A Didactic Module for the Energy Balance Models of the Earth Climate
Anastasia P. Hantsaridou, Antonios T.Theodorakakos and Hariton M. Polatoglou
Physics Department, Aristotle University of Thessaloniki, Greece 541 24
Paper presented at the annual European Conference on Educational Research, University of Crete, 22-25 September 2004
A didactic module for the energy balance models of the Earth climate.
It is fact that although scientists succeed to explain many of the subjects that concern peoples’ every day life, little effort has been made in order to promote their scientific knowledge to non - experts. For instance the climate and its changes and other atmospheric phenomena are subjects of great interest to anyone, but a few people understand how they work and even fewer can explain them. What we did in this project is to build a multimedia application, showing to people with basic scientific knowledge how the energy flows from one latitudinal zone of a planet to the next, modulating its climate. For this purpose we used the one–dimensional energy balance model. We visualized in Flash software the whole procedure and applied the method to 80 first year university physics students in Aristotle University of Thessaloniki, Greece, during 2002-2003 academic year, in order to study the feedback and make the appropriate corrections on the module, where necessary.
Conference paper presented at ECER Crete 2004 conference, 22-25/9/2004
Keywords: didactic module, energy, climate, energy balance model, multimedia application.
A didactic module for the energy balance models of the Earth climate.
A. P. Hantsaridou, A. T. Theodorakakos and H. M. Polatoglou, Physics Department,
Aristotle University of Thessaloniki, Greece 541 24
I. INTRODUCTION
It is widely known that there is a big confusion in people’s minds all over the world concerning the procedures that are taking place in the atmosphere and are responsible for many of the climatic phenomena that we observe. This confusion is due to the fact that until now no considerable efforts were made by scientists in order to present their special knowledge in a more common and understandable way. That came as a consequence of what they had been taught in university, where achieving old and new knowledge, was the main scope, while little or no effort was made to promote this knowledge to non-experts, for example students and common people.
Nowadays, despite of the fact that there are many examples of models that have been built (Bennett, 2002, Schpok et al., 2003, Dickinson & Sarachik, 1996) in order to explain the various atmospheric phenomena and some of them have already been visualized on the computer, we see that just a few are addressed to non-scientists and could be used as educational tools to everyone who is interested (Ibarra et al, 1999, Jennings & Kuhlman, 1997). In addition to that, the information overload that is observed due to modern technology (internet etc), as well as the media, can easily create a mess in pupil's mind (Fogarty and Bahls, 2002, Wraige, 2002, Schneider, 2002, Canning & Kilbourne, 2000). Since today technology allows us to rapidly create models on the computer that can explain science, it becomes necessary to construct useful tools in order to help people understand the various physical phenomena.
Two of the fundamental concepts that are used in atmospheric science in order to describe successfully many of its subjects, such as the climate, are energy and entropy. In the present work what we tried to do is to build a module, which could help people understand how the energy flows from one latitudinal zone of the planet to the next and comprehend though how the climate system of the Earth is modulated. For this case we used the energy balance model, which is one of the oldest and most-well known types of atmospheric science models. This model attempts to account for all energy coming in and all energy going out of a system and as a consequence helps to study the climate system of any planet in terms of its global energy balance.
Energy balance models are typically zero or one-dimensional models. As a result they represent particular features of the climate system in a very simple way and are therefore easier to integrate on computers. We used a latitudinal model, which is a one-dimensional model, in order to build a multimedia application with Macromedia Flash.
This application shows the energy flux between the latitudinal zones of the planet. Taking into account a number of parameters, such as the surface albedo, the fractional cloud cover of the zone we examine or the ratio correction of zone to incoming radiation, it calculates the individual average surface temperatures of each zone, the global mean temperature, the incoming and outgoing energy of each zone as well as the transport of energy between zones. Visualizing in Flash the whole procedure, people with basic scientific knowledge can easily workout some scenarios on the effect of various factors on the climate and estimate its usage in everyday life and especially in studying climate and undertaking climate simulation experiments. We applied the method to 80 first year university physics students during 2002-2003 academic year, in order to study the feedback and make the appropriate corrections on the module, where necessary.
II. THEORY
a. The structure of Energy Balance Models. The zero – dimensional Energy Balance Model
Energy balance models are of the most well - known types of atmospheric science models and very popular to climate modellers. There are many references in bibliography and internet describing how these models work (McGuffie & Henderson-Sellers, 2001). In general they are zero - dimensional or one – dimensional models. The models of the first case consider the planet as a single point in space having a global mean effective temperature. In the global energy balance, the term balance suggests that the system is at equilibrium, no energy is accumulated and the only variable is the effective temperature of the planet, Te. The climate can be simulated then, by considering the radiation balance of the system that we study, which in our case is the Earth. Mathematically we can describe the global model as follows:
Energy absorbed = energy emitted
πR2 (1-α) S = 4 πR2 σTe4 (1)
where R is the radius of the Earth, α is the planetary albedo, S is the solar constant (1370 W/m2) and σ is the Stefan – Boltzmann constant (5.67*10-8 W/m2K4). Because of the fact that the atmosphere of the Earth contains gases, which absorb thermal radiation, the mean global surface temperature Ts becomes
Ts = Te + ΔT (2)
where ΔT is known as the greenhouse increment and is a function of the efficiency of the infrared absorption. Due to the present atmosphere, for the Earth the greenhouse increment is about ΔT = 33K.
On the other hand the models of the second case consider the temperature as being latitudinally resolved. The fact that they are zero or one – dimensional models make them very popular, because they are simple, representing only particular features of the climate system and as a consequence are also simpler to integrate on the computers.
b. One – dimensional Energy Balance Models
In this case we study zonal models and as a result we must have some equation or a part of an equation that accounts for the flow of energy from one latitudinal zone to the next. If we want to describe mathematically the latitudinal model, as we have done in eqn. (1) for the global model, then eqn. (3) that follows would be appropriate:
Absorbed solar radiation = emitted infrared radiation + transport of energy between zones
Si (1-α (Ti)) = R (Ti) + F (Ti) (3)
where Si is the incoming radiation for a given zone i, α(Ti) the albedo at the zone i, R (Ti) is the emitted infrared radiation of the zone i, and finally the term F(Ti) gives the transport of energy between zones. In this model we need to take into account some features. For example, the average incoming radiation for a given zone varies from one latitudinal zone to the next, since the incident angle of the sun to a particular zone varies. Also each zone has its own zonal surface temperature, which usually includes the greenhouse increment.
In addition each zone has its own albedo, which depends on the ratio between land and water and the type of land covering. For a given zone the surface albedo depends on the surface temperature of that zone. If the temperature becomes below a critical value of temperature, which is –10 oC, then the land becomes ice covered. The albedo of the zone is the albedo of ice and its value becomes then 0.68. For temperatures above the critical temperature several equations are used, which consider the fractional cloud cover for the zone, the albedo of the clouds etc.
FIG. 1. One – dimensional Energy Balance Model.
In general the albedo is:
a(Ti) = 0.6 for TiTc and a(Ti) = 0.3 for -10<Ti0,
The transport of energy between zones is given by eqn. (4):
F (Ti) = K (Ti – Ts) (4)
where K is the transport coefficient (3.80 W/m2 oC), Ti is the average temperature of the zone i, and Ts is the mean global surface temperature. Finally the radiation leaving the top of the latitude zone is given by eqn. (5):
R (Ti) = A + BTi (5)
where A and B are empirically determined constants designed to account for the greenhouse effect of clouds, water vapour and CO2. Normally their values are: A = 204 W/m2 and B = 2.17 W/m2 oC.
Equation (3) incorporating eqns (4) and (5), calculates the temperature of the zone Ti:
(6)
Equation (6) is iterated until an equilibrium value is reached, determined by some user - defined tolerance value.
III. METHOD
First, in order to study the theoretical background of the students concerning to basic energy and heat transfer matters, as well as temperature matters, we prepare a written questionnaire. The questionnaire is passed to all of them, before the beginning of the teaching sequence, where we expose the basic theory of the model that is going to be used. It consists of 12 questions. All questions require basic knowledge that students gain from every day life and school, so they don’t have to be especially prepared in order to answer. Critical thought and consideration of answers is needed in most cases. Some questions are multiple-choice questions, while others demand a documented answer.
Few of the questions concern heat transfer matters, as mentioned before. We ask for example the students to answer if they should use a plastic glass, a ceramic cup or a thermos, in order to keep their coffee warm for longer time. Or the reason why we prefer not to wear dark clothes during the summer, especially in countries where the summer is hot and the sun is very shiny. Moreover to write down which factors modulate a room’s temperature, when an electrical stove, with constant energy flux, heats the room.
We are also concerned to see their background in relation to atmospheric and climate subjects. For instance we ask them to answer which factors, in their opinion, are responsible for the temperature that is formed over an area of the planet, since we know that there is a mean value for the solar constant; if the mean temperature over an area is the same during a cloudy and a cloudless night or whether the amount of the absorbed solar radiation remains still to what reaches the upper atmosphere. In addition we want them to answer in which case the solar radiation is mostly absorbed, if it is over an ice / snow covered area or over an area with thick vegetation.
In another question we give five temperatures and a picture of the Earth, where we have designed five latitudinal zones. Then we ask the students to match the temperatures and the zones, in order to see if they understand the differences in the temperature scale, when we are moving from equator to poles and vice versa. There is also a question where we examine by a multiple-choice answer their theoretical background concerning to the greenhouse effect and another one, where we ask them the meaning of the term “albedo”. Finally we want students to apply the energy conservation principle for the sun-earth system, in order to see if they understand how the solar radiation is distributed.
After we have finished with the questionnaire, we make a presentation of the necessary theory and the principles of the energy balance model, which we will use at a next step. During the presentation, unknown terms that the students will confront at a later time, such as the term “albedo”, are explained. We make a discussion in class. After a week, so that the students have embedded what they have heard, we give a set of exercises. These exercises demonstrate the energy balance model’s bahaviour and are representative examples of the type of climate simulation experiments that can be undertaken.
The whole task takes place on the computer, where we have installed a program that demonstrates the model. A member of our team, who is programmer, wrote this program in Flash language. Of course any other programming language, i.e. C++, could be also used. The main reason for this choice is that Flash language is a useful tool for internet applications. In fig. 2 we see a screenshot of the environment of the application.
FIG. 2. Screenshot of the energy balance model application.