The skill associated with
warm season rainfall predictions is low, both by absolute standards
and relative to predictions of cool season precipitation (Olson
et al., 1995). Our main purpose is to report the existence
of coherent warm season precipitation patterns that are continental
in scale and exhibit durations well in excess of typical mesoscale
convective lifecycles. We refer to the coherent rainfall
patterns as "episodes" to draw a distinction between
the largest and longest duration events and individual convective
systems. The time/space coherence of precipitation patterns
is suggestive of a heretofore unrecognized intrinsic predictability
associated with warm season rainfall. Herein, we provide
a basic statistical description of precipitation episodes for
the warm seasons 1997-2000, as derived from continent-scale analyses
of WSR-88D radar data at 2 km horizontal resolution.
We have not attempted a dynamical diagnosis of the
coherent precipitation patterns, though we discuss some candidate
mechanisms in light of the observations. Provided the causes
for rainfall coherence can be described dynamically and adequately
represented in models, an improved basis for specific predictions
at 6 to 48 h range can be established. Furthermore, statistical-dynamical
techniques may be developed for time scales up to seasonal when
associated with quasi-stationary forcings such as orography and
the North American monsoon circulation. Subsequent publications
will delve into the dynamical and predictability issues by various
means, including observationally-based case studies, idealized
simulations, and experimental numerical predictions.
Since we exhibit only a small fraction of the time
series discussed herein, a companion Technical Note (Ahijevych
et al., 2001) has been compiled and is now available from the
National Center for Atmospheric Research. A website, containing
all of the charts and links or instructions for access to base
data, is maintained here.
Several studies have focused on regional-scale forcings
of warm season precipitation over the continental United States.
Palmen and Newton (1969) describe a pronounced nocturnal maximum
and afternoon minimum in thunderstorm frequency from Texas to
Minnesota and attributed this, in part, to eastward movement of
squall lines from formation regions in the Rocky Mountains. Wallace
(1975) identified systematic diurnal variations in precipitation
and thunderstorm frequency using conventional hourly data.
Boundary layer convergence was attributed to at least three mechanisms,
including sea/land breezes; heating over sloped terrain (Holton,
1967; Lettau,1967); and changes in frictional drag associated
with diurnal variation of static stability (Blackadar, 1957).
Wallace concluded that the central U.S. nocturnal maximum in convective
activity was a direct consequence of the combined effects of heating
over sloped terrain and changes in frictional drag. This
was considered especially significant in the southern Great Plains
under SW flow and was associated with the low-level jet (Bonner,
1968). More recently, Dai et al.(1999) analyzed diurnal
variations in precipitation, surface pressure and static energy
over the U.S. from observations and a regional climate model.
They found that the solar-driven diurnal and semi-diurnal cycles
of surface pressure result in large scale convergence over most
of the western U.S. during the day and east of the Rockies at
night, thereby suppressing daytime convection and favoring nocturnal
convection east of the Rockies.
The extent to which warm season precipitation is
intrinsically predictable is limited by the non linear and chaotic
nature of convective storms. To some extent, the degree
of predictability is dependent upon the longevity of coherent
rainfall events. Apart from hurricanes, the longest reported
duration of organized convective systems is associated with mesoscale
convective complexes, MCCs (e.g. Maddox, 1980, 1983; Velasco and
Fritsch, 1987; Miller and Fritsch, 1991; Laing and Frisch, 1997;
Laing and Fritsch, 2000). As defined by satellite imagery-based
criteria, MCCs have average lifetimes of 8 to 12 h in the Americas,
China, Africa and Australia. Most of these systems originate
in the lee of steep topography; have an equatorward source of
moist static energy; and produce most of their precipitation at
night. Often these regions have distinct flow regime characteristics
such as a low level jet, a strong humidity gradient zone, and
a quasi-stationary front, all of which are common to central North
America. In addition, MCCs often initiate equatorward of
an upper level jet under divergent flow aloft (Uccellini
and Johnson, 1979).
The propagation of rainfall areas is intimately
linked to the maintenance of deep convection and the longevity
of mesoscale systems. Traveling convection may be influenced
by ambient tropospheric winds, vertical wind shear, negative buoyancy
production (in the lower troposphere) and positive buoyancy production
(in the middle/upper troposphere). In weakly-sheared environments
and in deep westerly shear at mid-latitudes, individual convective
storms tend to travel with "steering level" winds near
70 kPa (e.g. Ligda and Mayhew, 1954; Houze, 1993).
In jet-type profiles, where the direction of the vertical shear
vector reverses, mesoscale convective systems tend to travel in
the direction of the jet, and move at a speed slightly in excess
of the jet maximum. This is particularly common in the tropical
easterlies where a jet often exists near 70 kPa (e.g. Barnes and
Sieckman, 1984; Keenan and Carbone, 1992).
Mechanisms governing the sustained motion of organized
convective systems may be essentially external or internal to
a moist mesoscale circulation. Internal mechanisms include
shear-balanced gravity current propagation (e.g. Thorpe
et al., 1982; Rotunno et al., 1988); excitation of trapped gravity
waves in the nocturnal boundary layer (e.g. Crook, 1988; Raymond
and Rotunno, 1989; Carbone et al., 1990; Crook et al., 1990; Koch
et al., 1991); and propagating gravity waves produced by the convective
heating aloft (e.g. Moncrieff and Miller, 1976; Raymond, 1984;
Raymond, 1986; Lin and Li, 1988; Tripoli and Cotton, 1989).
Any of these mechanisms offer potential explanation for convective
system propagation rates that may exceed ambient winds.
At mid-latitudes, especially in spring and early
summer, convection is often associated with baroclinic waves,
extra-tropical cyclones and fronts. The propagation of such
"strongly-forced" systems should be consistent with
the (external) phase speed of synoptic forcing. This phase
relationship to synoptic scale features, while often investigated
with respect to genesis of individual convective systems,
has not been systematically examined with respect to the lifecycle
of coherent convective rainfall episodes.
Coherent regeneration of rainfall systems is yet
another aspect of rainfall episodes, especially when such episodes
exceed the duration of individual convective systems. Regeneration
is often associated with drylines, colliding mesoscale "boundaries"
(Wilson and Schreiber, 1986), gravity currents, bores, solitary
waves, and other forms of trapped gravity waves (Carbone et al.,
1990; Crook et al. 1990). Koch and O’Handley (1997)
identified mesoscale gravity waves in unbalanced flow at the synoptic
scale as a regeneration mechanism. Recent investigations
have firmly established the significant role of mesoscale convective
vortices (MCVs) in convective regeneration (Fritsch.et al., 1994;
Trier et al., 2000a; Trier et al., 2000b and Davis et al., 2001).
Our strategy is to apply very simple treatments
to massive quantities of data over a continent-scale domain. The
analyses are based exclusively upon U.S. National Weather Service
and related operational data. We have acquired a warm season
time series (1997-2000) from the WSR-88D (NEXRAD) Doppler
radar network, Geostationary Operational Earth Satellite (GOES)
rapid scans (1998-2000), all analyses and observations available
via NOAA's Family of Services, National Centers for Environmental
Prediction (NCEP) 2.5° Daily Data, and UHF wind profiler data
from the NOAA profiler network.
The focal point of this paper is examination of
WSR-88D national composite data from 1997 to 2000. While
WSR-88D data are limited in their capacity to represent local
rainfall rates or cumulative rainfall amounts (e.g. Klazura et
al., 1999), these are satisfactory to identify practically all
areas that experience precipitation east of the continental divide.
While observational gaps exist west of the divide, the fractional
area of coverage is sufficiently large to permit detection and
tracking of major mesoscale events. We examine these data
with respect to space/time coherency given the tacit assumption
that coherency provides clues as to the spatial and temporal scales
of intrinsic predictability. A smoothly varying continuum
of precipitation in time-space infers potential for developing
predictive skill, however, this property alone might prove to
Section 2 describes properties of the data, procedures
associated with calculations, and the presentation of quantities
derived from these calculations. Section 3 provides examples
of coherent rainfall regimes by means of Hovmoller (mainly time-longitude)
diagrams. The emphasis is on intra-seasonal and regional
variations over the four-season period of record. Section
4 examines the periodicity of rainfall within and beyond the diurnal
cycle. Section 5 provides probability density functions
of rainfall episodes and statistics related to the their translation
and propagation. Section 6 discusses the potential relevance of
various mechanisms governing the forcing, maintenance, propagation,
and regeneration of convection and their relationship to some
newly recognized characteristics.
We define the "warm season" as May through
August and we have compiled data for seasons 1997 through 2000.
All statistics presented herein encompass the computational domain
(Fig. 1) for these 16 months. Our principal focus is the
exploitation of information from a WSI Corporation NOWradTM
(national composite) product that has benefited from three levels
of quality control. Products such as NOWradTM,
while inadequate for some research purposes, have been the only
practical vehicle for access to complete spatial and temporal
coverage at high horizontal resolution within the WSR-88D network.
The properties of this NOWradTM product include
a ~2 km latitude/longitude grid with 15 min. resolution and 16
levels of radar reflectivity factor data (10 log Ze
(mm6 m-3)) at 5 dBZe intervals.
The precise algorithm for creating this composite is information
proprietary to WSI Corporation. It is commonly described
as the maximum value of dBZe as measured by any WSR-88D
radar at any height in a vertical column.
Figure 1. Computational domain for
radar-rainrate Hovmoller diagrams. For clarity, subdivisions
are shown with 1° vertical strips whereas, in actuality, there
are 740 strips of width 0.05° (~4 km). Diurnal echo
frequency diagrams use a similar domain with a western boundary
at 110 W.
The sensitivity of WSR-88D is high, equivalent to
rainfall rates < 0.1 mm h-1. Signals this
weak may not always represent water mass that reaches the ground
and some of the weak signals can originate from insects, seeds
and birds. A more serious problem for quantitative use of
these data is the error that results from quantization, which
corresponds to a factor of two in rainfall rate. It is well
known that reflectivity-rainfall rate (Z-R) relationships are
locally uncertain on several accounts, including the fact that
equilibrium drop-size distributions are uncommon within mid-latitude
convection (e.g. Carbone and Nelson, 1978). Given these
and other considerations, the averaged "rainfall rates"
illustrated in Section 3 should be viewed in relative terms, i.e.,
to indicate locally light or heavy rainfall, amplification and
Time-distance plots (often referred to as "Hovmoller
diagrams") are commonly used for the diagnosis of coherent
signals in climate science (e.g. Nakazawa, 1988). Carbone
et al. (1998), Knupp et al. (1998), and Wilson et al. (2001) have
recently applied this tool at the mesoscale to study the lifecycle
of precipitation systems using Doppler radar data. The standard
approach is to apply a power-law transformation, Ze
= aRb, in order to linearize the signal with respect
to rainfall rate where 1.2 < b < 1.8. The coefficient,
a, is typically 150-400 where rainfall rate, R, is expressed in
mm h-1. Herein, we have set the coefficients
a = 300 and b = 1.5 since these values render a relatively small
net bias in the global average when compared to national analyses
of rainfall (Klazura et al., 1999). While local biases may
exceed a factor of two, the reader should be mindful that rainfall
estimation per se is peripheral to our application.
Most of our diagrams exhibit longitude as the distance
dimension, since this is the principal direction of precipitation
system motion over North America. Figure 1 is the domain
of computation (~3300 by 1800 km). The 1° longitude
vertical columns are symbolic of meridional averaging intervals,
which are actually 0.05° (~4 km) wide. The estimated
rainfall rate is arithmetically averaged over each column (~1800
We have performed various calculations from the
Hovmoller diagrams for the purpose of quantifying event coherency,
longevity, zonal distance (hereinafter referred to as "span")
and the zonal component of propagation. Two-dimensional
autocorrelation functions are fit to the rainfall data in Hovmoller
space (Fig. 2). The function is rectangular in one
dimension and cosine-weighted in the other. For a given
time/longitude position, the 2-D function is rotated until the
correlation is maximized. The function is stepped through
all time/longitude positions (at 15 min./0.2° intervals).
Sequences of contiguous "fits" define the coherent span,
duration and propagation characteristics for each rain streak.
The rainfall rate threshold to initiate a fit is 0.1 mm h-1
and a correlation coefficient of 0.3 is required for the fit to
become part of the statistics. For the purpose of propagation
statistics, the rectangular pulse is long (~12°) in
order to have a stable measure of sustained movement of order
1000 km. For the purpose of span/duration statistics,
this dimension is relatively short (~3°), consistent
with the size of individual mesoscale convective systems, and
also able to exceed the correlation threshold when centered close
to the beginning and end of a rain streak. The cosine-weighting
in both applications (Fig. 2) is matched to ~3 h rainfall duration
at a given longitude, which is characteristic of the larger systems.
Figure 2. Sample radar-rainrate
Hovmoller diagram with autocorrelation fits superimposed (selected
for clarity). A cosine-rectangular weighting function (illustrated
in c)) is rotated in time-longitude space until it is maximized
along the axes shown. a) autocorrelations for phase speed;
b) autocorrelations for span and duration.
Most major episodes continuously produce at least
some detectable precipitation throughout the episode duration.
However, some events exhibit intermittency while retaining full
phase coherence. For example, if an eastward propagating
squall line dissipates and its remnant cold pool/gust front initiates
an MCS 100 km downstream, these systems, in effect, are classified
as causally-related and statistically recorded as one long duration
event (i.e., an episode). Such statistical determinations
are made objectively by means of phase coherence autocorrelation
and then manually checked for validity by inspection of animated
composites of radar data in two spatial dimensions. Subjectively
determined corrections, which take the form of disconnects and
reconnects of precipitation entities, occur in approximately 2%
of all cases.
A set of averaged Hovmoller diagrams has been created
to examine the phase-locked behavior of precipitation echo at
diurnal and higher frequencies. Every radar echo above ~10
dBZe constitutes an "event" at a given longitude/time
coordinate. The cumulative event frequency has been averaged
for monthly and seasonal periods permitting the elucidation of
regional, intra-seasonal and inter-seasonal variations.
In this section we present a few examples of coherent
rainfall patterns from the 1997-2000 period of record with emphasis
on a qualitative depiction of intra-seasonal variations.
The vehicle for this presentation is the radar-rainrate Hovmoller
diagram, within which organized rainfall systems appear as time-longitude
"streaks" of estimated rainfall rate.
The effects of synoptic scale modulation are most
pronounced in spring as illustrated in May 1999 (Fig. 3).
The longitude interval is 115-78W and average rainfall rates are
given in mm h-1. Sloping rain streaks are indicative
of propagating rainfall regions somewhere within the latitudinal
span of the domain (Fig. 1). The individual streaks represent
the zonal component of motion (typically 10-25 m s-1).
Streaks usually correspond to some form of organized convection
such as a squall line or a MCS. Characteristic dimensions
of the larger rain streaks are of order 1000 km and 20 h.
Figure 3. Radar-rainrate Hovmoller
diagram for the period (a) 1-15 May 1999, (b) 16-30 May 1999.
Note the slow eastward propagation of precipitation "envelopes"
in (a), within which there are faster propagating "rain streaks".
The shaded, elliptical area denotes one such "envelope."
In (b) there are mixed regimes including a more obvious component
of diurnal modulation late in the period.
The first half of May (Fig. 3a) exhibits well-defined
longitudinal limits of rainfall activity on any given day.
Between these limits, an "envelope" of activity is defined
and this propagates eastward over a period of days at a relatively
slow phase speed (~5 m s-1). One example of this is
highlighted by an ellipse on Fig. 3 from 9-15 May. Such
"envelopes" of rainfall activity are phase-coincident
with baroclinic waves in the westerlies as determined from examination
of National Centers for Environmental Prediction (NCEP) daily
2.5° analyses (e.g. Fig. 4). Phase-consistency with
strong synoptic forcing is observed in springtime, however, the
broader data set reveals significant insensitivity to transient
synoptic disturbances in the westerlies.
Figure 4. Hovmoller diagram of NCEP
2.5° data depicting anomalies of meridional wind for the period
1 through 9 May 1999, corresponding to most of Fig. 3a.
The anomaly phase speed is essentially identical to the precipitation
The second half of May 1999 (Fig. 3b) exhibits features
more consistent with the broader data set. Successive days
exhibit significant rainfall from the east slope of the continental
divide (~105 W) to the eastern domain boundary. Longitudinal
coherency and intermittency are also evident. In late May
(e.g. 29-30), one begins to observe non-propagating horizontal
structures across a broad longitudinal band, (~100 to 85 W).
As will become evident from subsequent figures, these structures
are associated with a diurnal maximum of "ordinary"
convection, typically between 1800 and 0000 UTC.
The first week of June 1997 (Fig. 5a, upper) illustrates
weakly-propagating and non-propagating convection across relatively
narrow spans of longitude. Genesis zones are initially evident
in the east and west and subsequently in the eastern Mississippi
valley (90 W). Precipitation episodes propagate no more
than 700 km during the first week of June 1997, a statistic quite
uncharacteristic of the broader period of record.
Figure 5. As in Figs. 3 for the
period 31 May 1997 through 29 June 1997. See text for explanation.
The remaining three weeks of June 1997 (Figs. 5a
lower and 5b) are more broadly representative of the mid-summer
condition in two aspects. Many rainfall streaks originate
near 105 W (east slope of the continental divide) and some of
these extend 1000 to 2000 km eastward. Propagation rates
vary from 10 to 20 m s-1. Non-propagating diurnal
convection, in phase with cumulative solar heating, is prominent
in the last week of June. Strongly propagating convection
occurs almost daily and coherency of the rain streaks is
sometimes maintained from the Rockies to the Appalachians.
Several amplifications and dissipations may occur along one continuous
streak together with a smoothly varying phase speed (slope).
For every continent-scale event of 20-40 h duration, there are
numerous shorter streaks, broadly consistent with the lifecycle
of MCSs (4-10 h). There are periods of 1 to 3 days duration
circa 85W (e.g. 20-22 June) that are indicative of quasi-stationary
forcing over orography in the southeastern United States.
July 1998 is archetypal of the mid-summer condition
(Figs. 6a, b). This period is often coincident in time with
an active North American monsoon circulation, which is known for
convection over the western cordillera and heavy rains in the
desert southwest. Propagating convection occurs
daily east of the continental divide. The major events span a
sizeable fraction of the continent. Non-propagating convection
can occur almost anywhere; is generally in phase with cumulative
diurnal heating; and is the dominant mode of convection west of
the continental divide. Westward-propagating convection occurs
intermittently (e.g. 17-23 July) and is mainly associated with
deep easterlies over the desert southwest. Variability in
the pattern of precipitation is associated with the amount of
convection west of 106 W; the suppression of propagating systems
from 16 to 18 July; and the degree to which enhanced rainfall
occurs over the eastern cordillera (e.g. 20-30 July).
Figure 6. As in Figs. 3 for the
period 30 June 1998 through 29 July 1998. See text for explanation.
Perhaps the signal of greatest significance in Figs.
6 is the widespread distribution of convective activity and the
dominance of diurnal forcing. This condition is consistent
with low skill in the dynamical prediction of convective precipitation.
Numerical weather predictions (via their data assimilation systems)
are based on the dynamical foundation of quasi-balanced flow and
synoptic scale forcing, the zonal variance of which may be secondary
for extended periods in summer when thermal forcing can prevail.
There is a propensity for nature to exploit widespread conditional
instability over the continent in mid summer.
In association with Figs. 6, we bring the reader’s
attention to a class of westward-propagating events that can evolve
from eastward-propagating systems with some regularity (e.g. 10-11,
15-16, 20-21 July). Westward propagation is slow (2 to 6
m s-1) and often associated with zonally oriented convective
lines that have a simultaneous southward component of motion (see
complete data set in Ahijevych et al. (2001) or the companion
The first half of August 1998 (Fig. 7a) has several
features in common with July including: non-propagating convection
associated with cumulative diurnal heating; essentially non-propagating
convection over the western cordillera; and coherent rain streaks
east of the continental divide. However, two aspects of
Fig. 7a differ significantly from July. Eastward-propagating
structures are markedly less coherent and highly intermittent.
Upon review of two-dimensional radar and satellite images, some
of the intermittent streaks are subjectively judged to be causally
related to each other (e.g. thin streaks in the 3-5 August period)
whereas others provide no indication of a dynamical relationship
(e.g. heavy streaks in the 12-14 August period).
From 2 to 11 August 1998, the strongest mid-summer synoptic
modulation is observed.
Figure 7. As in Figs. 3 for the
period 30 July 1998 through 28 August 1998. See text for explanation.
The second half of August 1998 (Fig. 7b) exhibits
frequent convective events across the continent; however, these
are both weaker and smaller in scale compared to the events in
July. The diurnal signal, while evident, is not as well
developed. Propagation distances, directions, and speeds,
while highly variable, are relatively small. Transcontinental
streaks, indicative of rapid propagation (30 m s-1),
reappear for the first time since June (e.g. 24 August).
The preceding charts have dealt exclusively with
the longitudinal distribution of rainfall and the zonal component
of motion. Propagation is less evident and spans shorter
distances in the meridional dimension (Ahijevych et al., 2001).
Figures 8a and b provide two examples of latitudinal rainfall
distribution and motion over the same computational domain. The
averaging of rainfall is performed in constant-latitude strips
Figure 8. Radar-rainrate Hovmoller
diagram, orthogonal to previous figures, in the meridional dimension.
(a) for the period 15 - 29 June 1998; (b) for the period 15-29
July 1999. While numerous coherent streaks are evident,
shorter distances and slower propagation speeds are indicated.
Note the low frequency oscillation in (a) around 40 N where convection
is most strongly forced. This pattern is much less evident
in (b) where diurnal variability and equatorward propagation prevail.
June 15-29 1998 (Fig. 8a) illustrates one common
pattern where a slow oscillation of 7-10 days defines the preferred
latitude band for strong convection. The convection is focused
within latitude bands and generally does not propagate far to
the north or south. Southward propagation (e.g. 19-20 June)
is preferred by the heavier rainfall systems. Slowly varying
latitudinal bands associated with quasi-stationary fronts are
easily diagnosed by numerical prediction systems and the forecasts
of heavy warm season rainfall often rely on the identification
of strong forcing at fronts such as these.
Figure 8b (15-29 July 1999) illustrates a less orderly
and, perhaps, less predictable condition. There is a preferred
latitudinal band for some of the heaviest rainfall events.
However, in this case, convection is latitudinally widespread
and rainfall systems occur in regions that are well removed from
any preferred forcing zone.
Figure 9. Regional Hovmoller computational
domain across southern tier of states. A leading-line, trailing
stratiform mesoscale convective system is present at 0700 UTC,
27 May 1998.
Figure 10. Radar-rainrate Hovmoller
diagram for 27-29 May 1998 in the southern region. Note
sudden changes in slope, coincident with (a) the MCS in Fig. 9;
(b) precipitation associated with a convectively generated mesoscale
convective vortex (MCV); (c) small squalls that are initiated
within the MCV but rapidly propagate eastward from it.
The 27-29 May 1998 episode (Fig. 9) originated under
upslope flow in northern New Mexico together with dryline and
cold pool initiations of convection in west Texas (~102-104W,
35-38N). Figure 9 shows a MCS over Texas at 0700 UTC on
27 May within a regional Hovmoller domain that extends from New
Mexico to the panhandle of Florida (105 to 85 W, respectively).
Figure 10 illustrates three phases of the episode. The first
phase is associated with the leading-line/trailing-stratiform
MCS depicted in Fig. 9, which propagated in a manner consistent
with cold pool dynamics (e.g. Rotunno et al., 1988) at 17-19 m
s-1. As the MCS dissipates, it spawns a mesoscale
convective vortex (Trier, et al., 2000a). This vortex (centered
at ~50-60 kPA) drifted slowly eastward with the 70 kPA winds (~4
m s-1) and was the principal forcing mechanism for
regeneration of convection (Trier et al., 2000a) on 28 May.
This period is marked by a steep slope in Fig. 10, when the rain
streak phase speed was only 2-3 m s-1. The vortex
dynamics and a stable nocturnal boundary layer (during most of
this period) apparently prevented organization of convection into
faster moving squalls. The mesoscale convective vortex weakened
on 29 May and descended to the lower troposphere. On the
southern and eastern flanks of the vortex, several small squall
lines developed and propagated eastward at 14-18 m s-1.
While the details of forcing and initiation are not well understood,
causal relationships among these successive events are evident.
The result is a continuum of rainfall events from New Mexico to
the panhandle of Florida.
Figure 11. Example of the "monsoon
regime": Left column is sequence of enhanced IR GOES images
over North America from (top) 1800 24 July 1998 through 1200 26
July 1998 (bottom). Center column is sequence of NOWrad
images at the same times. Right column, matched in time
to the GOES and radar images, is an expanded view of Fig. 6b for
the period indicated. Note the consistent continent-scale
A second example of complex coherence is associated
with the North American monsoon (Fig. 11); wherein southerly flow
from Mexico transports low- and mid-level moisture over the western
cordillera (e.g. Higgins et al., 1997). Exhibited are two
days in the midst of such a period when rainfall episodes over
the central continent had their origin over the east slope of
the Rockies (cf. Fig. 6b). The left hand column shows GOES
infrared imagery of North America and the center column shows
the corresponding NOWradTM images. The
coldest infrared cloud tops are dark blue and purple, nominally
corresponding to tropopause heights. Cold cloud tops proliferate
over the western cordillera at approximately 00 UTC on each day
in response to cumulative diurnal heating. What follows
is the eastward and southeastward propagation of one (or more)
cold cloud shields across the continent during nocturnal hours.
The convective systems underlying these cloud shields evolve into
less erect forms of convection and persist into the following
day. The Hovmoller representation of these events is depicted
in the right hand column, where the (vertical) center of each
GOES and radar image is at the time shown on the Hovmoller diagram
to its right. The evolution of propagating cold cloud tops
shows evidence of dissipation and regeneration of convection over
the two-day lifecycle of these episodes.
We employ two methods to examine the periodicity
and phase of rainfall. The first method examines coherent
structures associated with average radar echo-frequency within
the diurnal cycle. Hovmoller diagrams of radar echo-frequency
are averaged over months, seasons, and the entire period of record.
The second method performs discrete Fourier Transforms (DFTs)
along the time dimension of echo-frequency diagrams to isolate
signals in the power spectra that are associated with diurnal
and shorter periods of oscillation. A complete set of echo
frequency diagrams and DFT analyses are found on our website and
in Ahijevych et al. (2001).
We have counted the fraction of time that radar
echo is present at each longitude-time coordinate with 0.2°
and 1.0 h resolutions. Coherent patterns of average echo
frequency in this coordinate system can represent a "phase-locked"
occurrence of rainfall events. For example, diurnally modulated
convection over fixed heat sources (such as mountains) would fit
the phase-locked description in a local sense. Furthermore,
if such convection consistently propagates from the fixed source
region in a preferred direction and at a preferred speed, then
it may be referred to as phase-locked in a global sense.
Our focus herein is on the global aspects of phase-locked behavior
and also to further quantify the effects of diurnal and semi-diurnal
Figure 12. Diurnal echo-frequency
Hovmoller diagram for the entire period of record (1997-2000).
The diurnal cycle is repeated twice for clarity across the UTC
day boundary. The scale corresponds to the percentage of
days during which precipitation echo is present at the given longitude-UTC
hour coordinate. Four principal signals are evident including:
the diurnal oscillation, propagation from the western cordillera,
a semi-diurnal signal between the cordilleras (dashed lines),
and suppression of the in-phase diurnal maximum near 98-99 W (white
Figure 12, an average of warm seasons 1997-2000,
illustrates the diurnal cycle in a "back-to-back" format,
meaning the same data are repeated along the time axis to capture
features that span more than one UTC day. A value of 60
means that radar echo is detected at that coordinate (longitude,
UTC-hour) on ~60% of all days. Several features are plainly
evident in this echo climatology:
- A diurnal oscillation across the continent (maximum circa
- A maximum amplitude diurnal cycle associated with the Rockies
- A semi-diurnal maximum between the cordilleras (circa 1100
UTC, 98-86 W)
- Eastward propagation of a frequency maximum from the Rockies
- Suppression of the "in-phase" diurnal maximum near
- An apparent "rain shadow" east of longitude 82 W
The diurnal maximum between 2000 UTC and 0100 UTC
is plainly evident across the continent except near longitude
98-99 W where it is suppressed (Fig. 12, white arrow).
The most frequent "origin" of rainfall in the west is
at 105.5 W (circa 2100 UTC), which coincides with the eastern
most position of the continental divide (40 N). Thermal forcing
over the Rockies, when combined with deep westerly shear, favors
a solenoidal circulation to the east of the mountains (e.g. Wallace,
1975; Dai et al., 1999). The daytime upward branch over
the mountains and high plains is mass-compensated, primarily by
a descending branch to the east. This regional condition
suppresses a substantial fraction of afternoon convection circa
98-99 W, especially during the period of the North American monsoon
(Higgins et al., 1997). The implied rate of propagation
between 105 W and 94 W is 16 m s-1, considerably faster
than typical "steering level" winds (e.g. 70 kPa).
Despite the very high frequency of "echo origination"
near 106 W, this meridian has the lowest average daily
frequency of echo over the continent (east of 109 W). The
low average frequency is the result of near-zero activity throughout
most of the diurnal cycle.
One effect of eastward propagation from the western
cordillera is to produce a delayed-phase diurnal signal
that spans the nocturnal-to-sunrise period (0800 - 1200) eastward
to 96 W. Circa 98 W, this delayed-phase diurnal signal creates
(computationally) a very strong semi-diurnal signal.
Eastward from 96 W, a "pure" semi-diurnal signal at
1100 UTC is evident (Fig. 12, dashed line). Rainfall associated
with this semi-diurnal signal is often non-propagating.
East of 82 W there is an abrupt decrease in radar
echo frequency. This attribute of Fig. 12 is an artifact
of the eastern United States geography (Fig. 1). East of
82 W, radar coverage is absent both over Canada in the north of
our domain and over the Atlantic Ocean in the southern portion.
While area-normalization procedures could mitigate this artifact,
the effect of such a correction could be highly disproportionate
within each season and among them, so we elect not to make a corrective
calculation of this type.
Figure 13. Same as Fig. 12 but for
(a) May 1998, (b) June 2000, (c) July 1997. In July 1997,
the absolute maxima are near 90% at 83 and 90 W, circa 2200 UTC.
White arrows in a) and c) highlight suppression of the in-phase
diurnal maximum near 98-99 W. Diagonal dashed phase-lines
in c) highlight day-2 and day-3 phase-locked propagation.
See text for description of intra-seasonal variations.
Figure 13 shows examples of intra-seasonal variability
from May through July. We have selected three months from
the period of record that best illustrate the major features associated
with this variability, however, we encourage the reader to examine
the entire record (Ahijevych et al., 2001) owing to inter-seasonal
variations presumed to be associated with differences in large-scale
forcing. May 1998 (Fig. 13a) shows a diminished diurnal
amplitude compared to the seasonal average and the suppression
of an in-phase diurnal maximum circa 98 W (white arrow).
Propagation from the western cordillera is evident, as are the
nocturnal/morning maxima in the inter-cordillera region.
There is a weak suggestion of phase-locked propagation east of
June 2000 (Fig. 13b) retains similar major features
with a greatly strengthened diurnal signal and more activity overall.
An important difference between May and June is evidence supporting
a phase-locked day-2 propagation, located ~10° east of the
day-1 echo frequency maximum (e.g. 88W, 1200).
July 1997 (Fig. 13c) shows further evidence for
day-2 and day-3 propagation as indicated by the diagonal
white lines, which overlay the frequency maxima. Given the
trans-continental rain streak patterns exhibited in section 3,
evidence of multi-day propagation is not surprising. However,
we note the remarkable degree of phase-locking required to produce
the pattern observed in Fig. 13c over a monthly average.
Furthermore, such phase-locked behavior is suggested in somewhat
"blurred" form, for some four-season monthly averages,
and entire warm seasons (Ahijevych et al., 2001). Reference
to Fig. 12 reveals that the secondary semi-diurnal maximum (1100,
86 W) is coincident with the day-2 propagation signal. The
implied rate of propagation east of the Mississippi River is less
than in the western US (typically 9 to 13 m s-1).
We performed one-dimensional DFTs on the averaged
diurnal timeseries represented by Fig. 12. This eliminates
all spectral energy below the diurnal frequency and allows for
a greater sensitivity to spectral maxima at frequencies higher
than diurnal. The resulting power spectra (Fig. 14a) contain
three strong signals:
- A diurnal maximum over and near the Rockies
- A diurnal maximum over and near the Appalachians
- A semi-diurnal maximum between the cordilleras
The simplicity and symmetry of this result is surprising.
We find it to be fully consistent with the diagrams previously
presented herein and the historical literature regarding thermal
forcing in the presence of elevated and sloping terrain, and the
diurnal frictional variation.
The diurnal maxima exhibit somewhat different relationships
to their respective cordilleras. The western maximum stretches
eastward over sloping terrain, consistent with the observed propagation.
The eastern maximum sits squarely over the highest terrain, consistent
with less eastward propagation. The semi-diurnal maximum
(94 W) is very strong and it is located precisely at the eastern
terminus of sloping terrain. This longitude is also coincident
with the eastern edge of the low-level jet climatological zone
Figure 14. Power spectrum, (a),
and harmonic decomposition (b), (c), (d), of Fig. 13. The
power spectral density vs. longitude, (a), exhibits three signals;
diurnal oscillation over and near the eastern and western cordilleras,
and semi-diurnal oscillation between the cordillera. The
harmonic decompositions quantify the relative amplitudes of diurnal
and semi-diurnal oscillations in three longitude bands (b) west,
(c) central, (d) east. Thick, solid curve is echo frequency;
long-dashed is the 1st harmonic; short-dashed is the
Figures 14 b-d quantify the phase and amplitude
of the diurnal and semi-diurnal signals by illustrating a least
squares harmonic decomposition
in three meridional bands (west, 110-102 W; central, 98-90 W;
and east, 86-78 W). These figures quantify the exceptionally
large diurnal amplitude in the west (Fig. 14b); the dominance
of semi-diurnality in the central region (Fig. 14c); and an intermediate
condition in the east (Fig. 14d). In the west the semi-diurnal
amplitude is ~ 25% of the diurnal. It is associated
with slow decline of echo frequency in the nocturnal hours compared
to the rapid rise of echo frequency in daytime, a pattern that
mimics low cooling rates associated with outgoing long-wave radiation
and rapid warming associated with incoming short-wave radiation.
We cannot detect any semi-diurnal regeneration of rainfall in
In contrast, the amplitude of semi-diurnal oscillation
in the central region (Fig. 14c) is ~200% that of diurnal, however,
the total amplitude of variation is small. The east (Fig.
14d) is intermediate in all aspects with a semi-diurnal signal
that is ~40% of the diurnal. The semi-diurnal phase is fairly
uniform at all meridians with maxima near 1100 and 2300 UTC.
The diurnal maxima occur near 0100 UTC at the west and central
meridians and near 2300 UTC in the east.
We have presented evidence to support the notion
that rain streaks are mainly diurnal in frequency, have large
scale coherence in the zonal dimension and, to a limited extent,
exhibit phase-locked behavior. Here we attempt to quantify
the coherence and phase speed aspects by means of two-dimensional
autocorrelation analyses described in section 2b and supporting
analyses from the NCEP 2.5° data. We have examined both
zonal-span and duration properties from 5406 rain streaks over
492 warm season days, or approximately 11 per day. In addition,
we have calculated the zonal phase speeds and compared these to
both the zonal phase speed of upper tropospheric anomalies and
the zonal "steering-level" winds. Our statistics
represent only the zonal component of motion, U, which is defined
by U = S cos a, where S is total phase speed and a is the angle
of departure from zonal motion. Accordingly, conclusions
with respect to propagation rate (and span) are drawn from comparison
with other data where only the zonal component is considered.
The cumulative probability density distribution
(CPD) for rain streak span, as defined in section 2b, is logarithmically
linear in form (Ahijevych et al., 2001) to a distance of ~ 2500
km. Span statistics are relatively invariant over the four-season
period. The CPD may be approximated by a power law of the
N(S) = N0
where N(S) is the number
of rain streaks of span > S (km), N0 is the
total number of streaks, and L = 10-3 km-1.
The CPD for rain streak duration is also logarithmically linear
out to 65 h and it may be approximated by
where D is duration (h)
and G = 0.05 h-1. It can be shown
from (1) and (2) that a phase speed, U = S/D = G/L ~14 m/s, is
implied through the use of these expressions. The median
streak duration is 4.5 h, which is characteristic of ordinary
mesoscale convective systems. At 11 h duration (an average
MCC lifetime), the rain streak frequency is more than five times
that reported for MCCs by Augustine and Howard (1991).
Span and duration statistics are collectively summarized
in Table 1. We employ "recurrence frequency" as
a means to express the frequency of the "longest" 10%
of all episodes. Recurrence frequency is defined as
the average interval of time for recurrence of an event that equals
or exceeds a specified span or duration. At the recurrence
frequency of once per day, there are events of >
838 km span and > 18.5 h duration, thereby exceeding,
by a considerable margin, the average characteristics of individual
convective systems. To achieve this daily recurrence frequency
(as evinced, for example, by Fig. 6), "long" events
must occur on most days, portions of which are likely under synoptic
conditions less favorable than the mean. At the weekly recurrence
frequency, the coherency characteristics extend to 2000 km and
40 h. We find these results to be surprising, especially
since the "long" events are most frequent in mid-summer,
under conditions that are customarily described as "weakly
An inevitable conclusion is that large portions
of the continent routinely harbor conditions that are, in some
sense, favorable to (or cannot suppress) the initiation, maintenance
or transit of deep convection. We speculate that much of
the observed warm season rainfall results from strong thermal
forcing combined with as yet unidentified mechanisms underlying
convective system propagation. Convective system propagation
is a straightforward means to overcome inhibition (negative CAPE)
to convection where local forcing may be insufficient. For
example, forced lifting in the planetary boundary layer is a common
mode of convective initiation (Wilson and Schreiber, 1986) and
Phase speed characteristics of rain streaks are
of particular interest because these offer the opportunity to
diagnose dynamical organizations that underlie the structures.
We have examined the span/duration CPD statistics for phase speed
inferences and we have compared these to the slopes of the autocorrelation
data. More than 27,000 phase speeds were estimated on >
5400 rain streaks in the manner described in section 2b.
Approximately 4-6% of rain streaks exhibit slow westward motion
(U < 0). Such events are mainly confined to the desert
SW and the Gulf of Mexico coast in mid-late summer. For
the purpose of median zonal phase speed estimation, we restrict
our analyses to eastward-traveling systems.
Figure 15. Rain streak span vs.
duration data. Solid curve shows the median phase speed
(14.3 m s-1) for events > 1000 km and 20
h. Dashed curves locate the 30 m s-1 (upper)
and 7 m s-1 (lower) phase speeds, inclusive of most
"long" events. A correlation coefficient of 0.89
The span/duration statistics from Table 1 also provide
strong inferences of zonal phase speed, though the meaning of
these is slightly confounded by details of the autocovariance
function. Figure 15 shows the bivariate distribution (a
correlation coefficient of 0.89) and a phase speed line at 14.3
m s-1 corresponding to the median zonal speed for rain
streaks > 1000 km and 20 h duration. Most of the
events in Fig. 15 are bracketed by 30 and 7 m s-1 zonal
phase speed lines.
Table 2. summarizes three additional sets of zonal
phase speed estimates, stratified according to recurrence frequency.
The top row within each recurrence frequency is simply
the speed implied by each span/duration couplet in Table 1.
The bottom row within each recurrence frequency is the
median span/duration ratio (at the relevant scale of event) calculated
from the data in Fig. 15. The central row is an "exceedence
speed", defined as the average zonal phase speed that is
equaled or exceeded for each recurrence frequency. For example,
during the 492 day period of record, approximately 492 rain streaks
equaled or exceeded the phase speed of 23.9 m s-1 (an
average of 1 per day). "Long" events (frequency
of 1 to a few per week) exhibit slightly larger mean phase speeds,
however, the extrema of central measures over the period of record
maintain a relatively narrow range, from ~12 to 18 m s-1.
Zonal phase speed differences between seasons appear to be systematic
and may be related to mean zonal wind variations. For the
purpose of defining a global central measure of the zonal speed
component, 14 m s-1 appears to be robust with respect
to these various calculations.
We have examined the 1998 and 1999 NCEP 2.5°
data in latitude bands corresponding to the largest convective
events. We have compiled seasonal statistics on 30 kPa anomaly
phase speeds and zonal "steering" winds at 70, 50, 40,
30, and 25 kPa. The various zonal speed estimates were then
examined with respect to their propagation implications.
Our principal measure of upper tropospheric zonal
phase speed was derived from Hovmoller diagrams of meridional
wind anomalies (from climatology) at 30 kPa (e.g. Fig. 4).
This variable almost always revealed a phase speed signal associated
with traveling disturbances in the westerlies. On those
occasions when this failed, other fields (e.g., geopotential height,
temperature) were inspected and sometimes led to an improved definition
of zonal phase speed. The median zonal phase speeds were
determined simply by inspection of Hovmoller diagrams of the NCEP
data (e.g. Fig. 4) for the 35 N - 42.5 N latitude band.
Naturally occurring phase speed changes at 3 to 7 day intervals
led to the estimation of 45 values in 34 weeks. The variance
of median phase speeds was calculated and extreme values were
recorded for scales characteristic of the major rain streaks (~
1 day, 5° longitude).
The combined 1998-1999 statistics were quite stable
and exhibited consistency. The means of the median values
for each season were 2.6 and 3.3 m s-1 for 1998 and
1999, respectively. The standard deviation was 3 m s-1
for both years. The extrema in both seasons were -2 and
10 m s-1. On average, transient disturbances
can effectively extend the zonal "envelope" of convective
rain streaks by ~20% during the course of a 14 m s-1
(phase speed) event because these typically propagate eastward
at ~20% of the rain streak speed. The phase speeds indicated
by the NCEP 2.5° data are quite slow in comparison to commonly
held perceptions of upper-tropospheric short-wave speeds.
The 2.5° analyses include a spectral low-pass filter at T36
thereby damping structures below ~ 1000 km, which probably suppresses
evidence of most short-waves. It should be noted the group
velocities in the westerlies could account for much faster propagation
of atmospheric phenomena, however, group velocity structure was
not evident in the NCEP data throughout most of the warm seasons
"Steering Level" is defined as the lowest
standard pressure altitude at which median zonal wind speed, u,
equals or exceeds the locally-averaged rain streak phase speed
(U) within a 7-day x 5° (longitude) domain. Median zonal
steering winds were calculated from the NCEP data at a 1-week
and 5° longitude interval in the 35°-42.5° N latitude
band. Since organized convection is known to occur with
greater frequency just southward of stronger winds in the upper
troposphere (Laing and Fritsch, 2000), our samples included some
winds from 30-35 N or 42.5-47.5 N latitude bands, as appropriate,
if large convective systems were located far to the north or south.
In any given instance there will exist a spectrum of winds and
rain streak phase speeds, however, the 7-day x 5° aggregation
of data is sufficient to capture gradients associated with most
of the major changes while retaining a moderate degree of stationarity
within each 7-day x 5° bin.
Notably, we could not detect a statistically significant
correlation between the steering level and tropospheric wind speeds.
For example, the probability density histogram of steering levels
during the highest wind period (circa 1 June 1998) was statistically
indistinguishable from a period in August with minimum winds.
To the extent that standard pressure level data permit such discrimination,
it appears that steering level is approximately conserved.
Table 3 summarizes the various rain streak, anomaly,
and steering level wind speed information, with an eye toward
inferences about propagation. The upper tropospheric phase
speeds are only ~20% of rain streak phase speeds, therefore strong
relative propagation is indicated. Our attention is drawn
to steering level winds and the fraction of time these equal or
exceed rain streak phase speeds. Table 3 shows that lower
tropospheric steering (U=u) rarely occurs at 70 kPa, and most
frequently occurs at or above 50 kPa. The median steering
level is approximately 40 kPa and 29% of events have a steering
level above 30 kPa. No steering level is indicated for 6%
of events. These results are suggestive of one or more wave-like
propagation mechanisms that act in superposition with the steering
We have presented a litany of statistics without
much comment on the underlying physical and dynamical processes.
The statistics support the following conclusions:
- Coherent rainfall events, of order 1000 km in zonal span and
one-day duration, occur with high frequency (nearly one per
- Many of these events are of longer duration and a larger zonal
extent than is normally associated with mesoscale convective
systems, including mesoscale convective complexes.
- Such occurrences are believed to be compound events,
a coherent succession of convective systems. We refer
to these as "episodes."
- Coherent dissipation and regeneration of convective rainfall
within episodes suggests a causal relationship among successive
systems and, therefore, a suggestion of intrinsic predictability.
- The phase speed of episodes commonly exceeds the phase speed
of upper tropospheric anomalies and often exceeds zonal "steering
winds" in the low-to-mid troposphere. This is suggestive
of a convectively-generated propagation mechanism
- The steering level is not a strong function of wind speed
- The ensemble of episodes exhibits a globally phase-locked
behavior, consistent with the effects of thermal and topographical
forcing and subsequent propagation.
- The principal signals resulting from phase-locked events are
(1) diurnal forcing over both cordilleras and (2) semi-diurnal
forcing between the cordilleras.
Adequate representation of convection is generally
regarded as an unsolved problem in numerical weather and climate
prediction. Applications as diverse as short-range prediction
of precipitation and fundamental water cycle issues are dependent
upon appropriate representations of warm season rainfall processes
in forecast models at all timescales. Our findings contain
inferences of predictability, by reason of precipitation coherence
patterns, that exceed the dimensions of convective system lifecycles.
The coherence properties do not appear to be "tightly held"
by transient disturbances in the westerlies that precede (i.e.
have existed upstream of) the occurrence of convection over the
western cordillera. We hypothesize that the principal
significance of this study has its roots in lower boundary forcing,
dynamics at the mesoscale, and the capacity of organized convective
effects to scale upwards and to act remotely. One example
of "remote action" could be the creation of upper tropospheric
potential vorticity anomalies by convection over the Rockies that
subsequently advect eastward with the upper tropospheric winds.
The statistics establish a prima facie case
for dynamical linkages among successive convective systems.
The linkages exhibit phase coherence with respect to antecedent
convective systems that are often forced diurnally. Because
rain streaks are often not located optimally with respect to large
scale forcing, there is presumed to be a causal "upscale"
or "downstream" effect resulting from the antecedent
convection. Judging from the amplifications and dissipations
along many rain streaks, several generations of organized convection
may be causally related in this manner.
Convective precipitation lifecycles are poorly represented
in today's weather and climate forecast models. It would
seem advisable to communicate such forcings to the grid scale
to permit the propagation of convection and the attendant rainfall.
For example, we have illustrated precipitation patterns that are
suggestive of a "remote response" to the North American
monsoon condition, linking precipitation systems over central
and eastern North America to the western cordillera. The
challenge is to understand these dynamical linkages as a necessary
step toward proper representation.
What candidate mechanisms exist? We offer
a statistical result consistent with wave-like propagation.
At least two broad categories are evident:
- Density (or gravity) currents and various forms of trapped
gravity waves in the planetary boundary layer
- Gravity-inertia waves in the free troposphere, associated
with condensation of cloud water and freezing of hydrometeors
at mid- to upper tropospheric levels. This could also
include interfacial gravity waves.
There is ample evidence for the excitation of secondary
convection from convectively-generated boundary layer disturbances
of both the gravity current and gravity wave types (e.g. Purdom,
1982; Doviak and Ge, 1984; Wilson and Schreiber, 1986; Mueller
and Carbone, 1987; Carbone et al., 1990; Crook et al., 1990; Koch
et al., 1991; Carbone et al., 2000; Wilson et al., 2001).
Carbone et al. (1990) established linkages among three successive
mesoscale systems over one diurnal cycle and approximately 1000
km distance, including both the gravity current and undular bore
If one attempts to employ approximate calculations
of propagation speed as a means to identify dominant mechanisms
of MCS maintenance and regeneration, such efforts are thwarted
by results that are all too uncertain and inclusive. Density
current speed, V, is approximated by V2 = k2gh(Dr/r),
where k is of order unity, g is gravitational acceleration, h
is the current depth and r is ambient air density. This
leads to a plausible range of results (10 to 22 m s-1)
for commonly observed (buoyancy -1 to -5 %, 1 km deep) cold pools.
Observations and calculations of trapped gravity
wave phase speeds are similarly plausible. Koch et al. (1991,
Table 1), have summarized numerous observed cases over the U.S.
that propagate from 13 to 24 m s-1. Shallow-water
equation approximations under constant stratification and no shear
also yield plausible results (10 to 40 m s-1) for observed
nocturnal boundary layer conditions (N= 0.01 to 0.02 s-1,
h = 1 km) where N is the Brunt-Vaisala frequency. More realistic
calculations in shear and/or non-constant stratification yield
differing results but span a similar dynamic range (Crook, 1988;
Raymond and Rotunno, 1989).
Are planetary boundary layer disturbances the "connecting
tissue" among successive convective events that span and
duration statistics suggest? Long-lived density current
propagation in neutral (daytime) boundary layers followed by trapped
gravity waves in the stable nocturnal boundary layer offer a plausible
continuum. However, these mechanisms are either inherently
dissipative or dispersive and conditions may often be unfavorable
for the generation or maintenance of either.
Convective gravity wave excitation and maintenance
by the ensemble of latent heating in the free troposphere has
considerable appeal in its application to propagating episodes,
as evidenced by the sizeable body of literature associated with
the concept. These studies (e.g. Moncrieff and Miller, 1976;
Raymond, 1984, 1986; Tripoli and Cotton, 1989) are theoretical
for the most part. Attempts to verify the concepts have
been modest, mainly because verification based on observations
is costly and logistically difficult. The efforts
so far have generally met with inconclusive or negative results,
so a more vigorous exploration of this issue is required in light
of the findings herein.
Our calculations substantiate the plausibility for
wave-like propagation under sub-tropical conditions as described
by the idealized findings of Moncrieff and Miller (1976).
Their steady state model, when applied to an atmosphere with deep
shear of low magnitude, predicts that squall-type convection will
propagate (with respect to mid-level winds) c = ~0.3 (CAPE)1/2,
where c is in m s-1 and CAPE in J kg-1.
If we accept the propagation value of 8 m s-1, deduced
from the 70 kPa winds in Table 3, the inverse calculation implies
a characteristic CAPE of ~700 J kg-1. This is
a plausible value when averaged over the lifecycle of long-lived
Koch and O’Handley (1997) have provided relevant
information about typical steering levels for mesoscale gravity
waves associated with unbalanced flow at the synoptic scale.
The mean height of the observed critical levels was 467 hPa, broadly
consistent with the propagation statistics herein.
Another category of coherent regeneration is convective
forcing of quasi-balanced mesoscale circulations that either retain
a capacity to maintain organized convection (Raymond and Jiang,
1990) or later gain the capacity to regenerate it. A circulation
that fits this description is the mesoscale convectively-generated
vortex (MCV), a well known by-product of some mesoscale convective
systems (e.g. Bartels and Maddox, 1991; Fritsch et al., 1994;
Weisman, 1993). Recently Trier et al. (2000a) and Davis
et al. (2001) have established that there exists a greater number
of MCVs than previously documented. How frequently are MCVs
associated with significant regeneration of convection and to
what extent are these related to the "long" episodes
herein? MCVs are sometimes associated with non-propagating
episodes (e.g. section 3c) and, therefore, might not contribute
strongly to the statistics associated with propagating events.
Both weather and climate prediction are heavily
dependent upon an adequate representation of convective precipitation
processes. A speculative conclusion of this study is that
probabilistic precipitation forecasts of 6 to 48 h range might
be substantially improved through the combined use of dynamical
and statistical methods. Antecedent convection and its observed
propagation routinely place narrow bounds on the future meridional
position of heavy precipitation episodes, up to 48 h range.
Dynamical forecast models routinely identify the latitudinal bands
of mesoscale ascent and the associated production of thermodynamic
instability (e.g. Laing and Fritsch, 2000). The combined
strengths of meridional prediction by means of statistical expectation
and latitudinal prediction by means of numerical forecast models
may prove to markedly increase skill in warm season rainfall forecasts
at the short-range.