Energy Balance Models: Basic Concepts And Simulation

Energy Balance Models

Describe the basic idea behind any energy balance model. What is the variable calculated in an energy balance model?

The basic idea that establishes the concept of the EBM or the energy balance model is that the total amount of heat or incoming radiation that is received from the sun is not absorbed wholly rather a major portion of the heat is reflected back in terms of outgoing radiation from the earth. The balance of the energy budget of a planet (as for the earth here) is the integration of the incoming and outgoing radiation of heat and thereby trying to infer the climate on the surface of the earth. The EBM is a simulated model that calculates the surface temperature of the planet by balancing the incoming and the outgoing radiation measured over different variables. The EBM is designed in two different ways. The first one considers the earth as a single point and no dimension is added to it. This is known as the zero dimensional models. The second one considers the reception and reflection of the radiation into different latitudinal extensions and is termed as one dimensional model of EBM (Siler  Roe and Armour  2018).

The variables calculated in an EBM are the

• Planetary albedo (α)
• The solar constant (S)
• Zonal Surface temperature (T)

These parameters vary depending on the latitudinal variation of the planet.

The two major components of the energy balance model above the atmosphere include

• The ozone layer and
• The clouds.

The two major components are affected by the rate of evaporation and the generation of the Greenhouse Gases. The rate of evaporation increases the chances of the formation of clouds while emission of green houses affects the Ozone layer by absorbing infrared radiation creating imbalance in the heat budget.

• Lower the solar constant factor in steps of 0.02 and record the global mean temperature at each value. Stop when the Earth is completely glaciated (hint: you can look at the albedo of the latitude zones to see if the Earth is glaciated). At what value of the solar constant factor does this occur?

The following results were obtained by lowering the value of the solar constant in steps of 0.02

Initial condition:

A, B, C: 204, 2.17, 3.8

A _ice: – 0.62

T _crit: -10

Sol _con: 1368

Global Mean Temperature: 15.28891

At the solar constant value of 0.78, the earth seems to be glaciated.

The table beside reflects the situation when the earth is completely glaciated. The mean global temperature is recorded at -47.2° Celsius. The albedo value reflects the albedo value of ice at 0.62 which refers that the earth is in glaciated state.

The earth seems to exit from completely glaciated stage at the solar constant factor of 1.30. The global mean temperature is recorded at 44.7° Celsius. The Albedo values 0.5 to 0.254 from the polar to the equatorial zones.  This value of the albedo reflects the ice free condition and it can be inferred that the planet is free from glaciations.

Fig: 1 Plotting of the Global Mean Temperatures (From A and B)

Source : (created by the author)

The above schematic shows that the two different curves that represent the variation of the solar constant and the difference in the Global Mean Temperature. The red curve denotes the variations in the solar constant that tracks the temperature variation with changing solar constant till the glaciations of the planet. The green curve denotes the variation in temperature from glaciated stage to thawing of the ice and change of climate. The sudden jump is observed due to the drastic change in physical climatic conditions in the planet owing to the variation in the short wave solar radiation. The most common physical effect that will be responsible for this type of  and event is the transformation of an climatic phase. The glaciated phase will melt away to bring warmth and ocean circulation. Germination of plant and animal life might also initiate post this phase. On the contrary a planet moving from warm to a glaciated phase will experience rapid change in climatic conditions. Glaciations in the tropics might change the lithology of the planet. There would be drastic change in the atmosphere as well.  The pressure belts will also vary to great extent.

Effect of Albedo on Temperature

Solar constant Factor at critical value of 0°C

The planet will be completely glaciated at the solar constant factor of 0.88 with a critical temperature of 0° Celsius.

 The table beside gives a tabulation of the albedo values and the Global Mean Temperature at a Critical temperature of 0° Celsius. The critical temperature is the specified temperature that limits the onset of a            phase of climate change. Here in the case, the critical temperature is manipulated at 0° Celsius to find out the variation of the solar constant factor from the original factor. The global mean temperature is figured at -41.1° Celsius and the temperature denotes that with the change in the critical temperature the change in the climate can happen rapidly.  The other condition is the thawing of the glaciated period into ice free period.

The table to the right will show the thawing temperatures from the glaciated phase at a critical temperature of 0°C.  The table will represent that at a critical temperature of 0°C, if the planet is in a glaciated phase, the solar constant factor has to be changed till 1.46, which is higher than the earlier condition of thawing.  The Global Mean temperature is also a lot higher as compared to the earlier results. The change in the temperature is not just due to the rise in the critical temperature, but factors as albedo, the long wave radiation basically the outgoing radiation is affected largely, which causes much difference.

• Plotting of  T_70-80and T_80-90

Figure 2:  Plotting of T _20-10 and T _0-10

• Plotting of T_20-10 and  T _0-10 and

Figure 3: Plotting of T _20-10 and  T _0-10 and

With the change of A which refers to the long wave radiation loss, is actually the reflected heat that travels back to the atmosphere in the EBM. The variation of A with respect to latitude yielded results that determine the influence of the latitudes in the heat budget of the planet. The physical factors that determine the increasing or the decreasing Long wave radiation are the green house gases present in the atmosphere, the amount of clouds cover present in  the sky and the amount of the atmospheric carbon present.

The lower latitudes have higher water vapour content in the atmosphere as compared to the upper latitudes which is a one of the influencing factors of the long wave radiation. The higher latitudes have higher rate of albedo due to presence of ice caps which also influences the long wave radiation along the latitudes.  The low values of A at lower latitudes as compared to higher values of A at the higher latitudes describe the fact that these are not just effects of the spatial variation but also due to the factors of albedo, presence of green house gases and cloud cover and most importantly the moisture profile and atmospheric temperature indicates change in the long wave radiation.

Figure 4: Plotting of variables of C. (Transport coefficient)

The global mean temperature has not changed with the lower values of C. the higher value of C (4.8) shows evidence in the change of the Global Mean temperature. C refers to the transport coefficient of the energy. The lower latitudes have the C factor is directly proportional to the temperature along with the latitudes. With increasing the value of C there is substantial increase in the temperature but with the gradual decrease in the energy coefficient there is a decrease in temperature. The latitudinal factor does not imply much to this cause, with gradual rise the mean global there is an effect in the mean global temperature. Transport coefficient refers to the transport of energy along the latitudinal bands. This can mostly happen due the pressure belts and the wind circulation of the planet.  The C is expressed in terms of watts meter^-2 degrees C^-1 and signifies the amount of energy being transferred. This is actually influenced by the difference in temperature in various latitudes due to inclined radiation of the sun. The transfer of the heat from the regions of the low latitudes to the regions of higher latitudes. The average mean temperature is thus not affected by this constant.

(a) Increased greenhouse effect: To simulate increased greenhouse effect, the parameters of long wave radiation loss constants which depend on the carbon mono oxide, water vapour and effects of clouds (McGuffie and Henderson-Sellers, 2005).

(b) Melting sea ice: The melting of the solar ice depends on the solar constant. An increase in the solar constant will simulate the change in the model.

(c) Weakening ocean circulation: Ocean circulation will be weakened by freezing of ocean water. This will initiate the glaciated factor. A decrease in the solar constant will reflect weakening solar constant in the model.

(d) Injecting aerosols into the stratosphere to reduce shortwave radiation (geoengineering). The solar constant needs to be decreased to simulate the reduction in short wave radiation.

(e) Placing mirrors on major deserts (geoengineering). The albedo needs to be increased for the case, since placing mirror in the desert will change the albedo from the surface.

References

McGuffie, K. and Henderson-Sellers, A., 2005. A climate modelling primer. John Wiley & Sons.

Siler, N., Roe, G.H. and Armour, K.C., 2018. Insights into the zonal-mean response of the hydrologic cycle to global warming from a diffusive energy balance model. Journal of Climate, (2018).

North, G.R., Mengel, J.G. and Short, D.A., 1983. Simple energy balance model resolving the seasons and the continents: Application to the astronomical theory of the ice ages. Journal of Geophysical Research: Oceans, 88(C11), pp.6576-6586.

Dolman, A.J., 1993. A multiple-source land surface energy balance model for use in general circulation models. Agricultural and Forest Meteorology, 65(1-2), pp.21-45.

North, G.R., Cahalan, R.F. and Coakley Jr, J.A., 1981. Energy balance climate models. Reviews of Geophysics, 19(1), pp.91-121.

Sellers, W.D., 1969. A global climatic model based on the energy balance of the earth-atmosphere system. Journal of Applied Meteorology, 8(3), pp.392-400.

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