Design of Flood Protection in Hong Kong

Design of flood protection in Hong Kong

J.V.L. Beckers, F.L.M. Diermanse & A. Verwey Deltares, Delft, the Netherlands M.L. Tse Mott McDonald HK Limited, Hong Kong, China F.Y.F. Kan & C.C. Yiu Drainage Services Department, the Government of the Hong Kong Special Administrative Region, China

ABSTRACT: Design of waterways in the rapidly developing city of Hong Kong is commonly conducted based on the Stormwater Drainage Manual (SDM) of the Drainage Services Department. A pragmatic design rule, which is part of the SDM, was reviewed. Special interest was paid to the transition zone between coastal and riverine influences, where floods can be caused by intense rainfall, storm surges or by a combination of the two phenomena. The review shows that the pragmatic design rule provides a reasonable estimate of the fully probabilistic result. Where differences are found, the pragmatic design rule errs on the safe side. This finding can be of interest to delta regions around the world, where the combined influences of rainfall and storm surge pose a similar probabilistic challenge to design of flood protection.

1 BACKGROUND 1.1 Hong Kong flood hazard 1.2 Stormwater Drainage Manual The densely populated city of Hong Kong is a rap- Flood protection and drainage facilities in Hong idly developing coastal region on the South China Kong are designed according to a set of design stan- Sea with a population of over 7 million. The average dards laid down in the Stormwater Drainage Manual annual rainfall is about 2400 mm between 1981 and (SDM, 2000), which is issued by the Drainage Ser- 2010, which is high compared to other world cities. vices Department (DSD) of the Government of the Moreover, the rainfall distribution is far from uni- Hong Kong Special Administrative Region. The de- form. The city is often threatened by intense rain- sign rules in the SDM are based on probabilistic cri- storms in the wet season, between April and Octo- teria, that are: each part of the drainage system must ber. These rainstorms can be particularly severe be able to withstand a flood event with a predefined during May and June, with peaks of over 100 mm/hr, return period. The return period (T) depends on the causing traffic disruption, floods and sometimes type of area and on the type of element of the drain- human casualties. age system. The main trunks of the urban drainage Hong Kong is also subject to tropical cyclones or system are designed to have a flood protection level typhoons between May and November. About once of T=200 years. Smaller branches and rural drainage every 5 years a tropical cyclone of the highest cate- are designed to different return periods, see Table 1. gory (hurricane signal No. 10) strikes Hong Kong, often causing severe, damage, storm surges and Table 1: Design standards for drainage system elements. flooding of lower lying coastal areas. Less severe Element Return period tropical cyclones occur more often. On September Urban drainage: trunk 200 years 29, 2011, the Hong Kong Observatory hoisted a Urban drainage: branch 50 years tropical cyclone warning of Signal No. 8 for typhoon Rural catchment main 50 years Nesat, forcing many economic activities to be can- channel celled or postponed. Village drainage 10 years Flood protection and storm water drainage facili- Intensively used agricul- 2-5 years ties are an essential part of the Hong Kong urban in- tural land frastructure. The drainage and flood protection systems are also in constant need of extension, in The required capacities of the various elements of particular in the new towns, rural townships and ur- the drainage system are calculated using a design ban developments of the Northern New Territories rainstorm (hyetograph), rainfall runoff and hydro- (NNT), at the northern border of Hong Kong. logic/hydraulic routing model. The Hong Kong design rainstorms for several return periods are de- sea level and their probabilities of combined occur- scribed in the SDM, as well as the methods for set- rence are taken into account. As a case study, flood ting up rainfall runoff models. Similarly, design of levels are calculated for the Northern New Territo- drainage for tidal effect is based on frequency analy- ries (NNT) districts of Hong Kong (see Figure 1), sis of sea level measurements over the past decades. where new developments are taking place and local The SDM includes a table of extreme sea levels for drainage problems are actually experienced. The re- different return periods for four tide gauge stations at sults can thus be used for an upgrade of the local the Hong Kong coastline. More details of the SDM drainage system. method will be given in the next section. The transition zone between coastal and riverine influences poses a challenging problem. Elevated water levels in that area can be caused either by intense rainfall runoff or by a severe storm surge at sea, or by a combination the two phenomena. This implies that there is no single design condition, but rather a collection of likely and less likely combinations of extreme and less extreme rainstorms and storm surges. Together, these combinations consti- tute the design flood levels. To calculate the flood levels in the transition zone requires a probabilistic assessment of all possible hydraulic conditions and associated probabilities of occurrence. This is a complex and computationally demanding task. In order to simplify the necessary assessments, the SDM includes an approximate pragmatic design FigureThe 1: next NNT section Study area describes and test in locations. more detail the rule, which states that the T-year flood level is the maximum of two hydraulic conditions: a T-year sea The next section will describe in detail the SDM level in conjunction with relatively moderate X-year design procedures and the probabilistic methods that rainfall event and a T-year rainfall event in conjunc- are used to validate the SDM. Section 3 will present tion with a moderate X-year sea level. The return pe- the calculation results, including a comparison of the riod X of the conjugate event is either 2 or 10 years, probabilistic calculations to the pragmatic design depending on the return period of the main event T: rule. Section 4 discusses the findings and concludes this paper. X=10 years for T=50, 100 or 200 years X=2 years for T=2, 5 or 10 years 2 METHOD For example, to calculate the flood level of an ur- General approach ban drainage branch (design return period 50 years), 2.1 the design water level is calculated as the maximum Design of rainfall drainage and coastal flood protec- of two situations: (1) a T=50-year rainstorm event in tion systems should take into account many criteria, conjunction with a 10-year sea level and (2) a T=50- including economical, environmental, legal and es- years sea level in conjunction with a 10-year rainfall thetic considerations. The SDM focuses mainly on event. Instead of all possible combinations of sea the technical requirements regarding capacity of ele- level and rainfall intensity, only two situations need ments of the drainage system, such as storm water to be considered. This saves significant computing culverts, channels, pipelines and pumping facilities, and analysis time and makes the results easier to un- and on the flood levels for river bank and coastal derstand and explain. However, much depends on protection. The peak flows or flood levels that have the validity of the pragmatic design rule. In 2010, a to be accommodated are calculated in the following review was carried out on the SDM and, as part of steps: that, a validation of the pragmatic design rule.

• Determine design rainstorms for a range of re- 1.3 Objectives turn periods. The design storm profile consists of a point hyetograph and an areal reduction factor This paper presents the results of a review of the (ARF). The ARF is applied to take account of pragmatic design rule. The flood levels at test loca- the fact that, for larger areas, the T-year rainfall tions according to the pragmatic design rule are at different locations does not occur simultane- compared to the results of a fully probabilistic calcu- ously or even during the same storm. The point lation, in which many combinations of rainfall and hyetograph for the SDM is constructed from the Intensity-Duration-Frequency (IDF) curve. De- The safety standards for flood defence works are tails and variations of this method are described generally expressed in terms of a return period T. in (Keifer and Chu, 1957) and (Chow et al., For the Hong Kong area, water level variations in the 1988). drainage system and rivers are caused by rainfall and • Calculate the rainfall runoff for each catchment sea level variations. The relative influence of either in the area of interest. The runoff depends on the of the two causes differs for different locations. In rainfall intensity, catchment size and topography, the coastal zone, close to the sea, the sea level varia- soil type and land use. The SDM describes the tions will largely determine the local water level. In rational method, which is a relatively simple ap- riverine areas, the rainfall is the dominating factor. proach using a stationary flow assumption. More In the transition zone, between riverine and coastal advanced methods (e.g. Time-Area Method or influence, both processes are relevant. Because of Unit-Hydrograph Method), or numerical models the random nature of rainfall and sea level varia- should be used for catchments of more complex tions, water level probabilities in the transition zone geometry. must be based on a multivariate probabilistic model- • A hydrologic/hydraulic routing model calculates ling approach. the peak flows at locations of interest in the system. For the test cases in the Study Area, the Single matrix method SOBEK modeling suite (www.sobek.nl) was 2.2 used. Figure 3 displays part of the model sche- In order to calculate the maximum water levels for matization. a given return period, Binnie and Partners (1987) • Extreme sea levels for different return periods consider combinations of sea level and rainfall ex- are calculated using historical observations. A tremes in a two-dimensional matrix (see Figure 2). frequency analysis of annual maxima yields the Each matrix element represents a combination of sea estimated sea levels for return periods of interest. level and rainfall intensity, with associated probabili- • A probabilistic model combines peak flows and ties of exceedance. The corresponding water levels sea levels and calculates the probability of occur- in the drainage system can be calculated using a rence of various possible combinations. A hy- combination of a rainfall-runoff model and a hydrau- draulic model calculates the associated maxi- lic model. The probability of exceedance of a certain mum water level at the locations of interest. water level in the drainage system is then obtained Finally, the probabilistic model computes the by numerical integration of the probabilities over all maximum water level for a given return period matrix elements that exceed this particular water from the water levels for every combination and level. the associated probabilities.

This paper focuses on the last step in this procedure, which received special attention in the review of the SDM. Other aspects were also investigated and reviewed in the case study but will not be discussed here. Interested readers are referred to the online ver- sion of the SDM, available from www.dsd.gov.hk, or encouraged to contact the authors.

Figure 2: Matrix for calculation of probability of exceedance of water levels. Reproduced from Binnie & Partners (1985).

If sea level and rainfall are uncorrelated, the prob- Figure 3: SOBEK model for Hong Kong: D-Flow 1D ability of each matrix element can be obtained by Pipes and D-Flow 1D Open Water plus D-Rainfall Run- multiplying the individual probabilities of ex- off Open Water programmes. ceedance (per year) of the associated sea level and rainfall intensity. The result is the probability that a certain sea level and rainfall intensity are both ex- It is assumed that if a sea level and rainfall peak ceeded within the same year. However, since these occur on the same day, then the peaks coincide. In events may occur on different days of the year, the reality, there can be a time shift between the sea lev- probabilities should be divided by 700, which is el and rainfall peaks. The effect of time shifts be- roughly the number of tidal cycles per year. The fac- tween sea level and rainfall peak was investigated in tor of 1/700 represents the probability that the sea a separate study. The results indicate that the con- level and rainfall peaks coincide within the same stant sea level assumption leads to a conservative tidal cycle. This approach assumes total independ- design in the transition zone, with a maximum dif- ence between sea level and rainfall. In reality, ele- ference in water level of 47 cm at location A in the vated sea levels and rainfall are correlated, because transition zone (see Figure 1) for a T=50 year flood they both occur during storm events. The result of event. For locations in the riverine and coastal zone, this calculation therefore underestimates the ob- which are completely dominated by rainfall and sea served frequency of water levels in the drainage sys- level respectively, the timing effect vanishes. tem. The double matrix method takes into account the A simple correction to the assumption of total in- probability that a sea level and rainfall peak occur on dependence can be made by introducing a storm sea- the same day. Instead of using the overall (full time son. If the sea level and rainfall maxima only occur series) probability distribution, the conditional prob- during a certain part of the year (the storm season), abilities are used. That is, the probability of rainfall then the probability that they coincide is 1 over the given that there is a typhoon and the probability of a number of tidal cycles in that period, which is less sea level given that there is a rainstorm event. These than 700. This method was proposed by Binnie and conditional probabilities differ from the non- Partners (1987), who found that the observed water conditional (full year) probabilities, because there is levels seem to occur 1.5 times more frequently than a correlation between rainfall and sea level. By using indicated by independent events analysis. The cor- conditional probabilities, the method takes into ac- rection of all frequencies by 1.5 is, however, some- count part of the correlation between the probability what heuristic and calls for a more founded ap- distributions of sea level and rainfall peaks. proach. However, the double matrix method only dis- criminates between an event and a non-event. The conditional probability does not take into account Double matrix method 2.3 any correlation between the magnitude of the sea In order to account for some correlation between level and rainfall. In other words, it is assumed that sea level and rainfall, a double matrix method was there is no dependency between the intensity of the introduced by Mott MacDonald (1990a,b). This rainfall and the height of the maximum sea level. method considers two types of storm events: “typhoon” and “non-typhoon”. For each type of event a Copula description of correlations separate probability matrix is constructed, similar to 2.4 Figure 2 but with a conditional probability on one of To take fully into account the correlations requires the axes: a multivariate probability distribution, which is dif- • In the “typhoon” matrix, the sea level is the dom- ficult to establish for the extreme range because of inant determining variable. The probability of a the limited number of observations. Moreover, a certain sea level is obtained from annual maxi- straightforward description of the bivariate distribu- ma. The probability of rainfall is then calculated tion through a correlation coefficient is too simplis- as a probability conditional on a typhoon taking tic. Although the correlation coefficient is a strong place. indicator for the dependency between two variables, • In the “non-typhoon” matrix, the peak rainfall in- it provides only information about the average de- tensity is the dominant variable. The probability pendency between the two variables over their full of exceeding a certain sea level is defined as a range of values. In practice, the degree of correlation probability conditional on a non-typhoon rain- between two variables may vary and be very differ- storm taking place. ent for the average and extreme ranges. For each matrix and for each location, contours of For this type of problem, the correlation structure equal maximum water level are calculated. Next, the can be described by a copula function (de Matteis, probability of exceedance of different contour lines 2001). Imagine two random variables V and W, hav- is calculated using a numerical integration proce- ing two marginal probability of exceedance distribu- dure, such as described in Binnie and Partners tion functions FV(V) and FW(W). The bivariate prob- (1987) and DSD (1992). The frequencies of ex- ability distribution function is given by: ceedance of water levels from both matrices are added up to yield the overall frequencies of ex- Fvw( ,) = PV( ≤ vW , ≤ w ) (1) ceedance. The copula of function F is then defined as the Where D 1 is the Debye function with parameter two dimensional function C: [0,1] → [0,1] for k=1 (Abramowitz et al. 1965). The Archimedian which: copulas in Table 2 have only one parameter α, which also determines the average correlation, given by Kendall’s correlation coefficient. The correlation CFvF( V( ), W ( w)) = Fvw( , ) (2) structure, however, is determined by the type of gen- If the random variables V and W are independent erator function. then the copula is: Kendall’s correlation coefficient is a measure of the rank correlation between sea level and rainfall (in contrast to the more familiar Pearson’s correla- CFvF, w= FvFw (3) ( V( ) W ( )) ( ) ( ) tion coefficient, which is directly related to the co- variance). Kendall’s coefficient is defined as: In most practical applications, the bivariate distri-   bution function F(V,W) is unknown and so is the as- ρτ ( XY,) = Px( 1 − x 2)( y 1 −> y 2 ) 0  sociated copula function. The usual approach is to   (5) −Px( 1 − x 2)( y 1 −< y 2 ) 0  test several standard copulas, combine this with general knowledge about the dependency between the It can be calculated from the set of joint observations random variables and choose the best match with the of sea level (x 1) and rainfall intensity (x 2). observational data. Commonly used standard copula functions are the The procedure to find the copula that describes Archimedian copulas. These are produced from so- the correlation between the sea level and rainfall in- called generator functions ϕ, for which the following tensity is as follows: requirements apply: • Determine Kendall’s correlation coefficient for the combined observations of sea level and 1. The function ϕ must be valid on the range [0,1] rainfall; and the function result is [0, ∞]; • Construct Archimedian copulas from the corre- 2. ϕ is strictly decreasing; lation coefficient; 3. ϕ is convex; • Construct the empirical copula from the joint 4. ϕ (0)= ∞; observations of sea level and rainfall intensity; 5. ϕ (1)= 0; • Choose a copula function that matches the em- For two standard uniform random variables r and pirical copula and is in agreement with general s (rainfall and sea water level), a copula Cϕ can be knowledge about the correlation structure. constructed from: The empirical copula is determined from ob- −1 served marginal and joint exceedance frequencies of Crs( , ) =ϕ ϕ( r) + ϕ ( s )  (4) ϕ   sea level R and rainfall intensity S. The empirical marginal exceedance frequencies are given by: All copulas that are produced from a generator function ϕ by this procedure belong to the group of 1 FR()= NrR () > (6) Archimedian copulas. Three well known Archime- ()obs Nobs dian copulas and their generator functions are given 1 in Table 2. FS()=() NsS ( > ) (7) N obs obs Table 2: Archimedian copulas and generator functions. and the empirical joint exceedance frequency is de- Name Kendall’s ρρρ ϕϕϕ(t) fined as: 4 e−αt −1    −ln 1 Frank: 1− 1 − D1 ()α  −α  FRS(,)= NsSrR ( >∩> ) (8) α e −1  ()obs Nobs α This empirical exceedance frequency is compared 1 −α to the value predicted by the Archimedian copulas. Clayton: α + 2 ()t −1 α The best match is defined as the least mean squared difference.

Gumbel- 1 α 1− ()− ln t Hougard: α

3 RESULTS tions in the coastal and riverine zones, one of the two frequency curves typically dominates. Finally, the frequency curves can be used to cal- 3.1 Double matrix method culate a maximum water level for a given return period and used for design of flood protection. The water levels for all combinations of sea level and rainfall for both the typhoon and non-typhoon Non-cyclone series events were used to compute contour plots. An ex- Cyclone series Combined ample of a contour plot for non-typhoon events is given in Figure 4. Each contour line describes the 100 combinations of rainfall and sea levels that lead to the same maximum water level. Figure 4 is a contour plot for location A in the transition zone (see map in Figure 1), where both the influences of sea level and 10 Return period (years) rainfall are present. This leads to curved contour lines. If the sea level becomes extreme, the influence of the rainfall vanishes and vice versa. For locations in the coastal zone the influence of rainfall is always 1 2.5 3.0 3.5 4.0 4.5 5.0 weak and the contour lines are more vertical. For lo- Water level (mPD) cations in the riverine zone the contour lines are more horizontal. Figure 5: Water level exceedance frequency curve for location A, calculated as the sum of the exceedance

frequencies for the non-cyclone and cyclone matrix.

3.2 Correlations

As mentioned in the previous section, a correction

factor that accounts for the correlation between the

height of the sea level and magnitude of rainfall in-

tensity is calculated and applied to the joint ex-

ceedance frequencies. For positively correlated proc-

esses, this factor will be larger than 1. The

probability of joint occurrence of exceedance of high

threshold levels will be higher than for independent

phenomena.

The correlation between sea level maximum and

rainfall intensity was investigated based on joint ob-

servations in the Study Area. The correlation was Figure 4: Water level contour plot of the non- found weakly positive for the typhoon event data, cyclone matrix for location A in the transition zone. i.e. higher rainfall intensity for higher sea levels.

Kendall’s correlation coefficient is about 0.2. Pear- Next, the exceedance frequency as a function of son’s correlation coefficient has values between 0.17 water level is calculated. This was done by a nu- (1 hour duration) and 0.23 (4 hour duration). A scat- merical integration procedure described in Mott ter plot for 1 hour rainfall is shown in Figure 6. MacDonald (1990). The correlation between sea level and rainfall intensity is initially ignored. A cor- 80 rection factor to the exceedance frequency for this 70 60 correlation is later applied. This will be discussed in 50 the next section. 40 30 The exceedance frequency curves for the typhoon 20 and non-typhoon events are combined by adding the 10

max rainfall (mm/hr) exceedance frequencies from the two matrices. An 0 2 3 4 extrapolation is used to estimate the return periods TBT max sea level (mCD) for water levels outside the sampled range. Figure 6: Correlation between sea level at TBT and rainfall The result for location A is shown in Figure 5. intensity in the study area. For this location, the influences of sea level and rainfall are about equal. The frequency curves for non- For non-typhoon events, no correlation between typhoon and typhoon events are similar. For loca- rainfall and sea level was found. Pearson’s correlation coefficient is smaller than 0.03. Therefore, the rainfall intensity and sea level were assumed independent for non-typhoon events. As expected, an effect that depends on the return The data from the Study Area indicate that period is observed in the transition zone. For T=5, Frank’s and Clayton’s copula give the best match, the effect of enhanced rainfall in the typhoon event with almost identical mean squared differences. series is about 5 cm. For longer return periods, ef- However, Clayton’s is an asymmetric copula, exhib- fects between 0.1 and 0.3 m are observed. iting greater dependence in the negative tail than in Unexpectedly, a small effect of the correlated the positive. This correlation structure suggests that rainfall is also found at two locations in the riverine the correlation between sea level and rainfall be- zone. Differences of up to 5 cm are found for loca- comes very strong for very low values of either. In tions F and M for very long return periods (T>50). other words, the probability of rainfall during ty- This was investigated in detail and found to be phoon events having a very low sea level will be caused by numerical uncertainty in the extrapolation very small. This is in contrast to what is observed to these long return periods. There is no real influ- from the data and therefore Clayton’s copula is dis- ence of correlated rainfall in the typhoon event series missed on physical grounds. Frank’s copula is cho- at these locations. sen as the best representative of the correlation structure of the empirical data. This copula displays a Comparison to pragmatic design rule more or less constant correlation over the range of 3.3 values of both variates. The double matrix method requires a large num- From the copula function, a correction can be cal- ber of rainfall runoff and hydraulic model calcula- culated to the previously calculated joint probability tions. The results in the previous section are based distribution. The correction can be applied to either on 9*9+9*9=162 SOBEK model simulations. For of the marginal probability distributions. In this locations in the coastal and riverine zone, a more study, a correction was made to the rainfall probabil- simple approach can be followed, because the nor- ity conditional on the sea level. Frank’s copula was mative water levels are dominated by sea level and used to make a correction to the rainfall IDF that is rainfall respectively. For example, the 100 year re- input to the SOBEK simulations. The correction to turn period water level at an upstream location can the rainfall probability for very high sea levels was be found using a single runoff simulation of the found to be approximately 1.9. In other words, in- T=100 year rainfall design storm. tense rainfall becomes almost 2 times more probable The pragmatic design rule was compared to the in case of a very high sea level, compared to the av- double matrix results. Differences in results for both erage probability for all typhoon events. methods are given in Figure 8 for flood levels asso- This result was compared to the previous calcula- ciated with 5, 10, 50, 100 and 200-year return peri- tion without a correction to the rainfall in the ty- ods. It is found that the pragmatic method gives a phoon statistics, i.e. assuming independence between conservative estimate of the matrix method result. the intensity of rainfall and the height of the sea lev- On average, the pragmatic method water levels are el. The difference between the two calculations 24 cm higher than the results from the matrix meth- shows the effect of the correlation on the design wa- od. Largest differences of 45 cm are found in the ter levels. The largest effect is expected in the transi- transition zone. This corresponds to a factor of about tion zone, where a combination of high sea level and 2 for the return period. heavy rainfall cause the highest water levels. If the probability of such combinations increases, this will 0.50 enhance the design water levels. The difference be- 0.45 tween the two calculations is shown in Figure 7. 0.40 0.35 Effect of correlation 0.30 on design water levels 0.25 0.3 T=5 yrs 0.20 T=10 yrs 0.25 T=50 yrs 0.15 T=100 yrs T=200 yrs Difference in Water Level (m) 0.10 0.2 0.05 0.15 0.00 A5 A4 A3 A2 A1 A B D E F G H 0.1 Location

T=5 years T=10 years T=50 years T=100 years T=200 years 0.05

(m) level water in difference 0 Figure 8: Differen ces between pragmatic design rule and 0 5 10 15 20 25 double matrix approach. T=5 design water level (mCD)

Figure 7: Effect of correlation on design water levels. 4 CONCLUSIONS 5 REFERENCES

The double matrix approach takes into account only part of the correlation between sea level and Abramowitz, Milton; Stegun, Irene A., eds. (1965), rainfall. The analyses described in this paper show Handbook of Mathematical Functions with Formulas, that the rainfall during typhoon events is correlated Graphs, and Mathematical Tables, New York: Dover, pp. with sea level causing higher design water levels at 998, ISBN 978-0486612720 locations in the transition zone. The effect is of the order of 20 cm for long return periods (T>50 years) Binnie & Partners, 1987: New Territories Circular Road at specific locations. The correlation can be ac- Improvements, Au Tau to Fan Kam Road and vehicular counted for through a copula description and a cor- link at Lok Ma Chau. Downstream Flood Study. High- rection factor in the fully probabilistic method, how- ways Department (Hong Kong). ever at the cost of considerable analytical and computational efforts. Chow, 1988: Chow V.T., Maidment D.R. and Mays L.W. The pragmatic design rule as proposed in the 1988. Applied Hydrology. McGraw-Hill: New York. SDM (2000) is a much more straightforward method leading to somewhat conservative design flood lev- DSD, 1992: A study on a methodology of stormwater els. In the transition zone, the difference between the drainage analysis which considers the combined influ- flood levels from the pragmatic design rule and the ence of heavy rain and high sea level, Drainage Service matrix method, varies between 10 and 45 cm. For Department (DSD) technical report no 1, July 1992. the coastal and riverine zones, the results of the pragmatic method are identical to those obtained Keifer C.J. and Chu H.H., 1957: Synthetic storm pattern from the fully probabilistic method. for drainage design. Journal of the Hydraulics Division, The pragmatic design rule tends to err on the safe side and gives a better estimate of the flood level ASCE 83(4): 1–25. than simplistic assumptions of either total dependency or independency. Assuming total dependency Mott MacDonald, 1990a: Territorial Land Drainage and amounts to taking the T-year sea level in combina- Flood Control Strategy Study – Phase 1; Task 3: Specific tion with the T-year rainfall. This leads to overly Technical Considerations. Mott MacDonald Hong Kong conservative design. On the other hand, assuming to- Ltd, March 1990. tal independency ignores the fact that elevated sea level and intense rainfall typically occur simultane- Matteis, R. de: Fitting copulas to data, Diploma thesis, ously during storms. Obviously, this leads to too low Univ. Zurich (2001). estimates of the flood levels in the transition zone. The pragmatic design rule is therefore considered Mott MacDonald, 1990b: Topic Report No. 16: Urban a reasonable alternative to the fully probabilistic Drainage Modelling, West Kowloon Reclamation. Mott method for the test locations in the North New Terri- MacDonald Hong Kong Ltd, 1992. tories (NNT) districts of Hong Kong. A conservative margin of a few decimeters can be acceptable in SDM, 2000: Stormwater Drainage Manual; planning, de- some situations. It should be kept in mind that the sign and management, Drainage Services Department, frequency curves and hydraulic model results con- Government of the Hong Kong Special Administrative tain uncertainties. These uncertainties are likely to Region. Third Edition December 2000. also cause errors of a few decimeters. The pragmatic design rule can be of interest to delta regions around the world, where the combined influences of rainfall and storm surge pose a similar probabilistic challenge to design of flood protection. The appropriate return periods X of the conjugate events will typically depend on the area under con- sideration. For example, a strong correlation between rainfall and sea level leads to higher values of X. However, the basic approach is applicable to delta areas around the world. The pragmatic design rule offers a simple and efficient alternative design method if the fully probabilistic method is found too complex or time consuming.