data-driven predictions of space weather events without a ...€¦ · data-driven model ensemble...

Data-Driven Predictions of Space Weather Events

Without a Model

Erin Lynch

3/5/18 Weather Chaos Group Meeting 1

What is Space Weather?

SunCME

Earth

Carries energetic charged particles and magnetic field from the sun

Solar Wind

Magnetosphere

3/5/18 2Weather Chaos Group Meeting


SunCME

Earth

The Earth’s distorted dipole field interacts with the solar wind to create magnetospheric substorms

Magnetosphere

Solar Wind3/5/18 3Weather Chaos Group Meeting


SunCME

EarthDescribes the interactions that take place between the Solar Wind and the Magnetosphere and Ionosphere of the Earth

Magnetosphere

Solar Wind3/5/18 4

Space Weather

Weather Chaos Group Meeting

Space Weather events are difficult to forecast.


Modeling Challenges

ObservationalChallenges

• Many important scales to model• Model solar wind and magnetosphere • Some processes not well understood

• Lack of observations overall• Long record of AL index and

magnetometer measurements

Take full advantage of the time series observations that are available by combining techniques from nonlinear systems analysis and data assimilation

• Use ensemble data assimilation to improve the forecasts

• Specific applications to the thermosphere-ionosphere system include forecasting the AL index


Can we do data assimilation using time series observations, without knowing the model?

Data-Driven Model

Ensemble Transform Kalman Filter

• Exploit the low dimensional underlying dynamics of the system

• Phase space reconstruction from time series data using embedding technique to yield a dynamical model to make forecasts

Space Weather Time Series

Phase space reconstruction depends on underlying low dimensional dynamics.

3/5/18 Weather Chaos Group Meeting

7

Natural Phase Space Reconstructed Phase Space

AL Index

Time Delay Vectors

Embedding: preserves topology

Index computed from observations

Attractor manifold

Reconstructed attractor

Parameters:• Time delay between

components• Dimension of time

delay vectors

Model Forecasts are made by following the trajectory of points on the attractor.


Reconstructed phase space trajectories

Forecast by following evolution of trajectory

Singular Spectrum Analysis reduces the dimension of the phase space • Identify modes of variability• Keep modes that represent

most of the signal variance• Reject those that

correspond to noise

Ensemble Transform Kalman Filter (ETKF) with a Data-Driven Model

“Model” Forecast

Observations

Analysis

Nearest Neighbors (NN)Use a dense data set of points on the attractor (model) to advance NN analysis ensemble to the end of the analysis window

Observations of a single variable (i.e. the AL index) become multivariate when embedded

Locate nearest neighbors of analysis ensemble members to serve as analogs to make forecasts

Analysis ensemble members computed using the ETKF are the best estimates of the true state, but do not lie on the attractor


Forecasts are made in the state space of the principal components.


And then reconstructed to obtain a forecast of the AL index.


NN ETKF forecasts of the AL Index are more skillful than Persistence

Skill Score


Compare forecasts made using NN ETKF to persistence, i.e. assuming the value will remain the same over the forecast window

20 minute forecasts

40 minute forecasts

60 minute forecasts

SS = 0.60

SS = 0.80

SS = 0.37

Ensemble Spread and Extreme Events

3/5/18 13

No extreme events Extreme event

Figure from Palmer et al. 1999

• The ensemble spread can provide information about extreme events • In stable portions of the attractor, the spread remains relatively consistent in size• In the presence of an instability, the spread increases exponentially

Weather Chaos Group Meeting

AL Index and Ensemble Spread


• Dashed line shows observed value of AL index

• Colored dots located at ensemble mean prediction of the value of the AL index

• Color and size correspond to the ensemble spread

• Ensembles computed using NN ETKF

Summary• We have successfully applied data assimilation to a data-derived

model to produce forecasts of the AL index

• Ensemble forecasts using the ETKF improve predictions of the AL index

• We are able to identify the ensemble spread as an indicator of extreme events and can use as a precursor to predict their onset


References

• Published Manuscript:• E. Lynch, D. Kaufman, A. S. Sharma, E. Kalnay, and K. Ide. Brief

communication: Breeding vectors in the phase space reconstructed from time series data. Nonlin. Processes Geophys., 23: 127-141, 2016

• Manuscript in Preparation:• E. Lynch, K. Ide, A. S. Sharma, and E. Kalnay. Data Driven Time Series

Prediction using Time-Embedding and Ensemble Kalnman Filter Techniqes. 2018• E. Lynch, A. S. Sharma, and E Kalnay. Ensemble Spread as a Precursor for

Extreme Space Weather Events. 2018


data-driven predictions of space weather events without a ...€¦ · data-driven model ensemble...

Documents