Q: Modeling the Changing Weather A couple of years ago I asked you if the knowledge gained in controlling industrial processes would also be useful in modeling global ones, and you showed why it would. Now I would like to ask a more specific question. How would you go about modeling the thermodynamic processes which affect the changing weather on the East Coast of the United States? What sensors are needed to measure the present and estimate the future rate of warming of the East Coast as a function of the rate of concentration increase of CO2 in the atmosphere? Similarly, what detectors would be needed to measure the rate of melting of the ice at Greenland and approximate the time when that ice will be gone?
A: The past and present measurements of the water and air current flows, temperatures, heats of condensations (enthalpies), salinities, insolations, etc. are mostly available, and based on them, future trends can be estimated. Our data shows that as carbon dioxide emissions increase, the heat received by the East Coast rises. (Today mankind [numbering 7 billion] is yearly sending 35 billion tons of carbon into the air, nearly 5 tons per person. The global population is estimated to rise to 9 billion by 2050 and to 12 billion by 2100, and the per capita energy consumption in the third world is estimated to double. The carbon emission in the future will depend on the rate of conversion to the Post-Oil Energy Economy, http://www.amazon.com/Post-Oil-Energy-Technology-Solar-Hydrogen-Demonstration/dp/1420070258) The heat balance on the East Coast is influenced by the amount of insolation that it directly receives (Qs), by the heat which air and water currents (Qa & Qw) bring from the south, and the cooling caused by the melting of the ice at Greenland (Qi). (For the purposes of simplicity, I am disregarding the heating/cooling effect of the winds from the north and west.)
Using existing data, we can calculate and plot the relationship between the change in total heat input (ΔQt) and the change in CO2 concentration. From that plot, we can approximate the dead time and time constant (gain) of this heat transfer process.
The total heat input (Qt) can be estimated by Equation (1):
Qt = Qs + Qa + Qw – Qi (1)
In Equation (1), insolation (Qs) can be measured directly. On the East Coast it averages about 1200 kWhr/m2.
The heat conveyed by the air currents (Qa) move poleward. As evaporation increases near the equator, more heat is carried by the winds and hurricanes, which transport evaporated moisture up the East Coast, where it is released in the form of increased rain. The amount of this heat (Qa) can be measured by detecting the air flow and the heat of condensation of its moisture content.
The heat conveyed by the ocean currents (Qw) can similarly be measured by detecting the flow rates and temperatures of the arriving and returning currents. Making these measurements would also be useful to resolve the debate concerning the slowing of the Gulf Current (Figure 1). Some argue that the Gulf Current is slowing because the melting of the ice at Greenland lowers salinity (density) of the ocean, while others argue that this effect is smaller than the effect of the increased heating at the equator, which increases this flow.
As to the measurement of the rate of the melting of the ice (Qi) at Greenland, it could be detected indirectly by measuring the reduction in salinity of the receiving ocean.
Therefore, if a process control engineer was asked to model this overall heat transfer process, he/she would install sensors to measure the water and air current flows, temperatures, heats of condensations (enthalpies), salinities, insolations, rate of melting of the ice, etc., exactly the same way as we would model any other heat transfer process. Based on the above measurements, one could determine the dynamics of this control loop, including its time constants.
It should be emphasized that this is a batch process! In other words, the heat tranfer model would only be correct while there is still ice on Greenland. Once that ice is gone (like the ice in a glass of your gin and tonic at the pool in the summer, which stays cool only until the ice melts), the rate of warming would jump.
Q: Solids Level Measurement. I have a question relating to measuring the level of bulk solid using radar. I found the equation shown below for the level measurement of solids for the determination of the true dielectric constant of bulk solid:
True Dc = (Dc of solid - 1.0)(Bulk density/solid density) + 1.0