A review of global-local-global linkages in economic land-use/cover change models

Global change drivers of land-use/cover change (LUCC) like population dynamics, economic development, and climate change are increasingly important to local sustainability studies, and can only be properly analyzed at fine-scales that capture local biophysical and socio-economic conditions. When sufficiently widespread, local feedback to stresses originating from global drivers can have regional, national, and even global impacts. A multiscale, global-to-local-to-global (GLG) framework is thus needed for comprehensive analyses of LUCC and leakage. The number of GLG-LUCC studies has grown substantially over the past years, but no reviews of this literature and their contributions have been completed so far. In fact, the largest body of literature pertains to global-to-local impacts exclusively, whereas research on local feedback to regional, national, and global spheres remain scarce, and are almost solely undertaken within large modeling institutes. As such, those are rarely readily accessible for modification and extension by outside contributors. This review of the recent GLG-LUCC studies calls for more open-source modeling and availability of data, arguing that the latter is the real constraint to more widespread analyses of GLG-LUCC impacts. Progress in this field will require contributions from hundreds of researchers around the world and from a wide variety of disciplines.


Background and motivation
The world's land resources are critical to the attainment of various Sustainable Development Goals (SDGs) of the Agenda 2030 (Obersteiner et al 2016), but are under intense pressure from growing populations and rising per-capita consumptions (Godfray and Garnett 2014). Can the future demands for food security, renewable energy, clean water, conservation of biodiversity, climate change mitigation and poverty reduction be reconciled? Are we counting on the same area of land to satisfy conflicting SDGs? The sustainable development challenge-as viewed through the lens of the world's land resources-is a particularly 'wicked' problem because global sustainability solutions depend on national, regional or local circumstances, requiring fine-scale analyses of land-use/cover change (LUCC) 5 .
Even as local LUCC processes are often driven by remotely emanating global forces, regional responses to these pressures and the pursuit of local sustainability goals can, in turn, result in cross-border and international leakage (spillover) effects 6 , i.e. land initiatives in one place stimulating LUCC elsewhere (Delzeit et al 2018). Such leakage from national or subnational policies may affect the wider availability of land-based commodities and their prices, as well as local, regional, and global social and environmental conditions. Addressing these issues requires a multiscale approach that recognizes the linkages between global drivers and local responses (Rounsevell et al 2012), and their feedback at the regional, national, and global levels, i.e. global-to-local-to-global (GLG) analyses. While this terminology has gained recent attention in other fields, e.g. medical geography (Blatt 2015), it remains incipient in the LUCC literature.
Within the GLG-LUCC framework outlined in figure 1, global drivers represented by population dynamics, economic (and technological) development, and climate change shape global markets and migration patterns (Hunter et al 2015). These drivers affect global supply and demand for land-based resources, resulting in changes in international prices, as well as cross-border flows of commodities, capital and labor. The impacts from those drivers are filtered by national and subnational environmental and economic policies and institutions (e.g. exchange rate and trade regulations as well as land tenure) and market integration. National and subnational contexts, defined by natural resource availability, infrastructure and technology transfer, socioeconomic conditions (e.g. population size, income and education levels) and preferences (e.g. dietary choices, environmental and social awareness), modulate the impacts of global drivers on regional or local stressors. Once the impacts of global drivers reach domestic producers and consumers, they may induce production and behavioral changes related to land use/cover and socioeconomic preferences (e.g. for animal-sourced food) and conditions (e.g. income growth and energy consumption).
Negative impacts can result, for example, in overexploitation of natural resources, agriculture-induced water scarcity, higher food prices, exacerbated land conflicts, and socioeconomic hardship. Consequently, the impacts of global drivers are often followed by national or subnational responses such as changes in governance and regulations, as well as technological innovation, which can, in turn, feedback to the global level (figure 1).
The GLG-LUCC framework acknowledges that local impacts and responses can have important implications, not only locally or regionally, but also at the national and-often overlooked-global levels. If these responses are strictly localized, then it is unlikely that the feedback to international prices will be significant. However, if many localities respond to the influence of global drivers, GLG-LUCC feedbacks might affect global environmental and economic dynamics substantially. An example of this is provided by Liu et al (2017) who examine the impact of widespread irrigation water withdrawal restrictions on global food prices, food security and cropland conversion.
This review presents a summary of the recent history and status quo of the LUCC literature that has addressed key GLG linkages and feedbacks illustrated in our proposed GLG-LUCC framework (figure 1). Conceptual framework for global-to-local-to-global linkages of land-use/cover change. Global drivers, including population, income, climate, and technology drive the global supply and demand for land-based products, resulting in new market equilibria, price changes, and migration. When filtered through the national and subnational policies, global effects result in local stresses and responses which affect enterprises, households, and the environment, leading to policy changes and innovations, as well as to adjusted supplies and demands for land-based goods. Finally, the resulting changes in land use/cover attributed to both local and global factors may feedback to the global context. Our summary is complemented by a systematic review of recent and prominent peer-reviewed publications. By focusing on economic modeling of LUCC, our review does not capture context-specific social and political forces that often initiate LUCC at agricultural frontiers. As such, the lower panel of figure 1 identifies a set of forces that influence land use decisions at national level after land claims have been established. Finally, the review aims to identify literature gaps and outline future research directions to improve understanding and integrate the GLG framework into LUCC studies.

Methods
We conducted a systematic search for peer-reviewed articles published between 2009 and 2018 in ISI Web of Knowledge. We adopted a Boolean searching key 7 to filter unrelated climate, biodiversity, hydrology, and geology studies from the ones focused on LUCC. This search identified 727 articles, which were successively screened based on their titles, keywords, and abstracts, in accordance with the PRISMA approach for systematic reviews (Chatterjee et al 2018). For instance, many identified articles focused solely on global-to-local links, with no regard to local feedback, whereas others presented merely theoretical perspectives (e.g. on environmental governance and certification schemes) or even, despite our searching key, addressed issues unrelated to GLG-LUCC (e.g. satellite-mapping techniques, lifecycle analysis, and biological, geological or climate studies) or issues related to urbanization, which is considered out of the scope of this review. Those articles were excluded. Lastly, we adopted an additional filter based on the number of citations per year (10 yr −1 ) as an attempt to select the most prominent studies in the field (articles published in 2018 were scrutinized independently of the number of citations). The remaining 96 publications were added to a preliminary list for further screening. Of the list of identified studies, 81 articles addressing issues relevant to GLG linkages are referenced in this review. In addition to the systematically-selected recent publications, we also included what we consider key 'building block' studies (70 in total) that developed the basis for GLG analyses in the field of LUCC to provide a historical perspective on the topic or that complements our discussion, which led to the 151 articles cited in this review (figure A1). Table 1 provides an overview of the current GLG-LUCC literature based on this survey, along with key gaps and a discussion of future directions for GLG-LUCC studies, to which we refer in the subsequent sections of this review.

Results and discussion
Food production is one of the most common land uses worldwide. Agricultural products are widely traded, and cropland conversion for farming is one of the major drivers of LUCC, particularly in the tropics (Busch and Ferretti-Gallon 2017, Curtis et al 2018). As a result, and due to the focus of the modeling literature, our systematic review was largely populated by global agro-economic studies based on computable general equilibrium (CGE) and partial equilibrium (PE) models, with a lesser representation of studies focused on forestry or other land-based sectors and alternative methodologies (e.g. empirical studies).

Global LUCC models: a historical perspective
The first LUCC models, dating back to the 1960s, focused on the quantification of world food budgets and prospects for food production, emphasizing food availability rather than land uses (FAO 1962). The food crisis of the early 1970s led to the Club of Rome report (Meadows et al 1972) and an emphasis on finite land resources which were expected to be overtaken by a rapidly growing population. However, as with Malthus' (1798) original predictions, this work was eventually discredited as being overly pessimistic. The 1980s saw a flourishing of global agro-economic CGE and PE models such as IMPACT (Rosegrant et al 2008), GOL (Rojko 2017) andBLS (Fischer andFrohberg 1982). Of those, only the latter acknowledged the finite nature of land resources through endowment constraints considered at an aggregated regional level.
It was not until the 1990s that global LUCC models started to focus explicitly on the competition for land between agriculture and other activities within diverse agro-ecological zones (AEZs), such as the FARM model. FARM was developed at the United States Department of Agriculture (Darwin et al 1995) and built on the Global Trade Analysis Project (GTAP) database and modeling framework (Hertel 1997). The model was used by Darwin et al (1995) to investigate future climate impacts not through productivity shocks to existing crops (which was commonly studied), but rather as changes in the distribution of lands across AEZs. This novel, land-focused approach to global modeling sharpened the focus of LUCC models to AEZ land endowments, the activities undertaken within different AEZs, and their simulated responses to climate change. Findings from these type of studies typically emphasized the role of international trade in mediating LUCC and leakage effects between regions when the productivity and abundance of individual nations' land endowments are differentially affected 7 TS=(('land-use change' OR 'land use change' OR 'land-cover change' OR 'land cover change' OR 'land-use/cover change' OR 'land use/cover change' OR deforestation) AND model AND (economic OR simulation) NOT hydro * NOT runoff NOT fluvial NOT fish * NOT wildlife NOT habitat NOT species NOT precipitation NOT urban NOT climatolog * NOT atmospher * NOT meteorolog * NOT water * NOT wind NOT air NOT albedo NOT chemistry NOT physics NOT soil NOT geomorpholog * ). by biophysical forces, policies, and technological change (Reilly et al 2003. Roughly in parallel to the development of the FARM model, Sohngen and Mendelsohn (1998) introduced the Global Timber Model (GTM). By incorporating forest growth and harvesting dynamics into an economic model, the authors were able to examine a wide range of LUCC issues related to the forest sector. The GTM became an important tool for understanding the potential for forest carbon sequestration as part of a more comprehensive global climate policy (Sohngen 2010). The GTM is driven by global projections of growth in income and population. However, since the model represents consumption with one composite global timber demand function, it has been used less extensively for global leakage assessments since it does not specifically capture bilateral trade between regions of the world. Of necessity, it also aggregates regions to a much higher degree due to the computational challenges presented by a fully dynamic economic model (Sohngen and Mendelsohn 2003).
Growing interest in more comprehensive assessments of climate change mitigation (i.e. extending beyond fossil fuel emissions) promoted a series of longterm research projects aimed at building databases and modeling infrastructure for the analysis of land-based interventions . The GTAP-AEZ database and modeling framework resulted from that initiative (Lee et al 2009), forming the basis for much of the global LUCC studies focused on agricultural trade since that time (Schmitz et al 2014). Given the high degree of disaggregation (the current GTAP-AEZ database considers 140 national/subnational regions, with up to 18 AEZ each), the comprehensive treatment of greenhouse gas (GHG) emissions, the national representation of consumption, and the bilateral treatment of trade, the GTAP-AEZ-GHG models quickly assumed global prominence in leakage and indirect LUCC studies, in particular with the implementation of new biofuel mandates in the US and EU Another direction of global LUCC research over the past decade emanated from the earth system modeling literature, in particular, from improved representations of terrestrial ecosystems and the carbon fluxes associated with LUCC processes (Hurtt et al 2011). That literature is traditionally based on global gridded analyses and the developments in global circulation models undertaken in support of climate-related research (Intergovernmental Panel on Climate Change IPCC 2014). The initial demand for global-gridded LUCC projections was supported by downscaling regional results to the grid-cell level, allowing for the exploration of GLG-LUCC linkages at much higher resolutions (Reilly et al 2012, Schmitz et al 2014, Doelman et al 2018, Porfirio et al 2018. In addition to downscaling results, much of the literature also focused on upscaling local effects of climate impacts on land-based activities from global grids (Rosenzweig et al 2014). At the regional scale, a number of influential gridded simulation models have been developed and applied to assess future LUCC at high-spatial resolution and under alternative economic and policy scenarios (Verburg et al 2002, Soares-Filho et al 2006, Lapola et al 2010. A notable effort in this area is the Dynamic Conversion of Land Use and its Effects model (Dyna-CLUE) presented by Verburg and Overmars (2009). Dyna-CLUE integrates the allocation of topdown, multi-sectoral demand-driven LUCC with a bottom-up determination of conversions for specific land-use transitions at the grid-cell level and time considerations for natural vegetation regrowth. This 'softlinking' approach allows accounting for very detailed local and regional determinants of LUCC, but tends to ignore local-to-global feedback (Rutten et al 2014).

A gridded view of the world in economic LUCC models
Until recently, most of the global LUCC analyses relied on the downscaling of regional results in order to make predictions at the grid-cell level. Where gridded biophysical model results were required for use in the global model, they were aggregated to the level of the regions considered by the global models. Such approaches clearly limit the scope for full exploration of GLG linkages and raises questions of conceptual, data, and computational consistency. In response to these limitations, the Potsdam Institute for Climate Research (PIK) group developed the MAgPIE model . The objective function of MAgPIE is to satisfy agricultural demand for food, feed, bioenergy, and materials from ten world regions at minimum global costs (including the cost of capital, labor, inputs, investments in technology, and mitigation of GHG emissions), and given biophysical and socio-economic constraints. Cost-effective LUCC decisions at the grid cell-level are endogenous and based agricultural intensification, expansion, and relocation or trade (Kriegler et al 2017).
MAgPIE was later coupled with REMIND, also developed at PIK, resulting in the integrated assessment modeling framework REMIND-MAgPIE (Popp et al 2011). REMIND is an energy-economic equilibrium/macroeconomic growth model based on  The ever-growing demand for spatial disaggregation has been constrained both by data availability and by computational considerations (Lee et al 2015). Yet, given the rapid pace of improvement in both software and hardware, it is reasonable to expect computational constraints to diminish significantly in the near future. However, the collection and access to disaggregated (local) socioeconomic data is another matter. Hence, with some exceptions including agent-based modeling methods (Valbuena et al 2010, Murray-Rust et al 2014, West et al 2018, grid-based models coupled with agro-economic PE or CGE models are currently at the frontier of global and regional GLG-LUCC analyses. By integrating local biophysical, economic, and institutional information into a global framework, complex gridded models-developed by large research institutes and teams of collaborators-represent the most suitable approach to explore both the global drivers of local LUCC, as well as the feedback from national and subnational interventions to the global level

Global drivers in GLG-LUCC studies
The global-to-local focus dominates the LUCC literature; these studies conceptualize or quantify the effect of exogenous global drivers on national or subnational contexts. Climate, economic development, and population are commonly represented global drivers in LUCC studies, particularly among the ones based on agro-economic equilibrium models ( hidden) basic model parameters such as income and price elasticities, that define market behavior, besides data limitations on economic behavior and biophysical drivers. In addition, Hertel et al (2016) found that the ten models employed in the AgMIP inter-comparison exercise apply very different assumptions about the potential for intensification of production and cropland expansion. Moreover, in a recent study based on simulations from 18 LUCC models, the authors ascribed much of the differences in land-cover area projections (particularly in croplands) with the lack of consistency in the definitions of pasture and forest (Alexander et al 2017). The same authors also highlighted that similar model types are also more likely to share similar underlying assumptions and other commonalities, e.g. same model calibration data.
Which of the global drivers is most important in determining global-and regional-patterns of LUCC? Baldos and Hertel (2016) offer a decomposition of the drivers behind global cropland change over the period 1961-2006. They find that population growth was the dominant driver-far more important than income growth-with improved technology offsetting about half of the upward pressure on cropland expansion stemming from the population and income growth. This stands in contrast to the postulated 'Jevons paradox,' which suggests that improved technology might actually increase cropland use (Alcott 2005). These authors also consider LUCC projections to mid-century, for which they conclude that income growth will rival population growth as the major driver of future cropland expansion. This expected change is due to two main factors: (a) a slowdown in global population growth, and; (b) a shift of the composition of population growth towards lowincome regions (e.g. Africa), where current per-capita food consumption remains modest. Projections also suggest that bioenergy, water scarcity, and urbanization are likely to contribute far less to global LUCC.
While global drivers, such as population and technology, are often exogenous in LUCC studies and, in particular, in global agro-economic models, exceptions can be found. Moreover, policy scenarios can be simulated either with exogenous regulations that imply endogenous demand adjustments or with exogenous demand targets endogenously defining regulatory levels (Lefèvre et al 2018). Table 1 summarizes the key papers in our systematic review that study the global feedbacks of local responses to local stressors initiated by drivers of global change discussed in the previous section. An increasing number of theoretical and empirical studies consider bi-directional connections or 'telecoupling' between remote regions (Liu et al 2013). Telecoupling exists when market or non-market linkages between regions translate interventions or shocks in one region into corresponding changes in another. In seminal work, (Yu et al 2013) estimated 33%, 50%, and 92% of the total land use for consumption in US, EU, and Japan to be displaced from other (developing) countries, respectively. In contrast, agricultural lands in Brazil (47%) and Argentina (88%) are estimated to be driven by consumption demands outside of their territories, mainly in EU and China. Moreover, the same authors highlight that highly-populated emerging economies like China and India are likely to continue increasing land demands, which are expected to be met by African and Latin American countries, and Russia. Similarly, Yao et al (2018) applied a telecoupling framework to analyze the economic and environmental consequences of the Brazilian soy boom. They found the Chinese macroeconomic growth to have boosted soybean production and exports from Brazil and the US. Soy productivity growth and the associated area expansion in Brazil were also associated with a loss of US soy market share in the Chinese market and reducing soy production growth in the US. Telecoupling can also affect domestic patterns of LUCC. For example, da Silva et al (2017) demonstrate how the increase in international soy trade between Brazil and China led to changes in the Brazilian maize production.

GLG linkages: responses and feedbacks in LUCC studies
As a result of telecoupling, national or subnational interventions to promote sustainable land use or conservation may have unintended and indirect spillover effects within and across countries, depending on regional and international trade linkages (Meyfroidt et al 2013). A well-studied example of such local (national) to global LUCC effects is the impact of US and EU biofuel policies on other crop producing world regions You 2018, Somé et al 2018). These policies represent national responses to expected climate change-related stressors and looming fossil fuel scarcity. The renewed impetus of US and EU biofuel policies in the wake of oil price rises after 2006 sharply focused attention on the nature of the market teleconnections leading to LUCC leakage (Searchinger et al 2008). Searchinger et al (2008) used a PE model of the world economy based on integrated global markets for agricultural commodities (i.e. the law of one price). Simulations suggested that countries with larger areas (China, India, and Brazil) would have the largest cropland responses as a consequence of the US biofuels program, regardless of their exposure to international markets. However, when subjected to statistical testing, the integrated markets hypothesis has been rejected by Villoria and Hertel (2011). They find that bilateral trade flows do not change as rapidly as would be the case with a unified global market for commodities. This has important implications for the geographic transmission of local interventions across the globe.
Armington (1969) recognized that the relative stability of bilateral trade flows could be captured in a framework in which products are differentiated by their country of origin. Empirical evidence suggests that even relatively homogeneous products such as rice and wheat display markedly rigid patterns of international trade (Hillberry et al 2005). These rigid patterns of trade result in segmented markets wherein supply responses to distant shocks depend on the intensity of competition between trading partners in specific markets. Considerations of market segmentation led to more moderate estimates of global GHG emissions from LUCC, although these still largely offset the benefits from domestic reductions (Hertel et al 2010b). Local-to-global interactions are also crucial to explain LUCC due to technological progress in agriculture, but have been somewhat less studied than global-to-local linkages. Even though the role of technology in achieving a more sustainable global food system is widely cited (Godfray et al 2010, Tilman et al 2011, technological progress can also increase the returns to farming, thereby leading to agricultural expansion, as suggested by 'Jevons paradox' (Alcott 2005). As demonstrated theoretically and via model simulation by Hertel, Ramankutty, and Baldos (Hertel et al 2014), this seemingly paradoxical situation depends in part on the observer's point of view. Globally, food demand is highly inelastic (Muhammad et al 2011), so better technologies, as captured by growth in overall productivity, are likely to result in global land savings. However, for farmers in a single country that is well-integrated into world markets, local demand is likely quite price-elastic, due to the potential to displace other producers with lower-cost products. Thus, access to better technology tends to encourage local cropland expansion and, potentially, the conversion of native vegetation (Angelsen and Kaimowitz 2001). Indeed, Villoria (2019) finds that, in most countries of the world, productivity growth is either uncorrelated or is positively associated with cropland expansion. However, when one adopts a global perspective, the expansion in the innovating region is likely to displace production elsewhere in the world. Depending on relative yields and emissions factors, these distant reductions-in the form of land abandonment and avoided deforestation-may offset the local increases due to LUCC in the innovating region, thereby leading to global land savings.
Recent studies also reported how productivity growth may spillover across countries and continents. Gasparri et al (2016), for example, documented public and private sector linkages that indicate innovationinduced telecoupling between Southern African and South American agricultural frontiers. In South America, the emergence of genetically modified soy varieties has been an enabling factor in the expansion of soy production in the Amazon and the Dry Chaco biomes (Bindraban et al 2009, Goldfarb andZoomers 2013, Leguizamón 2014). The transfer of knowledge and capital accumulated in the South American frontier development may thus accelerate Southern African frontier expansion with associated social costs and benefits that still need to be systematically assessed (Gasparri et al 2016).
Our review of selected local-to-global linkages illustrates the various mechanisms at play when we observe linkages between LUCC in spatially separate locations (table 1). First, shocks or interventions arise in individual countries or regions; if sufficiently large to affect aggregate global supply, land use/cover can change in other regions through changes in global commodity prices. Secondly, beyond this price mechanism, spatially distant LUCC impacts of local interventions can be induced by cross-border and international flows of capital, people, knowledge, and technology. Thirdly, the time-dependent innovation process leading to agricultural productivity growth and land use change remains an important research topic. While this may save land globally, it is not immediately clear whether such productivity growth will benefit ecologically sensitive and globally valued ecosystems. An important knowledge gap, therefore, is whether-and to what extent-the land saving effects of agricultural productivity growth have historically contributed to the conservation of native biomes at global scale. The answer clearly depends on where on the planet global mass of cropland contracts and expands over time. In principle, cropland abandonment is less desirable, from a conservation perspective, than avoided expansion into natural ecosystems. Linking biofuel demand and technological change to spatially-explicit LUCC patterns and their drivers at national scale could provide geographically more accurate estimates of such of the local impacts of such drivers of LUCC (Wright et al 2017).
National governments under pressure from local stressors, including violent land conflicts at agricultural frontiers or loss of ecosystem services provided by native vegetation, often resort to land-use and conservation policy instruments. The possibility of regional and transnational LUCC leakage induced by such interventions has been demonstrated over a decade ago in simulation exercises (Sohngen and Brown 2004). More recently, empirical evidence related local to global linkages is emerging in the South American context. In 2004, Brazil initiated a major forest governance reform (e.g. intensification of forest monitoring and law enforcement, land tenure regularization, rural credit access restrictions, and promotion of zero-deforestation supply chains), which has allegedly reduced Amazon forest loss by over 70%  (2017), who show that military action to suppress illegal gold-mining and related deforestation in French Guiana led to comparatively large additional forest losses in Suriname.

GLG linkages in LUCC studies: barriers, gaps, and the course ahead
In the previous sections, we explored how GLGlinkages can produce unanticipated LUCC outcomes that involve complex interactions and leakage effects from market and non-market mechanisms. Before we discuss potentially useful approaches to incorporating related features in global simulation or statistical models and fine-scale LUCC analyses, we should emphasize that empirical knowledge of the functioning and strength of these mechanisms is still limited (Baylis et al 2016). Causal inference is inherently difficult in analyses of spatially separated cause-effect relationships, i.e. when local interventions produce outcomes in telecoupled regions. Often, no credible counterfactual outcome can be established in standard quasi-experimental studies, because outcomes materialize in units of observations with very different characteristics than those in treatment locations. Empirical work must thus increasingly rely on structural models, new (and big) data sources, and methodological innovations, e.g. synthetic control approaches, based LUCC data with high temporal and spatial resolution (Börner et al 2016). Moreover, such studies are paramount to corroborating underlying assumptions and relationships in global agroeconomic and other simulation models used to investigate GLG-LUCC linkages.
3.5.1. Summary functions: a bridge from local to global across LUCC models One response to the need for capturing endogenous global responses to local land-use policies has been to create summary functions which embody all of the economically relevant information about local or regional responses to global changes and which could be directly embedded into the global model. Summary functions (sometimes dubbed transfer functions) are widely used to summarize complex biophysical properties which cannot be incorporated into more aggregate models. One example is the rate of nitrate leaching resulting from the application of nitrogen fertilizer in crop production. It is well known that the leaching rate depends on a variety of highly localized factors, such as fertilizer application rate and timing, crop choice, management practices (including cover crops and irrigation), soils, drainage management, and weather, among other things (Kucharik and Brye 2003). Incorporating all of these factors into a national or global gridded model seems nearly impossible. However, by independently estimating grid cellspecific transfer functions and incorporating them into a gridded economic model, it is possible to incorporate grid cell-specific transfer functions. The ensuing model can then be used to explore LUCC leakage effects of non-point source pollution policies at the grid cell level .
Britz and Hertel (2009) developed a summary function to provide the linkage between the highly disaggregated CAPRI model (operating at the level of 250 sub-regions) for EU agriculture and the global GTAP-AEZ model. They did so by estimating a system of supply functions which described the aggregate responses of EU agriculture to price changes, as embodied in the CAPRI model. This permitted them to estimate the global land use impacts of EU-based biofuel policies. In later work, the same authors extended this summary function approach to incorporate a specific, land-based policy lever-in this case, an index of the stringency of the EU agricultural land set-aside program. This allowed them to simulate the spillover effects of this very specific EU-land use policy in a global model, and then link the EU market price results back to the disaggregated CAPRI model in order to assess the detailed effects of this intervention at the regional level (Pelikan et al 2014). Summary functions have also been used to represent land use change in hydrological models (Hundecha and Bárdossy 2004). However, the estimation of internally consistent summary functions is a non-trivial task. For example, Britz and Hertel (2009) were able to exploit the fact that the CAPRI model adheres to well-understood theoretical economic properties, which may not be the case with other models.
Just as summary functions can be used as a bridge from local to global analyses, so, too, can they be used as a means of incorporating a summary of key global responses into local analyses of LUCC and leakage. This could allow for better harmonization and interpretation of cross-model simulations (Schmitz et al 2014, von Lampe et al 2014, Alexander et al 2017, Popp et al 2017. Such summaries of composite economic responses can also allow for rapid insights into the potential impacts of local LUCC in response to various interventions. Consider, for example, local assessments of the impacts of agricultural technology improvements. Hertel et al (2014) demonstrate that, all of the relevant information about global demand for the commodity in question, as well as supply response in the rest of the world, is embodied in one parameter-the price elasticity of excess demand. If the value of this parameter is greater than one, then economic theory predicts that cropland will expand in response to the technological innovation, otherwise, land use will contract. The value of this parameter can be readily estimated from any global model, simply by perturbing the local supply function and observing the ensuing change in equilibrium quantity and price.
Researchers focusing on local LUCC should consider eliciting this excess demand elasticity from appropriately configured global models (Plevin et al 2015), thereby allowing them to leverage the relevant global information without having to run the global model repeatedly.

Model validation: the 'Holy Grail'
In the context of GLG-LUCC linkages, we find that the question of model validity is rarely explored in global models. In particular, we found that global agro-economic model validity tends to deteriorate as models become more complex and more disaggregated (McCalla and Revoredo 2001). This is unfortunate given the perceived demand for additional disaggregation in the LUCC literature.
Validation is a critical piece of the puzzle if global simulation models are to have broader relevance for science and policy. Two types of validation have been undertaken with global agro-economic models: ex post validation and historical validation (or hindcasting). Ex post validation, i.e. comparing model predictions with actual outcomes realized at a later date, is rarely practiced. A notable exception is McCalla and Revoredo (2001), who evaluate how actual outcomes deviated from the modeling teams' earlier projections of global food output. Based on their analysis, the FAO projections improved over time for wheat but were less accurate for oilseeds, which grew dramatically over this period. This contrasts sharply with their assessment of the global commodity projections made by IFPRI and USDA over this period. The deviations of these agencies' predictions from actual outcomes grew over time. The authors argued this was due to the demands for greater regional disaggregation. Indeed, their review suggests that forecast errors were larger, the smaller the economy-often due to low-quality data. In addition, they found evidence of large projections errors for the US and EU where changing agricultural policies exerted an inordinate influence. The authors concluded their review by suggesting it is difficult for global models to reach clear conclusions about the evolution of agricultural production and consumption in specific countries. Their findings pose a challenge for those undertaking global gridded modeling, where the objective is to project outcomes for highly resolved subnational regions.
Historical validation or 'hindcasting,' the second and most common approach to the validation challenge in global modeling, relies on the comparison of simulated outputs to historical 'real-world' data. This method has become standard in climate modeling The reportedly limited experience with model validation also suggests that much more attention needs to be paid to the land-use/cover data being used in these models, as well as the estimation of key behavioral parameters in LUCC models (Filatova et al 2013). This includes the price and income responsiveness of food demand, the potential for endogenous intensification of crop production, the responsiveness of cropland area to economic signals, and the extent of integration with international commodity markets. For example, Verburg and Overmars (2009) highlight the fact that land-cover databases such as the 1990 and 2000 CORINE European land-cover maps do not effectively distinguish between recently abandoned farmland and grassland or identify alternative land uses of former agricultural areas. Moreover, Alexander et al (2017) suggested that the greater research efforts placed on the roles of cropland and European land led to greater consistency among multiple modelsʼ simulations due to lower variance in initial areas. Many models also derive forest area change from changes in cropland, without consideration for potential demands for forest products or non-market ecosystem services (Schmitz et al 2014). With less attention paid to other land types in global economic models, agricultural areas may inadequately account for the interactions between demands for other uses, e.g. timber (Alexander et al 2017).

Gridded data and parameters: a critical limitation
It is difficult to overstate the importance of accurate, detailed data on crops and related land-use practices (e.g. irrigation and fertilization) for high-resolution global-level modeling efforts. The pioneering work of Monfreda et al (2008), though anchored nearly two decades ago, circa 2000, still remains one of the most frequently used data products for the global spatial distribution of harvested areas and yields 8 (175 FAO crops). Another key piece of information for GLG-LUCC analysis is the spatial location of cropland, pastures, and natural land covers such as forests and grasslands. Land-cover products based on automated processing of satellite data are relatively current (e.g. GlobCover from the European Spatial Agency updated to 2010), but they tend to underestimate the cropland statistics compiled from FAO (Fritz et al 2013). A recent land-cover dataset from NASA that is representative of 2015, in contrast, identified 15%-20% more cropland than formerly assessed (Congalton et al 2017). Alternative datasets that are cropland specific are representative of land use in the first decade of the 2000s (Goldewijk 2001, Klein Goldewijk et al 2007, Fritz et al 2015. We still lack globally consistent data on other key aspects related to land use such as labor allocation, the location of processing plants (e.g. bio-refineries) and the distribution of agricultural input and output prices. Exceptions are the global map on fertilizer application (Potter et al 2010) and irrigation maps (Siebert et al 2010), both representative of the early 2000s.
An obstacle to improving the globally gridded data available to researchers is the generalized perception that the data offered by international organizations, combined with the increasing availability of data and computing capabilities for data processing and visualization, automatically translates into impressive maps and state-of-the-art datasets that can improve GLG-LUCC analysis. As evidenced by the short discussion above, this is simply not the case. Given the advances in satellite imagery processing and the experiences mapping national and subnational information, the time seems ripe for a globally coordinated effort geared toward the continuous improvement of the data needed by the scientific community. As discussed by Fritz et al (2013), better algorithms to process global moderate resolution satellite data are a promising solution for annually updated cropland maps, although considerable methodological refinements are needed to make these maps accurate. One methodological refinement is in the recent work of Graesser et al (2015) which shows that the interpretation of moderate-resolution satellite data can be significantly improved by validation through sampling and expert interpretation of the high-resolution imagery offered by Google Earth. Another is the use of machine learning to identify patterns of burning and plantation establishment in Indonesia (Jia et al 2016).
Regarding crop level information, Lobell (2013) and Burke and Lobell (2017) have shown that satellite imagery can be used to infer yields and yield gaps. The data fusion methods of Monfreda et al (2008), whereby land-cover information from satellite imagery is combined with detailed data on agricultural area and production from national censuses with subnational information, could be enhanced and automated so new information can be digested and incorporated, shortening the time span between data updates. New research using simple discrete-choice regression techniques for downscaling subnational data seems a promising area of endeavor (Song et al 2018). The experiences with crowdsourcing from See et al (2015) offers a glimpse into how to collaborate with the broader community to validate and improve the cropland and other maps over time.
The root cause of the lack of improvement in the global gridded datasets over time, despite increasing availability of satellite data, is the fact that most of these efforts are based on one-time academic and institutional projects, which quickly become outdated and lack inter-operability (Hertel et al 2010a). This is a consequence of several factors. Firstly, the incentives for the development and maintenance of data sets in academia are quite limited. Even those authors who have garnered widespread citations for published data sets do not have a strong incentive to update them. In addition, these data sets often entail collaboration across disciplines (e.g. agronomy, hydrology, climate science, geography and economics), further increasing the challenge for many academics. The provision of such public goods is the natural domain of governmental bodies. However, this is expensive and cutting data collection and maintenance is often one of the first ways agencies come to grips with budget reductions. Given the skill-specific nature of global gridded data, once a team is disbanded, it is costly to reassemble, and the all-important continuity in time series data is typically lost.
While competing approaches are a desirable attribute that allows for new and improved discovery, data users often lack guidance in terms of data product accuracy. An ideal system would involve a research environment that produces updated data, with protocols that can ensure consistency across research groups and a vetting system that can guide users to select the best datasets while encouraging ongoing improvements (Hertel et al 2010a).
A related concern is the lack of parameter estimates that regulate economic behavior in LUCC models. For instance, the elasticities of factor supplies (i.e. land, labor, and agriculture) are among the most important parameters explaining LUCC in the recent past (David et al 2013, Baldos and Hertel 2016). These are also the parameters about which we know the least, and what is known comes from efforts three or four decades ago, generally focusing in the developed world. Parameter estimation does not necessarily depend on the availability of spatially explicit data, but when these data are available, the understanding of many phenomena is greatly enhanced. For example, Lubowski (2002) exploits the spatially-explicit LUCC information (e.g. cropland, forest, range, and pastures) in the US Crop Data Layer to estimate LUCC transition elasticities in the US; these elasticities underpin most of the global-to-local analysis based on the GTAP-AEZ framework (Ahmed et al 2008). Their results predict LUCC reasonably correlated with observed changes across the continental US while identifying opportunities to increase estimation accuracy by incorporating data about the location of biorefineries and other processing facilities. In contrast, many global agro-economic models deriving LUCC from changes in agricultural areas (Schmitz et al 2014) often disregard the key roles of biophysical attributes (e.g. distance to roads, slope, and soil and climate suitability) well-known to be strongly correlated with agricultural land uses (Busch and Ferretti-Gallon 2017, Kleemann et al 2017, Restivo et al 2018.
Even if spatially-explicit data does not allow for parameter estimation, it can be used to spatialize existing country-level parameters. For example, Villoria and Liu (2018) used data on biophysical attributes and global market access maps prepared by Verburg et al (2011) to estimate land supply elasticities at the gridcell level-the land supply elasticity in this context is the percentage change in cropland area given a one percent change in agricultural rents. This parameter is crucial in LUCC modeling because it determines the extensive margin of the supply response to changes in the expected profitability of agricultural production. In addition to land quality, transport costs to markets are key determinants of these supply elasticities. Transport costs, in turn, vary with relative prices and can be substantially modified by investments in infrastructure such as roads (Chomitz and Gray 1996) or biorefineries (Li et al 2019). The combination of maps of market access with well-established econometric models of land use choice allows to capture the effects of investments in reducing transportation costs (Chomitz and Gray 1996), which are a key determinant of deforestation and cropland expansion (Pfaff 1999, Laurance et al 2014. This further underscores the need to intensify collaboration between economists, biophysical scientists, and geographers.

Summary and future research directions
While there is a great deal of important work underway in GLG-LUCC modeling, most current approaches fall prey to one or more of the following three key limitations. The first of these is that many studies remain a prisoner of an excessive disciplinary orientation. LUCC science specifically, and the sustainability challenges facing the world today more generally, are fundamentally interdisciplinary in nature. Approaches driven solely by geographers, agronomists, ecologists or economists will ultimately prove too narrow in their analyses. This interdisciplinary thrust is evident from the LUCC work currently being undertaken at the large international institutions. However, we believe that future GLG-LUCC analyses and leakage will benefit from even greater interdisciplinary collaboration, particularly on the part of individual academic researchers working in this field.
A second limitation of much of the work to date on GLG-LUCC and leakage, as reflected in this review, is that most of the work focuses on the global-to-local component, with far fewer studies characterizing the local-to-global linkages. As mentioned above, by their very nature, land-based sustainability challenges usually require local solutions, with the preferred approach depending on current use, soil characteristics, topography, access to water and agricultural inputs, infrastructure, as well as socio-economic conditions and governance. However, local analyses, disconnected from national and global contexts, cannot foresee future system stresses nor can they anticipate the spillovers and broader consequences of local solutions (Rounsevell et al 2012).
Where the full GLG-LUCC nexus has been developed, as with the global gridded modeling projects discussed above, we observe an excessive reliance on proprietary and complex analysis frameworks. It is hardly surprising that this kind of major undertaking has typically been undertaken in large national and international institutions. However, most of these modeling frameworks have been proprietary in nature. While there are currently significant efforts underway to make several of the leading integrated assessment models open-source (e.g. GCAM and MAgPIE), it is hard to get serious uptake due to the complexity of the underlying modeling frameworks that are often not well documented and are being continually expanded to address new challenges and new projects. It is hard to think of any example where outsiders have been able to effectively use and modify these global gridded modeling frameworks. If one is to build a community of practice around GLG-LUCC analyses, the underlying models and data should be open-source and developed from the very beginning with the premise that they will be used by a variety of individuals, from various institutions, with differing backgrounds and skill levels. This calls for a suite of models that are simple enough to be accessible to a wide range of users, while not being so simple that they abstract from key issues underpinning global LUCC and leakage. Open-sourcing will also permit more ground-truthing of local data and behavioral assumptions. One open-source source effort known as Global to Local Analysis of Systems Sustainability seeks to provide researchers with the entire workflow behind GLG-LUCC analyses-starting with the data and parameters underlying the open-source models provided on the GeoHub (https://mygeohub.org/ groups/glass). This type of project is complementary to efforts to foster a global community working on sustainable land use in a global context, of which the Global Land Program (https://glp.earth/) is the most prominent example. It is only through such collaboration that the 'wicked problems' posed by GLG-LUCC and leakage in the 21st century can be adequately addressed.