Sediment transportSediment transport is the movement of solid particles (sediment), typically due to a combination of gravity acting on the sediment, and the movement of the fluid in which the sediment is entrained. Sediment transport occurs in natural systems where the particles are clastic rocks (sand, gravel, boulders, etc.), mud, or clay; the fluid is air, water, or ice; and the force of gravity acts to move the particles along the sloping surface on which they are resting.
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.
Bed loadThe term bed load or bedload describes particles in a flowing fluid (usually water) that are transported along the stream bed. Bed load is complementary to suspended load and wash load. Bed load moves by rolling, sliding, and/or saltating (hopping). Generally, bed load downstream will be smaller and more rounded than bed load upstream (a process known as downstream fining). This is due in part to attrition and abrasion which results from the stones colliding with each other and against the river channel, thus removing the rough texture (rounding) and reducing the size of the particles.
Fluvial processesIn geography and geology, fluvial processes are associated with rivers and streams and the deposits and landforms created by them. When the stream or rivers are associated with glaciers, ice sheets, or ice caps, the term glaciofluvial or fluvioglacial is used. Fluvial processes include the motion of sediment and erosion or deposition on the river bed. The movement of water across the stream bed exerts a shear stress directly onto the bed.
Gamma distributionIn probability theory and statistics, the gamma distribution is a two-parameter family of continuous probability distributions. The exponential distribution, Erlang distribution, and chi-squared distribution are special cases of the gamma distribution. There are two equivalent parameterizations in common use: With a shape parameter and a scale parameter . With a shape parameter and an inverse scale parameter , called a rate parameter. In each of these forms, both parameters are positive real numbers.
Hyperexponential distributionIn probability theory, a hyperexponential distribution is a continuous probability distribution whose probability density function of the random variable X is given by where each Yi is an exponentially distributed random variable with rate parameter λi, and pi is the probability that X will take on the form of the exponential distribution with rate λi. It is named the hyperexponential distribution since its coefficient of variation is greater than that of the exponential distribution, whose coefficient of variation is 1, and the hypoexponential distribution, which has a coefficient of variation smaller than one.
Abrasion (geology)Abrasion is a process of erosion which occurs when material being transported wears away at a surface over time. It is the process of friction caused by scuffing, scratching, wearing down, marring, and rubbing away of materials. The intensity of abrasion depends on the hardness, concentration, velocity and mass of the moving particles. Abrasion generally occurs in four ways: glaciation slowly grinds rocks picked up by ice against rock surfaces; solid objects transported in river channels make abrasive surface contact with the bed and walls; objects transported in waves breaking on coastlines; and by wind transporting sand or small stones against surface rocks.
Multimodal distributionIn 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 discrete data can all form multimodal distributions. Among univariate analyses, multimodal distributions are commonly bimodal. When the two modes are unequal the larger mode is known as the major mode and the other as the minor mode. The least frequent value between the modes is known as the antimode.
Erlang distributionThe Erlang distribution is a two-parameter family of continuous probability distributions with support . The two parameters are: a positive integer the "shape", and a positive real number the "rate". The "scale", the reciprocal of the rate, is sometimes used instead. The Erlang distribution is the distribution of a sum of independent exponential variables with mean each. Equivalently, it is the distribution of the time until the kth event of a Poisson process with a rate of .
Meta-analysisA meta-analysis is a statistical analysis that combines the results of multiple scientific studies. Meta-analyses can be performed when there are multiple scientific studies addressing the same question, with each individual study reporting measurements that are expected to have some degree of error. The aim then is to use approaches from statistics to derive a pooled estimate closest to the unknown common truth based on how this error is perceived. It is thus a basic methodology of Metascience.
Phase-type distributionA phase-type distribution is a probability distribution constructed by a convolution or mixture of exponential distributions. It results from a system of one or more inter-related Poisson processes occurring in sequence, or phases. The sequence in which each of the phases occurs may itself be a stochastic process. The distribution can be represented by a random variable describing the time until absorption of a Markov process with one absorbing state. Each of the states of the Markov process represents one of the phases.
GravelGravel (ˈɡrævəl) is a loose aggregation of rock fragments. Gravel occurs naturally on Earth as a result of sedimentary and erosive geological processes; it is also produced in large quantities commercially as crushed stone. Gravel is classified by particle size range and includes size classes from granule- to boulder-sized fragments. In the Udden-Wentworth scale gravel is categorized into granular gravel () and pebble gravel (). ISO 14688 grades gravels as fine, medium, and coarse, with ranges for fine and for coarse.
Marine sedimentMarine sediment, or ocean sediment, or seafloor sediment, are deposits of insoluble particles that have accumulated on the seafloor. These particles have their origins in soil and rocks and have been transported from the land to the sea, mainly by rivers but also by dust carried by wind and by the flow of glaciers into the sea. Additional deposits come from marine organisms and chemical precipitation in seawater, as well as from underwater volcanoes and meteorite debris.
Negative binomial distributionIn probability theory and statistics, the negative binomial distribution is a discrete probability distribution that models the number of failures in a sequence of independent and identically distributed Bernoulli trials before a specified (non-random) number of successes (denoted ) occurs. For example, we can define rolling a 6 on a dice as a success, and rolling any other number as a failure, and ask how many failure rolls will occur before we see the third success ().
Turbidity currentA turbidity current is most typically an underwater current of usually rapidly moving, sediment-laden water moving down a slope; although current research (2018) indicates that water-saturated sediment may be the primary actor in the process. Turbidity currents can also occur in other fluids besides water. Researchers from the Monterey Bay Aquarium Research Institute found that a layer of water-saturated sediment moved rapidly over the seafloor and mobilized the upper few meters of the preexisting seafloor.
Stable distributionIn probability theory, a distribution is said to be stable if a linear combination of two independent random variables with this distribution has the same distribution, up to location and scale parameters. A random variable is said to be stable if its distribution is stable. The stable distribution family is also sometimes referred to as the Lévy alpha-stable distribution, after Paul Lévy, the first mathematician to have studied it. Of the four parameters defining the family, most attention has been focused on the stability parameter, (see panel).
Lomax distributionThe Lomax distribution, conditionally also called the Pareto Type II distribution, is a heavy-tail probability distribution used in business, economics, actuarial science, queueing theory and Internet traffic modeling. It is named after K. S. Lomax. It is essentially a Pareto distribution that has been shifted so that its support begins at zero. The probability density function (pdf) for the Lomax distribution is given by with shape parameter and scale parameter .
UnimodalityIn mathematics, unimodality means possessing a unique mode. More generally, unimodality means there is only a single highest value, somehow defined, of some mathematical object. In statistics, a unimodal probability distribution or unimodal distribution is a probability distribution which has a single peak. The term "mode" in this context refers to any peak of the distribution, not just to the strict definition of mode which is usual in statistics. If there is a single mode, the distribution function is called "unimodal".
Clastic rockClastic rocks are composed of fragments, or clasts, of pre-existing minerals and rock. A clast is a fragment of geological detritus, chunks, and smaller grains of rock broken off other rocks by physical weathering. Geologists use the term clastic to refer to sedimentary rocks and particles in sediment transport, whether in suspension or as bed load, and in sediment deposits. Clastic sedimentary rocks are rocks composed predominantly of broken pieces or clasts of older weathered and eroded rocks.
Mixture distributionIn probability and statistics, a mixture distribution is the probability distribution of a random variable that is derived from a collection of other random variables as follows: first, a random variable is selected by chance from the collection according to given probabilities of selection, and then the value of the selected random variable is realized. The underlying random variables may be random real numbers, or they may be random vectors (each having the same dimension), in which case the mixture distribution is a multivariate distribution.
