Lake stratificationLake stratification is the tendency of lakes to form separate and distinct thermal layers during warm weather. Typically stratified lakes show three distinct layers: the epilimnion, comprising the top warm layer; the thermocline (or metalimnion), the middle layer, whose depth may change throughout the day; and the colder hypolimnion, extending to the floor of the lake. Every lake has a set mixing regime that is influenced by lake morphometry and environmental conditions.
Probability density functionIn probability theory, a probability density function (PDF), density function, or density of an absolutely continuous random variable, is a function whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can be interpreted as providing a relative likelihood that the value of the random variable would be equal to that sample.
TurbulenceIn fluid dynamics, turbulence or turbulent flow is fluid motion characterized by chaotic changes in pressure and flow velocity. It is in contrast to a laminar flow, which occurs when a fluid flows in parallel layers, with no disruption between those layers. Turbulence is commonly observed in everyday phenomena such as surf, fast flowing rivers, billowing storm clouds, or smoke from a chimney, and most fluid flows occurring in nature or created in engineering applications are turbulent.
Probability mass functionIn probability and statistics, a probability mass function is a function that gives the probability that a discrete random variable is exactly equal to some value. Sometimes it is also known as the discrete probability density function. The probability mass function is often the primary means of defining a discrete probability distribution, and such functions exist for either scalar or multivariate random variables whose domain is discrete.
Probability distributionIn probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. It is a mathematical description of a random phenomenon in terms of its sample space and the probabilities of events (subsets of the sample space). For instance, if X is used to denote the outcome of a coin toss ("the experiment"), then the probability distribution of X would take the value 0.5 (1 in 2 or 1/2) for X = heads, and 0.
Ocean stratificationOcean stratification is the natural separation of an ocean's water into horizontal layers by density, which is generally stable because warm water floats on top of cold water, and heating is mostly from the sun, which reinforces that arrangement. Stratification is reduced by wind-forced mechanical mixing, but reinforced by convection (warm water rising, cold water sinking). Stratification occurs in all ocean basins and also in other water bodies.
Conditional probability distributionIn probability theory and statistics, given two jointly distributed random variables and , the conditional probability distribution of given is the probability distribution of when is known to be a particular value; in some cases the conditional probabilities may be expressed as functions containing the unspecified value of as a parameter. When both and are categorical variables, a conditional probability table is typically used to represent the conditional probability.
Probability theoryProbability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of axioms. Typically these axioms formalise probability in terms of a probability space, which assigns a measure taking values between 0 and 1, termed the probability measure, to a set of outcomes called the sample space.
LakeA lake is a naturally occurring, relatively large body of water localized in a basin surrounded by dry land. A lake generally has a slower-moving flow than the inflow or outflow stream(s) that serve to feed or drain it. Lakes lie completely on land and are separate from the ocean, although, like the much larger oceans, they form part of the Earth's water cycle by serving as large standing pools of storage water. Most lakes are freshwater and account for almost all the world's surface freshwater, but some are salt lakes with salinities even higher than that of seawater.
TemperatureTemperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer. Thermometers are calibrated in various temperature scales that historically have relied on various reference points and thermometric substances for definition. The most common scales are the Celsius scale with the unit symbol °C (formerly called centigrade), the Fahrenheit scale (°F), and the Kelvin scale (K), the latter being used predominantly for scientific purposes.
EnergyIn physics, energy () is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of heat and light. Energy is a conserved quantity—the law of conservation of energy states that energy can be converted in form, but not created or destroyed. The unit of measurement for energy in the International System of Units (SI) is the joule (J).
Dimictic lakeA dimictic lake is a body of freshwater whose difference in temperature between surface and bottom layers becomes negligible twice per year, allowing all strata of the lake's water to circulate vertically. All dimictic lakes are also considered holomictic, a category which includes all lakes which mix one or more times per year. During winter, dimictic lakes are covered by a layer of ice, creating a cold layer at the surface, a slightly warmer layer beneath the ice, and a still-warmer unfrozen bottom layer, while during summer, the same temperature-derived density differences separate the warm surface waters (the epilimnion), from the colder bottom waters (the hypolimnion).
Lake ecosystemA lake ecosystem or lacustrine ecosystem includes biotic (living) plants, animals and micro-organisms, as well as abiotic (non-living) physical and chemical interactions. Lake ecosystems are a prime example of lentic ecosystems (lentic refers to stationary or relatively still freshwater, from the Latin lentus, which means "sluggish"), which include ponds, lakes and wetlands, and much of this article applies to lentic ecosystems in general. Lentic ecosystems can be compared with lotic ecosystems, which involve flowing terrestrial waters such as rivers and streams.
Monomictic lakeMonomictic lakes are holomictic lakes that mix from top to bottom during one mixing period each year. Monomictic lakes may be subdivided into cold and warm types. Cold monomictic lakes are lakes that are covered by ice throughout much of the year. During their brief "summer", the surface waters remain at or below 4 °C. The ice prevents these lakes from mixing in winter. During summer, these lakes lack significant thermal stratification, and they mix thoroughly from top to bottom. These lakes are typical of cold-climate regions (e.
HypolimnionThe hypolimnion or under lake is the dense, bottom layer of water in a thermally-stratified lake. The word "hypolimnion" is derived from λιμνίον. It is the layer that lies below the thermocline. Typically the hypolimnion is the coldest layer of a lake in summer, and the warmest layer during winter. In deep, temperate lakes, the bottom-most waters of the hypolimnion are typically close to 4 °C throughout the year. The hypolimnion may be much warmer in lakes at warmer latitudes.
Posterior probabilityThe posterior probability is a type of conditional probability that results from updating the prior probability with information summarized by the likelihood via an application of Bayes' rule. From an epistemological perspective, the posterior probability contains everything there is to know about an uncertain proposition (such as a scientific hypothesis, or parameter values), given prior knowledge and a mathematical model describing the observations available at a particular time.
Exponential distributionIn probability theory and statistics, the exponential distribution or negative exponential distribution is the probability distribution of the time between events in a Poisson point process, i.e., a process in which events occur continuously and independently at a constant average rate. It is a particular case of the gamma distribution. It is the continuous analogue of the geometric distribution, and it has the key property of being memoryless. In addition to being used for the analysis of Poisson point processes it is found in various other contexts.
Characteristic function (probability theory)In probability theory and statistics, the characteristic function of any real-valued random variable completely defines its probability distribution. If a random variable admits a probability density function, then the characteristic function is the Fourier transform of the probability density function. Thus it provides an alternative route to analytical results compared with working directly with probability density functions or cumulative distribution functions.
Richter magnitude scaleThe Richter scale (ˈrɪktər), also called the Richter magnitude scale, Richter's magnitude scale, and the Gutenberg–Richter scale, is a measure of the strength of earthquakes, developed by Charles Francis Richter and presented in his landmark 1935 paper, where he called it the "magnitude scale". This was later revised and renamed the local magnitude scale, denoted as ML or .
Exponential functionThe exponential function is a mathematical function denoted by or (where the argument x is written as an exponent). Unless otherwise specified, the term generally refers to the positive-valued function of a real variable, although it can be extended to the complex numbers or generalized to other mathematical objects like matrices or Lie algebras. The exponential function originated from the notion of exponentiation (repeated multiplication), but modern definitions (there are several equivalent characterizations) allow it to be rigorously extended to all real arguments, including irrational numbers.
