The Conversion of Total Column Ozone Data to Numerical Weather ...

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The Conversion of Total Column Ozone Data to Numerical Weather Prediction Model Initializing Fields, with Simulations of the 24–25 January 2000 East Coast Snowstorm DOROTHY DURNFORD,* JOHN GYAKUM,

AND

EYAD ATALLAH

McGill University, Montreal, Quebec, Canada (Manuscript received 18 January 2008, in final form 29 April 2008) ABSTRACT Satellites are uniquely capable of providing uniform data coverage globally. Motivated by such capability, this study builds on a previously described methodology that generates numerical weather prediction (NWP) model initial conditions (ICs) from satellite total column ozone (TCO) data. The methodology is based on three principal steps: 1) conversion of TCO to mean potential vorticity (MPV) via linear regression, 2) conversion of two-dimensional MPV to three-dimensional potential vorticity (PV) via vertical mapping onto average PV profiles, and 3) inversion of the three-dimensional PV field to obtain modelinitializing height, temperature, and wind fields in the mid- and upper troposphere. The overall accuracy of the process has been significantly increased through a substantial reworking of the details of this previous version. For instance, in recognition of the fact that TCO ridges tend to be less reliable than troughs, the authors vertically map an MPV field that is a synthesis of ozone-derived MPV troughs and analysis MPV ridges. The vertical mapping procedure itself produces a more physical three-dimensional PV field by eliminating unrealistically strong features at upper levels. It is found that the ozone-influenced upper-level initializing fields improve the quantitative precipitation forecast (QPF) of the 24–25 January 2000 East Coast snowstorm for two of the three (re)analyses. Furthermore, the best QPF involves ozone-influenced upper-level initializing fields. Its high threat scores reflect a superior placement, amplitude, and structure. This best QPF is apparently superior to a forecast of the same case where TCO data were assimilated using four-dimensional variational data assimilation.

1. Introduction Our work seeks to improve quantitative precipitation forecasts (QPF). Although manual precipitation forecasts are more skillful than numerical weather prediction (NWP) forecasts, the skill levels of the two are closely related (Fritsch and Carbone 2004). Thus, improving numerical QPFs should lead to more accurate manual QPFs. The error of initial conditions (ICs) is an important component of the NWP error (Rabier et al. 1996; Richard et al. 2003). Where there are no observations for the model to assimilate, the first-guess field becomes

* Current affiliation: Environment Canada, Dorval, Quebec, Canada.

Corresponding author address: Dorothy Durnford, Air Quality Research Division, Environment Canada, 2121 Trans-Canada Highway 424, Dorval, QC H9P 1J3, Canada. E-mail: [email protected] DOI: 10.1175/2008MWR2534.1 © 2009 American Meteorological Society

the analysis and the model is left to drift (Hello and Arbogast 2004). Grimit and Mass (2002), Faccani et al. (2003), and Hello and Arbogast (2004) document the sensitivity of forecasts to IC errors. Unfortunately, both Canada and the waters surrounding the United States are relatively data sparse. Moreover, the North American radiosonde network has degraded since the 1980s (Bosart 1990). The U.S. carriers’ Aircraft Communication Addressing and Reporting System (ACARS) reports are a new type of data. They are valid typically at 250–200 hPa. Unfortunately, the frequency of these reports varies considerably with the time of day, the day of week, and weather conditions (Moninger et al. 2003). The assimilation of satellite data in otherwise datasparse regions has been found to improve NWP model performance by Buehner (2002), Leidner et al. (2003), and Pendelbury et al. (2003). Some satellite data contain dynamical information. Demirtas and Thorpe (1999) found satellite water vapor imagery and upperlevel potential vorticity (PV) features to be collocated. Unfortunately, the extraction of this dynamical information is complex, subjective, and qualitative (Swar-

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brick 2001). However, dynamical information may be objectively derived from satellite total column ozone (TCO) data (e.g., Davis et al. 1999, hereafter D99). Although TCO is the vertical integral of all the ozone molecules in a column, it is primarily composed of tracer molecules residing just above the tropopause (Schoeberl and Krueger 1983; Bowman and Krueger 1985; Peuch et al. 2000). Dobson and collaborators (e.g., Dobson and Harrison 1926) noticed that high and low values of TCO are associated with cyclonic and anticyclonic conditions, respectively. High-valued TCO regions will, therefore, be referred to hereafter as “troughs.” Ertel potential vorticity (EPV) acts as a stratospheric tracer when mixing processes are more important than diabatic heating gradients (Hoskins et al. 1985; Danielsen 1968). Ridges and troughs are associated with low and high values of EPV, respectively. A summary of deep-layer atmospheric dynamics is provided by the mean potential vorticity (MPV) in Eq. (1): MPV ⫽

1 ptop ⫺ pbottom

冕

ptop

PV共p兲 dp,

共1兲

pbottom

where p is pressure and the variable PV may represent EPV, PV derived from the stream function and the geopotential, or any other type of potential vorticity. Though the choice of ptop is important, since the PV– ozone mixing ratio correlation becomes anticorrelation above 22 km (⬃50 hPa; Danielsen 1983), the value of pbottom is less significant, given that tropospheric PV values tend to be small. As with TCO, high-MPV regions will be referred to as troughs. TCO and MPV are most strongly correlated during winter and spring (Allaart et al. 1993). The TCO–MPV correlation is stronger in troughs than in ridges (Barsby and Diab 1995; D99). Photochemistry and latent heating negatively impact the TCO–MPV correlation most strongly during spring–summer and winter, respectively (Beekman et al. 1994). Ozone data have been assimilated into numerical models for use in radiative transfer calculations (Derber and Wu 1998; Dethof and Holm 2004) and in order to extract tropopause-level wind information (Peuch et al. 2000; Dethof and Holm 2004). Dethof and Holm (2004) found that, while significant improvements in both wind and temperature fields could be realized, the results were extremely sensitive to observational errors. Riishøjgaard (1996), who linked assimilated ozone data dynamically, also noted a sensitivity to data quality. Jang et al. (2003) and Zou and Wu (2005) assimilated dynamically linked TCO data using four-dimensional variational data assimilation (4DVAR) assimilation.

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The latter study presented no results, while the former study exhibits a partly improved, partly degraded precipitation forecast. A known problem in the assimilation of TCO is the incorrect vertical distribution of these data (Riishøjgaard 1996; Dethof and Holm 2004). Assimilating ozone profiles as well as TCO data can mitigate this problem (Struthers et al. 2002). Our procedure to extract the dynamical information inherent in TCO data is based on the D99 method, which is less computationally expensive than variational assimilation. This method maps a regressed ozone-derived MPV field vertically onto average PV profiles. The resulting three-dimensional (3D) PV field is then inverted, yielding model-initializing height, temperature, and nondivergent wind fields. D99 found that ozone-derived and analysis winds differed sometimes in the vicinity of sharp ridges, indicating either faulty TCO values or the decorrelation of ozone and PV as a result of diabatic heating. We have reworked the details of the D99 methodology, thereby increasing the overall accuracy of the process. Our method generates a fairly independent ensemble member. Furthermore, developed techniques are adaptable to variational assimilation. We apply our method to the unforecasted, record-breaking East Coast snowstorm of 24–25 January 2000. Before it can be of use to operational centers, our procedure must be tested on a more substantial dataset; parameter values must be refined and the procedure’s generality be established. The remainder of this article is organized as follows: section 2 describes datasets used, section 3 introduces the event simulated, section 4 presents our NWP model ICs-generating procedure, section 5 discusses our simulations of the event, and Section 6 presents our conclusions. The reader is referred to Durnford (2007) for a more complete discussion of any section.

2. Datasets This project uses 1° latitude ⫻ 1.25° longitude, version 8, gridded daily average TCO fields measured by the Earth Probe’s Total Ozone Mapping Spectrometer (TOMS). Northern Hemispheric ozone measurements are valid near local noon or approximately 1800 UTC for North America, with eastern values valid at an earlier time than western values (McPeters et al. 1998). Pressure-level fields were provided by the 40-yr European Centre for Medium-Range Weather Forecasts (ECMWF) Re-Analysis (ERA-40; Uppala et al. 2005), the National Centers for Environmental Prediction– National Center for Atmospheric Research (NCEP– NCAR; Kalnay et al. 1996) reanalysis (hereafter the NCEP reanalysis), the Global Environmental Multi-

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FIG. 1. Accumulated liquid water equivalent precipitation for 24–26 Jan 2000 [contours at 5 mm and every 10 mm from 10 mm, with the 20-mm contour dashed, the 40-mm contour heavy, and light (dark) shading from 50 (80) mm; adapted from BL05].

scale model (GEM; Côté et al. 1998) and the Eta (Black 1994). ERA-40, NCEP, and GEM (re)analyses are on 1.125°, 2.5°, and approximately 0.9° latitude–longitude global grids, respectively. January 2000 Eta analyses are on a regional 32-km grid.

3. The 24–25 January 2000 East Coast snowstorm The 24–25 January 2000 East Coast snowstorm generated a significant amount of precipitation along the U.S. eastern seaboard, as demonstrated with respect to the Carolinas and Virginia by Fig. 1. Even though some of the precipitation fell as rain, freezing rain, and sleet, the storm total snowfall record was broken at the Raleigh–Durham, North Carolina airport with 51.6 cm. Daily snowfall records were broken in the District of Columbia region [(National Climatic Data Center) NCDC 2000]. Locations in 15 states along the eastern seaboard received more than 25.0 cm of snow. The total cost of the storm for the state of North Carolina alone was estimated at 800 million U.S. dollars. Unfortunately, the prediction of this storm was “one of the major failures of the operational forecast system” (Zupanski et al. 2002); all National Weather Service (NWS) operational models failed. (An analysis of the operational forecasts can be viewed online at http:// www.emc.ncep.noaa.gov/mmb/research/blizz2000/.) Forecasts initialized as late as 1200 UTC 24 January were still predicting that the heavy precipitation would remain offshore. The almost nonexistent lead time earned the event the media label of the “surprise snowstorm” (NCDC 2000).

The generation of onshore precipitation was heavily influenced by the upper-level trough; ERA-40 fields suggest that minimal, if any, warm-air advection occurred onshore from 1800 UTC 24 January through the remainder of the event in the southeastern U.S. (not shown). During the event, latent heating eroded the southern portion of the trough and eventually a midlevel cutoff low formed. On 22 January 2000, the surface cyclone associated with this event was located over the Great Plains (not shown). The cyclone subsequently tracked eastward through the Gulf of Mexico, then northeastward along the eastern seaboard. The central pressure plunged from 1003 hPa at 1800 UTC 24 January to 993 and 979 hPa at 0000 and 1800 UTC 25 January, respectively. Articles published on this storm (Buizza and Chessa 2002; Langland et al. 2002; Zhang et al. 2002; Zupanski et al. 2002; Jang et al. 2003; Zhang et al. 2003; Brennan and Lackmann 2005, hereafter BL05; Kleist and Morgan 2005; Zhang 2005) focus primarily on the first half of the event prior to 1200 UTC 25 January 2000. They are from a variety of perspectives. These studies’ consensus is that the forecasting of the 24–25 January 2000 East Coast snowstorm is extremely sensitive to model ICs. Therefore, simulating this event is a significant test of our technique. The fact that the event is located over the data-rich U.S., where (re)analyses should be at their most accurate, augments the challenge; if our ozoneinfluenced fields are able to perform comparatively well under these conditions, producing a forecast on the same order of accuracy as the (re)analyses, they can be expected to perform reliably in data-sparse regions, where (re)analyses are at their least reliable. The performance of reanalysis ICs is represented by our “ERA” experiment.

4. The conversion of TCO data to NWP model ICs a. The conversion of TCO to MPV 1) SPATIAL

INTERPOLATION OF

TCO

We first interpolate all fields to a global 1.125° latitude–longitude grid. Eta fields are interpolated to a subdomain of the ERA-40 domain. Since TCO datavoid regions are arbitrarily assigned a zero value by the National Aeronautics and Space Administration (NASA), the spatial interpolation assigns unrealistically low values to neighboring grid points; a location halfway between a data-void region and a 400–Dobson unit (DU) region is unlikely to be valued at 200 DU. Data-void regions exist at high winter latitudes where there is no sunlight and at low latitudes, where the satellite’s altitude is insufficient to provide complete

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coverage. Points in and neighboring data-void regions are bypassed in calculations.

2) TEMPORAL

INTERPOLATION OF

TCO

We interpolate the local noon TCO field to 1800 UTC, local noon at 90°W. Our temporal interpolation scheme, mathematically identical to that of D99, is purely advective. However, whereas we use dynamic tropopause winds to advect the TCO field itself at the beginning of the procedure, D99 use pressure-leveladvecting winds to interpolate the ozone-derived 3D PV field at a much later stage in the procedure. The D99 system is unfortunate for two reasons: the regression is performed on temporally and, therefore, spatially, misaligned fields, which surely degrades the regression; and individual pressure-level PV fields are interpolated, which, given the variation in both direction and speed of winds with atmospheric level, surely distorts the vertical PV profiles that were created during the vertical mapping process. Since our regression fields are spatially aligned, and our constructed 3D PV field is left unaltered, it can be expected that our temporal interpolation system increases the overall accuracy of the procedure. Our temporal interpolation of the TCO field itself is also of practical importance. D99 process one quarter of the globe at a time, such that local noon at the central longitude corresponds to an NCEP grid time. There is no flexibility in the location of the model domain. In contrast, our model domain is unrestricted as to size and location; the ozone data can be interpolated temporally to any domain. Thus, while D99’s fixed boundaries may result in only some of the features relevant to a developing system being captured in the model ICs, our ICs are able to capture all aspects. Our choice of analysis dynamic tropopause winds as the advecting agent enables us to interpolate the TCO field itself. This choice is made viable by the fact that the large majority of the ozone molecules resides just above the dynamic tropopause (Salby and Callaghan 1993). As implied by D99, our advecting winds are halved. Given that wind strengths are maximized at the tropopause, while the majority of the ozone molecules reside just above the tropopause where the winds are weaker, it is understandable that reducing the strength of the advecting winds increases the correlation coefficient (not shown). The temporal interpolation scheme is defined by Eq. (2):

␦ longitude ⫽ ␦ latitude ⫽

u共␭ ⫺ ␭c兲 and ␻R cos共lat兲

␷共␭ ⫺ ␭c兲 , ␻R

共2兲

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where u and ␷ are zonal and meridional advecting winds (m s⫺1); ␭ (radians) is the longitude of a given grid point; ␭c (radians) is the longitude (90°W) at which local noon represents the specified universal time (1800 UTC); ␻ is the planetary angular velocity, which is valued at 7.27 ⫻ 10⫺5 s⫺1; R is the radius of the earth (m); and lat is the latitude of the given grid point (radians). An inverse Cressman method (Cressman 1959) calculates the ozone value at the determined longitude and latitude. D99 use the nearest grid point’s value. Our temporal interpolation is conducted in 3-hourly or 45° segments. The first segment uses advecting winds valid at 1800 UTC, the second uses winds that are interpolated linearly between 1800 and either 1200 or 0000 UTC of the next day, the third uses winds valid at 1200 or 0000 UTC, and so on until the interpolation is complete. The multiple interpolation segments permit a curved trajectory. D99, with their fixed domain size, use a single interpolation segment of no more than 3 h. Figure 2 presents the original local noon and temporally interpolated TCO fields in our region of interest for 24 January 2000. The interpolation scheme has stretched the local noon field outward from 90°W where the winds are westerly. The effect is greatest where the winds are strong and/or the longitudinal distance from 90°W is large.

3) TCO–MPV

REGRESSION SCHEME

We perform a least squares method linear regression following Eqs. (3) and (4) (Hastings 1997): b⫽

1 n

n

兺

yi ⫺ m

i⫽1 n

n m⫽

兺

n

兺x,

共3兲

i

i⫽1

冉 兺 冊冉 兺 冊 冉兺 冊 n

xiyi ⫺

i⫽1

n

xi

yi

i⫽1

n

n

1 n

兺 共x 兲 ⫺

i⫽1

n

2

i

i⫽1

xi

,

共4兲

2

i⫽1

where b is the intercept and m is the slope of the best-fit line describing the relationship between fields X and Y, which consist of n x and y points, respectively. The regression domain extends between 17.35°–65.94°N and 150.95°–39.08°W. Unless explicitly stated otherwise, all figures in this subsection are based on data points from all latitudes of the domain combined and 10–23 January 2000, with MPV calculated using ERA40 PV from 400–50 hPa. The TCO–MPV regression uses MPV calculated from PV(⌿, ⌽), with ⌿ as the streamfunction and ⌽ as the geopotential, so that the form of PV on which ozone-influenced PV is based is identical to the form of

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FIG. 2. Plotted for 24 Jan 2000 are (a) the original TCO field valid at local noon with ERA-40 dynamic tropopause winds valid at 1800 UTC [(half) barb equals (2.5) 5 m s⫺1, pennant equals 25 m s⫺1], and (b) the time-mapped TCO field valid at 1800 UTC. The ozone fields are plotted with a contour interval of 25 DU, where smaller values are shown in lighter shades of gray, and shading from 350 DU.

PV that is inverted. PV(⌿, ⌽) is derived from EPV by assuming a hydrostatic, nondivergent state (Davis and Emanuel 1991). Since the TCO–MPV correlation coefficient unquestionably varies with latitude, some studies have assumed that the ozone–MPV regression scheme should also vary either with latitude (D99; Jang et al. 2003) or air mass (Zou and Wu 2005). However, the low-latitude points follow the same general direction as the points from the other latitude bands (Fig. 3); the lower correlation may be more a result of the less elongated region covered by the filtered low-latitude data points and less an indication that this air mass behaves fundamentally differently. Furthermore, the fact that the highest correlation (␳; top left corner of each panel in Fig. 3) of all

is obtained by points from all latitude bands combined, for which the slope and intercept are, following the low-latitude behavior, smaller and larger, respectively, than those of the three higher-latitude bands (see Table 1), and the fact that all latitude bands have similar numbers of filtered points (N; top left corner of each panel in Fig. 3), indicating that the low-latitude filtered points are not dominating the set of filtered points from all latitudes, together suggest that the low-latitude points do not belong to a separate regime. Likewise, the fact that the 30°–40°N latitude band is the most highly correlated latitude band suggests that the intercepts from the two most northerly latitude bands are unrealistically low. Therefore, our regression uses the filtered points from all latitude bands combined; this set of

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FIG. 3. TCO (DU)–MPV (PVU) data points from the indicated latitude bands are shown with the respective regressed lines. Available (filtered) points are plotted in black (gray). The heavy line along the abscissa is created by points from data-void regions.

points is the most highly correlated and there is no evidence that the regression scheme should vary with latitude. Table 2 suggests that the MPV upper-bounding pressure level should be at least 50 hPa. Despite the ability of the 30-hPa upper level to produce high correlation coefficients, this upper-level value is rejected as being unwise, given that ozone and PV become decorrelated above approximately 50 hPa. Thus, we select the 50-hPa

upper-bounding level. This agrees with the value chosen by D99 and Zou and Wu (2005), but is higher than the 100-hPa value used by Jang et al. (2003). With a 50-hPa upper level, the 300-hPa lower level produces a slightly higher correlation coefficient than does the 400-hPa lower level. However, given that no published study has used such a high lower-level value and given that the difference in correlation value is minimal, we chose a 400-hPa lower level. Zou and Wu

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TABLE 1. Regression slopes and intercepts for the indicated latitude bands. Lat band (°N) Slope (DU PVU Intercept (DU)

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⫺1

)

All

⬍30

30–40

40–50

⬎50

19.9 215

16.7 224

21.7 212

22.6 201

21.4 199

as 10 days, decreases the correlation coefficient calculated. We use a 14-day period, which yields the highest correlation coefficient of this table. This is equal or comparable to the 14- and 12-day periods used by Zou and Wu (2005) and Jang et al. (2003), respectively. D99 used a 1-month period.

4) TCO (2005) also used 400 hPa as the lower level, while D99 and Jang et al. (2003) used 500 hPa. The correlation coefficients obtained using MPV calculated from the GEM, NCEP, and ERA-40 (re)analyses are 0.875, 0.888, and 0.893, respectively. These differences may not be significant, given that the spatial and temporal interpolation errors may be greater than these small coefficient differences. However, if the differences are significant, then these coefficients indicate two interesting points: 1) the quality of the (re)analysis has a greater impact than its resolution, since lowerresolution NCEP reanalyses produce a higher correlation coefficient than GEM operational analyses; and 2) extrapolating the trend of increasing correlation coefficient with increasing (re)analysis quality suggests that using an even more accurate set of fields than that provided by the ERA-40 would increase the coefficient further. This implies that the TCO fields are, on the whole, more accurate than even the ERA-40 fields. Our regression uses ERA-40 fields for the TCO–MPV regression. Although it would be desirable to perform the TCO– MPV regression using a time period from the current year centered on the target date, it is not possible to do so in an operational setting; fields from after the target date are still unknown. Also, the base level of TCO varies from year to year (Geller and Smyshlyaev 2002). Thus, our regression time period is taken from the days leading up to the target date. The correlation coefficients calculated using a time period of 10, 14, 18, and 22 days are, respectively, 0.880, 0.893, 0.887, and 0.891. Given the presence of errors owing to the spatial and temporal interpolations, these small coefficient differences may not be significant. However, they do suggest that a short time period, such

TABLE 2. Correlation coefficients (dimensionless) calculated using the indicated MPV upper- and lower-bounding pressure levels. Across: lower level (hPa) Down: upper level (hPa)

500

400

300

250

70 50 30

0.880 0.890 0.891

0.885 0.893 0.894

0.889 0.894 0.893

0.885 0.888 0.885

REGRESSION

The TCO field is converted to an MPV field using the best-fit line parameters calculated previously. The MPV field is then smoothed using Eq. (5) with weightings defined by Eq. (6): I⫹n

MPVI, J ⫽

J⫹n

兺 兺

wi, jMPVi, j

i⫽I⫺n j⫽J⫺n I⫹n

,

J⫹n

兺 兺

共5兲

wi, j

i⫽I⫺n j⫽J⫺n

for i ⫽ I otherwise: wi, j ⫽

and j ⫽ J: wi,j ⫽ a; 1⫺a

共2n ⫹ 1兲2 ⫺ 1

,

共6a兲 共6b兲

where a is the smoothing coefficient and n determines the number of points involved in the summations. The denominator of Eq. (6b) represents the number of noncentral points involved in a summation. Since very light smoothing yields the best results, we set a to 0.995. The initial smoothing pass is conducted with n set at unity. If, at a given grid point, no valid data points are encountered during this pass, the grid point is assigned a missing data value. A second smoothing pass is then conducted to replace missing data values. During this pass, where each grid point is processed until its MPV value is determined, and where n is initially set to unity, the value of n increments by 1 until at least one valid point is encountered. The regressed MPV field (Fig. 4a) faithfully reproduces the features exhibited by the temporally mapped TCO field (Fig. 2b). The regressed and analyzed MPV fields, though very similar in general terms, are not identical (Fig. 4). The water vapor imagery of Fig. 5 suggests that neither field is completely accurate: while only the regressed MPV field extends the eastern seaboard trough into the Atlantic Ocean, the ERA-40 ridge seemingly penetrates insufficiently northward in the western part of the continent, resulting in overdeveloped coastal depressions; the strength and extent of the ozone-derived coastal depressions are likely more reasonable. Latent heating due to heavy precipitation off the eastern seaboard has previously warmed the upper troposphere (not shown), where warmth is subsequently advected eastward. Since diabatic processes constitute

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FIG. 4. (a) Regressed and (b) ERA-40 MPV valid at 1800 UTC 24 Jan 2000. These fields are plotted using a contour interval of 1 PVU for solid lines (where smaller values are represented by paler shades of gray), a dashed line at 5.5 PVU and shading from 7 PVU.

a source/sink for PV but not for ozone, the TCO field is unable to “see” the ridge building. This deficiency is exhibited by the overly weak regressed Atlantic ridge and the overly important regressed trough extension into the Atlantic.

5) SYNTHESIS MPV

OF OZONE-DERIVED AND ANALYSIS

As mentioned in the previous section, TCO fields do not immediately exhibit ridges built by latent heat release. TCO values may also be less reliable in the vicinity of ridges than of troughs given that, in cloudy regions, which are often associated with ridging, the TOMS algorithm uses tropospheric ozone values deduced from climatological tropospheric ozone profiles and climatological cloud heights. Since the regressed MPV field seems to be slightly unreliable, owing to

inaccurate TCO ridges, we strengthen the reliability of the ozone-derived MPV field by synthesizing regressed troughs and analyzed ridges. Our synthesis is conducted, at latitudes no more than 61°N, in recognition of the decorrelation between MPV and TCO that occurs within the polar vortex by the following: 1) copying the analysis MPV field to the synthesized field. 2) Overlaying all synthesized values of at least 7 potential vorticity unit (PVU; shaded regions in Fig. 4b; 1 PVU ⬅ 1 ⫻ 10⫺6 K m2 kg⫺1 s⫺1) with regressed values, as long as the regressed value is no less than 3 PVU; in other words, analysis troughs are erased. 3) Overlaying all synthesized values with regressed values of at least 7 PVU (shaded regions in Fig. 4a). This inserts ozonederived troughs into the synthesized field. 4) Overlaying all synthesized values with analyzed values of 5.5 PVU or less (the region of pale solid contours in Fig. 4b

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FIG. 5. Shown for the indicated Jan 2000 day–UTC time are (a), (c) Geostationary Operational Environmental Satellite-10 (GOES-10), and (b), (d) GOES-8 water vapor images.

enclosed by the dashed contour). Thus, analysis ridges are permitted to replace ozone-derived troughs, as diabatic heating does in the real atmosphere. ERA-40 fields at 1800 UTC 24 January 2000 indicate that MPV values of 5.5 and 7 PVU translate, respectively, to approximately 552–558 and 546 dam at 500 hPa, which could be considered fairly general ridge and trough bounding values at this time of year. Given the seasonal variation of climatological mass fields (Bluestein 1993), the boundary MPV values would change with season. Inverted and forecast fields exhibit virtually no sensitivity to variations in MPV ridgebounding values for values between 5 and 6 PVU, owing, most likely, to the smoothing effect of the PV inversion. The 3-PVU limiting value is designed to eliminate TCO synoptic-scale minima, which represent the superposition of a tropopause-level ridge and an independent midstratospheric equatorward extrusion of ozonepoor polar vortex air (Allen and Nakamura 2002). They are characterized by TCO values of at least 70 DU less than that region’s climatological value (James and Pe-

ters 2002). Figure 3 suggests that the mean January TCO value for mid- and high latitudes is approximately 350 DU, so that ozone values less than 280 DU, corresponding to about 3 PVU, represent a minihole. The 3-PVU limiting value can be expected to change with season. A 300-DU value represents a 3-mm-thick layer of ozone at standard temperature and pressure. The synthesized MPV field clearly exhibits the analyzed Atlantic and western ridges and the regressed troughs (Figs. 4 and 6), although the spatial extent of the regressed eastern seaboard trough’s southern portion has been reduced. On the other hand, the southern extension of the analyzed western trough and the small analyzed Pacific Ocean depression have been erased. MPV calculated from rawinsonde data, analyzed onto a 1.125° latitude–longitude grid using Gempak’s Barnes objective analysis with ERA-40 first-guess fields, is presented in Fig. 7, along with ERA-40 MPV fields valid at the same times. MPV fields presented in previous figures are all valid at 1800 UTC 24 January, while Fig. 7’s fields are valid at 1200 UTC 24 January and 0000 UTC 25 January. The strong rawinsonde-

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FIG. 6. The (a) synthesized MPV field for 1800 UTC 24 Jan 2000 is shown, with a contour interval of 1 PVU for solid lines (where smaller values are represented by paler shades of gray), a dashed line at 5.5 PVU and shading from 7 PVU. The straight lines indicate the location of the cross sections of Figs. 9–11.

FIG. 7. Shown for the indicated dates, where “24/12” denotes 1200 UTC 24 Jan 2000 are (a), (c) MPV calculated from analyzed rawinsonde data and (b), (d) ERA-40 MPV. The contour interval is 1 PVU for solid lines (where smaller values are represented by paler shades of gray), with a dashed line at 5.5 PVU and shading from 7 PVU. Triangles (squares) mark sounding stations contributing data at all (some of the) ten pressure levels contributing to the MPV calculation.

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derived MPV ridge over Georgia at 1200 UTC 24 January, presumably generated diabatically by the precipitation described in BL05, has likely weakened the east coast MPV trough. Rawinsonde-derived diabatic heating over the Carolinas and Virginia, evident at 0000 UTC 25 January, has likely continued to weaken the trough further. The ERA-40 MPV field exhibits insufficient ridging both over Georgia at the earlier time and over South Carolina at the later time. This results in an ERA-40 trough that extends too far south at the earlier time, while, at the later time, the cutoff low and the bend in the dashed contour over South Carolina are both too far north. Though our synthesizing process improves the regressed MPV field’s trough by reducing its southerly extent, the southern region of the synthesized trough remains both too strong, owing to the inability of the TCO field to see the MPV-destroying diabatic processes, and too extensive, owing to the ERA-40’s underestimation of the local ridging (Fig. 7). Thus, at 1800 UTC, while the ERA-40 trough is probably fairly accurate, the synthesized trough is too strong.

b. MPV to PV conversion 1) CONSTRUCTION

OF AVERAGE

PV

PROFILES

The conversion of the two-dimensional (2D) MPV field to a 3D PV field is conducted by mapping the synthesized MPV field onto average PV profiles, following D99. However, whereas D99 provided two average profiles, one each for ridges and troughs, we provide a set of 12. The first step in the construction of a grid point’s appropriate average PV profile is the calculation of the mean MPV value and standard deviation (␴) for that grid point’s set of ERA-40 space–time points. The manner in which the set of points is established is discussed below. The algorithm next determines to which of the 12 available MPV categories the grid point’s synthesized MPV value belongs, the categories having the 11 boundaries consisting of the mean MPV value ⫾2.5␴, representing an extreme ridge or trough: ⫾2␴, ⫾1.5␴, ⫾1␴, ⫾0.5␴, and 0␴. The first and last categories consist of MPV values less than or equal to the mean ⫺2.5␴ and greater than the mean ⫹2.5␴, respectively. The average PV value for each level is then calculated using all points from the full set of space–time points that have an MPV value within the determined MPV category. The average PV profile is constructed by stacking the individual levels’ average PV values vertically. The MPV value of this constructed profile is labeled the “average” MPV value. If a grid point’s synthesized MPV value represents

FIG. 8. Average PV profiles (PVU) at two latitudes (30.91° or 54.64°N) and two longitudes (143.04° or 82.02°W) constructed using space–time points having an MPV value between the mean MPV ⫹ 0.5 std dev (␴) to the mean ⫹ 1 std dev, representing local troughs of identical relative strengths.

either an extreme ridge or an extreme trough, it is possible that that grid point’s set of space–time points will contain no elements characterized by an MPV value lying within the appropriate MPV category. In such a situation, the boundaries of the MPV category are shifted, starting with the boundary nearest the mean, until at least one point is found. Given the seasonal variation of climatological mass fields (Bluestein 1993), the set of space–time points must include only points from the same season as the target date. Since a large number of space–time points is desired, points from the target date’s month from a long (e.g., 40–50 yr) dataset would be optimal. However, for our demonstration of the vertical mapping process, points from the two weeks prior to the target date plus the target date itself are used, which cannot be done operationally, but that does provide points with anomalously high low-latitude PV values. Average trough profiles at four grid points are presented in Fig. 8. These profiles are constructed using space–time points characterized by MPV values bounded by the grid point’s mean MPV value ⫹ 0.5␴ and the grid point’s mean MPV value ⫹ 1.0␴. Thus, the four profiles represent troughs of identical relative strengths. Given the variation, both latitudinal and longitudinal, between these average PV profiles, it is nec-

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TABLE 3. The factork values. Level (hPa)

600

500

400

300

250

200

150

100

70

50

factork (dimensionless)

0.30

0.60

0.90

0.60

0.20

⫺0.75

⫺0.85

⫺0.95

⫺0.98

0.00

essary to restrict the extent of the region providing space–time points. If too small a region is used, insufficient points will be available to contribute to extreme ridge–trough profiles. Therefore, we use a 10° latitude– longitude region centered on the grid point being processed. D99 calculated statistical profiles as a function of latitude.

PVmap; i, j,k ⫽

冋

MPVsyn; i, j MPVavg; i, j

⫹

冉

2) VERTICAL

The 2D synthesized MPV field is converted to a 3D PV field by mapping each grid point’s MPV value onto the appropriate average PV profile. The mapped PV value at a given grid point (i, j) and level k, is calculated using Eq. (7):

MPVsyn; i, j MPVavg; i, j

where MPVsyn; i, j is the synthesized MPV value at grid point (i, j), MPVavg; i, j is the MPV value of the grid point’s average PV profile, PVavg; i, j,k is the value of the grid point’s average PV profile at level k, and factork is the level-dependent multiplicative factor. The first occurrence of the ratio of the synthesized and average MPV values in Eq. (7) constitutes a constant mapping coefficient. Since 12 average profiles are available, this ratio is close to unity, rendering the term multiplied by factork a small adjustment to the constant mapping coefficient. The presence of the factork term transforms the constant mapping coefficient into a level-varying mapping coefficient. Our factork values are presented in Table 3. A constant mapping coefficient assigns the MPV increment predominantly to upper levels: if an average

MAPPING

冊

册

⫺ 1 共factork兲 PVavg; i, j,k,

共7兲

PV profile has a 70-hPa value of 15 PVU and a 250-hPa value of 5 PVU, and if the MPV ratio is 1.1, then the mapped values become 16.5 and 5.5 PVU, representing a difference of 1.5 and 0.5 PVU, respectively; the positive MPV increment has been converted into a trough that is stronger in the midstratosphere than in the lower stratosphere/upper troposphere (see Fig. 9a). This is unrealistic. Our level-varying coefficient, on the other hand, assigns the MPV increment predominantly to the upper troposphere/lower stratosphere (see Fig. 9b), which is far more realistic. Given that the vertical distribution of the TCO or ozone-derived increment is a known problem (Riishøjgaard 1996), even for variational assimilation (Dethof and Holm 2004), it might be useful to adapt our level-varying mapping coefficient for variational assimilation.

FIG. 9. For 1800 UTC 24 Jan 2000, cross sections of PV are shown along the line indicated in Fig. 6, where the PV fields have been vertically mapped using (a) a constant mapping coefficient, and (b) a level-varying mapping coefficient. The PV fields are plotted every 1 to 13 PVU and every 2 from 13 PVU, with shading from 2 to 3 PVU.

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FIG. 10. Cross sections of PV for 1800 UTC 24 Jan 2000 along the lines indicated in Fig. 6 are presented from the following sources: (a) vertical mapping of ozone-influenced MPV using a level-varying mapping coefficient, (b) ERA-40 PV(⌿, ⌽), (c) EPV calculated from ozone-influenced inverted fields, and (d) ERA-40 EPV. The PV fields are plotted every 1 to 13 PVU and every 2 from 13 PVU, with shading from 2 to 3 PVU.

The vertical mapping is conducted automatically from 50 to 400 hPa, continuing to 600 hPa if either the profile’s or mapped PV value on the level above remains at least 1.5 PVU. For more elevated tropopauses, ERA-40 PV values are transferred unmapped to the ozone-influenced profile below 400 hPa. The mapping is conducted iteratively at each grid point until either the mapped PV profile’s MPV value is within 1.0 ⫻ 10⫺3 PVU of the synthesized MPV value or 250 iterations have been completed, at which point the synthesized and mapped MPV values tend to agree to two decimal places. The ozone-influenced cross section of PV(⌿, ⌽) obtained using a level-varying vertical mapping coefficient (Fig. 10a) is very similar to the ERA-40 PV(⌿, ⌽) cross section (Fig. 10b) to first order, in that they both have collocated primary troughs with flanking ridges. However, the analysis cross section exhibits a PV minimum at 150 hPa; our vertical mapping procedure is incapable

of producing a minimum above a maximum as, on average, PV increases with altitude at these levels. Furthermore, the ozone-influenced trough is deeper and wider than that of the analysis. This difference was evident in the MPV fields (Figs. 4 and 6) and was amplified during the vertical mapping. The mapping exaggerates the upper-tropospheric wave in order to counteract the PV inversion’s smoothing.

c. PV inversion The ozone-influenced 3D PV field is inverted following Davis and Emanuel (1991). However, a spurious height field dipole was generated when we used a single inversion domain; the boundary conditions may not have been able to guide the inversion sufficiently in our 3626-point domain. We, therefore, divide the domain into six subdomains. Each subdomain’s outer three rows of points, where the boundary conditions have the strongest influence on output field values, are dis-

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FIG. 11. Cross sections of PV along the line indicated in Fig. 6 are shown for 1800 UTC 24 Jan 2000 using (a) EPV calculated from the original ERA-40 fields, and (b) EPV calculated from fields produced by inverting ERA-40 PV(⌿, ⌽). Full PV fields are plotted every 1 to 13 PVU and every 2 from 13 PVU. In (a), the difference of the two ERA-40 EPV fields are also shown [inverted minus original; shading intervals of 0.5 PVU with a solid (dashed) contour at ⫹ (⫺) 0.5 PVU].

carded. The remaining seven gridpoint sponge zone between adjacent subdomains ensures smooth field transitions. The inversion outputs model-initializing height, temperature, and nondivergent wind fields on the original vertical mapping levels from 600 to 50 hPa, as well as on the bounding levels of 700 and 30 hPa. As a result of the smoothing produced by the PV inversion (demonstrated by Fig. 11), and the fact that EPV fields are somewhat smoother than PV(⌿, ⌽) fields (cf. Figs. 10b,d), the ozone-influenced EPV (Fig. 10c) cross section is far smoother than the ozoneinfluenced inversion input PV(⌿, ⌽) section (Fig. 10a). The ozone-influenced EPV cross section trough is now slightly weaker than that of the ERA-40, although its greater width has been maintained. Reflecting the MPV fields, the ozone-influenced 500hPa inverted eastern seaboard height field trough is deeper than that of the ERA-40, while the southern extension of its western trough is weaker (Fig. 12). ERA-40 500-hPa winds tend to be slightly stronger than inverted ozone-influenced winds, owing not only to the nondivergence of the ozone-influenced winds, but also to the inversion’s smoothing of the flanking ridges. According to rawinsonde-derived fields (Fig. 13), the strengths of the ERA-40 and ozone-influenced 500-hPa height field troughs are likely approximately correct and definitely too great, respectively. However, the significant curvature in the leading edge of the ozoneinfluenced trough is likely more accurate than the lesser curvature of the ERA-40 trough. The water vapor imagery (Fig. 5) also suggests a significantly curved trough. Our simulations indicate that this curvature is

of the utmost importance for the generation of this event’s onshore precipitation.

d. Comparison of the proposed procedure and the D99 method Table 4 compares the proposed and D99 procedures. Our early performance of the temporal interpolation scheme, our regression scheme’s use of grid points from all latitudes combined, our synthesis procedure, and our use of a level-varying mapping coefficient are believed to be the most important differences between the two methodologies.

5. Simulations of the 24–25 January 2000 East Coast snowstorm a. Experimental setup Simulations are performed by the Mesoscale Compressible Community model (MC2; Benoit et al. 1997), using version 4.9.8 of the dynamics and version 4.1 of the physics package. The MC2 is a limited-area, fully compressible, nonhydrostatic model with a semiimplicit, semi-Lagrangian scheme. We use Kain–Fritsch deep convection (Kain and Fritsch 1990) and Kong– Yau explicit microphysics (Kong and Yau 1997) schemes. The boundary layer scheme is based on turbulent kinetic energy (more information available online at http://collaboration.cmc.ec.gc.ca/science/rpn/ physics/physic98.pdf). We perform six experiments (see Table 5). Since model settings remain constant and identical ERA-40 6-hourly lateral boundary conditions are provided, the

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FIG. 12. Shown at 500 hPa for 1800 UTC 24 Jan 2000 are (a) ozone-influenced inverted and (b) ERA-40 height (12-dam contour interval, with a wider 540-dam contour) and wind fields [(half) barb equals (2.5) 5 m s⫺1, pennant equals 25 m s⫺1]. Note that the inverted winds are nondivergent while the ERA-40 winds are full.

experiments are differentiated solely by their ICs. The six experiments are divided into three pairs involving three different (re)analyses. Both experiments of a pair use the same low-level and moisture fields; their difference lies in the fact that the “ozone” experiment uses ozone-influenced upper-level initializing fields. All ozone-influenced initializing fields stem from the same ozone-influenced 3D PV field. This 3D PV field is inverted three separate times, using first-guess and boundary condition fields provided by ERA-40 reanalysis, GEM analysis, or operational Eta analysis fields. A single source thus provides each ozone experiment with PV inversion boundary conditions, including horizontal boundary condition fields at 700 hPa, lowlevel model-initializing fields up to and including 700 hPa, and moisture fields at all levels. Since the inversion

guarantees output fields that are stable internally, and a single source provides 700-hPa fields and 700-hPa boundary conditions, stability between the upper- and lower-level sets of fields across 700 hPa is ensured. Unfortunately, GEM analyses provide no 600-hPa fields. To promote consistency between PV inversions, 600-hPa GEM fields are created: temperature and wind fields are calculated as the average of the 500- and 700hPa fields with respect to the natural logarithm of pressure, while the height field is calculated hypsometrically (Bluestein 1992) using 600-hPa virtual temperatures. Similarly, operational Eta analyses provide fields at 75 and 50 hPa, but not at 70 or 30 hPa. Therefore, ERA-40 fields are used at 70, 50, and 30 hPa when inverting PV with Eta boundary conditions and firstguess fields. It is unlikely that this borrowing of ERA-

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FIG. 13. Shown at 500 hPa for the indicated dates, where “24/12” denotes 1200 UTC 24 Jan 2000 are (a), (c) analyzed rawinsonde heights (6-dam contour interval, with a wider 540-dam contour) with observed heights (dam) and winds [(half) barb equals (2.5) 5 m s⫺1, pennant equals 25 m s⫺1], and (b), (d) ERA-40 heights and winds, plotted using the same conventions.

40 fields at these elevated levels will significantly affect our experiments’ short-term forecasting results. The 32-km horizontal resolution of our extensive domain, which encompasses the region shown in Fig. 2, is

similar or identical to resolutions used by Zupanski et al. (2002), Zhang et al. (2002), Jang et al. (2003), and BL05. The experiments are initialized at 1800 UTC on both 23 and 24 January 2000, which is close to the TCO

TABLE 4. Comparison of the proposed procedure with the method of D99.

Fields Temporal interpolation

Regression Management of ozone data’s weaknesses Vertical mapping

PV inversion

Proposed procedure

D99

Full; 1.125° lat–lon grid Of TCO field using dynamic tropopause winds; Cressman scheme; near start of procedure; unlimited temporal–longitudinal mismatch; unrestricted domain location Not function of latitude; ERA-40 MPV from 400 to 50 hPa; 14-day period Synthesis of ozone-derived MPV troughs and analysis MPV ridges 12 available avg PV profiles; profiles defined for a 10° lat–lon box; level-varying mapping coefficient 6 subdomains; 600–30 hPa

5-day anomaly; 2.5° lat–lon grid Of 3D PV field using pressure-level winds; nearest grid point; near end of procedure; max 3-h temporal–45° longitudinal mismatch; set domains Function of latitude; NCEP MPV from 500 to 50 hPa; 1-month period None 2 available avg PV profiles; profiles are function of latitude; constant mapping coefficient (assumed) Single domain; 1000–50 hPa using NCEP fields below 500 hPa

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DURNFORD ET AL. TABLE 5. Numerical experiments.

Expt name

600⫺30-hPa fields

ERA Ozone/ERA

ERA Ozone-influenced (inverted) Eta Ozone-influenced (inverted) GEM Ozone-influenced (inverted)

Eta Ozone/Eta GEM Ozone/GEM

1000⫺700-hPa fields, moisture at all levels ERA ERA Eta Eta GEM GEM

data’s time of validity over North America. Note that the precipitation started near 1200 UTC 24 January in South Carolina. The simulations end at 1200 UTC 25 January, after which time little precipitation fell in the Carolinas. Precipitation analyses vary widely between articles. Since rain gauge data are suspect for heavy snow events in general (Colle et al. 1999; see also online at http:// www.weather.gov/asos/tipbuck.htm) and the Raleigh– Durham, North Carolina, gauge is known to have underestimated the precipitation by over 65% for this event (BL05), we use the BL05 precipitation analysis for 24–26 January 2000 (Fig. 1; adapted from their Fig. 1) as our truth field. This analysis is based on approximately 240 cooperative observer network liquid water equivalent precipitation observations per day from Virginia, North Carolina, South Carolina, and Georgia (M. Brennan 2006, personal communication). Because the U.S. Unified Precipitation Dataset fields for 1200 UTC 24 January–1200 UTC 25 January and 1200 UTC 25 January–1200 UTC 26 January (not shown) indicate that relatively little precipitation was produced in the Carolinas/Virginia area from 1200 UTC 25 January– 1200 UTC 26 January, the BL05 analysis, which is valid from 1200 UTC 24 January to 1200 UTC 26 January can be considered an excellent approximation for 1200 UTC 24 January to 1200 UTC 25 January. The BL05 analysis of Fig. 1 indicates that the 24–25 January 2000 East Coast snowstorm produced 40 mm of precipitation over approximately half of the Carolinas, with two maxima of 80–90 mm along the border between the two Carolinas and a third similarly valued maximum in South Carolina near the border with Georgia.

b. Modeling results 1) SIMULATIONS INITIALIZED JANUARY 2000

AT

1800 UTC 24

Of the three (re)analyses, the Eta onshore QPF is the worst, being characterized by the lowest onshore pre-

177

cipitation values and, consequently, the lowest overall threat scores and biases (Figs. 14 and 15). Moreover, the Eta onshore precipitation contours are meridional, whereas the lower-valued contours of the BL05 analysis are parallel to the coastline. GEM produced the best onshore QPF of the three nonozone forecasts, exhibiting the highest values, a well-located maximum near the border of the Carolinas, good inland penetration, and the correct contour orientation for contours under 40 mm. These features earned the GEM QPF the highest overall threat scores and biases of the three (re)analyses. The ozone-influenced upper-level initializing fields degrade the ERA onshore QPF, according to both subjective and objective evaluations, owing to the lesser inland penetration of the precipitation region. Objectively, the ozone fields degrade the Eta QPF as well, as a result of diminished North Carolina values. However, these fields also increase South Carolina values. This shifting of the precipitation is extremely important, as it creates an onshore QPF that resembles the analyzed field far more closely in terms of field shape. In consideration of this significant improvement of the QPF shape as well as the increased penetration of the 5-mm contour in the Carolinas, the objective evaluation is overridden and the ozone-influenced upper-level initializing fields are deemed to improve the Eta forecast. The best overall onshore QPF is produced by ozone/ GEM: this forecast shows the deepest inland penetration of the 40-mm contour, and is the only forecast to exhibit a self-contained onshore maximum, which is located almost perfectly across the border of the Carolinas. Consequently, this forecast earns the top threat scores and biases at almost all thresholds (Fig. 15). Unfortunately, the precipitation values of even this forecast are low by approximately 20 mm in North Carolina and even more in South Carolina; the late initializing time and lack of spinup may be partly to blame for the latter problem. Table 6 ranks the simulations’ onshore QPFs. The subjective evaluation of the forecasts overrules the objective rankings, determined by the threat scores, only by placing the ozone/Eta forecast above that of Eta, for the reasons cited above. Compared to published 24-h onshore QPFs ending at 1200 UTC 25 January, the ozone/GEM, GEM, and ERA forecasts far surpass the Buizza and Chessa (2002) deterministic forecast and surpass or are comparable to their ensemble 30% probability of 20 mm of precipitation forecast. Zupanski et al.’s (2002) 3DVAR forecast is surpassed by those of the ozone/GEM, GEM, ERA, and ozone/ERA simulations, while their 4DVAR forecast is surpassed only by those of the two

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FIG. 14. Precipitation [contours at 5 mm and every 10 mm from 10 mm, with the 20-mm contour dashed, the 40-mm contour heavy, and light (dark) shading from 50 (80) mm] accumulated during the indicated experiments from the start of the simulation at 1800 UTC 24 Jan to 1200 UTC 25 Jan 2000 is shown.

GEM experiments. The Jang et al. (2003) simulation that assimilated both radiosonde and TCO data produced their most inland-penetrating precipitation region. This degree of penetration is improved with the ozone/GEM forecast. Furthermore, the ozone/GEM forecast does not exhibit the unwanted North Carolina coastal maximum seen in the Jang et al. (2003) forecast. Thus, our ozone-influenced upper-level initializing

fields produce an onshore QPF that is superior to their ozone-influenced 4DVAR assimilation forecasting of the case, despite the technological superiority of 4DVAR assimilation. Furthermore, the ozone/GEM onshore accumulated precipitation forecast is unambiguously superior to that of GEM, while the Jang et al. (2003) ozone-influenced forecast is only partially better than their control forecast. Unfortunately, none of Fig.

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FIG. 15. Calculated for the indicated experiments and thresholds are the (a) threat scores and (b) bias for the precipitation accumulated from the start of the simulation at 1800 UTC 24 Jan to 1200 UTC 25 Jan 2000. The BL05 analysis constitutes the truth field.

14’s precipitation fields display the heavy South Carolina precipitation region produced by the Jang et al. (2003) control forecast. The Zhang et al. (2002) 30- and 3.3-km forecasts, which are initialized at 0000 UTC 24 January, are inferior to the ozone/GEM and GEM forecasts and comparable to that of ERA. However, the BL05 forecast of precipitation accumulated from 0900 UTC 24 January to 0000 UTC 26 January surpasses all forecasts of Fig. 14: this forecast contains an

TABLE 6. Onshore QPF rankings for simulations initialized at 1800 UTC 24 Jan 2000. Simulation

Ranking

Ozone/GEM GEM ERA Ozone/ERA Ozone/Eta Eta

1 2 3 4 5 6

179

onshore, correctly valued and located 90-mm maximum on the border of the Carolinas, while the collocated ozone/GEM maximum reaches only 60 mm. Note, however, that much of this particular discrepancy may be a result of the later ending time of the BL05 accumulation period, given that, according to the U.S. Unified Precipitation Dataset, over 20 mm of precipitation accumulated in the region of this maximum from 1200 UTC 25 January to 1200 UTC 26 January (not shown). More importantly, the BL05 field exhibits a 40-mm tongue extending from their maximum across South Carolina toward Georgia. Although this represents a 30-mm underprediction, it is missing entirely from the ozone/GEM forecast. Thus, although far from perfect, the two GEM forecasts, particularly the ozone/GEM forecast, are superior to almost all of the published precipitation forecasts. When even the ozone/GEM forecast is surpassed by a published forecast, the most significant difference lies in South Carolina. The ozone/GEM underprediction in this area is likely due to this simulation’s late initialization time of 1800 UTC 24 January, at which point precipitation had already been falling for 6 h in South Carolina. The ozone/GEM forecast earned excellent threat scores ranging from 0.31 to 0.79 for thresholds of 40 mm or less, including 0.59 (0.46) at 20 (30) mm, despite the forecast’s being characterized by biases less than unity (see Fig. 15), which increases the difficulty of earning high threat scores. This forecast’s 20- and 30-mm threat scores far surpass the average day-1 threat score of approximately 0.24 earned by the National Oceanic and Atmospheric Administration (NOAA) Hydrometeorological Prediction Center in 2000 for 24-h forecasts of 1.00 in (25.4 mm) or more of precipitation (Fritsch and Carbone 2004), despite the extreme unpredictability of this event. The exceptional threat scores of the ozone/ GEM forecast, together with the above comparison of Fig. 14’s forecasts to published forecasts demonstrate that ozone-influenced upper-level initializing fields are capable of producing excellent precipitation forecasts. Of particular importance is the superiority of the ozone/GEM QPF over the 4DVAR Jang et al. (2003) ozone-influenced precipitation forecast. The most accurate QPF of this event is that of BL05. Their simulation was initialized by RUC analyses and did not involve ozone data. By 0000 UTC 25 January, the RUC 500-hPa vorticity and height analyses exhibit significant curvature in the trough’s leading edge (their Fig. 8); the conditions that eventually produced this curvature were likely present in the BL05 ICs at 0900 UTC 24 January. Their QPF is, therefore, superior to ours for several reasons: their earlier initializing time

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permits them to forecast the onset of the event, their ICs most likely include the crucial trough-shaping features, and their ICs are free of the errors generated during our procedure. Jang et al. (2003) generated ozone-influenced ICs using a state of the art technique. However, these authors assimilated ozone data that had not yet reacted to diabatic ridge building, resulting in an incorrectly shaped trough. Furthermore, their ozone assimilation, which likely used the 4DVAR equivalent of a constant mapping coefficient, reduced the downward penetration of the upper-level trough, weakening it (their Fig. 9). Thus, their ICs were flawed. Our technique, which excludes ozone-derived ridges via the synthesis and employs a level-varying mapping coefficient, generates more realistic ICs, which produce a superior QPF. In conclusion, while a successful QPF requires an accurately shaped upper-level trough, the source of the data is not important. However, when working with ozone data, the technique used is of critical importance. The fact that a single source (GEM) provides lowlevel and moisture initializing fields for both the best nonozone and the best ozone QPF, while a single source (Eta) is associated with both the worst ozone and nonozone forecasts indicates that the source of the low-level and moisture fields has a greater impact on the quality of the QPF than whether or not ozoneinfluenced upper-level initializing fields are used. Nonetheless, the ability of our ozone-influenced initializing fields, even over the data-rich eastern United States, to improve the QPF for two out of three sources of low-level and moisture fields is impressive. An accurately forecasted sea level pressure cyclone is not a sufficient condition for the production of an accurate onshore QPF for this event: the GEM (secondbest precipitation forecast) cyclone’s location is the worst of all six experiments at 0000 UTC 25 January, and overly weak double cyclones are present at 0600 UTC 25 January (see Fig. 16). These double cyclones also develop in the ozone/GEM (best precipitation forecast) simulation. On the other hand, the Eta (worst precipitation forecast) cyclone’s position and strength are both excellent at 0000 UTC 25 February and 0600 UTC 25 January. Similarly, the two GEM 540-dam troughs in the 1000–500-dam thickness field are the weakest of all, while the Eta trough is one of the deepest, matching the rawinsonde-derived contour well at 0000 UTC 25 January. Note, however, that the southerly extent of the two GEM simulations’ 534-dam contours is comparable to those of the other simulations. The three ozone troughs in both the dynamic tropopause potential temperature field and the 250-hPa height field most resemble each other throughout the

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simulation period (not shown). This suggests that dynamical features at the top of the troposphere, at least during this period, are of slight relevance for the successful forecasting of this event’s onshore precipitation. Note that ozone-influenced 250-hPa initializing winds gained a divergent component within 6 h (not shown). The importance of 500-hPa ascent is indicated by the fact that the onshore accumulated precipitation fields of Fig. 14 correspond closely in shape to the sum of the simulations’ 500-hPa ascent regions (not shown). Given this correspondence, it is not surprising that ozone/ GEM and GEM consistently exhibit the strongest onshore ascent values, with the former’s values usually the stronger of the two (Fig. 17). Compared to the two GEM simulations’ ascent regions, the Eta ascent region exhibits values of half the magnitude at 0000 UTC 25 January (Fig. 17), and penetrates inland far less at 0600 UTC 25 January (not shown). The importance of 500hPa fields in this case, combined with the slight relevance of features at the dynamic tropopause and at 250 hPa, suggests that the features of the greatest dynamical importance at this time were located in a narrow atmospheric layer. The close association between 500-hPa ascent and geostrophic absolute vorticity advection in these simulations indicates that an accurate 500-hPa height field is a prerequisite for the production of this event’s onshore precipitation. Therefore, it is not surprising that ozone/ GEM and GEM have the most accurate 500-hPa height fields; only the two GEM height fields exhibit the distinct curvature observed in the leading edge of the rawinsonde-derived trough (see Figs. 17and 18). The fact that the curved region of the ozone/GEM height field is farther north than that of GEM, though it is still not sufficiently north according to the rawinsonde-derived field, is responsible for its superior QPF. The fact that the shape of the trough’s leading edge is found to be of such dynamical importance agrees with Langland et al. (2002); their region of greatest sensitivity for the 24-h forecast initialized at 1200 UTC 24 January was aligned along the leading edge of the 500-hPa height field trough (their Fig. 7). The superiority of the ozone/GEM 500-hPa fields over those of the other two ozone fields suggests that the GEM PV inversion boundary condition fields, particularly at 700 hPa, exert a positive influence on the ozone/GEM 500-hPa fields. Although, at 0000 UTC 25 January, Eta does produce the desired vorticity advection onshore accompanied by ascent, confirming the fairly high accuracy of the height field (Fig. 17), at 0600 UTC 25 January the Eta ascent region appears to be pushed to the east and north by the overly large cutoff low (not shown). The strength of the Eta initializing trough (not shown), which was the

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FIG. 16. Sea level pressure (solid, 4-hPa contour interval, 1000-hPa contour heavy) and 1000–500-hPa thickness (dot–dashed, 6-dam contour interval with a heavy, solid line for the 540-dam contour) fields are shown for experiments initialized at 1800 UTC 24 Jan 2000. ERA-40 sea level pressure cyclone locations are plotted in gray, with the central pressure value for a given column’s time marked at the top of each column. Also shown, at 0000 UTC 25 Jan 2000, are rawinsonde-derived thickness contours (dashed, 6-dam contour interval with a heavy gray line for the 540-dam contour). Titles indicate the experiment name, and date–time. Note that the date–time varies by column and the experiment by row.

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FIG. 17. For experiments initialized at 1800 UTC 24 Jan 2000: (a)–(f) the 500-hPa ascent (shading intervals at ⫺5 ⫻ 10⫺3 hPa s⫺1 then every 10 ⫻ 10⫺3 hPa s⫺1 from ⫺10 to ⫺70 ⫻ 10⫺3 hPa s⫺1) field and the advection of cyclonic absolute vorticity by the geostrophic winds (positive-valued gray contours every 2 ⫻ 10⫺9 s⫺2), (g)–(l) the 500-hPa height fields (every 1.5 dam from 538.5 to 552 dam, with the 540- and 546-dam contours dashed and the contours between these two values heavy), and (m)–(r), on a more localized domain, 850and 700-hPa equivalent potential temperature difference [4-K interval, positive (negative) values solid (dashed) denoting potential instability (stability), ⫺8- and 0-K contours heavy] and 850-hPa ascent (shading intervals as per at 500 hPa) fields. The heavy gray contours represent the ⫺8- and 0-K rawinsonde-derived temperature difference contours. Titles indicate the experiment name and actual date–time.

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FIG. 18. The rawinsonde-derived 500-hPa height field (every 1.5 dam from 538.5 to 552 dam, with the 540- and 546-dam contours dashed and the contours between these two values heavy) at 0000 UTC 25 Jan 2000.

deepest of the three (re)analyses, likely spawned the problematic cutoff low. The two GEM simulations are initialized with the least midtropospheric potential stability over Georgia and both Carolinas, indicated by 850- and 700-hPa equivalent potential temperature differences that are either zero valued or only slightly negative (not shown). This correlation of onshore QPF quality and initializing potential instability in Georgia supports Zupanski et al.’s (2002) results that the initializing moisture content in Georgia is a crucial factor in determining the quality of the onshore QPF; equivalent potential temperature is proportional to the moisture content. However, 6 h later at 0000 UTC 25 January, while the GEM, compared to rawinsonde-derived values, is overly potentially unstable, ozone/GEM is more often overly potentially stable than unstable (Fig. 17). Furthermore, ERA is also overly potentially unstable at 0000 UTC 25 January (Fig. 17). Thus, while the lesser stability of the two GEM initializing atmospheres will have facilitated the generation of precipitation, it is unlikely that stability was a determining factor in the production of the greater GEM and ozone/GEM precipitation values. Equivalent potential temperatures at 925 hPa reinforce the notion that low-level stability does not distinguish the various simulations. The Eta exhibits the most potentially stable initializing midtropospheric atmosphere (not shown) and remains overly stable at 0000 UTC 25 January (Fig. 17). Because the onshore accumulated precipitation fields, including the significant inland penetration of the ERA 5- and 10-mm contours, are associated strongly with ascent at 500 not 850 hPa (not shown), the fact that both Eta and ERA exhibit a large onshore region of ascent at 850 hPa at 0000 UTC 25 January is

not important (Fig. 17). This finding agrees with Kleist and Morgan’s (2005) determination that the onshore precipitation was associated with ascent at upper levels. While GEM, ozone/GEM, and Eta all duplicate the observed temperature profile at CHS (Charleston, South Carolina) at 0000 UTC 25 January admirably, apart from the surface-level cool layer (see Fig. 19), none of these simulations captures the extent of the observed potential instability, indicated by the dry layer shown in Fig. 19a above 700 hPa over a moist layer, and confirmed by the equivalent potential temperature profiles shown in Fig. 19b. The two GEM simulations exhibit a deep layer (700–400 hPa) of basically neutral potential stability (Fig. 19b), with ongoing static destabilization of the atmosphere indicated by cold advection from 700 to 400 hPa overlying warm advection (Fig. 19a), which destabilization is confirmed by the observed winds. Cold (warm) advection is signified by the counterclockwise (clockwise) rotation of the winds with increasing height. Perhaps most importantly, the two GEM simulations exhibit the strongest onshore moisture transport from 1000 to 775 hPa (Fig. 19b). The Eta simulation is characterized by potential instability from 600 to 500 hPa, but it lacks cold advection from 700 to 400 hPa, and its moisture transport is insufficiently onshore. Note that the ozone/GEM static destabilization and onshore moisture transport are both stronger than those of GEM.

2) SIMULATIONS INITIALIZED JANUARY 2000

AT

1800 UTC 23

All six forecasts of precipitation accumulated from 1200 UTC 24 January to 1200 UTC 25 Janury during the experiments initialized at 1800 UTC 23 January 2000 are extremely poor, in that onshore precipitation values are either very low or nonexistent (not shown). Low threat scores and biases confirm this subjective assessment (not shown). The three ozone forecasts’ scores are the worst of all, owing to the almost uniform nonexistence of onshore precipitation; ozone/Eta earns zero-valued threat scores and biases. The ERA forecast, by virtue of its inland penetration, earns the best scores overall, followed by that of GEM. Ozone and nonozone QPFs are ordered identically; for both groups, the ERA forecast is the best followed by the GEM forecast. This indicates that the source of the low-level, moisture, and PV inversion boundary condition fields strongly influences the precipitation forecasts. Given the strong association found between the onshore 500-hPa ascent and precipitation fields in the simulations initialized at 1800 UTC 24 January (later simulations), and given the lack of onshore 500-hPa

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FIG. 19. Shown at CHS (Charleston, SC) at 0000 UTC 25 Jan 2000 for simulations initialized at 1800 UTC 24 Jan 2000, and as observed are (a) a skew T–logp plot of temperature (°C, solid) and dewpoint temperature (°C, dashed) with the 300-, 325- and 350-K moist adiabats, along with horizontal winds [(half) barb equals (2.5) 5 m s⫺1, pennant equals 25 m s⫺1], and (b) a logp vs temperature plot of equivalent potential temperatures (K), along with moisture transport vectors (cm s⫺1), where the length of the 1000-hPa Eta moisture transport vector represents 12.3 cm s⫺1.

ascent produced by the simulations initialized at 1800 UTC 23 January (earlier simulations; see Fig. 20), it is not surprising that the earlier simulations produced minimal, if any, onshore precipitation. What is perhaps more interesting is that 500-hPa ascent is strongly as-

sociated with geostrophic absolute cyclonic vorticity advection in the later but not earlier simulations (see Figs. 17 and 20). Even the three ozone simulations, which generate no onshore precipitation, exhibit onshore geostrophic absolute cyclonic vorticity advection. This sug-

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FIG. 20. For experiments initialized at 1800 UTC 23 Jan 2000: (a)–(f) ascent and advection of cyclonic absolute vorticity by geostrophic winds at 500 hPa, (g)–(l) height fields at 500 hPa, and (m)–(r) 850- and 700-hPa equivalent potential temperature difference and 850-hPa ascent fields (plotted as in Fig. 17).

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gests that static stability is greater in the earlier simulations. This notion is reinforced by the lack of 850-hPa onshore ascent (Fig. 20). Indeed, the three ozone experiments tend to be characterized by a greater midtropospheric potential stability at 1800 UTC 24 January than their respective pairs (not shown), while, at 0000 UTC 25 January, only the two Eta simulations are overly potentially unstable onshore compared to rawinsonde-derived values (Fig. 20). The lesser ozone 500-hPa vorticity advection, which is likely responsible for the degradation of the QPFs, is partly a consequence of the weakness of the ozone 500hPa height field troughs. This weakness can be traced back to the TCO field of 23 January. Its origin has not been investigated. It is possible that the ozone field did not react sufficiently quickly to trough-deepening diabatic cooling. It is also possible that a midstratospheric southward extrusion of ozone-poor air from the polar vortex reduced TCO values in the area. Considering the depth of the TCO trough only 24 h later, at a latitude unaffected by polar vortex extrusions, the latter explanation seems more likely. Unfortunately, given the poor performance of all six experiments, the simulations initialized at 1800 UTC 23 January are unable to indicate with any precision the length of lead time that ozone-influenced initializing fields are capable of providing; the poor performance of the ozone experiments is not linked to errors in the upper-level initializing fields alone. The fact that the ozone QPFs were not significantly worse than the nonozone QPFs suggests that the ozone fields should be capable of providing some lead time for other events.

6. Discussion and conclusions a. Limitations of the proposed method Analyses are employed in the temporal interpolation and regression of the TCO field, the synthesizing of the MPV fields, and the generation of average PV profiles. Analyses also provide PV inversion boundary condition and first-guess fields. Thus, the accuracy of our process is limited by the accuracy of the analyses used. However, if our procedure were used operationally to generate an ensemble member, such as ozone/GEM, every other member might incorporate identical analysis errors; the ozone-influenced member, being strongly influenced by independent data, might, in fact, be the most accurate member of all. Given that our vertical mapping system employs average PV profiles, it will never be able to reproduce observed details and will always, therefore, represent a source of error. However, it seems likely that the de-

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gree of smoothing induced by PV inversion poses a stronger limit on the accuracy of the overall procedure. The exaggeration of upper-tropospheric/lower-stratospheric features during the vertical mapping was introduced in order to mitigate the impact of this smoothing. Inaccurate TCO values most likely constitute our procedure’s greatest source of error. Such values occur mainly in ridge areas, according to a subjective comparison of TCO and ERA-40 MPV fields. The errors seem to be caused primarily by the inability of the ozone field to respond quickly to the elevating of the tropopause during diabatic ridge building. Our synthesizing process was devised to eliminate this source of error. We have demonstrated that this process can improve the accuracy of the ozone-influenced MPV field greatly. Unfortunately, ozone-influenced ridges that are not undergoing diabatic heating are also erased during the synthesizing process; these ridges may be more accurate than the analysis ridges. Furthermore, the overlaying of an inaccurately located analysis ridge may partially erase a correctly located ozone-derived MPV trough. If this is found to occur frequently, the MPV ridge bounding value could simply be decreased.

b. Potential uses of the proposed method The presented procedure can be used as described to generate an ensemble member, such as ozone/GEM. An ozone-influenced member would be fairly independent of the operational data assimilation system. The weighting for this member could be adjustable; when numerical forecasts vary substantially, either between models or initializing times, indicating IC errors, its weighting could be augmented. Specific processes from our procedure could be adapted individually for the variational assimilation of TCO data. Our temporal interpolation scheme could be used in 3DVAR systems. Both 3DVAR and 4DVAR assimilation schemes could adopt our experimentally determined regression parameters. The synthesizing process and our level-varying vertical mapping coefficient could also be adapted for variational assimilation. The 4DVAR assimilation of TCO for 1800 UTC 24 January 2000 by Jang et al. (2003) strengthens the eastern seaboard trough’s PV distribution above 350 hPa while weakening its distribution from 400 to 460 hPa (their Fig. 9). It seems highly likely that this lessening of the downward penetration of the upper-level trough is a result of the use of the 4DVAR equivalent of a constant mapping coefficient. It is possible that our levelvarying coefficient could also be useful during the variational assimilation of other 2D satellite fields or single-level data. Furthermore, Jang et al. (2003) as-

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similated TCO data indiscriminately; they included observations from the overly weak Atlantic ridge and the unwanted Atlantic extension of the eastern seaboard trough. I strongly suspect that if these authors had adapted our level-varying coefficient and our synthesizing process to their assimilation system, their ozoneinfluenced precipitation forecast would have improved.

PV inversion program. The NCAR scientific computing division provided the streamfunction-calculating program. Marco Carrera supplied the operational Eta analyses and forecasts. I appreciate the reviewers’ suggestions, which greatly improved this manuscript.

c. Conclusions

Allaart, M. A. F., H. Kelder, and L. C. Heijboer, 1993: On the relation between ozone and potential vorticity. Geophys. Res. Lett., 20, 811–814. Allen, D. R., and N. Nakamura, 2002: Dynamical reconstruction of the record low column ozone over Europe on 30 November 1999. Geophys. Res. Lett., 29, 1362, doi:10.1029/ 2002GL014935. Barsby, J., and R. D. Diab, 1995: Total ozone and synoptic weather relationships over Southern Africa and surrounding oceans. J. Geophys. Res., 100, 3023–3032. Beekman, M., G. Ancellet, and G. Mégie, 1994: Climatology of tropospheric ozone in southern Europe and its relation to potential vorticity. J. Geophys. Res., 99, 12 841–12 853. Benoit, R., M. Desgagné, P. Pellerin, S. Pellerin, Y. Chartier, and S. Desjardins, 1997: The Canadian MC2: A semi-Lagrangian, semi-implicit wideband atmospheric model suited for finescale process studies and simulation. Mon. Wea. Rev., 125, 2382–2415. Black, T. L., 1994: The new NMC mesoscale Eta model: Description and forecast examples. Wea. Forecasting, 9, 265–278. Bluestein, H. B., 1992: Synoptic-Dynamic Meteorology in Midlatitudes. Vol. I, Principles of Kinematics and Dynamics, Oxford University Press, 421 pp. ——, 1993: Synoptic-Dynamic Meteorology in Midlatitudes. Vol. II, Observations and Theory of Weather Systems, Oxford University Press, 584 pp. Bosart, L. F., 1990: Degradation of the North American radiosonde network. Wea. Forecasting, 5, 527–528. Bowman, K. P., and A. J. Krueger, 1985: A global climatology of total ozone from the Nimbus 7 Total Ozone Mapping Spectrometer. J. Geophys. Res., 90, 7967–7976. Brennan, M. J., and G. M. Lackmann, 2005: The influence of incipient latent heat release on the precipitation distribution of the 24–25 January 2000 U.S. east coast cyclone. Mon. Wea. Rev., 133, 1913–1937. Buehner, M., 2002: Assimilation of ERS-2 scatterometer winds using the Canadian 3D-Var. Atmos.–Ocean, 40, 361–376. Buizza, R., and P. Chessa, 2002: Prediction of the U.S. storm of 24–26 January 2000 with the ECMWF ensemble prediction system. Mon. Wea. Rev., 130, 1531–1551. Colle, B. A., K. J. Westrick, and C. F. Mass, 1999: Evaluation of MM5 and Eta-10 precipitation forecasts over the Pacific Northwest during the cool season. Wea. Forecasting, 14, 137– 154. Côté, J., S. Gravel, A. Méthot, A. Patoine, M. Roch, and A. Staniforth, 1998: The operational CMC-MRB Global Environmental Multiscale (GEM) model. Part I: Design considerations and formulation. Mon. Wea. Rev., 126, 1373–1395. Cressman, G., 1959: An operational objective analysis system. Mon. Wea. Rev., 87, 367–374. Danielsen, E. F., 1968: Stratospheric-tropospheric exchange based on radioactivity, ozone and potential vorticity. J. Atmos. Sci., 25, 502–518. ——, 1983: Ozone transport. Ozone in the Free Atmosphere, R. C.

We have presented a methodology for generating NWP model ICs from satellite TCO data. Our methodology contains many important innovations. It can be used to generate an ensemble member that is fairly independent of operational analyses. Alternatively, many of the techniques developed can be adapted for the variational assimilation of TCO. Ozone-influenced initializing fields improved the QPF in two out of our three experiments. Furthermore, our best QPF, which utilized these fields, is surpassed by only one published forecast of the same event; it is superior to an ozone-influenced 4DVAR forecast. The performance of our initializing fields is impressive, given that the event was located over the data-rich eastern United States. We hope that our ozone-influenced upper-level initializing fields will be useful to operational forecast centers, particularly in association with weather systems originating in data-sparse areas. However, before using our methodology operationally, it should be tested on more cases; the regression scheme may be slightly case dependent, while the level-varying vertical mapping coefficient’s values and the synthesizing bounding values may need to be refined. Simulating multiple events would also help to clarify the lead time that ozoneinfluenced initializing fields are capable of providing. Furthermore, although our synthesizing process is an important tool, it should optimally be replaced by an initial correction of TCO values. Such a correction would be based on a knowledge of how these data actually respond to diabatic heating and how they should respond in order to preserve the TCO–MPV correlation. Acknowledgments. Funding for the lead author’s Ph.D. work, on which this article is based, was provided by the Natural Sciences and Engineering Research Council of Canada; the Cooperative Program for Operational Meteorology, Education and Training; the Canadian Foundation for Climate and Atmospheric Sciences; and Environment Canada. Environment Canada’s Recherche en Prévision Numérique made available their IBM supercomputers, the MC2 model, and associated software. Rick Danielson provided the

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