A Functional Landscape Protoype to simulate Water Resource Competition between Plants Vincent Le Chevalier Laboratory MAS Ecole Centrale of Paris, France [email protected] Xing Mei LIAMA, CASIA, China [email protected]

Marc Jaeger INRIA-Futurs, DigiPlante Team CIRAD AMAP, Montpellier, France [email protected]

Aurelien Lesluye LIAMA, CASIA, China Chalmers University, Sweden [email protected]

Abstract Vegetation ecosystem simulation and visualisation are a challenging topic involving multidisciplinary aspects. We present here a generic frame focused on functional plant growth models under environmental resource conditions: the growth model is coupled to the climatic conditions (temperature, rainfalls) and the competition between plants is taken into account, according to soil hydrological budget. A simple architecture and simulation scheme are proposed to synchronise the water cycles updating (daily based) and the plant growth cycles. A voxel space is used to store the water resource, and layers hold the interfaces between the environmental data and landscape components. The prototype simulator is operative on PC and HPCs with in-line and off-line visualisation tools. Despite the rough implementation level of the underlying bio-physical models, we could simulate realistic behavior of a simple vegetation model in heterogeneous environmental conditions, in space and time.

1. Introduction Realistic simulation of eco-systems is a hot challenging topic, involving bio-physical, ecological, social, economical and human aspects. We focus hereby on vegetation growth in interaction with resources, mainly temperature and water, over a delimited domain. Nowadays, more and more process based vegetation models (PBM) and functional structural models (FSPM) [4] become mature. Some of them are currently able to model plant, crop development and production, under constraints

Paul-Henry Cournède Laboratory MAS Ecole Centrale of Paris, France [email protected]

from a variable resource environment, especially in terms of light, water and temperature [3]. Nevertheless, in such approaches, the interaction between plant models and resources is limited. Another point is that such models cannot usually be easily extended at crop, plantation and higher spatial levels (landscape). Significant results were gained in the case of homogeneous crops, but competition for resources and heterogeneity in terms of space and time, make such extensions not obvious at all. The proposed work is to define some simple basis to allow plant and environment to interact, both ways. In this paper, we mainly focus on water resources, conservative, to be shared among the components of a crop, plantation or landscape. Water resource availability and supply is one of the main human interests, since human activities depend on them as well. All the elements of the water cycle have to be modeled, not only plants but soil and climate as well. Next section briefly presents some interesting pioneering works in this frame, while section three introduces the principles of the proposed landscape simulator. Section four details some specific models and their interaction with resources. Section five presents the techniques used to visualise simulation results. Some study cases are then illustrated before concluding.

2. Previous work Landscape modelling is a difficult subject, mainly because of the complex interactions at various time and space scales. Historically, the first goal was to reach a satisfying visual simulation of landscapes, and thus contributions came from Computer Graphics specialists. A pioneering study in

this domain is certainly the work J. Hammes [7] introducing for the first time the word of ecosystems in Computer Graphics, proposing a multilevel texture based approach to synthetise such systems. Relief definition was also studied, including erosion [11] and hydraulic aspects, as well as vegetation generation ([6], [5], and recently [1]). Shortcomings of these approaches are mainly lack of retroaction between elements of the landscape, as well as unrealistic dynamics. Physical accuracy is not sought in these studies since only the visual aspect is desired. Landscape submodels, on the other hand, are getting more and more complex and accurate. Plant models, soil models, hydrological models, are all constantly improving. However, they are rarely integrated together to allow a coherent simulation of the whole landscape. Such is also the case regarding scientific visualisation of bio-physical approaches at the landscape level where such techniques do exist on specific limited domains (runoff [12]).

3. Functional landscapes’ architecture The idea behind functional landscapes is to simulate the multiple interactions taking place inside ecosystems at the landscape level, with tools to visually investigate these interactions and the resulting quantitative variability. The notion was first introduced in [8], and has been the subject of further reflexions described in this work. However, this definition is to consider in a very restrictive way. The term of ‘functional’ did not (in the citation) include any biophysical, social, nor economical evolution except vegetation development and its interaction with the water cycle simulation.

3.1. Resources Our approach focuses on the evolution of resources accross the landscape. Resources are physical quantities that follow conservative laws. Components of the landscape compete for those resources, because they are in limited availability. Resources are thus one of the main ways for the components to interact. The water cycle is our primary concern, since water is the usual limiting resource for plants growth. The water cycle is a well-known phenomenon, described for example in [10, 2] (see figure 1). Water resource offers nice challenges in modeling, covering a wide range of motions with various time scales. It is, as such, a good test case for functional landscape architecture. Nevertheless, the proposed architecture could be used for other resources as well: nutrients, carbon, etc. Resources in the landscape are spatially distributed. In our implementation we use a voxel space discretisation to

Figure 1. The water cycle. On the left, the descending part of the cycle: water falls on the soil and vegetation, and is finally absorbed into the soil. On the right, the ascending part: water is absorbed through roots and released in athmosphere during plant transpiration, or even directly evaporated from the soil.

store the water resource level and the soil properties. Resolution of this 3D space is related to the terrain definition; it may be important, typically terrains with 256 by 256 by 64 voxels space are used in this paper. Landscape processes as well as climatic data do not interact directly with the voxel space but rather with specific spatialised interfaces called layers. They are divided into regular cells and their resolution is usually also related to that of the terrain definition, typically 256 by 256 cells in our case. However, specific data may not follow this scheme and interpolation methods are then required in order to allow communication between layers and the voxel space.

3.2. Simulation loop The proposed architecture implementation mimics the water cycle loop, that can be summarised as follow in a daily simulation loop: • read climat conditions (or user requests) • rain fall (if any) • runoff and soil absorption • deep water soil diffusion • plant growth and water uptake • evaporation / evapotranspiration The time step is chosen to be daily, being a compromise between fast processes (runoff for instance), slower processes (plant growth for instance), and data availibility (rain, temperature). These processes may thus be subject to specific implementation or interfaces in order to synchronise their interactions to resources, as described further on.

3.3. Model specifications

as a simple plant Process Based Model simply expressed by the following equation:

Models should be adapted in order to run within our framework. Specifically, they should become resourceoriented, in order to communicate nicely with other models. This poses no big problem for models already dedicated to the motion and transfers of resources, for example soil water model or runoff model. A bit more work is required concerning plant models, because they are generally geared more towards biomass and growth. Models should not assume that resources are always available. Functionning under a shortage of resources is a key point for the simulation of competition. Functionning with an excess of resources is generally less problematic, but must be ensured as well. It is also prefered that models do not involve the disparition (or appearance) of a resource. While it can be easier in certain cases, it makes resource accounting at the landscape scale difficult whithout interfering with individual models. Ideally, in such cases, the models should for example put the resource in a virtual stock (that has no physical support in the landscape), so that its exit point is known.

4. Landscape submodels 4.1. The Functional Plant Model

Qn = E

Qn−1 A + B.Qn−1

(2)

where n is the current plant development cycle, Qn is the biomass produced in the cirrent cycle, Qn−1 is the biomass produced in the previous cycle, A is the leaf petiol resistivity, B is the leaf limb resistance and E is the environment factor. Expression of this simple model is very straightforward since a single new leaf appears at each cycle, and dies at end of it. Expansion is supposed to be immediate. Note also that, with such simplifying assumptions, under non limiting environmental conditions (i.e. E = 1), the biomass production reaches a fixed maximum value Qmax . Synchronising the growth cycle with calendar time can be difficult, with possible side-effects in days when a cycle ends. We adopted an approach that is valid when the cycle duration is at least several time step. At the end of each cycle, the biomass produced is allocated to the organs of the plant according to the demands of the organs computed at the previous cycle Between two development cycles, we may consider (if the temperature allows it) that plants do still grow and uptake water in soil. Therefore, while performing the simulation, we had to compute on a daily base: • first the cycle increase according to the thermal time

The GreenLab plant model has been used in our simulation. It is a functional-structural model, which means that it includes both a growth model and a representation of the structure of the plant, interacting together. Details can be found in [4]. The relatively low number of parameters and advanced mathematical formalisation allows calibration of the model and thus reproduction of the behaviour of existing plants. In the frame of this work we did implement a basic degraded case of this model. Expression of the full model was a bit too complex to start with; a simple model was used to experiment the approach, nevertheless corresponding to a simple plant structure and simple plant fonctioning. Plant development is not defined from calendar time but rather from thermal time. That is, new organs appear at integer values of the cycle n: n=

Z

0

t

max(0, T − Tb ) dt Tg

(1)

where Tb is the base temperature below which development pauses, Tg is the number of degree-day necessary to complete a growth cycle. Plant model structure is simplified to a unique development axis, with leaves limited to a one cycle life span. Under the precited conditions, the proposed model can be seen

• then, check if this increase leads to a new cycle (case 1) or not (case 2) In case 1 (no new development cycle), potential growth is computed for the cycle increase Ca , according to the water resource availibilty, the corresponding daily biomass Ba produced is stored, and the corresponding water uptake in the soil deduced from soil water content. In case 2 (a new cycle will appear), the cycle increase is splitted in 2: the part belonging to the previous cycle (Ca ), and the part belonging to the next cycle called Cb . Ca is then processed P in the same way then case 1. The sum of biomass ( qa = Qn ) is computed and sent to the plant generator for a new development cycle. Tables summarising total biomass production are updated. Plant cycle is increased and the new production equation is used. The growth and water uptake is then performed with Cb as done with Ca , but on the new cycle n + 1. To model the water uptake, we restrict it to the first layer of soil. Uptake of plants is defined on a cell of soil, containing plants at a density δ, as: W =δ

Qn wue

where wue is the water use efficiency of the plant.

(3)

The parameter E is the primary way of interaction between plants and their environment. We give it a value of 1 unless water stress happens. Indeed, the plant could attempt to take more water than is available. This is when E is given a value less than 1. It is computed so that the plant does not take any more water than is available in soil.

4.2. Soil water movement This section describes the model chosen to represent water movement inside the soil, under the surface of the terrain, as well as on the soil surface. The water motions inside the soil was modelled by the linear form of Richards’ equation: ∂θe ∂ 2 θe ∂θe = D0 2 − K0 ∂t ∂z ∂z

(4)

which is a classical advection-diffusion equation. The water that is not absorbed flows on the soil surface as described below.

lay in the time scale of both phenomena, and the numbers of neighbours considered (26 cells in 3D respectively 8 cells in 2D). A less than satisfactory algorithm is implemented for runoff, emulating the greater speed of runoff by loops of diffusion on the surface. Such approaches may be satisfactory as prototypes, but show high costs in terms of computation time as the number of loops for runoff is related to the terrain resolution. They also have high costs in memory, the number of 3D cells inside soil being related to terrain resolution cubed. Proposed algorithm should be revisited for pratical cases.

4.3. A simple evaporation model Evaporation process is considered from vegetation (transpiration) and soil (evaporation). Vegetation case is implicitely covered by the functional plant model, on the basis of the water efficiency use balance. While biomass production is poor or vegetation not present a simple model is used. Classical literature offers many models, such as Penman equation, quite precise, but parameter-heavy. We chose the simple Turc’s formula for water evaporation over soil and water areas, defined here for a 10 day period: ET P = µ.(Rg + 50).

Ta Ta + 15

(6)

where µ is a coefficient (0.13 for 10 days), Rg is the solar radiation for 10 days, expressed in cal/cm2 , and Ta the average daily temperature on the period. A simple corrective ratio is applied when water covered areas, such as lakes, are concerned, and the ETP value is proportionaly scaled to a daily value to be evaluated in the daily cycle.

Figure 2. Water movements involved in Runoff

4.4. Environmental models Runoff quantity can be modeled thanks to a very simple balance equation: Ro = max(0, Ri + r − A − E)

(5)

where Ri is the input runoff, arriving in the cell, Ro is the output runoff, r is the rain, A is absorption in the cell, and E is evaporation, as illustrated on figure 2. The quantity Ro is then redistributed among lower neighbours of the cell, according to the slope between the cell and the neighbour (i.e. the lowest cell gets most of the water). There are other approaches for the distribution, and the paper [13] gives a good overview of them. We chose the basic proportional model because while simple, it gives realistic results. On the basis that both processes can be considered as diffusive movements, tri-dimensional inside the soil and twodimensional on the surface, a similar approach is used to simulate diffusion in soil and runoff. The main differences

Temperature and precipitations are considered as data for our simulator. There is no retroaction from plants to temperature, for instance. The simulator demanded daily values for temperature and precipitations at each point of the landscape. We established algorithms to procedurally generate data at this level of detail, based on real data corresponding to the region of Montpellier, France, in 2005, available from the Internet. These real values were monthly based, and of course not dependent on the position in the landscape. From these, daily values were procedurally generated. The daily values could also be modulated according to the position in the landscape, taking into account simple effects such as vertical temperature gradient. Here, the goal was not to work with accurate weather conditions models, but just to allow spatial and temporal heterogeneity, that may be defined from real measurements or specific simulators.

5.

Implementation and Visualization techniques

5.1. Implementation The proposed simulator, called ‘LandVol’ was implemented in C++ language under QT development environment on a PC Linux Fedora Core 4 system. Graphical developments, described below, are using OpenGL library. System interface is shown in Figure 3. Qt environment offers easy multi-thread managing functions. Those are used in the simulator to speed up the simulation. Each process corresponding to a specific task in the simulation loop is embedded in a separate thread. Typically, the graphical thread is independant from all others, export requests too. Within the water cycle loop, each process is embedded as well in a specific thread, However, specific care is taken in order to synchronise processes. For instance, plant growth process can only occur once water runoff and absorption is performed. The prototype was successfully tested on a 16 processor BULL Novascale 5000 Computer.

• an export of all the scene, including the voxel space with its water contents • an export of specific user selected interface layers

5.2. Simple embedded simulator controls The Simple visualiser embeded in the simulator allows fast control of water floods, and cumulated biomass on the terrain. This visualiser basically displays the terrain meshes. Geometry is defined from the terrain altitude mesh and a simple illumination with a constant color (brown) is applied on the terrain meshes.

Figure 4. Visualisation modes. Left up: simple terrain mesh; right up terrain with flooded areas; bottom: terrain with biomass, color blended (left), represented as simple crowns (right)

Figure 3. The LandVol simulator Interface

With a daily based approach, updating several layers interactions, simulation result visualisation and analysis tools are necessary. A classical year simulation set output is composed by 8 to 10 channels, at resolution of the Digital Elevation Model (thus 0.1 to 2 million cells), for 365 days; thus leading to a total storage of 0.2 to 6 Gigabytes. Such an amount of data makes visualisation and analysis tools necessary. The simulation tool offers three may ways to analyse and visualise results: • a simple visualisation tool, embeded in the simulator, allowing simple 3D control on the fly

This geometry may include (or not) water flows, changing to blue color the mesh vertices where the terrain is flooded. Cumulated biomass can also be added through color blending or simple tree representation. In the blending color mode, the terrain color (with potential water flood) is blended with green color according to the cumulated biomass value (the blending ratio is proportional to the biomass, up to a threshold value). In the simple tree representation mode, each biomass production within a cell (i.e. terrain mesh) is represented by a simple ‘tree crown’, whose diameter is representative of the biomass value. Figure 4 illustrates these four representation modes. The visualiser offers interactive rotation and translation at the current simulation day. This low level visualiser is a fast way to overview and control the simulation process.

5.3. Full simulation export In this functionality, the simulator dumps all data to disk on user request at current simulation step. More precisely, any layer (water in soil, water flood, vegetation biomass, cumulated biomass, temperature ...) can be stored as a floating

point image on disk. This also concerns the 3D voxel volume. For instance, both labels defining the various kind of soil, and values (water content) are exported. Such an export allows further simulation load and resume, but can of course not be extended to analyse and visualise the dynamics day per day of a full year simulation. It can be usefull for specific close ups, especially concerning water distribution within the soil, and for a detailled day analysis. The multichannels (layers) and volume sets can be visualised and analysed on a similar basis then medical imaging exams, with specific tools and technics related to remote sensing. Such output allows many visual combinations, including on the fly feature extraction, and 3D gradients evidence.

Figure 5. Volume rendering, including shadow computations from simulator voxel space and layers exports

Easy merge with other tools based on voxel space is also possible. Data analysis is open to a wide range of investigations, mainly related to multichannel 2D and 3D image analyses [9]. In our case, on the basis of past research work, we use the AMBIOS volume imaging plateform for analysis and volume rendering [8] as illustrated in Figure 5.

5.4. Exploring simulation channels For each simulated day, a binary multichannel layer record is dumped on the disk. This record is a table of the spatialised cells, each of them containing the scalar values of the user selected channels. Typicall exports contains 2 to 7 channels: terrain elevation, water depth, water contents in soil, water runoff, temperature, plant functioning biomass production, cumulated biomass. A new tool is currently developed, inspired from [12], extending the simulator in-line visualiser into a real time multi-layer visualiser. It aims at interactively visualizing any combination of channels (from a single one to four), combining geometrical, color mapping and color blending aspects for a given simulated day. Simple classical 3D navigation and navigation through day and time is allready im-

plemented. Up to now, geometry rendering is still similar to the in-line visualiser but offers more color combinations, and visualisation of any other exported chanel. Exemple of such visualisation are shown if Figure 8. Moreover, the visualiser includes simple statistical curves display, corresponding to the selected channels all over the year, as shown in Figure 6.

6. Results We present hereby some simulation results corresponding to simple cases. Those examples can not be considered as validations, but, beside their academic interest, were used for consistency check (resource water conservative aspect, comparisons with simple crop models, etc.) Many aspects could be used to illustrate this work. We present here some results with very few changes in environmental conditions. Despite the fact that the simulator holds variable local properties for vegetation and soil we consider here a single vegetation species homogeneously seeded (with a given constant density) all over the terrain. Soil parameters (except altitude) are also chosen constant, as well as rain fall level all over the terrain. Nevertheless, the proposed and developed simulation and visualisation tools are not restricted to these constraints, mainly related to the availability of consistent data.

6.1. Rain Level effect Current example is held on a synthetic terrain (see figure 7), with real rain and temperature conditions (see 4.4). Plant development parameters are inspired from annual crop behaviour with a limited development cycle, and a fast development rate (nearly 1 cycle per week at average daily temperature of 25 degres). In this experiment, the rain level is multiplied tenfold. Daily and cumulated biomass production are compared with the reference case in figure 6. One can note that plant development speed is not affected by rain conditions; growth cycle curves are identical in both cases. While the average daily biomass production is similar in late winter (climat values are mediterranean), the production quickly reaches the asymptotic value Qmax in the rainy case. On the contrary, in the reference case, production drops down, due to water resource limitation at the same date. A drop in production can then be observed in both cases early in spring, due to a colder week. After this point, daily biomass production is mainly related to water availability, and thus is maximum for the second case, while rain level in the reference case strongly affects biomass production.

Figure 6. Effect of rain level. Curves show average daily value on synthetic terrain. Cumulated biomass in orange, daily biomass in Green, Plant cycle in black, water in soil in red. Top: reference curves. Bottom with rain level multiplied by a factor 10, leading to a water saturated soil as shown on red curve.

Figure 7. The synthetic terrain used.

6.2. Full Simulation, plants, water, terrain and temperature We have held a possibly realistic simulation case on a user defined Digital Elevation Model downloaded from http://www.terragen.org . This example was chosen since it possesses different topographic areas: a main valley, small hills and plateau. Climate conditions were also downloaded from the Web site of an official weather forecast institutions, corresponding to real temperature and rain precipitation data from a town in south of France (year 2005). Plant parameters, as defined in equation 2 are set to A=0.3, B=0.5 and the seed value Q0 is set to 0.01. Simulations run on a pseudo-realistic terrain model illustrate how temperature and water interplay could create temporal and spatial variability. Results are commented here, and shown on figure 8. It illustrates 4 stages of the vegetation correponding to the fonctional biomass of the vegetation at dates of March 10, April 15, May 15 and June 12. Biomass production level is coded by colours from yellow (low level) to green (high level). On this example one may notice appearance of biomass in warm areas, oriented south, south-east in first view. Biomass production is then spread to higher altitudes and on the plateau. Then, in May,

Figure 8. Daily biomass production simulation from March (top left) to June (bottom right). Climatic conditions are related to real data for southern France. Level of production (if any) is color-mapped from yellow (low) to green (high)

biomass production is spread to the hills. In June, water shortage effect can be seen on slopes, due to low rain precipitation and vegetation competition.

7. Conclusion and further work This preliminary study, trying to interface a simple plant growth model and a simple water cycle model, both spacialised, is promising. Regular spatial partitioning offers fast local resource access to models to interact with them. A very simple dynmanic water cycle model is proposed, delivering a spatialised water resource level potential. Biomass production models, even very simple ones, can be used easily, interacting with simple climatic conditions (rain and temperature), updating locally the water resources. Basic tests and experiments show realistic behaviors, interesting for model tests and communication. However, the proposed approach has underlined several aspects to develop. Models first, and more precisely plant growth model as well as runoff models are too simplifyied for reasonable further uses. We are currently working on the full expression of the plant growth model, allowing also density effect, and reliable for agronomical applications, calibrated on real measured data. We are also developping a more efficient runoff simulation algorithm. While plant models and soil absorbtion models should

be complexified, it seems that deep water soil movements could be simplified, leading to simple layers as the soil water storage structure, rather than voxels, which have a high memory cost. An interesting challenge in landscape modelling is the consistency of the results. If we were to compare the output of two different simulation runs concerning two slightly different areas, during the same period, we should get similar results. This imposes an indexation of all data according to time and to geographical location. Another key point concerns validation, at three levels. The bio-physical models level, that might not always be extended to a time-spacialised cell. Validation concerning the implementation of the model, especially the way to process the ‘borders’ of the scene have or may have a drastic effect on the whole simulation, but such may also be the case while defining various model synchronising implementation, or spatialised data explorations. And last, but not least, validation of the simulation results themselves; simple synthetic and real cases under ‘controlled’ environment could help too for this task. From this preliminary work, we did also learn that, for each bio-physical process, defining the appropriate models, the appropriate level of description, the qualitative and quantitative level of interaction with the resources may be complex. It requires exchanges between scientists from various domains, underlining the need of advanced analysing and visualisation tools for mutual knowledge understanding and sharing.

8. Acknowledgements The authors would like to adress their thanks to BULLAsia headquaters in Beijing (CHINA) for their kind assistance on developments, and computing tests on BULL Novascale 5000. This work is supported by National HighTech Research and Development Plan of China under Grant No. 2006AA01Z301; and by LIAMA funding within GreenLab project.

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