The area density (also known as areal density, surface density, superficial density, areic density, mass thickness, column density, or density thickness) of a two-dimensional object is calculated as the
mass
Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different elementar ...
per unit
area
Area is the quantity that expresses the extent of a region on the plane or on a curved surface. The area of a plane region or ''plane area'' refers to the area of a shape
A shape or figure is a graphics, graphical representation of an obje ...
. The
SI derived unit is the kilogram per square metre (kg·m
−2).
A related ''
area number density'' can be defined by replacing
mass
Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different elementar ...
in by
number of particles
The particle number (or number of particles) of a thermodynamic system, conventionally indicated with the letter ''N'', is the number of constituent particles in that system. The particle number is a fundamental parameter in thermodynamics which is ...
or other
countable quantity
A dimensionless quantity (also known as a bare quantity, pure quantity, or scalar quantity as well as quantity of dimension one) is a quantity to which no physical dimension is assigned, with a corresponding SI unit of measurement of one (or 1) ...
.
In the paper and fabric industries, it is called
grammage
Grammage and basis weight, in the pulp and paper industry, are the area density of a paper product, that is, its mass per unit of area. Two ways of expressing grammage are commonly used:
* Expressed in grams (g) per square meter (g/m2), regardle ...
and is expressed in grams per square meter (g/m
2); for paper in particular, it may be expressed as pounds per
ream
Ream may refer to:
* Paper ream, unit of 500 sheets of paper
* Ream (surname)
* Reamer, tool used to widen a hole
* Ream, West Virginia
* Ream, the name of Rama in the Khmer version of the Ramayana, the Reamker
* Ream National Park, a national pa ...
of standard sizes ("basis ream").
Formulation
Area density can be calculated as:
or
where,
Column density
A special type of area density is called ''column (mass) density'' (also ''columnar mass density''), denoted ''ρ''
A or ''σ''. It is the
mass
Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different elementar ...
of
substance
Substance may refer to:
* Matter, anything that has mass and takes up space
Chemistry
* Chemical substance, a material with a definite chemical composition
* Drug substance
** Substance abuse, drug-related healthcare and social policy diagnosis ...
per unit
area
Area is the quantity that expresses the extent of a region on the plane or on a curved surface. The area of a plane region or ''plane area'' refers to the area of a shape
A shape or figure is a graphics, graphical representation of an obje ...
integrated along a path;
[
] It is obtained integrating
volumetric density
Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematicall ...
over a column:
In general the integration path can be slant or oblique incidence (as in, for example,
line of sight propagation in
atmospheric physics
Within the atmospheric sciences, atmospheric physics is the application of physics to the study of the atmosphere. Atmospheric physicists attempt to model Earth's atmosphere and the atmospheres of the other planets using fluid flow equations, che ...
). A common special case is a vertical path, from the bottom to the top of the medium:
where
denotes the vertical coordinate (e.g., height or depth).
Columnar density
is closely related to the vertically averaged volumetric density
as
where
;
,
, and
have units of, for example, grams per cubic metre, grams per square metre, and metres, respectively.
Column number density
''Column number density'' refers instead to a
number density
The number density (symbol: ''n'' or ''ρ''N) is an intensive quantity used to describe the degree of concentration of countable objects (particles, molecules, phonons, cells, galaxies, etc.) in physical space: three-dimensional volumetric number ...
type of quantity: the number or count of a substance—rather than the mass—per unit area integrated along a path:
Usage
Atmospheric physics
It is a quantity commonly retrieved by
remote sensing
Remote sensing is the acquisition of information about an object or phenomenon without making physical contact with the object, in contrast to in situ or on-site observation. The term is applied especially to acquiring information about Earth ...
instruments, for instance the
Total Ozone Mapping Spectrometer
The Total Ozone Mapping Spectrometer (TOMS) was a NASA satellite instrument, specifically a spectrometer, for measuring the ozone layer. Of the five TOMS instruments which were built, four entered successful orbit. The satellites carrying TOMS ins ...
(TOMS) which retrieves ozone columns around the globe. Columns are also returned by the
differential optical absorption spectroscopy (DOAS) method
[
] and are a common retrieval product from
nadir
The nadir (, ; ar, نظير, naẓīr, counterpart) is the direction pointing directly ''below'' a particular location; that is, it is one of two vertical directions at a specified location, orthogonal to a horizontal flat surface.
The direc ...
-looking
microwave
Microwave is a form of electromagnetic radiation with wavelengths ranging from about one meter to one millimeter corresponding to frequencies between 300 MHz and 300 GHz respectively. Different sources define different frequency ran ...
radiometers
A radiometer or roentgenometer is a device for measuring the radiant flux (power) of electromagnetic radiation. Generally, a radiometer is an infrared radiation detector or an ultraviolet detector. Microwave radiometers operate in the microwave wa ...
.
[
][
]
A closely related concept is that of ice or
liquid water path Liquid water path - in units of g/m2 is a measure of the total amount of liquid water present between two points in the atmosphere.
LWP is an important quantity in understanding radiative transfer in the atmosphere. It is defined as the integral o ...
, which specifies the volume per unit area or depth instead of mass per unit area, thus the two are related:
:
,
Another closely related concept is
optical depth
In physics, optical depth or optical thickness is the natural logarithm of the ratio of incident to ''transmitted'' radiant power through a material.
Thus, the larger the optical depth, the smaller the amount of transmitted radiant power through ...
.
Astronomy
In Astronomy the column density is generally used to indicate the number of atoms or molecules per square cm (cm
2) along the line of sight in a particular direction, as derived from observations of e.g. the 21-cm
hydrogen line
The hydrogen line, 21 centimeter line, or H I line is the electromagnetic radiation spectral line that is created by a change in the energy state of neutral hydrogen atoms. This electromagnetic radiation has a precise frequency of , w ...
or from observations of a certain molecular species. Also the
interstellar extinction
In astronomy, extinction is the absorption and scattering of electromagnetic radiation by dust and gas between an emitting astronomical object and the observer. Interstellar extinction was first documented as such in 1930 by Robert Julius Trumple ...
can be related to the column density of H or H
2.
The concept of area density can be useful when analysing
accretion disk
An accretion disk is a structure (often a circumstellar disk) formed by diffuse material in orbital motion around a massive central body. The central body is typically a star. Friction, uneven irradiance, magnetohydrodynamic effects, and other fo ...
s. In the case of a disk seen face-on, area density for a given area of the disk is defined as column density: that is, either as the
mass
Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different elementar ...
of
substance
Substance may refer to:
* Matter, anything that has mass and takes up space
Chemistry
* Chemical substance, a material with a definite chemical composition
* Drug substance
** Substance abuse, drug-related healthcare and social policy diagnosis ...
per unit
area
Area is the quantity that expresses the extent of a region on the plane or on a curved surface. The area of a plane region or ''plane area'' refers to the area of a shape
A shape or figure is a graphics, graphical representation of an obje ...
integrated along the vertical path that goes through the disk
(line-of-sight), from the bottom to the top of the medium:
:
where
denotes the vertical coordinate (e.g., height or depth), or as the number or count of a substance—rather than the mass—per unit area integrated along a path (column number density):
:
Data storage media
Areal density is used to quantify and compare different types media used in data storage devices such as
hard disk drives
A hard disk drive (HDD), hard disk, hard drive, or fixed disk is an electro-mechanical data storage device that stores and retrieves digital data using magnetic storage with one or more rigid rapidly rotating hard disk platter, platters ...
,
optical disc drives and
tape drives
A tape drive is a data storage device that reads and writes data on a magnetic tape. Magnetic tape data storage is typically used for offline, archival data storage. Tape media generally has a favorable unit cost and a long archival stability.
A ...
. The current unit of measure is typically gigabits per square inch.
Paper
The area density is often used to describe the thickness of paper; e.g., 80 g/m
2 is very common.
Fabric
Fabric "weight" is often specified as mass per unit area, grams per square meter (gsm) or
ounce
The ounce () is any of several different units of mass, weight or volume and is derived almost unchanged from the , an Ancient Roman units of measurement, Ancient Roman unit of measurement.
The #International avoirdupois ounce, avoirdupois ounce ...
s per square yard. It is also sometimes specified in ounces per yard in a standard width for the particular cloth. One gram per square meter equals 0.0295 ounces per square yard; one ounce per square yard equals 33.9 grams per square meter.
Other
It is also an important quantity for the
absorption of radiation.
When studying bodies falling through air, area density is important because resistance depends on area, and gravitational force is dependent on mass.
Bone density
Bone density, or bone mineral density, is the amount of bone mineral in bone tissue. The concept is of mass of mineral per volume of bone (relating to density in the physics sense), although clinically it is measured by proxy according to optica ...
is often expressed in grams per square centimeter (g·cm
−2) as measured by x-ray absorptiometry, as a proxy for the actual density.
The
body mass index
Body mass index (BMI) is a value derived from the mass (weight) and height of a person. The BMI is defined as the body mass divided by the square of the body height, and is expressed in units of kg/m2, resulting from mass in kilograms and he ...
is expressed in units of kilograms per square meter, though the area figure is nominal, being simply the square of the height.
The
total electron content
Total electron content (TEC) is an important descriptive quantity for the ionosphere of the Earth. TEC is the total number of electrons integrated between two points, along a tube of one meter squared cross section, i.e., the electron columnar nu ...
in the ionosphere is a quantity of type columnar number density.
Snow water equivalent
Snow science addresses how snow forms, its distribution, and processes affecting how snowpacks change over time. Scientists improve storm forecasting, study global snow cover and its effect on climate, glaciers, and water supplies around the worl ...
is a quantity of type columnar mass density.
See also
*
Linear density
Linear density is the measure of a quantity of any characteristic value per unit of length. Linear mass density (titer in textile engineering, the amount of mass per unit length) and linear charge density (the amount of electric charge per unit ...
*
Paper density
Paper density is a paper product's mass per unit volume. The density can be calculated by dividing the grammage of paper (in grams per square metre or "gsm") by its caliper (usually in micrometres, occasionally in mils).
The "ISO 534:2011, Pap ...
References
{{DEFAULTSORT:Area Density
Atmospheric physics
Density
Classical mechanics