Giuseppe Gentili 
  
Where C is a coefficient related to the geometry and the roughness (material) of the constriction, 4 refers to the section 
downstream from the constriction and , to the upstream section. The other symbols are as previously defined. 
The step backwater computational method solves the basic flow equation between sections by trial and error 
solution within specified tolerances. It is one of the many used to calculate water surface profiles under gradually varied 
flow conditions and it is considered one of the best when applied to natural streams. It can be applied to subcritical and 
supercritical flow conditions with the proviso that cross sectional calculations be made in an upstream direction for 
subcritical flow and in a downstream direction for supercritical flow. The theory assumes also that Manning s formula, 
derived for uniform flow, is also applicable to varied flow conditions. It is assumed that the following conditions are 
applicable: 
1) Flow is permanent, 2) Slopes are small enough to accept the measured depths as equivalent to the 
vertical ones, 3) Water level is constant across the section, 4) Effects due to sediment load and air 
entrapment are insignificant, 5) All the energy losses are taken into account 
Design flood derivation 
Concerning the determination of the design flood discharge(s) to be applied, be that the maximum recorded or, 
better, that with a given probability of occurrence, it all depends on what hydrologic data are available. Under the best 
conditions there is a hydrologic station on the river stretch being studied with tens of years of record. In other cases, 
with less precision in determining the flood flow, there is a hydrologic station nearby within the same basin. With lesser 
precision yet, but probably mirroring reality more closely, there are no hydrologic stations in the basin and one must 
rely on extrapolating regional estimates of flow (Benson, 1962) to the segment of river being investigated. In the first 
case, when the hydrologic station is within the river stretch under study, the procedure to determine the flood flow, let s 
say the 100 year flood (probability of occurrence of 0.01), is straight forward. The annual maximum peak flood 
discharges for the period of record are ordered from the largest to the smallest. The probability of each flood is 
calculated from the formula m/(n+1) where m is the rank of the ordered series, 1,2,3 ..n and n is he total number of the 
data, that is the number of years of record. In practice the inverse of the probability is calculated, the so called return 
period, and thus the formula used is (n+1)/m. Next the data are plotted on Gaussian log probability paper or on a similar 
one, taking the flood values (or their logs if using normal probability paper) as the ordinates and the return period (or 
the probability) as the abscissa. If the data are aligned in such a manner that a straight line can be drawn safely through 
the points the line is extended graphically to intercept the value of the discharge at the return period of 100 or the value 
of 0.01 if using probability. Although it is always of help to obtain a graphic plot of the data one can calculate 
analytically the values from the appropriate Gaussian (or other) distribution equations as, by definition, a straight line 
drawn on a probability paper implies that the data that define the line come from that distribution or can be accepted as 
that. If the data do not follow a straight line but rather define a curve one can try to follow it to extrapolate the value 
wanted but only if the extrapolation is very short (the record is long). Alternatively one can search for a distribution 
that will linearize the data better; the choice is ample. 
If the existing hydrologic record is from stations outside the area of interest one may resort to regional 
techniques of flood flow analysis to obtain an estimate of the 100 year flood where needed (Dalrymple, 1960). 
Perhaps the most complex and documented study of mapping design floods in urban areas is that of Anderson 
(1970) relative to the tributaries of the Potomac river in Virginia within the Washington, D.C.,. metropolitan area This 
study made use of aerial photography combined with field surveys to assess the river geometry and included also the 
evaluation of the increased flood levels brought about by the urbanization process; one should consult the cited paper 
for details. 
When the appropriate design flood has been determined, one proceeds with the hydraulic equations 1-3 to 
calculate the relative flood levels along the river banks and subsequently draw the corresponding flood inundation 
maps. Traditionally the river cross sections used for the calculations are surveyed in the field, a time consuming work 
that has not facilitated flood mapping (Giusti, 1984). The recent appearance on the market of laser instruments that can 
be mounted on aircraft to sense altimetry with a precision of less than 20 cm and with an equivalent planimetric 
positioning by differential GPS promises to improve the future of flood mapping by indirect methods. 
LASERSCAN APPLICATION TO THE PARMA RIVER 
A general laserscan survey test was made by the Compagnia Generale Ripreseaeree of Parma in collaboration 
with the German TopoSys Company, a leading producer of laserscan operating systems in Europe (Casella et al, 1998). 
Various surveys were made over the Province of Parma and one was conducted over the city itself covering the segment 
of the Parma River that crosses it. The characteristics of the survey were as follows: Flight speed 350km/hr; Flight 
height 810m above ground; Aircraft twin engine Piper Navajo Chief PA31; Camera RC 30 with 150mm lens; 
  
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000. 337