Rain gaugeA rain gauge (also known as udometer, pluviometer, pluviameter, ombrometer, and hyetometer) is an instrument used by meteorologists and hydrologists to gather and measure the amount of liquid precipitation over a predefined area, over a period of time. It is used to determine the depth of precipitation (usually in mm) that occurs over a unit area and measure rainfall amount. The first known rainfall records were kept by the Ancient Greeks, at around 500 BCE.
RainRain is water droplets that have condensed from atmospheric water vapor and then fall under gravity. Rain is a major component of the water cycle and is responsible for depositing most of the fresh water on the Earth. It provides water for hydroelectric power plants, crop irrigation, and suitable conditions for many types of ecosystems. The major cause of rain production is moisture moving along three-dimensional zones of temperature and moisture contrasts known as weather fronts.
Snow gaugeA snow gauge is a type of instrument used by meteorologists and hydrologists to gather and measure the amount of solid precipitation (as opposed to liquid precipitation, which is measured by a rain gauge) over a set period of time. The first use of snow gauges were precipitation gauges that was widely used in 1247 during the Southern Song dynasty to gather meteorological data. The Song Chinese mathematician and inventor Qin Jiushao records the use of gathering rain and snowfall measurements in the Song mathematical treatise Mathematical Treatise in Nine Sections.
Jacobi elliptic functionsIn mathematics, the Jacobi elliptic functions are a set of basic elliptic functions. They are found in the description of the motion of a pendulum (see also pendulum (mathematics)), as well as in the design of electronic elliptic filters. While trigonometric functions are defined with reference to a circle, the Jacobi elliptic functions are a generalization which refer to other conic sections, the ellipse in particular. The relation to trigonometric functions is contained in the notation, for example, by the matching notation for .
Trigonometric functionsIn mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial mechanics, geodesy, and many others. They are among the simplest periodic functions, and as such are also widely used for studying periodic phenomena through Fourier analysis.
Precipitation typesIn meteorology, the different types of precipitation often include the character, formation, or phase of the precipitation which is falling to ground level. There are three distinct ways that precipitation can occur. Convective precipitation is generally more intense, and of shorter duration, than stratiform precipitation. Orographic precipitation occurs when moist air is forced upwards over rising terrain and condenses on the slope, such as a mountain.
HygrometerA hygrometer is an instrument which measures the humidity of air or some other gas: that is, how much water vapor it contains. Humidity measurement instruments usually rely on measurements of some other quantities such as temperature, pressure, mass and mechanical or electrical changes in a substance as moisture is absorbed. By calibration and calculation, these measured quantities can lead to a measurement of humidity.
PrecipitationIn meteorology, precipitation is any product of the condensation of atmospheric water vapor that falls from clouds due to gravitational pull. The main forms of precipitation include drizzle, rain, sleet, snow, ice pellets, graupel and hail. Precipitation occurs when a portion of the atmosphere becomes saturated with water vapor (reaching 100% relative humidity), so that the water condenses and "precipitates" or falls. Thus, fog and mist are not precipitation but colloids, because the water vapor does not condense sufficiently to precipitate.
Theta functionIn mathematics, theta functions are special functions of several complex variables. They show up in many topics, including Abelian varieties, moduli spaces, quadratic forms, and solitons. As Grassmann algebras, they appear in quantum field theory. The most common form of theta function is that occurring in the theory of elliptic functions. With respect to one of the complex variables (conventionally called z), a theta function has a property expressing its behavior with respect to the addition of a period of the associated elliptic functions, making it a quasiperiodic function.
Lemniscate elliptic functionsIn mathematics, the lemniscate elliptic functions are elliptic functions related to the arc length of the lemniscate of Bernoulli. They were first studied by Giulio Fagnano in 1718 and later by Leonhard Euler and Carl Friedrich Gauss, among others. The lemniscate sine and lemniscate cosine functions, usually written with the symbols sl and cl (sometimes the symbols sinlem and coslem or sin lemn and cos lemn are used instead), are analogous to the trigonometric functions sine and cosine.
