Assimilating lightning data into numerical forecast models use of the ensemble kalman filter
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Assimilating Lightning Data Into Numerical Forecast Models: Use of the Ensemble Kalman Filter. Greg Hakim, Cliff Mass, Phil Regulski, Ryan Torn Department of Atmospheric Sciences University of Washington. Vaisala ILMC Meeting Tucson, April 24-25, 2008.

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Assimilating Lightning Data Into Numerical Forecast Models: Use of the Ensemble Kalman Filter

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Assimilating Lightning Data Into Numerical Forecast Models: Use of the Ensemble Kalman Filter

Greg Hakim, Cliff Mass, Phil Regulski, Ryan Torn

Department of Atmospheric Sciences

University of Washington

Vaisala ILMC Meeting

Tucson, April 24-25, 2008

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

  • Earlier studies have generally used fairly primitive assimilation approaches or were completed during earlier periods without the massive amounts of observations that are now available from satellite and aircraft.

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

Poorly Forecast 1993 Superstorm

Lots of lightning during its early developmental stages over the Gulf

Alexander Study: 1993 Superstorm

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

  • Precipitation based on satellite microwave information was also used.

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

500 mb height errors in meters

Assimilation of Pacific Lightning Data into a Mesoscale NWP Model

Antti Pessi, Steven Businger, and Tiziana Cherubini

University of Hawaii

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

Vaisala Thunderstorm Group Inc. Tucson, AZ

Conversion of Lightning Rate to Moisture Profile

  • Determined the relationship between convective rainfall and lightning rate.

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

  • Thus, Lightning rate => rainfall rate => moisture profile

  • Nudged moisture in MM5 model towards the moisture profile



Reducing Forecast Error over the Eastern Pacific


Assimilation of lightning data results in a significantly improved forecast of storm central pressure (December 18-19, 2002).

The Big Questions

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

The Big Questions

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

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

The University of Washington Lightning Assimilation Project

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

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

EnKF Primer

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

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

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

Covariance structures in 3dvar



Data 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 Covariance Matrices







Summary of Ensemble Kalman Filter (EnKF) Algorithm

  • Begin with a large ensemble of forecasts.

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

  • Ensemble analyses with new observations using these covariance structures. Many analyses and uncertainty information.

  • Make short forecasts of all ensemble members until the next observation time.

Mesoscale Example: cov(|V|, qrain)

A nice example: the Puget Sound Convergence Zone

Eastern Pacific Ocean

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

Other studies with similar domain

Pessi/Businger previously studied domain for lightning assimilation

Experiment Design


Control case


Surface stations (ASOS, ship, buoy)


Cloud drift winds (no sat. radiances)

Experimental cases

Control observations


Experiment Design

The WRF Model.

WRF 2.1.2 (Jan 27, 2006)

100 by 86 grid

45-km horizontal resolution

33 vertical levels

270 second timestep

Shortwave: Dudhia

Longwave: Rrtm

Surface: Noah land-sfc

PBL: MYJ TKE scheme

Cumulus: Kain-Fritsch (new Eta)

Experiment Design

EnKF Setup

90 ensemble members

6-hr Analyses

24-hr Forecasts (starting every 12 hours)

8 assimilations period for “spin-up” before lightning assimilations

Square root filter (Whitaker and Hamill, 2002)

Horizontal localization – Gaspari and Cohn 5th order piecewise

Fixed covariance perturbations to lateral boundaries

Zhang covariance inflation method

Localization radius – 2000 km

Experiment Design

Experiment observations exampleACARS observations spatial distribution

Experiment observations exampleCloud track wind observations spatial distribution

Experiment observations exampleRadiosonde, surface station and buoy observations

  • Radiosonde Obs

  • Surface Stations

  • Buoys

Experiment observations exampleLightning Observations

Test Cases

  • Test Case #1

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

  • Test Case #2

    • October 4-8, 2004

  • Test Case #3

    • November 8-12, 2006

Lightning Assimilation Techniques

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

Lightning Assimilation

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

  • We tried thinning and not thinning the lightning observations.

  • We tried assimilating the lightning over various periods.

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

Lightning Assimilation Techniques

  • Non-thinned Lightning Experiment

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

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

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

Lightning Assimilation Techniques

  • Thinned Lightning Experiment

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

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

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

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

Results from the latest experiment

  • Thinned lightning

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

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

  • Comparisons to GFS analysis

    • Although generally the best analysis provided by NCEP, the GFS analysis is certainly imperfect, especially for fine scale features.

Question 1: Is their a significant impact from lightning data?

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

Question 3: Is lightning improving the 12 and 24h forecasts compared to the no-lightning control?

Future Work

  • Evaluation of other approaches to connecting lightning with meteorological variables:

    • One approach would be to connect lightning with graupel, or with some combination of strong vertical motion and cloud ice. Perhaps more general.

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

  • Increasing frequency to 3hr.

  • Weight lining with the lightning detection efficiencies.

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