Step-wise modifications of the Vegetation Optimality Model

The Vegetation Optimality Model (VOM, Schymanski et al., 2009, 2015) is an optimality-based, coupled water-vegetation model that predicts vegetation properties and behaviour based on optimality theory, rather than calibrating vegetation properties or prescribing them based on observations, as most conventional models do. In order to determine wheter optimality theory can alleviate common shortcomings of conventional models, as identified in a previous model inter-comparison study along the North Australian Tropical Transect (NATT) (Whitley et al., 2016), a range of updates to previous applications of the VOM have been made for increased generality and improved comparability with conventional models. To assess in how far the updates to the model and input data would have affected the original results, we implemented them one-by-one while reproducing the analysis of Schymanski et al. (2015). The model updates included extended input data, the use of variable atmospheric CO2-levels, modified soil properties, implementation of free drainage conditions, and the addition of grass rooting depths to the optimized vegetation properties. A systematic assessment of these changes was carried out by adding each individual modification to the original version of the VOM at the flux tower site of Howard Springs, Australia. The analysis revealed that the implemented changes affected the simulation of mean annual evapo-transpiration (ET) and gross primary productivity (GPP) by no more than 20 %, with the largest effects caused by the newly imposed free drainage conditions and modified soil texture. Free drainage conditions led to an underestimation of ET and GPP, whereas more fine-grained soil textures increased the water storage in the soil and resulted in increased GPP. Although part of the effect of free drainage was compensated for by the updated soil texture, when combining all changes, the resulting effect on the simulated fluxes was still dominated by the effect of implementing free drainage conditions. Eventually, the relative error for the mean annual ET, in comparison with flux tower observations, changed from an 8.4 % overestimation to an 10.2 % underestimation, whereas the relative errors for the mean annual GPP stayed similar with a change from 17.8 % to 14.7 %. The sensitivity to free drainage conditions suggests that a realistic representation of groundwater dynamics is very important for predicting ET and GPP at a tropical open-forest savanna site as investigated here. The modest changes in model outputs highlighted the robustness of the optimization approach that is central to the VOM architecture.

Informing the Sustainable Pursuit of Happiness

Although most people want to be happy, the pursuit of happiness involves an overwhelming number of choices and great uncertainty about the consequences. Many of these choices have significant implications for sustainability, which are rarely considered. Here, we present an optimality model that maximizes subjective happiness, which can eventually account for sustainability outcomes. Our model identifies the optimal use of time or energy to maximize happiness. Such models tell people how to invest in domains of happiness (e.g., work vs. leisure) and how to choose activities within domains (e.g., playing a computer game vs. playing a board game). We illustrate this optimization approach with data from an online survey, in which people (n = 87) either recalled or imagined their happiness during common activities. People reported decelerating happiness over time, but the rate of deceleration differed among activities. On average, people imagined spending more time on each activity than would be needed to maximize happiness, suggesting that an optimality model has value for guiding decisions. We then discuss how such models can address sustainability challenges associated with overinvesting (e.g., excessive CO2 emissions). To optimize happiness and explore its implications for sustainability over long periods, models can incorporate psychological processes that alter the potential for happiness and demographic processes that make lifespan uncertain. In cases where less objective approaches have failed, a quantitative theory may improve opportunities for happiness, while meeting sustainability outcomes.

The influence of carbon costs and benefits on predicted vegetation behaviour along a precipitation gradient using the Vegetation Optimality Model

<p>Vegetation properties such as rooting depths and vegetation cover play a key role in coupling ecological and hydrological processes. These properties are however highly variable in space and/or time and their parametrization generally poses challenges for terrestrial biosphere models (Whitley et al., 2016). Models often use static values for dynamic vegetation properties or prescribe values based on observations, such as remotely sensed leaf area index. Here, vegetation optimality provides a way forward in order to predict such vegetation properties and their response to environmental change (Schymanski et al., 2015).</p><p>In this study, we explore the utility of a combined water-vegetation model, the Vegetation Optimality Model (VOM, Schymanski et al., 2009), to predict vegetation properties such as rooting depths, foliage cover, photosynthetic capacity and water use strategies. The VOM schematizes perennial trees and seasonal grasses each as a single big leaf with an associated root system and optimizes leaf and root system properties in order to maximize the Net Carbon Profit, i.e. the difference between the total carbon taken up by photosynthesis and all the carbon costs related to the construction and maintenance of the plant organs involved. The VOM was applied along the North-Australian Tropical Transect, which consists of six savanna sites equipped with flux towers along a strong rainfall gradient between 500 and 1700 mm per year. The multi-annual half-hourly measurements of evaporation and CO<sub>2</sub>-assimilation at the different sites were used here to evaluate the model.</p><p>The VOM produced similar or better results than more traditional models even though it requires much less information about site-specific vegetation properties. However, we found a persistent bias in the predicted vegetation cover. More detailed numerical experiments revealed a likely misrepresentation of the foliage costs in the model, which are based on a linear relation between leaf area and fractional vegetation cover. This finding, and the already favourable comparison with traditional models, implies that optimization of vegetation properties for Net Carbon Profit is a very promising approach for predicting the soil-vegetation-atmosphere exchange of water and carbon in complex ecosystems such as savannas.</p><p><strong>References<br></strong>Schymanski, S.J., Roderick, M.L., Sivapalan, M., 2015. Using an optimality model to understand medium and long-term responses of vegetation water use to elevated atmospheric CO2 concentrations. AoB PLANTS 7, plv060. https://doi.org/10.1093/aobpla/plv060</p><p>Schymanski, S.J., Sivapalan, M., Roderick, M.L., Hutley, L.B., Beringer, J., 2009. An optimality‐based model of the dynamic feedbacks between natural vegetation and the water balance. Water Resources Research 45. https://doi.org/10.1029/2008WR006841</p><p>Whitley, R., Beringer, J., Hutley, L.B., Abramowitz, G., De Kauwe, M.G., Duursma, R., Evans, B., Haverd, V., Li, L., Ryu, Y., Smith, B., Wang, Y.-P., Williams, M., Yu, Q., 2016. A model inter-comparison study to examine limiting factors in modelling Australian tropical savannas. Biogeosciences 13, 3245–3265. https://doi.org/10.5194/bg-13-3245-2016</p>

A repeatable and reproducible modelling workflow using the Vegetation Optimality Model and RENKU

<p>Numerical experiments become more and more complex, resulting in workflows that are hard to repeat or reproduce. Even though many journals and funding agencies now require open access to data and model code, the linkages between these elements are often still poorly documented or even completely missing. The software platform Renku (https://renkulab.io/), developed by the Swiss Data Science Center, aims at improving reproducibility and repeatability of the entire scientific workflow. Data, scripts and code are stored in an online repository, and Renku records explicitly all the steps from data import to the generation of final plots, in the form of a knowledge graph. In this way, all output files have a history attached, including linkages to scripts and input files used generate them. Renku can visualize the knowledge graph, to show all scientific links between inputs, outputs, scripts and models. It enables easy re-use and reproduction of the entire workflow or parts thereof.</p><p>In the test case presented here, the Vegetation Optimality Model (VOM, Schymanski et al., 2009) is applied along six study sites of the North-Australian Tropical Transect to simulate observed canopy-atmosphere exchange of water and carbon dioxide. The VOM optimizes vegetation properties, such as rooting depths and canopy properties, in order to maximize the Net Carbon Profit, i.e. the total carbon taken up by photosynthesis minus all the carbon costs of the plant organs involved. The vegetation is schematized as one big leaf for trees and one leaf for seasonal grasses, and is combined with a water balance model. Flux tower measurements of evaporation and CO2-assimilation, and remotely sensed vegetation cover are used for model evaluation, in addition to meteorological data as input for the model. A numerical optimization, the Shuffled Complex Evolution, is used to optimize the vegetation properties for each individual site by repeatedly running the model with different parametrizations and computing the net carbon profit over 20 years. The optimization was repeated several times for each site to analyze the sensitivity of the results to a range of different input parameters.</p><p>This case demonstrates an example of a complex numerical experiment with all its associated challenges concerning documenting model choices, large datasets and a variety of pre- and post- processing steps. Renku assured the repeatability and reproducibility of this experiment, by documenting this in a proper and systematic way. We demonstrate how Renku helped us to repeat analyses and update results, and we will present the knowledge graph of this experiment.</p><div> <p><strong>References<br></strong>Schymanski, S.J., Sivapalan, M., Roderick, M.L., Hutley, L.B., Beringer, J., 2009. An optimality‐based model of the dynamic feedbacks between natural vegetation and the water balance. Water Resources Research 45. https://doi.org/10.1029/2008WR006841</p> </div>