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Scientific Method to Mathematical Models




From the SCIENTIFIC METHOD to Predictions, Projections and Models.

Scientists to be both risk takers and conservative thinkers when they use the Scientific Method.

Scientists must first make an observation. E.g. bubbles form in cold, fresh water as it warms. Then the scientist must ask a question. E.g. what causes bubbles to form in cold, fresh water as it is heated? The answer to the question involves taking a risk or making a guess. This guess or hypothesis must try to answer the question. In this case, if the hypothesis is that water holds more dissolved gases at cooler temperatures, then the experiment must be designed to prove this hypothesis.

When designing the experiment to test their guess or hypothesis, scientists must be objective or unbiased. They must try to isolate and test the factors or variables that may be responsible. Scientists try to test one variable at a time in an experiment. For example, for the hypothesis “increased heat energy causes the bubbles to form in cold, fresh water” then cold, fresh water can be heated in the laboratory to observe the number and size of the bubbles formed as the water is heated. When only one variable or factor is changed in the conditions of the experiment, that single variable is most likely to be the reason for the change seen in the results.

Accurate observations and records of procedures are critical to experiments. In this example, charts of volumes of water, starting temperatures, temperature changes, time, heat source, and material of the container should be recorded as well as the number and size of the bubbles. Video taping or digital photography of the experiment, with a ruler in the photo for scale measurements, would provide additional records. A graph of the number of bubbles and temperature would show the effect of temperature increase on the number of bubbles formed.

When drawing conclusions based on their experimental observations, scientists become very conservative and only interpret the results with respect to the question asked and the answer /hypothesis tested. E.g. a diagonal line on the graph shows a direct relationship between temperature and bubbles seen. Experimental results from one scientist will not be accepted until duplicated independently by other scientists. New discoveries are treated as theories until agreement is reached- which may take centuries.

Scientists must also take a risk by guessing which observations are most important to pursue for the next experiment. In our example the scientist may wish to vary the pressure conditions for the same volume of water and temperature range to check out a second hypothesis. A third design might be to see what the combined effects of both variables, temperature and pressure are on the same volume of water – to see if the change in one variable affects the change in another. All other conditions must remain the same such as the heat source, the thermometer, the rate of heating, the container, the volume of water etc. so that only the conditions of temperature and pressure are changed.

Precautionary Principle

Scientists must guess the possible implications or applications of their conclusions. Scientists must also be conservative and use the “precautionary principle” when thinking about a change in procedure or an application of their findings. There is an understanding among scientists that there are unknown effects for any change made. This means that the most conservative estimates are used. Citizen scientists like ourselves would say, “Better to be on the safe side” when planning to undertake new challenges.

PREDICTIONS are best estimates for a future condition based on the best data from the past and the present. Scientific predictions assume no new factors or variables will be introduced to change the conditions that are involved. Using this known data, scientists set up a mathematical model to calculate and predict a pattern that in fact has already happened as a test of the model. The scientist is then ready to make the best estimate or prediction of the unknown future using this tested or “calibrated” model. E.g. weather predictions

Proxy data

Data from our past can be “proxy” data that it is NOT directly measured. The proxy data taken from cores of ice for gas analysis and cores of lake sediments for pollen grains, for example, uses specialized equipment and techniques to allow us to look at past concentrations. We can also DIRECTLY measure the CO2 concentration in our atmosphere today. Proxy data of the carbon dioxide concentrations in ice cores begins 1000’s of years ago. The tested mathematical model combines directly measured data with ice core data so that predictions of future concentrations can be more reliable.

Or we can predict the past! By knowing what growing conditions are needed for today’s white pines, we can approximate the climate conditions of yesterday when their pollen grains are found in a sample core.

Predictions of new oil discoveries are based on knowledge of today’s clues from past climates.

Thus, predictions, based on facts about the conditions we know and can rely on, enable scientists to guess the unknown, that is, predict, hypothesize or project conditions that have no present data.

Scientific work generally moves forward in small steps, which are based on previous scientific findings.

PROJECTIONS are predictions, which add in assumptions for further studies. They show the affect that a proposed change might have when introduced into a system which is already being studied. E.g. introduction of an assumption concerning an effect of human impact into an already operating system model. The scientist takes a risk by making an assumption about changes that might influence the future of what is being studied. Mathematical equations are designed to carry out the projection.

For example, an assumption could be made that the Earth’s present atmosphere is to become one degree warmer each decade. The projection of temperature for Earth’s systems at the end of the decade could then be made based on this assumption and on the predictions of known factors that affect the Earth’s temperature. Each factor used is known to have a cooling or heating effect. A mathematical equation would then be written to represent the effect of that factor in the assumption. A mathematical model could link or couple several factors to make a more reliable projection based on the assumption.

CLIMATE MODELS, designed by teams of meteorologists, mathematicians and computer specialists, have been under development for several decades. They are becoming more complex as more factors are built-in. See the chart of the historical development above. The more factors that are linked or coupled for consideration by the model, the closer the projections are to simulating the natural conditions and events that affect climate. Even so, climate models are still simplified versions of the complexities of nature they are simulating. Climate models are tested or validated by using past data to project known “future” conditions for which we have present data. This validation increases the credibility of the models projected future conditions.

Note that SCENARIOS describe how the future may develop. Scenarios are often based on projections and use additional information from other sources. E.g. scenario for CO2 concentrations will include data about CO2 emissions from burning of fossil fuels. See 2.3 for more information on scenarios and the Canadian and international climate change models.

Activities are listed in individual sub-sections.