4.1 Energy Budget#
We will analyze water and energy flux data collected in different biomes to better understand the measurements, processes, and regional exchanges of water and energy. This relates to the grand challenges of understanding basic climate and boundary layer dynamics and Earth’s energy budget and radiative forcing. This module also relates to the geoscience literacy themes of energy sources driving Earth processes and Earth system changes that occur at multiple scales and the interconnections between the water and energy cycles. Two of the primary learning goals are to better understand how the conservation of mass and energy result in the water and energy budget equation and to be able to explore and extract data from CZO flux databases.
In this module we will:
Use water and energy cycle diagrams to discuss how water and energy are partitioned at the watershed scale.
Learn about the instrumentation used to collect water and energy flux data.
Examine radiative forcings collected from various CZO sites to compare various climatic and site-specific influences.
Explore and visualize energy flux data from CZO and related database.
Calculate a measure of Effective Energy and Mass Transfer (EEMT) related to the potential for CZ evolution.
Use CZO micro-meteorological data to calculate reference evaporation at a site of their choice.
Solar Energy#
Energy released from the Sun is radiant energy, which travels in waves through space. These electromagnetic waves have electrical and magnetic properties that allow them to travel long distances at the speed of light. Electromagnetic waves move like ocean waves, with crests and troughs, but they do not move matter. Radiant energy is carried by atomic particles; when it is absorbed by an object, radiant energy is converted to heat.
Electromagnetic energy is the term for all energy traveling in waves through space, including light, heat, X-rays, radar, and radio waves. Each type of wave has a specific wavelength and frequency. The spectrum of all possible wavelengths of electromagnetic energy is the electromagnetic spectrum.
The Sun emits radiant energy composed of \(\pu{8 \%}\) ultraviolet, X-ray, and gamma-ray wavelengths; \(\pu{47 \%}\) visible light wavelengths; and \(\pu{45 \%}\) infrared wavelengths.
Fig. 23 The electromagnetic spectrum showing various properties across the range of frequencies and wavelengths. Image source: Electromagnetic spectrum - Wikipedia#
An important physical law states that all objects radiate energy in wavelengths related to their individual surface temperatures: The hotter the object, the shorter the wavelengths emitted. This law holds true for the Sun and Earth.
Heat and Temperature#
Temperature and heat are different, but related, concepts. Temperature is a measure of the average kinetic energy (or average speed) of individual molecules in matter. If molecular movement increases, temperature increases. In contrast, heat is a form of energy that transfers between molecules and thus between bodies or substances. Heat is the flow of kinetic energy between molecules or from one body or substance to another resulting from a temperature difference between them.
Heat is a form of energy, while temperature is related to the amount of energy in a substance. Heat is the energy that crosses a system boundary in response to a temperature gradient. Because temperature is a measure of the average kinetic energy of individual molecules in matter, temperature is a measure of heat. An object with a “hot” temperature contains more heat energy; an object with a “cold” temperature contains less heat energy.
Heat always flows from matter at higher temperature to matter at lower temperature. Heat flow between objects or substances stops when the temperatures—that is, when the amounts of kinetic energy—become equal.
Applying these concepts to the Sun and Earth, we see that the hot Sun radiates shorter wavelength energy, concentrated around \(\pu{0.5 \mu m}\), with the majority falling in the visible region of the electromagnetic spectrum. Because Earth is a cooler radiating body, it emits longer wavelengths, mostly in the infrared portion of the spectrum, centered around \(\pu{10 \mu m}\).
As electromagnetic energy moves through Earth’s atmosphere, gases such as water vapor and carbon dioxide absorb certain wavelengths. These gases vary in their response to radiation received, being transparent to some wavelengths while absorbing others.
Fig. 24 Of the \(\pu{340 W m-2}\) of solar energy that falls on the Earth, \(\pu{29 \%}\) is reflected back into space, primarily by clouds, but also by other bright surfaces and the atmosphere itself. About \(\pu{23 \%}\) of incoming energy is absorbed in the atmosphere by atmospheric gases, dust, and other particles. The remaining \(\pu{48 \%}\) is absorbed at the surface. Image source: Climate and Earth’s Energy Budget (nasa.gov)#
For more information see Climate and Earth’s Energy Budget (nasa.gov).
Earth-Atmosphere Energy#
The inputs for our Earth–atmosphere energy budget consist of shortwave radiation (ultraviolet light, visible light, and near-infrared wavelengths). Only a portion of the insolation (incoming solar radiation) that enters Earth’s atmosphere reaches Earth’s surface; the remainder is either reflected back out to space or absorbed by Earth’s atmosphere. Insolation arrives at Earth’s surface as either direct or diffuse radiation—the direct sunlight that causes shadows or the diffuse, shadowless light cast in shaded areas or on cloudy days. This energy is absorbed by Earth’s surface and converted to heat. The outputs of our energy budget consist of shortwave radiation (the light reflected before reaching Earth’s surface) and longwave radiation in thermal infrared wavelengths.
Fig. 25 The earth-atmosphere energy balance is the balance between incoming energy from the Sun and outgoing energy from the Earth. Energy released from the Sun is emitted as shortwave light and ultraviolet energy. When it reaches the Earth, some is reflected back to space by clouds, some is absorbed by the atmosphere, and some is absorbed at the Earth’s surface. Image source: The Earth-Atmosphere Energy Balance (weather.gov)#
Types of Energy Transfers#
Insolation, or incoming solar radiation, is the single energy input driving the Earth–atmosphere system, yet it is not equal at all surfaces across the globe. Throughout the equatorial and tropical latitudes, minor variations in daylength and high Sun altitude produce fairly consistent insolation values (about \(\pu{180–220 W m-2}\). Insolation decreases toward the poles, from about \(\pu{25 ^\circ}\) latitude in both the Northern and the Southern Hemispheres. In general, greater insolation at the surface occurs in low-latitude deserts worldwide because of frequently cloudless skies.
Insolation encounters an increasing density of atmospheric molecules as it travels toward Earth’s surface. These gases, as well as dust, cloud droplets, water vapor, and pollutants, physically interact with insolation to redirect radiation, changing the direction of the light’s movement without altering its wavelengths. Scattering is the name for this phenomenon, which accounts for a percentage of the insolation that does not reach Earth’s surface but is instead reflected back to space. Incoming energy that reaches Earth’s surface after scattering occurs is diffuse radiation.
A portion of the arriving solar energy bounces directly back into space—this is reflection. Clouds reflect about \(\pu{20 \%}\) of insolation over the course of a year, far more than is reflected by Earth’s surface. Air pollutants, either natural or anthropogenic, also reflect incoming energy. We discuss the role of clouds and aerosols in the Earth–atmosphere energy budget ahead.
The reflective quality, or intrinsic brightness, of a surface is albedo, an important control over the amount of insolation that reaches Earth. We report albedo as the percentage of insolation that is reflected: \(\pu{0 \%}\) is total absorption; \(\pu{100 \%}\) is total reflectance.
Insolation, both direct and diffuse, that is not part of the \(\pu{31 \%}\) reflected from Earth’s surface and atmosphere is absorbed, either in the atmosphere or by Earth’s surface. Absorption is the assimilation of radiation by molecules of matter, converting the radiation from one form of energy to another. Solar energy is absorbed by land and water surfaces (about \(\pu{45 \%}\) of insolation) as well as by atmospheric gases, dust, clouds, and stratospheric ozone. At Earth’s surface, it is converted into either longwave radiation or chemical energy, such as by plants during photosynthesis. The process of absorption raises the temperature of the absorbing surface.
Heat Transfer at Earth’s Surface#
Two types of heat energy are important for understanding Earth–atmosphere energy budgets. Sensible heat can be “sensed” by humans as temperature because it comes from the kinetic energy of molecular motion. Radiant energy from the Sun must be absorbed before it can be felt as sensible heat. Latent heat (“hidden” heat) is the energy gained or lost when a substance changes from one state to another, such as from liquid water to water vapor or from liquid water to ice. Latent heat transfer differs from sensible heat transfer in that as long as a physical change in state is taking place, the substance itself does not change temperature (although the surroundings do gain or lose heat). The latent heat absorbed in the process of evaporation is an important output of the Earth–atmosphere energy system.
Heat energy is known as thermal energy and can be transferred throughout Earth’s atmosphere, land, and water bodies by several processes. Radiation is the transfer of heat in electromagnetic waves.
Conduction is the molecule-to-molecule transfer of heat energy as it diffuses through a substance. As molecules warm, their vibration increases, causing collisions that produce motion in neighboring molecules, thus transferring heat from warmer to cooler material.
Gases and liquids also transfer energy by convection, the transfer of heat by mixing or circulation. In the atmosphere or in bodies of water, warmer (less dense) masses tend to rise, and cooler (denser) masses tend to sink, establishing patterns of convection. This physical mixing usually involves a strong vertical motion. When horizontal motion dominates, the term advection applies.
Fig. 26 The four fundamental modes of heat transfer processes illustrated with a campfire. Image source: Heat transfer - Wikipedia#
Energy Balance at Earth’s Surface#
Energy and moisture are continually exchanged with the lower atmosphere at Earth’s surface—this is the boundary layer. Specific characteristics of Earth’s surface, such as the presence or absence of vegetation and local topography, affect the energy balance in the boundary layer. The height of the boundary layer is not constant over time or space.
The surface in any given location receives and loses shortwave (\(SW\)) and longwave (\(LW\)) energy according to the following simple scheme:
Net radiation (\(R_n\)) is the sum of all radiation gains and losses and varies with daylength through the seasons, the amount of cloud cover, and latitude.
In and over most soil surfaces, heat is transferred by conduction through the soil, predominantly downward during the day (or in summer) and toward the surface at night (or in winter). Energy exchange with the surface or with surrounding materials becomes negligible at a certain depth, usually less than a meter. Energy moving from the atmosphere into the surface is reported as a positive value (a gain), and energy moving outward from the surface, through sensible and latent heat transfers, is reported as a negative value (a loss) in the surface account.
Effective Energy and Mass Transfer#
An integrated framework based on thermodynamic theory to characterize the CZ as a system open to energy and mass fluxes that are forced by radiant, geochemical, and elevational gradients. Rasmussen et al (2011) showed the relative importance of solar radiation, water, carbon, and physical/chemical denudation mass fluxes to the CZ energy balance by using rates of effective energy and mass transfer (\(EEMT\), \(\pu{W m-2}\)) to quantify the relevant flux-gradient relations.
\(EEMT\) includes inputs of energy associated with reduced carbon from primary production (\(E_{BIO}\)) and heat influx to soil from precipitation minus evapotranspiration and surface runoff (\(E_{PPT}\)):
The balance of energy and mass flux involved in CZ development (Λ) may then be stated as:
Each term is defined below:
The energy and mass flux associated with evapotranspiration, \(E_{ET}\) (\(\pu{W m-2}\)): \(E_{ET} = ET \cdot h_\nu\), where \(ET\) is mass flux of precipitation to evapotranspiration (\(\pu{kg m−2 s−1}\)), and \(h_\nu\) is latent heat of vaporization (\(\pu{J kg−1}\)) and quantifies the fraction of radiant energy used to evaporate a mass of water. This energetic flux is largely fluxed out of the CZ and returned back to the atmosphere.
Water mass flux converted to energy flux, \(E_{PPT}\) (\(\pu{W m-2}\)): \(E_{PPT} = F \cdot c_w \cdot \Delta T\), where \(F\) is mass flux of precipitation to base flow from the water balance (\(\pu{kg m−2 s−1}\)), \(c_w\) is specific heat of water (\(\pu{J kg−1 K−1}\)), and \(\Delta T = T_{ambient} − T_{ref}\) where \(T_{ambient}\) is taken as the ambient water temperature at the time of water flux (assumed equal to the ambient air temperature) and \(T_{ref}\) is a reference temperature (\(\pu{273 K}\)). When \(T_{ref} > T_{ambient}\), \(E_{PPT} = 0\).
Carbon mass flux (\(NPP\)) can be converted to energy flux, denoted as \(E_{BIO}\) (\(\pu{W m-2}\)): \(E_{BIO} = NPP \cdot h_{BIO}\) where, \(NPP\) is net primary production (\(\pu{kg m−2 s−1}\)), and \(h_{BIO}\) is the specific biomass enthalpy (\(\pu{J kg−1}\)). We assume an average \(h_{BIO} = \pu{22e6 J kg−1}\) biomass based on the average of values for a range of organic materials derived from calorimetric analyses.
Physical denudation may be expressed in energy flux units as \(E_{ELV}\) (\(\pu{W m-2}\)), based on the change in potential energy of uplifted sediment: \(E_{ELV} = m · g · U\), where \(m\) is mass of sediment per unit area (\(\pu{kg m−2}\)), \(g\) is the gravitational constant (\(\pu{9.81 m s−2}\)), and \(U\) is uplift rate (\(\pu{m s−1}\)). The mass of sediment available for transport may be approximated using rock density, \(\rho\) (\(\pu{kg m−3}\)) and regolith depth, \(H_S\) (\(\pu{m}\)), where \(m = ρ · H_S\), assuming all soil and saprolite layers have the potential to be physically transported.
The mass and energy flux associated with chemical denudation and specific mineral transformations, \(E_{GEO}\) (\(\pu{W m-2}\)), may be approximated using the Gibbs free energy (\(Δ _{rxn}G^\circ,\ \pu{J mol−1}\)) of a given mineral transformation reaction (determined for the relevant environmental conditions) and the associated mass flux: \(E_{GEO} = N Δ_{rxn}G^\circ\), where \(N\), the mass flux per unit area (\(\pu{mol m−2 s−1}\)), is a function of reaction rate and a stoichiometric coefficient.
ξ encompasses net energy flux associated with any additional material flux into the system such as dust, atmospheric solutes, or anthropogenic inputs such as fertilizers or other amendments.
In general, some energetic fluxes are negligible relative to the other terms, but may be relevant for specific ecosystems. The relative magnitude of the individual fluxes over annual time scales indicate latent heat transfer by evapotranspiration is the largest energy flux; however, as noted above this energy is largely transferred out of the CZ back to the atmosphere and hence has a less direct impact on subsurface development.
Given the range of values, the key parameters for quantifying the flux of energy into and through the subsurface CZ are \(E_{PPT}\) and \(E_{BIO}\). These parameters describe the fraction of energy and mass effectively transferred into and through the subsurface CZ and are the two parameters originally included in the \(EEMT\) term.
Water Budget#
The hydrological cycle is important to the transport and cycling of nutrients and energy. Quantifying the various components of the hydrological cycle, referred to as constructing water budget for a defined area, is an important framework for wise and equitable water management. The hydrological cycle has changed as the result of human activity affecting specific components of the water budget and the movement of water between the components.
Fig. 27 Global water cycle, as well as how human water use affects where water is stored, how it moves, and how clean it is. Image source: Water Cycle Diagrams | U.S. Geological Survey (usgs.gov)#
Water budget provides a quantitative method for evaluating availability and sustainability of water supply. A water budget simply states that the rate of change in water stored in an area, such as a watershed, is balanced by the rate at which water flows into and out of the area. An understanding of water budget and the underlying hydrologic processes provides a foundation for effective water-resource and environmental planning and management. Observed changes in water budgets of an area over time can be used to assess the effects of climate variability and human activities on water resources. Comparison of water budgets from different areas allows the effects of factors such as geology, soils, vegetation, and land use on the hydrologic cycle to be quantified. Water budget also plays an important role in quantifying energy and mass transfer with the Earth’s CZ.
The water balance equation in its most simple form is shown as:
In this equation, change in water storage (\(\Delta S\)) in a system and is equal to the difference in the inflow (\(i\)) and the outflow (\(q\)). This water balance equation can be expanded to be a little more informative as follows:
where, \(Q\) is water flow into (\(Q_{In}\)) or out (\(Q_{Out}\)) of a watershed (can be separated into groundwater and surface water components), \(P\) is precipitation, \(ET\) is evapotranspiration (sum of evaporation from soils, surface water bodies, and plants), and \(\Delta S\) is change in water storage within the system.
To calculate an annual water budget for a specific location, meteorological and stream data will be required.
Precipitation is commonly measured using a automated or a manual rain gage. To calculate \(P\) for a watershed, often multiple measurements are collected across the watershed and an average value is estimated. In order to estimate this value, the watershed boundary also needs to be identified (watershed delineation). There are now automated tools available that help in this process. Try StreamStats (usgs.gov) to identify the delineate the watershed of your interest.
Evapotranspiration (\(ET\)) is a process that dominates the water balance and controls soil moisture content, ground water recharge, and streamflow. Evapotranspiration is responsible for returning a significant portion of precipitation falling on the land back to the atmosphere. Generally, \(ET\) is viewed as a loss from the water budget in that it reduces the amount of streamflow, storage, and the available groundwater. There are multiple methods to measure \(ET\) (potted plants, lysimeters, etc.), but the eddy covariance flux method is commonly used at many research sites. Because \(ET\) is difficult to measure, several methods have been developed to estimate it.
Ground water movement is explained using Darcy’s law for saturated flow through porous media as follows:
where, \(Q_{GW}\) is groundwater discharge, \(k_s\) is saturated hydraulic conductivity (function of type of rock or aquifer), \(A\) is area of cross-section and \(dh/dl\) is the hydraulic gradient (slope of the flow.)
Streamflow in streams is commonly measured using the velocity-area method as shown below:
where, \(Q_{SW}\) is stream discharge, \(A\) is cross-sectional area of a stream, and \(V\) is the average velocity at a given location. In smaller streams with diffuse flows, “flumes” are installed In large streams, complex methods are used to measure discharge. See How Streamflow is Measured | U.S. Geological Survey (usgs.gov). USGS measures streamflow and makes these data available in real time at USGS | National Water Dashboard. For example, Click Here to see stream data for greater Charleston area. You can also create runoff simulations at Model My Watershed® - WikiWatershed.