* Finally, along the lines of predicting system behavior, researchers may want to know what conditions will lead to an optimal outcome of some property of the system. This type of analysis is essential to informed policy decisions and often cannot be performed without an integrated model of natural and human systems. * At the next level, after empirical measurements had been taken, models can be used to test assumptions about the system. (including spatial and temporal interpolation) * Models can be used to gain a conceptual picture of how a system of interest might work. In many cases, these types of models are generated before any field or laboratory studies have been conducted, and their main purpose is to examine what features are the most critical in determining system behavior. WHY MODELING? Scientists may be led to modeling for a number of reasons. Hall and Day (1977) consider three uses of models: understanding, assessing, and optimizing.

Substance: The stuff we're interested in (water, carbon, N). What units do we use to measure the quantity of a substance? Better to use volume or mass. Mass might be preferable to volume, because mass in conserved, while volume is not

We'll use the term 'stock' (abbreviated S) to refer to the amount of substance in a reservoir. The problem of estimating the stock of a reservoir (i.e. the quantity of substance that it holds) is non-trivial, and often important. Using units of volume, the ocean, for example, has a stock (=volume) of Volume = Area x Height (depth), and is measured in km 3 Using units of mass, the ocean has a stock (= mass) of Mass = Density x Area x Height, and is measured in kg comp1 Reservoir: Place that holds or stores a substance

Stock per unit volume: amount of a stock in a unit volume (abbreviated s) If the stock of substance has units of X, then s has units of X per distance cubed. For example, if the substance is mass of water with units of kilograms, then s has units of kilograms per meter cubed: kg/m3. Stock = (Stock per unit volume) x Volume S = s V Note that when the substance is mass, then the substance per unit volume is "density".

Transport: moving a substance between reservoirs (abbreviated T) comp1 flow1

Flux: rate of transporting a substance (abbreviated F) If the substance has units of X, then flux has units of X per unit time. For example, if the substance is mass of water with units of kilograms, then the flux has units of kilograms per second. Transport = Flux x Time T = F x time If a quantity is conserved, then: (Flux in - Flux out) x Time = Increase in Reservoir Stock; or Rate of Growth in Reservoir Stock = (Flux in - Flux out) dS/dt = Fin - Fout

Flux per unit area: rate of transporting a substance across a surface (abbreviated f) If flux has units of X per unit time, then flux per unit area has units of X per unit time per unit area. For example, if the substance is mass of water with units of kilograms, then the flux per unit area has units of kilograms per second per meter squared: kg/m2s Flux = (flux per unit area) x Area F = f x A Note that when the stock is volume of a material, then the flux per unit area is "velocity".

Time-dependent reservoir models: dS/St = Fin - Fout = Fnet No Feedback: Fnet(t) a proscribed function of time, t, and is not a function of stock, S. Positive Feedback: Fnet increases with stock, S. Negative Feedback: Fnet decreases with stock, S

Solution of time-dependent problems Mathematically, we must solve the ordinary differential equation, dS(t)/dt = Fnet(t), and its associated initial condition, S(t=0) = S 0. Examples: dS/dt=C, S(t)=S 0 +C t dS/dt=C+at, S(t)=S 0 +C t +at 2 /2 dS/dt=aS, S(t)=S 0 exp(at) dS/dt=-aS, S(t)=S 0 exp(-at) dS/dt=C-aS, S(t)=(C/a>(1-exp(-at)) Once solution is found, behavior at long time can be analyzed.

Between the qualitative conceptual model and the computer code, there are many software packages that can help convert conceptual ideas into a running model. Usually, there is a trade-off between universality and user-friendliness. At one extreme are computer languages that can be used to translate any concept and any knowledge into working computer code. At the other extreme are implementations of particular models that are good only for the individual systems and conditions for which they were designed. In between there are a variety of more universal tools. Among them we can distinguish between modeling languages, which are computer languages designed specifically for model development, and extendible modeling systems, which are modeling packages that allow specific code to be added by the user if the existing methods are not sufficient for their purposes. In contrast, there are also modeling systems, which are completely prepackaged and do not allow any additions to the methods provided. There is a remarkable range among these packaged and extendible systems in terms of their user- friendliness. In general, the less power the user has to modify the system, the fancier the graphic user interface (GUI) and the easier the system is to learn. Extendible models, are individual models that can be adjusted for different locations and case studies. In these, the model structure is much less flexible, the user can make choices from a limited list of options and it is usually just the parameters and some spatial and temporal characteristics that can be changed.

Visual modelling: (1) drawing of diagrams that show the main features of the model. (2) fleshing-out the model- diagram elements with quantitative information: values and equations. System Dynamics: … as compartments (stocks, levels) whose values are governed by flows in and flows out. (visual language for representing differential-equation models, with a compartment representing a state variable, and the rate-of-change being the net sum of inflows minus outflows. Disaggregation: defining how one class behaves, then specifying that there are many such classes. Object-based modelling: define how one member behaves, then specify that there are many such members. Spatial modelling: a special form of disaggregation.One spatial unit (grid square, hexagon, polygon...) is modelled, then many such units are specified. Each spatial unit can be given spatial attributes (area, location), and the proximity of one unit to another can be represented. Modular modelling: allows any model to be inserted as a submodel into another model. Efficient computation: Models can be run as compiled C++ programs. … Customisable output displays and input tools: can design and implement their own input/output procedures, independently of the Simile developers. In particular, you can develop displays for model output that are specific to your requirements. Once developed, these can be shared with others in your research community. Declarative representation of model structure: A Simile model is saved in an open format …also opens the way for the efficient of models across the Internet (as XML files), and for the sharing of models between different modelling environments.