Thanks Dear Ljubomir and Dear Mohan for the pertinent links selected. According to one of the links that Ljubomir selected “Estimating Storm Water Runoff” from 2012, by John Poullain (PE):

“Limitations of the Formula: The major limitation is that the Rational Formula only produces one point on the runoff hydrograph--the peak discharge rate. When basins become complex, and where sub-basins combine, the Rational Formula will tend to overestimate the actual flow. The over estimation will result in the oversizing of stormwater management systems.”

In fact I obtained results in the opposite direction. The classic Rational Method is a kinematic method (i.e., it assumes that the maximum flow occurs when whole upstream drainage basin is contributing for the formation of the flow in the sewer section, for a time of precipitation, Tp, equal to the time of the concentration of the basin in that section, Tc), assuming implicitly a symmetric triangular hydrograph of base 2Tc. The intensity of precipitation decreases, in the curves of Intensity-Duration-Frequency (IDF curves), for a given Period of Return, TR, when the time of precipitation increases. Higher Intensities of precipitation during periods shorter than Tc can produce higher peak flows, even if not all area of the drainage basin contributes for the formation of the peak flow. The decrease of the intensity of precipitation with the time of transportation in the pipe sewers in the rational method may produce a larger decrease in the peak flow than the effects of propagation, attenuation and storage in the pipe sewers, as I demonstrated with a very simple example in the conference article from 1996 in attachment of my first answer. I confirmed those results also for tree-like networks (arborescent networks) in a more elaborated example that I developed on that time.

According to results that I obtained in the decade of nineties, the classic rational method may underestimate the storm water peak flow rate in the sewers, even for relatively small drainage basins.

Conference Paper Modelação Hidráulica em Colectores de Sistemas Urbanos de Dr...

It is true, you can underestimate the peak flows using the rational formula but that is if the factors are not region specific. But in well developed areas, standard design criteria has been developed historically from experience to be relevant for that region's climate, topography, soil conditions, receiving waters or drainage wells, tidal conditions especially impacting coastal communities, etc. Most states in the US have their own customized stormwater design criteria, thus for a desert like state, the C factor can be different than for a less arid or more tropical state. And with safety factors applied or using the higher 100-year rainfall event rather than the standard 25-year event, it usually comes out right in urbanized areas. What can go wrong is when a region or country which has no rules decides to implement by importing somebody else's design manuals and criteria without adjusting and customizing it specifically for that area.However, this looks like an research opportunity see how things currently stand or have changed since your last results. Some links from various design manuals and studies below:

http://udfcd.org/wp-content/uploads/uploads/resources/technical%20papers/20-yrs%20Stormwater%20Managemet%20Evolution%201999.pdf

http://www.fws.gov/southwest/es/Documents/R2ES/LitCited/4TX_Sal/Booth_1991_Urbanization_and_the_Natural_Drainage_System.pdf

http://www.nrcs.usda.gov/Internet/FSE_DOCUMENTS/stelprdb1083019.pdf

http://erode.evsc.virginia.edu/papers/howard-detach-94.pdf

http://www.pdhonline.org/courses/h119/stormwater%20runoff.pdf

http://www.ct.gov/deep/lib/deep/water_regulating_and_discharges/stormwater/manual/Chapter_7.pdf

http://www.iwmi.cgiar.org/Publications/IWMI_Research_Reports/PDF/pub056/Report56.pdf

http://ocw.unesco-ihe.org/pluginfile.php/493/mod_resource/content/1/Urban_Drainage_and_Sewerage/7_System_Components_and_Design/Chapter_7-System_components_and_Design_part2_for_PDF.pdf

http://ocw.unesco-ihe.org/pluginfile.php/445/mod_resource/content/1/Urban_Drainage_and_Sewerage/3_Urban_Hydrology/Urban_Hydrology/Urban_hydrology_note.pdf

http://nepis.epa.gov/Adobe/PDF/P100EA7H.pdf

https://www.fhwa.dot.gov/engineering/hydraulics/pubs/10

http://www.pub.gov.sg/abcwaters/ABCWatersProfessional/Documents/managingUrbanRunoff.pdf

http://redac.eng.usm.my/EAD/EAD512/MSMA.pdf

http://eng.lacity.org/techdocs/stormdr/lacounty/Contents/hydman.pdf

http://www.nj.gov/dep/stormwater/bmp_manual/NJ_SWBMP_5%20print.pdf

http://earth.geology.yale.edu/~ajs/2001/Apr_May/qn10t100432.pdf

Some more links and some for a different perspective like the UN legal one definig hydrology of water in 1979: 

http://cdn.intechweb.org/pdfs/10998.pdf

http://www.nat-hazards-earth-syst-sci.net/14/1417/2014/nhess-14-1417-2014.pdf

http://coweeta.uga.edu/publications/2164.pdf

http://soilandwater.bee.cornell.edu/Research/VSA/papers/BernierJH86.pdf

http://legal.un.org/ilc/documentation/english/a_cn4_320.pdf

http://www.geog.ucsb.edu/~kclarke/Geography232/Markda

http://www.unep.org/dewa/giwa/publications/finalreport/giwa_final_report.pdfvid.pdf

This is interesting, dear António.

Quite useful and modern in terms of our urban societies in an era of constant and unexpected climate changes and the so-called Global Warming.

Congratulations on your question and interesting field of work. It is not at all my specialty, but I'll certainly follow the results of this thread that I consider of utmost importance and actuality.

Thank you !

Thanks Dear Maria: In fact, this is one of my focus of research interest that is waiting, since a long time ago, for sun shining days. I would like to know what the experts in this area consider nowadays with respect to this subject, given that I suppose that many procedures were developed in the past for the reduction of the peak flow resulting from the application of the classic rational method. The current Portuguese regulation from 1995, for example, includes a procedure of this type. Of course that wrong politics, the increase of the impermeable surfaces in urban areas, and the observed changes of the climate (?) do not help too.

I have found some resources for computing the peak storm water flow rates in urban drainage systems. I hope that I have not duplicated some link from @Mohan's answer. It is much better to attach links by pasting it under post, not in answer box.

http://www.nj.gov/dep/stormwater/bmp_manual/NJ_SWBMP_5%20print.pdf

http://ocw.unesco-ihe.org/pluginfile.php/493/mod_resource/content/1/Urban_Drainage_and_Sewerage/7_System_Components_and_Design/Chapter_7-System_components_and_Design_part2_for_PDF.pdf

http://www.pdhonline.org/courses/h119/stormwater%20runoff.pdf

Thanks Dear Ljubomir and Dear Mohan for the pertinent links selected. According to one of the links that Ljubomir selected “Estimating Storm Water Runoff” from 2012, by John Poullain (PE):

“Limitations of the Formula: The major limitation is that the Rational Formula only produces one point on the runoff hydrograph--the peak discharge rate. When basins become complex, and where sub-basins combine, the Rational Formula will tend to overestimate the actual flow. The over estimation will result in the oversizing of stormwater management systems.”

In fact I obtained results in the opposite direction. The classic Rational Method is a kinematic method (i.e., it assumes that the maximum flow occurs when whole upstream drainage basin is contributing for the formation of the flow in the sewer section, for a time of precipitation, Tp, equal to the time of the concentration of the basin in that section, Tc), assuming implicitly a symmetric triangular hydrograph of base 2Tc. The intensity of precipitation decreases, in the curves of Intensity-Duration-Frequency (IDF curves), for a given Period of Return, TR, when the time of precipitation increases. Higher Intensities of precipitation during periods shorter than Tc can produce higher peak flows, even if not all area of the drainage basin contributes for the formation of the peak flow. The decrease of the intensity of precipitation with the time of transportation in the pipe sewers in the rational method may produce a larger decrease in the peak flow than the effects of propagation, attenuation and storage in the pipe sewers, as I demonstrated with a very simple example in the conference article from 1996 in attachment of my first answer. I confirmed those results also for tree-like networks (arborescent networks) in a more elaborated example that I developed on that time.

In the link below “A Self-Learning Manual - Mastering Different Fields of Civil Engineering Works (VC-Q&A Method)”, By Vincent T. H. CHU, from 2010, in pages 156/157, a basic elementary question and the respective answer is given:

“Rational Method should not be used for large catchments in estimating peak runoff. Is it true?

One of the assumptions of Rational Method is that rainfall intensity over the entire catchment remains constant during the storm duration. However, in case of a large catchment it stands a high probability that rainfall intensity varies in various part of the large catchment. In addition, for long duration of rainfall, it is rare that the rainfall intensity remains constant over the entire rainstorm and a shorter duration but a more intense rainfall could produce a higher peak runoff. Moreover, a reduction of peak runoff is also brought about by the temporary storage of stormwater like channels within the catchment.”

Effects of attenuation, propagation, and storage in the surface drainage basins, and particularly detention ponds not anticipated, natural or artificial in the urban basins, that are not directly considered in the classic rational method, and that may eventually increase with the increase of the area of the urban drainage basin served (?), may possibly reduce significantly the peak flows in the pipe sewers, but intense rainfalls of short duration may produce larger peak flows than the estimation obtained with the classic rational method.  

http://www.iemauritius.com/upload/files/a_self-learning_manual_-_mastering_different_fields_of_civil_engineering_works_(vc-q&a_method).pdf

Antonio - I believe it comes down to how well urban drainage basins have been studied and data modified/fine tuned over time to provide proper drainage.  Every region has its own unique characteristics. Flooding is going to occur if the same rainfall amount in one hour period instead of being spread out over 24 hours. Last week in Miami, we had 9-inches of rainfall in 24-hours in the western part while it was about 3-inches on the eastern part - the rainfall was evenly spread out virtually non-stop. The roads were flooded in the western part but once the rain stopped, within an hour the road floodwaters receded whereas in other areas it took a few more hours. The rainfall event exceeded the design capacity but its intensity ensured serious flooding did not occur. Another time, there was 11 inches of rain in less than 24-hours and people could not leave their homes for 2-days waiting for waters to recede

Last year, I experienced an extremely intense storm event, 2-inches rain event in less than a hour, and the roads and businesses flash flooded next to the river  washing away cars  despite storm discharge receiving rivers right next to the road. And then been through 3 direct hurricanes up to 130 mph, the rainfall intensity was very high with roads flooding but was high and dry because it was designed above the 100-year flood elevation and in a well drained area.

What you have pointed out is that the rational method parameters developed which works in one place cannot be applied elsewhere. And this means more research and studies to determine the best methods - which is a good thing!!

Some links on a recent article on Miami's coastal flooding and a finding age of water below:

http://www.newyorker.com/magazine/2015/12/21/the-siege-of-Miami

http://pubs.acs.org/doi/pdf/10.1021/acs.est.5b03227

https://uwm.edu/news/uwm-scientist-develops-new-way-to-find-age-of-drinking-water/

Dear Antonio,

The following material may be of interest to you.

Regards,

Antonis D. Koussis

The so-called rational method, introduced about 150 years ago and credited either to Mulvaney (1851) or to Kuichling (1889) (Chow, 1964, p. 14-6), is still being used widely around the world today in the design of “small” urban storm drainage systems, despite lacking rigorous basis in hydraulics and also verification. Chief reason for this method’s popularity among hydrologists and authorities alike is certainly its simplicity. The model consists of the single equation Qp = Cia that purports to estimate the peak discharge Qp from a drainage basin of area a, the hydraulic characteristics of which are supposed to be encapsulated in the value of the dimensionless constant runoff coefficient C, when the drainage basin receives a gross rainfall of constant intensity i over a time period equal to or longer than the basin’s time of concentration or time to equilibrium. It should be noted, however, that while the rational formula is applied typically to ungauged drainage basins of size, say, on the order of a ~100 ha, e.g., a < 40 ha (Kirpich, 1940), Giandotti (1934) has applied it to drainage basins from 170 to 70000 km2 area size.

Application of the rational formula, even to small, well-defined urban basins, requires, aside from the non-trivial task of selecting appropriate C-values, estimating a characteristic rainfall duration, which determines the rainfall intensity through the use of an intensity-duration-frequency curve. Huber (1987) criticised the concept of the time of concentration or time to equilibrium as ambiguous, astutely asserting that the proper characteristic time is the wave travel time from the most remote point of a basin to its outlet. Thusly defined, the time of concentration tc is the time that results in maximum flow rate at the basin outlet. Hydraulic theory shows the wave travel time as inversely proportional to the rainfall (nonlinearity, the wave celerity increases with the flow rate, e.g., Koussis (2009, 2010)), therefore the travel time is not constant (e.g., Grimaldi et al., 2012). However, proper flood wave propagation is ignored in the context of the rational method in regard to discharge concentration (and to pipe flow, commonly computed as steady uniform flow), largely because the practical calculation of travel time for overland flow in natural drainage basins based on the well-established theory of flood wave motion is fraught with uncertainties. Efstratiadis et al. (2014) compared measured peak flow to Qp calculated with the rational formula, estimating the time of concentration by four popular empirical formulas as tc(a, Dz = an elevation difference, L = a length of streamflow), and obtained greatly disparate results.

 The implementation of the rational method is based on the following procedure:

The rational method’s elementary concept and mathematical simplicity mislead towards a recipe-like application. In reality, however, all steps of the procedure described above involve critical assumptions and estimations for which open research questions exist. To gauge the significant uncertainty in the results of the rational method, due to inherent uncertainties in the estimation of its input parameters, the rational method should be placed in a non-deterministic framework. Efstratiadis et al. (2014) show that the rational method’s deterministic application can give significantly lower peak flows compared to upper-quantile results of related Monte Carlo simulations, also noting that: “The different aspects of uncertainty in flood modelling are only partially represented by the return period of the design rainfall. A more consistent approach would require integrating the uncertainties of all associated components, including model input, model parameters and initial conditions. Such an option can be offered by stochastic simulation, which is the most effective and powerful technique for analysing systems of high complexity and uncertainty. In particular, the model parameters (many of which are, in fact, variable) reflect the high complexity of the flood system. In the context of stochastic simulation, these should be treated as random variables, to which are assigned proper statistical distributions.” Excerpts from Efstratiadis et al. (2014) follow.

Section 2, Handling flood design by means of “recipes”: lessons learned from the rational method

“In the flood design context, the probabilistic measure of the return period of an event, T, is set a priori to represent the acceptable risk for all relevant quantities (peak flow, flood volume, flow depths and velocities, inundated areas, etc.). Yet, the risk related to these flooding outcomes cannot be estimated statistically, i.e. by evaluating their statistical distributions, due to common scarcity or even lack of observed data. Therefore, the return period is assigned to the input, i.e. the rainfall, for which it is easier to find records of sufficient length and accuracy. In fact, the design rainfall itself is an uncertain quantity. Typically, this is estimated from an ombrian curve, which is nothing more than a statistical model, the parameters of which are inferred from historical samples. The quantification of the uncertainty of ombrian curves is difficult, because analytical expressions for its confidence limits do not exist, except for few distributions (e.g. normal, exponential), which are however unsuitable for describing rainfall maxima.”

 “The basin’s response to rainfall is also governed by inherent uncertainties, due to the complexity of flood processes, their nonlinear interactions and their dependence on the antecedent soil moisture conditions. In the rational method, which employs a very simple rainfall–runoff transformation that avoids process descriptions, these uncertainties are reflected in the model parameters, i.e. the time of concentration, the areal reduction factor and the runoff coefficient. Yet, by using the rational method with known parameters we erroneously assume that a single value of Qp exists for a specific return period of rainfall (Viglione and Blöschl, 2009). In a deterministic context, the actual statistical behaviour of the peak discharge is represented only partially through the ombrian curve.”

From the Conclusions

“Flood design and modelling is more than blind application of “recipes”, regardless of the sophistication of the underlying predictive tools. Caution is recommended, because few of the methodologies and modelling tools available in the literature, of any level of complexity, have been tested extensively against flood data observed in many different catchments worldwide. In this vein, hydrological experience (and, why not, intuition) is of key importance to prevent misuse of these tools as well as to properly account for underlying uncertainties, which are apparent in all aspects of flood modelling.

Particularly regarding predictions in ungauged basins, (a) the user must know a model’s validation basis, statistical and physical, and (b) predictions with modelling tools that use regionalized parameters cannot be trusted before validation at some local setting.”

References

Chow, V.T. 1964. Runoff, Chapter 14, Handbook of Applied Hydrology, McGraw-Hill, New York, NY.

Efstratiadis, A., A.D. Koussis, D. Koutsoyiannis and N. Mamassis, 2014. Flood design recipes vs. reality: can predictions for ungauged basins be trusted?, Nat. Hazards Earth Syst. Sci., 14(1), 1–12.

Giandotti, M., 1934. Previsione delle piene e delle magre dei corsi d’acqua, Memorie e Studi Idrografici, Ministero dei Lavori Pubblici, Roma.

Grimaldi, S., A. Petroseli, F. Tauro, and M. Porfiri. 2012. Time of concentration: A paradox in modern hydrology, Hydrological Sciences Journal, 57(2), 217–228.

Huber, W.C. 1987. Discussion of “Estimating urban time of concentration” by R.H. McCuen et al., J Hydraul. Eng., 113(1): 122-124.

Kirpich, Z. P., 1940. Time of concentration of small agricultural watersheds, Civil Engineering, 10(6), 362.

Koussis, A.D. 2009. An assessment review of the hydraulics of storage flood routing 70 years after the presentation of the Muskingum method, Hydrological Sciences Journal, 54(1): 43 – 61.

Koussis, A.D. 2010. Reply to the Discussion of An assessment review of the hydraulics of storage flood routing 70 years after the presentation of the Muskingum method by M. Perumal, Hydrol. Sci. J., 55(8): 1431 – 1441.

Kuichling, E. 1889. The relation between rainfall and runoff of sewers in populous districts, Trans. ASCE, 20.

Mulvaney, T.J. 1851. On the use of self-registering rain and flood gauges in making observations of the relations of rainfall and flood discharges in given catchments, Trans. Inst. Civil Engrs., Ir. (Dublin) 4(pt. 2), p. 18.

My Sincere thanks Dear Antonis for your long answer with pertinent references and some input that may complement my main questions. I do not know if you saw the last figure of the conference paper that I posted in my first answer (example of application of a dynamic wave numerical model that I developed in the decade of 90). Urban drainage systems of storm water and sanitary wastewater is my area of research in my University since 1988 (project of the systems, optimization, management and rehabilitation). In fact, sometimes we have no time to make our answers simpler and shorter.

Dear Antonio,

I am glad that my answer was useful to you.

If I understood it right, the last figure in your conference paper refers to the flow inside the drainage network. This is, of course, an important part of the system. However, most of the uncertainty in the design of storm drainage systems derives from the modelling of the processes in the discharge concentration phase, which I believe was also the object of your question.

Regarding flood routing through the storms drains, you should consider the diffusive wave (DW) model in its storage routing form. The DW model is a parsimonious flood routing option with a wide applicability range (see my papers cited in my first answer and also Bowen et al. (1989) Storm Drain Design-Diffusive Flood Routing for PCs, J. Hydraulic Eng., ASCE, 115(8), pp. 1135-1150). The high efficiency of the DW model makes it very suitable for stochastic simulation, as suggested in my first answer regarding the rational method.

Best regards,

Antonis D. Koussis       

Dear Antonis, thanks again. I concur with you. In fact, I underlined already before the great importance of the effects in the superficial runoff in the urban drainage basin that in my understanding contribute decisively for the formation of the peak flow; not so much inside the pipes in a project phase given that it is supposed that sewers operate in open channel flow, and the current trend suggests the limitation of the extension of the pluvial networks as much as possible, due to the high capital costs involved. I do not know the paper you mention, but I will give a look to it, as for your papers too. Nevertheless, the model I developed (and that I applied on that simple example that I formulated) is a complete dynamic model, i.e., it considers all terms (and all effects) of the momentum equation in the sewers open channel flow. Currently we have for example the storm water management model (SWMM) of USEPA fully available in the INTERNET (I suppose it is a dynamic complete model too, but I do not know yet fully its details).

Dear @Antonio, dear colleagues, there are thousands of available articles on this issue, here at ResearchGate. Link follows!

https://www.researchgate.net/publicliterature.PublicLiterature.search.html?type=keyword&search-keyword=methods+for+computing+the+peak+storm+water+flow+rates+in+urban+drainage+systems&search-abstract=&search=Search

Thanks for your kind words and friendship, Dear Barbara, which I appreciate. I could guess. Nevertheless, this theme may be related with climatic changes, as Maria wisely pointed, and perhaps also with other areas of science, particularly with studies in socioeconomic areas, and with environment that I suppose is an area of your interest.

Some links below on "Voodoo Hydrology" on calculation methods:

http://www.foresteruniversity.net/slides/voodoo-hydrology-pitfalls-urban-hydrology-methods.pdf

http://www.paep.org/meetings/08/presentations/PAEP_Stormwater_Management_Seminar.pdf

http://www.eng-tips.com/viewthread.cfm?qid=165345

http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=20&cad=rja&uact=8&ved=0ahUKEwjYyu2Qt_LJAhXGMyYKHb-lDnY4ChAWCE0wCQ&url=http%3A%2F%2Ffiles.engineering.com%2Fdownload.aspx%3Ffolder%3D098c1eb3-4a1d-4575-b0c0-1cd1ea099838%26file%3Dh131content.pdf&usg=AFQjCNGG0CEiqJF6VVD1Y8BDC6hm2LnjDQ&bvm=bv.110151844,d.eWE

http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=26&cad=rja&uact=8&ved=0ahUKEwjbqem-ufLJAhWFNSYKHYm5DRM4FBAWCDMwBQ&url=http%3A%2F%2Fdelcocd.org%2Fworkshop%25203-26-2010%2FAYC_Stormwater_Program%5B1%5D.ppt&usg=AFQjCNG74TeqVidWwB_OryiA48S1t2C1Fw&bvm=bv.110151844,d.eWE

http://www.chesco.org/DocumentCenter/View/7380

Dear António Manuel Abreu Freire Diogo

I hope you can get benifit from this links:

- http://ocw.unesco-ihe.org/pluginfile.php/493/mod_resource/content/1/Urban_Drainage_and_Sewerage/7_System_Components_and_Design/Chapter_7-System_components_and_Design_part2_for_PDF.pdf

- http://www.njstormwater.org/bmp_manual/NJ_SWBMP_5%20print.pdf

Regards

Raid

A RG link to my most recent paper in this area

https://www.researchgate.net/publication/332447065_Peak_Flows_and_Stormwater_Networks_Design-Current_and_Future_Management_of_Urban_Surface_Watersheds

Hello António Manuel Abreu Freire Diogo

The best and simplest method for estimating peak discharge in a large

urban drainage system is CLARK's synthetic unit hydrograph method.

It is simple to learn and can be using for areas as large as 5000 km2.

This method is explained in books on hydrology.

The rational method Q= CIA is fraught with the danger of guessing the runoff coefficient C especially for a drainage basin consisting of different run-off surfaces.

Many thanks Dear Amaechi J. Anyaegbunam for your answer mentioning the “CLARK's synthetic unit hydrograph method” that, according to your words, seems your preferred method for guessing peak flows in basins “as large as 5000 km2”, seems well “explained in books on hydrology” and is “simple to learn”. I will take a look on it. The rational method and its application in stormwater networks can be used for small urban areas, is explained practically everywhere, and particularly very well in manuals of project practice and scientific works. However, if you wish more details, particularly in the Portuguese practice, see

https://www.researchgate.net/publication/271847229_Optimizacao_Tridimensional_de_Sistemas_Urbanos_de_Drenagem

@ António Manuel Abreu Freire Diogo

Although the unit hydrograph model was developed for large watersheds

it has been found applicable to small watersheds from 0.5 Ha to 25 sq.Km.