An optimality-based model of the dynamic feedbacks between natural vegetation and the water balance
Authors:
S. J. Schymanski, M. Sivapalan, M. L. Roderick, L. B. Hutley, and J. Beringer
Abstract:
The hypothesis that vegetation adapts optimally to its environment gives rise to a novel framework for modeling the interactions between vegetation dynamics and the catchment water balance that does not rely on prior knowledge about the vegetation at a particular site. We present a new model based on this framework that includes a multilayered physically based catchment water balance model and an ecophysiological gas exchange and photosynthesis model. The model uses optimization algorithms to find those static and dynamic vegetation properties that would maximize the net carbon profit under given environmental conditions. The model was tested at a savanna site near Howard Springs (Northern Territory, Australia) by comparing the modeled fluxes and vegetation properties with long-term observations at the site. The results suggest that optimality may be a useful way of approaching the prediction and estimation of vegetation cover, rooting depth, and fluxes such as transpiration and CO2 assimilation in ungauged basins without model calibration.
Reference:
- Water Resources Research, 45, doi:10.1029/2008WR006841.
- Weblink to publisher's web page.
- Postprint of this manuscript (accepted version of the paper formatted by author).
Figure 1: Net carbon profit as the difference between carbon acquired by photosynthesis and the carbon used for the construction and maintenance of organs necessary for its uptake. As CO2 uptake from the atmosphere is inevitably linked to loss of water from the leaves, the root system as well as water transport and storage tissues are essential to support photosynthesis. The atmosphere (sunlight and water demand) and the soil (water supply) constitute the environmental forcing. Within these constraints, vegetation is assumed to optimize foliage, water transport and storage tissues, roots, and stomata dynamically to maximize its net carbon profit. Figure taken from Schymanski [2007] and Schymanski et al. [2007].
Figure 2: Flow diagram of the coupled water balance and vegetation optimality model. Input variables are at the top, while model outputs are separated into state variables (dashed boxes) and fluxes (along arrows). Symbols are explained in the text (the subscript i denotes a vector over all soil layers). For clarity, only selected model outputs are drawn. See the main text for parameter definitions.
Figure 3: Representation of the (left) perennial and (right) seasonal vegetation components. The perennial vegetation component was assumed to be composed of evergreen trees with a constant cover MA,p and rooting depth yr,p, while the seasonal component was assumed to be composed of annual grasses with variable cover MA,s and a rooting depth yr,s limited to 1 m. Note that deep rooting trees need larger vascular systems per unit horizontal cover than shallow rooting annuals.
Figure 4: Subdivision of measured net ecosystem CO2 uptake (FnC, solid black line) into soil respiration (Rs, dashed line), foliage CO2 uptake (Ag,tot, solid grey line), and woody tissue respiration (Rw, not shown). Rs and Rw are modeled on the basis of measurements, while Ag is taken as the sum of FnC, Rs, and Rw. For clarity, all fluxes have been plotted as negative values for carbon uptake and positive values for carbon release (note the signs in the legend).
Figure 5: Sensitivity of the optimized parameters to the value of crv. Each column illustrates the optimal parameter values from four model runs, where the run with the highest NCP is marked in bold. (a–d) Parameters defining the sensitivity of the water use parameters λs and λp to soil moisture. (e) Optimal fractional cover and rooting depth of perennial vegetation (MA,p and yr,p respectively).
Figure 6: Sensitivity of the achieved net carbon profit and simulated fluxes to the value of crv. Each column illustrates the results from four model runs, where the run with the highest NCP is marked in bold. (a) Total net carbon profit achieved over 30 years. (b) Simulated mean annual transpiration. (c) Simulated mean annual soil evaporation. (d) Simulated mean annual evapotranspiration. (e) Simulated mean annual gross primary production (Ag,s + Rl,s + Ag,p + Rl,p).
Figure 7: Simulated seasonal dynamics in canopy properties and observed rainfall between 2001 and 2005. (a) Electron transport capacity (Jmax25) of the seasonal and perennial components (Jmax25,s and Jmax25,p, respectively), (b) area fraction covered by vegetation compared with satellite-derived estimates [Donohue et al., 2008], (c) slopes between Et and Ag for the seasonal and perennial components (λs and λp, respectively), and (d) observed daily rainfall. Note that the satellite-derived data include flooded areas during the wet season.
Figure 8: Modeled (black) and observed (grey) daily (a) evapotranspiration rates (ET) and (b) net CO2 assimilation rates (Ag,tot). The dashed line shows scaled daily averages of the validity flag values, ranging from -0.2 for a whole day of valid measurements to -0.4 for a whole day of gap-filled data using a neural network approach. The plots also display the means of the time series as well as the mean absolute errors (MAE) and Pearson’s r values of the simulations.
