,t) γ i. (w o. w m. N Wi(x

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2 tendency terms to prognostic equations based on the difference between model- and observed states. The relationship between lightning rates and rain rates was used to relate lightning rates with moisture profiles. Seven vertical moisture profiles typical for a range of rainfall rates were constructed (Fig. 3). The model predicted vertical moisture profiles were nudged towards moisture values derived from lightning data. The observational nudging method was used, which nudges the model at every observation time and model level. User can define the radius of influence for observations both in the horizontal and vertical, time window of influence, and nudging coefficient G. The nudging equation can be written (Stauffer and Seaman, 1990) p * w t N [ 2 Wi (x j,t) γ i (w o w m ) i ] = F(w, x j,t) + G w p * i=1 N Wi(x j,t ) i=1, (1) where F represents model s all physical forcing terms, G is the nudging coefficient, W is 4-D weighting function which is used to determine G, γ is observational quality factor (between 0 and 1), w 0 locally observed mixing ratio and w m model mixing ratio interpolated to observation location. The model equations are written in flux form, where the prognostic variables for horizontal wind, temperature and mixing ratio are mass weighted by p* (p* = p s - p t where p s is surface pressure and p t is constant pressure at the top of the model). If the nudging coefficient G is increased, the observations have more effect on the model run. However, if G>1/timestep the model becomes numerically unstable. The lightning data were assimilated during the first eight hours of the 24-hour model simulation. The initial conditions were taken from GFS model and GFS boundary conditions were read every six hours. One disadvantage of the moisture-profile method is the strong dependence of the saturation mixing ratio (w s ) on temperature. For example, if the surface temperature on the different sides of a cold front is 0 C and 10 C, w s will range from ~4 to 8 g/kg across the front. w s = w s (T,p) = ε*(e s /(p-e s )), (2) where e s = e s (T) = 6.112*exp(17.67T/(T+243.5)) In Equation 2, w s is the saturation water vapor mixing ratio, e s saturation vapor pressure (Bolton, 1980), p pressure, T temperature and ε=r a /R w =0.622, where R a and R w are specific gas constants of dry air and water vapor, respectively. 2.2 Latent heating assimilation method In a second experiment, lightning data from PacNet were assimilated into MM5 using a latent heating assimilation method (e.g. Manobianco et al., 1994). The method was implemented by modifying the Kain-Fritch convective parameterization scheme and constructing an input data file. The method scales the model's vertical latent heating profiles at each grid point and model level depending on the ratio between model predicted rainfall and rainfall derived from lightning data. Scaling is done only if the observed rain rate (derived from lightning) is greater than model produced rain rate. To prevent excessive latent heating values and model instability, the scaling coefficient was limited to three. As before, if the observed rain rate was zero, no assimilation was done, as the absence of lightning does not imply the absence of rain. If the rain rate derived from lightning observations at any grid point was greater than zero, but the model rain rate was zero, a search algorithm was used. Initially the algorithm searches the adjacent model grid points for similar rainfall rates as those observed. If no matching rain rate is found, further grid points are gradually included in the search until a match is found. The vertical latent heating profile from the matching grid point is used and the levels where the heating rate is positive are saturated.

3 The input file was created by relating lightning rates to rainfall rates. The ratio of lightning to convective rainfall was determined using the method described in section 1. The lightning rates were computed over 1x1 deg. squares centered at each grid point and over 30 min time window centered at each time step. The lightning data were assimilated in the latent heat runs also the first eight hours of the 24 hour model simulation and the boundary conditions were read every six hours. The method reads the input data file and nudges model s tendency equations every model time step (81 s). One advantage of the latent heating method is that just one static lightning-rainfall ratio file is needed, whereas moisture profile method also requires construction of rainfall-moisture profiles before each model run. The method can be made more robust in the future by refining the lightning-rainfall ratio and possibly deriving the relationship empirically for different MM5 domains and for each season or air mass. 3. RESULTS Preliminary results assimilating PacNet sferics data into MM5 are promising (Pessi et al. 2005). Two cases were analyzed using the available long-range lightning data, a squall-line passage over Hawaii and a poorly forecast mid-latitude cyclone that approached the US west coast. 3.1 Tropical Squall-line over Hawaii A subtropical cyclone (kona low) impacted the Islands of Hawaii during the period February 2004, causing heavy rain, thunderstorms, extensive flooding and two storm-related deaths. The MM5 6- hour precipitation forecast without lightning data shows a squall line over Oahu and Molokai (Fig. 4a). Lightning and satellite observations place the rainband ~150 km to the east (Fig. 4b). The forecast location of the squall line in the MM5 simulation with lightning data shows a much better match with observation (Fig. 4c,d). The 06 UTC surface analysis on 28 February placed the 1000 hpa low pressure center 300 km north of Maui. The location of the center does not vary much between the runs, but the surface pressure drops ~2 hpa to the same value as observed using the assimilation techniques. The rainfall amounts are yet to be verified using the Hawaiian rain gauge and radar networks. 3.2 Extratropical storm on the northeast Pacific Beginning on 16 December 2002, an extratropical cyclone produced a large amount of lightning as it moved across the east Pacific Ocean. On December 18, the center of the storm was located near 43 N latitude and 135 W longitude, northeast of Hawaii and west of Oregon. Most of the lightning activity was associated with the cold front (Fig. 5). Preliminary results for both the FDDA and latent heat nudging of MM5 are promising (Fig. 6), with the storm central sea-level pressure tracking much closer to the observations, when lightning data are assimilated. The surface analysis (Fig. 7a) showed 972 hpa storm central pressure whereas the MM5 control forecast (Fig. 7b) was 982 hpa. During the early hours of the control forecast the model does not produce any rain or the rain rates are very small. When we specified diabatic heating sources (latent heating) derived from lightning observations, using the lightning data assimilation method, the model s spin-up time was reduced and the production of rainfall started earlier in the forecast cycle. The intensity of the forecast storm more closely matches the observations in the MM5 simulations that include lightning data (Fig. 8). The storm was almost stationary on 19 December 12 UTC and the storm center location at the surface differ less than 125 km between control-fdda-latent runs. The exact true position is difficult to obtain due to lack of observations, especially at the upper-levels. Fig. 9. shows the difference in sea-level pressure and rainfall between the FDDA and control runs. The biggest pressure differences are found near the storm center and to the east and south of the center. It is interesting to note that practically no lightning was observed north of 45 th latitude during the assimilation period (Fig. 5). However, the FDDA run shows a large addition in rainfall compared to control run between 45 th and 48 th latitude, to the east-northeast of the storm center. Presumably this moisture

4 has advected there from the lightning active areas to the south. The cold front and the cold pool trailing it were also very active electrically, resulting in a substantial increase in precipitation. The storm 500 hpa heights (Fig. 10) are very close together in control and FDDA runs (5220 and 5217 gpm, respectively). Using the latent heat method, the height was lowered to 5196 gpm. The model produces more precipitable water when using latent heat method than the control run and even more when FDDA is used. The storm center location at 500 hpa differs less than 65 km between control-fddalatent runs. 4. CONCLUSIONS Two different methods to assimilate lightning data into MM5 were implemented and tested. All numerical simulations used 27-km grid spacing without nesting. The model solved most of the cold front rain explicitly, with ~33% added by the cumulus parameterization scheme. The moisture profile method used Four-Dimensional Data Assimilation (FDDA) to nudge the model s vertical mixing ratio profiles according to observed lightning rate at each grid point. The latent heating assimilation method scaled the model s convective latent heating rates according to the number of lightning strikes observed around each grid point. Both methods improved the northeast Pacific storm s central pressure forecast and were able to locate a squall line in Hawaii better than the control runs. Quantitative estimation of moisture profiles for FDDA runs is difficult due to uncertainties in lightning-rainfall-moisture relationship. Since mixing ratio is a strongly nonlinear function of temperature, the temperature must be well known when the moisture profiles for the model run are constructed. Therefore, the results using FDDA are especially sensitive to the choice of moisture profiles used. In addition the results are sensitive to the value of the nudging coefficient. Increasing the nudging coefficient G has the same effect as increasing moisture profile values but the model becomes numerically unstable if G 1/ t. The FDDA runs in this experiment proved to be unstable even at smaller nudging coefficients. To address the sensitivity of the moisture profile to surface temperature, the relationship between rainfall and moisture profile could be divided into several temperature categories. Then the relationship would be between rainfall rate at a certain temperature and moisture profile. However, this methodology is difficult to implement as the temperature at each grid point and each time step should be known before the model run begins, at the time when FDDA input file is created. The estimate of the temperature field could be retrieved from previous model forecast, but especially in the case of fast moving frontal systems, there would be uncertainties in the temperature field using this method. Because only ~33% of the rain was produced by the cumulus parameterization scheme, convective latent heating rates were relatively modest, and therefore the latent-heat approach in scaling the cumulus latent heating does not change the overall latent heating greatly. Instead, if the model is dry in areas where lightning is observed, the latent-heating algorithm has more influence. The search function of the latent-heat approach works best when model rainfall rates close to those estimated from lightning rates are found in the vicinity of dry areas exhibiting lightning. Both the methods can be tuned by user chosen options. The FDDA method is relatively stable with several options in the configuration file. The latent heating method can be tuned by modifying the convective parameterization scheme, but the modifications have to be carefully chosen in order to conserve mass balance and keep the model stable. The advantage of the latent heating assimilation method over FDDA is that it requires only an empirically derived lightning-rainfall relationship and lightning observations before each model run and can be made operational relatively easily allowing 8 hours of assimilation in the beginning of the forecast. 5. REFERENCES Alexander, G. David, Weinman, James A., Karyampudi, V. Mohan, Olson, William S., Lee, A. C. L..

5 1999: The Effect of Assimilating Rain Rates Derived from Satellites and Lightning on Forecasts of the 1993 Superstorm. Monthly Weather Review: Vol. 127, No. 7, pp Anthes, R., Ying-Hwa Kuo and John R. Gyakum. 1983: Numerical Simulations of a Case of Explosive Marine Cyclogenesis. Monthly Weather Review: Vol. 111, No. 6, pp Bolton, D., 1980: The computation of equivalent potential temperature. Mon. Wea. Rev., 108, Calheiros, R.V., Zawadzki, I. 1987: Reflectivity-Rain Rate Relationships for Radar Hydrology in Brazil. Journal of Applied Meteorology, 26, Chang, Dong-Eon, Weinman, James A., Morales, Carlos A., Olson, William S. 2001: The Effect of Spaceborne Microwave and Ground-Based Continuous Lightning Measurements on Forecasts of the 1998 Groundhog Day Storm. Monthly Weather Review: Vol. 129, No. 8, pp Manobianco, J., S. Koch, V. M. Karyampudi, and A. J. Negri, 1994: The impact of assimilating satellite-derived precipitation rates on numerical simulations of the ERICA IOP4 cyclone. Mon. Wea. Rev., 122, Papadopoulos, A., T. Chronis and E. N. Anagnostou, 2004: Improving Convective Precipitation Forecasting Through Assimilation of Regional Lightning Measurements in a Mesoscale Model, Monthly Weather Review (in review). Pessi, A., S. Businger, K.L. Cummins, T.Turner, On the Relationship Between Lightning and Convective Rainfall Over the Central Pacific Ocean. Preprints, 18th International Lightning Detection Conference, 7-9 June 2004, Helsinki, Finland. Pessi, A.T., S. Businger, T. Cherubini, K. L. Cummins, and T. Turner, 2005: Toward the assimilation of lightning data over the Pacific Ocean into a mesoscale NWP model. 85 th Annual AMS Meeting held January 2005 in San Diego, CA. Pessi, A., S. Businger, T. Cherubini, Progress in Assimilation of Lightning Data into a Mesoscale NWP Model. 17 th Conference on Numerical Weather Prediction, Washington, D.C., Aug , Amer. Meteor. Soc. Petersen, W.A., and S.A. Rutledge, 1998: On the relationship between cloud-to-ground lightning and convective rainfall. J. Geophys. Res., 103, Stauffer, D. and Nelson L. Seaman. 1990: Use of Four-Dimensional Data Assimilation in a Limited- Area Mesoscale Model. Part I: Experiments with Synoptic-Scale Data. Monthly Weather Review: Vol. 118, No. 6, pp Zipser, E. J.,1994: Deep cumulonimbus cloud systems in the tropics with and without lightning. Mon. Wea. Rev., 122,

6 Fig. 1. Convective rainfall rate over the northeast Pacific storm on 19 December 2002 derived from TRMM s TMI sensor and averaged over 0.5x0.5 degree squares (contours) and lightning strikes over 30 minute time window centered at the satellite overpass time (shaded).

7 Fig. 2. Composite analysis of 15 storms in the central Pacific. Blue line is fitted function R = 2.2L 0.52 where R is rainfall rate and L lightning rate. Moisture profiles Mixing Ratio (kg/kg) No rain 1-3 mm/h 3-6 mm/h >6 mm/h Fig. 3. Four typical MM5 moisture profiles corresponding to four rainfall categories. Data were obtained during a Northwest Pacific storm on 19 December 2002.

8 Fig. 4 a) MM5 6-hr forecast without lightning data of precipitation (shading) and sea-level pressure (contours) valid at 0600 UTC on 28 February b) Lightning strikes observed UTC. c) MM5 6-hr forecast with lightning data using FDDA and d) latent heat method

9 Fig. 5 (a) Satellite image at 1800 UTC on 18 December 2002 and (b) 0300 UTC December 19 (right) and c) 1200 UTC December 19. ILRN Lightning detected between ~15-18 UTC, UTC and UTC December (left, right, bottom, respectively). Red dots indicate lightning during the last hour and yellow dots during the previous two hours

10 Sea-Level Pressure Dec FDDA CTRL OBS LAT Time Fig. 6. Comparison of observed storm central pressure (yellow) with that predicted by MM5 on 19 December 2002 with (white and blue) and without (purple) lightning data (Pessi et al. 2005). Fig. 7 Surface analysis (left) and twelve-hour forecast of sea-level pressure and 3-hr accumulated rainfall (right) over the eastern North Pacific Ocean valid at 1200 UTC on 19 December 2002

11 Fig 8. As in Fig. 7, but with lightning data using latent heating method (left) and FDDA (right). Fig. 9. The difference in sea-level pressure and rainfall between the FDDA and control runs.

12 Fig hpa height (gpm) and vertically integrated precipitable water (cm). a) Control run b) FDDA and c) latent heat method