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Flash Flood Forecasting: An Ingredients-Based Methodology
C
HARLES
A. D
OSWELL
III, H
AROLD
E. B
ROOKS
,
AND
R
OBERT
A. M
ADDOX
NOAA/Environmental Research Laboratories, National Severe Storms Laboratory, Norman, Oklahoma
(Manuscript received 31 August 1995, in final form 5 June 1996)
ABSTRACT
An approach to forecasting the potential for flash flood–producing storms is developed, using the notion of
basic ingredients. Heavy precipitation is the result of sustained high rainfall rates. In turn, high rainfall rates
involve the rapid ascent of air containing substantial water vapor and also depend on the precipitation efficiency.
The duration of an event is associated with its speed of movement and the size of the system causing the event
along the direction of system movement.
This leads naturally to a consideration of the meteorological processes by which these basic ingredients are
brought together. A description of those processes and of the types of heavy precipitation–producing storms
suggests some of the variety of ways in which heavy precipitation occurs. Since the right mixture of these
ingredients can be found in a wide variety of synoptic and mesoscale situations, it is necessary to know which
of the ingredients is critical in any given case. By knowing which of the ingredients is most important in any
given case, forecasters can concentrate on recognition of the developing heavy precipitation potential as mete-
orological processes operate. This also helps with the recognition of heavy rain events as they occur, a chal-
lenging problem if the potential for such events has not been anticipated.
Three brief case examples are presented to illustrate the procedure as it might be applied in operations. The
cases are geographically diverse and even illustrate how a nonconvective heavy precipitation event fits within
this methodology. The concept of ingredients-based forecasting is discussed as it might apply to a broader
spectrum of forecast events than just flash flood forecasting.
1. Introduction
Flash flooding has become the convective storm–
related event annually producing the most fatalities.
Whereas the system for reducing casualties from tor-
nadoes, including not only forecasts and warnings but
also public preparedness, has improved steadily since
the 1950s and continues to improve, the comparable
system for flash floods has experienced less progress.
A major challenge associated with flash flooding is the
quantitative character of the forecast: the task is not just
to forecast the occurrence of an event, which is difficult
enough by itself, but to anticipate the magnitude of the
event. It is the amount of the precipitation that trans-
forms an otherwise ordinary rainfall into an extraordi-
nary, life-threatening situation. This challenge is ex-
acerbated by the interaction of the meteorology with
hydrology. A given rainfall event’s chances to produce
a flash flood are dramatically affected by such factors
as antecedent precipitation, the size of the drainage ba-
sin, the topography of the basin, the amount of urban
Corresponding author address: Dr. Charles A. Doswell III, Na-
tional Severe Storms Laboratory, 1313 Halley Circle, Norman, OK
73069.
E-mail: doswell@nssl.uoknor.edu
use within the basin, and so on. Thus, a flash flood
event is the concatenation of a meteorological event
with a particular hydrological situation. We are not pre-
pared to treat the hydrological aspects of the flash flood
problem in this paper, but we are by no means implying
their lack of relevance.
As noted by Spiegler (1970), albeit in a different
context, quantitative precipitation forecasting (QPF) is
a ‘‘formidable challenge.’’ Rainfall, per se, is a quite
ordinary event, which is why it can be difficult to rouse
public concern when rainfall becomes life threatening.
The public has no difficulty becoming concerned about
the threat associated with extraordinary weather events
such as tornadoes, but rain is both common and benign
in the vast majority of circumstances. The fact that QPF
is difficult to do [see Mostek and Junker (1989) and
Olson et al. (1995) for some QPF verification results]
makes the task that much more challenging; forecast
credibility is certainly part of the problem. Even if
we could do QPF with perfect skill, rousing the public
to recognition of the threat might continue to be a
problem.
Many operational studies associated with QPF are
local or regional in scope (e.g., Belville and Johnson
1982). Moreover, such studies typically are empirical,
in that they are based heavily on statistical associations
between candidate precipitation predictors and precip-
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itation (e.g., Charba 1990), without establishing a
physical connection between predictor and predictand.
We want to provide forecasters with a basic framework
for understanding the occurrence of heavy precipitation
that is neither limited in geographical application nor
based on statistical relationships. Instead, we wish to
develop a physical basis for understanding why heavy
precipitation occurs that is not region specific and is
not prone to obsolescence through advances in science
and/or technology. In fact, when the basis is properly
constructed, it permits an easy and obvious integration
of new scientific concepts. We believe that a QPF
scheme using an ‘‘ingredients’’ basis can be improved
and refined through advances in scientific understand-
ing and technological tools, but the basis itself should
remain essentially unchanged, barring perhaps a true
revolution in our understanding (a pervasive ‘‘para-
digm change’’).
Accordingly, in section 2, we develop what we be-
lieve to be such an ingredients-oriented basis for pre-
dicting heavy precipitation. In section 3, we will pro-
vide an overview of the meteorological processes as-
sociated with bringing these ingredients together,
primarily in midlatitudes. The same ingredients are as-
sociated with tropical occurrences of heavy precipita-
tion, but the processes by which they are brought to-
gether may be different in important ways. Section 4
then provides three case examples that serve to illus-
trate the ideas developed in sections 2 and 3, and sec-
tion 5 offers a summary and discussion.
2. Ingredients for flash floods
a. Ingredients for heavy precipitation
1) A
SIMPLE CONCEPT OF HEAVY PRECIPITATION
There is an almost absurdly simple concept of how
heavy precipitation comes about that by its very sim-
plicity makes the issues leading to heavy precipitation
quite clear. It takes the form of a simple statement (at-
tributable to C. F. Chappell) of quantitative precipita-
tion forecasting: the heaviest precipitation occurs
where the rainfall rate is the highest for the longest
time. That is, at any point on the earth,
1
if R
V
is the
average rainfall rate and D is the duration of the rain-
fall, then the total precipitation produced, P, is simply
U
P
Å
RD.
Flash flood events arise from high to extremely high
rainfall rates, whereas river flood events are associated
with rainfall events over days and perhaps months. The
infamous northern Mississippi and Missouri River
1
The point of view here is Eulerian and the development that fol-
lows continues in this perspective.
floods of 1993 clearly were due to the persistence of
rainfall over many weeks, but there were flash floods
with quite high rainfall rates embedded within the sum-
mer events of 1993. Flash floods caused many of the
deaths during the summer of 1993; flash floods, of
course, are the main concern within this paper.
We have not provided quantitative thresholds for
what we consider to be ‘‘high’’ or ‘‘extremely high’’
rainfall rates, nor have we done so for ‘‘long’’ or ‘‘ex-
tremely long’’ durations. Thresholds can be intellectual
traps for the unwary and what constitutes an important
threshold in one hydrometeorological situation may be
quite unimportant in another, as we shall illustrate be-
low. Broadly speaking, moderately high rainfall rates
begin at about 25 mm (
Ç
one in.) h
01
, and moderately
long durations begin at about 1 h, but these should be
considered only as the crudest of guidelines.
2) I
NGREDIENTS FOR HIGH PRECIPITATION RATE
With this simple ‘‘law’’ in mind, one key issue is to
consider how heavy precipitation rates occur: from a
synoptic viewpoint, precipitation is produced by lifting
moist air to condensation. The instantaneous rainfall
rate at a particular point, R, is assumed to be propor-
tional to the magnitude of the vertical moisture flux,
wq, where w is the ascent rate and q is the mixing ratio
of the rising air.
2
This means rising air should have a
substantial water vapor content and a rapid ascent rate
if a significant precipitation rate is to develop. The ver-
tical moisture flux can be related to the condensation
rate, which in turn is the ultimate source for precipi-
tation. Of course, not all the water vapor flowing into
a cloud falls out as precipitation. This naturally brings
up the subject of precipitation efficiency. The precipi-
tation efficiency, E, is the coefficient of proportionality
relating rainfall rate to input water flux, so that
R
Å
Ewq.
Precipitation efficiency is defined as the ratio of the
mass of water falling as precipitation, m
p
, to the influx
of water vapor mass into the cloud, m
i
, such that E
Å
m
p
/m
i
. The details of this definition are given in the
appendix. Figure 1 illustrates this process schemati-
cally to show that precipitation efficiency is most log-
ically understood as a time average over the history of
a precipitation-producing weather system. If calculated
at any particular instant, precipitation efficiency might
be zero (as when no rainfall is occurring early in the
life cycle of the system) or it might be infinite (as when
2
Note that the instantaneous flux of water vapor into the thunder-
storm is not directly equal to the precipitation rate. Many issues in-
fluence the rate at which input water vapor falls out of a thunderstorm.
Our simplifying assumption is that the higher the input flux, the
greater the precipitation rate.
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. 1. Schematic illustration of the time variation of water vapor input (cross-hatched area) and the precipitation output (vertical bars)
over the lifetime of a precipitation system. The units are arbitrary, so the system being portrayed can be any precipitating process with a
developing phase (time
Å
0–3 units), a mature phase (time
Å
3–6 units), and a dissipating phase (time
Å
6–10 units). For this example,
the areas under the respective curves give a precipitation efficiency of about 44%.
rain is continuing to fall from a dissipating system in
which the water influx has gone to zero). The smallest
unit for which it makes sense to calculate precipitation
efficiency is a convective cell. However, if a system
contains many individual convective cells, the precip-
itation efficiency of any one of them is likely to be of
little more than academic interest, because the precip-
itation efficiency of individual cells could vary consid-
erably across a large convective system. Note that E is
not necessarily a constant, but can be a function of
space and time. Strictly speaking, in the relationship R
Å
Ewq, all quantities have been averaged over the life-
time of a precipitating system.
Broadly speaking, therefore, calculation of a single
cell’s precipitation efficiency is of minor significance;
what matters is being able to anticipate the efficiency
in a general sense. How likely is it that the potential
flood-producing storm is going to have high precipi-
tation efficiency? Of the input water vapor in a con-
vective storm, virtually all of it will condense, since a
convective updraft is typically tall enough that the sat-
uration mixing ratio at the storm top is on the order of
0.1 g kg
01
. This value is roughly 1% of a typical input
mixing ratio, implying that 99% of the input water va-
por condenses. What happens to the condensed water
vapor? Some of it falls as precipitation, some of the
cloud particles are swept away by the winds aloft to
evaporate elsewhere, and some condensate evaporates
in downdrafts in the vicinity of the storm. In other
words, that which does not fall as precipitation even-
tually evaporates. What promotes evaporation? There
are some microphysical aspects to this question, in-
volving such issues as the droplet size spectrum, the
fraction of ice in the condensate, and so on. These cur-
rently are unobservable in the operational arena, and
whatever role they might play is unknown to a fore-
caster.
Another factor in precipitation efficiency is the en-
trainment rate, since bringing environmental air that is
unsaturated into a cloud tends to promote evaporation.
This, too, is unlikely to be known by a forecaster, ex-
cept in general terms: an isolated cloud is more likely
to suffer substantial entrainment than a cloud embed-
ded within a larger cloud system, since the environment
of the latter typically is much more nearly saturated
than that in the vicinity of an isolated cloud. This brings
up the key observable factor related to evaporation: en-
vironmental relative humidity. As the relative humidity
decreases, the evaporation rate increases and the pre-
cipitation efficiency falls. There can be other environ-
mental factors, such as wind shear, that alter precipi-
tation efficiency. Interested readers should consult
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Fankhauser (1988) for additional discussion about
precipitation efficiency and the factors that might con-
trol it.
Thus, if at least one of the three factors (E, w, and
q) for high rainfall rates is large (or likely to become
large) while the other ingredients are at least moderate,
the potential for high R exists. Obviously, the potential
for high R increases as E, w, and q increase and the
relationship is multiplicative and, hence, nonlinear.
b. Ingredients for deep, moist convection
From the preceding, it should be clear why flash
flood–producing storms are usually convective in na-
ture. Deep, moist convection normally occurs during
the warm season when high moisture content is possi-
ble and buoyant instability promotes strong upward
vertical motions. Thus, the rainfall rates associated with
convection tend to be higher than with other rain-pro-
ducing weather systems. Precipitation efficiency typi-
cally is not an important issue unless there is reason to
believe that it will be unusually low (as might be the
case for high-based convection, e.g., over much of the
interior Rockies). Therefore, although flash flood
events of a nonconvective nature do occur (as we shall
show), they are sufficiently uncommon that the search
for flash flood potential generally begins with a search
for the potential for convection.
Again using an ingredients-based approach, deep,
moist convection
3
is associated with buoyancy. This
buoyancy virtually always arises because the lapse rate
of a rising saturated parcel (i.e., ascending a moist adi-
abat) is less than that of the environment, so that the
rising parcel eventually becomes warmer than its en-
vironment. This is simple parcel theory, of course; even
with all its limitations, simple parcel theory is a pow-
erful tool for anticipating deep, moist convection.
In order to produce buoyancy and deep convection,
then, 1) the environmental lapse rate must be condi-
tionally unstable, 2) there must be sufficient moisture
that some rising parcel’s associated moist adiabat has
a level of free convection (LFC), and 3) there must be
some process by which a parcel is lifted to its LFC. As
discussed in Doswell (1987), the lift required to raise
a parcel to its LFC generally must be supplied by some
process operating on subsynoptic scales, because the
rising motions associated with synoptic-scale processes
usually are too slow to lift a potentially buoyant parcel
to its LFC in the required time. We shall return to this
topic later.
3
The term ‘‘deep, moist convection’’ is used instead of ‘‘thun-
derstorm’’ because not all cases of the former involve lightning (and
its associated thunder). We wish to avoid excluding nonthundering
convection, so we are using the more general term.
When deep, moist convection is already under way,
it is obvious that the ingredients are already in place.
In situations where convection is not happening at fore-
cast time, the forecasters must determine whether or
not those ingredients will be in place at some time in
the future. This involves assessing the possibility that
the missing ingredient will become available, while the
other ingredients will remain in place. Existing con-
vection’s future evolution should be considered in the
same light: the existing convection will continue as
long as the ingredients remain present and will cease
when one or more of the ingredients is no longer fa-
vorable.
c. The character of flash flood–producing storms
We already have considered the topics related to
rainfall rate, so the question of the rainfall associated
with an event now becomes one of determining the
duration. As noted by Chappell (1986), most impor-
tant flash floods are produced by quasi-stationary con-
vective systems, wherein many convective cells reach
maturity and produce their heaviest rainfall over the
same area. By this means, a convective event achieves
a relatively long duration, since individual convective
cells have lifetimes that almost always are too short to
produce heavy rainfall even though the individual con-
vective cell rainfall rates can be high.
For a convective system made up of a number of
convective cells, the duration of the high precipitation
rate in any location is related to 1) system movement
speed, 2) system size, and 3) within-system variations
in rainfall intensity. When a system moves very slowly,
the other factors may not be very important for those
locations that are experiencing the most intense rainfall
in the system. For large systems, the duration of mod-
erate or greater intensity rainfall can be quite long
(Maddox 1983; Fritsch et al. 1986), regardless of the
system movement speed. Nevertheless, as a general
rule, flash floods are associated with slow-moving pre-
cipitation systems.
Obviously, system movement, denoted by the sys-
tem motion vector
C
s
, can affect the duration, but an
Eulerian view requires knowledge of the system size
along
C
s
; denote this length by L
s
. The idea is illus-
trated in Fig. 2; as already noted above, the rainfall
total from the system is simply R
V
D, where now D can
be expanded to
01
D
Å
L (
É
C
É
).
ss
Long duration is associated with systems that have a)
slow movement, b) a large area of high rainfall rates
along their motion vector, or c) both of these. A squall
line with a large motion normal to the line will not
produce long-lasting precipitation at any point (as il-
lustrated by Fig. 3a), whereas the same line with the
majority of its motion parallel to the line will take a
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. 2. Schematic illustrating the concept of the length of a system,
L
s
, as it passes a point. The system motion vector is denoted by
C
s
,
and the system is shown (a) as it first encounters the point, (b) half-
way through the encounter, and (c) as it is leaving the point. For the
asymmetric system shown, different points would have different val-
ues for L
s
, and different orientations for
C
s
would yield different
values for L
s
at the same point.
longer time to pass a point (as in Fig. 3b), resulting in
more rainfall. Mesoscale convective systems with a
large region of ‘‘stratiform’’ precipitation
4
trailing a
leading convective line may end up with a long dura-
tion of moderate-to-heavy rain showers following a rel-
atively brief intense rainfall associated with the leading
convective line, exacerbating the effect of the heavy
rainfall (as illustrated in Fig. 3c). Obviously, the case
where many intense convective cells pass in succession
over the same spot, the so-called train effect, is the
situation producing the highest rainfall totals (as in
Fig. 3d).
Chappell (1986) indicates that convective cell
movement,
C
c
, is related to
V
m
, the mean wind through
some deep tropospheric layer (in which the cloud is
embedded). Thus, slow system movement could be as-
sociated with weak winds. This is indeed the case on
some occasions (e.g., Maddox et al. 1978; Maddox et
al. 1979). However, having strong winds within the
troposphere by no means excludes the potential for
4
The term ‘‘stratiform’’ may not be an entirely accurate descrip-
tion of the precipitation that trails behind a convective line within an
MCS, but we will continue to employ it here in view of its widespread
usage.
convective precipitation to have long duration at some
given location. Convective system movement,
C
s
,is
the vector sum of the contributions from
C
c
and the so-
called propagation effect, denoted by
P
s
. In the context
of convective storms, ‘‘propagation’’ is the contribu-
tion to system movement from the development and
dissipation of individual convective cells. A convective
precipitation system is not a ‘‘thing’’ in the sense that
it is an object made up of the same elements over some
period of time, as a stick or a book is a thing. Rather,
convective systems are processes made up of a number
of subprocesses (convective cells), through which air
parcels are flowing. It is the near cancellation of the
cell movement via propagation effects that results in
slow system movement (Fig. 4).
Anticipating cell movement is relatively simple,
since cells generally move more or less with
V
m
. That
is, simple advection dominates cell movement in most
cases. Forecasting the contribution from propagation is
much more difficult, because the convection can inter-
act with its environment to develop new convection in
preferred locations relative to the existing cells. New
convective development can be influenced heavily by
the outflow boundary produced from the existing (and
previous) cells. This boundary is a storm-scale source
of intense lift when the boundary-relative moist inflow
is large. Strong boundary-relative flow can arise in two
quite distinct ways: 1) ambient flow is weak but the
boundary is moving rapidly, or 2) ambient flow is
strong but the boundary is moving slowly. Obviously,
only in case 2 can the duration of a convective event
be large at a given location. Rapid boundary movement
is virtually never associated with long-duration rainfall
at a point.
Again speaking generally, the outflow location rel-
ative to an updraft is determined by the updraft-relative
flow within the precipitation-bearing layer. Since pre-
cipitation forms in the middle and upper troposphere,
the outflow usually is located downstream (in the up-
draft-relative framework) with respect to the middle-
and upper-tropospheric winds. The precipitation cas-
cade region usually is under the anvil of a convective
storm. An ideal situation for a long-duration convective
rainfall event is when the cells move roughly parallel
to a slow-moving outflow boundary, leaving a quasi-
stationary segment of the boundary behind into which
a substantial moist boundary-relative flow is imping-
ing, creating new cells that repeat the motion of their
predecessors. The new cells reinforce the boundary,
maintaining its position against the inflow. Such a sys-
tem can persist for many hours, as long as the moist,
unstable inflow is maintained. The Johnstown, Penn-
sylvania, event (Maddox et al. 1979) was of this sort.
In the Johnstown case, the southeastern part of the
boundary and its associated convective line moved rap-
idly southeastward, while the northwestern part of the
boundary remained quasi-stationary, and repeated new
