Thermal Pollution

Introduction

Fig. 1: The black-body radiation curve for different temperatures. The power across all wavelengths is obtained by integrating under the curve. (Source: Wikimedia Commons)

Thermal pollution refers to the dissipation of heat into the environment as a consequence of human activity. Here we shall take a brief look at both the local (water, urban heat island effect) and global impacts of thermal pollution.

Localized Thermal Pollution

At a local level, thermal pollution typically refers to the introduction of waste heat into nearby bodies of water. Any process that uses energy to do work will generate waste heat in accordance with the second law of thermodynamics. To rid themselves of this heat, industrial plants will partition a cooler water stream and run it through a heat exchanger, thereby increasing the temperature of the exiting stream. This is often then reintroduced to the original body of water.

Within the United States at least one third of all electricity generated uses cooling schemes which release waste heat into rivers, lakes or oceans at an average of 8°C to 12°C above the intake temperature. [1] The Mississippi river is notable for the absolute magnitude of thermal pollution it experiences - the river receives thermal emissions of nearly 60,000 MW, translating to a temperature increase of 3°C for up to 9% of the total river flow during a year. [2] In Europe the Rhine river experiences the greatest absolute change in temperature with one third of its flow subject to a 5°C temperature increase primarily driven by heat waste of nuclear power plants. [2] For rivers, 14 of the 15 largest thermal polluters are nuclear power plants due to their high energy capacity. [2]

Empirically, aquatic ecosystems are highly sensitive to minute changes in temperature with a 1°C increase in temperature responsible for a 10% decreases in biological activity and a 7°C increase responsible for a 50% decrease in biological activity. [1] Efforts to address thermal pollution such as the Clean Water Act in the United States focus on curtailing temperature increases to within specified boundaries. Mitigation strategies including limiting electricity generation, distributing industrial plants, employing advanced water recycling schemes and simply waiting for evaporative cooling before discharging water back into the environment.

Local thermal pollution also contributes to the urban heat island effect - the phenomena of increased temperatures in large cities. Unlike thermal pollution into rivers, heating is primarily caused by installation of pavement and construction of large buildings which absorb more solar radiation and retain larger amounts of heat. [3] Other causes include consumption of energy for transportation and building heating/cooling. Tokyo, infamous for prolific urban heat, experiences temperature increases of up to 6.5°C, of which up to 1°C is estimated to be directly caused by consumption of energy. [4] The urban heat island effect has been shown exacerbate heat waves and cause a measurable increase in heat-related mortality in Shanghai. [5]

Global Thermal Pollution and Global Warming

To understand the impact of thermal pollution at a global level, we calculate the expected increase in mean global temperature attributed to energy consumption alone (ignoring greenhouse gas effects).

At a high-level the Earth's energy budget can in part be understood by careful book keeping of the flux of energy or heat (W m^-2) at different boundaries of the Earth. Inherent challenges in weather science and atmospheric dynamics mean the following estimates derived by Kleidon are subject to an error bar but are in large part in agreement with released material by NASA and other agencies. [6] Virtually all of Earth's energy comes from the sun, with incoming solar irradiance providing an average of 341 W m^-2. Part of this radiation (103 W m^-2) is reflected back into space but the majority is absorbed by the Earth's surface (168 W m^-2) and turned into heat. The remainder is distributed between solar and thermal flux within the Earth's atmosphere. Next, although the mantle is part of Earth, it's worth noting geothermal heat from the Earth's interior to the surface is 0.1 W m^-2. Finally, heat from the Earth's surface is emitted as black-body radiation into space (238 W m^-2) in accordance with the Stefan-Boltzmann Law which has a fourth order dependence on temperature - this is depicted in the black-body radiation curves in Fig. 1. As temperatures on Earth's surface increase, more energy is radiated into space. Consequently, emittance of black-body radiation is how the Earth rids itself of excess heat and stays in a thermal equilibrium with no net energy flux. The aforementioned figures are intended to capture the big picture they omit nuanced breakdowns of heat and solar flux within the atmosphere as well as carbon and hydrologic cycling. Nonetheless they paint a good enough picture to allow us to understand the magnitude of thermal pollution.

We now calculate an upper bound on the thermal pollution dissipated by global energy consumption and procurement. According to the BP Statistical Review of World Energy, in 2020 the total primary energy consumption was 5.6 × 10²⁰ J. This figure includes the energy overhead for power generation with an efficiency of 40.5%. [7] Assuming the Earth has a surface area of 5.1 × 10¹⁴ m² we can calculate the total thermal pollution as:

In accordance with Stefan-Boltzmann's Law this excess heat will have the effect of slightly increasing the mean surface temperature of the Earth until the power radiated into space equilibrates with that absorbed by Earth's surface. Assuming the Earth is roughly a black-body we calculate this as follows where P is the power radiated in Watts, A is the surface area of Earth in m², σ is the universal Stefan-Boltzmann constant and T is the mean temperature in Kelvin:

To find the change in temperature for a given change in power we take the derivative with respect to temperature:

Rearranging terms and multiplying by (T/T) we obtain:

We can cancel the area from the top and bottom terms to obtain an expression in terms of energy flux. Using our calculated change in energy flux .035 W m^-2, the total energy flux to the Earth's surface 168 W m^-2, and a mean temperature of 298°K we calculate thermal pollution inducing a mean surface temperature change of:

The magnitude of human-derived thermal pollution appears astonishingly small compared to big players in Earth's energy budget. This number is further put into context when compared to estimates of global warming from the past 100 years: the IPCC reports a 0.85°K mean surface temperature change from 1880 to 2012. [8] This is in-line with the IPCC conclusions that anthropogenic forcing (energy flux) increases of 2.29 W m^-2 from 1750 to 2011 have been primarily caused by the increasing concentration of CO₂ and other greenhouse gases in the environment. [8] Taken together these numbers suggest heat pollution has a minor role, if any, in contributing to global warming.

Conclusion

Thermal pollution remains small on a global scale, paling in comparison to increased heat retention from greenhouse gas emissions. While global impacts may be mild, localized thermal pollution still remains a threat to immediate ecosystems affected by dissipated heat including cities and bodies of water. [9]

© Alexander Conklin. The author provided no input other than typesetting and referencing guidelines. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.

References

[1] N. Madden, A. Lewis, and M. Davis, "Thermal Effluent from the Power Sector: an Analysis of Once-Through Cooling System Impacts on Surface Water Temperature," Environ. Res. Lett. 8, 035006 (2013).

[2] C. E. Raptis, M. T. H. van Vliet, and S. Pfister, "Global Thermal Pollution of Rivers From Thermoelectric Power Plants," Environ. Res. Lett. 11, 104011 (2016).

[3] L. Kleerekoper, M. Van Esch, and T. B. Salcedo, "How to Make a City Climate-Proof, Addressing the Urban Heat Island Effect," Resour. Conserv. Recycl. 64, 30 (2012).

[4] G. J. Zhang, M. Cai, and A. Hu, "Energy Consumption and the Unexplained Winter Warming over Northern Asia and North America," Nat. Clim. Change. 3, 466 (2013).

[5] J. Tan et al., "The Urban Heat Island and its Impact on Heat Waves and Human Health in Shanghai," Int. J. Biometeorol. 54, 75 (2010).

[6] A. Kleidon, "Nonequilibrium Thermodynamics and Maximum Entropy Production in the Earth System," Naturwiss. 96, 1 (2009).

[7] "BP Statistical Review of World Energy 2021," British Petroleum, June 2021.

[8] Climate Change 2013: The Physical Science Basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change, (Cambridge University Press, 2014).

[9] L. V. Vinnå, A. Wüest and D. Bouffard, "Physical Effects of Thermal Pollution in Lakes," Water Resour. Res. 53, 3968 (2017).