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Data-drivenModeling,PredictionandPredictability:TheComplexSystemsFramework
Surja Sharma,ErinLynchandEugeniaKalnayUniversityofMaryland,CollegePark
V.KrishnamurthyGeorgeMasonUniversity,Fairfax
GSFC AI WorkshopNov. 2018
Nonlinear Dynamics and Complexity Dynamics (Lorenz, 1963)
Deterministic dynamics, ChaosQuantitative resultsWeak connection with data
Structure (Mandelbrot, 1977)Real objects in nature
(Trees, clouds, coastline, etc.)Fractals and Multifractals
Dynamics + StructureSpatio-temporal DynamicsData-driven modeling in Complex Systems Framework
Machine Learnimg / Artificial Intelligence
Reconstruction of Dynamics
“Geometry from a time series”(Packard et al., 1980)
Embedding theorem (Takens, 1981)Time series data: x(t)Time-delay embedding:
xk(ti) = x(ti + (k-1)τ)Reconstructed space:
Xi = {x1(ti), x2(ti), x3(ti), ..}(Broomhead and King, J. Phys. A, 1986)
Actual
Reconstructed
Time series data
Complex Systems Framework:• Low-dimensional (data-driven) modeling• Dynamical prediction (Dynamics)• Predictability analysis (Statistics)
SpaceWeather:PredictionandPredictability
Data-drivenModeling:Phasespacereconstructionofdriver(solarwind)– response(magnetosphere)• Storms(Dst)• Substorms (AL)• Killerelectronflux
FirstPredictions[Sharma,Rev.Geophys.,1995]
EarlycontributionstoAI/MachineLearning
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Solar wind (VBs)
Past data: auroral electrojet index AL
Predicted ALandPredictability
[Ukhorskiy et al., 2002, 2004].
PredictabilityofSpaceWeatherGlobalorCoherentaspectsoftheMagnetosphere
Demonstratedby• Low-dimensionality– reconstructionof
phasespace[Vassiliadis etal.,1990;Sharmaetal.,1993]
• Modeling[Bakeretal.,1990]• Phenomenology[Siscoe,1991]• Phasetransition-likebehaviorfromdata-
drivenmodelingandMHDsimulations
impliesPredictability
Fundamentalcontributionbasedondata-drivenmodeling(AI/MachineLearning)
Similartoearlyresultsondynamicalbehavioroftheatmosphere
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Transition from higher (orange)to lower (green) level.AL index data – observed andfrom global MHD simulations.
ExtremeeventsandEnsembleforecasting
• Data-drivenmodelswithoutgoverningequations
• ForecastsusingEnsembleTransformKalman Filter(ETKF)
• Ensemblespreadasanindicatorofextremeevents
Forecast ensemble
Erin Lynch, Ph. D. thesis (2018)
Data-drivenPredictionofMonsoonPhase space reconstruction model (PSRM).
Rainfall data on 0.25 deg longitude × 0.25 deg latitude grid for 1901-2009(1800 stations)
Climate Forecasting System (CFSv2 )State of the art numerical model (NOAA )
Modeling by Reconstruction using Rainfall and CFSv2 data.
Improvement of predictability
Krishnamurthy and Sharma, Geophys. Res. Lett. (2017)
ComparisonofpredictionsofPSRMandCFSv2
Key results and conclusions:
Intraseasonal oscillations are predictable
Predictability of intraseasonalphenomena such as MJO and midlatude processes
Data-driven modeling provides higher predictability
Modeling and prediction of spatio-temporal structure of space weather
Spatio-temporal Data: Networks of monitoring stations
Krishnamurthy and Sharma, Geophys. Res. Lett., 2017
ComplexSystemsFrameworkØ Data-drivenModelingØ Dynamicalprediction(globalandspatiallyextended)Ø CharacterizationofpredictabilityØ Extremeevents:QuantificationofpredictabilityØ PredictabilityofextremeeventsfromBigDataØ Quantitativemeasureofthelikelihoodofextremespaceweatherevents(data-drivenmodeling)
Ø PredictionofIntraseasonal climate(IndianMonsoon)Ø Applicationsandaframeworkforartificialintelligence, andmachinelearning
Ø Fourthparadigm– Data–enabledscience
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