22 23 24 26 24 20 21
2.4.3.6 Average maximum dew points. Another method of obtaining smoothing in maximum dew points is to average over six or twelve hours. The maximum average 6-hr. dew point in the above series is 25.00C (two consecutive observations) while the maximum average 12-hr. value (3 consecutive observations) is also 25.00C.
2.4.3.7 Single observation maximum dew point. Single observation dew point maximums may be used as the maximum moisture index provided the record is examined for dubious values and the synoptic test of paragraph 2.4.3.3 is applied. These tests should be applied in any event, but are particularly necessary to appraise single observation maximum dew points.
2.4.3.8 Storm dew point. To select the saturation adiabat representing the observed storm moisture, the highest dew points in the warmest airmass flowing into the storm are identified on surface weather charts. This determination may be made in the rain area but not necessarily so. Dew points at stations between the rain area and the sea should also be considered. This tolerance
is to insure that the dew points are in the warmest airmass involved.
In some storms, particularly storms related to warm fronts, surface dew points in the rain area may represent only a shallow layer of cold air and not the temperature distributions in the convective clouds that are releasing the rain. Figure 2.18 illustrates
schematica11y a weather map on which the storm dew point determination is made. On each consecutive weather map for the duration of a
storm the maximum dew point is average over several stations as
14
•
H EA VY RAI N AR.EA
16
•
•
24•
23•
2419
•
Figure 2.18 - Determination of maximum dew point in a storm.
Representative dew point for this map time is average of values in boxes
ESTIMATION OF MAXIMUM FLOODS
illustrated in the figure. Occasionally for lack of data it is necessary to rely on the dew point at only one suitably located station.
2.4.-3~9 The maximum dew points, one value per map from
each consecutive weather map, determined as described in paragraph 2.4.3.8, forma serie~. The representative storm dew point is then abstracted from this series by the same rules followed ,in determining climato10gical maximum dew points, be it single observation, average, or persisting maximum.
2.4.4 Combihedrlli:ixirnization and tran~position
adjustment for moi~ture
2.4.4.1 Where a storm is both maximized for .mo;isture and transposed with'a:-n{oisture'a-djustment, the two adjustmeIl;ts,may be combined into a single ratio. Using a precipita.ble water type_
of adjusi~ent, the transposition adjustment is:
The maximization ratio is:
Obviously the combined adJ'ustment ratio, r ' is
tm'
w ,
W , and Ware respectively the precipitable water correspondingt x s
to the maximum wet-bulb potential temperature at transposed locati9n, the maximum where the storm occurs, and the representative storm value. The transposition adjustment, r
t , may be less or greater than 1.0, depending on whether the transposition is toward
greater or less moisture; the maximization ratio, r
m, is never less than 1.0.
2.4.5 Maximization from precipitable water measurements 2.4.5.1 Intelligent smoothing is required in developing reliable maximum values of most hydrometeorological variables. The representative maximum storm dew points are smoothed areally by averaging several stations on each weather map (par. 2.4.3.8). The climatological maximum dew points are smoothed or enveloped
areally by constructing isopleths on maps on which the basic data are station values. Time smoothing is provided by the procedure of figure 2.15. Vertical smoothing is discussed in the next paragraph.
2.4.5.2 Long records of radiosonde observations open up the possibility of adjusting storms for moisture, by measurements of atmospheric water vapour integrated through a layer, rather than by surface dew point alone. Both the maximum atmospheric moisture and the storm moisture would be derived from the radiosonde observa-tions. This method has not been fully developed because of (a) the considerable added expense in processing the upper air data records, (b) the lesser density of radiosonde stations as compared with surface stations, and (c) the lack of radiosonde stations in early years of climatological records. It would seem desirable to explore this method, and base the moisture adjustment on
precipitable water integrated through the atmosphere ~vith emphasis on the bottom 1000 to 2000 meters, the most significant inflow layer in storms.
74 ESTIMATION OF MAXIMUM FLOODS
2.4.6 Wind maximization
2.4.6.1 I·and maximization is most commonly used in mountainous regions wi th storm types "lhich it can logically be
considered that if the strength of the wind blowing against the mountain range in the observed storm had been increased, the precipitation would have been increased in proportion. The most direct way to apply a wind adjustment is to compare the total daily air movement (w·ind) at a coastal station,· or other station suitably located between the storm and the sea, with the maximum daily air movement in a considerable period of record at the same place and season. Only days with wind direction from a sector appropriate to storms are considered in arriving at this maximum value. The wind maximization ratio is then the ratio of
the maximum air movement to the storm air movement.
2.4.6.2 Wind maximization.may also be applied to large-area long-duration storms in regions not necessarily mountainous but far enough away from warm seas that the inflow of moisture during the storm is an important limiting factor on the amount of rain that may be produced. Such a wind maximization is calculated in the manner just described. The low-level 24-hr. wind movement is an index of the movement through a layer, just as the surface dew point is an index of the water content of a layer. This type of wind maximization was applied in an evaluation of probable
ma~imum precipitation in Iran, and is described briefly by Koelzer and Bitoun (15).
2.4.7 Maximization of orographic storms
2.4.7.1 In regions where the major contribution to heavy
rainfall results from strong winds impinging on steep mountain slopes rather than from convective or convergence activity (par. 2.4.7.4), storms are maximized by use of the orographic model of paragraph 2.1.2. This procedure involves several steps. Maximum dew points on the windward side of the mountain are determined as described in section 2.4.3. From this, the saturation adiabatic assumption gives the corresponding maximum inflow specific humidity at each level. Temperature is set equal to dew point, where saturation is assumed (see 2.4.7.3). Maximum winds are abstracted at several levels from rawinsonde observations where available. Smoothing bet1;veen stations and months compensates for short periods of
record. Also, because of the short record, the maximum winds are extrapolated statistically to some return period such as 25 or 50 years rather than using the simple maximums. This extrapolation may be done by the extreme value analysis procedures outlined in chapters 5 and 6. The winds are restricted to those from directions characteristic of storms. Lacking rawinsonde measure-ments, pilot balloon observations may be used~ The problem here is that there is a bias resulting from lack of observations on storm days of rain, low clouds and high wind speeds. A third method, used in the absence of upper-level wind measurements, is to use maximum values of pressure differences between two
meteorological stations along a line approximately normal to the storm wind inflow for estimating geostrophic wind values, then to convert to assumed profiles of the wind in the vertical by use of empirical relationships. The use of all of these methods is described In u.b. weather BureCl.u E,ydrometeorulogicCl.l Revort 1~o6. 36 cLnd 43 (25,32).
16
ESTIMATION OF ~~XIMmi FLOODS2.4.7.2 Given the maximum winds normal to a mountain, and the maximum temperature and moisture as described in the preceding two paragraphs, the resulting theoretical orographic rainfall is computed in the manner described in paragraph 2. L 3.3.
2.4.7.3 Calibration. It is important to test the applicability of the orographic laminar flow model by attempting to reprodureobserved storm rainfall amounts from observed winds, temperature, and moisture. Such tests are described in- the t\VO previously cited reports of the D.S. Weather Bureau (25, 32).
These tests have shmm that, under favourable circumstances in the most intense part of orographic storms, the model can account for the observed precipitation moderately well. During the weaker part of 2- or 3-day storms the model tends to overcompute the precipitation if saturation is assumed. Procedures for allowing for non-saturation during some parts of the storm are described in
(ll) .
2.4.7.4 Orographic-convergence separation method. The storm processes that release precipitation over relatively flat terrain or over the sea also release precipitation over mountainous areas. For purposes of analysis and maximization we may regard the precipitation on the windward slope ofa mountain as a combination of an orographic component - that yielded by assumed laminar
flmv of air in accordance with the orographic model - and the precipitation that would occur in the absence of the mountains.
The latter is sometimes called the convergence component of precipitation for lack of-a more satisfactory title, because it results from convergence of the air. Convergence precipitatio~
so defined, is probably never absent in important rain storms. The foregoing orographic model procedure for maximizing storms is t~en
valid only if the orographic component dominates and the convergence component is small by comparison. These conditions may pertain on steep slopes well exposed to strong winds. For general application over more varied terrain the previously cited studies of the U.S.
Weather Bureau (2S, 32) separate storm rainfall into orographic and convergence components and maximize these separately. The
orographic component is maximized by the orographic model procedures just described while the convergence component is maximized for moisture by the procedure described in section 2.4.2. 11aximum
values of each are assumed to occur simultaneously. This assumption is in itself a maximization step and is taken into account in
weighing the several maximization steps against the "sufficiency of storm sample" referred to in section 2.4.11. Knox (14) in a study of maximum precipitation rates on a major mountain range in the western United States also applies the principle of super-position of orographic and convergence components of rainfall. For
full maximization of the convergence component he proposes enveloping parametric values of the convergence rainfall rate computed from SOO-mb. vertical velocities in storms. These vertical velocities, which are non-orographic, are in turn computed from vorticity
appraisal of the large-scale storm through a model. For more restricted maximization, Knox adds the convergence component estimated to have occurred in a single selected extreme storm to
the maximized orographic precipitation.
78 ESTHJIATION OF r1IAXnmm FLOODS
2.4.8 Composite maximization
2.4.8.1 ~1ajor rain floods on the larges t rivers are generally caused by a succession of heavy rainfalls rather than by single storms. A logical maximization for such river
basins is the comuosite method of forming past storms into sequences.
Both spatial and sequential maximization is involved. Such a procedure was the predominant one in establishing the design flood for the largest river in the United States, the lower Hississippi (29), and has been employed else'\1here. In pursuing the composite method of maximization, guidelines on acceptable combinations must be developed from a study of the characteristics of a number of storms. In the Hississippi River study referred to, the minimum rainless time interval between storms for various storm types was determined on the basis of synoptic meteorology. This is amplified in chapter 2.5.
The composite method could also be used for smaller basins with a concentration time of a day or so, and research in this direction would be valuable.
2.4.9 Herschfield statistical-empirical method of estimating probable maximum precipitation
2.4.9.1 Hershfield in a paper available in the Journal of the Hydraulic Division, Proceedings of the American Society of Civil Engineering (13) has derived a statistical technique for estimating extreme values of 24-h point rainfall.
Required for this method are the series of maximum annual daily rainfalls at an observing point. Hershfield's estimating equation is:
where:
Xmax x + 15 s (7)
Xmax extreme rainfall to be estimated
X mean of series of maximum annual values s
=
standard deviation of this series15 is an empirically derived factor.
2.4.9.2 Basis of Method Hershfield's equation is an adaptation of the generalized frequency equat'ion (Chmv, 15, 16):
(8)
where X is the mean annual maximum, X
t is the annual maximum with return period of t years, s is the standard deviation of the series of annual maxima, and Kt a "frequency factor" depending only on t and the probability distribution assumed. In this usage Kt is computed mathematically irrespective of the data sample.
Hershfield wished to avoid specification of either a return period, t, or a particular form of frequency distribution, but rather to rely on processing a large body of.data without preconceived ideas as to the distribution form the values ma~
follow. In similation of the extreme rainfall estimation required, he withholds the largest annual maximum daily rainfall and calculates K required to yield this value from the remainder of the samnle:
m
~vhere:
+ (9)
X largest observed annual maximum rainfall
m
Xl mean of annual maxima, excluding largest
SI standard deviation of annual maxima, excluding largest