Cellular Automata based Modeling for the Assessment of ... · Giuseppe Mendicino, Jessica Pedace, Alfonso Senatore* Department of Environmental and Chemical Engineering, University

Procedia Environmental Sciences 19 ( 2013 ) 311 – 320

1878-0296 © 2013 The Authors. Published by Elsevier B.V Open access under CC BY-NC-ND license.Selection and/or peer-review under responsibility of the Scientific Committee of the Conferencedoi: 10.1016/j.proenv.2013.06.036

Available online at www.sciencedirect.com

Four Decades of Progress in Monitoring and Modeling of Processes in the Soil-Plant-

Atmosphere System: Applications and Challenges

Cellular Automata based modeling for the assessment of ecohydrological dynamics at the hillslope scale: preliminary

results

Giuseppe Mendicino, Jessica Pedace, Alfonso Senatore* Department of Environmental and Chemical Engineering, University of Calabria, Italy

Abstract

An improved version of a Cellular Automata (CA)-based ecohydrological model developed using a Macroscopic CA approach was applied in a numerical experiment over a large hillslope. The original model was made up of a Vegetation Dynamic Model (VDM) coupled to a Soil–Vegetation–Atmosphere Transfer (SVAT) scheme and to a three-dimensional unsaturated flow and heat diffusion model. It was built in a problem solving environment that uses macroscopic CA both as a tool to model and simulate dynamic complex phenomena and as a computational model for parallel processing. The new version of the ecohydrological model adds flow generation and flow routing modules, allowing to govern liquid water interactions between surface and subsurface domains, to account for depression storage, obstruction storage exclusion and changing surface roughness owing to vegetation dynamics. This paper shows the preliminary results of the analysis of vegetation-hydrology dynamics performed on a ‘reference’ hillslope, with the same morphological characteristics of the Biosphere 2 hillslope experiment, hypothesized fully vegetated with alfalfa grass. Soil moisture and turbulent fluxes spatial and temporal variability was assessed for a period characterized by a single wetting event followed by a dry-down period. The computational performance of the CA-based model allowed a sensitivity analysis over the hillslope, varying both precipitation intensity and soil moisture initial conditions. Surface runoff, soil moisture, evapotranspiration and Leaf Area Index space-time distributions were evaluated for each scenario, highlighting the main differences depending on the changing features of the experiments.

© 2013 The Authors. Published by Elsevier B.V. Selection and/or peer-review under responsibility of the Scientific Committee of the conference.

Keywords: Cellular Automata; Fully-coupled models; Vegetation Dynamics Models (VDM); Soil–Vegetation–Atmosphere Transfer (SVAT) schemes; 3D unsaturated flow models; Flow generation; Flow routing; Biosphere 2; Evapotranspiration; LAI

* Corresponding author. Tel.: +39-0984-496614; fax: +390984-494050. E-mail address: [email protected].

© 2013 The Authors. Published by Elsevier B.V Open access under CC BY-NC-ND license.Selection and/or peer-review under responsibility of the Scientific Committee of the conference

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312 Giuseppe Mendicino et al. / Procedia Environmental Sciences 19 ( 2013 ) 311 – 320

1. Introduction

Cellular Automata (CA) [1,2,3] are discrete dynamic systems, where space is divided in regular cells, whose global evolution is derived from the simultaneous application of a unique local rule (transition function) governing the interactions between each cell (which embeds a finite automaton as its computational device) and its neighbors. The CA computational paradigm is directly compatible with parallel programming and makes CA capable to support the modelling of large-scale systems requiring complex and computationally expensive simulations.

The possibility of exploiting for fluid dynamics applications the CA specific attitude of being executed ‘easily’ in parallel systems was investigated since ‘70s of last century [4,5], focusing on the microscopic scale, but the first effective approach of CA to flow modeling came later, with Lattice Gas Automata (LGA) models proposed by [6]. LGA represented the state of each cell in the regular lattice as a pure boolean, not allowing to express the velocity in explicit form. This drawback was overcome by the Lattice Boltzmann method (LBM), where the state variables can take continuous values, representing the density of fluid particles [7,8]. LBM has been used also to model flow in porous media, but they also focus mainly on a microscopic approach. In order to simulate macroscopic flow phenomena, an extension of the original CA definition was developed, introducing Macroscopic CA (MCA) [9,10]. In the MCA an almost unlimited number of states is allowed for the cells, and each state is expressed by a Cartesian product of sub-states, each one describing a specific feature of the space portion related to its own cell. Nevertheless, most of the MCA applications [e.g. 11,12] use transition functions based on parameters whose physical meaning is not clear, so they need heavy calibration phases.

The first example of MCA modeling in hydrology using a transition function based on physical laws is given by [13], who developed a three-dimensional model which simulates water flux in unsaturated soils. With the aim of completely modeling complex surface-subsurface ecohydrological dynamics by means of MCA, the model was extended by adding Vegetation Dynamic Models (VDMs) coupled to a Soil–Vegetation–Atmosphere Transfer (SVAT) scheme, and tested against both field data and numerical benchmarks, also considering heterogeneous or sloping terrains [14,15]. Furthermore, recently [16] suggested a solution for the main restriction of the approach proposed by [13], i.e. the direct and stringent dependence of the time step on the spatial grid and the hydraulic properties of the cells, by developing a framework with an unconditionally stable computational algorithm based on the approach of [17].

In this paper the objective of fully-coupled modeling of surface-subsurface ecohydrological dynamics by means of MCA is pursued by adding the schematization of runoff generation and flow routing processes to the system shown in [13,14,15]. Several hydrological models describe in great detail surface-subsurface-groundwater interactions (e.g. the reviews in [18,19], and [20,21]), but a much smaller number is aimed at the simulation of the hydrological system in a more comprehensive way, accounting for the complex interactions with the atmospheric boundary layer and vegetation (Rhessys [22], GeoTop [23], tRIBS+VEGGIE [24], Tethys-Chloris [25]). Nevertheless, a complete ecohydrological model considering these feedbacks is potentially the perfect ‘virtual laboratory’ [26,27] for performing analyses that would be difficult to achieve with idealized analytical solutions or would otherwise require huge investments in monitoring instruments. Among the obstacles preventing the development and the operational use of fully-coupled ecohydrological models, one of the most challenging is given by huge computational requirements [28,29]. From this point of view CA can significantly contribute to a greater usability of these models, considering that multi-core processors allowing parallel computing are becoming more readily available.

The fully-coupled MCA model is intended in this paper for a highly detailed analysis at the hillslope scale, i.e. at the scale of the hydrological element generating runoff and first routing water flow. Understanding surface and subsurface water flow in a hillslope is crucial also for other reasons, e.g.


rainfall induced landslides or nutrient transport. The features of the hillslope used for this study are the same of the Biosphere 2 hillslope experiment [30]. Next Section describes the main features of the new runoff generation and flow routing schemes in the MCA model; in Section 3 design of numerical experiments is briefly described, and preliminary results of simulations with varying rainfall and initial soil moisture conditions are shown.

2. Methods

This section describes the new features of the fully-coupled MCA model. For details about VDM, SVAT scheme, three-dimensional unsaturated soil flow model and their interactions, readers are completely referred to [13,14,15], where also more details about the CA problem solving environment used for developing the system are given [31].

2.1. Overland flow

MCA approach requires a discrete formulation of the overland flow. Such as described in [13], also in this case the discrete mass balance equation can be expressed by the following general equation:

1c cc

c

m St

(1)

where c is the cell where the water mass balance is performed, is the generic direction obtained linking the center of cell c with that adjacent, c is the mass flux (L3T-1), c is the fluid density (ML-3), mc is the mass inside the single cell c (M), t is the time step (T), mc/ t (MT-1) is the mass-time variation in the cell, and Sc is the mass source term (L3T-1). Equation (1) is valid both for internal nodes of the discrete domain and for boundary nodes.

Adopting the diffusion wave model as an approximation of the full Saint Venant equations (where gradually varied flow conditions are assumed, with uniform velocity over the cross-section, water level across the section represented by a horizontal line and small bed slope), and using Chezy equation with Manning’s coefficient in order to express the friction slope, the discrete mass flux over a square regular mesh is given by:

2/3

c

c c cc

c

R H H= An l

(2)

where Hc and H are respectively the water surface elevations (L) in the cell c and in the contiguous cell along direction (H = h + z, with h flow depth and z land surface elevation); A c is the surface area where the flux passes through (L2); l c is the distance between the centers of the cells c and (L); R c is the hydraulic radius corresponding to A c; n c is the Manning’s coefficient (L-1/3T), calculated as the average of the cells values. With respect to previous versions of the MCA model, variable h is a new sub-state related only to surface cells of the domain.


Mass-time variation in the cell can be expressed by the following equation:

c cc c

m h= At t

(3)

where Ac is the area of the upper (horizontal) surface of cell c (L2), c is the fluid density (ML-3) and hc/ t is the flow depth variation in the cell during time step t.

Substituting Eqs. (2) and (3) to Eq. (1) the complete overland flow equation is obtained:

2/3

c

c c cc c c

c

R H H hA + A = Sn l t

(4)

Eq. (4) corresponds to the transition function for the overland flow, that is applied to each cell of the domain, in order to estimate the only unknown term, i.e. hc.

2.2. Accounting for depressions and obstructions

Modeling of depression storage and obstruction storage exclusion is based on the introduction of volumetric height VH [32], which is defined as the height from land surface of an equivalent volume of water without depressions or obstructions. Figure 1 shows that, up to the maximum storage height hs, given by the sum of the height of depression storage hds (equal to the height at which overland flow starts to occur) and the height of storage within obstructions hos, the relationship between h and VH can be expressed by a parabolic equation, while above that height the relationship is linear.

Fig. 1. Conceptual model for depression storage and obstruction storage exclusion, modified from [32]. Symbols are explained in the text.

Substituting VH to overland flow Eq. (4) leads to the following modified equation, accounting for depressions and obstructions:


2/3

c

c c cc c c

c

R H H VHA + A = Sn l t

(5)

Two remarks are relevant concerning variable hs. The first is that it roughly corresponds to vegetation height, that is not a static parameter. VDM allows to estimate vegetation growth in terms of evolution of Leaf Area Index LAI, that can be related to vegetation height for specific land uses (e.g. [33]). Hence, VDM interacts with the overland flow module by varying the height of storage obstructions and the relationship h = h(VH), depending on the parameter hs value. Another way VDM, through dynamic parameter hs, affects overland flow is the variation of Manning’s coefficient. In fact, according to [34], the flow resistance exerted on vegetation is usually classified by the relative flow depth to the height of vegetation. Hence, Manning’s coefficient varies depending on h and hs.

2.3. Source term and surface-subsurface interactions

Source term Sc in Eq. (1) is given by the sum of three terms, namely incoming precipitation, evaporation from water stored on the surface and flow between surface and subsurface (i.e. infiltration or exfiltration). The evapotranspiration module in the SVAT scheme is affected by the presence of water on the surface. Referring to Figure 1, if 0 < h hds, the estimate of latent heat flux from bare soil Eg is limited only to the fraction of surface not covered by water (1 – krgo, where krgo varies between zero at land surface elevation and unity at hds), while for the fraction krgo evaporation from wet surface Ed is calculated. Furthermore, also partial or total submersion of vegetation cover, i.e. hds < h hds + hos, is considered, accounting for a submersion factor fs, varying between zero (up to the height where it is assumed that plant transpiration begins to be hindered) and one (total submersion). In case of partial or total submersion, transpiration of vegetation Etr is usually limited also by moisture excess, and this is accounted for in the stomatal resistance evaluation.

According to [32], the flux across the total interface area Ac, expressed as Qgo (L3T 1), is given by the following equation (negative for flow out of the surface):

go rgo c go g oQ k A K H H (6)

where Hg and Ho are the water hydraulic head within the surface cell (i.e., the hydraulic head in the first soil layer) and the water surface elevation (i.e. the hydraulic head over the ground surface) respectively, while Kgo (T 1) is the leakance across the ground surface to the subsurface. This leakance may include a skin layer effect, or it may be defined as the vertical hydraulic conductivity of the topmost subsurface cell divided by its half-thickness (since the hydraulic head within the cell is calculated in its center).

3. Preliminary results

The fully-coupled model was applied to an ideal test-case, based on a hillslope with the same morphological features of the Biosphere 2 experiment (30 m × 15 m × 1 m constant depth; Fig. 2, [30]), considering two different initial conditions (dry i.c., uniform total head H involving average soil moisture

= 0.20; wet i.c., uniform H involving = 0.28). The soil hydraulic parameters, chosen in order to emphasize the differences between dry and wet i.c., and corresponding to a clay loam, were: hydraulic conductivity Ks = 2.69×10-7 m s 1; residual water content r = 0.0778; saturation water content s = 0.3783; van Genuchten equations coefficients: L = 1.3168, n = 1.29, and = 1.4551 m 1. Input data


were half-hourly series of precipitation, air temperature, wind speed, atmospheric pressure, relative humidity, incoming solar radiation and albedo taken from a micrometeorological station placed in a peach orchard and directly managed by the authors, from 05.06.2012 up to 20.06.2012 (15 days). The chosen period was characterized by an initial rainy event (scenario P, 4.5 hours, with a cumulated value of 28.4 mm), and a following summertime dry-down period (with temperatures ranging from 12.2 °C to 34.2 °C, average value 23.5 °C). For both the dry and wet i.c., initial precipitation was also doubled (scenario 2P) and halved (scenario 0.5P), leading to a total of 6 different scenarios. The hypothesized vegetation covering the hillslope was alfalfa grass, with initial LAI = 0.4. Boundary conditions were of no flux all around the hillslope, except the closing surface section 15 m wide (Fig. 2; water can flow out only from the surface, not along the vertical soil plane). The dimension of each cell of the Automata was 1 m × 1 m × 0.05 m along the vertical axis (total number of cells: 9000). Following, the main results achieved by the simulations are briefly described.

Fig. 2. Biosphere 2 hillslope with the upstream (U) and downstream (D) control points for monitoring soil moisture evolution.

The hydrographs (Fig. 3) are limited only to the first 5 hours of simulations, when runoff occurs. Owing to low soil hydraulic conductivity and precipitation intensity, overland flow occurs almost in every simulation, even though precipitation duration is not very long (no contributions of subsurface flow). Such as it was expected, precipitation intensities (0.5P, P and 2P) significantly impact on peak flows, that

Fig. 3. Outflow from the hillslope during the first 5 hours of simulation: (a) dry initial conditions; (b) wet initial conditions.


instead are not much influenced by initial soil moisture conditions, since in both cases saturated surface conditions are reached during the simulations. However, soil moisture affects total runoff volume, as it is shown in Fig. 3b, where for all precipitation scenarios new minor peaks arise.

Two reference soil columns, one upstream (cell U, Fig. 2) and the other one downstream (cell D, Fig. 2) were analyzed for assessing soil moisture evolution. Figs. 4 and 5 show several soil moisture profiles at the beginning of the simulation (0.00 days), at the end of the rainy event (0.19 d), and then during the dry-down period (days 1.00, 1.75, 5.00 and 15.00). The left and center graphs of both Figs. 4 (dry i.c.) and 5 (wet i.c.) show, for the upstream soil column, that effects of different precipitation (0.5P and 2P) only produces significant differences in the top layers of 0.19 d profile. The same happens to the downstream soil column (comparison not shown). Also center and right graphs in Fig. 4 (same precipitation 2P, but different soil columns, U and D) are similar, excluding the slight shift due to the i.c. profile. In all dry cases the 15.00 d profile shows a typical s-shape, meaning that the initial precipitation still influences the first soil layers, while the wet front slowly goes down. The same happens for the upstream wet i.c. soil column (Fig. 5, left and center graphs), but a different profile is shown for the downstream wet i.c. soil column (Fig. 5, right graph). Different behavior is due to the quasi-saturated soil moisture i.c. of much of the soil profile, and the consequent higher hydraulic conductivity, allowing a faster dry-down of the profile, even though the mean water content in the D profile remains higher than in the U profile for the whole simulation period.

Fig. 4. Soil moisture profiles for upstream (U) and downstream (D) with different precipitation intensities; dry initial conditions.

Fig. 5. Same as Fig. 4, but with wet initial conditions.


Faster dry-down of wet i.c. case is linked to a higher actual evapotranspiration rate ET. Half-hour evolution of spatially averaged simulated E with dry i.c. is very similar for each precipitation scenario (0.5P, P and 2P), excluding only the first day, when the rainy event happens (graphs not shown). The same behavior is given by the three wet i.c. simulations. On the contrary, assuming the same precipitation scenario, more marked differences are shown between wet and dry i.c. simulations, even though the half-hour evolutions of E (graphs not shown) highlight daytime differences not higher than 10 Wm-2 from the 5th to the 15th day, up to 20 Wm-2 during the 1st and 4th day, and close to 50-70 Wm-2 only during the 2nd and 3rd day (peak values of E reach 600 Wm-2 in the 1st rainy day, and about 3-400 Wm-2 later on). Figure 6 shows the spatial pattern of cumulated actual ET after 15 days of simulation, for the same precipitation scenario P, but with different i.c. (left graph: dry i.c.; right graph: wet i.c.). The distribution pattern of the variable is similar considering the two surfaces, with higher values in the water collecting cells and in the downstream cells. However, the scales used for the two graphs are different. Owing to the slight differences in terms of initial upstream and downstream soil moisture conditions (see Fig. 4, center and right graph), cumulated ET in the dry case only varies from about 61.1 to 62.7 mm (range of 1.6 mm, cumulated ET can be considered as uniformly distributed). In the wet case, owing to higher differences in initial soil moisture conditions (Fig. 5, center and right graph), cumulated ET varies from about 62.0 up to 77.0 mm at the closure section (with a more significant range of 15 mm). Different values in the legends were plotted in order to let the reader appreciate the spatial pattern of cumulated ET also with dry i.c.

Fig. 6. Spatial distribution of cumulated actual ET after 15 days of simulation and precipitation intensity P. Left: dry initial conditions; right: wet initial conditions. Please note different values in the legends.

A similar behavior to ET distribution pattern is given by LAI maps (Fig. 7), that are obviously strictly connected to this previous variable. Specifically, with dry i.c. variability of LAI ranges from 1.35 to 1.43, while with wet i.c. it ranges from 1.45 to 2.00. Such as it is usually experienced in natural hillslopes, higher vegetation density can be observed in the water collecting areas and in the downstream area.

Fig. 7. Spatial distribution of LAI after 15 days of simulation and precipitation intensity P. Left: dry initial conditions; right: wet initial conditions. Please note different values in the legends.


4. Conclusions

In this paper a fully-coupled virtual ecohydrological laboratory based on Macroscopic Cellular Automata (MCA) is presented, by showing numerical applications at the hillslope scale and the inter-related results of runoff generation and routing, unsaturated soil moisture fluxes, subsurface-surface-atmosphere energy and water fluxes, and vegetation growth dynamics (which implicitly accounts for CO2 flux exchanges between surface and atmosphere). This potentially very powerful tool, characterized by a computational paradigm directly compatible with parallel computing, needs to be tested over reliable benchmarks. Few models nowadays allow a comprehensive comparison of all the output variables provided by the MCA model. The Biosphere 2 experiment should allow a complete control at the hillslope scale of many ecohydrological processes, by carefully measuring them.

Further developments of the model will concern numerical and, where possible, observed data comparisons, and the analysis of computational efficiency. The modular architecture of the fully-coupled model allows since now to add new modules, for example analyzing geotechnical aspects or nutrient transport phenomena at the hillslope scale.

Acknowledgements

The authors gratefully acknowledge Dr. Valeriy Ivanov (University of Michigan) for providing the original DTM of Biosphere 2. The research was partly funded through a grant provided by the program “Borse Post-doc all’estero UniCal”, POR Calabria FSE 2007/2013, Axis 4 “Capitale umano”, Operative objective M.2.

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Cellular Automata based Modeling for the Assessment of ... · Giuseppe Mendicino, Jessica Pedace, Alfonso Senatore* Department of Environmental and Chemical Engineering, University