Connecting processes and formalizing the biophysical understanding
The study of complex systems requires the formulation of hypothesis and the development of functions to describe quantitatively the processes. Modeling consists in the elaboration of the precise organization of those hypotheses (de Parcevaux and Huber, 2007). Modeling thus provides a holistic approach by connecting inter-dependent processes. Process-based models provide a mathematical framework to (1) produce research questions and hypothesis; (2) explain/decompose the variability in observed data, i.e. help summarize and interpret field data; (3) predict system behavior in unknown conditions; (4) down-scale or up-scale processes (D. Baldocchi, Adv. biometeorogy course, UC. Berkeley; de Parcevaux and Huber, 2007). AFS typically require process-based models to further and systematize our understanding of the complex interactions involved, especially microclimatic. Process-based models for monoculture stands (in the forestry or agronomic fields) are now simulating canopy processes with great accuracy (e.g. Brisson et al., 2003 for crop models ; Hanson et al., 2004 for a set of forest models). The most refined models embark detailed canopy processes including the complex effects of turbulence or the description of short and long wave radiations (Baldocchi and Harley, 1995). Those models generally deal with spatially averaged canopies virtually divided in one or multiple layers. Fluxes are represented in 1D. Those models helped solving a great number of ecophysiological/agronomical issues in those systems: effect of clumping, LAI and percentage of diffuse radiations on crop light use efficiency (Medlyn, 1998), linear relationship between aPAR and plot scale NPP (Monteith and Moss, 1977), etc. They also helped in finding key and emerging processes for up-scaling. For example, locally influent turbulence effect may be canceled at larger scales (de Parcevaux and Huber, 2007). Representing the canopy by a single layer separated into sun and shade leaves is sufficient to simulate satisfactorily light absorption and photosynthesis (De Pury and Farquhar, 1997; Roupsard et al., 2008; Ryu et al., 2011). The coupling of 2 vertical canopy-layers (i.e. shade tree canopy + crop canopy) or multiple vertical layers systems create new interactions, such as microclimate feedback, that were not modeled by single canopy-layers models. Those models only describe vertical gradients of fluxes (e.g. Cannell et al., 1998). Spatially disaggregated (e.g. Mobbs et al., 1998b) or explicit 3D (e.g. Wang and Jarvis, 1990a) models account for lateral fluxes. Those models consider uniquely the radiative transfer in 3D; in most cases energy, water and wind fluxes are still modeled according to a vertical gradient. The modeling of the 3D nature of those fluxes remains a huge challenge in AFS and heterogeneous systems in general.
F. Charbonnier Synthesis 19 Impact of those non-modeled lateral fluxes in certain AFS may be important (see the Sahelian windbreak example cited above) or perhaps may be neglected (e.g. humid climate).
Bringing continuous variables into heterogeneous plots and helping experimental designs
AF research provided legions of articles trying to assess experimentally the effect of shade on productivity, pests and diseases incidence, crop quality, pollination (a simple google search allows to access the wide variety of studied effects of shade)… Those effects are generally weak, display a high variability and are sometimes contradictory between studies. Spatially explicit models are expected to produce maps of processes that could not be easily inferred solely from measurements, for example a map of light available for the understorey, a map of canopy temperature, a map of photosynthesis, etc. Those maps may provide local values of processes integrated over user-defined time scale. Models are thus requested to produce explanatory variables for field experiments. We argue here that those continuous variables could help explaining much more variability than the usual full sun/ shade dichotomy used in AFS experimental designs. Meaningful covariates that could be mapped and used in experimental designs: e.g. total transmitted radiations to the crop, crop canopy temperature… Models also provide a quantification of local (or plant scale) fluxes (integrated over time) that can be coupled to plant productivity measurements to produce significant ratios in plant physiology: biomass produced per unit of absorbed radiation (light use efficiency), of water transpired (water use efficiency) or of carbon assimilated by photosynthesis (carbon use efficiency). Studying the determinants of the variability of those ratios may give significant insights on the effect of shade trees on local canopy processes.
The importance of virtual simulation for the design of innovative AFS
By definition, process-based models are expected to produce reliable predictions even outside their validation range, even if verification is recommended. They are thus suitable to predict the system behavior in after varying the physical constraints. A typical question in AF research is related to the optimal density, arrangement and row orientation of shade trees, so that the crop production is only marginally affected. AF or forestry models were already used to optimize the absorbed radiations or photosynthesis (Grace, 1988). Such simulations were attempted by Talbot (2011) who simulated the effects of tree arrangements on the tree and crop yield using a 3D light interception model for trees coupled to a crop model (Hi-Safe; Dupraz et al., 2005). In the simulation, the author compares the evolution of tree and crop yield compared to sole plots during 40 years for various shade tree density and line orientations (Fig. 7). The author demonstrates that it is difficult even a posteriori to determine which variables influenced more the variations in crop productivity, because in a complex dynamic crop model nearly none of the explanatory variables were independent.
Modeling to assess the resilience of AFS
Given the spatial heterogeneity and species diversity, AFS are assumed to be intrinsically more resilient (i.e the capacity of the system to recover production after a climate disruption such as a drought or an extended period with high temperatures) than a monoculture (Anderson and Sinclair, 1993). If we can easily state a large resilience of traditional agroforests that mimic the ecological functioning of rainforests (e.g. Michon et al., 1983), the resilience of modern AFS with 2-3 species is not so obvious. Unlike undisturbed ecosystems, the resilience of AFS is intrinsically linked to management practices. An absence of adequate management in an AFS would rapidly lead to a loss of production. In practice, it would be interesting to separate an intrinsic AFS resilience (so-called “ecological resilience”) from a “global resilience” including economic and social factors (O. Roupsard, Pers. Comm.). Theoretically, the “ecological resilience” would be the inherent capacity of the system to absorb environmental stresses and recover stability. In practice, AFS is already a managed system receiving energetic inputs (fertilizers, pesticides, etc). Its intrinsic resilience would thus be biased by the absence of nutrient limitations. The system resilience should be a step by step assessment that would include: 1/ an AFS managed with realistic levels of fertilization (i.e. system recycling + fertilizers produced in the farm; context of organic farming); 2/ an AFS with generally admitted levels of oil-derived inputs; 3/ an AFS with economical and social constraints. Those 3 level resilience profiles should be established under various scenarios such as: climate projections scenarios locally downscaled, effect of strong disturbing climatic events (e.g. hurricanes or strong drought), effect of considered time scale, and effect of economic scenarios on the crop-value chain or on the price of raw materials such as oil prices… The assessment of those resilience profiles is a huge scientific challenge in such complex context. Obviously, mechanistic models that couple biophysical and economic models would be needed. Environment, the management and the economic factors do impact the system. That’s why models should be dynamic in order to account for feedback loops. Few attempts were made to couple biophysical and economical models: to our knowledge only the “Silvoarable AgroForestry for Europe” project (SAFE) developed an economic model (Graves et al., 2011) coupled to a dynamic and simplified biophysical model designed for long term run (van der Werf et al., 2007). However, the simplified biophysical model would not allow studying “ecological resilience” of systems. The same team is being developing a daily time step model to study the above and below ground intra-plot Charbonnier Synthesis 21 biophysical interactions using 3D approach that would be able to make such study (Hi-Safe) (Dupraz et al., 2005). A recently accepted French project (ANR agrobiosphère MACACC) aims at studying resilience profiles of 3 perennial plantations, including coffee AFS to increased temperature, decreased precipitations and under nutrient constraints. They plan to study specifically the buffering capacity of shade trees in maintaining adequate microclimate (temperature) for the under-storey under different downscaled climate change scenarios and nutrient limitations. They plan to use a 3D soil-vegetation-atmosphere transfer model adapted to AFS (MAESPA; Duursma and Medlyn, 2012) coupled with a model of carbon allocation and growth (GO+: Loustau et al., 2012) to model the 3 perennial plantations.
Justifying our choice of MAESTRA/MAESPA
We have shown that the only way to study the interactions occurring in an AFS (between shade tree and crop, soil and atmosphere) in a holistic way, was to study the canopy processes relying on physic laws (energy and mass transfers) that take into account the multiple non-linearities involved in the different processes (radiative, heat, water and carbon transfers). SVAT models are the only kind of models to provide such framework. In vertically and horizontally heterogeneous systems, simplified 3D models appear as an ideal way of simulating plant to plot canopy processes when studying the intra-plot variability (or the local effects of shade trees). More sophisticated 3D models such as architectural models (e.g. Dauzat et al., 2001; de Reffye et al., 1995) beside their extremely complex parameterization, are until now hardly compliant to simulate plot scale or yearly scales fluxes (Fig. 13). Half-hourly time scales are the only scale able to study microclimates effects introduced by shade trees on crop canopy processes, according to sun course, season and latitude and meteorological inputs. The model should be able to run a full year because it is the minimum time needed to have an overview on the whole system phenological cycle. Farquhar et al. (1980) model is a widely accepted mechanistic description of photosynthesis. It is generally coupled to a stomatal conductance model (Ball et al., 1987; Jarvis, 1978; Leuning, 1995; Medlyn et al., 2011). The coupling between, stomatal conductance and photosynthesis is empiric, but to date there is no reliable and widely applicable mechanistic alternative. This couple photosynthesis – stomatal conductance approach has to be preferred to more empirical approaches. MAESTRA is an array model with a long and prestigious development history that come back to the late 70s (for details see: Medlyn, 2004). It was one of the first spatially explicit model representing individual plants by simple geometrical shapes (Fig. 15a). MAESTRA is able to simulate intercepted radiations of individual plants in PAR, near infrared and thermal infrared wavelengths, in a crown divided in various vertical layer and various point per layer (for details see: Norman and Welles, 1983; Wang and Jarvis, 1990a). MAESTRA was the first array model to represent the vertical and horizontal spatial distribution of leaves within the crown and assess its importance (Wang et al., 1990). MAESTRA is coupled to a photosynthesis stomatal conductance model, allowing balance closure for all fluxes (Ball et al., 1987; Jarvis, 1978; Leuning, 1995; Medlyn et al., 2011). MAESTRA potentials to model AFS were highlighted when Dr Jennifer Grace used it to study the sensitivity of plant (and plot) absorbed light and photosynthesis to tree rows orientation and spatial arrangement (Grace, 1988; Grace, 1990). Lawson et al. (1995) used MAESTRA in its 1st explicit AF application during the Agroforestry Modeling Project. The authors showed the strong overestimation of light interception assuming homogeneous canopies when compared to spatialized crowns simulated with MAESTRA. MAESTRA was further abandoned for this trial due to 1/ the huge amount of time needed for calculations 2/ the inability of the model to account for water stress in a Sahelian environment.
Table of contents :
1. Potential role of agroforestry in a new paradigm of agriculture
B. Definition of agroforestry and historical aspects of agroforestry research
C. Agroforestry and ecosystem services
i. Hydrological services and soil erosion
ii. Biodiversity conservation
iii. Carbon sequestration
iv. Primary productivity and resource use efficiency
v. Mitigation of the effects of climate change
2. Specificity of interactions in agroforestry systems
A. Competition, Facilitation, Complementarity
B. Seasonal interactions: phenology and synchronicity
C. Highlight on the competition for light
D. Effect of microclimate on processes
i. Changes of heat fluxes
ii. Effect of wind
3. Why modeling canopy processes in AFS?
A. Connecting processes and formalizing the biophysical understanding
B. Bringing continuous variables into heterogeneous plots and helping experimental designs
C. The importance of virtual simulation for the design of innovative AFS
D. Modeling to assess the resilience of AFS
4. How to model processes in AFS?
A. Which processes to simplify? Which processes to ignore?
B. How to model the AFS structure?
5. Measuring and modeling processes in AFS
F. Charbonnier Synthesis 2
A. Field measurements for parameterization and model verification
i. Studying the structure heterogeneity of AFS
ii. Measuring canopy processes
B. Modeling strategies
i. Static models
ii. Dynamic models
iii. Justifying our choice of MAESTRA/MAESPA
6. Conclusions: our contribution to AFS understanding: modeling the effects of microclimate modifications on understorey fluxes
A. Mapping the absorbed radiation in a plot with a plant resolution
B. Using the absorbed radiation as a covariate for experimentation
C. Intra-plot variability of photosynthesis and of LUE
A. Possible limitations of MAESTRA-MAESPA
B. Our scientific strategy