Modeling and Environmental Science: In Conclusion Environmental Science It sounds like a modern idea, but if you view it broadly, it s a very old idea: Our ancestors survival depended on their knowledge of the environment Science is a process, a way of knowing It results in conclusions, generalizations, and sometimes scientific theories and even scientific laws People often confuse the process of science with a fied set of beliefs the results BUT science does not lead to so much to a fied set of beliefs as to a set of beliefs that, at the present time, account for all known observations about a kind of phenomenon
Science Change Science is a process of discovery, thus scientific ideas change through time, and this can make applying the results of science frustrating. For eample: 1. Scientists cannot agree what is the best diet for people. 2. A chemical can be considered as dangerous in the environment for a while, and then later be determined not be 3. Wild fire was considered to be undesirable disturbance, and then it was decided that it is an important and necessary natural phenomenon It is more accurate to think of science as a continuing adventure with ever improving approimations of how the world works
How Does Science Work? Science begins with Observations of the world From these observations, scientists formulate hypotheses that can be tested Modern science does not deal with things that cannot be tested by observations, such as the eistence of a supernatural being It is generally agreed today that the essence of the scientific method is disprovability A statement can be said to be scientific if someone can state a method by which it can be disproved
Scientific Statements Let s come up with a few scientific statements How could we disprove them? For eample: Deforestation changes stream water flow peaks and water quality This is a scientific statement as we can come up with an eperiment to disprove it or test if the above statement is true or false In some sense, progress in science is not so much limited by our ability to conceive of scientific statements, but our ability to come up with ways to test them
Assumptions of Science 1. Events in the natural world follow patterns that can be understood through careful observation and analysis 2. The basic patterns, or rules, that describe the behavior of events in the natural world are the same everywhere 3. Science is based on a type of reasoning known as induction; it begins with specific observations about the natural world and etends to generalizations 4. Generalizations can be subjected to tests that may disprove them; if such a test cannot be devised, then a generalization cannot be treated as a scientific statement 5. Although new evidence can disprove eisting scientific theories, science can never provide absolute proof of the truth of its theories
The Methods of Science 1 Observation of nature (Contet: Current scientific theories and social values) Yes Reject No hypothesis? 7 2 Form some inferences about how we think things work Perform data collection to allow us to conduct the test 6 3 Create a model that relates the inferences in order to eplain the observations Test the hypothesis 5 Hypothesis deduced from the model 4
What is a Model? Just what are we talking about when we use the word model here? There are a wide range of possible definitions, but here is a simple description that suits our purposes: A model can be thought of as a means of codifying how a set of processes functions, simplifying the compleity of the real world in which the processes operate. Anderson, M.G. and T.P. Burt. 1985. Modelling Strategies. In Anderson, M.G. and T.P. Burt (Eds.), Hydrological Forecasting, John Wiley and Sons, Great Britain, 1-13. At the mention of the word model you might think of computer software, or a particular STELLA file, but the model itself is the idea encoded therein, a particular representation of how something works
Modeling in Env. Science Observations & Epectations 1 2 Observation of nature (Contet: Current scientific theories and social values) Form some inferences about how we think things work The precursors to models are sets of observations that form the basis of what we know about the world From those we develop a set of epectations (or inferences) about how things work we make some sort of guess (informed and logical or otherwise) about how the system functions This is where the deep thinking takes place
Modeling in Env. Science Synthesis & Integration 1 2 3 Observation of nature (Contet: Current scientific theories and social values) Form some inferences about how we think things work Create a model that relates the Inferences in order to eplain the observations One way we use models is to take our observations and epectations, and synthesize and integrate them to create a formal, coherent epression of how we think a particular system functions Quite often in science, this is done mathematically, with some objective (statistical) criterion establish and used to see if our idea can be easily dismissed
Modeling in Env. Science The Role of Computers Reject hypothesis? 7 Perform data collection to allow us to conduct the test Hypothesis deduced from the model 6 Test the hypothesis 5 4 The limitation on the progress of scientific ideas on how things work is to some etent controlled by what sorts of representations of reality that we can build and eventually test This is where software comes into the picture: It allows us to build representations that would otherwise be utterly unmanageable, and test ideas that before we could not
Modeling in Env. Science The Role of Computers While computers provide us with a means of epanding our representations of how the world functions, they are by no means a panacea; we still must come up with those key inferences ourselves An anonymous quote about the division of labor between people and computers epresses the situation quite well: The computer is incredibly fast, accurate, and stupid. Man is unbelievably slow, inaccurate, and brilliant. The marriage of the two is a challenge and opportunity beyond imagination. Walesh, S.G. 1989. Urban Surface Water Management. John Wiley and Sons, U.S.A. While the possible rewards are tremendous, the effort epended following blind alleys can also be huge
Modeling in Env. Science Prediction and Forecasting Once we have a built a model, tested it, and decided that it is satisfactory for some purpose (i.e. possessing sufficient structural and predictive validity), we can make use of it in a few ways The emphasis in this course has been from a problem solving point of view: Identify an environmental issue, build a model of how the system will function under a range of conditions, and use model output to help us understand what is likely to happen. We can view this problem solving process as a multi-stage linear process:
Modeling in Env. Science Prediction and Forecasting The first step (between the real world and the model) is that of conceptualization or abstraction, where we epress our epectations and draw inferences Here, we conceive of how our model will represent the real world, and difficult decisions are made as to what simplifying approach can best achieve the problem-solving objective
Modeling in Env. Science Prediction and Forecasting The second step (between the model and a decision or some results) is that of implementation, testing (and decision-making) In many ways, this is less difficult than the conceptual portion of model building (as signified in the diagram by the much wavier line between the real world and model than the very straight line between the model and decision especially using STELLA!)
Modeling in Env. Science Prediction and Forecasting However, making operational decisions by interpreting model results can be very tricky! How sure are we that the model results are accurate / reliable / applicable to our problem? Yes, we can use the various quantitative / objective means of evaluating the structural and predictive validity of our model as detailed in the Strategies portion of the course to get a numerical sense of the validity of the model but how sure are we? In order to safely use the results of modeling in decisionmaking, it is useful to be able to epress the degree of uncertainty associated with model output, I.e. what is the range of values around the prediction where the true value is likely to fall?
Uncertainty, Error, and Sensitivity We need to be able to estimate uncertainty and error associated with our input data, as errors that are present in our representation of reality are likely to result in errors in our output We also need to be able to estimate error and sensitivity in our models computation: Some parameters in our model can be very sensitive to error (this is one reason we perform sensitivity analysis), such that a small change in the value input to a model can potentially result in a large error in the output
Errors in Model Input Data When an error is made in interval or ratio input data attributes, the error usually distorts a measurement by some small amount (unlike with nominal data, where the attribute is either correct or incorrect there are not smaller or larger errors) When describing errors in interval/ratio input data, we need to distinguish between two characteristics: Accuracy refers to the amount of distortion from the true value in a measurement Precision refers to the variation among repeated measurements, and also to the amount of detail in the reporting of a measurement
Precision and Accuracy These related concepts are often confused: Precision refers to the eactness associated with a measurement (i.e. closely clustered) Accuracy refers to the etent of systematic bias in the measurement process (i.e. centered on the middle) Precise & Accurate Precise & Inaccurate Imprecise & Accurate Imprecise & Inaccurate
Error Propagation in our Models When we use our input data in our model, we often combine data to produce output (through the calculation of what is in the stocks at the end of each time step in the case of using STELLA) In order to estimate the error in the output we must combine the input errors in some fashion Error propagation addresses the effects of errors and uncertainty on the results of modeling Almost every input to a model is subject to error and uncertainty and in principle, every output should have confidence limits or some other epression of uncertainty that reflects the error in the analysis output
Error Propagation in our Models In computational models like those we have been using in STELLA, calculating the error associated with the output can be fairly straightforward, provided we have good estimates of the error in the inputs This is simply a question of using equations that are closely related to the difference equations that STELLA uses to calculate the contents of stocks at each time step to calculate the uncertainty associated with those estimates As models get more comple (with more inputs and more calculations that transform the values) this becomes an increasingly burdensome bookkeeping problem In etremely comple models, it might be difficult to come up with a good estimate of the resulting error
Simplicity vs. Compleity in our Models The difficulties associated with error propagation in comple models is amongst the reasons that we strive to make simple models Models should be made as simple as possible, but not simpler Albert Einstein There are two ways to construct a model: 1. Make the model so simple that there are obviously no deficiencies 2. Make the model so comple that there are no obvious deficiencies While simplicity is the more desirable approach, it also the more difficult; we aim for parsimony
Simplicity vs. Compleity in our Models Merriam-Webster s Online Dictionary defines parsimony as: 1 a : the quality of being careful with money or resources : THRIFT b : the quality or state of being stingy 2:economy in the use of means to an end; especially : economy of eplanation in conformity with Occam's razor: In science (and modeling), we can interpret this to mean a preference for the least complicated eplanation for an observation (or least complicated model that accurately matches the observation) We need or models to be comple enough to capture the behavior of the system, but as simple as possible in order to minimize the possible errors involved