Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Propagation of Uncertainty from Systematic Error01:10

Propagation of Uncertainty from Systematic Error

893
The atomic mass of an element varies due to the relative ratio of its isotopes. A sample's relative proportion of oxygen isotopes influences its average atomic mass. For instance, if we were to measure the atomic mass of oxygen from a sample, the mass would be a weighted average of the isotopic masses of oxygen in that sample. Since a single sample is not likely to perfectly reflect the true atomic mass of oxygen for all the molecules of oxygen on Earth, the mass we obtain from this...
893
Propagation of Uncertainty from Random Error00:59

Propagation of Uncertainty from Random Error

1.1K
An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...
1.1K
Random Error01:04

Random Error

1.6K
Random or indeterminate errors originate from various uncontrollable variables, such as variations in environmental conditions, instrument imperfections, or the inherent variability of the phenomena being measured. Usually, these errors cannot be predicted, estimated, or characterized because their direction and magnitude often vary in magnitude and direction even during consecutive measurements. As a result, they are difficult to eliminate. However, the aggregate effect of these errors can be...
1.6K
Parametric Survival Analysis: Weibull and Exponential Methods01:14

Parametric Survival Analysis: Weibull and Exponential Methods

624
Parametric survival analysis models survival data by assuming a specific probability distribution for the time until an event occurs. The Weibull and exponential distributions are two of the most commonly used methods in this context, due to their versatility and relatively straightforward application.
Weibull Distribution
The Weibull distribution is a flexible model used in parametric survival analysis. It can handle both increasing and decreasing hazard rates, depending on its shape parameter...
624
Prediction Intervals01:03

Prediction Intervals

2.3K
The interval estimate of any variable is known as the prediction interval. It helps decide if a point estimate is dependable.
However, the point estimate is most likely not the exact value of the population parameter, but close to it. After calculating point estimates, we construct interval estimates, called confidence intervals or prediction intervals. This prediction interval comprises a range of values unlike the point estimate and is a better predictor of the observed sample value, y. 
2.3K
Estimating Population Mean with Unknown Standard Deviation01:22

Estimating Population Mean with Unknown Standard Deviation

8.3K
In practice, we rarely know the population standard deviation. In the past, when the sample size was large, this did not present a problem to statisticians. They used the sample standard deviation s as an estimate for σ and proceeded as before to calculate a confidence interval with close enough results. However, statisticians ran into problems when the sample size was small. A small sample size caused inaccuracies in the confidence interval.
William S. Gosset (1876–1937) of the...
8.3K

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Introduction to the Focus Issue: Nonautonomous dynamics in the climate sciences.

Chaos (Woodbury, N.Y.)·2026
Same author

Introduction to Focus Issue: Nonautonomous dynamical systems: Theory, methods, and applications.

Chaos (Woodbury, N.Y.)·2026
Same author

Topological modes of variability of the wind-driven ocean circulation.

Chaos (Woodbury, N.Y.)·2025
Same author

Bayesian inference for geophysical fluid dynamics using generative models.

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences·2025
Same author

Intraseasonal atmospheric variability under climate trends.

Chaos (Woodbury, N.Y.)·2025
Same author

Exponential stability for a forecast-assimilation process with unstable dynamics.

Chaos (Woodbury, N.Y.)·2025
Same journal

Exact computation of Lyapunov exponents via system parameters in multi-triangle chaotic maps: Bifurcation analysis and circuit realization.

Chaos (Woodbury, N.Y.)·2026
Same journal

Integrating score-based generative modeling and neural ODEs for accurate representation of multiscale chaotic dynamics.

Chaos (Woodbury, N.Y.)·2026
Same journal

A data-driven tuberculosis model with behavioral changes and saturated treatment: Optimal control and cost-effectiveness study.

Chaos (Woodbury, N.Y.)·2026
Same journal

Breathers, rational solutions, and their exact physical spectra in F = 1 spinor Bose-Einstein condensates.

Chaos (Woodbury, N.Y.)·2026
Same journal

Finite invariant sets with bridging points in logistic IFS.

Chaos (Woodbury, N.Y.)·2026
Same journal

Reputation-gated funding sustains cooperation: A spatial production game with selective investment.

Chaos (Woodbury, N.Y.)·2026
See all related articles
  1. Home
  3. Forecast Error Growth: A Dynamic-stochastic Model.
  1. Home
  3. Forecast Error Growth: A Dynamic-stochastic Model.

Related Experiment Video

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
04:35

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Published on: July 3, 2020

3.4K

Forecast error growth: A dynamic-stochastic model.

Eviatar Bach1,2,3, Dan Crisan4, Michael Ghil4,5,6

  • 1Department of Environmental Science and Engineering and Department of Computing and Mathematical Sciences, California Institute of Technology, Pasadena, California 91125, USA.

Chaos (Woodbury, N.Y.)
|July 9, 2025

View abstract on PubMed

Summary
This summary is machine-generated.

This study introduces a new nonlinear stochastic differential equation (SDE) model for forecast error growth in numerical weather prediction (NWP). The model accurately captures both mean and probabilistic error growth features.

More Related Videos

A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data
10:46

A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data

Published on: December 9, 2015

10.8K
Characterization of Complex Systems Using the Design of Experiments Approach: Transient Protein Expression in Tobacco as a Case Study
20:24

Characterization of Complex Systems Using the Design of Experiments Approach: Transient Protein Expression in Tobacco as a Case Study

Published on: January 31, 2014

16.6K

Related Experiment Videos

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
04:35

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Published on: July 3, 2020

3.4K
A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data
10:46

A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data

Published on: December 9, 2015

10.8K
Characterization of Complex Systems Using the Design of Experiments Approach: Transient Protein Expression in Tobacco as a Case Study
20:24

Characterization of Complex Systems Using the Design of Experiments Approach: Transient Protein Expression in Tobacco as a Case Study

Published on: January 31, 2014

16.6K

Area of Science:

  • Atmospheric sciences
  • Meteorology
  • Data science

Background:

  • Numerical weather prediction (NWP) models have historically used simple error growth models.
  • Existing models capture key properties but can be improved with advanced techniques.

Purpose of the Study:

  • To propose a novel dynamic-stochastic scalar model for forecast error growth.
  • To incorporate multiplicative noise within a nonlinear stochastic differential equation (SDE).

Main Methods:

  • Developed a nonlinear stochastic differential equation (SDE) incorporating multiplicative noise.
  • Analyzed the SDE's properties, including error growth curves and stationary distribution.
  • Fitted the model to operational NWP error growth data.

Main Results:

  • The proposed SDE model demonstrates well-posedness and positivity of solutions.
  • The model shows good agreement with both mean and probabilistic aspects of NWP error growth.
  • The model's dynamic-stochastic approach offers a robust framework for error prediction.

Conclusions:

  • The new dynamic-stochastic error growth model provides an accurate representation of NWP error dynamics.
  • This modeling approach has potential applications beyond meteorology in various predictive sciences.