A Toy Model for Frameworks and Toolkits Comparisons

http://giee.uvm.edu/AV/Frameworks/

	Background
	Model Overview
	Model Equations
	Data Sets
	Frameworks, Toolkits, Packages

Background

A workshop was held in July 2001 at the Institute for Ecological Economics, University of Maryland Center for Environmental Sciences (UMCES) at Solomons, Maryland, USA. The workshop was attended by modellers, environmental scientists, and developers and expert users of three toolkits and frameworks developed so far: the Spatial Modelling Environment (SME, T. Maxwell), Tarsier (F. Watson) and the Integrated Catchment Management System (ICMS, M. Reed). In common for the three frameworks is the ability to formalize and run spatial process based models. The goal of the workshop was to compare the three frameworks, figure out their strengths and peculiarities, better understand how they can be integrated if at all. As one of the venues for comparison, it was decided to formulate a "simple environmental problem" and to apply each of the three frameworks to this problem. In this way, the objective was to compare the three frameworks in their application to a single problem and to identify the relative strengths and weaknesses.

The purpose of this web site is to describe the Toy Model and offer it as sample application to implement and run in yet other frameworks and toolkits available. In that way we can expand this comparison to alternative software packages and approaches that may be currently available. These pages provide all the formalism, equations and data sets that may be required to implement the model. If you decide to do it, we will be most happy to publish the results of your application on this web site and add your modeling tool to the suit of toolkits presented here.

Model Overview

To select the pilot system we were looking for one that would require a mix of local and spatially distributed processes evolving in time. A simple runoff-erosion problem seemed to be a perfect candidate system. Let us consider a small watershed, described by its elevation map. For this watershed we have daily NetRainfall data, that represents the total of Rainfall and Evapotranspiration. The rainfall creates erosion, as a result the runoff carrying sediment is transported downhill towards the drainage point with the lowest elevation. At the drainage point there is a dam as if in a retention pond. Whenever the stage is higher than the dam level water is released from the watershed. As the sediment fills the pond the height of the dam will be gradually decreasing.

Model Equations

At any point in the watershed the amount of water (mm) is described by the following equation:

Water(t+dt) = Water(t) + Runoff_in - Runoff_out - Infiltration + NetRainfall

The Runoff is descibed by a piecewise linear function:

Runoff = { 0,      if Water < A

Water/(B-A) - A/(B-A)    if A ≤ Water ≤ B

Water,      if Water > B

where A = Low Water threshold = 2 mm; B = High Water Threshold = 10 mm.

The infiltration is assumed constant, dependent on the soil type provided by the Soil coverage:

Soil Type Infilitration rate (mm/day) Map category

water 0 1

sand 100 29

sandy clay 20 11

clay 1 31

The sediment transport equation is similar to the one for runoff:

Sediment = { 0,      if Runoff < D

Runoff·C/(E-D) - D·C/(E-D)    if D ≤ Runoff ≤ E

C,      if Runoff > E

where C = Max Sediment concentration = 100 g/m³; D = Low Water threshold = 2 mm/day; E = High Water Threshold = 10 mm/day.

The dam equation is

Runoff = { 0, if Water < H

Water - H if Water ≥ H

where H = Dam Height = 4000 mm.

Data Sets

The Data Sets include one timeseries and 3 maps.

NetRainfall. The negative values stand for evaporation.
Elevation map. Units = meters.
Soil map. Legend: 11=sandy clay, 31=clay, 29=sand, 1=water
Link map. Legend: 2=NE, 3=EE, 4=SE, 5=SS, 6=SW, 7=WW, 8=NW, 9=NN
You may use your own link map (if your software can create it, or use the one posted here.