Assimilating Lightning Assimilating Lightning Data Into Numerical Data Into Numerical

Forecast Models: Use of Forecast Models: Use of the Ensemble Kalman the Ensemble Kalman

FilterFilterGreg Hakim, Cliff Mass, Phil Regulski, Ryan Greg Hakim, Cliff Mass, Phil Regulski, Ryan

TornTorn

Department of Atmospheric SciencesDepartment of Atmospheric Sciences

University of WashingtonUniversity of Washington

Vaisala ILMC MeetingTucson, April 24-25, 2008

Use of Lightning Data in Numerical Use of Lightning Data in Numerical Weather Prediction (NWP): Previous Weather Prediction (NWP): Previous

StudiesStudies Earlier studies have generally used fairly Earlier studies have generally used fairly

primitive assimilation approaches or were primitive assimilation approaches or were completed during earlier periods without completed during earlier periods without the massive amounts of observations that the massive amounts of observations that are now available from satellite and are now available from satellite and aircraft.aircraft.

Several of these studies have noted Several of these studies have noted substantial forecast improvements using substantial forecast improvements using lightning data.lightning data.

Poorly Forecast 1993 Poorly Forecast 1993 SuperstormSuperstorm

Lots of lightning during its early developmental stages over the Gulf

Alexander Study: 1993 Alexander Study: 1993 SuperstormSuperstorm

A relationship between lightning flash rate A relationship between lightning flash rate and convective precipitation was used to and convective precipitation was used to alter the latent heating rate in the MM5 alter the latent heating rate in the MM5 during a spin-up period.during a spin-up period.

Precipitation based on satellite microwave Precipitation based on satellite microwave information was also used.information was also used.

The model was then run in forecast mode, The model was then run in forecast mode, improving predictions when satellite and improving predictions when satellite and lightning data were used.lightning data were used.

500 mb height errors in meters

Assimilation of Pacific Lightning Data Assimilation of Pacific Lightning Data into a Mesoscale NWP Modelinto a Mesoscale NWP Model

Antti Pessi, Antti Pessi, Steven BusingerSteven Businger, and Tiziana Cherubini, and Tiziana Cherubini

University of HawaiiUniversity of Hawaii

K. Cummins, N. Demetriades, and T. TurnerK. Cummins, N. Demetriades, and T. Turner

Vaisala Thunderstorm Group Inc. Tucson, AZVaisala Thunderstorm Group Inc. Tucson, AZ

Conversion of Lightning Rate to Conversion of Lightning Rate to Moisture ProfileMoisture Profile

Determined the relationship between convective rainfall and Determined the relationship between convective rainfall and lightning rate.lightning rate.

Determined the relationship of rainfall with the moisture profile using Determined the relationship of rainfall with the moisture profile using MM5 data. MM5 data.

Thus, Lightning rate Thus, Lightning rate =>=> rainfall rate rainfall rate ==> moisture profile> moisture profile Nudged moisture in MM5 model towards the moisture profileNudged moisture in MM5 model towards the moisture profile

Moisture profiles

0

5

10

15

20

25

30

35

40

0 0.002 0.004 0.006 0.008

Mixing Ratio (kg/kg)

Sigma Level

No rain

1-3 mm/h

3-6 mm/h

>6 mm/h

972972

L 983L 972

Reducing Forecast Error Reducing Forecast Error over the Eastern Pacificover the Eastern PacificAssimilation of lightning data results in a Assimilation of lightning data results in a significantly improved forecast of storm significantly improved forecast of storm central pressure (December 18-19, 2002).central pressure (December 18-19, 2002).

The Big QuestionsThe Big Questions

What is the potential What is the potential impact of lightning, impact of lightning, particularly over the particularly over the oceans, now that there oceans, now that there are massive amounts of are massive amounts of satellite information satellite information from cloud and moisture from cloud and moisture track winds, as well as track winds, as well as increasing number of increasing number of satellite vertical satellite vertical soundings and soundings and scatterometer winds. scatterometer winds. Plus, increasing aircraft Plus, increasing aircraft observations.observations.

The Big QuestionsThe Big Questions

Does lightning data provide Does lightning data provide information content and information content and potential forecast potential forecast improvements that are not improvements that are not available from conventional and available from conventional and satellite assets?satellite assets?

What is the impact of new data What is the impact of new data assimilation approaches that assimilation approaches that allow better use of conventional allow better use of conventional and non-conventional data? and non-conventional data? Will this allow a more effective Will this allow a more effective use of lightning data? Or will it use of lightning data? Or will it make lightning data redundant make lightning data redundant with other data sources?with other data sources?

The University of The University of Washington Lightning Washington Lightning

Assimilation ProjectAssimilation Project The UW has has been working for several The UW has has been working for several

years, both in research and operational years, both in research and operational modes, with a new type of data assimilation modes, with a new type of data assimilation that has a number of potential advantages that has a number of potential advantages over more traditional types of data over more traditional types of data assimilation, such as nudging and 3D-VAR.assimilation, such as nudging and 3D-VAR.

Known as the Known as the Ensemble Kalman Filter (EnKF)Ensemble Kalman Filter (EnKF), , this approach is this approach is essentiallyessentially probabilistic and probabilistic and makes use of the modeling system as a central makes use of the modeling system as a central component of the data assimilation process.component of the data assimilation process.

EnKF PrimerEnKF Primer

Modern data assimilation systems combine the Modern data assimilation systems combine the background (or model first guess) fields and background (or model first guess) fields and observations to produce an optimal analysis.observations to produce an optimal analysis.

A key element of such data assimilation systems A key element of such data assimilation systems is the is the background error covariance matrixbackground error covariance matrix, which , which spreads errors in the background fields both spreads errors in the background fields both spatially and among other parameters. spatially and among other parameters.

Current data assimilation approaches, such a 3D-Current data assimilation approaches, such a 3D-Var spread the errors using simplified structures Var spread the errors using simplified structures and functions that are not necessarily realistic.and functions that are not necessarily realistic.

Covariance structures in Covariance structures in 3dvar3dvar

Cov(Z500,Z500) Cov(Z500,U500)

Data AssimilationData Assimilation

•Data assimilation should be probabilistic, providing uncertainty information regarding the analyses and the forecasts derived from them.

•Data assimilation should also spread information among parameters, say using a precipitation (or lightning) observation to update other parameters such as wind or temperature.

•Ensemble-based data assimilation and particularly the Ensemble Kalman filter offers a way to do this.

•Makes use of an ensemble of forecasts to produce state-dependent error covariance structures, uncertainty information for analyses and forecasts, and allows the spread of information among parameters.

State-dependent State-dependent Covariance MatricesCovariance Matrices

EnKF“3DVAR”

Cov(Z500,Z500)

Cov(Z500,U500)

“3DVAR”EnKF

Summary of Summary of EnsembleEnsemble Kalman Filter (Kalman Filter (EnKFEnKF) )

AlgorithmAlgorithm(1)(1) Begin with a large ensemble of forecasts.Begin with a large ensemble of forecasts.

(2)(2) Ensemble Ensemble forecastforecast provides background provides background error covariance statistics (B) for new error covariance statistics (B) for new analyses. (How to spread errors)analyses. (How to spread errors)

(3)(3) Ensemble Ensemble analysesanalyses with new observations with new observations using these covariance structures. Many using these covariance structures. Many analyses and uncertainty information.analyses and uncertainty information.

(4)(4) Make short forecasts of all ensemble Make short forecasts of all ensemble members until the next observation time.members until the next observation time.

Mesoscale Example: cov(|Mesoscale Example: cov(|V|, qV|, qrainrain))

A nice example: the Puget Sound Convergence Zone

Experiment DesignExperiment Design Eastern Pacific OceanEastern Pacific Ocean

Relatively low observation Relatively low observation density; location of important density; location of important storm tracks; errors propagate storm tracks; errors propagate downstream to mainland United downstream to mainland United StatesStates

Other studies with similar domainOther studies with similar domain Pessi/Businger previously Pessi/Businger previously

studied domain for lightning studied domain for lightning assimilationassimilation

Experiment DesignExperiment DesignObservationsObservations

Control case Control case RadiosondesRadiosondes Surface stations (ASOS, ship, Surface stations (ASOS, ship,

buoy)buoy) ACARSACARS Cloud drift winds (no sat. Cloud drift winds (no sat.

radiances)radiances)

Experimental casesExperimental cases Control observationsControl observations LightningLightning

Experiment DesignExperiment DesignThe WRF Model. The WRF Model.

WRF 2.1.2 (Jan 27, 2006)WRF 2.1.2 (Jan 27, 2006) 100 by 86 grid100 by 86 grid 45-km horizontal resolution45-km horizontal resolution 33 vertical levels33 vertical levels 270 second timestep270 second timestep Shortwave: DudhiaShortwave: Dudhia Longwave: RrtmLongwave: Rrtm Surface: Noah land-sfc Surface: Noah land-sfc PBL: MYJ TKE schemePBL: MYJ TKE scheme Cumulus: Kain-Fritsch (new Eta)Cumulus: Kain-Fritsch (new Eta)

Experiment DesignExperiment DesignEnKF SetupEnKF Setup

90 ensemble members90 ensemble members 6-hr Analyses6-hr Analyses 24-hr Forecasts (starting every 12 24-hr Forecasts (starting every 12

hours)hours) 8 assimilations period for “spin-up” 8 assimilations period for “spin-up”

before lightning assimilationsbefore lightning assimilations Square root filter (Whitaker and Square root filter (Whitaker and

Hamill, 2002)Hamill, 2002) Horizontal localization – Gaspari and Horizontal localization – Gaspari and

Cohn 5th order piecewiseCohn 5th order piecewise Fixed covariance perturbations to Fixed covariance perturbations to

lateral boundarieslateral boundaries Zhang covariance inflation methodZhang covariance inflation method Localization radius – 2000 kmLocalization radius – 2000 km

Experiment observations exampleExperiment observations exampleACARS observations spatial distributionACARS observations spatial distribution

Experiment observations exampleExperiment observations exampleCloud track wind observations spatial distributionCloud track wind observations spatial distribution

Experiment observations exampleExperiment observations exampleRadiosonde, surface station and buoy observationsRadiosonde, surface station and buoy observations

•Radiosonde Obs

•Surface Stations

•Buoys

Experiment observations exampleExperiment observations exampleLightning ObservationsLightning Observations

Test CasesTest Cases Test Case #1Test Case #1

December 16-21, 2002 (already considered by Businger December 16-21, 2002 (already considered by Businger and Pessi)and Pessi)

Test Case #2Test Case #2 October 4-8, 2004October 4-8, 2004

Test Case #3Test Case #3 November 8-12, 2006November 8-12, 2006

Lightning Assimilation Lightning Assimilation TechniquesTechniques

Converted the density of lighting observations into convective rainfall using the Pessi/Businger Lightning rate/Convective Pessi/Businger Lightning rate/Convective

rainfall rate relationshiprainfall rate relationship

Lightning AssimilationLightning Assimilation

Then the convective rainfall was assimilated Then the convective rainfall was assimilated using the ensemble-based covariances to using the ensemble-based covariances to influence a wide variety of parameters.influence a wide variety of parameters.

We tried thinning and not thinning the We tried thinning and not thinning the lightning observations.lightning observations.

We tried assimilating the lightning over We tried assimilating the lightning over various periods.various periods.

We verified both the quality of the analyses We verified both the quality of the analyses and forecasts.and forecasts.

Lightning Assimilation Lightning Assimilation TechniquesTechniques

Non-thinned Lightning ExperimentNon-thinned Lightning Experiment

Lightning strike observations are converted into 30 minute Lightning strike observations are converted into 30 minute lightning density rate from nearby LTNG observations. lightning density rate from nearby LTNG observations.

Lightning rate converted into “observation” of convective Lightning rate converted into “observation” of convective rainfall rate using Pessi/Businger convective rain rainfall rate using Pessi/Businger convective rain rate/lightning rate relationshiprate/lightning rate relationship

Convective rainfall (mm) is assimilated into WRF-EnKFConvective rainfall (mm) is assimilated into WRF-EnKF

Lightning Assimilation Lightning Assimilation TechniquesTechniques

Thinned Lightning ExperimentThinned Lightning Experiment Same as the previous experiment except that any lightning Same as the previous experiment except that any lightning

strikes used in the density calculation are no longer allowed strikes used in the density calculation are no longer allowed to be an assimilation point, resulting in a thinning out of the to be an assimilation point, resulting in a thinning out of the lightning “observations” (although strikes will be used to lightning “observations” (although strikes will be used to calculate nearby densities)calculate nearby densities)

One hour and six hour lightning assimilation One hour and six hour lightning assimilation experiments. In all cases we calculate the lightning-experiments. In all cases we calculate the lightning-based convective rainfall using lighting plus or based convective rainfall using lighting plus or minus one hour from the nominal observing time.minus one hour from the nominal observing time.

One hour-compared that rate to the one hour convective rainfall One hour-compared that rate to the one hour convective rainfall in model.in model.

Six hour-scaled it to 6 hr and compared to six hour precipitation Six hour-scaled it to 6 hr and compared to six hour precipitation in model.in model.

Results from the latest Results from the latest experimentexperiment

Thinned lightningThinned lightning

1-hr precipitation assimilation (which should be 1-hr precipitation assimilation (which should be more realistic)more realistic)

Realistic error variance for lightning Realistic error variance for lightning precipitation retrieval (5 mm)precipitation retrieval (5 mm)

Comparisons to GFS analysis Comparisons to GFS analysis Although generally the best analysis provided by Although generally the best analysis provided by

NCEP, the GFS analysis is certainly imperfect, NCEP, the GFS analysis is certainly imperfect, especially for fine scale features.especially for fine scale features.

Question 1: Is their a Question 1: Is their a significant impact from significant impact from

lightning data?lightning data?

Question 2: Is lightning Question 2: Is lightning improving the analysis improving the analysis compared to the no-compared to the no-

lightning control?lightning control?

Question 3: Is lightning Question 3: Is lightning improving the 12 and 24h improving the 12 and 24h

forecasts compared to forecasts compared to the no-lightning control?the no-lightning control?

Future WorkFuture Work

Evaluation of other approaches to connecting Evaluation of other approaches to connecting lightning with meteorological variables:lightning with meteorological variables: One approach would be to connect lightning with One approach would be to connect lightning with

graupel, or with some combination of strong vertical graupel, or with some combination of strong vertical motion and cloud ice. Perhaps more general.motion and cloud ice. Perhaps more general.

Improvements in the WRF EnKF, including Improvements in the WRF EnKF, including experiments with varying EnKF settings (localization experiments with varying EnKF settings (localization ratios, etc).ratios, etc).

Increasing frequency to 3hr.Increasing frequency to 3hr.

Weight lining with the lightning detection Weight lining with the lightning detection efficiencies.efficiencies.