1. Introduction
Carbone et al. (2002) identified a coherence of warm-season, continental precipitation on time- and space scales greatly exceeding those of individual convective systems, yet not associated with traveling synoptic-scale disturbances in any obvious way. The zonal translation of synoptic-scale disturbances appears distinct from the propagation of convective episodes in time–longitude (Hovmöller) diagrams of rainfall. During the height of the warm season, the respective phase speeds characterizing synoptic-scale motions slow to a mere 3 m s−1, whereas the convective episodes maintain a characteristic phase speed of nearly 14 m s−1.
Carbone et al. (2002) also noted that convective episodes leave a fundamental signature on the overall diurnal cycle of warm-season rainfall. In general, an axis of propagation is apparent from roughly the Continental Divide (about 105°W) to about 90°W longitude in a diurnally averaged time–longitude “echo” frequency diagram (Fig. 1). Shown is the frequency of meridionally averaged rainfall exceeding 0.1 mm within strips 0.2° longitude wide, spanning from 30° to 48°N latitude. This propagation creates a phase-lagged diurnal signal over the Plains states (105°–95°W), with a nocturnal rainfall maximum (note that 0000 UTC is 1900 LST over much of the region of interest). Near 90°W, a semidiurnal signal is evident, with rainfall occurring in the early evening and just after sunrise. In some months, the propagating signal extends over two and sometimes three diurnal cycles. Given the mean phase speed of about 14 m s−1, these recurring episodes span more than 2000 km and are therefore nearly continental in scale.
The observed coherence of rainfall is indicative of some, yet unquantified, element of enhanced predictability of warm-season rainfall. Because of the extremely low skill of dynamically based deterministic predictions of warm-season rainfall (Olson et al. 1995), the promise of enhanced predictability is most welcome. The observations force us to consider whether the poor skill of warm-season rainfall prediction by numerical models is related to their inability to capture the basic climatology of warm-season rainfall. We will present strong evidence that this is indeed the case (section 3). Furthermore, we present strong evidence that cumulus parameterizations contribute substantially to errors in the statistics of predicted rainfall. We will also show that models exhibit considerably more skill in predicting the latitude of rainfall than the longitude, which is tantamount to predicting the “corridors” of rainfall coherence but not the propagation that defines the coherence. This result suggests that a combination of observed rainfall statistics containing propagation information with NWP predictions will offer a significant improvement in warm-season rainfall prediction.
2. Data and methods
As we are primarily concerned with precipitation prediction, the data used in this study are 3-hourly accumulated precipitation derived from the National Centers for Environmental Prediction (NCEP) stage-IV analyses (Fulton et al. 1998) and corresponding 3-hourly accumulations from two NWP models, the operational NCEP Eta Model (Black 1994) and the Weather Research and Forecast (WRF) model (Michalakes et al. 2001). Data were obtained for periods during the warm seasons of 2001 (July–August) and 2002 (June–July). These two periods represent equal samples featuring markedly different continental-scale patterns of rainfall and therefore offer an opportunity to evaluate the applicability of our findings in different regimes.
The stage-IV data are a combination of radar [Weather Surveillance Radar-1988 Doppler (WSR-88D)] and rain gauge precipitation estimates analyzed to a 4-km mesh covering the continental United States (CONUS), available with hourly time resolution. Three-hourly accumulations of precipitation were used herein. The stage-IV data were nearly complete during the periods of interest. We performed no formal quality control of the dataset; however, because of the averaging performed (see below), localized, sporadic errors are tolerable. Errors involving lack of radar coverage or missing radars in regions without adequate rain gauge coverage will tend to result in an underestimate of rainfall. Because of the inherent difficulties in obtaining rainfall rates from radars, and the potential unrepresentativeness of gauges, we will emphasize spatial–temporal patterns of rainfall instead of amounts.
Output from the NCEP Eta Model was received on a 40-km grid containing forecasts initialized daily at 0000 and 1200 UTC. The forecasts extended to 48 h at 3-h increments. The Eta Model was run on a 22-km grid covering the CONUS in 2001 and on a 12-km grid during the warm season of 2002. The physics in the Eta Model, while evolving somewhat between years, consisted of the Betts–Miller–Janjic cumulus parameterization and a Mellor–Yamada closure for the planetary boundary layer (Janjic 1994). During the warm season of 2001, the cloud physics was treated using the scheme described in Zhao and Carr (1997). In this scheme, only cloud mixing ratio was predicted; precipitation hydrometeors were diagnosed. In November 2001, the NCEP Grid-Scale Cloud and Precipitation Scheme of 2001 (NGCP01) was introduced, in which mixing ratios of rainwater and cloud ice were added to the prognostic variables (Ferrier et al. 2002).
The WRF model was run twice daily over the CONUS with a 22-km grid spacing, initialized at 0000 and 1200 UTC from the Eta 00-h forecast obtained from NCEP on a 40-km domain. In 2001, the WRF model consisted of a nonhydrostatic height-coordinate dynamical core and employed a version of the Betts–Miller–Janjic cumulus scheme similar to that used in the Eta Model. In addition, the Medium-Range Forecast (MRF) model planetary boundary layer scheme (Hong and Pan 1996) and a two-category cloud microphysics scheme were integrated. This latter scheme consisted of only a single prognostic equation for hydrometeors (rain at temperatures greater than 0°C and snow at lower temperatures) and another equation for cloud water (T > 0°C) and cloud ice (T < 0°C). In 2002, the WRF model integrated a mass-coordinate dynamical core and employed the Kain–Fritsch cumulus parameterization (Kain and Fritsch 1993) and a five-category cloud microphysics scheme consisting of two categories of cloud particles (water and ice crystals, assumed to have zero fall speed) and three categories of hydrometeors (rain, snow, and graupel).
Both Hovmöller and diurnally averaged time–longitude echo frequency diagrams (hereafter referred to as time–longitude frequency diagrams) were constructed for the periods July–August 2001 and June–July 2002 using the 3-hourly precipitation data from the stage-IV analyses, and WRF and Eta Model output. June 2001 was excluded from our sample because the WRF model physics changed substantially between June and July 2001, in addition to changes implemented to correct coding errors. August 2002 was not included because of numerous forecasts missing from the WRF model during the period. All datasets were interpolated or averaged to identical grids of 10-km spacing. WRF (22- and 10-km grids) and Eta forecasts (archived on a 40-km grid) were remapped using bilinear interpolation. Stage-IV data were remapped from a 4-km grid to the 10-km grid by averaging all 4-km grid cells that fully or partially overlapped a given 10-km grid cell. Model forecasts were separated into 0000 and 1200 UTC initializations. Only forecasts initialized at 0000 UTC will be presented. The 2-month period from each year was spanned by a contiguous string of 12–36-h forecasts spanning each 24-h period 1200–1200 UTC. While there were some differences obtained using forecasts from 1200 UTC, or different 24-h segments of forecasts initialized at 0000 UTC (such as 24–48-h forecasts), all of the principal conclusions presented herein are invariant to such permutations. Note that we avoided using 0–24-h forecasts because errors resulting from model adjustments over the first few hours of integration left notable signatures on the rainfall statistics. This problem has been widely recognized within the NWP community for some time and will therefore not be further discussed herein.
3. Propagation and diurnal aspects of rainfall in NWP models
a. 2001
We begin by showing a comparison between observed and WRF depictions of time–longitude diagrams of rainfall for 2001 (Fig. 2). Propagating rainfall signals are evident in the WRF model and in the stage-IV precipitation data. The period shown, late August 2001, reveals numerous coherent rain streaks spanning 1000–2000 km. While plenty of pointwise inconsistencies can be noted, streaks of comparable duration and speed are evident in the WRF forecasts as well as in the observations. The diurnal cycle of rainfall is clearly evident in both the stage-IV and WRF forecasts. The WRF model also accurately identifies particularly active periods of convection (e.g., 9–19 August). This example is representative of several, broadly similar periods of active convection during 2001 and 2002. The propagating aspects of convection are evident in the observations despite the use of 3-hourly data, and the character of the rain streaks is qualitatively similar to those presented in Carbone et al. (2002).
Despite the presence of what look to be realistic diurnal and propagating signals in the predicted rainfall (Fig. 2), averaging by time of day to produce time–longitude frequency diagrams reveals some striking forecast errors (cf. Figs. 3 and 4). These diagrams are constructed in a manner similar to that described in Carbone et al. (2002). Specifically, we averaged 3-h rainfall within strips of 0.1° longitudinal width extending from 30° to 45°N latitude. An event was designated as average rainfall within a strip exceeding 0.1 mm in 3 h. Figure 4 shows the percentage occurrence of rainfall exceeding this threshold as a function of longitude and time within the diurnal cycle.
For July–August 2001, we find the following errors:
Neither model correctly predicts the timing or longitude of most frequent diurnal rainfall. The WRF model maintains a maximum between 90° and 95°W, with a maximum frequency occurring at about 1800 UTC, 3 h earlier than observed. The Eta Model maintains its diurnal frequency maximum around 1500 UTC, with a small diurnal amplitude over the eastern part of the domain.
Neither model captures the primary propagation axis between about 105° and 90°W. The frequency of nocturnal precipitation, probably in the form of elevated convection, is poorly predicted by both models.
The reader may be wondering why the seemingly ubiquitous rain streaks produced by the WRF, seen in Fig. 2b, are absent from the time–longitude frequency diagram. One reason is that many of the apparent streaks were nonpropagating and occurred at a nearly fixed universal time across a wide range of longitude. However, there were periods, such as the latter half of July 2001, during which numerous propagating streaks were predicted with phase speeds that at least qualitatively agreed with observations. To examine how the propagating signal was eroded from the longtime average, we computed a series of time–longitude frequency diagrams for increasing averaging periods ranging from 1 to 17 days. As the averaging time increased, the propagating component of the rainfall decorrelated rapidly such that by the time the averaging interval exceeded about 7–11 days, the time–longitude frequency diagram strongly resembled the 2-month climatology (Fig. 5). Thus, even when rain streaks were present in the forecasts, they were not phase locked to the diurnal cycle as in the real atmosphere (Carbone et al. 2002).
Notable errors in the diurnal cycle of precipitation were found in regional climate models by Dai et al. (1999). Apparently, such first-order errors are also a property of at least some mesoscale models performing short-range forecasts. The large spatial and temporal errors of the diurnal cycle of precipitation suggest that large-scale circulations, such as the mountain–plains solenoid (MPS), may be poorly handled. Limitations in the parameterization of deep convection are probably a key to the poor performance. In 2001, both models utilized the Betts–Miller–Janjic cumulus parameterization, which is designed mainly for large-scale models. In traditional applications of this scheme, downdrafts are weak. This could imply that one key to correctly predicting the propagation of convection across the Plains states is a realistic incorporation of downdraft physics.
The WRF forecasts integrated on a 10-km grid1 using a Kain–Fritsch parameterization of deep convection (Kain and Fritsch 1993) exhibit behavior similar to that of the forecasts on the 22-km grid (Fig. 6). Little evidence of nocturnal, propagating rainfall exists. The diurnal maximum occurs at about the same time and longitude as forecasts using coarser grid spacing and is therefore too early and too far west relative to the observations. Overall, our results are qualitatively invariant with respect to horizontal grid spacing and choice of cumulus parameterization. However, we have not explored systematically the use of cloud-resolving grid spacing (4 km or less).
Examination of time–latitude diagrams reveals a somewhat different picture of model performance. Figure 7 shows time–latitude diagrams for August 2001 from stage IV and the WRF model. Slow meandering of rainfall areas is characteristic of time–latitude diagrams, with the varability corresponding mainly to the diurnal cycle and the movement of synoptic-scale fronts. From inspection of Fig. 7, one may infer that WRF has considerable skill in predicting the latitude of rainfall. However, it is difficult to judge directly from Hovmöller diagrams whether the model better predicts the latitude or longitude of rainfall (cf. Figs. 2 and 7).
As with any two-dimensional depiction of rainfall, it is possible to construct an equitable threat score (ETS). Given time and latitude as the two dimensions, we computed the ETS for the rainfall in Figs. 2 and 7 exceeding 0.1 mm in 3 h. We obtained a score of about 0.25 for the longitudinal Hovmöller and about 0.31 for the latitudinal Hovmöller rainfall fields for July–August 2001, implying that the WRF model more skillfully predicted the latitude of rainfall than the longitude of rainfall during this period.
Perhaps a more insightful measure of relative skill is obtained by examining the distribution of errors in rainfall location, conveniently represented by the distribution of errors in predicting the median latitude or longitude of rainfall. Here, the median is the location dividing an equal number of points with rainfall greater than 0.1 mm on either side (in latitude or longitude). As in the Hovmöller diagrams, rainfall is averaged within either meridionally or zonally elongated strips, as defined earlier for time–longitude and time–latitude diagrams, respectively. We display the distribution of errors in the prediction of median rainfall position from the WRF model for July–August 2001 in Fig. 8. For time–longitude diagrams, there was a systematic and significant difference in behavior between forecasts valid for daytime (1200–0000 UTC) versus nighttime (0000–1200 UTC). Hence, we group our statistics accordingly. Forecasts verifying between 1200 and 0000 UTC (daytime) had a median rainfall that was consistently too far west. Modeling the distribution as a Gaussian and applying the Student's t test yielded a confidence of 95% for rejecting the null hypothesis that the mean is not significantly different from zero. The opposite was true for forecasts verifying between 0000 and 1200 UTC (nighttime), wherein the predicted longitude was systematically too far east. Again, the mean was significantly different from zero with greater than 95% confidence.
Following 0000 UTC, the forecast errors were characterized by a poorly predicted evening initiation of eastward-propagating rainfall. By virtue of missing initiation over the western portion of our domain (105°–85°W), the forecast acquired an eastward bias in rainfall location during the night. As the observed convection propagated eastward of 95°W (the center of our domain) around 12 UTC, and the model failed to capture the ensuing suppression of High Plains rainfall during the morning and early afternoon, the WRF model acquired a westward bias.
Concerning time–latitude diagrams, we note that there is no statistically significant bias in latitude. Moreover, the standard deviation of the distribution of errors is notably smaller than for the distribution of longitude errors for forecasts verifying between 0000 and 1200 UTC. Our conclusion is therefore that, at least for forecasts verifying at night, the WRF model better forecast the latitude of rainfall than the longitude of rainfall. This is essentially equivalent to the statement that the WRF model predicted the corridors within which rainfall coherence occurred but did not forecast the coherence itself. The most probable reason for the superior prediction of the latitude of rainfall versus the longitude is that the latitudinal axis of rainfall was often determined by the location of synoptic-scale features such as frontal zones, and these are more likely zonally oriented (that is, elongated west to east) than meridionally oriented during the warm season. To the extent that the east–west elongated frontal zones are quasi-stationary, even daily persistence will produce a skillful forecast.
b. 2002
The 2002 warm season offered a notable departure from 2001 and, more generally, from the previous 5 yr of rainfall over the central United States, especially during the months of June and July. A persistent, zonally elongated upper-tropospheric anticyclone formed in June 2002, confining the westerlies to the northernmost states in the Midwest and Plains and allowing the easterlies to expand northward to nearly 35°N (not shown). The result of this anomalous pattern of precipitation is evident in Fig. 9, in which the time–latitude frequency diagrams for July–August 2001 and for June–July 2002 are shown. The averaging was performed between 105° and 85°W. The axis of rainfall in 2002 was shifted poleward by nearly 6° latitude, relative to its axis in 2001. In addition, there was a hint of southward propagation of the nocturnal rainfall in 2001 and slightly poleward propagation in 2002. In 2002, nocturnal rainfall dominated the rainfall frequency poleward of 40°N. Immediately to the south of 40°N, rainfall frequency was suppressed, with a maximum during the late afternoon. Farther south, the amplitude of the diurnal cycle of rainfall frequency increased, again with most rainfall most commonly occurring in the late afternoon.
Comparison of the time–longitude frequency diagrams from stage-IV analyses, the Eta Model, and the WRF model during June–July 2002 is shown in Fig. 10. Because 40°N approximately divides two distinct regimes in the observations, we separate the time–longitude frequency diagrams into precipitation data averaged between 40° and 48°N, and between 30° and 40°N (Fig. 10).
In general, the diurnal cycle was better in the WRF and Eta Models as compared with the 2001 warm season. However, south of 40°N and approaching 85°W, the event frequency amplitude of the diurnal cycle in the Eta Model diminished to less than half of what is observed. On the other hand, the WRF model exhibited a diurnal cycle with very nearly the correct phase and amplitude east of 100°W. Between 100° and 105°W, the WRF and Eta Models underestimated the morning suppression of rainfall.
Poleward of 40°N, nocturnal convection dominated, but both models maintained their greatest frequency of convection in the late afternoon. There was a propagating axis of rainfall emanating from around 104°W in the observations that was completely missed by both models. This axis was less pronounced than in 2001. The climatology also differs from 2001 in that a second, apparently separate, region of nocturnal convection was centered between 90° and 95°W. There was little evidence of propagation in this region. The nocturnal rainfall in the Eta Model was displaced about 3° to the east of what was observed, whereas the WRF model placed its nocturnal region more accurately. The diurnal cycle eastward of about 90°W and poleward of 40°N was poorly handled by both models.
It is not immediately clear why the propagation characteristics of rainfall varied so greatly between 2001 and 2002. One factor may be that the terrain (defined by, say, the 1000-m elevation line) is north–south–oriented south of about 41°N but slopes westward with increasing latitude to the north. To the extent that the phase of propagating convection is tied to orography, we might expect a less-clear signal of eastward propagation where the orography departs radically from a north–south alignment. Regardless, the numerical models considered here are unable to replicate the nocturnal convection.
4. Interpretation
The causes for the large errors in NWP model representation of the diurnal and propagating characteristics of warm-season rainfall are as yet unquantified. In this section we advance some possibilities.
The errors pervade a range of horizontal grid spacing and choices of physics in models. It may be that higher-resolution forecasts improve model performance by making models less reliant upon implicit precipitation schemes that have questionable relevance. Treatment of downdrafts and the resulting cold-pool dynamics is often poor in models with grid spacing of 10 km or more.
To illustrate the nature of errors introduced by cumulus parameterizations, we performed a simple set of idealized simulations with the WRF model in two dimensions, initialized within a horizontally homogeneous environment characterized by a single sounding. The sounding (Fig. 11) was adapted from a composite sounding ahead of mesoscale convective systems, modified to reduce convective inhibition. The convective available potential energy (CAPE) experienced by a hypothetically lifted air parcel characterized by potential temperature and water vapor averaged over the lowest 50 hPa was 2800 J kg−1, and the convective inhibition was 25 J kg−1. The wind profile featured easterlies of 10 m s−1 at the surface, linearly sheared to zero velocity at 3 km AGL and maintained at zero velocity above. Convection was initiated using a semi-infinite cold pool with a maximum buoyancy deficit of 5 K at the surface, linearly decaying to zero at 2.5 km AGL.
All simulations were performed using the five-category ice physics scheme configured nearly identically to that used in the real-time forecasts made during 2002. The reference simulation was performed on a 1-km grid, with 50 levels, spaced 300 m apart near the ground, and stretched gradually to a spacing of about 1.8 km near the lid placed at about 23.3 km. A second simulation, initialized with the same cold-pool,2 environmental sounding and on the same vertical grid, was integrated on a 12-km horizontal grid with the addition of the Kain–Fritsch cumulus parameterization. In both simulations, the Coriolis parameter was set to zero.
To compare these simulations, Hovmöller diagrams of hourly rainfall were created. Output from the 1-km simulation was spatially averaged over 12-km intervals and placed on the identical grid as the coarser-resolution simulation. The reference simulation produced a quasi-steady, leading-line, trailing stratiform squall line that moved at about 7 m s−1 relative to the wind at 3 km AGL (which was zero) (Fig. 12a). This speed agrees well with the 8 m s−1 propagation speed of rain streaks (relative to the 700-hPa wind) estimated by Carbone et al. (2002).
Convection in the coarse-mesh simulation required over 2 h to organize, moved less than 1 m s−1 relative to the steering flow, and did not attain the upshear-tilted structure characteristic of the system in the cloud-resolving simulation. We also performed an analogous 12-km-mesh simulation using the Betts–Miller–Janjic scheme. An even weaker convective system resulted, and again, little propagation was discernable (not shown). This simple comparison strongly implicates currently used cumulus parameterizations as an important contributor to the poor model performance described earlier. For instance, it may explain the relative inability of convection to move rapidly eastward from its origin near the Continental Divide. Furthermore, it may explain the excessive temporal width of many of the predicted longitudinally extensive features seen in Fig. 2. A lack of propagation would tend to extend existing precipitation features too far in time at a given longitude. Simulations of a multiday convective episode over the central United States by Moncrieff and Liu (2003), using resolved and parameterized convection in two and three dimensions, respectively, in “real data” situations are consistent with our idealized simulations. They show a dominance of nonpropagating rainfall systems during a 10-day period in July 1998, when the real atmosphere was dominated by long, rapidly propagating rain streaks.
There are other potential errors in NWP models that could contribute to the poor reproduction of observed rainfall statistics. Although the diurnal cycles of temperature and moisture may appear adequate locally in these models, there is some question as to whether the larger-scale diurnally forced topographic circulations, such as the MPS, and their interaction with deep convection (Tripoli and Cotton 1989) are well represented. Baldwin et al. (2002) demonstrated that the NCEP Eta Model, using the Betts–Miller–Janjic scheme, tends to remove capping inversions because of its shallow mixing parameterization, causing convection to develop too early in the day (recall Figs. 3 and 10). The problem may be particularly pronounced over the Great Plains where the subsidence branch of the MPS tends to create an inversion that inhibits convection during the daytime. It is possible that excessive mixing removes this inversion and allows convection to trigger too early, thus preventing the correct diurnal and propagating rainfall. Errors in the time of initiation of organized convection may result in the inability of forecasts to correctly phase lock the rainfall in the diurnal cycle (Fig. 5) and hence hinder the development of a coherent propagating signal in time–longitude frequency diagrams, as is observed (Fig. 3).
Another potential source of systematic error is the coupling between the surface and boundary layer, especially the rainfall–surface water vapor exchange feedbacks that modulate regional rainfall distributions. Both the WRF and Eta Models used a similar derivative of the Oregon State University land surface model (Pan and Mahrt 1987; Chen and Dudhia 2001) and hence could be prone to similar errors. However, because the Eta data assimilation system (EDAS) incorporates observed precipitation (Lin et al. 1998), it is unlikely that the associated errors in forcing soil moisture changes are large enough or accumulate rapidly enough to alter the prediction of rainfall in a short-range forecast.
It is possible that other components of the modeling system are partially to blame for the poor performance. For example, because the WRF model was initialized using Eta Model initial conditions, deficiencies in the analysis of moisture, for instance, could affect the ability of each model to correctly simulate the timing of convection. To address this issue, it would be necessary to look at the results of other initialization techniques or examine other modeling systems. Even that, however, will be insufficient if there are significant initial errors introduced owing to a lack of observations.
5. Conclusions
We have examined the macroscopic aspects of warm-season rainfall forecasts from the NCEP Eta Model and the WRF model, concentrating on diurnal and propagating characteristics of precipitation. Apart from the western United States, the diurnal cycle of rainfall in both models is poorly represented, especially in regimes characterized by nocturnal convection over the central United States and the Appalachian Mountains. We have noted a marked tendency for rainfall to occur too early in the day over the central and eastern United States in the Eta Model, sometimes almost exactly out of phase with the observed diurnal cycle. While some improvement may be inferred in 2002 over areas with a strong diurnal cycle and an afternoon peak in convection, the failure to capture nocturnal convection occurs in both models and with different physical parameterizations in each model.
Using simplified two-dimensional simulations with the WRF model, we have shown that shortcomings of shallow and deep cumulus parameterizations produce errors consistent with the apparent inability of the NWP models examined herein to represent the propagation of warm-season rainfall. Further investigation of the statistics of cloud-resolving models, especially in three dimensions, is required to address whether the improvement in propagation afforded by using cloud-resolving grids will substantially improve rainfall statistics.
We found that even in periods when forecasts exhibited realistically propagating rainfall features, the lack of phase locking of rain streak initiation to diurnal and orographic forcing prevented the appearance of propagation in diurnally averaged statistics. We believe that the lack of phase locking is related to shortcomings in the prediction of the mountain–plains solenoid, boundary layer evolution, and convective triggering.
There are some potentially significant implications of our results. Because the gross statistics of rainfall are poorly represented in state-of-the-art NWP models, one must question the current partitioning of effort in NWP that emphasizes model and data assimilation enhancements designed for short-term, location-specific prediction with only an indirect consideration of model “climatology.” It would seem that a concerted effort to improve the statistics of rainfall representation in short-range NWP models could begin the realization of some of the apparent predictability inferred by Carbone et al. (2002). This effort must begin by a deeper probing of the mechanisms of observed rainfall coherence and further delineation of salient dynamics or physical processes missing from NWP models. Detailed diagnosis and comparison of kinematic and thermodynamic fields in models and observations is an obvious next step in better understanding the cause of the systematic prediction errors described herein.
Because models are currently deficient, a blending of rainfall propagation statistics and NWP model prediction might be highly beneficial for improving short-range rainfall prediction. We have shown that the WRF model is more adept at predicting the latitude of rainfall than the longitude. To a first approximation this amounts to predicting the corridors along which rainfall is coherent, but not the coherence itself. Perhaps the most straightforward combination of model and statistics lies in the calibration of ensemble forecasts from NWP models using the probability of rain-streak span and duration derived from observations. Beyond this, it is conceivable that semiempirical, probabilistic forecasts could be derived purely from the observations or in combination with numerically based probabilistic forecasts. Work is currently underway in this area and will be reported in a future article.
Acknowledgments
The authors would like to thank James Bresch and Wei Wang of NCAR for performing the WRF forecasts, Sherrie Fredrick of NCAR for assistance with graphics of the idealized WRF simulations, and David Ahijevych and Mitchell Moncrieff of NCAR, David Stensrud of NSSL, and an anonymous reviewer for their comments on the manuscript. This research was sponsored by National Science Foundation support to the U.S. Weather Research Program.
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Time–longitude rainfall frequency diagram, averaged over four warm seasons (1997–2000). Shown is the number of occurrences of meridionally averaged (30°–48°N) estimated rainfall exceeding 0.1 mm h−1 within latitudinal strips of 0.2° longitude width [adapted from Carbone et al. (2002)]
Citation: Monthly Weather Review 131, 11; 10.1175/1520-0493(2003)131<2667:COWCRI>2.0.CO;2
Time–longitude diagrams of meridionally averaged (30°–48°N), 3-h rainfall within strips of 0.1° longitude width. Light shading denotes rainfall greater than 0.16 mm; dark shading denotes rainfall greater than 0.64 mm. Data are from Aug 2001
Citation: Monthly Weather Review 131, 11; 10.1175/1520-0493(2003)131<2667:COWCRI>2.0.CO;2
Time–longitude rainfall frequency diagram for Jul–Aug 2001 using 3-h stage-IV data averaged meridionally within strips of 0.1° longitude width between 30° and 48°N. The diurnal cycle is repeated
Citation: Monthly Weather Review 131, 11; 10.1175/1520-0493(2003)131<2667:COWCRI>2.0.CO;2
Same as Fig. 3, but for (a) Eta and (b) WRF forecasts initialized at 0000 UTC during Jul–Aug 2001
Citation: Monthly Weather Review 131, 11; 10.1175/1520-0493(2003)131<2667:COWCRI>2.0.CO;2
(a) Hovmöller diagram for 20–23 Jul 2001; (b) diurnal frequency diagram for 20–23 Jul 2001; (c) Hovmöller diagram for 18–25 Jul 2001; and (d) diurnal frequency diagram for 18–25 Jul 2001
Citation: Monthly Weather Review 131, 11; 10.1175/1520-0493(2003)131<2667:COWCRI>2.0.CO;2
Diurnal time–longitude diagrams for (a) observed and (b) simulated rainfall echo frequency from WRF forecasts on a 10-km, sub-CONUS grid
Citation: Monthly Weather Review 131, 11; 10.1175/1520-0493(2003)131<2667:COWCRI>2.0.CO;2
Same as Fig. 2, but a time–latitude diagram. Rainfall is averaged from 105° to 85°W within strips of 0.1° latitude width
Citation: Monthly Weather Review 131, 11; 10.1175/1520-0493(2003)131<2667:COWCRI>2.0.CO;2
Histograms of errors in (a) median longitude and (b) median latitude of rainfall, computed from longitudinal and latitudinal Hovmöller diagrams, respectively. The abscissas have been scaled so that physical distances are comparable
Citation: Monthly Weather Review 131, 11; 10.1175/1520-0493(2003)131<2667:COWCRI>2.0.CO;2
Diurnally averaged time–latitude rainfall frequency diagrams derived from stage-IV data for (a) Jul–Aug 2001 and (b) Jun–Jul 2002
Citation: Monthly Weather Review 131, 11; 10.1175/1520-0493(2003)131<2667:COWCRI>2.0.CO;2
Same as Fig. 3, but for (a) stage-IV analyses, (b) Eta, and (c) WRF diurnally averaged rainfall frequency diagrams, meridionally averaged from 40° to 48°N. (d), (e), (f) Same as (a), (b), (c), except the averaging is from 30° to 40°N
Citation: Monthly Weather Review 131, 11; 10.1175/1520-0493(2003)131<2667:COWCRI>2.0.CO;2
Skew-T–logp representation of thermodynamic sounding used to initialize idealized, 2D WRF simulations. Heavy dashed line represents hypothetically lifted surface parcel
Citation: Monthly Weather Review 131, 11; 10.1175/1520-0493(2003)131<2667:COWCRI>2.0.CO;2
Hovmöller diagrams of hourly rainfall from idealized, 2D WRF simulations. (a) Simulation on a 1-km grid, averaged to a 12-km grid. (b) A simulation performed on a 12-km grid using a Kain–Fritsch cumulus parameterization. Light gray, medium gray, and dark gray shadings represent 1, 12, and 36 mm, respectively. The heavy, solid line in (b) marks the approximate axis of maximum rainfall in (a)
Citation: Monthly Weather Review 131, 11; 10.1175/1520-0493(2003)131<2667:COWCRI>2.0.CO;2
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The 10-km domain extended from roughly 32° to 45°N and 110° to 90°W. Hovmöller diagrams created from output on this domain contain rainfall averaged from 32° to 45°N. Stage-IV precipitation data were likewise averaged from 32° to 45°N for the comparison shown in Fig. 5.
Because the initial cold pool abruptly decayed to zero across one grid box, the discrete gradient depends on the grid spacing. However, the adjustment of the cold-pool structure to the model grid occurs on a much shorter timescale than the initiation of convection.
