age, all adequately nourished and optimally cared for children will have simi lar, predictable growth rates (WHO 2006). In addition to this food intake-related burden, if socioeconomic conditions are poor, there is an additional risk of stunting from non food causes and their interaction with food causes, for example, high rates of diarrhea associated with inadequate sanitation. We do not consider it probable that a country will lack sufficient food but otherwise have "optimal" socio economic conditions; our conception is theoretical.
Using the data set, we estimated the pre dictable but unknown physiologically based relationship between under nourishment and stunting at level k (β k ) as (The operator min i,j {•} means the minimum of the argument in {•}.) This minimum pro portion was obtained by finding the mini mum value of the ratio of y ijk to x ij among all the countries in all regions, where, as defined above, y ijk represents the proportion stunted < 5 years of age in country i, in region j, and stunting level k; and x ij represents the pro portion of the population under nourished in county i, in region j. Because it is unlikely that all stunting in a country is caused by food causes alone, our estimate of β k will be an overestimate of the purely physiological relationship between food and stunting. In practice, because the minimum observed value may be too low because of data errors, we chose to use the 5th percentile of the distribution of y ijk /x ij as the best estimate of β k and used the 1st and 10th percentiles as the boundaries of its plausible range (see "Estimating future stunting," below).
Once the above relationship was found, onefifth of the data set (37 records) was ran domly selected and reserved for model valida tion; the remainder (149 records) was used to parameterize the equations. (To obtain the best possible estimate, and considering that our method of estimation provides a rough approximation, we used the entire data set to estimate β k .) We parameterized the equations in a step wise manner. In the first step, we used β k to attribute a proportion of stunting to food causes in all countries in the parameterization data set: where r ijk is the proportion of stunting attributable to food causes in country i, in region j, at level k.
In the second step, we attributed the remaining proportion of stunting to non food causes and the interaction between food and non food causes: where s ijk is the proportion of stunting attrib utable to non food causes and the interaction between food and non food causes in coun try i, in region j, at level k. We then used lin ear methods to estimate the parameters (α k , γ k , θ k ) of the bilinear model: The model was validated by comparing levels of stunting predicted by the model to observed stunting in the reserved portion of the data set (37 records).
For α k , γ k , and θ k we used the standard errors of the estimates to describe the plau sible range of their true values. We carried out our analysis with Stata (version 11; StataCorp, College Station, TX, USA).
Estimating future population under nourished. The model required estimates of future PoU with and without climate change. Calculation of PoU requires data for a) the coef ficient of variation for withinpopulation calorie distribution, b) the average minimum calorie requirements to avoid under nourishment in the population, and c) per capita calorie avail ability (FAO 2003). Because projection data for a) and b) are not available, we assumed they remain at baseline levels. For c), we used esti mates made by Nelson et al. (2009) (2000)]. The two climate scenarios were used to address uncertainty in the climate system; the NCAR model is warmer and wetter than the CSIRO model. The global average increases in maximum temperature and precipi tation over land by 2050 were 1.9°C and 10%, and 1.2°C and 2% for the NCAR and CSIRO scenarios, respectively. For details of the assumptions in the crop modeling (e.g., carbon dioxide fertil ization, irrigation, and adaptation responses), extrapolations to other food groups, and the trade model, see Nelson et al. (2009). For additional information on PoU estimation, see Supplemental Material, Annex 2 (http://dx.doi. org/10.1289/ehp.1003311).
Estimating future stunting. The principal input to our simulation model was future countrylevel PoU derived from Nelson et al. (2009). We ensured withinscenario consis tency by using the same GDP (G. Nelson To account for parameter uncertainty, we used a standard Monte Carlo approach. Each of α k , γ k , and θ k were assumed to be nor mally distributed about their point estimates as defined by their respective standard errors. β k was assumed to be uniformly distributed between the 1st and 10th percentiles of the distribution of y ijk /x ij . This method produced probability density functions (PDFs) of future stunting.
We aimed to base each PDF on 100,000 estimates. We selected the first 100,000 esti mates that were > 0 and < 1. By rejecting low and high estimates, we potentially intro duced an upward or downward bias; to assess this, we quantified the proportion of rejected results [see Supplemental Material, Final estimates were produced at the regional level for South Asia and four regions in subSaharan Africa [SSA; central, east, south, and west; see Supplemental Material, Table 2 (http://dx.doi.org/10.1289/ehp.1003311)]. We aggregated stunting from the country to regional level using population weighting. We ran the simulation using MATLAB (version 2009b; MathWorks, Natick, MA, USA). Table 1 summarizes the data set used to parameter ize our model. The correlation coefficients between stunting and PoU were 0.16 and 0.19 for moderate and severe stunting, respec tively. For univariate analysis of stunting and the development score, R 2 was 0.40 for mod erate stunting and 0.45 for severe stunting; when PoU was added to these models, R 2 was unchanged. That is, using a datadriven approach, including PoU as an explanatory variable would not improve the model fit to estimate stunting in the present compared with using the development score alone. This supported our approach using a theorybased model that accounts for both food access and socioeconomic conditions. The model parameter estimates are shown in Table 2. The β parameter is an estimate of the assumed physiological relationship volume 119 | number 12 | December 2011 • Environmental Health Perspectives between a lack of food and stunting. Thus, the central estimate of β = 0.35 for moder ate stunting suggests that for every 1% of the population who are under nourished, on aver age 0.35% of children < 5 years of age will be moderately stunted. Using the validation data set, the predicted and observed values are well correlated, with correlation coefficients of 0.78, 0.66, and 0.80 for no/mild, moderate, and severe stunting, respectively [for scatter plots, see Supplemental Material, Figure 1 (http://dx.doi.org/10.1289/ehp.1003311)].

Estimates of future proportions under nourished.
The proportions of regional pop ulations projected to be under nourished in 2050 are shown in Table 3. Countries for which complete data were not available were excluded [see Supplemental Material, Table 2 (http://dx.doi.org/10.1289/ehp.1003311)]. The estimates suggest that climate change will increase PoU compared with a future without climate change, and also that climate change and population growth will increase it to above current levels in all regions.

Projections of stunting in 2050.
We estimate that climate change will increase stunting in all regions (Table 3), with severe stunting increas ing by 30-50%. The estimated relative change in stunting was smaller than the estimated rela tive change in under nourishment. Figure 1 shows the uncertainty in the stunting estimates as histograms of probabilistic outcomes derived from the Monte Carlo simulation.
We compared our stunting estimates with underweight estimates made by Nelson et al. (2009) (Table 4). The results are not directly comparable, but we have assumed that the ratio of underweight to stunting at baseline remains constant in the future. The final column shows this ratio as a regional, populationweighted average calculated using the most recent estimates of underweight and stunting (FAO 2010).

Discussion
We have developed the first global model to estimate the impact of climate change on future stunting-a more relevant outcome measure for human population health than "population at risk of hunger" (i.e., under nourishment) or underweight. Additionally, our model distin guishes moderate from severe stunting, which bring substantially different health risks (Black et al. 2008). Based on our conservative assump tions, the model suggests that climate change will have significant effects on future under nutrition, even when the beneficial effects of economic growth are taken into account. This is particularly so for severe stunting, with a 62% increase in South Asia and a 55% increase in east and south SSA. The health implica tions of this are large: according to Black et al.  β k is the physiological relation between undernourishment and stunting [5th percentile (1st-10th percentile)]; α k is the regression constant, γ k relates the development score to stunting, and θ k relates the interaction between undernourishment and the development score to stunting (regression estimate ± SE). (2008), moderate stunting increases the risk of allcause death 1.6 times (95% CI: 1.3, 2.2) and severe stunting increases the risk 4.1 times (95% CI: 2.6, 6.4). Comparing our results with those of Nelson et al. (2009) should be done cau tiously because the outcome measures are dif ferent. Our estimates for stunting are lower than estimates from Nelson et al. (2009) for underweight in both South Asia and SSA (Table 4). Our estimates for SSA are closer but still lower. It is likely these differences are largely explained by how the models account for socioeconomic conditions. Nelson et al. (2009) estimated underweight using a complex model that accounted for many socio economic factors, but because of a lack of data, all the factors (except for food access) were held at baseline levels. Our stunting equation repre sents socioeconomics more simply but is able to account for expected changes over the next 40 years. World Bank projections suggest that in South Asia, GDP will increase nine times between 2005 and 2050-an absolute increase of about $7,000 billion (year 2000 US$); in SSA the figures are five times and $1,700 bil lion. Hence, allowing for these changes results in lower future stunting estimates, with a greater reduction in South Asia.
Model approximations and assumptions. We used a theorybased rather than statisti cally based approach to modeling. Although we accept that a statistical approach would  a Calculated as [(moderate + severe underweight)/(moderate + severe stunting)] using data for the present (FAO 2010) and as a regional, population-weighted average. b Underweight estimates for 2050 are from Nelson et al. (2009). c Stunting estimates are the sum of the numbers moderately and severely stunted, based on the mean estimates of the empirically derived PDFs.
volume 119 | number 12 | December 2011 • Environmental Health Perspectives be sound if our aim were to estimate current stunting, our aim was to estimate future stunt ing. Thus, we developed a model that was driven as much as possible by a relationship that can reasonably be expected to remain con stant over time. We assumed that the physi ological relationship between stunting and under nourishment will remain constant and approximated this relationship in the first step. After this, because the relationship between stunting and GDP (which is mediated by, among other things, political and social con ditions) may vary significantly over time, we fitted the development score and interaction term as a second step. We made several key approximations in constructing the model. The first approxi mation was to fit a separate bilinear regres sion model to two of the stunting levels and then use these to estimate no/mild stunting. Although a more rigorous approach would fit the three regression models simultane ously while ensuring that the proportions (for each country) are positive and always add up to unity, this could lead to an imbalance in the goodness of model fit of one level at the expense of another. The second approximation was to treat the food causes and the product of the food causes and non food causes as two independent variables in the least squares fit. This, of course, would introduce errors because the variables are correlated. Nevertheless, the approximation was validated against a data set different from that on which it was based. The third approximation concerns the approach we adopted for the probabilistic (Monte Carlo) simulations. Simulated values that were either < 0 or > 1 were discarded. This could intro duce bias, and we quantified this potential. No estimates were rejected for being > 1, mean ing there is no risk of downward biasing. For estimates < 0, no moderate stunting estimates were rejected, but severe stunting estimates were rejected in all regions [see Supplemental Material, Table 1 (http://dx.doi.org/10.1289/ ehp.1003311)], meaning there is some poten tial for upward bias. Because more estimates were rejected in the "no climate change" future compared with the "climate change" future, this may have reduced the apparent impact of climate change on severe stunting.
The fourth approximation was the estimate of the physiological relationship between stunt ing and a lack of food (as represented by under nourishment). We ran our model assuming that a uniform distribution of values between the 1st and 10th percentile of the ratio of stunting to under nourishment adequately represented the true value. In support of our estimates, our parameters suggest that about 60% of stunt ing could not be directly attributed to a lack of food; this is in line with previous estimates that around 40-60% of under nutrition could be attributed to environmental conditions (predominantly a lack of water and sanitation) (PrussUstun and Corvalan 2006).
Although a more elaborate approach could have been used, inevitably there is always a tradeoff between model complexity and ease of model use. We have tilted more toward model simplicity but at the same time quanti fied the errors induced by the approximations, as far as possible.
We made estimates of future under nourishment from projected calorie availability. In doing so we assumed that both withincoun try food distribution and average minimum calorie requirement remained at baseline levels. In support of these assumptions, we note that FAO estimates of withincountry food distribu tion are based on extrapolations of infrequently collected data from relatively few countries and are restricted to lie between values represent ing a given maximum and minimum equity of distribution (based on estimated require ments). Varying values within this range has been found to have little impact on PoU in countries with low calorie availability (FAO 1996;Svedberg 2002). Considering mini mum calorie requirements, the estimated mean change in requirements across all countries was just 0.1% per year over the period 1990-1992-2006(FAO 2010. Further, accord ing to FAO data (FAO 2010), the average minimum calorie requirements are increasing in most lowincome countries and are higher (and increasing) in middleincome countries. This means our estimate may be conservative. Finally, Svedberg (2002) estimated that over a 20year period, 88% of the change in regional under nourishment was explained by changes in per capita calorie availability.
We assumed that, once per capita GDP reached $10,000 (2000 US$; with an associ ated Gini coefficient of 0.38), socioeconomic conditions no longer contributed to stunt ing. We tested the sensitivity of the model to this assumption by rerunning it without this assumption. This made a negligible difference to estimates (data not shown).
Finally, a limitation of the overall model ing strategy is that climate change is assumed to enter the system only through its impact on crop production. First, this allows only a par tial consideration of future food security: food availability and, to a degree, access are mod eled, but stability and utilization are not (for a discussion, see Schmidhuber and Tubiello 2007). Second, climate change is likely to affect under nutrition by a variety of routes, including plant diseases, extreme drought events, infectious disease, labor productivity, water availability, and overall impact on GDP. So far, these aspects have not been accounted for, and we recommend that future assess ments (of all health impacts, not just under nutrition) attempt to account for the multiple effects of climate change.
Model behavior. We examined model behavior over the range of plausible input vari able values. When either under nourishment or the development score are high (a high develop ment score indicates poor socio economic conditions), moderate stunt ing decreases. However, this is accompanied by increases in severe stunting, provid ing that under nourishment is not too high [for the model's equations surface plots, see Supplemental Material, Figure 2 (http://dx.doi. org/10.1289/ehp.1003311)]. As with any model, output for input variable values falling outside the range within which the model was fitted should be interpreted with caution. In the data used to parameterize the equations, the maximum value for under nourishment was 76% (Table 1), and the surface plots suggest that above this value, stunting estimates may be invalid. In our future estimates, only under nourishment in central SSA under climate change exceeded this (80% and 81%; Table 3); although these PoU estimates are only just out side the fitting range, the resulting stunting estimates should be interpreted cautiously.
The model's equations suggest that, as either food access or general socioeconomic conditions worsen, severe stunting increases more rapidly than moderate stunting; that is, more children shift from moderate to severe stunting than shift from no/mild stunt ing to moderate stunting. It is likely that this behavior is partly because the model assumes that, regardless of conditions, the distribu tion of access to food remains constant. This assumption is a property of the FAO under nourishment model (FAO 2003) and of our development score (i.e., the Gini coefficient is assumed to remain constant at baseline levels). We believe that allowing distributions to vary should be considered in future work.
The θ parameters have negative values. This was unexpected but, when considered in the context of the full equation and in terms of observed model behavior, the model equa tions predicted stunting changes as expected. Thus, if either food or non food causes are high and those causes are then reduced, the impact on stunting is greater than if both food and non food causes are high and only one vari able is lowered. This suggests, as expected, that to best deal with stunting it is necessary to address both food and non food causes.
Dealing with uncertainty. It is axiomatic that there are uncertainties in any risk assess ment model. In this assessment, we have addressed parametric uncertainty in the stunting model through the use of Monte Carlo simula tions. Structural uncertainty will be addressed in future work by exploring non linear interactions. It was not possible to assess the uncertainty in the upstream models (e.g., climate models, crop models, trade model) that drive our model (i.e., the input uncertainties associated with x ij and w ij ) because we lacked the necessary infor mation. Future assessments should use a wide range of climate and socioeconomic scenarios in order to capture the uncertainty of future emission pathways and the world in which the climate impacts will occur.

Conclusions
Previous studies have shown that climate change is likely to have negative effects on future hunger and under nutrition (Nelson et al. 2009(Nelson et al. , 2010Parry et al. 1999Parry et al. , 2004Rosenzweig and Parry 1994), and our results are consistent with these. This reinforces the evidence base for action to be taken to reduce carbon emissions and the impacts of the cli mate change to which we are already commit ted. Additionally, our model suggests that to reduce and prevent future under nutrition, it is necessary to both increase food access and improve socioeconomic conditions.
Quantifying the size of the impact pres ents difficulties. Our work illustrates the importance of the outcome considered-for example, under nourishment versus stunting, and moderate stunting versus severe stunting. These outcomes have different implications for adaptation and decision making (e.g., whether adaptation policies should focus only on food supplies or consider water and sani tation provision) and different implications for health (e.g., severe stunting is a much greater health threat than is moderate stunt ing). Further, future socioeconomic condi tions must be considered; this involves both developing new data sets and designing mod els that recognize data constraints. Above all, because none of the above issues will be easily overcome, modeling efforts should explicitly describe their assumptions and limitations.