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Integrating Agent-Based Models of Subsistence Farming with Individual-Based Models of Trees and Dynamic Models of Water Distribution

Integrating Agent-Based Models of Subsistence Farming with Individual-Based Models of Trees and Dynamic Models of Water Distribution

Subsistence farming communities are dependent on the landscape to provide the resource base upon which their societies can be built. A key component of this is the role of climate, and the feedback between rainfall, crop growth, land clearance, and their coupling to the hydrological cycle. Temporal fluctuations in rainfall, on timescales from annual through to decadal and longer, changes the spatial distribution of water availability, mediated by the soil-type, slope and landcover. This in turn determines the locations within the landscape that can support agriculture, and controls sustainability of farming practices. We present an integrated modelling system to represent land use change that couples three simple process models:- An agent based model of subsistence farming; an individual-based model of tree growth; and a spatially extended version of TOPMODEL for the prediction of distributed soil moisture and stream discharge. In this way we can, for example, investigate how demographic changes and associated removal of forest cover influence agricultural production through changes in ground water availability and how land-use change affects river regimes and influences flood frequency and magnitude.

Introduction

This work seeks to couple together three simple dynamical models, all of which are spatially distributed. Trees are represented by an individual based model that represents all trees over 5 years in age over the study region. Over time the trees grow, and are cut down by people, represented as individual agents, each with their own unique behaviour. This modifies the hydrology, largely through changes in hydraulic conductivity, leading to differences in soil moisture deficit and discharge. The model is applied to a 4.2km sub-catchment in the Nepal middle hills (the Bore Khola), for which there is considerable variation in land use, from farmed lowland to heavily forested uplands

Land Use

Land use within the Bore Khola is largely divided between three types, with most of the farming taking place in the lower part (Khet), where approximately 80 households are situated.

Land use

Elevation and Shade

Elevation is based on a 20m resolution DTM derived from digitized contours, mapped at 1:5000 scale with a 10m interval.
High relief in the Bore Khola valley leads to significant self-shading of the landscape. The figure shows those parts of the catchment in shadow for solar zenith angle 65° and azimuth 100°E

Trees

The tree model is a simplification of the SORTIE methodology developed by Pacala et al (1996).

In this individual based model growth of individual trees is limited by competition for light.

  • Sapling survival and growth are controlled by shading.
  • Tree height and depth allometrically related to trunk diameter.
  • Death rate is 1% per annum in the absence of other disturbances.
  • New saplings are produced with a distance from parent that depends on species.

For the current study we limit the number of species to two - a shade tolerant low dispersal species and a less shade tolerant but wide dispersing gap species.


The basal area of shade-tolerant and gap species as a function of time, illustrating the gradual dominance of the shade tolerant trees. When people are introduced at year 600, both species are rapidly reduced in area. Most of the reduction takes place in the lower half of the catchment, although higher reaches get thinned gradually also. Basal area of shade-tolerant and gap species as a function of time

Shade tolerant trees are in red and the gap species in yellow.
The model was run for 1200 years to allow the effects of initial transients to decay.
Plots are shown for the intial state and then every 600 years thereafter.
Actual forest cover near Bore Khola
Shade tolerant trees in red and gap species in yellow Actual forest cover near Bore Khola
[Click for a larger version of image]

Hydrology

Hydrology is represented by a spatially distributed dynamic model, based on TOPMODEL, but with explicit flow routing between points in the catchment (Brasington et al 1998).

Each cell in the model represents an idealised vegetated soil profile, with interception store (CAP), a root zone store (SRMAX) and a dynamic transition between root zone and water table.
Model results described below are based on a year's time series of rainfall data.
The two panels show the first 4000 hours of rainfall and the associated discharge observed.

People

The agent-based model of people is an extension of the the design of Ziervogel et al (2004).

  • Households need a field of size 1 ha. to feed a family of 8 people.
  • Fuelwood and fodder requirements are 1 cubic metre of wood per person per year
  • Trees are cleared annually until wood and field requirements are met
  • Only trees with trunks between 10cm and 1m are cut down
  • The population starts with 3 households at year 600, and doubles in size every 30 years

People [click for larger version]
[Click image for larger version]

On the far left the impact of tree cutting can be seen. Bright green shows fields and bright yellow degraded forest (less than 125 trees per hectare) at 60 year intervals as the people remove the forest cover. In the centre are the resulting changes in the soil moisture deficit, and on the right the accompanying changes in total discharge. Earlier discharge peaks are better captured as the distribution of land use approaches that of the current catchment.

Conclusion

The combination of agent based modelling, Individual-based ecological modelling and distributed dynamic hydrological modelling can be applied to real-world situations with some degree of success. The current framework can now be extended to bring in more realistic behaviour for the human agents, and the feedbacks between soil moisture, hydrology and land use explored in detail, including, for example, the effects of landslides. Other extensions will include realistic self-shading by the topography and its impact on tree growth (see above), and the effects of transpiration and root-zone water extraction by plants on the hydrology and inter-plant competition.

References

  • Brasington, J., El-Hames, A. And Richards, K., 1998. In "The Sustainable Management of Tropical Catchments", Harper,D. And Brown, T. Eds. Wiley.
  • Pacala, S.W., Canham, C.D., Saponara, J., Silander, J.A. Jr., Kobe, R.K. And Ribbens, E., "Forest Models Defined by Field Measurements, Estimation, Error Analysis and Dynamics", Ecological Monographs, 66, 1-42, 1996
  • Ziervogel, G., Bithell, M., Washington, R. And Downing, T. (2005) "Agent-based social simulation: A method for assessing the impact of seasonal climate forecast applications among smallholder farmers.", Agricultural Systems, 83, 1-26
  • M. Bithell, M and J. Brasington, (2005), Integrating Agent Models of Subsistence Farming With Dynamic Models of Water Distribution, Eos Transactions AGU, 85(47), SF33A-0725