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Related Concept Videos

Precipitation Processes01:12

Precipitation Processes

The experimental conditions in a gravimetric analysis should be optimized to maximize the particle size and purity of the obtained precipitate. Ideally, the concentration of the precipitating reagent should be low with effective stirring to maintain low relative supersaturation for the growth of large crystals. In homogeneous precipitation, the precipitant is slowly generated by a chemical reaction in the solution to avoid local reagent excesses. For example, urea decomposes gradually to...
Precipitation and Co-precipitation01:17

Precipitation and Co-precipitation

Precipitation and coprecipitation methods can be used to separate a mixture of ions in a solution. In qualitative inorganic analysis, ions that form sparingly soluble precipitates with the same reagent are separated based on the differences in solubility products. For example, consider the separation of Cu(II) and Fe(II) ions by precipitation as insoluble sulfides. First, copper(II) sulfide is precipitated by the addition of acidic H2S, where the dissociation of H2S is suppressed. Adding H2S...
Precipitation Gravimetry01:03

Precipitation Gravimetry

Precipitation gravimetry is based on converting an analyte into a sparingly soluble precipitate, which is separated by filtration and weighed. An ideal precipitate should be pure, insoluble, of known composition, and easily filtered from the reaction mixture.
In determining nickel by gravimetric analysis, a precipitant of ethanolic dimethylglyoxime is added to a hot nickel salt solution. This is quickly followed by the dropwise addition of dilute ammonia solution until precipitation occurs. A...
Absolute and Local Extreme Values01:22

Absolute and Local Extreme Values

The highest and lowest values of a function, relative to a reference axis, are known as extreme values. These include absolute maximum and absolute minimum values, which represent the highest and lowest points the function reaches across its entire domain. Within a restricted portion of the function, the highest and lowest values are referred to as local maximum and local minimum values, respectively.Periodic functions, such as sine and cosine, show extreme values at infinitely many points due...
Types of Coprecipitation01:10

Types of Coprecipitation

Coprecipitation is the contamination of a precipitate by otherwise soluble species and occurs via different processes. In colloidal precipitates, coprecipitation occurs via surface adsorption. For instance, barium sulfate has a primary layer of adsorbed barium ions and a secondary layer of nitrate counterions. This results in contamination of the precipitate by barium nitrate.
Sometimes, ions in a crystal lattice can undergo isomorphous replacement by inclusions of similar charge and size. For...
Precipitation of Ions03:11

Precipitation of Ions

Predicting Precipitation
The equation that describes the equilibrium between solid calcium carbonate and its solvated ions is:

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Related Experiment Video

Updated: May 10, 2026

Simulating Impacts of Ice Storms on Forest Ecosystems
06:27

Simulating Impacts of Ice Storms on Forest Ecosystems

Published on: June 30, 2020

A HIERARCHICAL MAX-STABLE SPATIAL MODEL FOR EXTREME PRECIPITATION.

Brian J Reich1, Benjamin A Shaby

  • 1Department of Statistics, North Carolina State University, Raleigh, NC 27560 brian_reich@ncsu.edu.

The Annals of Applied Statistics
|June 25, 2013
PubMed
Summary

Researchers developed a new random effects model to analyze extreme spatial dependence in precipitation data. This approach overcomes limitations of existing max-stable processes, enabling Bayesian analyses for climate modeling.

Keywords:
Gaussian extreme value processgeneralized extreme value distributionpositive stable distributionregional climate model

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Simulating Impacts of Ice Storms on Forest Ecosystems
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Watershed Planning within a Quantitative Scenario Analysis Framework
12:44

Watershed Planning within a Quantitative Scenario Analysis Framework

Published on: July 24, 2016

Area of Science:

  • Environmental Science
  • Statistical Modeling
  • Extreme Value Theory

Background:

  • Extreme environmental phenomena, like heavy rainfall, display significant spatial dependence.
  • Max-stable processes are used to model spatial extremes but lack tractable joint likelihoods for complex analyses, hindering Bayesian applications.
  • Existing models struggle to represent spatial dependencies in extreme values across multiple locations.

Purpose of the Study:

  • To propose a novel random effects model for accurately capturing spatial dependence in extreme environmental events.
  • To develop a flexible modeling framework that overcomes the limitations of traditional max-stable processes, particularly for Bayesian inference.
  • To enable robust analysis of spatially dependent extreme precipitation data.

Main Methods:

  • Introduced a new random effects model designed to explicitly account for spatial dependencies.
  • Demonstrated that the proposed model's random effect distribution converges to a max-stable process, including the Gaussian extreme value process (GEVP) as a special case.
  • Applied the developed model to analyze yearly maximum precipitation data from a regional climate model.

Main Results:

  • The proposed random effects model effectively captures spatial dependence in extreme precipitation.
  • The model provides a flexible alternative to existing max-stable processes, allowing for Bayesian analyses.
  • The Gaussian extreme value process (GEVP) is identified as a limiting case of the new model specification.

Conclusions:

  • The novel random effects model offers a powerful and flexible tool for analyzing spatially dependent extreme environmental data.
  • This approach significantly enhances the applicability of extreme value modeling, particularly within Bayesian frameworks.
  • The model facilitates more accurate climate change impact assessments by improving the analysis of extreme precipitation patterns.