4.3: Quantifying and Managing Soil Erosion on Cropland
Jaana Uusi-Kämppä
Water Quality Impacts, Natural Resources
Natural Resources Institute Finland (Luke)
Key Terms
| Detachment | Water erosion | Universal Soil Loss Equation |
| Transport | Wind erosion | Measurement |
| Deposition | Tillage erosion | Monitoring |
Variables
Introduction
Soil is a major natural resource in food production and therefore it is important to take care of soil in a sustainable manner. In cropland areas, topsoil is degraded by depleting available nutrients and by the removal of soil material from the soil surface via erosion caused by water or wind. Erosion usually occurs more rapidly when the soil is disturbed by human activity or during extreme weather conditions such as high precipitation or drought. Soil loss from a field decreases soil fertility and hence crop yield because of depletion of nutrients, reduction in soil organic carbon, and weakening of soil physical properties (Zhang and Wang, 2006). Recent global estimates suggest that soil erosion removes between 36 and 75 billion tonnes of fertile soil every year (Borelli et al., 2017; Fulajtar et al., 2017) causing adverse impacts to agricultural land and the environment.
In addition to the loss of fertile soil from cropland, erosion processes cause burying of crops and many environmental problems, such as siltation and pollution of receiving watercourses and degradation of air quality. Agrichemicals such as phosphorus and some pesticides adsorbed to eroded soil particles may be transported from croplands. In receiving water bodies, the chemicals may desorb and cause algal blooms or damage the local ecosystems. Due to the many harmful effects caused by soil erosion, it is important to understand erosion processes and how to monitor and prevent them, as well as how to reduce harmful environmental impacts both in the source and impacted (or target) areas. These topics are explored in more detail in this chapter.
Outcomes
After reading this chapter, you should be able to
- • Define soil erosion and explain erosion mechanics and transport mechanisms
- • Describe measurement and monitoring methods for quantifying erosion
- • Explain and apply the Universal Soil Loss Equation (USLE) to estimate soil loss by water
- • Calculate average annual soil loss and the effect of different tillage practices on erosion rates
Concepts
What is Soil Erosion?
Soil erosion is a natural geomorphological process by which surface soil is loosened and carried away by an erosive agent such as water or wind. Other agents, such as freezing and thawing, gravity, tillage, and biological activity cause soil movement. Human activity has accelerated erosion for many years, with changes in land use making soil prone to accelerated erosion so that loss is more rapid than replenishment. Tillage, and especially plowing, generally keeps the soil surface bare during winter. Bare soil is prone to erosion, whereas permanent grass or winter plant cover (i.e., cover crop or stubble) on the soil surface protects soils from erosion. Soil erosion is a local, national, and global problem. In the future, erosion processes may be intensified due to the increase in extreme weather events predicted with climate change. New erosion areas also appear due to deforestation, clearing land for cultivation, and global warming.
Soil Erosion Processes
The process of soil erosion consists of three different parts: detachment, transport, and deposition. First, soil particles are detached by the energy of falling raindrops, running water, or wind. Soil particles with the least cohesion are easiest to be loosened. The detached soil particles are then transported by surface runoff (also known as overland flow) or wind. Finally, the soil particles start to settle out, or deposit, when the velocity of overland flow or wind and sediment transport capacity decrease. Deposited particles are called sediment. Heavier particles, such as gravel and sand, deposit first, whereas fine silt and clay particles can generally be carried for a longer distance and time before deposition. Although particles of fine sand are more easily detached than those of a clay soil, clay particles are more easily transported than the sand particles in water (Hudson, 1971).
In addition to the energy of water or wind used in both detachment and transport of soil particles, gravity may impact erosion either directly, i.e., soil moving downhill without water (e.g., slump mass-movement), or indirectly (e.g., pulling rain to the Earth or drawing floodwaters downward). Bioturbation, which is reworking of soils and sediments by animals or plants, may also play an important role in sediment transport. For example, uprooted trees, invertebrates living underground and moving through the soil (e.g., earthworms), and many mammals burrowing into soil (e.g., moles) can cause soil transport downslope (Gabet et al., 2003).
In some other erosion processes, cycles of freezing and thawing or wetting and drying of clay soils weaken or break down soil aggregates and make the soil more susceptible to erosion. In boreal areas (i.e., northern areas with long winters and short, cool to mild summers), soil erosion may be high during snowmelt periods as a result of soils saturated by water, limited vegetation cover, and high overland flow (Puustinen et al., 2007). Soil erodibility is high in recently thawed soils, since high water content decreases the cohesive strength of soil aggregates (Van Klaveren and McCool, 1998).
Tillage Erosion
Soil erosion caused by tillage has also become more important with the development of mechanized agriculture, while soil erosion caused by water and wind has moved the Earth for millions of years. Tillage erosion has intensified with increased tillage speed, depth, and size of tillage tools, and with the tillage of steeper and more undulating lands (Lindstrom et al., 2001). The amount of soil moved by tillage can exceed that moved by interrill and rill erosion (Lindstrom et al., 2001). In agricultural areas, tillage is the main contributor to accelerated erosion rates. In certain areas, e.g., the U.S. and Belgium, tillage erosion has created soil banks of several meters high near field borders (Lindstrom et al., 2001). The net soil movement by tillage is generally presented as units of volume, mass, or depth per unit of tillage width (e.g., liter m −1 , kg m −1 , or cm m −1 , respectively).
Types of Soil Erosion Caused by Water on Cropland
Soil erosion caused by water can be classified into several forms including splash, sheet, interrill, rill, gully and bank (Toy et al., 2002). Splash erosion is caused by raindrop impact (Fernández-Raga et al., 2017). Small soil particles are broken off of the aggregate material by the energy of falling drops and are splashed into the air (Figure 4.3.1). Particles may deposit on the soil surface nearby or on flowing water.
Sheet erosion occurs when a thin layer of soil is evenly removed from a large area by raindrop splash and runoff water moving as a thin layer of overland flow. It occurs generally on uniform slopes. Sheet erosion is assumed to be the first phase of the erosion process, and the soil losses are assumed to be rather small (Toy et al., 2002).
Rills are small channels, less than 5 cm deep. They exist when overland flow (or surface runoff) begins to concentrate in several small rivulets of water on the soil surface. Detachment of soil particles is caused by surface runoff (Toy et al., 2002). In general, if a small channel can be obliterated with normal farming operations, it is a rill rather than a channel. After obliteration, rills tend to form in a new location.
The areas between rills are called interrill areas, and the erosion there is defined as interrill erosion (Toy et al., 2002). Interrill erosion is a type of sheet erosion because it is uniform over the interrill area. Detachment occurs by raindrop impact, and both surface runoff and detached soil particles tend to flow into adjacent rills.
Gullies are large, wide channels that are carved by running water (Figure \(\PageIndex{2}\)). Ephemeral gullies may occur on croplands and they are able to be filled with soil during tillage operations (Toy et al., 2002). The macrotopography of the surface allows the formation of ephemeral gullies after refilling by tillage. Gullies may sometimes be large enough to prevent soil cultivation. These gullies are called permanent, or classic, gullies. This kind of gully erosion causes severe damage to a field and produces high sediment loads to water.
Bank erosion is direct removal of soil particles from a streambank by flowing water. Bank erosion is the progressive undercutting, scouring and slumping of the sides of natural stream channels and constructed drainage channels (OMAFRA, 2012b).
Types of Wind Erosion
Suspension, saltation, and surface creep are three types of soil movement during wind erosion (Figure \(\PageIndex{3}\)). The dominant manner of erosion depends principally on soil type and particle size. Pure sand moves by surface creep and saltation. Soils with high clay content move under saltation. The sediment moved by creep and saltation may deposit very near the source area, along a fence, in a nearby ditch, or a field (Toy et al., 2002). In suspension, fine particles (diameter less than 0.1 mm) are moved into the atmosphere by strong winds or through impact with other particles. They can be carried extremely long distances before returning to earth via rainfall or when winds subside. In saltation, bouncing soil particles (diameter 0.1–0.5 mm) move near the soil surface. A major fraction of soil moved by wind is through the saltation process. In surface creep, large soil particles (diameter 0.5–1 mm), which are too heavy to be lifted into the air, roll and slide along the soil surface. Particles can be trapped by a furrow or a vegetated area.
Factors Influencing Water and Wind Erosion
Soil erosion is affected by several factors such as climate, rainfall, runoff, slope, topography, wind speed and direction, soil characteristics, soil cover like vegetation or mulch, and farming techniques. For example, in arid climates with steep slopes without good plant cover, during heavy rains the soil erosion is much higher than in level fields with robust plant cover in a mild climate. As another example, soils with high organic matter are naturally more cohesive and, thus, less susceptible to detachment than soils with low organic matter.
Water erosion occurs in areas where rainfall intensity, duration, and frequency are high enough to cause runoff. Wind erosion is most common in arid and semi-arid areas where dry and windy conditions occur. When rainfall water exceeds infiltration (i.e., permeation of water into soil by filtration) into the soil surface, runoff starts to occur. Infiltration capacity depends on soil type. For example, water infiltrates more rapidly into sandy soils than into clay soils; however, water infiltration can be improved in clay-textured soil by aggregate formation. The aggregates, consisting of fine sand, silt, and clay, are typically formed together with a mixed adhesive including organic matter, clays, iron (Fe) and aluminum (Al) oxides, and lime. At first, rainwater runoff has an impact on light materials (i.e. silt, organic matter, and fine sand particles) in soil, whereas during heavy rainfalls, larger particles are also carried by runoff water. Topography (i.e., slope length and gradient) is also an important factor for water erosion, with longer or steeper slopes being associated with greater erosion rates.
Soil surfaces covered by dense vegetation or mulches are less prone to water erosion due to their protection against the erosive power of raindrops and runoff water. Plants also use water, and their roots bind soil particles. Wind erosion can be counteracted by vegetation, which provides shelter from wind, intercepts wind-borne sediment, and keeps the soil surface moist.
Mechanical disturbance (e.g., soil tillage) buries vegetation or residues that would ordinarily serve as protection from erosion. Anthropogenic, i.e., human-induced, influences, such as changes in land management (animal production vs. crop production) and crop pattern (crop rotation vs. monoculture), use of heavier agricultural machinery, and soil compaction, increase the water and wind erosion potential of soils. Reduced tillage and no-till practices on croplands have been successful in reducing erosion. Globally, intensive deforestation causes soil erosion in new agricultural areas, increasing the net erosion rate.
Estimation and Modeling of Soil Erosion
The average annual erosion rate can be estimated using mathematical models. One of the most widely used models for estimating soil loss by water erosion is the Universal Soil Loss Equation, USLE (Wischmeier and Smith, 1978), and its update the Revised Universal Soil Loss Equation (RUSLE) or Modified Universal Soil Equation (MUSLE). According to the USLE, the major factors affecting erosion are local climate, soil, topography (length and steepness of cropland), cover management, and conservation practices.
The standard erosion plot is 22.13 m long and 4.05 m wide, with a uniform 9% slope in continuous fallow, tilled up and down the slope (Wischmeier and Smith, 1978), and is the experimental basis for the development of the empirical USLE model. The soil loss is evaluated as follows by the USLE:
\[ A = R\ K\ LS\ C\ P \]
where A = computed average annual soil loss (Mg ha −1 yr −1 ) from sheet and rill erosion
R = rainfall erosivity factor (MJ mm ha −1 h −1 yr −1 )
K = soil erodibility factor (Mg ha h ha −1 MJ −1 mm −1 )
LS = topographic factor (combines the slope length and the steepness factors L and S ) (dimensionless)
C = crop management factor (dimensionless, ranging between 0 and 1)
P = conservation practice factor (dimensionless, ranging between 0 and 1; the high value, 1, is assigned to areas with no conservation practices)
Each value on the right can be estimated from figures or tables. To minimize soil loss ( A ), any one value on the right needs to decrease. The units of R and K in Equation 4.3.1 are a result of adapting the USLE to use in SI units. The USLE was derived using customary U.S. units (e.g., tons, inches, acres). With international application of USLE, adoption of SI units was important. Several authors (e.g., Foster et al., 1981) have described approaches for use of the USLE in SI units.
Rainfall Erosivity Factor (R)
The rainfall and runoff factor ( R ), is related to the energy intensity of annual rainfall, plus a factor for runoff from snowmelt or applied water (irrigation) (Wischmeier and Smith, 1978). Rainfall erosivity defines the potential ability of the rain to produce erosion. Erosivity depends solely on rainfall properties (e.g., drop velocity, drop diameter, rainfall rate and duration) and frequency of a rainstorm. The greatest erosion occurs when rainfall with high intensity beats a bare soil surface without any plant cover. Plants or stubble are good cover against rainfall erosivity.
The National Soil Erosion Research Laboratory has presented a figure of the aerial erosion index for different areas of the U.S. varying from <200 to 10,000 (Foster et al., 1981). Several regional and global rainfall erosivity maps (e.g., ESDAC, 2017) are available. Erosivity also varies according to the season (Toy et al., 2002), being highest during winter and early spring in boreal areas.
Soil Erodibility Factor (K)
The soil erodibility factor is the soil loss rate per erosion index unit for a specified soil as measured on a standard erosion plot. It is based on the soil texture, soil structure, percent organic matter, and profile-permeability class (Wischmeier and Smith, 1978; Foster et al., 1981) and reflects the susceptibility of a soil type to erosion. Soils high in clay content have low K factor values because the clay soils are highly resistant to detachment of soil particles. In general, there is little control over the K factor since it is largely influenced by soil genesis. However, some management choices can result in small changes to the K factor. For example, by increasing the percent of organic carbon in soil, the K factor can be decreased, since organic matter increases soil cohesion.
The K factor in SI units (Mg ha h ha −1 MJ −1 mm −1 ) can be estimated using a regression equation that considers soil texture, organic matter content, structure, and permeability (Mohtar, n.d.):
\[ K = 2.8 \times 10^{-7} \times M^{1.1.4} (12 - a) + 4.3 \times 10^{-3} (b-2) + 3.3 \times 10^{-3} (c - 3) \]
where M = particle size parameter = (% silt + % very fine sand) × (100 – % clay)
a = organic matter content (%)
b = soil structure code (very fine granular = 1; fine granular = 2; medium or coarse granular = 3; blocky, platy, or massive = 4)
c = soil profile permeability class (rapid = 1; moderate to rapid = 2; moderate = 3; slow to moderate = 4; slow = 5; very slow = 6)
The K factor can also be read from nomographs, e.g., Foster et al. (1981) provided a nomograph in SI units.
In reality, soil erodibility is more complicated than Equation 4.3.2 suggests. How erodible a soil is depends not only on the physical characteristics of the soil but also its treatment, which effects how cohesive the soil aggregates are. Some variations of the USLE, such as the Second Revised USLE (RUSLE2) use a more complicated and dynamic K factor to account for management effects.
Topographic Factor (LS)
The topographic factor (called also slope length factor) describes the combined effect of slope length and slope gradient. This factor represents a ratio of soil loss under given conditions to that on the standard plot with 9% slope. Thus, LS = 1 for slope steepness of 9% and slope length of 22.13 m (Wischmeier and Smith, 1978); LS > 1 for steeper, longer slopes than that, and <1 for gentler, shorter slopes. For example, LS factor values for a 61 m long slope with steepness of 5%, 10%, 14%, and 20% are 0.758, 1.94, 3.25, and 5.77, respectively. The LS factors for 122 m and 244 m long slopes with constant steepness of 10% are 2.74 and 3.87, respectively. The steeper and longer the slope, the higher the erosion risk. The LS factor can be determined from a chart or tables in standard references (Wischmeier and Smith, 1978), or from equations where both slope length and steepness have been taken into consideration, e.g., Wischmeier and Smith (1978):
\[ LS = (\frac{\lambda}{22.13})^{m} (65.41\ sin^{2}\theta+4.56\ sin\theta+0.065) \]
where λ = slope length (m)
θ = angle of slope
m = 0.5 if the slope is 5% or more, 0.4 on slopes of 3.5 to 4.5%, 0.3 on slopes of 1 to 3%, and 0.2 on uniform gradients of less than 1%
Equations such as Equation 4.3.3 were derived for specific conditions, so care must be taken in using the appropriate equation for the given situation. These equations can be found in various USLE references. There is limited ability to change the LS factor, except for, notably, breaking a long slope into shorter slope lengths through the installation of terraces.
Cover Management Factor (C)
The cover management factor is a ratio that compares the soil loss from an area with specified cover and management to that from an identical area in tilled continuous fallow. The value of C on a certain field is determined by several variables, such as crop canopy, residue mulch, incorporated residues, tillage, and land use residuals (Wischmeier and Smith, 1978).
The factor may roughly be determined by selecting the cover type and tillage method that corresponds to the field and then multiplying these factors together (OMAFRA, 2012a). The height and density of a canopy reduces the rainfall energy. Residue mulch near the soil surface is more effective to reduce soil loss than equivalent percentages of canopy cover (Wischmeier and Smith, 1978). For example, incorporating plant residue at the soil surface by shallow tillage offers a greater residual effect than moldboard plowing. The C factor for crop type varies from 0.02 (hay and pasture) to 0.40 (grain corn). The C factor for tillage method varies from 0.25 (no-till or zone tillage) to 1.0 (fall plow). However, local investigation of the C factor is highly recommended because of varying cultivation practices, and because of the interaction of the timing of crop cover development and the timing of rainfall energy, which varies from place to place. Selection of crops and tillage systems can have a huge impact on the C factor.
Conservation Practice Factor (P)
The conservation (also support practice or erosion control) factor reflects the effects of various practices that will reduce the amount and rate of water runoff and, thus, reduce the erosion rate (Wischmeier and Smith, 1978). The most commonly used supporting cropland practices are cross-slope cultivation, contour farming, and strip cropping. The highest P factor value of 1 is given in the case when no influences from conservation practices are considered. The value of 1 is also given to “up and down slopes,” while “strip cropping, contour” gets the lowest value of 0.25 in the factsheet of Ministry of Agriculture, Food and Rural Affairs Ontario (OMAFRA, 2012a).
Measurement and Monitoring
Scientific research and erosion measurements are needed to understand erosion processes. Erosion is measured for three principal reasons (1) erosion inventories, (2) scientific erosion research, and (3) development and evaluation of erosion control practices (Toy et al., 2002). Measurements are also needed for the development of erosion prediction technology and implementation of conservation resources and development of conservation regulations, policies, and programs (Stroosnijder, 2005). Erosion measurements are used for development, calibration, and validation of methods of erosion prediction.
Temporal and Spatial Measurements
Erosion measurements are made at various temporal and spatial scales (Toy et al., 2002). For example, sampling duration can vary from a single rainstorm or windstorm to several years.
Spatially, water erosion measurements can range from interrill and rill sediment sources on hillslope or experimental plots to sediment discharge from watersheds. The presence of rills gives evidence of the possible erosion problems on the field. Sediment discharge from watersheds is used in reservoir design. Wind erosion measurements range also from small plots to agricultural fields and to entire regions.
Erosion Inventories
In planning erosion inventory measurements, the following issues should be included (Toy et al., 2002): selection of measurement site(s), measurement frequency and duration at the sites, and suitable measurement techniques. The selection of sites is made according to a sampling strategy. The measurement duration should be long enough to capture the temporal variability of erosion processes. The measurement technique is selected according to erosion type and study question.
How to Measure?
Erosion research is possible in the field (outdoor) or in the laboratory (Toy et al., 2002). Stroosnijder (2005) presents the following five fundamental ways to measure erosion: (1) sediment collection from erosion plots and watersheds, (2) change in surface elevation, (3) change in channel cross section dimensions, (4) change in weight, and (5) the radionuclide method. Both direct measurements and erosion prediction technology are used in erosion inventories. Commonly used erosion measurement techniques are cheap and fast but not very accurate. More accurate methods are costly and beyond the budget of many projects.
Experimental Fields and Catchments
In outdoor research settings, experimental plots, cropland fields or catchments are in use and runoff may be caused by natural or artificial rainfall. Temporal surface runoff (overland flow movement of water exclusively over the soil surface, down slope, during heavy rain) and subsurface discharge (drainage flow) from these sites can be measured and water sampled for sediment analyses. Sampling can be done automatically according to water volume or time. For indoor studies, soil blocks under a rainfall simulator (e.g., stationary drip-type rainfall simulator) can be used (Uusitalo and Aura, 2005). In both cases, representative water samples are collected for the sediment concentration analyses in the laboratory.
To predict the sediment load for a certain study area and time period, the concentration of analyzed water samples is multiplied by the water volume of the sampling period. Water flow (L s −1 ) can be measured in stream with a flow meter or V-notch weir, and on croplands with tipping buckets. Erosion amount (kg ha −1 ) is estimated by multiplying water flow (L s −1 ) by the time (s) and sediment concentration (g L −1 ) and finally dividing by the size of the study area (ha).
Also, continuously operating sensors for turbidity measurements from water can be used for measuring erosion from a study area. Turbidity is the degree to which water loses transparency due to suspended particles like sediment; the murkier the water, the more turbid it is. Turbidity sensors need good calibration and control water samples to evaluate sediment content. They must also be equipped with an automatic cleaning mechanism.
Change in Surface Elevation (Hillslope Scale)
The change in elevation is based on the principle that erosion and deposition by water or wind change the elevation of the land surface (Toy et al., 2002). The difference between the two measurements indicates the effect of erosion and deposition during that time interval. A lower elevation indicates erosion and higher elevation at the end of time interval indicates deposition.
One approach to measure change in elevation is to implant stakes or pins that remain in place in the soil for the duration of the study. The distance from the top of the stake or pin to the ground is measured at set time intervals. A decrease in distance corresponds to sedimentation whereas an increase means erosion (Stroosnijder, 2005). By multiplying the change in elevation by the soil bulk density, it is possible to convert the measurement to a mass of soil (Toy et al., 2002). In Figure 4.3.4, a soil roughness meter is used to measure changes in the surface of soil. The soil roughness meter has a set of pins that sit on the surface, so that soil surface position measurements can be made relative to the top of the structure of the roughness meter. By making repeated measurements at the same location, small changes in the surface elevation can be measured. It may also be used to determine soil erosion in rills.
Change in Channel Cross Section
Channel erosion can be estimated by measuring cross sections at spaced intervals, repeating this after some time and comparing and determining the change in volume of soil. The measurement can be done either manually or using airborne laser scanners (Stroosnijder, 2005). This technique is also suitable for estimating rill or gully erosion on croplands.
Change in Weight (Collected by Splash Cups and Funnels)
This method is based on the principle that the erosion process removes material from the source area (Toy et al., 2002). Test soil, packed in a cup or funnel placed in the soil, is weighed before and after an erosion event, and loss of weight is the erosion measurement. This technique is used in studies of soil detachment and transport by raindrop force (Stroosnijder, 2005). While affordable, and accurate at a small scale, the results using this method are representative of only a very small area, and may not scale well to the field level.
Radionuclide Method
Environmental radionuclides can be used as tracers to estimate soil erosion rates (Stroosnijder, 2005). A human-induced radionuclide of cesium (Cs137) was released into the atmosphere during nuclear weapon tests in the 1950s and 1960s. It spread to the stratosphere and gradually deposited on the land surface. In studies using this method, an undisturbed reference site, on which no or minimal erosion or sedimentation occurs, is needed (Fulajtar et al., 2017). The Cs137 concentration in the study soil is compared to the concentration in the reference site. If the study site contains less Cs137 than the reference site, erosion occurs there. If the study site has more Cs137 than the reference, sedimentation (deposition of soil particles) has occurred. In radionuclide studies, the time scale is usually much longer than in agronomic or environmental studies (Stroosnijder, 2005).
Wind Erosion Measurements
Wind erosion measurements require different measurement plans and equipment than water erosion measurements (Toy et al., 2002). While water erosion follows topography and water flow paths, windblown sediment cannot be collected at a single point (Stroosnijder, 2005). Soil gains and losses due to wind erosion require a number of measurement points, followed by geostatistical analyses. Since wind blows from various directions during the year and during a storm, sediment samplers must rotate with changing wind directions. Measurements must be made at various heights to determine the vertical distribution of the sediment load (Toy et al., 2002).
Impacts of Soil Erosion In-Field and Downstream
Soil erosion has impacts both on croplands where the erosion process starts (detachment) and in the place where it ends up (deposition, sedimentation) (Figure 4.3.5).
Impacts in Fields
In fields, fertile top soil material can be lost due to erosion processes. The finest particles from topsoil are generally transported from field areas under convex slopes making the areas less productive. The loss of finest particles reduces further the physical structure and fertility of soils (Hudson, 1971). Removal of fine particles or entire layers of soil or organic matter can weaken the structure and even change the texture, which can in turn affect the water-holding capacity of the soil, making it more susceptible to extreme conditions such as drought (OMAFRA, 2012b). Erosion of fertile topsoil results in lower yields and higher production costs.
Sediment may either increase fertility of soil or impair its productivity on productive land. For example, in Egypt, the fields along the Nile River are very productive due to nutritious sediments from the river water. In some cases, the sediment deposited on croplands may inhibit or delay the emergence of seeds, or bury small seedlings (OMAFRA, 2012b). Dredging of open ditches, sedimentation ponds, and waterways, in which sediment is mechanically removed, is becoming more common. However, it is questionable whether dredged sediment can be recycled back to agricultural fields (Laakso, 2017). The sediment may contain substances that are harmful to crops (herbicides) or decrease soil fertility (e.g., aluminum and iron hydroxides).
Impacts Downstream and in Air
In streams and watercourses, sediment can prevent water flow, fill in water reservoirs, damage fish habitats, and degrade downstream water quality. With an enrichment of nutrients, pesticides, salts, trace elements, pathogens, and toxic substances in soil particles in the field, soil erosion causes contamination of downstream water sources, wetlands, and lakes (OMAFRA, 2012b; Zhang and Wang, 2006). Because of the potential harmful impacts of deposited soil particles in water, the control of soil erosion in the field is important. Siltation of watercourses and water storages decreases the storage capacity of water reservoirs.
In addition, fine particles (<0.1 mm) transported by wind may also cause visibility problems on roads. They may also penetrate into respiratory ducts causing health problems.
Applications
For best results, erosion control should begin at the source area, by preventing detachment of soil particles. One of the most effective ways to prevent erosion is through crop and soil management. Detached particles can be trapped by different tools both on cropped field, field edges, and outside fields.
Decreasing the Effects of Erosivity ( R ) and Erodibility ( K )
Erosivity is rather difficult to decrease since there are no tools to affect rainfall. Soil erodibility can be decreased by increasing soil organic matter in soil, e.g., by adding manure or other carbon sources to soil. Practices that reduce or mitigate loss of soil carbon in cropped land can also decrease erodibility. These methods include managing residue to return carbon to the soil and minimizing tillage to reduce the conversion of soil carbon to carbon dioxide gas. Decreasing soil erosion caused by water on highly erodible soils requires additional methods such as permanent grass cover or zero tillage.
The addition of manure, compost, or organic sludge into soil increases aggregate stability, porosity, and water-holding capacity (Zhang, 2006). Both inorganic (stone, gravel, and sand) and organic mulches (crop residue, straw, hay, leaves, compost, wood chips, and saw dust) are used to absorb the destructive forces of raindrops and wind. All these materials also obstruct overland flow and increase infiltration (Zhang, 2006). Mulch reduces erosion until the seedlings mature to provide their own protective cover. In addition, soils treated with amendments like gypsum or structure lime are more durable against erosion than untreated soils (Zhang, 2006). The effect of these soil amendments lasts for a certain period depending on soil and environmental conditions. To maintain the effect, the amendment must be reapplied at intervals.
Soil moisture can prevent erosion. A moist soil is more stable than a dry one, since the soil water keeps the soil particles together. Soil moisture is higher in untilled soils due to a higher percent of organic carbon and minimal evaporation from the soil covered by plant residues. For example, wind erosion can be controlled by wetting the soil.
Reducing the Effect of Topography
Long slopes can be shortened by establishing terraces, but it is difficult to make steep slopes gentler. Reducing the field width (e.g., by windbreaks) protects cropped land against the effects of wind (Figure 4.3.6).
Increasing the Effect of Cover and Management
Plants are excellent in the protection of soil. They keep the soil in place with their roots, intercept rainfall, provide cover from wind and runoff, increase water infiltration into soil, increase soil aggregation, and provide surface roughness that reduces the speed of water or air movement across the surface. Dense perennial grasses are the most effective erosion controlling plants.
Soil management techniques that disrupt the soil surface as little as possible are excellent at maintaining soil cover and structure. For example, eliminating tillage (called no-till, e.g., direct drilling) keeps the soil surface covered all year round (Figure 4.3.7). This method, where seed is placed without any prior soil tillage in the stubble, has become common in many dry growing regions to decrease erosion potential. In winter, the stubble remaining after harvest effectively reduces soil erosion compared to bare fields (e.g., plowed in fall). Reduced, or conservation, tillage is also a better choice than fall plowing that leaves the soil surface uncovered. Tillage decreases the organic matter in soils and, thus, has a negative effect on the aggregate stability of clay soils (Soinne et al., 2016). Tillage also disturbs soil structure and, thus, reduces infiltration capacity.
Controlled grazing causes less erosion than tilled croplands; however, the number of grazing animals must be kept low enough to prevent erosion caused by over-grazing. Crop rotation and use of cover crops also maintain soil fertility and, thus, help control erosion.
Increasing the Effect of Support Practices
On steep slopes, erosion can be controlled by support practices like contour tillage (Figure 4.3.8), strip cropping on contour, and terrace systems (Wischmeier and Smith, 1978). Strip cropping protects against surface runoff on sloping fields and decreases the transport capacity of soil.
Tillage and planting on the contour is generally effective in reducing erosion. Contouring appears to be most effective on slopes in the 3–8% range (Wischmeier and Smith, 1978). On steeper slopes, more intervention is usually needed. Contour strip cropping (Figure 4.3.9) is a practice in which contoured strips of dense vegetation, e.g., grasses, legumes, or corn with alfalfa hay, are alternated with equal-width strips of row crops (e.g., soybeans, cotton, sugar beets), or small grain (Wischmeier and Smith, 1978). In erodible areas, grass strips usually 2 to 4 m wide are placed at distances of 10 to 20 m (Figure 4.3.10). They can be placed on critical areas of the field and the main purpose of these strips is to protect the land from soil erosion. Terracing can be combined with contour farming and other conservation practices making them more effective in erosion control (Wischmeier and Smith, 1978).
In terrace farming, plants may be grown on flat areas of terraces built on steep slopes of hills and mountains. Terracing can reduce surface runoff and erosion by slowing rainwater to non-erosive velocity. Every step (terrace) has an outlet which channel water to the next step.
If soil detachment and transport have taken place, the next consideration is to control deposition before the runoff enters a receiving watercourse. Narrow, 1 to 5 m wide, buffer strips under perennial grasses and wider buffer zones under perennial grasses and trees (Figure 4.3.11) have been established along rivers to prevent sediment transport to watercourses (Haddaway et al., 2018, Uusi-Kämppä et al., 2000). Grassed waterways (Figure 4.3.10) are established on concentrated water flows in fields to decrease water flow and, thus, decrease the erosion process in a channel.
Sediment basins, ponds and wetlands are also used to trap sediment (Uusi-Kämppä et al., 2000). Large particles and aggregates settle over short transport distances, while small clay and silt particles can be carried over long distances in water before their sedimentation.
Country-Specific Perspectives on Soil Erosion
Due to climatic factors ( R ), soil characteristics ( K ), landscape features ( LS ) and cropping practices ( C ), soil erosion varies geographically. Soil erosion by water is highest in agricultural areas with high rainfall intensity ( R factor). In the U.S., the erosion index is great (1200–10,000 MJ mm ha −1 h −1 yr −1 ) in eastern, southern, and central parts where tropical storms and hurricanes occur. In Europe, the R factor is highest in the coastal area of the Mediterranean, from 900 to >1300 MJ mm ha −1 h −1 yr −1 (Panagos et al., 2015). In addition to climate, changes in cropping systems ( C factor) influence the amount of erosion.
In northern Europe, the most erodible agricultural areas exist in southeast Norway (soil types are silty clay loams or silty clay), southern and central Sweden, and in southwestern Finland (with clay) due to the K factor. In these boreal areas, erosion risk is highest during late fall, winter, and spring due to surface runoff in frozen soil. Soil was previously covered by snow in winter; however, these areas have more frequently been subject to melting and runoff in winter during the last centuries due to climate change ( R factor).
In the 1900s, global cropland area increased causing a similar reduction in grassland area ( C factor). In Norway, the change in land use doubled soil erosion by water. In addition, extensive land levelling and putting brooks into pipes increased agricultural area in the same region in the 1970s and led to a two-to-three fold increase in erosion (Lundekvam et al., 2003), because levelling, i.e., creating smooth slopes instead of undulating ones, tended to increase the LS factor. Intensive erosion research started in the 1980s and since then Norwegian farmers have received national payments to implement erosion reducing methods, e.g., zero-tillage and growing cover crops in fall ( C factor), or establishment of grassed waterways, buffer strips, and sedimentation ponds ( P factor). Also, re-opening of piped brooks (decrease in L factor), and conversion of fall-tilled fields with high erosion risk into permanent grassland ( C factor) have been subsidized.
In Finland, typical soil erosion processes in field are sheet erosion, rill erosion, and tillage erosion. Although the mean arable soil loss rate is low (460 kg ha −1 yr −1 ) according to estimations of the RUSLE2015 model (Lilja et al., 2017), there are areas where the erosion risk is higher than this. These high risk areas, with steep slopes and high percent crop production, exist in southwestern parts of the country. In Finland, erosion is mitigated to decrease losses of phosphorus, which can be desorbed from detached soil particles into receiving water bodies where it may cause eutrophication and harmful algal blooms. To decrease soil erosion, some agri-environmental measures are subsidized by the European Union and Finland. For example, fall plowing has been replaced by conservation tillage practices, e.g. no-tillage and direct drilling ( C factor) or fields may be left under green cover crops for the winter ( C factor). Grass buffer zones, erosion ponds, or wetlands may be installed and maintained between fields and water bodies to trap soil particles rich in phosphorus ( P factor).
Examples
Example \(\PageIndex{1}\)
Example 1: Calculate average annual soil loss
Problem:
Use the USLE model to calculate the annual soil loss from a Finnish experimental site (slope steepness 6%, length 61 m, 60°48′N and 23°28′E). Annual rainfall is 660 mm, and erosivity is 311 MJ mm ha −1 h −1 yr −1 (Lilja et al., 2017). The site is plowed (up and down slope) in the fall and sown with spring wheat. Particle distribution: clay (<0.002 mm) 30%, silt (0.002–0.02 mm) 40%, very fine sand (0.02–0.1 mm) 25%, and sand (>0.1 mm) 5%. Organic matter in the soil is 2.8%. Soil structure is fine granular, and permeability is slow to moderate.
Solution
Determine the value of each factor in Equation 4.3.1:
\( A = R\ K\ LS\ C\ P \) (Equation \(\PageIndex{1}\))
R = rainfall erosivity factor; given in problem statement = 311 MJ mm ha −1 h −1 yr −1
K = soil erodibility factor; calculate using Equation 4.3.2:
\( K = 2.8 \times 10^{-7} \times M^{1.14} (12-a) + 4.3 \times 10^{-3} (b -2) + 3.3 \times 10^{-3} (c-3) \) (Equation \(\PageIndex{2}\))
where M = particle size parameter
\( =( \text{% silt} +\text{% very fine sand}) \times (100 - \text{% clay}) = 65\% \times (100 - 30\%) = 4550 \)
a = organic matter content (%) = 2.8
b = soil structure code = 2 (fine granular)
c = soil profile permeability class = 4 (slow to moderate)
Thus, substituting values in Equation 4.3.2 yields:
\( K = 0.041\text{ Mg ha h ha}^{-1} MJ^{-1} mm^{-1} \)
LS = topographic factor; find from a published table, e.g., table 3 (Wischmeier and Smith, 1978) or the following excerpt from Factsheet table 3A (OMAFRA, 2012a):
| Slope Length (m) | Slope (%) | LS Factor |
|---|---|---|
|
61 |
10 |
1.95 |
|
8 |
1.41 |
|
|
6 |
0.95 |
|
|
5 |
0.76 |
|
|
4 |
0.53 |
For a slope length of 61 m and a slope steepness of 6%, LS = 0.95, or calculate LS using Equation 4.3.3:
\( LS = (\frac{\lambda}{22.13})^{m} (65.41\ sin^{2}\theta+4.56\ sin\theta+0.065) \) (Equation \(\PageIndex{3}\))
\( LS = (\frac{61}{22.13})^{0.5} (65.41\ sin^{2}(6\%)+4.56\ sin(6\%) + 0.0065) = 0.95 \)
C = crop management factor = 0.35 for cereals
P = conservation practice factor = 1.0 for fall plowing up and down slope (OMAFRA, 2012a).
Substitute the values for each factor in Equation 4.3.1:
\( A = R\ K\ LS\ C\ P \) (Equation \(\PageIndex{1}\))
\( = 311 \times 0.041 \times 0.95 \times 0.35 \times 1 \text{ Mg ha}^{-1} \text{ yr}^{-1} = 4.24 \text{ Mg ha}^{-1} \text{ yr}^{-1} \)
Example \(\PageIndex{2}\)
Example 2: Effect of different tillage practices on erosion rates
Problem:
Use the USLE model to evaluate the change in erosion rate in the field runoff of the previous example when fall plowing (up and down slope) is changed (a) to spring plowing (cross slope) or (b) to no-till (up and down slope).
Solution
- (a) Using Equation 4.3.1 with:
\( R = 311 \text{ MJ mm ha}^{-1} h^{-1} yr^{-1} \)
\( K = 0.041 \text{ Mg ha h ha}^{-1} MJ^{-1} mm^{-1} \)
LS = 0.95
\( C = 0.35 (\text{cereals} \times 0.9 (\text{spring plow)} = 0.315 \)
\( P= 0.75 (\text{cross slope)} \)
\( A = R\ K\ LS\ C\ P = 2.86 \text{ Mg ha}^{-1}yr^{-1} \)
- The erosion rate is 32% less due to cross slope plowing in spring compared to up and down plowing in fall.
- (b) Using Equation 4.3.1 with:
\( R = 311 \text{ MJ mm ha}^{-1} h^{-1} yr^{-1} \)
\( K = 0.041 \text{ Mg ha h ha}^{-1} MJ^{-1} mm^{-1} \)
LS = 0.95
\( C = 0.35 (\text{cereals} \times 0.25 (\text{no-till)} = 0.0875 \)
\( P= 1 (\text{up and down slope)} \)
\( A = R\ K\ LS\ C\ P = 1.06 \text{ Mg ha}^{-1}yr^{-1} \)
- The erosion rate is 75% less due to direct drilling compared to up and down plowing in fall.
Image Credits
Figure 1. USDA Natural Resources Conservation Service. (CC By 1.0). (2020). Splash erosion. Retrieved from https://photogallery.sc.egov.usda.gov/photogallery/#/
Figure 2. USDA Natural Resources Conservation Service. (CC By 1.0). (2020). Gully erosion Retrieved from https://photogallery.sc.egov.usda.gov/photogallery/#/
Figure 3. USDA ARS. (CC By 1.0). (2020). Wind erosion process. Retrieved from https://infosys.ars.usda.gov/WindErosion/weps/wepshome.html
Figure 4. Risto Seppälä / Luke. (CC By 4.0). (2020). Soil roughness meter.
Figure 5. USDA Natural Resources Conservation Service. (CC By 1.0). (2020). Sediment chokes. Retrieved from https://photogallery.sc.egov.usda.gov/photogallery/#/
Figure 6. USDA Natural Resources Conservation Service. (CC By 1.0). (2020). Field windbreaks. Retrieved from https://photogallery.sc.egov.usda.gov/photogallery/#/
Figure 7. USDA Natural Resources Conservation Service. (CC By 1.0). (2020). No-till drilling. Retrieved from https://photogallery.sc.egov.usda.gov/photogallery/#/
Figure 8. USDA Natural Resources Conservation Service. (CC By 1.0). (2020). Contoured field. Retrieved from https://photogallery.sc.egov.usda.gov/photogallery/#/
Figure 9. USDA Natural Resources Conservation Service. (CC By 1.0). (2020). Alternating strips. Retrieved from https://photogallery.sc.egov.usda.gov/photogallery/#/
Figure 10. USDA Natural Resources Conservation Service. (CC By 1.0). (2020). Grass helps. Retrieved from https://photogallery.sc.egov.usda.gov/photogallery/#/
Figure 11. USDA Natural Resources Conservation Service. (CC By 1.0). (2020). Multiple rows of trees. Retrieved from https://photogallery.sc.egov.usda.gov/photogallery/#/
References
Borrelli, P., Robinson, D. A., Fleischer, L. R., Lugato, E., Ballabio, C., Alewell, C., . . . Panagos, P. (2017). An assessment of the global impact of 21st century land use change on soil erosion. Nature Commun. , 8 (1), 1-13. https://doi.org/10.1038/s41467-017-02142-7 .
ESDAC. (2017). European soil data centre, Global rainfall erosivity. Retrieved from https://esdac.jrc.ec.europa.eu/content/global-rainfall-erosivity .
Fernandez-Raga, M., Palencia, C., Keesstra, S., Jordan, A., Fraile, R., Angulo-Martinez, M., & Cerda, A. (2017). Splash erosion: A review with unanswered questions. Earth-Sci. Rev. , 171 , 463-477. https://doi.org/10.1016/j.earscirev.2017.06.009 .
Foster, G. R., McCool, D. K., Renard, K. G., & Moldenhauer, W. C. (1981). Conversion of the universal soil loss equation to SI metric units. JSWC , 36 (6), 355-359.
Fulajtar, E., Mabit, L., Renschler, C. S., & Lee Zhi Yi, A. (2017). Use of 137Cs for soil erosion assessment. Rome, Italy: FAO/IAEA.
Gabet, E. J., Reichman, O. J., & Seabloom, E. W. (2003). The effects of bioturbation on soil processes and sediment transport. Ann. Rev. Earth Planetary Sci. , 31 (1), 249-273. https://doi.org/10.1146/annurev.earth.31.100901.141314 .
 Uusi-Kämppä, J. (2018). The multifunctional roles of vegetated strips around and within agricultural fields. Environ. Evidence , 7 (14), 1-43. https://doi.org/10.1186/s13750-018-0126-2 .
Hudson, N. (1971). Soil conservation. London, U.K.: B. T. Batsford.
Laakso, J. (2017). Phosphorus in the sediments of agricultural constructed wetlands. Doctoral thesis in Environmental Science. Helsinki, Finland: University of Helsinki, Department of Food and Environmental Sciences. Retrieved from https://helda.helsinki.fi/bitstream/handle/10138/224575/phosphor.pdf?sequence=1&isAllowed=y .
Lilja, H., Hyväluoma, J., Puustinen, M., Uusi-Kämppä, J., & Turtola, E. (2017). Evaluation of RUSLE2015 erosion model for boreal conditions. Geoderma Regional , 10 , 77-84. https://doi.org/10.1016/j.geodrs.2017.05.003 .
Lindstrom, M. J., Lobb, D. A., & Schumacher, T. E. (2001). Tillage erosion: An overview. Ann. Arid Zone , 40 (3), 337-349.
Lundekvam, H. E., Romstad, E., & Øygarden, L. (2003). Agricultural policies in Norway and effects on soil erosion. Environ. Sci. Policy , 6 (1), 57-67. https://doi.org/10.1016/S1462-9011(02)00118-1 .
Mohtar, R. H. (no date). Estimating soil loss by water erosion. https://engineering.purdue.edu/~abe325/week.8/erosion.pdf .
OMAFRA. (2012a). Universal soil loss equation (USLE). Factsheet Order No. 12-051. Ontario Ministry of Agriculture, Food and Rural Affairs. Retrieved from http://www.omafra.gov.on.ca/english/engineer/facts/12-051.htm#1 .
OMAFRA. (2012b). Soil erosion—Causes and effects. Factsheet Order No. 12-053. Ontario Ministry of Agriculture, Food and Rural Affairs. Retrieved from http://www.omafra.gov.on.ca/english/engineer/facts/12-053.htm .
Panagos, P., Ballabio, C., Borrelli, P., Meusburger, K., Klik, A., Rousseva, S., . . . Alewell, C. (2015). Rainfall erosivity in Europe. Sci. Total Environ , 511, 801–814. https://doi.org/10.1016/j.scitotenv.2015.01.008 .
Puustinen, M., Tattari, S., Koskiaho, J., & Linjama, J. (2007). Influence of seasonal and annual hydrological variations on erosion and phosphorus transport from arable areas in Finland. Soil Tillage Res. , 93 (1), 44-55. https://doi.org/10.1016/j.still.2006.03.011 .
Soinne, H., Hyväluoma, J., Ketoja, E., & Turtola, E. (2016). Relative importance of organic carbon, land use and moisture conditions for the aggregate stability of post-glacial clay soils. Soil Tillage Res. , 158 , 1-9. https://doi.org/10.1016/j.still.2015.10.014 .
Stroosnijder, L. (2005). Measurement of erosion: Is it possible? CATENA , 64 (2), 162-173. https://doi.org/10.1016/j.catena.2005.08.004 .
Toy, T. J., Foster, G. R., & Renard, K. G. (2002). Soil erosion: Processes , prediction , measurement , and control. Hoboken, NJ: John Wiley & Sons.
USDA ARS. (2020). United States Department of Agriculture, Agricultural Research Service. Washington, DC: USDA ARS. Retrieved from https://infosys.ars.usda.gov/WindErosion/weps/wepshome.html .
Uusi-Kämppä, J., Braskerud, B., Jansson, H., Syversen, N., & Uusitalo, R. (2000). Buffer zones and constructed wetlands as filters for agricultural phosphorus. JEQ , 29 (1), 151-158. doi.org/10.2134/jeq2000.00472425002900010019x.
Uusitalo, R., & Aura, E. (2005). A rainfall simulation study on the relationships between soil test P versus dissolved and potentially bioavailable particulate phosphorus forms in runoff. Agric. Food Sci. , 14 (4), 335-345. https://doi.org/10.2137/145960605775897713 .
Van Klaveren, R. W., & McCool, D. K. (1998). Erodibility and critical shear of a previously frozen soil. Trans. ASAE , 41 (5), 1315-1321. https://doi.org/10.13031/2013.17304 .
Wischmeier, W. H., & Smith, D. D. (1978). Predicting rainfall erosion losses . A quide to conservation planning. Agriculture Handbook No. 537. Supersedes Agriculture Handbook No. 282. Washington, DC: USDA. Retrieved from https://naldc.nal.usda.gov/download/CAT79706928/PDF .
Zhang, T., & Wang, X. (2006). Erosion and global change. In R. Lal (Ed.), Encyclopedia of soil science (2nd. ed., Vol. 1, pp. 536-539). New York, NY: Taylor & Francis.
Zhang, X.-C. (2006). Erosion and sedimentation control: Amendment techniques. In R. Lal (Ed.), Encyclopedia of soil science (2nd ed., Vol. 1, pp. 544-552). New York, NY: Taylor & Francis.


1: Functional Organization
Learning Objectives
Upon completion of this unit the learner should be able to:
- Describe functional organization of the computer
- Explain the basic principles of organization, operation and performance of modern-day computer systems
- Outline the architectural design of the computer system
This unit introduces learners to functional organization of a computer. The unit provides you with basic concepts and techniques that will get you started in understanding and analysis of hardware and software interaction in computer systems.
-
- 1.5: Unit 1 Summary
- At the end of this unit, you will be conversant with the advanced functional organization of computer. This is by learning how data transfers occurs in the computer, the architecture of the microprocessor, the types of transfer of instructions within the computer and the processor and system performance of the computer.


2: Periodic Properties of the Elements
Last chapter, we presented the contemporary quantum mechanical model of the atom. In using this model to describe the electronic structures of the elements in order of increasing atomic number, we saw that periodic similarities in electron configuration correlate with periodic similarities in properties, which is the basis for the structure of the periodic table. For example, the noble gases have what is often called filled or closed-shell valence electron configurations. These closed shells are actually filled s and p subshells with a total of eight electrons, which are called octets ; helium is an exception, with a closed 1 s shell that has only two electrons. Because of their filled valence shells, the noble gases are generally unreactive. In contrast, the alkali metals have a single valence electron outside a closed shell and readily lose this electron to elements that require electrons to achieve an octet, such as the halogens. Thus because of their periodic similarities in electron configuration, atoms in the same column of the periodic table tend to form compounds with the same oxidation states and stoichiometries. Last chapter ended with the observation that, because all the elements in a column have the same valence electron configuration, the periodic table can be used to find the electron configuration of most of the elements at a glance.
In this chapter, we explore the relationship between the electron configurations of the elements, as reflected in their arrangement in the periodic table, and their physical and chemical properties. In particular, we focus on the similarities between elements in the same column and on the trends in properties that are observed across horizontal rows or down vertical columns. By the end of this chapter, your understanding of these trends and relationships will provide you with clues as to why argon is used in incandescent light bulbs, why coal and wood burst into flames when they come in contact with pure F 2 , why aluminum was discovered so late despite being the third most abundant element in Earth’s crust, and why lithium is commonly used in batteries. We begin by expanding on the brief discussion of the history of the periodic table and describing how it was created many years before electrons had even been discovered, much less discussed in terms of shells, subshells, orbitals, and electron spin.
-
- 2.1: Development of the Periodic Table
- The periodic table arranges the elements according to their electron configurations, such that elements in the same column have the same valence electron configurations. Periodic variations in size and chemical properties are important factors in dictating the types of chemical reactions the elements undergo and the kinds of chemical compounds they form. The modern periodic table was based on empirical correlations of properties such as atomic mass.
-
- 2.2: Shielding and Effective Nuclear Charge
- The calculation of orbital energies in atoms or ions with more than one electron (multielectron atoms or ions) is complicated by repulsive interactions between the electrons. The concept of electron shielding, in which intervening electrons act to reduce the positive nuclear charge experienced by an electron, allows the use of hydrogen-like orbitals and an effective nuclear charge to describe electron distributions in more complex atoms or ions.
-
- 2.3: Sizes of Atoms and Ions
- Ionic radii share the same vertical trend as atomic radii, but the horizontal trends differ due to differences in ionic charges. A variety of methods have been established to measure the size of a single atom or ion. The covalent atomic radius (rcov) is half the internuclear distance in a molecule with two identical atoms bonded to each other, whereas the metallic atomic radius (rmet) is defined as half the distance between the nuclei of two adjacent atoms in a metallic element.
-
- 2.4: Ionization Energy
- Generally, the first ionization energy and electronegativity values increase diagonally from the lower left of the periodic table to the upper right, and electron affinities become more negative across a row. The energy required to remove successive electrons from an atom increases steadily, with a substantial increase occurring with the removal of an electron from a filled inner shell.
-
- 2.5: Electron Affinities
- The electron affinity (EA) of an element is the energy change that occurs when an electron is added to a gaseous atom to give an anion. In general, elements with the most negative electron affinities (the highest affinity for an added electron) are those with the smallest size and highest ionization energies and are located in the upper right corner of the periodic table.


4.9: Function Composition
The following graphic is once again from the OER textbook Business Calculus by Calaway, Hoffman and Lippman, 2013 and is used with permission (Creative Commons Attribution 3.0 United States License).
The notation \(f(g(x))\) and \(g(f(x))\) may be easier to understand than using the composition operator. For \(f(g(x))\), think of wrapping a package. The gift is put into the box (the gift is \(g(x)\), the box is \(f(x)\)) and the wrapped present, \(f(x)\), contains the gift \(g(x)\).
If \(f(x) = x^2 − 2\) and \(g(x) =\sqrt{x}\), find:
- \(f(g(x))\) and the domain of the composite function
- \(g(f(x))\) and the domain of the composite function
Solution
- The composition of functions, \(f(g(x))\) is:
\(\begin{aligned} f(g(x)) &&\text{ Function composition, }f \text{ of }g\text{ of }x \\ f(\sqrt{x}) &&\text{ Replace } g(x)\text{ with }\sqrt{x} \\ ( \sqrt{x})^2 − 2 && \text{ In the function } f(x)\text{, every }x \text{ is replaced with } g(x) =\sqrt{x} \\ x − 2 && f(g(x))\text{, answer simplified.} \end{aligned}\)
The domain of the composite function contains the restrictions of the domain of the inner function, as well as the restrictions of the composite function.
The domain of the inner function, \(g(x) = \sqrt{x}\) is that \(x\) must be nonnegative, or in interval notation \([0, \infty )\)
The domain of the composite function, \(x − 2\) is all real numbers, \((−\infty , \infty )\)
Therefore, the domain of \(f(g(x))\) is \([0, \infty )\).
- The composition of functions, \(g(f(x))\) is:
\(\begin{aligned} g(f(x)) &&\text{ Function composition, }g \text{ of } f \text{ of } x \\ g(x^2 − 2)&& \text{ Replace }f(x)\text{ with } x^2 − 2 \\ \sqrt{x^2 − 2} &&\text{ In the function } g(x)\text{, every }x \text{ is replaced with } f(x) = x^2−2 \\ x^2 − 2 && g(f(x))\text{, answer simplified. }\end{aligned}\)
The domain of the composite function contains the restrictions of the domain of the inner function, as well as the composite function.
The domain of the inner function, \(f(x) = x^2 − 2\) is all real numbers, or in interval notation \((−\infty , \infty )\)
The domain of the composite function, \(\sqrt{x^2} − 2\) is that the quantity \(x^2 −2\) must be nonnegative, or \(x^2 −2 \geq 0\).
Solving \(x^2 − 2 \geq 0\) for \(x\), \(x \geq 2\) and \(x \leq −2\). In interval notation, \((−\infty , −2] \cup [2, \infty )\)
Therefore, the domain of the composite function, g(f(x)) is the more restrictive domain, \((−\infty , −2] \cup [2, \infty )\).
If \(f(x) = \dfrac{1 }{x − 4}\) and \(g(x) = \dfrac{5 }{x} + 4\), find:
- \(f(g(x))\) and the domain of the composite function
- \(g(f(x))\) and the domain of the composite function
Solution
- The composition of functions, \(f(g(x))\) is:
\(\begin{aligned} f(g(x)) \text{ Function composition, } f\text{ of }g \text{ of }x\\ f\left( \dfrac{5}{ x} + 4\right) && \text{ Replace }g(x)\text{ with }\dfrac{5 }{x} + 4 \\ \dfrac{1 }{\left(5 x + 4\right)− 4} && \text{ In the function } f(x)\text{, every x is replaced with } g(x) = \dfrac{5}{ x} + 4 \\ \dfrac{1 }{\dfrac{5 }{x}}&&\text{ Simplify} \\ \dfrac{x }{5} && f(g(x))\text{, answer simplified. }\end{aligned}\)
The domain of the composite function contains the restrictions of the domain of the inner function, as well as the restrictions of the composite function.
The domain of the inner function, \(g(x) = 5 x + 4\) is all values of \(x\) such that \(x\) must not be 0, or in interval notation \((−\infty , 0) \cup (0, \infty )\)
The domain of the composite function, \(\dfrac{x }{5}\) is all real numbers, \((−\infty , \infty )\) Therefore, the domain of \(f(g(x))\) is \((−\infty , 0) \cup (0, \infty )\)
- The composition of functions, \(g(f(x))\) is
\(\begin{aligned} g(f(x))&&\text{Function composition, } g \text{ of } f\text{ of }x \\ g\left( \dfrac{1 }{x −4}\right) &&\text{Replace } f(x) \text{ with }\dfrac{1}{ x − 4}\\ \dfrac{5 }{\dfrac{1 }{x − 4}} + 4 &&\text{In the function } g(x)\text{, every x is replaced with } f(x) = \dfrac{1 }{x − 4}\\ 5(x − 4) + 4 && \text{ Simplify the fraction} \\ 5x − 20 + 4 &&\text{ Simplify more}\\ 5x − 16 && g(f(x))\text{, answer simplified.} \end{aligned}\)
The domain of the composite function contains the restrictions of the domain of the inner function, as well as the composite function.
The domain of the inner function, \(f(x) = \dfrac{1}{ x − 4 }\) is that \(x\neq 4\), or in interval notation \((−\infty , 4) \cup (4, \infty )\)
The domain of the composite function, \(5x − 16\) is all real numbers, \((−\infty , \infty )\).
Therefore, the domain of the composite function, \(g(f(x))\) is the more restrictive domain, \((−\infty , 4) \cup (4, \infty)\).
For the given functions, find both \(f(g(x))\) and \(g(f(x))\), and find the domain of the composite function.
- \(f(x) = 3x^ 2 + x − 10\), \(g(x) = 1 − 20x\)
- \(f(x) = 3x − 2\), \(g(x) = \dfrac{1}{ 3} x + \dfrac{2 }{3}\)
- \(f(x) = 4x − 1\), \(g(x) = \sqrt{6 + 7x}\)
- \(f(x) = 5x + 2\), \(g(x) = x^2 − 14x\)
- \(f(x) = x^ 2 − 2x + 1\), \(g(x) = 8 − 3x ^2\)
- \(f(x) = x ^2 + 3\), \(g(x) = \sqrt{5 + x^2} \)


1.24: Big Bang Nucleosynthesis - Observations
The build-up of the chemical elements
We usually think of heavy elements as a product of nucleosynthesis (formation of nuclei) in stellar fusion and supernovae. Over billions of years of stellar processing and an overall increase in heavy element abundances, the chemical abundances of stars become richer with elements besides hydrogen, such as helium, oxygen, and iron. In a given star, we typically see a direct correlation between its oxygen abundance and iron abundance. If a star is oxygen-rich, it is likely a newer star made from dust clouds containing heavier elements, and thus likely has a high iron content as well. We can see this relationship in Figure 1, which plots the oxygen and iron content of many stars. This observed relationship supports our hypothesis that these elements were formed together over time with stellar processing.
Figure \(\PageIndex{1}\): Relative abundances of oxygen-to-hydrogen and iron-to-hydrogen. We see a trend in which low-iron stars tend to have low-oxygen, while iron-rich stars are also oxygen-rich. This is because iron and oxygen were formed together over billions of years of stellar processing.
Observations of helium abundances gives us a different relationship, which can be seen in Figure 2. As with iron and oxygen, an oxygen-rich star is likely to contain more helium, which indicates that both helium and oxygen have been created over time with stellar processing. The difference is that we see a significant abundance of helium even in very old stars formed by gas clouds containing little to no heavy elements. This points to a primordial abundance of helium that existed even before stellar processing. Where did this helium come from?
Figure \(\PageIndex{2}\): Relative abundances of oxygen-to-hydrogen and helium-to-hydr ogen in stars. While there is still a trend in which stars with low O/H also have lower He/H, even the most oxygen-poor stars contain a significant abundance of helium. This is because all these objects formed with a primordial abundance of helium, whereas there is essentially no primordial abundance of oxygen. (credit: Ned Wright)
In 1948, Gamow explored the very early universe as a source of elements heavier than hydrogen. He extrapolated Einstein’s theory of an expanding universe with certain assumptions of what the universe is made of, and concluded that the universe was infinitely dense at a finite time in the past. He theorized that this early universe could be a prodigious source of heavier elements. If the universe began at infinitely high density and temperatures and underwent rapid expansion and cooling, atomic nuclei would form within a window of just a few minutes. Before this window, high-energy radiation did not permit any nuclei to survive, and after this window, temperatures were too low for the nuclear collisions to overcome the Coulomb repulsion.
Gamow’s important discovery was that in order to avoid overproduction of helium and other heavy elements, the ratio of nucleons to photons had to be small. Since the number of photons in black body radiation is proportional to temperature cubed, this means that the “Big Bang” had to be very, very hot. From these parameters, Gamow theorized that we should see a background of heat and light from this period of high temperature and photon density. This background was discovered later in 1964 and is known as the Cosmic Microwave Background.
The Ashes of the Big Bang
Gamow's (and soon after, Ralph Alpher's) realization that chemical elements could be made during the early Universe paved the way for what is now referred to as Big Bang nucleosynthesis, which is the end-product of putting neutrons and protons in a hot, expanding universe. The original motivation of their work was to explain the origin of the abundance of all chemical elements, including hydrogen, helium, and all heavy elements. However, a few physical processes were neglected in their calculation, and as a result, the calculations by Alpher and Gamow produced orders of magnitude too many elements heavier than lithium, but roughly the correct amount of helium. In Chapter 23: Big Bang Nucleosynthesis - Predictions , we derived the amount of helium produced during the Hot Big Bang under some simplifying assumptions. Detailed calculations that include a full nuclear reaction network and all of the relevant physical processes can be used to estimate the complete set of nuclides that are created during these first few moments.
Only the lightest elements of the periodic table were made during Big Bang nucleosynthesis, including hydrogen (H), helium (He), and a trace amount of lithium (Li). The relative amounts of these nuclides depend on a competition between the expansion rate of the Universe and the rates of a network of nuclear reactions. This competition is parametrized by the relative number density of baryons to photons, commonly referred to as the baryon-to-photon ratio. Numerical calculations of these primordial nuclides have allowed us to understand the sensitivity of each primordial nuclide to the physics of the early Universe. For example, if there were an additional particle outside of the Standard Model, this might change the expansion rate of the Universe or interact with baryons in a way that changes the production and destruction of the primordial nuclides. Turning this statement around, if we could measure the relative abundance of the primordial elements, and combine this with a model of Big Bang nucleosynthesis, then we can learn about particle physics and cosmology a few minutes after the Big Bang.
The challenge is to find places in the Universe that have not significantly altered the primordial nuclides from their initial abundances set a few minutes after the Big Bang. This usually means that we have to find environments that have very few of the elements made by stars (e.g. oxygen, iron). Historically, the goal is to measure the number density of one primordial nuclide relative to hydrogen (i.e. the protons that are left over following Big Bang nucleosynthesis). While many nuclides are made during Big Bang nucleosynthesis, only the most abundantly produced primordial elements can currently be measured, including: deuterium (D, which is a heavy isotope of hydrogen), helium-3 ( 3 He), helium-4 ( 4 He), and lithium-7 ( 7 Li). We will discuss the current techniques and measurements of each of these primordial elements in turn.
Deuterium: A way to weigh the Universe
Deuterium is a heavy stable isotope of hydrogen, and Big Bang Nucleosynthesis makes just \(\sim25\) deuterons for every one million protons (a deuteron is the nucleus of a deuterium atom). The nucleus of deuterium contains one neutron and one proton, and it has very similar energy levels to the hydrogen atom. However, as a result of the neutron in the nucleus, the energy levels of a deuterium atom are shifted relative to that of hydrogen. This presents us with a problem, because if we want to measure the relative number of deuterium and hydrogen atoms of a pristine environment, we need to detect the atomic transitions of both deuterium and hydrogen. To estimate this shift, we can consider the Bohr model of the atom. The energy levels based on this model are given by: \[\frac{1}{\lambda}= R\bigg(\frac{1}{n_{f}^{2}} - \frac{1}{n_{i}^{2}}\bigg) \nonumber \]where \(\lambda\) is the wavelength of the transition between levels \(n_{f}\) and \(n_{i}\) and \(R\) is the Rydberg constant of that atom. Since deuterium has an extra neutron in the nucleus, this changes the centre of mass of the atom, so the Rydberg constant is slightly different for deuterium and hydrogen. The ratio of the deuterium and hydrogen wavelengths is just the ratio of their Rydberg constants, which is simply the ratio of the reduced masses: \[\frac{\lambda_{D}}{\lambda_{H}}=\frac{R_{H}}{R_{D}}= \frac{1+\frac{m_{e}}{m_{D}}}{1+\frac{m_{e}}{m_{H}}} \label{DeuteriumIsotopeShift} \] where \(m_{e}\), \(m_{H}\) and \(m_{D}\) are the rest masses of the electron, proton and deuteron. The isotope shift, expressed as a velocity shift, is \(c(\lambda_{D}-\lambda_{H})/\lambda_{H}\simeq -81.6~{\rm km~s}^{-1}\). So, if we want to detect deuterium and hydrogen transitions, we require that the environment must not contain Doppler motions that exceed this value.
In 1976, it was realized that there might be clouds of gas in the high redshift Universe that have very low Doppler motions, such that absorption by deuterium and hydrogen transitions could be imprinted on the light of a bright, unrelated background light source. The idea is similar to looking at a lighthouse on a foggy night. We know that there is fog between us and the lighthouse because we don't see all of the light from the lighthouse. The brightest "lighthouses" in the early Universe are quasars, which are rapidly accreting supermassive black holes in the centers of galaxies. By obtaining a spectrum of a quasar, we can study the clouds of gas that are between our telescopes and the distant quasars. Furthermore, because the Universe is expanding, the absorption lines of all these gas clouds are redshifted by different amounts, leading to a plentiful forest of absorption lines (between a wavelength of \(3500-4800\) in the example shown in Figure E); the absorption lines in this figure are almost entirely due to hydrogen atoms that are along the line-of-sight to the quasar.
Figure \(\PageIndex{3}\): A spectrum of a quasar is shown (black data). Galactic and intergalactic gas along the line-of-sight to this quasar absorb the quasar light at the wavelengths corresponding to atomic transitions. The expansion of the Universe causes these transitions to redshift relative to each other, leading to a forest of absorption lines, mostly comprised of hydrogen lines. There are also some absorption lines from heavy elements, called "metals", including oxygen and iron (credit: John Webb).
In some quasar spectra, there could be as many as several hundred hydrogen absorption lines, and all of these gas clouds have deuterium atoms in them as well. However, most of these gas clouds have Doppler motions that exceed the isotope shift of \(81.6~{\rm km~s}^{-1}\), and cannot be used to measure the relative number of deuterium and hydrogen atoms. While this technique (called "quasar absorption line spectroscopy") was very promising, it took more than two decades of research and the advent of the 10 meter diameter Keck telescopes to find the first gas clouds where deuterium and hydrogen atomic transitions could be measured. An example of the deuterium and hydrogen absorption lines detected in a gas cloud using this technique is shown in Figure 4, where the transitions from from principal quantum number \(n=1\) to higher energy levels (a.k.a. the Lyman series of hydrogen and deuterium) are shown.
Figure \(\PageIndex{4}\): The black data shows an example of a deuterium and hydrogen absorption line system. The deuterium absorption is indicated with the green line at \(-81.6~{\rm km~s}^{-1}\), and the hydrogen line is shown with the red tick mark above the data. The red curve is a model fit to the data (black histogram). (credit: Ryan Cooke).
These same gas clouds also contain absorption lines from heavy elements (see Figure 3 for an example). This tells us that these gas clouds are not pristine reservoirs that have been untouched since the Big Bang; instead, their chemistry has been slightly altered by enrichment from stars. By measuring how many metals have been made relative to hydrogen in these environments, we can estimate how contaminated these environments are.
Since these first measurements were made, the technique used to identify these deuterium absorption systems has been refined. However, despite considerable work since the year 2000, the deuterium abundance has only been reliably and consistently measured for just seven gas clouds, demonstrating how challenging and rare this measurement is. These seven measurements are shown as the blue symbols in Figure 5, as a function of the amount of contamination by stars (represented by the oxygen abundance, [O/H]). Even though these seven independent gas clouds have had a different amount of stellar processing, they are all statistically consistent with each. This tells us that the gas clouds where these measurements were made have retained a primordial relative composition of deuterium and hydrogen, and their ratio is the same as the value set just minutes after the Big Bang.
Figure \(\PageIndex{5}\): Seven independent measures of the deuterium abundance (i.e. the relative number of deuterium to hydrogen atoms) of gas clouds (blue symbols with error bars). The x-axis shows the oxygen abundance, displayed on a log scale relative to solar (i.e. -2 is one-hundredth of the number of oxygen atoms in the sun relative to hydrogen, while -3 represents one-thousandth of the number of oxygen atoms). All seven measures are consistent with each other. The red horizontal lines represent 68 and 95 per cent confidence interval of the weighted mean value of these seven measures. (credit: Ryan Cooke).
Calculations of Big Bang nucleosynthesis indicate that the relative abundance of deuterium and hydrogen atoms is highly sensitive to the expansion rate of the Universe and the density of baryons (i.e. ordinary matter). If we assume the Standard Model of particle physics and cosmology, this sets the expansion rate of the Universe, and under this assumption, we can use the deuterium abundance to estimate the universal density of baryons. The baryon density is also a fundamental quantity that can be measured from the cosmic microwave background temperature fluctuations. Quite amazingly, the baryon density that is inferred from the seven measures of D/H agrees with the baryon density derived from the cosmic microwave background at one per cent precision. The astounding agreement of these two baryon density measures, based on completely independent physics, and based on two epochs of the Universe separated by almost 400,000 years, represents one of the strongest confirmations of our Standard cosmological model.
Helium-4 and the search for physics beyond the Standard Model
As discussed in Chapter 23: Big Bang Nucleosynthesis - Predictions , 4 He is the main nuclide produced during Big Bang nucleosynthesis. Calculations of Big Bang nucleosynthesis tell us that the amount of 4 He that is made depends primarily on the expansion rate of the Universe. There are three approaches to measure the primordial abundance of 4 He: (1) spectroscopic observations of metal-poor star-forming dwarf galaxies; (2) quasar absorption lines; and (3) the damping tail of the Cosmic Microwave Background temperature fluctuations. These approaches will now be discussed in turn.
Galaxies that are currently forming a new generation of stars are referred to as "star-forming galaxies", and usually have blue colors owing to the presence of massive (and therefore short-lived) stars of spectral type O and B. These hot stars produce significant quantities of photons that are capable of ionizing the atoms in the surrounding area. Electrons that have been ionized from atoms eventually recombine with another atom and produce emission lines as the electron cascades down the energy levels. An image and a spectrum of one of the most metal-poor star-forming galaxies currently known is shown in Figure 6; this galaxy is called I Zwicky 18 (where the "I" is the roman numeral for 1, and is pronounced "one Zwicky eighteen"). The ionized gas surrounding the O and B stars are generally referred to as "H II regions", because almost all of the hydrogen atoms have had their electron ionized ("H I" refers to regions that are mostly neutral, whereby most of the protons have captured an electron).
Figure \(\PageIndex{6}\): An image of I Zwicky 18 (left panel; credit: NASA, ESA, and A. Aloisi) and an optical spectrum (right panel; credit: SDSS). Note the blue appearance of the galaxy image and the emission lines that are detected in the spectrum, indicating that hot O and B stars are ionizing the gas in this galaxy. The relative strengths of the emission lines can tell us about the physical and chemical properties of the gas.
Figure \(\PageIndex{7}\): The helium abundance of a sample of galaxies with different metallicities (measured as O/H) shows a gentle increase from the primordial value, \(y_{p}\) (credit: O. A. Kurichin).
The relative strengths of the emission lines emanating from H II regions depend on the chemistry of the gas (i.e. the relative abundance of each chemical element) and the physical conditions of the gas (e.g. the density, temperature, ionization fraction, etc.). Most of the emission lines that come from H II regions have a different dependence on density, temperature, etc. and by combining the information from many lines simultaneously, it is possible to determine both the physical and chemical properties of the gas. Measurements of the 4 He/H ratio in different galaxies indicate that the 4 He abundance gradually increases as stars produce heavy elements (see Figure 2). Therefore, the helium abundance that we measure in these star-forming galaxies does not reflect the primordial composition. Instead, we need to measure the helium abundance in many galaxies covering a range of metallicity, fit a linear relation to the helium and metal abundance, and extrapolate this linear fit to zero metallicity (see Figure 7). Current determinations of the primordial helium abundance using this approach are limited by systematic uncertainties at the \(\sim1\) per cent level.
The second approach that has been used to infer the primordial helium abundance uses quasar absorption line spectroscopy (see the section on Deuterium, above, for an explanation of this technique) of metal-poor gas clouds at high redshift (\(z\sim1-2\)). This approach is qualitatively similar to the approach used to measure the deuterium abundance, however, there is a key difference between these approaches. For deuterium, one tries to find mostly neutral gas clouds to facilitate the detection of many deuterium Lyman series transitions. However, these mostly neutral gas clouds absorb essentially all of the background quasar photons with energies greater than the ionization potential of hydrogen (13.6 eV \(\equiv\ 912\)Å). Since all of the helium transitions occur at wavelengths \(<912\)Å, there is insufficient quasar flux to detect helium absorption. Therefore, in order to detect both helium and hydrogen absorption lines, the gas cloud needs to be transparent to photons at wavelengths \(<912\)Å; this occurs for gas clouds that are mostly ionized, with a column density of neutral hydrogen \(N({\rm H I}) < 10^{17}~{\rm atoms~cm}^{-2}\). The helium abundance has only been measured in one gas cloud with a metallicity of 1/30 solar, which is a similar metallicity to the most metal-poor star-forming galaxies used to measure the helium abundance. The measurement precision of this technique is currently at the \(\sim10\) per cent level.
The third approach that is currently employed to infer the primordial 4 He abundance uses the Cosmic Microwave Background temperature fluctuations (see Chapter 27: Cosmic Microwave Background Anisotropies ). For further details about this technique, see the Advanced Topic at the end of this chapter.
Lithium-7 and the Cosmic Lithium Problem
The best available observational determination of the primordial 7 Li abundance is based on measurements of the 7 Li absorption from the atmosphere's of metal-poor stars in the Milky Way. This is not a straightforward measurement, because stars are extremely good at burning 7 Li. Convective motions (particularly in cool stars) mix the 7 Li near the surface of the star into the deeper layers where 7 Li is burned. Meanwhile 7 Li-deficient material is brought to the surface. To mitigate this process, observations typically focus on the hottest metal-poor stars, which have thin convective zones, and the measured 7 Li abundance does not correlate with temperature. This key realization came from F. Spite and M. Spite in 1982, who reported the first measurement of the 7 Li abundance in metal-poor stars; using only the hottest halo stars, Spite & Spite found that the 7 Li abundance of these stars is independent of temperature and metallicity, and has a very small scatter. This seemingly constant 7 Li abundance is referred to as the "Spite Plateau" (see Figure 8), and this value has remained impressively constant over the last few decades.
For many years, it was assumed that the Spite plateau was representative of the primordially produced abundance of 7 Li/H. However, at the turn of the millennium, the first WMAP results provided an impressively tight bound on the baryon density, and this revealed that the Spite plateau disagreed significantly with the Standard Model value, based on the CMB-derived baryon density. This problem has come to be known as the "Cosmic Lithium Problem". Many groups have re-measured the lithium abundance with increasing detailed models of stellar atmosphere's, and the result was essentially unchanged (actually this made the agreement with the Standard Model a little worse). Several nuclear physics groups searched for resonances with the reaction rates involving 7 Li, with the expectation that an unidentified resonance might alter the primordially predicted 7 Li abundance; the refined measurements of the reaction rates made the disagreement even more pronounced.
Figure \(\PageIndex{8}\): The chemical evolution of 7 Li in the Milky Way. The x-axis shows the iron abundance on a log scale relative to solar (i.e. 0 is the solar iron abundance, -1 is one-tenth solar, etc.). The primordial 7 Li abundance assuming the Standard Model is shown by the black symbol with error labeled "BBN". As the Universe becomes more enriched with iron, some 7 Li is made by stars and cosmic rays. The build-up of 7 Li as the iron abundance increases is shown by the green solid line, and the solar value is given by the \(\odot\) symbol. The measured value in stars is shown by the purple and blue hatched region. The "Spite Plateau" refers to the roughly constant value of 7 Li/H between -2.5 < [Fe/H] < -1.0. At extremely low metallicities, [Fe/H] < -2.5, the Spite Plateau declines. The 7 Li abundance of the Small Magellanic Cloud (based on interstellar absorption line spectroscopy) is shown as the red and black symbol with an error bar (Credit: J. C. Howk).
It's fair to say that most, but far from all, of the community believe that Cosmic Lithium Problem can be solved with a better understanding of 7 Li burning in stars; this is currently the favored explanation for the relatively low abundance of lithium in metal-poor stars. Moreover, several groups have now measured the 7 Li abundance in extremely metal-poor stars, and found that the Spite Plateau appears to break down at metallicities less than 1/300th of solar (see Figure 8), giving further weight to the idea that the Cosmic Lithium Problem is a result of stellar burning of 7 Li. In an attempt to mitigate the problem of 7 Li burning in stars, a measurement of the interstellar abundance of 7 Li was made in the lowest metallicity environment where this measurement is currently possible - the Small Magellanic Cloud (SMC), which has an iron abundance about one-fifth of the solar metallicity. The technique used is similar to quasar absorption line spectroscopy (see description in the section on deuterium, above), but instead of a quasar, a bright O star is used as the background light source probing the interstellar medium of the galaxy. Coincidentally, this measurement is consistent with the Standard Model primordial value; however, we expect that the interstellar medium of the Small Magellanic Cloud is enriched with some 7 Li made by stars and cosmic rays. Subtracting the 7 Li produced by stars and cosmic rays in the Small Magellanic Cloud would result in a value that is consistent with the Spite Plateau, and marginally inconsistent with the Standard Model value. Thus, further work is needed to elucidate the cosmic chemical evolution of 7 Li, and pin down with confidence an observational determination of the primordial 7 Li abundance.
Helium-3
3 He has proven to be a very challenging primordial nuclide to measure. First, almost all 3 He and 4 He transitions are very close in wavelength (the difference is one neutron in the nucleus - see the section above on deuterium for a discussion about isotope shifts). The proximity of these transitions, and the fact that 4 He is 10,000 times more abundance than 3 He, has rendered measurements of the 3 He abundance to be nearly impossible. To date, 3 He has only been measured in the Milky Way, including a small handful of H II regions and a few environments in our Solar System (Jupiter, in particular, provides a good estimate of the pre-solar 3 He/ 4 He abundance). Unfortunately (for measurements of the primordial abundances), the Milky Way has experienced a significant amount of chemical enrichment, and the 3 He abundances measured in the Solar System and in some of the Milky Way H II regions do not reflect the primordial value. Nevertheless, despite the significant build-up of metals in the Milky Way, the latest models of Galactic chemical evolution suggest that the abundance of 3 He in the outskirts of galaxies like the Milky Way may be close to primordial (see the red curve in Figure 9).
The most common approach currently used to infer the primordial 3 He abundance utilizes the 8.7 GHz spin-flip transition of 3 He + (i.e. singly ionized 3 He). The key benefit of this approach is that 3 He has a non-zero nuclear spin, while the nuclear spin of 4 He is zero. The ground state of 3 He is therefore split into two hyperfine structure levels; this splitting does not occur for 4 He, so the detection of 3 He in emission is made somewhat less difficult. Over many decades of work, there are just five reliable measurements of the 3 He abundance in Galactic H II regions. The most distant, and well-characterized of these H II regions is called "S209", and is 16 kpc from the Galactic centre, where models of Galactic chemical evolution predict a very modest enhancement in the amount of 3 He above the primordial value (see Figure 9). The value measured in this H II region agrees with the Standard Model value to within \(\sim30\) per cent.
Figure \(\PageIndex{9}\): The present-day radial distribution of 3 He in the Milky Way (symbols with error bars) together with a detailed model of Galactic chemical evolution (red curve) and the primordial abundance (gray horizontal band labeled "BBN Standard Model"). The blue curves show Galactic chemical evolution models that do not include outflowing gas. The black points correspond to measurements of the 8.7 GHz fine-structure line of 3 He + , while the red symbol represents a measure of the 3 He/ 4 He isotope ratio of the Orion Nebula, using absorption line spectroscopy (Credit: R. Cooke).
An alternative approach uses the same 8.7 GHz transition to detect 3 He + in absorption against the light of a radio-bright background quasar close to helium reionization at redshift \(z\simeq3.5\). While the astronomical telescope facilities do not currently exist to perform this measurement, this is an exciting goal for future facilities, because the intergalactic regions that would be probed with this technique are almost certainly of near-primordial composition.
Finally, a recent measurement of the helium isotope ratio of the Orion Nebula was reported using absorption line spectroscopy of a star in Orion to study the gas that lies at the edge of the Orion Nebula. This approach is qualitatively similar to the approach used to measure the deuterium abundance of gas clouds at high redshift (see the section on the deuterium abundance above for a discussion about this approach). Future measurements using this technique may help to precisely pin down the Galactic chemical evolution of 3 He, and also obtain a determination of the primordial helium isotope ratio from the outskirts of the Milky Way. It is also possible to apply this technique to gas clouds at higher redshift, where the Universe has had less time to pollute the primordial signature.
Advanced Topic - Helium-4 and the Cosmic Microwave Background
Figure \(\PageIndex{10}\): The power spectrum of the Cosmic Microwave Background radiation (top panel), and the deviations of the power spectrum (in per cent) due to changes of the helium abundance. The blue dashed and solid black lines represent a decrease and increase of the primordial helium abundance by 10 per cent. (credit: Trotta & Hansen 2003).
An alternative and very promising approach to measure the helium abundance utilizes the power spectrum of temperature fluctuations imprinted on the Cosmic Microwave Background radiation. This approach has the advantage that helium is purely primordial during recombination, because there are no channels (i.e. stars) to produce/destroy 4 He during the first 400,000 years after Big Bang nucleosynthesis.
The key physical process that is sensitive to the helium abundance is diffusion damping. Note also that if more 4 He is produced during Big Bang nucleosynthesis, that means less hydrogen is made, and vice-versa. Diffusion damping (sometimes referred to as Silk damping) is a process whereby the temperature fluctuations are smoothed out on small scales (high multipoles). The damping is a result of photons being constantly scattered by charged particles (mostly electrons) prior to recombination. Photon scattering stops when the temperature of the Universe drops to the point that electrons can recombine with nuclei, at which point photons can free stream. Electrons recombine with helium first, followed later by hydrogen recombination; this is because helium has a higher ionization potential than hydrogen (i.e. it is more difficult to ionize an electron from helium once it has recombined). If more helium is made during Big Bang nucleosynthesis, there are fewer electrons between helium and hydrogen recombination, leading to less scattering. This allows photons to free stream further, damping the perturbations and reducing the CMB power at small scales. The effect is relatively small (see Figure 10), and the current inference on the primordial helium abundance using this approach is \(\sim10\) per cent. Future CMB experiments that target small angular scales aim to measure this quantity to much higher precision.