Hypsometry () is the measurement of the

elevation The elevation of a geographic location is its height above or below a fixed reference point, most commonly a reference geoid, a mathematical model of the Earth's sea level as an equipotential gravitational surface (see Geodetic datum § ...

and depth of features of the Earth's surface relative to

mean sea level There are several kinds of mean in mathematics, especially in statistics. Each mean serves to summarize a given group of data, often to better understand the overall value ( magnitude and sign) of a given data set. For a data set, the '' ...

. On Earth, the elevations can take on either positive or negative (below sea level) values. The distribution is theorised to be

bimodal In statistics, a multimodal distribution is a probability distribution with more than one mode. These appear as distinct peaks (local maxima) in the probability density function, as shown in Figures 1 and 2. Categorical, continuous, and d ...

due to the difference in density between the lighter continental crust and denser oceanic crust. On other planets within this solar system, elevations are typically

unimodal In mathematics, unimodality means possessing a unique mode. More generally, unimodality means there is only a single highest value, somehow defined, of some mathematical object. Unimodal probability distribution In statistics, a unimodal p ...

, owing to the lack of oceans on those bodies. EarthHypso

Hypsometric curve

A hypsometric curve is a

histogram A histogram is an approximate representation of the frequency distribution, distribution of numerical data. The term was first introduced by Karl Pearson. To construct a histogram, the first step is to "Data binning, bin" (or "Data binning, buck ...

cumulative distribution function In probability theory and statistics, the cumulative distribution function (CDF) of a real-valued random variable X, or just distribution function of X, evaluated at x, is the probability that X will take a value less than or equal to x. Eve ...

of elevations in a geographical area. Differences in hypsometric curves between landscapes arise because the geomorphic processes that shape the landscape may be different. When drawn as a 2-dimensional histogram, a hypsometric curve displays the elevation (''y'') on the vertical,

y-axis A Cartesian coordinate system (, ) in a plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, measured in ...

and area above the corresponding elevation (''x'') on the horizontal or x-axis. The curve can also be shown in non-dimensional or standardized form by scaling elevation and area by the maximum values. The non-dimensional hypsometric curve provides a

hydrologist Hydrology () is the scientific study of the movement, distribution, and management of water on Earth and other planets, including the water cycle, water resources, and environmental watershed sustainability. A practitioner of hydrology is calle ...

or a geomorphologist with a way to assess the similarity of watersheds — and is one of several characteristics used for doing so. The hypsometric integral is a summary measure of the shape of the hypsometric curve. In the original paper on this topic, Arthur Strahler proposed a curve containing three parameters to fit different hypsometric relations: :

y = \left frac \cdot \frac\right z

, where ''a'', ''d'' and ''z'' are fitting parameters. Subsequent research using two-dimensional landscape evolution models has called the general applicability of this fit into question, as well as the capability of the hypsometric curve to deal with scale-dependent effects. A modified curve with one additional parameter has been proposed to improve the fit. Hypsometric curves are commonly used in

limnology Limnology ( ; from Greek λίμνη, ''limne'', "lake" and λόγος, ''logos'', "knowledge") is the study of inland aquatic ecosystems. The study of limnology includes aspects of the biological, chemical, physical, and geological characteris ...

to represent the relationship between lake surface area and depth and calculate total lake volume. These graphs can be used to predict various characteristics of lakes such as

productivity Productivity is the efficiency of production of goods or services expressed by some measure. Measurements of productivity are often expressed as a ratio of an aggregate output to a single input or an aggregate input used in a production proces ...

, dilution of incoming chemicals, and potential for water mixing.

Hypsometric curve

See also

References

Further reading