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    Grid points and terrain (m) for the simulations.

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    The 0235 UTC rain rates inferred from the microwave brightness temperatures (mm h−1) and the 0300 UTC surface frontal analysis from Kocin et al. (1995). The lowest surface pressure was 981 mb. No measurements were available from the white area in this and subsequent images.

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    SSM/I rain rates and tie points at 0305 UTC and 1525 UTC 12 Mar and 0235 UTC 13 Mar.

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    Morphing and standard interpolation were applied to rain-rate fields derived from two IR brightness temperature images (1230 UTC 12 Mar and 1530 UTC 12 Mar) to estimate the rain-rate field for 1400 UTC 12 Mar. These estimates are compared to rain-rate fields derived from the observed brightness temperatures at 1400 UTC 12 Mar. Differences (estimated minus observed) are shown for (a) morphed and (b) interpolated rain-rate fields. Contour interval is 1 mm h−1, with solid (dashed) contours indicating positive (negative) errors. Zero contour is omitted.

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    The rain rates computed from the SSM/I technique at 0305 UTC, 0930 UTC, 1525 UTC, and 2130 UTC 12 Mar, and 0235 UTC 13 Mar.

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    Infrared brightness temperatures at 0330 UTC 12 Mar, 1530 UTC 12 Mar, and 0330 UTC 13 Mar.

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    Infrared brightness temperatures vs SSM/I rain rates at 0305 UTC 12 Mar, 1525 UTC 12 Mar, and 0235 UTC 13 Mar.

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    Infrared rain rates computed from the histogram-matching technique at 0305 UTC and 1525 UTC 12 Mar and at 0235 UTC 13 Mar.

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    The rain rates computed from the SSM/I–IR technique at 0305 UTC, 0930 UTC, 1525 UTC, and 2130 UTC 12 Mar, and 0235 UTC 13 Mar.

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    Flashes observed by the NLDN in the 60-min periods surrounding 0305 UTC 12 Mar, 1525 UTC 12 Mar, and 0235 UTC 13 Mar.

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    Flashes observed by the NLDN (right) and UKMO (left) networks in the 60-min period surrounding 0235 UTC 13 Mar. Note the cutoff south of 24°N lat.

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    Flash rates observed by the NLDN and UKMO networks between 0000 UTC 12 Mar and 0300 UTC 13 Mar.

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    The convective fractions derived from SSM/I measurements at 0305 UTC 12 Mar, 1525 UTC 13 Mar, and 0235 UTC 13 Mar.

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    The convective rain rates derived from SSM/I measurements at 0305 UTC 12 Mar, 1525 UTC 13 Mar, and 0235 UTC 13 Mar.

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    The rain rates computed from the SSM/I–IR–lightning technique at 0305 UTC, 0930 UTC, 1525 UTC, and 2130 UTC 12 Mar, and 0235 UTC 13 Mar.

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    Total rain assimilated into the model for the three techniques between 0000 UTC 12 Mar and 0250 UTC 13 Mar.

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    Accumulated rain for the three techniques and from the rain gauge network for 0000–0600 UTC 12 Mar.

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    The convective rain rate (mm h−1) computed in the four simulations at 0600 UTC 12 Mar.

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    As in Fig. 18 except at 1200 UTC 12 Mar.

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    The 500-mb geopotential error (m) at 1200 UTC 13 Mar for the four simulations.

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    The 500-mb geopotential error (m) at 0000 UTC 14 Mar for the four simulations.

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    Minimum sea level pressure of Superstorm for 0000 UTC 12 Mar through 14 Mar from the mesoanalyses of Kocin et al. (1995) and from the MM5 simulations.

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    Location of the minimum sea level pressure for Superstorm for 0000 UTC 12 Mar through 14 Mar from the mesoanalyses of Kocin et al. (1995) and from the MM5 simulations.

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    Precipitation field at 0900 UTC 13 Mar from the WSR-57 radar network and from the MM5 simulations. Simulated rain rates less than 0.5 mm h−1 are not shown.

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    As in Fig. 24 except at 1200 UTC 13 Mar.

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    Tracks and positions (UTC/day; Mar 1993) of PV anomalies A, C, and D, denoted by dashed, dotted, and long dash–dotted lines, respectively. Solid line denotes the track of Superstorm, with the “L” locating the cyclone position every 12 h. Adapted from Dickinson et al. (1997).

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    Difference fields (forecast minus observed) of θT (solid/dashed for positive/negative differences, every 8 K), potential temperature advection [heavy solid line every (20 K) (12 h)−1], and pT (dotted line every 25 mb) at 1200 UTC 13 Mar.

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The Effect of Assimilating Rain Rates Derived from Satellites and Lightning on Forecasts of the 1993 Superstorm

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  • 1 Universities Space Research Association, and Microwave Sensors Branch, NASA/Goddard Space Flight Center, Greenbelt, Maryland
  • | 2 Microwave Sensors Branch, NASA/Goddard Space Flight Center, Greenbelt, Maryland
  • | 3 Science Systems and Applications, Inc., Mesoscale Atmospheric Processes Branch, NASA/Goddard Space Flight Center, Greenbelt, Maryland
  • | 4 Caelum Research Corporation, and Mesoscale Atmospheric Processes Branch, NASA/Goddard Space Flight Center, Greenbelt, Maryland
  • | 5 Remote Sensing Instruments Branch, U.K. Meteorological Office, Farnborough, Hants, United Kingdom
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Abstract

Inadequate specification of divergence and moisture in the initial conditions of numerical models results in the well-documented “spinup” problem. Observational studies indicate that latent heat release can be a key ingredient in the intensification of extratropical cyclones. As a result, the assimilation of rain rates during the early stages of a numerical simulation results in improved forecasts of the intensity and precipitation patterns associated with extratropical cyclones. It is challenging, however, particularly over data-sparse regions, to obtain complete and reliable estimates of instantaneous rain rate. Here, a technique is described in which data from a variety of sources—passive microwave sensors, infrared sensors, and lightning flash observations—along with a classic image processing technique (digital image morphing) are combined to yield a continuous time series of rain rates, which may then be assimilated into a mesoscale model. The technique is tested on simulations of the notorious 1993 Superstorm. In this case, a fortuitous confluence of several factors—rapid cyclogenesis over an oceanic region, the occurrence of this cyclogenesis at a time inconveniently placed in between Special Sensor Microwave/Imager overpasses, intense lightning during this time, and a poor forecast in the control simulation—leads to a dramatic improvement in forecasts of precipitation patterns, sea level pressure fields, and geopotential height fields when information from all of the sources is combined to determine the rain rates. Lightning data, in particular, has a greater positive impact on the forecasts than the other data sources.

Corresponding author address: James A. Weinman, NASA/Goddard Space Flight Center, Code 975, Greenbelt, MD 20771.

Email: weinman@sensor.gsfc.nasa.gov

Abstract

Inadequate specification of divergence and moisture in the initial conditions of numerical models results in the well-documented “spinup” problem. Observational studies indicate that latent heat release can be a key ingredient in the intensification of extratropical cyclones. As a result, the assimilation of rain rates during the early stages of a numerical simulation results in improved forecasts of the intensity and precipitation patterns associated with extratropical cyclones. It is challenging, however, particularly over data-sparse regions, to obtain complete and reliable estimates of instantaneous rain rate. Here, a technique is described in which data from a variety of sources—passive microwave sensors, infrared sensors, and lightning flash observations—along with a classic image processing technique (digital image morphing) are combined to yield a continuous time series of rain rates, which may then be assimilated into a mesoscale model. The technique is tested on simulations of the notorious 1993 Superstorm. In this case, a fortuitous confluence of several factors—rapid cyclogenesis over an oceanic region, the occurrence of this cyclogenesis at a time inconveniently placed in between Special Sensor Microwave/Imager overpasses, intense lightning during this time, and a poor forecast in the control simulation—leads to a dramatic improvement in forecasts of precipitation patterns, sea level pressure fields, and geopotential height fields when information from all of the sources is combined to determine the rain rates. Lightning data, in particular, has a greater positive impact on the forecasts than the other data sources.

Corresponding author address: James A. Weinman, NASA/Goddard Space Flight Center, Code 975, Greenbelt, MD 20771.

Email: weinman@sensor.gsfc.nasa.gov

1. Introduction

Inadequate specification of divergence and moisture in the initial conditions of numerical models result in a well-known “spinup” problem (e.g., Davidson and Puri 1992). Observational studies indicate that latent heat release can be a key ingredient in the intensification of extratropical cyclones (e.g., Uccellini 1991; Petty and Miller 1995). As a result, the assimilation of rain rates in early stages of a numerical simulation results in improved forecasts of the intensity and precipitation patterns associated with extratropical cyclones (e.g., Manobianco et al. 1994; Jones and Macpherson 1997). It is challenging, however, particularly over data-sparse regions, to obtain continuous and accurate estimates of instantaneous rain rate. Here, we describe a technique through which data from a variety of sources—passive microwave sensors, infrared sensors, and lightning flash observations—along with a classic image processing technique (digital image morphing) may be combined to yield a continuous time series of rain rates, which may then be assimilated into a mesoscale model and result in an improved forecast.

Remote observations of rain rates may be derived from numerous sources, including infrared (IR) brightness temperatures (Adler and Negri 1988), microwave brightness temperatures (Negri et al. 1995), radar reflectivity (Burgess and Ray 1986), and cloud-to-ground lightning flashes (Petty 1995; Petersen and Rutledge 1998; Chèze and Sauvageot 1997). Each of these sources of rain rates has its advantages and disadvantages. For example, rain rates derived from IR brightness temperature sensors aboard geostationary satellites have excellent temporal coverage, but suffer from contamination from cirrus clouds and other drawbacks, which depend on factors including geography, season, latitude, and environment (Adler and Negri 1988). Moreover, there is often a time lag between peak convective rain rates and peak IR-derived rain rates. Microwave-derived rain rates are generally considered to be more accurate than infrared-derived rain rates (e.g., Ferraro 1997), but because the Special Sensor Microwave/Imager (SSM/I) sensors are placed on low earth orbiting Defense Meteorological Satellite Program (DMSP) satellites, their temporal and spatial coverage is limited. Rain rates derived from radar reflectivity depend upon assumptions made about the hydrometeor field and microphysical processes, and coverage is generally available only over developed land areas. A proportionality between convective rain rates and lightning flash rates was reported by Workman and Reynolds (1949) and numerous subsequent investigators. Although Petersen and Rutledge (1998) showed that the proportionality can vary by orders of magnitude between differing climatic regimes, it appears to be stable over several hours within any given storm system. Thus lightning data, tuned with appropriate microwave measurements, can provide continuous estimates of convective rainfall between SSM/I overpasses.

If one is able to assemble a reasonably accurate time series of rain rates, the assimilation of these rain rates into forecast models can result in improved forecasts. For example, Karyampudi et al. (1998) demonstrated the positive impact of assimilation of rain rates on forecasts of Hurricane Florence. In their study, the synthesized SSM/I–Geostationary Operational Environmental Satellite IR (GOES-IR) technique described by Manobianco et al. (1994) was employed to derive the spatial fields of rain rate. In the Manobianco et al study, they assimilated SSM/I and IR rain rates into simulations of a rapidly intensifying Atlantic cyclone and improved forecasts of the central mean sea level pressure, frontal positions, and low-level vertical-motion patterns.

With ground-based lightning detection systems now becoming more common, it is possible to continuously obtain large-scale estimates of lightning activity. This new source of data represents a fertile source of information for testing theories on using lightning as a proxy for convective variables and for model data assimilation purposes. It is the purpose of this paper to demonstrate one case in which a fortuitous confluence of several factors—rapid intensification of a major extratropical cyclone over an oceanic region during a time of heavy thunderstorm activity—allowed the assimilation of rain rates determined from SSM/I, IR, and lightning data to improve mesoscale model forecasts. This paper is organized as follows. In section 2, we describe the details of the the case study of the March 1993 “Superstorm” and the model that we used to simulate it—the Pennsylvania State University–National Center for Atmospheric Research Mesoscale Model version 5 (PSU–NCAR MM5). In section 3, we describe the morphing technique used to interpolate rain rate and integrated water vapor (IWV) distributions between satellite overpasses. These morphed data are fed into the model during the rainfall assimilation simulations. Section 4 presents the techniques used to assimilate specific humidity profiles in all of the rainfall assimilation simulations. Section 5 describes the algorithms used to derive rain-rate distributions and the methods of rain-rate interpolation that we have tested, including SSM/I only, combined IR and SSM/I, and combined lightning, SSM/I, and IR. Section 6 describes the rain-rate assimilation methodology. In section 7, the results of the various model simulations are analyzed and the impact of the different rain-rate retrievals on the forecasts is examined. Finally, our results are summarized in section 8.

2. Simulation

a. Model description

The mesoscale model used for the simulations described here is the nonhydrostatic version of version 1 of the MM5. All of the simulations are run in the nonhydrostatic mode with explicit treatment of cloud water, rainwater, snow, and ice (see Dudhia 1993). Unresolved convection is represented by the Kain–Fritsch (1990) cumulus parameterization scheme. The Blackadar high-resolution planetary boundary layer model, which includes surface fluxes of sensible heat, latent heat, and momentum, is used (Zhang and Anthes 1982). Davies relaxation boundary conditions (Davies and Turner 1977) are used for the lateral boundary conditions, which are time and inflow/outflow dependent. At the model top, a radiative boundary condition is used, allowing wave energy to pass through unreflected (see Klemp and Durran 1983; Bougeault 1983). The atmospheric radiation scheme in the PSU–NCAR MM5 accounts for the interaction of longwave and shortwave radiation with the atmosphere including cloud and precipitation fields as well as with the surface (see Dudhia 1989). The radiative tendencies are updated every 15 min.

The initial conditions are provided by the National Meteorological Center’s [NMC, now known as the National Centers for Environmental Prediction (NCEP)] gridded (2.5° × 2.5°) analysis (available on 13 mandatory levels), which were interpolated to the MM5 mesh using a 16-point, two-dimensional parabolic function. In each simulation, the horizontal grid spacing is 40 km (120 × 100 grid points), with 23 vertical levels. The horizontal domains, horizontal grid points, and model topography for each simulation are depicted in Fig. 1. The resolution of the vertical levels is highest in the planetary boundary layer and decreases above there, with the middles of the vertical layers located at σ = 0.025, 0.075, 0.125, 0.175, 0.225, 0.275, 0.325, 0.375, 0.425, 0.475, 0.525, 0.575, 0.625, 0.675, 0.725, 0.775, 0.825, 0.87, 0.91, 0.945, 0.97, 0.985, and 0.995. The model uses a time-splitting technique in which terms involved with sound waves are separated from terms that vary more slowly. The model’s long time step is 60 s.

b. Case study

The test case that we have chosen for the MM5 simulations described here is the 12–14 March 1993 Superstorm, which brought an unusually widespread area of severe weather to central and eastern North America, setting all-time records of snowfall amounts and low surface pressure at many cities along the East Coast. The National Oceanic and Atmospheric Administration (NOAA 1994) estimated that some 200 deaths and $1.6 billion in property loss were caused by the snowfall and flooding associated with this storm. The operational forecasts for the storm failed to predict its rapid intensification over the Gulf of Mexico and as a result it has since been analyzed by researchers such as Forbes et al. (1993), Kocin et al. (1995), and Dickinson et al. (1997). One conclusion from those analyses was that insufficient data were available during the incipient phase of its development. The present study attempts to overcome this limitation by assimilating improved latent heating rates dervied from spaceborne and lightning-derived rainfall measurements to more accurately derive the precipitation associated with this storm. Our simulations were initialized at 0000 UTC 12 March, when the storm was nothing more than a ripple of low pressure in northern Mexico. The simulations were integrated forward 48 h to 0000 UTC 14 March when the NMC analysis indicated that Superstorm’s minimum sea level pressure was 960 mb.

One of the SSM/I orbits passed directly over the full-fledged Superstorm at approximately 0235 UTC 13 March 1993 over the central Gulf of Mexico. The precipitation field, derived using the retrieval algorithm of Kummerow et al. (1996) and Olson et al. (1996), indicates an elongated squall line several hundred miles ahead of the observed low pressure center and trailing surface cold front (Fig. 2). The frontal mesoanalysis of Kocin et al. (1995) indicates three fronts—a leading cold front, a trailing cold front, and a warm/stationary front. The squall line is located well ahead of both cold fronts. The control simulation of the MM5 failed to simulate this observed squall line. Simulations attempted with both the Kuo (1974) and Grell (1993) convective parameterizations also failed to simulate this prefrontal squall line. As discussed in Kocin et al. (1995), rapid intensification of the storm between 1200 UTC 12 March and 0000 UTC 13 March was accompanied by a large outbreak of convection near the cyclone. Kocin et al. argued that the advection of cold air over the Gulf at midlevels may have supported the development of the convection by reducing the static stability. They also suggested that the latent heating from this convection may have contributed to the strengthening of the downstream 500-mb jet over the mid-Atlantic states, resulting in a rapid deepening of the cyclone in a fashion similar to that described for other cyclones (e.g., Chang et al. 1982; Uccellini 1991). Thus, we hypothesize that because the MM5 failed to simulate this convection near the center of the storm, the simulated cyclone failed to deepen nearly as much as was observed. For example, the control simulation generates a minimum central pressure of only 985 mb at 1200 UTC 13 March, compared to 971 mb in the 1200 UTC 13 March NMC analysis. There is also a significant displacement error, with the cyclone forecast approximately 180 km to the south-southwest of its observed location. The analysis of Dickinson et al. (1997) suggested that the early intensification of the storm occurred over the Gulf of Mexico where critically needed conventional meteorological measurements were unavailable. There was, however, evidence from lightning observations that convection was intensifying during this formative period. To improve our forecast, we employed the rain-rate assimilation technique of Karyampudi et al. (1998) during the first portion of our forecast. This technique requires a continuous time series of rain-rate fields to be fed into the model.

3. Data morphing

Microwave data from SSM/I were measured only at approximately 12-h intervals and IR imagery from GOES was mainly available at 3-h intervals from archived data. The MM5 model runs in this study assimilated rainfall and IWV derived from these sources at every model time step. Those quantities were therefore morphed from the directly retrieved quantities to fill the gaps at intervening time steps. This technique used the image warping technique described by Alexander et al. (1998) in which a source image is transformed into a target image. We briefly recap the highlights of that technique and describe how it is augmented to seamlessly morph one image into another. For the purposes of illustration we use SSM/I data to describe the method. We then demonstrate how morphing differs from simple interpolaton with an illustration of rainfall derived from GOES-IR imagery.

For Superstorm, there were overpasses by the DMSP F-10 satellite at 0305 and 1525 UTC 12 March and by the DMSP F-11 at 0235 13 March. Figure 3 shows the rain-rate distributions retrieved at those times. Each SSM/I product image is morphed into the subsequent SSM/I product image (a linear evolution of features is assumed). Thus, two pairs of rain rate and IWV images are morphed. For the first pair, the 0305 UTC 12 March image is the source image and the 1525 UTC 12 March image is the target image. For the second pair, the 1525 UTC 12 March image is the source image and the 0235 UTC 13 March image is the target image.

For each pair of images, before the morphing is carried out, the rain-rate fields are interpolated to the MM5 mesh, and K paired tie points connecting similar features of the source and target images are selected manually. The morphing is performed by a coordinate transformation in which the coordinates of a pixel, (x, y) at time t, were mapped to a new location (x′, y′) at time t′ by a third-order polynomial coordinate transformation. While third-order morphing requires that at least 10 tie-point pairs be chosen, we employ 36 tie points for each image. Thus, the warped coordinate transformation, with coefficients (ai,j, bi,j) fitted the target image in a least squares sense that satisfies
i1520-0493-127-7-1433-e1
where the polynomial coefficients ai,j and bi,j are chosen to minimize the mean-square error between the set of 36 target tie points (xk, yk) and the corresponding polynomial estimates for the source tie points (xk, yk). The SSM/I tie points used in this study are shown in Fig. 3.
The output image is formed by mapping each individual rectangular region in the input image, composed of four neighboring pixels, through the transform and onto the output plane in the form of a polygon. The polygon is filled onto the output plane using scan-line bilinear interpolation. Any deformation of the rain-rate distribution implies that the mass density must be scaled to conserve moisture in each warped MM5 grid box. That is,
i1520-0493-127-7-1433-e2
where the mass density in the transformed coordinates is scaled by the Jacobian of the transformation described in (1):
i1520-0493-127-7-1433-e3

This scaling simply accounts for the change in the area covered by a grid box caused by the grid morphing process.

The procedure described above yields polynomial weighting coefficients ai,j and bi,j, which define the warped coordinate system (x′, y′). The warped coordinates fit only the measured data at t′ in the least squares sense, while the data at t were actually measured. To keep the errors at t and t′ consistent, the morphing algorithm was applied twice to each pair of images. The image Mt(x, y) is first morphed forward to Mt(x′, y′). The “forward” morphed coordinates [xf(t"), yf(t")] at each time step are linearly interpolated between the original coordinate system and the final warped coordinate system:
i1520-0493-127-7-1433-e4
where Mt1 at t = t1 (0300 UTC 12 March) was warped forward to the image Mt2 at t′ = t2 (1525 UTC 12 March).

The “backward” coordinates [xb(t"), yb(t")] were interpolated similarly, except that the coordinates were now warped backward in time from t = t2 to t′ = t1.

The final morphed coordinates are just the mean of the forward and backward coordinates:
i1520-0493-127-7-1433-e6

The magnitudes of the IWV and rain rates are interpolated between the Mt1 and Mt2 in the same manner as the coordinates in (4)–(7).

This process was repeated for the second pair of microwave images: Mt2 at t = t2 (1525 UTC 12 March) was warped forward to the Mt3 image at t′ = t3 (0235 UTC 13 March) and then Mt3 was warped backward in time from t = t3 to Mt2 at (t′ = t2) as for the previous image pair.

Because the distinguishing features of the rain-rate images and the IWV images correspond to one another, the same tie points that were used for the rain-rate morphing were also used to morph the IWV fields. After the morphing is completed, we have a continuous time series of both IWV and rain rate over the ocean during the assimilation period. This procedure assumes that the rain rate and IWV fields propagate at a constant velocity and that the magnitudes of those quantities vary monotonically with time between the SSM/I overpasses.

To compare the morphing procedure described here with standard interpolation as described in Manobianco et al. (1994), we have applied both techniques to a pair of IR-derived rain-rate images (1230 UTC 12 March and 1530 UTC 12 March) to obtain estimated rain-rate fields at the time halfway in between (1400 UTC 12 March). Then, we compared the rain rates derived using each procedure with the rain rates derived from the observed IR brightness temperatures at 1400 UTC 12 March. The differences between the estimated and observed fields (estimated minus observed) are shown in Fig. 4. The interpolated field is blurred over the combined area of the initial and final fields, whereas the morphed field is advected eastward and retains a more compact shape. Although the magnitudes of the errors for the two techniques are comparable at 2 mm h−1, the areal extent of the morphed errors is smaller.

4. Retrieval and nudging of IWV

a. IWV retrieval

The SSM/I microwave radiometer provides brightness temperatures at 19.3, 37.0, and 85.5 GHz, all of which are measured with horizontal and vertical polarization (see Hollinger et al. 1990). Different combinations of the brightness temperatures, TBν,p (where ν is the frequency in GHz and p is the horizontal or vertical polarization), can be used to compute both the IWV and rain rate. All of the rainfall-derived heating rate experiments utilized specific humidity profiles derived from the SSM/I IWV retrievals and MM5 model output. The IWV retrievals have been shown to be acceptable, with errors of about 10% when compared to radiosonde measurements (e.g., Alishouse et al. 1990). Numerous statistical and physical–statistical algorithms are available to retrieve IWV from microwave brightness temperatures. Algorithms used to retrieve IWV depend primarily on the 22.2-GHz brightness temperatures (Schluessel and Emory 1990), as that frequency is near the center of a weak water vapor absorption line. Brightness temperatures at other SSM/I channels are used in IWV retrieval algorithms to reduce the error by accounting for varying surface wind speeds or liquid water content (Deblonde et al. 1995). Retrievals of IWV were implemented only over water because the higher emissivity of land compared to ocean renders such retrievals difficult.

Values of IWV were determined at the SSM/I overpasses using the algorithm of Alishouse et al. (1990),
19υ37υ22υ22υ
which was modified by Colton and Poe (1994) using a cubic correction of the IWV in the low- and high-IWV regimes:
23

b. IWV nudging

The morphed IWV fields obtained over the Gulf of Mexico were assimilated into the model using the Newtonian nudging technique of Kuo et al. (1993) based on the work of Stauffer and Seaman (1990). Here, we apply analysis nudging, in which model fields are nudged toward gridpoint analyses of observations. In analysis nudging, for a given variable α, the model’s prognostic equation is written as
i1520-0493-127-7-1433-e10
where F includes the normal model forcing terms, αobs is the gridpoint analysis toward which the model is being nudged, G is the nudging coefficient, and p* is defined at pspt, where ps is the surface pressure and pt is the pressure at the model top. We choose G to be 3 × 10−4 s−1, following Kuo et al. (1993). For each simulation, the nudging is applied continuously during the rain assimilation period (0000 UTC 12 March–0235 UTC 13 March).
IWV is a two-dimensional variable, so Eq. (12) cannot be used for nudging toward observations of IWV. However, Kuo et al. (1993) described a technique through which a three-dimensional field of specific humidity may be derived from the IWV observations. First, the observed IWV (IWVobs) is computed by applying Eqs. (10) and (11) to the observed brightness temperature fields. Then, one can compute the model saturation IWV using
i1520-0493-127-7-1433-e11
where g is gravitational acceleration, and qsat(k) is the model saturation specific humidity at each of the model’s KP σ levels. If IWVobs > IWVsat, then the “observed” specific humidity qobs(k) is set to the model saturation specific humidity qsat(k). Otherwise the following iteration procedure is performed:
  • use the model humidity field qm(k) as the first guess of the observed specific humidity q(1)obs(k);

  • calculate the quantity IWV(n)obs,
    i1520-0493-127-7-1433-e12
    initially n = 1,
  • if |(IWVobs/IWV(n)obs) − 1| < 0.01, q(n)obs(k) is the observed specific humidity qobs(k) and the iteration ends; otherwise,

  • calculate
    i1520-0493-127-7-1433-e13
  • set q(n+1)obs(k) = qsat(k) at level k where q(n+1)obs(k) > qsat(k), and go back to (b).

This procedure typically converges with just a few iterations.

5. Rain-rate retrievals

a. Overview

To assess the impact of including progressively larger amounts of information in our rain-rate estimates, we have determined the rain-rate fields using three different techniques. In the first technique, rain-rate data from only the SSM/I are used. Because SSM/I rain rates were available only approximately every 12 h, intermediate rain rates are determined using the image morphing technique described in section 3. In the second technique, rain rates inferred from IR brightness temperatures are combined with the SSM/I rain-rate fields. In the final technique, rain rates inferred from two ground-based lightning detection networks are included along with rain rates derived from the other two sources (SSM/I, IR). The three techniques are described individually below.

b. SSM/I

Maps of SSM/I rain rates used in all three techniques were determined from the microwave brightness temperature fields using the algorithm of Olson et al. (1996) and Kummerow et al. (1996). In their technique, three-dimensional cloud-resolving simulations from the Goddard cumulus ensemble model were used as input to radiative computations of upwelling microwave brightness temperatures at selected microwave sensor frequencies. The cloud/radiative calculations formed the basis of a Bayesian precipitation profile retrieval method that yielded estimates of the expected values of the rain rates. These rainfall retrieval techniques were validated against ground-based radars in Darwin, Australia, by Kummerow et al. (1996). They found a bias of the order of 30% and a correlation coefficient of the order of 0.8. Those values are representative of several spaceborne retrievals (see Barrett et al. 1994) and appear to be sufficient for this study.

The SSM/I microwave brightness temperatures were measured during the overpasses on 0305 and 1525 UTC 12 March and on 0235 UTC 13 March. The first experiment to continuously assimilate rainfall data utilized the morphing technique described in section 3 to generate rainfall distributions at 1-min intervals. Figure 5 shows the rain-rate distributions from the original SSM/I data and two examples of distributions at the intermediate times 0930 UTC and 2130 UTC 12 March. One can see by inspection that the morphed images contain some of the obvious shape characteristics of the images derived from the actual SSM/I data. This technique assumes that the rainfall distribution evolves monotonically with time, a condition that was not met with this storm.

c. SSM/I–IR

The technique described above used only data from the SSM/I observations. Because no information was available at intermediate times, we were forced to assume a constant evolution of features between SSM/I overpasses. Temporal resolution of the SSM/I data can be improved by employing rain rates inferred from infrared brightness temperatures. GOES-IR brightness temperature images were obtained every 3 h, from 0030 UTC 12 March until 0330 UTC 13 March, and were interpolated to the model grid points. To convert infrared brightness temperatures to rain rates, IR images at 0330 UTC 12 March, 1530 UTC 12 March, and 0230 UTC 13 March (Fig. 6) were matched to the SSM/I rain-rate images at 0305 UTC 12 March, 1525 UTC 12 March, and 0235 UTC 13 March, respectively. Then, the technique described in Manobianco et al. (1994) was used to calibrate the threshold IR brightness temperatures based on the SSM/I rain-rate estimates. The technique is briefly recapped here.

  1. Determine the area (i.e., total number of pixels) in the 0330 UTC 12 March SSM/I rain-rate image where the rain rates are greater than or equal to 1 mm h−1.

  2. Within this area, generate cumulative sums of the number of SSM/I pixels greater than discrete (integer) precipitation rates and generate cumulative sums of the number of IR pixels colder than discrete (integer) IR brightness temperatures.

  3. For each whole number SSM/I-derived precipitation rate from 1 mm h−1 to the maximum rate, choose a threshold brightness temperature from the IR data such that the sum of pixels at or below that brightness temperature most closely matches the cumulative pixel count from the SSM/I data.

  4. Repeat steps 1–3 for the other two SSM/I–IR image pairs.

Because three SSM/I–IR pairs are compared, there will be three different temperature–rain-rate relationships—these are shown in Fig. 7. For intermediate IR brightness temperature images, the relationships are interpolated accordingly. For example, at 0330 UTC 12 March, a 215-K IR brightness temperature corresponds to a 10 mm h−1 rain rate while at 1530 UTC 12 March a 215-K IR brightness temperature corresponds to a 16 mm h−1 rain rate. Thus, for the 0930 UTC 12 March image, a 215-K brightness temperature would be assigned a rain rate of 13 mm h−1.

Such variations are consistent with the results of other derivations of rain rates from combined microwave and IR data. C. Kidd (1997, personal communication) noted that the rainfall retrieved in this manner had a correlation coefficient on the order of 0.5 with respect to rainfall from the Tropical Ocean Global Atmosphere Coupled Ocean–Atmosphere Response Experiment radar and a bias factor of 2. It was not clear, however, whether the radar or the microwave-IR rainfall retrieval introduced the greatest errors.

The technique described above gives us IR rain-rate maps every 3 h between 0030 UTC 12 March and 0230 UTC 13 March. Figure 8 shows the rain rates given by applying this histogram-matching technique to brightness temperatures at 0330 UTC 12 March, 1530 UTC 12 March, and 0330 UTC 13 March. Comparing rainfall distributions obtained from GOES-IR with those from SSM/I shows that the IR retrieval distributes rain rates of less than 10 mm h−1 over a larger area than the microwave retrieval.

Although the GOES images can be obtained at half-hour intervals in real time over the United States, geostationary satellite images are available only at 3-h intervals over many parts of the world. Moreover, the cost of retrieving more frequent geostationary IR imagery from archives is not insignificant. In view of these considerations, morphing was applied to nine IR image pairs (0030 12 March/0330 12 March, 0330 12 March/0630 12 March, 0630 12 March/0930 12 March, 0930 12 March/1230 12 March, 1230 12 March/1530 12 March, 1530 12 March/1830 12 March, 1830 12 March/2130 12 March, 2130 12 March/0230 13 March). Again, as for the SSM/I morphing, 36 paired tie points are chosen for each morphing pair (not shown). The validity of this procedure was described section 3.

The SSM/I and IR rain rates obtained as described above are blended together using the method of Manobianco et al. (1994). At times close to the SSM/I overpasses, the rain-rate estimates are heavily weighted toward the SSM/I estimates, whereas at other times, the IR estimates become increasingly predominant. Thus, the SSM/I and IR rain rates are computed separately at each model time step and then combined according to
w1w2
where w1 varies linearly from 0 to 1 back to 0 in the 4-h period surrounding each SSM/I overpass, and w2 = 1 − w1. Figure 9 shows the rain-rate fields obtained using the SSM/I–IR technique at the times of the SSM/I overpasses and at two intermediate times.

d. SSM/I–IR–lightning

The final technique for creating observed rain-rate fields at every model time step exploits the strengths of the techniques described above as well as the correlation between convective rain rates and lightning flashes. During the assimilation period, observations from two ground-based lightning detection networks showed Superstorm to be extremely electrically active during its developing phases. The two networks are briefly described below.

The National Lightning Detection Network (NLDN) is a commercial network operated by Global Atmospheres, Inc. that consists of about 105 stations that monitor cloud-to-ground lightning strokes across the contiguous United States (e.g., Cummins et al. 1998). The remote antennas are connected to a central processor that records the time, polarity, signal strength, and number of strokes of each cloud-to-ground lightning flash. A combination of arrival-time difference and magnetic direction finding technology is used to locate the flash. Depending on the location within the network, the location accuracy is 2–4 km, with a detection probability between 80% and 90%. The flash time is accurate to within 2 ms. Spatial coverage is from approximately 24°N to 53°N and from 60°W to 130°W. Figure 10 shows the flashes observed by the NLDN in 60-min periods encompassing the three SSM/I overpasses of Superstorm. Note in Fig. 10 that because no data are given south of 24°N, the flashes documented by the NLDN stop abruptly at that latitude.

Observations from a lightning detection network operated by the United Kingdom Meteorological Office (UKMO) (see Lee 1986) showed that the squall line extended farther south. We therefore employed those data to extend the range of coverage. The UKMO system consists of a network of seven receivers dispersed over the United Kingdom and the Mediterranean. A given lightning stroke produces sferic wave forms, which are detected through their vertical electric field between 8.1 and 11.7 kHZ at the seven receivers. Each outstation stores all of the data that it observes above an analog threshold, and forwards selected data to the control station. The service area covered by the UKMO system ranges between 30°N to 70°N and 40°W to 40°E, with location accuracy of 2–20 km (Lee 1989). However, the sources of sferics can be located from regions well outside this area out to ranges of several thousand kilometers with a resolution of 200 km × 200 km. The UKMO system detects mainly cloud-to-ground strokes. It is estimated that the UKMO system detects about one-quarter of all strokes; the limitations were caused by computer processing speeds and the communications links between the outstations and the control station. Figure 11 shows the flashes observed by the UKMO network in a 1-h period surrounding the 0235 UTC 13 March SSM/I overpass in comparison to the flashes observed by the NLDN during the same period. Because the UKMO receivers are located much farther from the Gulf of Mexico than the NLDN receivers, the total number of flashes observed by the UKMO network is much less than the total number observed by the NLDN (Fig. 12).

There is no universal relationship between lightning flash density and rainfall—in fact, this ratio can vary by as much as three orders of magnitude or more between different climatic regimes, and can vary by as much as an order of magnitude for any given location (e.g., Zipser 1994; Petersen and Rutledge 1998). In particular, the relationship between lightning and rainfall is very sensitive to whether the storms are occurring over land or ocean. Price and Rind (1992) note that because marine convective clouds have updrafts about a factor of 5 less intense than equivalent-sized clouds over land, they have a much lower lightning rate, even though the precipitation rate may be roughly the same. However, over a particular climatic regime and a limited geographic region, lightning is well correlated to convective rainfall (e.g., Zipser 1994). Here, we take advantage of this correlation in order to estimate convective rain rates at times between the SSM/I overpasses.

The retrieved rain rates at the SSM/I overpasses were partitioned into convective rain rates and stratiform rain rates, again using the algorithm of Olson et al. (1996) and Kummerow et al. (1996). Figure 13, for example, shows the convective fraction at each of the three SSM/I overpasses, and Fig. 14 shows the resulting convective rain rates. The convective rain per flash relationship is then determined for each SSM/I overpass as follows:

  1. Determine the convective rain flux for each overpass. To do this, we assume that the rain rate detected at the time of the overpass is representative of a 60-min period flanking the time of the overpass.

  2. Count the number of lightning flashes or sferics in a 60-min period flanking the time of the overpass. For the 0235 UTC 13 March overpass, lightning flashes were detected by both detection networks—the number of flashes from each network is counted separately.

  3. For each overpass, divide the total convective rain flux by the number of flashes or sferics to obtain the convective rain flux for each lightning event—again, at 0235 UTC 13 March, there is a separate relationship for each detection network.

  4. To convert the convective flux per flash or sferic relationship to convective rain rate per flash or sferic, assume that the convective rain rate persists for 30 min (a typical lifetime for a convective cell).

The convective rain rate per flash relationship for the NLDN is determined by averaging this relationship at all three overpasses. For the UKMO network, only one overpass is used to determine the relationship, since it detected no lightning at the other overpasses. For Superstorm, the technique described above yielded a relationship of 1.05 mm h−1 per flash for NLDN and 32.99 mm h−1 per sferic for the UKMO network.

Once the convective rain rate per flash or sferic is determined, a time series of convective rain rate may be constructed between 0000 UTC 12 March and 0250 UTC 13 March. To compute the total rain rate, this convective rain rate is then added to the stratiform rain rate, which is determined by multiplying the morphed stratiform fraction fields (the Fig. 3 tie points are used) by the SSM/I–IR rain-rate fields. Figure 15 shows the rain-rate maps given by the combined SSM/I–IR–lightning technique at the times of the SSM/I overpasses and two intermediate times.

e. Comparison of techniques

Figure 16 shows the total rain assimilated into the MM5 using each of the three rain assimilation techniques (SSM/I only, combined SSM/I–IR, combined SSM/I–IR–lightning). Note that when lightning is used to derive rain rates, the first peak in total rain rate occurs approximately 6 h earlier than for either IR or combined SSM/I–IR. For SSM/I only, this maximum does not appear at all, of course, because of the linear evolution of the fields, which is assumed. This difference appears, for example, in the rain-rate maps in Fig. 5, Fig. 9, and Fig. 15 for 0930 UTC 12 March. At this time, the NLDN indicates that frequent lightning is occurring in areas ranging from the south Texas coastline to several hundred kilometers offshore, implying the existence of convective precipitation, which was not picked up by either the SSM/I or SSM/I–IR techniques. Thus, when lightning data are used to determine convective rain rates, additional areas of heavy precipitation are included over the western Gulf of Mexico.

A natural question to ask is whether the rain rates implied by the lightning data are reasonable. One way of testing this is to compare the rain rates computed by the three different techniques to rain rates observed over land areas by the rain gauge network at times when copious lightning is occurring over land. Here, in order to facilitate the comparison, we have smoothed the estimates of precipitation from the SSM/I, SSM/I–IR, and SSM/I–IR–lightning techniques from their original 40 km × 40 km grid to match the average spacing of the rain gauge network. Figure 17 shows this comparison for the first 6 h of the rain assimilation period, between 0000 UTC and 0600 UTC 12 March, where the accumulated rain from the three techniques is compared to the rain gauge observations. Comparing the four panels, it is evident that the SSM/I and SSM/I–IR techniques underestimate the accumulated precipitation and the SSM/I–IR–lightning technique appears to provide the best representation of the the observed precipitation. The SSM/I–IR–lightning technique provides the best match to the rain gauge observations, although the precipitation amounts appear to be slightly overestimated in the region of the two precipitation maxima. These errors are attributable to uncertainty in (a) the exact relationship between convective rainfall and flash rate and (b) the exact proportion of the rainfall that is convective.

6. Rain-rate assimilation method

The continuously generated rainfall distribution obtained from the method described in section 5 was assimilated into the MM5 using the scheme of Karyampudi et al. (1998). That method was adapted from the scheme described by Manobianco et al. (1994), which was used to simulate the evolution of a rapidly developing extratropical cyclone that occurred during the Experiment on Rapidly Intensifying Cyclones over the Atlantic. The Karyampudi scheme considers three regimes. The first regime includes areas in which both satellite (Ps) and model-predicted (Pm) rainfall rates are greater than zero. The second regime includes areas where Ps = 0 but Pm > 0. The third regime includes areas where Ps > 0 but Pm = 0. In regime 1, the scheme scales the MM5-predicted latent heating by a factor α = (PsPm)/Pm. However, if Ps > 2Pm in region 1, the rainfall predicted by the MM5 is assumed to be unreliable, and hence a parabolic heating profile (with a midlevel heating maximum at 500 mb) typical of cloud clusters containing a combination of convective and stratiform precipitation (Frank and McBride 1989) is specified. In regime 2, the model-predicted latent heating is not allowed. In regime 3, a parabolic heating profile equivalent to that described above is imposed. The primary difference between the Manobianco et al. (1994) scheme and the Karyampudi et al. (1998) scheme is that instead of specifying a parabolic profile in region 3, the former scheme searched from a model-predicted heating profile corresponding to ±20% of the satellite rainfall within a 320-km radius.

The rain rates computed using the three techniques—SSM/I, SSM/I–IR, and SSM/I–IR–lightning—were assimilated into the MM5 for approximately 26 h, between 0000 UTC 12 March and 0235 UTC 13 March. The simulations were then allowed to run until 0000 UTC 14 March. In the following section, the results of the three simulations are compared to a control simulation in which no rain assimilation or IWV assimilation was performed.

7. Results and discussion

a. Overview

As we show in the following subsections, while all of the simulations in which the Karyampudi et al. (1998) rain assimilation and Kuo et al. (1993) IWV assimilation are used perform better than the control simulation, the improvement is most dramatic in the simulation in which lightning data are used as a proxy for convective rain rates during the assimilation period. As discussed in section 5e and shown in Fig. 16, the abundance of lightning between 0000 UTC and 1200 UTC 12 March resulted in a significantly greater amount of rain being assimilated in the SSM/I–IR–lightning assimilation during this time, contemporaneous with the observed rapid deepening of Superstorm. To demonstrate the difference in the behavior of the simulations during this time, we show in Figs. 18 and 19 the simulated convective rain rates at 0600 UTC and 1200 UTC 12 March, respectively. While there is essentially no difference between the control simulation, the SSM/I assimilation simulation, and the SSM/I–IR assimilation simulation, at both times the SSM/I–IR–lightning simulation is generating convective precipitation over a larger region. The difference is particularly notable at 1200 UTC, when the SSM/I–IR–lightning simulation is generating heavy precipitation in the region in the Gulf of Mexico directly south of Louisiana—just to the north and east of the cyclone center. In the following subsections, we discuss the impact of these differences in convective precipitation early in the simulation on later forecasts of geopotential height, sea level pressure, and precipitation.

b. 500-mb geopotential height

Figure 20 shows the 500-mb geopotential height errors for the four simulations at 1200 UTC 13 March, where the NMC analysis is used as the benchmark. All of the simulations forecast the geopotential height to be too high over the southeastern United States, particularly over south Georgia. However, the errors are reduced significantly when rain assimilation is used, and in fact become progressively smaller as one increases the amount of information used to piece together the time series of rain rates. Over the geographic region depicted in Fig. 20, the 500-mb geopotential root-mean-square error (rmse) is reduced by 54%, from 63.9 m to 29.6 m, in the SSM/I–IR–lightning simulation compared to the control simulation. Over the entire domain shown in Fig. 1, the rmse is reduced by 41%, from 28.9 m to 17.0 m.

Figure 21 shows the 500-mb geopotential height errors for the four simulations at 0000 UTC 14 March. The behavior of the error fields is similar to that at 1200 UTC 13 March, except now the maximum errors appear over the Delmarva Peninsula region. Over the geographic region depicted in Fig. 21, the rmse in the SSM/I–IR–lightning simulation is reduced by 59% compared to the control simulation, from 65.3 m to 26.9 m. Over the entire domain shown in Fig. 1, the rmse is reduced by 60%, from 64.4 m to 26.0 m.

c. Sea level pressure

The sea level pressure error for the four simulations at 1200 UTC 13 March, where the NMC analysis has been used as the benchmark, are also improved in all of the simulations (not shown). As for the 500-mb geopotential errors, the errors are largest for the control simulation and decrease as one progresses through the other simulations. The forecast sea level pressure is much too high over the Carolinas and north Georgia and is somewhat low over the northeast Gulf of Mexico. Over the geographic region depicted in Fig. 20, the rmse in the SSM/I–IR–lightning simulation is reduced by 67%, from 6.73 mb to 2.19 mb compared to the control simulation. Over the entire domain shown in Fig. 1, the rmse is reduced by 32%, from 3.74 mb to 2.16 mb.

Figure 22 shows the forecast minimum sea level pressure for Superstorm between 0000 UTC 12 March and 0000 14 March for the four simulations as well as the observed minimum pressure given by the mesoanalyses of Kocin et al. (1995). The control forecast performs the most poorly, with errors in minimum pressure of 14 mb at 1200 UTC 13 March and 8 mb at 0000 UTC 14 March. The SSM/I and SSM/I–IR assimilation simulations perform somewhat better than the control, generally improving minimum sea level pressure forecasts by a few mb at most times. However, only the SSM/I–IR–lightning assimilation simulation does a credible job reproducing Superstorm’s observed minimum pressure, with errors of less than 2 mb in the final 12 h of the simulation.

Figure 23 shows the forecast location of Superstorm’s center between 1800 UTC 12 March and 0000 UTC 14 March for the four simulations compared to the observed locations given by the mesoanalyses of Kocin et al. (1995). Until 1800 UTC 13 March, all of the simulations except the SSM/I–IR–lightning simulation trail the observed location of the cyclone center by several hundred kilometers. By 0000 UTC 14 March, there are relatively small displacement errors for all four of the simulations.

d. Precipitation

Above, we have shown that the forecast fields of geopotential height and sea level pressure are much improved in the SSM/I–IR–lightning simulation compared to all of the other simulations. Here, we show that this is also the case for the forecast precipitation fields. The primary deficiency of the control simulation was its failure to simulate the intense squall line, which formed in the Gulf of Mexico ahead of the main cold front at approximately 0000 UTC 13 March. Over the next 12 h, this squall line was observed to propagate across Florida and into the western Atlantic Ocean. The use of rain-rate assimilation enabled the simulations to simulate this squall line. Furthermore, as the amount of information included in the rain-rate estimates was increased, the forecasts of the squall line progressively improved.

Figure 24 shows the forecast rain-rate fields for the SSM/I, SSM/I–IR, and SSM/I–IR–lightning simulations at 0900 UTC 13 March compared to the rain rates derived from the 0930 UTC 13 March radar summary [the reflectivity is converted to rain rates using the default WSR-88D algorithm described in Woodley et al. (1975)]. The control simulation failed to simulate a squall line and is not shown. Note that this time is approximately 6 h after all rain assimilation has ended. The SSM/I assimilation simulation begins to reveal the observed squall line near the Florida peninsula, although the organization is scattered and some convection is placed too far to the west. As IR rain rates are added to the SSM/I rain rates during the assimilation period, the simulated squall line shows better linear organization. Finally, as information from lightning data is added to the assimilated rain rates, the model not only forecasts a well-organized squall line, but the orientation of the squall line is forecast more accurately as well.

Figure 25 shows the forecast rain-rate fields for the SSM/I, SSM/I–IR, and SSM/I–IR–lightning simulations at 1200 UTC 13 March compared to the rain rates derived from the 1230 UTC 13 March radar summary. Comparison to radar observations becomes more difficult here, as a portion of the squall line has moved out of radar range. However, the SSM/I–IR–lightning simulation is the only simulation in which all of the strong convection clears Florida, as shown by the radar observations. All of the simulations still do not correctly forecast the convection observed by radar just off the Outer Banks.

e. Discussion

In the results shown above, we wish to stress the following point: In the control simulation, the simulation in which precipitation inferred from SSM/I-derived rain rates was assimilated into the model, and the simulation in which precipitation inferred from a combination of SSM/I and IR-derived rain rates was assimilated into the model, the model did not replicate either (a) the observed rapid intensification of Superstorm over the Gulf of Mexico or (b) the existence and structure of the squall line, which developed over the Gulf and raced across Florida in the following hours. The only simulation that replicated (a) and (b) was the simulation in which the rain rates inferred from lightning data were included in the assimilated precipitation. The inclusion of rain rates derived from lightning data was the only difference between the successful simulation and the other two assimilation simulations. Here, we will address the following question: Why did only the SSM/I–IR–lightning assimilation simulation work?

Bosart et al. (1996) and Dickinson et al. (1997) discussed the synoptic factors underlying Superstorm’s cyclogenesis (Fig. 26). Prior to cyclogenesis, two potential vorticity (PV) anomalies are present in the subtropical jet stream. These anomalies (C and D) can be tracked as they cross the west coast of North America on 10 March. The stronger anomaly, D, dives southeastward toward Texas where it dissipates by 0000 UTC 12 March. The weaker anomaly, C, drops southeastward to a location near Las Cruces, New Mexico, by 0000 UTC 12 March. As Bosart et al. note, cyclogenesis is triggered just off the coast of Texas between 0000 and 1200 UTC 12 March as anomaly C tracks over northern Mexico toward Corpus Christi, Texas. Concurrent with anomaly C’s arrival in the western Gulf, lower values of potential temperature at the dynamic tropopause (θT) are advected over the same area. Meanwhile, lower levels are being increasingly warmed and moistened by a persistent southeasterly flow over the western Gulf of Mexico. As a result, the difference between (θT) and the 850-mb equivalent potential temperature (θe) becomes more and more negative, indicating ripening conditions for deep convection. Finally, explosive cyclogenesis occurs as another PV anomaly (A), located in the northern branch of westerlies, skirts just north of the activity in the Gulf and begins to interact with PV anomaly C by 0000 UTC 13 March. The intensification of the cyclone is associated with a tightening gradient of θT in a band stretching from the Ozarks to Lake Erie after 1200 UTC 12 March as well as a tightening gradient of pressure at the dynamic tropopause (pT) downstream of PV anomalies A and C (see Fig. 3 of Dickinson et al. 1997). As Dickinson et al. explain, the poleward bulge in the isentropes between 0000 and 1200 UTC 12 March cannot be explained by quasi-horizontal advective processes alone, but instead it must be associated with the release of latent heat associated with deep convection. The advection patterns of θT and pT are associated with a “compaction” of PV anomaly C beginning at 1200 UTC 12 March, an important harbinger of cyclogenesis (Lackmann et al. 1997).

Dickinson et al. (1997) suggested that the inability of the National Centers for Environmental Prediction (NCEP) Medium-Range Forecast model to capture the observed rate of cyclogenesis was a result of the model not properly simulating the bulk effects of cumulus convection of the troposphere. In our simulations, we have already seen the differences in the convective precipitation rates forecast between 0000 and 1200 UTC 12 March. Only in the SSM/I–IR–lightning simulation does convection occur to the extent indicated by the NLDN observations. Thus, we have hypothesized that the inability of all but one of our model simulations (the one in which rain rates inferred from lightning were included) to properly forecast the rapid intensification of Superstorm is related to failure of the model to trigger the amount of convection that was observed. To identify the errors in our forecast fields, the NMC analyses are subtracted from the forecast fields at the verification time. Here, we consider the differences in the 12-h forecast verifying at 1200 UTC 12 March for our four simulations. Figure 27 shows the forecast errors in θT, θT advection, and pressure at the dynamic tropopause (pT). In the control, SSM/I, and SSM/I–IR simulations, the θT forecast is over 30 K too low. The errors are largest for the control simulation, but are also substantial for the SSM/I and SSM/I–IR simulations. On the other hand, in the SSM/I–IR–lightning simulation, the maximum error is less than 10 K. Likewise, in the control, SSM/I, and SSM/I–IR simulations, the pressure at the dynamic tropopause is forecast to be around 40 mb too high in a broad area to the north of the storm. On the other hand, in the SSM/I–IR–lightning simulation, the errors are limited to about 20 mb, and are confined to a much smaller area. These results show that that the control, SSM/I, and SSM/I–IR simulations are forecasting the dynamic tropopause to be too low and too cold in a northeast–southwest-oriented band ahead of PV anomaly C. In all but the SSM/I–IR–lightning simulation, the MM5 is not forecasting the nonconservation of θT. As a result, the model is not capturing the significant advection of lower values of θT over the rapidly intensifying center of Superstorm. Only the SSM/I–IR–lightning simulation correctly diagnoses this favorable cyclogenesis pattern. Similarly, at 0000 UTC 13 March, in the control, SSM/I assimilation, and SSM/I–IR assimilation simulations, the MM5 forecasts of pT are forecast nearly 100 mb too high (the dynamic tropopause is too low) across the southeastern United States to the east of the cyclone center, while the maximum errors in the SSM/I–IR–lightning simulation are only about 25 mb (not shown). Thus, our results are consistent with those found by Dickinson et al. in their analysis of the MRF forecasts of Superstorm. Clearly, the effects of the convective outbreak shown by the lightning observations are not reproduced in the control, SSM/I, or SSM/I–IR simulations. Although one might speculate that the poor quality of these forecasts could be blamed on inadequacies in the cumulus parameterization scheme, it is not the intent of this paper to critique the performance of that, or any other cumulus parameterization scheme. Instead, we have tried to show how utilizing a unique source of data (lightning) was the key to improving forecasts of an exceptional case of cyclogenesis.

8. Summary

In this study, we continuously assimilated latent heating profiles into the MM5 mesoscale model. Those data were derived from SSM/I rainfall retrievals separated by approximately 12 h that were (a) smoothly interpolated by morphing, (b) interpolated in combination with more frequent IR images, and (c) interpolated in combination with both IR images and continuously available lightning data. The morphed SSM/I retrievals could not respond to intense convective development during the early development of Superstorm. The IR imagery responded only to the convection 6 h after it actually occurred, when sufficient cirrus anvils and tall clouds had formed. The best estimate of continuous rainfall distributions was obtained from a combination of IR to identify stratiform rain, and lightning data that responded rapidly to the occurrence of strong convection, tuned with rainfall distributions derived from SSM/I data. Because SSM/I and archived IR images are spaced several hours apart, the technique of digital image morphing is employed in order to “bogus” in gaps in temporal coverage. Of course, the lightning data do not suffer from the same problem, and in fact were temporally smoothed. Recognizing that lightning is a better proxy for convective rain rate than total rain rate, we employed the multichannel microwave retrieval algorithm in order to separate the rain into convective and stratiform components. In our simulation in which lightning data are used to estimate only the convective rain rates, the SSM/I and IR convective rain rates are discarded and replaced by convective rain rates inferred from the number of observed lightning flashes. The amount of convective rain represented by each lightning flash is determined a priori by dividing the total amount of convective rain observed at the SSM/I overpasses by the total number of lightning flashes observed in a 1-h period surrounding the time of the overpass.

We have shown that in the case of the 1993 Superstorm, using lightning data as a proxy for convective rain has particular utility because of the paucity of conventional information needed to initialize the forecast model. A fortuitous confluence of factors for this particular case study enabled the assimilation of lightning data to impact the forecast in such a positive way. These factors include 1) rapid cyclogenesis over an oceanic region out of the range of operational radars, 2) the occurrence of this cyclogenesis at a time inconveniently placed in between SSM/I overpasses, 3) intense lightning (and presumably convective rain) during this time, and 4) a poor forecast in the control simulation. Certainly there will be other cases in which lightning data is of little value either because other data sources (such as radar) do a good job of determining where precipitation is falling or because lightning is not occurring in conjunction with heavy precipitation.

However, our present results suggest that there are occasions in which lightning data have practical uses that have heretofore been unexploited. While here we have employed ground-based lightning networks, space-borne continuous lightning sensors such as the lightning mapping sensor (Christian et al. 1989) are likely to be operational within a decade. In light of the success of lightning data as a commercial product, it is likely that ground-based lightning observing networks will expand their coverage area as well.

Acknowledgments

We thank Ramesh Kakar of NASA’s Mission to Planet Earth for his financial support of this study. Robert Adler and Wei-Kuo Tao are thanked for making the computing facilities of the Goddard Mesoscale Atmospheric Processing Branch available to us. We thank Jack Schols for providing the code for the morphing algorithm used here. We thank Bob Fox of the University of Wisconsin Space Science and Engineering Center and Hal Pierce of NASA/Goddard for assisting us in obtaining GOES IR brightness temperature images. George Lai is thanked for providing an initial version of the rain-rate assimilation code and for his help in obtaining the NMC analyses. Also, thanks to Eric Nelkin for providing the code used to retrieve the SSM/I data from tape. The rain gauge precipitation estimates were obtained from the National Climatic Data Center. We wish to thank the anonymous reviewers for their thought-provoking comments, which motivated us to present the results of this study more clearly. This work was supported by NASA Contract NAS5-32484.

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Fig. 1.
Fig. 1.

Grid points and terrain (m) for the simulations.

Citation: Monthly Weather Review 127, 7; 10.1175/1520-0493(1999)127<1433:TEOARR>2.0.CO;2

Fig. 2.
Fig. 2.

The 0235 UTC rain rates inferred from the microwave brightness temperatures (mm h−1) and the 0300 UTC surface frontal analysis from Kocin et al. (1995). The lowest surface pressure was 981 mb. No measurements were available from the white area in this and subsequent images.

Citation: Monthly Weather Review 127, 7; 10.1175/1520-0493(1999)127<1433:TEOARR>2.0.CO;2

Fig. 3.
Fig. 3.

SSM/I rain rates and tie points at 0305 UTC and 1525 UTC 12 Mar and 0235 UTC 13 Mar.

Citation: Monthly Weather Review 127, 7; 10.1175/1520-0493(1999)127<1433:TEOARR>2.0.CO;2

Fig. 4.
Fig. 4.

Morphing and standard interpolation were applied to rain-rate fields derived from two IR brightness temperature images (1230 UTC 12 Mar and 1530 UTC 12 Mar) to estimate the rain-rate field for 1400 UTC 12 Mar. These estimates are compared to rain-rate fields derived from the observed brightness temperatures at 1400 UTC 12 Mar. Differences (estimated minus observed) are shown for (a) morphed and (b) interpolated rain-rate fields. Contour interval is 1 mm h−1, with solid (dashed) contours indicating positive (negative) errors. Zero contour is omitted.

Citation: Monthly Weather Review 127, 7; 10.1175/1520-0493(1999)127<1433:TEOARR>2.0.CO;2

Fig. 5.
Fig. 5.

The rain rates computed from the SSM/I technique at 0305 UTC, 0930 UTC, 1525 UTC, and 2130 UTC 12 Mar, and 0235 UTC 13 Mar.

Citation: Monthly Weather Review 127, 7; 10.1175/1520-0493(1999)127<1433:TEOARR>2.0.CO;2

Fig. 6.
Fig. 6.

Infrared brightness temperatures at 0330 UTC 12 Mar, 1530 UTC 12 Mar, and 0330 UTC 13 Mar.

Citation: Monthly Weather Review 127, 7; 10.1175/1520-0493(1999)127<1433:TEOARR>2.0.CO;2

Fig. 7.
Fig. 7.

Infrared brightness temperatures vs SSM/I rain rates at 0305 UTC 12 Mar, 1525 UTC 12 Mar, and 0235 UTC 13 Mar.

Citation: Monthly Weather Review 127, 7; 10.1175/1520-0493(1999)127<1433:TEOARR>2.0.CO;2

Fig. 8.
Fig. 8.

Infrared rain rates computed from the histogram-matching technique at 0305 UTC and 1525 UTC 12 Mar and at 0235 UTC 13 Mar.

Citation: Monthly Weather Review 127, 7; 10.1175/1520-0493(1999)127<1433:TEOARR>2.0.CO;2

Fig. 9.
Fig. 9.

The rain rates computed from the SSM/I–IR technique at 0305 UTC, 0930 UTC, 1525 UTC, and 2130 UTC 12 Mar, and 0235 UTC 13 Mar.

Citation: Monthly Weather Review 127, 7; 10.1175/1520-0493(1999)127<1433:TEOARR>2.0.CO;2

Fig. 10.
Fig. 10.

Flashes observed by the NLDN in the 60-min periods surrounding 0305 UTC 12 Mar, 1525 UTC 12 Mar, and 0235 UTC 13 Mar.

Citation: Monthly Weather Review 127, 7; 10.1175/1520-0493(1999)127<1433:TEOARR>2.0.CO;2

Fig. 11.
Fig. 11.

Flashes observed by the NLDN (right) and UKMO (left) networks in the 60-min period surrounding 0235 UTC 13 Mar. Note the cutoff south of 24°N lat.

Citation: Monthly Weather Review 127, 7; 10.1175/1520-0493(1999)127<1433:TEOARR>2.0.CO;2

Fig. 12.
Fig. 12.

Flash rates observed by the NLDN and UKMO networks between 0000 UTC 12 Mar and 0300 UTC 13 Mar.

Citation: Monthly Weather Review 127, 7; 10.1175/1520-0493(1999)127<1433:TEOARR>2.0.CO;2

Fig. 13.
Fig. 13.

The convective fractions derived from SSM/I measurements at 0305 UTC 12 Mar, 1525 UTC 13 Mar, and 0235 UTC 13 Mar.

Citation: Monthly Weather Review 127, 7; 10.1175/1520-0493(1999)127<1433:TEOARR>2.0.CO;2

Fig. 14.
Fig. 14.

The convective rain rates derived from SSM/I measurements at 0305 UTC 12 Mar, 1525 UTC 13 Mar, and 0235 UTC 13 Mar.

Citation: Monthly Weather Review 127, 7; 10.1175/1520-0493(1999)127<1433:TEOARR>2.0.CO;2

Fig. 15.
Fig. 15.

The rain rates computed from the SSM/I–IR–lightning technique at 0305 UTC, 0930 UTC, 1525 UTC, and 2130 UTC 12 Mar, and 0235 UTC 13 Mar.

Citation: Monthly Weather Review 127, 7; 10.1175/1520-0493(1999)127<1433:TEOARR>2.0.CO;2

Fig. 16.
Fig. 16.

Total rain assimilated into the model for the three techniques between 0000 UTC 12 Mar and 0250 UTC 13 Mar.

Citation: Monthly Weather Review 127, 7; 10.1175/1520-0493(1999)127<1433:TEOARR>2.0.CO;2

Fig. 17.
Fig. 17.

Accumulated rain for the three techniques and from the rain gauge network for 0000–0600 UTC 12 Mar.

Citation: Monthly Weather Review 127, 7; 10.1175/1520-0493(1999)127<1433:TEOARR>2.0.CO;2

Fig. 18.
Fig. 18.

The convective rain rate (mm h−1) computed in the four simulations at 0600 UTC 12 Mar.

Citation: Monthly Weather Review 127, 7; 10.1175/1520-0493(1999)127<1433:TEOARR>2.0.CO;2

Fig. 19.
Fig. 19.

As in Fig. 18 except at 1200 UTC 12 Mar.

Citation: Monthly Weather Review 127, 7; 10.1175/1520-0493(1999)127<1433:TEOARR>2.0.CO;2

Fig. 20.
Fig. 20.

The 500-mb geopotential error (m) at 1200 UTC 13 Mar for the four simulations.

Citation: Monthly Weather Review 127, 7; 10.1175/1520-0493(1999)127<1433:TEOARR>2.0.CO;2

Fig. 21.
Fig. 21.

The 500-mb geopotential error (m) at 0000 UTC 14 Mar for the four simulations.

Citation: Monthly Weather Review 127, 7; 10.1175/1520-0493(1999)127<1433:TEOARR>2.0.CO;2

Fig. 22.
Fig. 22.

Minimum sea level pressure of Superstorm for 0000 UTC 12 Mar through 14 Mar from the mesoanalyses of Kocin et al. (1995) and from the MM5 simulations.

Citation: Monthly Weather Review 127, 7; 10.1175/1520-0493(1999)127<1433:TEOARR>2.0.CO;2

Fig. 23.
Fig. 23.

Location of the minimum sea level pressure for Superstorm for 0000 UTC 12 Mar through 14 Mar from the mesoanalyses of Kocin et al. (1995) and from the MM5 simulations.

Citation: Monthly Weather Review 127, 7; 10.1175/1520-0493(1999)127<1433:TEOARR>2.0.CO;2

Fig. 24.
Fig. 24.

Precipitation field at 0900 UTC 13 Mar from the WSR-57 radar network and from the MM5 simulations. Simulated rain rates less than 0.5 mm h−1 are not shown.

Citation: Monthly Weather Review 127, 7; 10.1175/1520-0493(1999)127<1433:TEOARR>2.0.CO;2

Fig. 25.
Fig. 25.

As in Fig. 24 except at 1200 UTC 13 Mar.

Citation: Monthly Weather Review 127, 7; 10.1175/1520-0493(1999)127<1433:TEOARR>2.0.CO;2

Fig. 26.
Fig. 26.

Tracks and positions (UTC/day; Mar 1993) of PV anomalies A, C, and D, denoted by dashed, dotted, and long dash–dotted lines, respectively. Solid line denotes the track of Superstorm, with the “L” locating the cyclone position every 12 h. Adapted from Dickinson et al. (1997).

Citation: Monthly Weather Review 127, 7; 10.1175/1520-0493(1999)127<1433:TEOARR>2.0.CO;2

Fig. 27.
Fig. 27.

Difference fields (forecast minus observed) of θT (solid/dashed for positive/negative differences, every 8 K), potential temperature advection [heavy solid line every (20 K) (12 h)−1], and pT (dotted line every 25 mb) at 1200 UTC 13 Mar.

Citation: Monthly Weather Review 127, 7; 10.1175/1520-0493(1999)127<1433:TEOARR>2.0.CO;2

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