NEVENKA O@ANI]
CROATIAN WATERS, Rijeka, G. Ciotta 17 b, Croatia
JOSIP RUBINI]
CROATIAN WATERS, Labin, Zelenice 18, Croatia
Summary
PROBLEMS IN CALCULATIONS OF PRECIPITATION WATER
DRAINAGE IN URBAN AREAS
Flood appearance in urban areas is commonly caused by the urban areas precipitation’s themselves. The reason for their appearance are often inevitable e.g. extreme rainfalls, hydrological runoff conditions or the degree of drainage systems development, but sometimes the damages caused by flood appearance are the result of methodological mistakes in hydrological calculations. Such mistakes in hydrological calculations are sometimes so expressed that whole constructions for precipitation water draeinage system in urban areas became questionable and the main reason for these mistakes is that basic hydrological principals are ignored. Therefore, present paper analyzes the possibilities for minimalization of these mistakes in hydrological calculations of precipitation water drainage as one of possible ways for non-structural flood protection in urban areas.
Because most of the methods for hydrological calculations of high waters in urban areas are almost universal, the mistakes are certainly widespread in distribution also. The incorrect methodological application of hydrological calculations, although without good reason, is very rarely the subject of professional papers. Therefore this work emphasizes the most frequent mistakes in calculations of maximal runoff values. First of all the real characteristics of short-termed intensive precipitation regime are often ignored as well as the time of concentration and the runoff pattern in canal network. Besides that the mode of evacuation of longer returning period precipitation, than the one that was used for the dimensioning of drainage system, are often not considered as well.
Key words :

Urban drainage (runoff) system, hydrological calculations, calculation mistakes, intensity of precipitation
1. Intorduction
The main condition for proper water management is to understand the way they behave. The knowledge of hydrological characteristic of high waters is therefore one of the basic elements for successful flood control in urban areas. Flood appearance in urban areas is mostly caused by high water flows. Therefore the hydrological characteristics of these water flows are best studied and known and these characteristics are a basement for the development of technical measures for flood control and protection. Specialists in the field of hydrology mostly perform hydrological studies of such water flows.
On the other hand a greater number of other designers are involved in the planing and designing of system for urban areas water drainage. Therefore very frequently the basic principals of hydrological calculations are disregarded besides the fact that exactly these calculations are the main input parameters for such designs. If the specialty is not governed by state regulations, such circumstances may be the cause for bad and uneconomical technical constructions for water drainage and for the appearance of sudden floods caused by rainfalls precipitating directly on urban areas. Although such events are spatialy limited they can cause a great damage on buildings and other urban objects. Therefore an effort to minimalize such methodological mistakes during hydrological calculations of precipitation water drainage can be accepted as one of possible ways for non-structural flood protection in urban areas.
2. Basic elements of hydrological calculations
The main purpose of this paper is not to present some new hydrological calculation method or to recommend some of already existing methods but to point on basic methodological errors that appear in calculations of water drainage in urban areas. The discussion has conducted according to the very simple equation that is still in use for calculation of maximal runoffs - so called rationale Loyd-Davies method. The calculation of peak value of maximal runoff (Q) for selected returning period (p) is performed by the equation:

Q p
= k * C * i p
* A (1) where: i k - factor of correction
C - mean runoff cofficient p
- precipitation intensity
A - surface of catchment area
During the determination of parameters for the equation it is necessary to decide the degree of protection for desired object expressed as the probability of a maximal flow through appearance, e.g. its returning period. That can be done using precipitation intensity of selected returning period. For the selection of proper precipitation intensity, besides its returning period it is necessary to calculate the time of concentration (T c
) for each part of road, according to the rational method equation: where:
T c
= T k
+ T s
+ T g
(2)
T k
- the surface concentration time (s)
T s
- the time of flow through secondary canals (s)
T g
- the time of flow through main canals (s)
The determination of previously mentioned flow through and surface concentration times can be performed using proper equations and numerous tables and nomograms, so further comentary of these methodologies is not necessary.
3.
Mistakes in returning periods determination
The selection of returning period for dimensioning of canal system for drainage must be based on economical analysis of ratio between damages that could result in case of flood appearance

and expenses for building up the system for precipitation water drainage. However, with the exception of bigger systems for urban drainage, such analysey are not usual. Therefore the selection of returning period is mostly done according to the present standards for the drainage of respective urban area, usualy between 0.5 and 5 years.
The main mistake in designing the technical documentation for urban areas drainage is that precipitations for returning periods longer than one that was used for the dimensioning of closed canal system are not considered. Table 1 represents an example of interrelation between the intensity of strong precipitations on the impermeable surface in station Rijeka for
20 minutes period considering different returning periods of 2, 10 and 100 years. It can be noticed that exceptional appearance of maximal precipitations for longer returning periods are followed by considerably greater amounts of water on the protected area. For 10 years returning period the amount is approximately 29% greater and for 100 years returning period the amount is greater for 63%.
Table 1. Interrelation between 20-minutes strong period intensity for different returning periods (Rijeka) returning period
2 years
10 years
100 years
H (mm)
27,8
36,0
45,4
I (l/s/ha)
232
300
378
I pp
/I
2
(%)
100
129
163
The error is even greater when ground configuration supports considerable surface outfow. In case when surface evacuation of these waters is not planned, such situations can result in great damages especially in urban areas valuable economic activities are located in groun floors
(public buildings, commercial or other special purpose zones...). Therefore, during hydrological calculations of water drainage it is necessary to consider the mode for evacuation of waters that appear less frequently than one that was used for the dimensioning of closed drainage canal system.
4.
Mistakes in the determination of time of concentration
The mistake that is most frequently done in hydrological calculations for smaller urban areas is that constant values of precipitation durations are considered and the time of concentration

is not calculated at all. Such hydrological calculation considers only previously adopted values of precipitation intensity, catchment area and runoff coefficients but disregards the physics of runoff in urban area.
Therefore in certain regions in Croatia, and probably elsewhere, it is usual to consider
20-minutes precipitation duration for all the analysed profiles. Such calculations result in fact that the drainage systems with shorter time of concentration are as a rule underdimmensioned and others with longer concentration time are over dimmensioned.
Table 2 represents maximal precipitation intensity values for 10 years returning period for station Rijeka for the duration from 10 minutes (420 l/s/ha) to 2 hours (134 l/s/ha). It can be noticed that calculated intensities for different durations differ significantly from that calculated for previously mentioned 20-minutes duration time (300 l/s/ha). The differences are expressed in percents and it can be seen that the values are in range from -27% for
10-minutes period to +124% for 2-hours period. It is logicaly to presume that maximal flow through calculation error would be in the same range if only 20-minutes precipitation intensity would be considered in these calculations as a constant value.
Table 2. ranged
The comparison between 20-minutes precipitation intensity with the duration
Duration l/s/ha
Difference (%) from 10 minutes to 24 hours (Rijeka - 10 years returning period)
10’
410
-27
15’
342
-12
20’
300
0
30’
251
+20
40’
220
+36
1 h
184
+63
2 h
134
+124
5. Mistakes during precipitation intensity determination
Calculation of precipitation water drainage for urban areas usualy includes methods that include the knowledge of characteristics of short-termed intensive precipitation rainfall regime. Such analyses are usualy based on DDP (depth of rainfall, duration, returning period) or IDP (rainfall intensity, duration, returning period) curves that are not always available to the drainage designers and sometimes the designers are not even interested for their availability.
On the contrary, some designers, even now, avoid to use the data regarding maximal precipitation intensities for calculations of maximal runoff quantities. Maximal flows through

are therefore, sometimes, determined considering for example annual rainfalls quantities.
Such calculations are certainly unacceptable.
An analysis of data obtained from 10 pluviographs located in wider region of Zagreb in
Croatia (Bonacci,1984) established that there is no statistical conections between annual precipitation quantities and maximal precipitation intensities of any duration within analysed range from 10 minutes to 24 hours. Correlation coefficients obtained in that study suggest weak statistical connection of these parameters only with 24 hours data. Practicaly, the durations of intensive precipitations that are usefull for the determination of maximal flows through are much shorter than 24 hours. Just for illustration Table 3 summarizes average coefficients of correlation obtained by previously mentioned analysis and coefficients for analysed station Zagreb-Gri~ in a series of data from 71 years.
Table 3. Correlation coefficients between maximal short-termed intensities and annual precipitation quantities
Duration 10’ 20’ 30’ 40’ 1 h 2 h 4 h 8 h
Zagreb-Gri~ 0,10 0,15 0,18 0,19 0,18 0,08 0,16 0,23
Average 0,32 0,30 0,31 0,30 0,28 0,20 0,23 0,25
12 h
0,36
0,35
24 h
0,47
0,45
Besides that, in designers practice, it is almost usual to get the data regarding the characteristics of maximal precipitation intensity by extrapolating from DDP curves these data that are out of the range of analysed input parameters. Therefore, if ombrographic data regarding the real characteristics of short-termed intensive precipitations are not available they are usualy extrapolated from the daily data or even from data for more than one day.
Such calculations can result in great discrepancies between the real and calculated precipitation characteristics (Table 4). Such analyses can have a great influence on technical realization of drainage systems that are, therefore, frequently underdimensioned (if shorter precipitation duration data are used) or overdimensioned (if longer precipitation duration data are used).
Table 4. extrapolated
The values of maximal precipitation intensities according to DDP curve from daily data (Rijeka - 10 year returning period)
Duration H h
-according
DDP curve
(mm)
H e
-from daily precipitation data
(mm)
H e
/H h
(%)

10’
20’
30’
40’
1h
2h
6h
12h
24h
24,6
36,0
45,1
52,8
66,1
96,1
125,0
147,3
173,7
42,3
50,9
56,7
61,3
68,3
82,2
110,2
132,6
156,2
243
175
144
125
103
74
68
70
72
These previously mentioned examples of mistakes resulting from using the data regarding the characteristics of short-termed intensive rainfalls are not the only ones that appear during hydrological calculations of drainage systems, but they are certainly the most frequent ones.
There are certainly other mistakes that include primary analysis of ombrographic data and the defining of DDP curves, but such analyses are not usually performed by rainfall water drainage system designers and therefore they should be discussed elsewhere.
6. Mistakes in the determination of runoff coefficient
Very frequent mistake during the calculation of maximal flows through is also a disregarding of precipitation’s infiltration variability and consequently disregarding of the fact that function of effective precipitation is non-linear. Uncritical use of mostly older methodologies for calculations of maximal flows through results in acceptance of constant average runoff coefficients and therefore maximal flow through values are simply functionaly connected with calculated maximal precipitation quantities for certain returning periods.
As an example for unacceptability of such calculation principals Table 5 represents maximal precipitation values for Rijeka for the duration of 20 minutes and for the 10 years returning period. Table also represents the respective calculated values of effective precipitation by SCS method that take into account the non-linear character of infiltration during rainfall precipitation. Table consists values for meadow ground and for four analysed soil groups
(A-D). From such calculated values of effective precipitation and respective runoff coefficients can be noticed that the infiltration possibility influences significantly on the quantity of effective precipitation and consequently on maximal runoff and flow through values.

Table 5. The comparison of rainfall and effective precipitations returning period
2 years
10 years
100 years
H
(mm)
27,8
36,0
45,4
Pf
11,5
18,0
25,9
A
K
0,41
0,50
0,57
Pf
20,7
28,6
37,7
B C
K Pf K
0,78 23,4 0,84
0,79 31,5 0,88
0,83 40,8 0,90
Pf
25,1
32,8
42,2
D
K
0,90
0,91
0,93
7. Mistakes during catchmenta area surface determination
These mistakes are directly connected with previously mentioned mistakes of runoff coefficient determination and disregarding the non-linear relation between rainfalls and runoffs. The catchment area surface determination is a task that is independent on methodology of drainage calculations and it should not be a problem at all. But the determination of catcment area boundaries in urban areas often is followed by mistakes. The real surface of catchment area is often diminished, sometimes even considerably. Extreme rainfalls in such cases cause flood waters considerably more than it can be predicted.
Extreme rainfall appearance of less frequent returning periods causes surface flow on both, the urbanised areas and other still not urbanised gravitating surfaces within catchment area.
Such conditions activate complete catchment area, and such possibilities are often disregarded during calculations. To make the mistake even greater, the mode of evacuation of water exceeding the capacity of closed canal drainage system is often not even considered and that often result in flood appearance in urbanised areas.
The analyses of the degree of building up in urban areas and of the functioning of drainage systems in such extreme situations are frequently omitted. Namely, building up of urban areas and roads influence on the natural water running conditions. In such conditions of extreme precipitation, the roads collect surface running water and therefore, sometimes even independently from closed drainage system, contribute to the formation of extreme flows through on locations where, in natural state, high waters were not gravitating in such degree.
8. Analysis of the high water appearance in the town of Veli Lo{inj on October, 30 th

1995
High waters in urban areas that are a consequence of a local precipitation are normal phenomena although of not very frequent returning periods. The fact that is not normal is the disregarding of such phenomena although they are present, especially in cases of the closed canal drainage systems existence. The existence of drainage system apparently enables flood water evacuation even in conditions of extreme runoffs. Surface waters that appear in such conditions are threatening in economic sense and for population as well.
We are going to present the degree of such events on the example of high water appearance on the area of Veli Lo{inj, small town located on the island Lo{inj in Croatia (Fig.1). During usual precipitation conditions surface runoffs do not appear, and whole water is evacuated by constructed canal drainage system.
Flood waters at this particular location have been caused by the appearance of the extreme precipitation of about 200 mm on 30 October 1995. On approximately 2 km far away located gage-station Mali Lo{inj 129 mm of precipitation was recorded that day and such precipitation had the characteristics of 25 years returning period. The duration of this intensive precipitation was very short (Table 6). Therefore formation of flood wave and its consequences were enormous. Precipitation that was lasted for about 2 hours on Veli Lo{inj location exceeded values of intensities ever recorded in Croatia. Figure 2 represents comparison of these values with a remark on fact that the values for Veli Lo{inj are approximated.
Table 6.
30
Precipitation recorded according to the measurement at Mali Lo{inj station on
October 1995.
Duration (min/hours) Precipitation (mm)
10'
30'
45'
1 h
2 h
24 h
20,3
50,9
76,0
81,0
109,0
129,0

1000
100
Mali Lo{inj
Veli Lo{inj max. in Croatia
10
0.1
1 10
Tim e (hour)
Figure 2. Maximal precipitation of different duration for Croatia region
Precipitation mentioned before have caused the appearance of strong surface runoff even on overgrown impermeable ground made up of karst cretaceous lime-stones and the appearance of flood waves on urban surfaces. Total amount of rainfall that was recorded during previous month was 4.6 mm. Evaluation of maximal flow through was performet by SCS method with approximation of runoff hydrogram by approximation triangle. Maximal flow through obtained like that was 7.5 m 3 s -1 for catchment area surface of 0.334 km 2 . The value of maximal flow through obtained by hydraulical presumptions according to water traces was
7.3 m
3 s
-1
. The best illustration of the degree of flood wave can be seen on Fig. 3. This photograph was taken in one street located in the centre of the town approximately 20 minutes after the peak runoff has happened. The appearance of flood water threatened the safety of local population, and caused considerable material damages on objects in the town. Just for illustration, the costs of repairing the damages just on infrastructural communal objects were about $ 100 000 and the total damages caused by this disaster on residential and other public objects exceeded this value far more.

Figure 3. Flood wave formed in one of the streets of Veli Lo{inj
It is definitely sure that canal network of drainage systems could not be dimensioned on values that would provide complete protection of urban areas from flood appearances.
However, resulting damages of such events could be reduced on minimal level if surface evacuation of water that exceeds the capability of canal drainage system is predicted and planned ahead.
All of us are whiteness’ that such events and damages caused by them on infrastructural and other objects are unfortunately forgotten far to soon. To avoid that it is necessary tu analyse and record them. These analyses and records would be the basement for future designing of urban drainage systems and for planning the purpose of certain urban areas.
9. Conclusion
This work, although it refers on problems of urban areas flood protection does not suggest any

method for calculation or some revolutionary strategic solution for achieving better results in this field. The purpose of this paper is to highlight most frequent mistakes in hydrological calculations for urban areas and to suggest that with their minimalization is possible to obtain positive movements in present designer’s practice. Complete and reliable hydrological elaboration of high precipitation water appearance besides giving the basic elements for drainage systems designing gives also necessary information even for other activities that can be included in flood protection in urban areas, especially for appropriate spatial planning designs.
10. Literature
1. Bonacci, O., (1984) Meteorolo{ke i hidrolo{ke podloge (Meteolological and Hydrological bases), Priru~nik za hidrotehni~ke melioracije I kolo - Odvodnjavanje, Dru{tvo za odvodnjavanje i navodnjavanje Hrvatske: 39-130, Zagreb
2. Bonacci, O., (1994) Oborine - glavna ulazna veli~ina u hidrolo{ki ciklus (Precipitations -
Major Impute Value for Hydrological Circle), Geing - 341, Split
3. Chow, W.T., (1964) Handbook of Applied Hydrology, New York
4. Linsley, R.K., Kohler, M.A., Paulhus, J.L.H., (1972) Hydrology for Engineers,
McGraw-Hill, New York
5. Rubini}, J., Gaji}-^apka, M., Milinkovi}, J., O`ani}, N., (1995) Intenziteti oborine-problemi obrade i interpretacije u praksi (Rainfall Intensity - Analytical and
Interpretative Problems in Practise), Zbornik radova okruglog stola Uloga hidrologije u strukturi gospodarstva Hrvatske: 53-69, Zagreb
6. Rubini}, J., O`ani}, N., Breulj, D., (1995) Analiza upotrebe hidrolo{kih prora~una u praksi projektiranja prometnica (The Analysis of Exploitation of Hydrological Calculations in a Road Desinging Practise), Zbornik radova Prvog hrvatskog kongresa o cestama, Opatija
CORRESPONDING AUTHOR:

dr. NEVENKA O@ANI] addres: Hrvatske vode, VGO Rijeka
G. Ciotta 17b,
51000 Rijeka
Croatia
Phone: +385/51/339755 fax: +385/51/336947
E-mail: hrvatska-vodoprivreda@ri.tel.hr dr. NEVENKA O@ANI]
CROATIAN WATERS - Rijeka
G. Ciotta 17b, Croatia
IRTCUD-RCTC
International Workshop on Nonstructural
Flood Control in Urban Areas
Prof. B. Braga
Av. Brigaderio Luis Antonio, 317-cj.33
01317-901 Sao Paulo, SP Brazil

Rijeka, 20.11.1997.
Dear Colleague:
I am sending to you Paper for International Workshop on Nonstructural Flood Control in
Urban Areas, which will take place in April 20-22, 1998 in Sao Paulo, Brazil.
Your truly,
Nevenka O`ani}
--------------------------------------------------------------------------------------------------------------- dr. NEVENKA O@ANI] addres: Hrvatske vode, VGO Rijeka
G. Ciotta 17b,
51000 Rijeka
Croatia
Phone: +385/51/339755 fax: +385/51/336947
E-mail: hrvatska-vodoprivreda@ri.tel.hr

Duration Precipitation
(min/hours) (mm)
10'
30'
45'
1 h
2 h
24 h
20,3
50,9
76,0
81,0
109,0
129,0
1000
100
Mali Lo{inj
Veli Lo{inj max. in Croatia
10
0.1
1
Tim e (hour)
10