Introducing leakywell concept for stormwater quantity control in Dhaka, Bangladesh
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Abstract
Dhaka, the capital city of Bangladesh with rapid and unplanned urbanization, is subjected to annual average rainfall of 2,076 mm. The intensity of rainfall during 10 years recurrence interval and 1 h duration of the city is 98 mm/h. The stormwater drainage systems of the city are often unable to manage peak runoff volume and hence urban flooding is common after medium to heavy rainfall events. A proposal to introduce leakywells using water sensitive urban design (WSUD) principles was investigated for Dhaka’s drainage network to transfer the present unsatisfactory situation into one which is sustainable. The regime in balance strategy was considered to control the stormwater for 100 years recurrence interval. We applied scaling theory to 57 years (1953–2009) daily rainfall data for the estimation of subdaily rainfall intensity values. It was found that two leakywells; each with depth H = 2.0 m and diameter D = 2.0 m, in 500 m^{2} allotment can improve the situation. The emptying (drain) time of the proposed device is around 1.25 days, which meets the standard criterion. Groundwater table, soil hydraulic conductivity and topographic slope of Dhaka also support for installations of leakywells.
Keywords
Leakywell Water sensitive urban design Regime in balance Emptying time Stormwater Source controlAbbreviations
 A
Catchment area (km^{2})
 C
Effective runoff coefficient
 D
Diameter of leakywell (m)
 F
Factor of proportionality
 H
Height of leakywell (m)
 H*
Scaling exponent
 I
Rainfall intensity (mm/h)
 K_{h}
Soil hydraulic conductivity (m/s)
 K_{o}
Observed infiltration rate (m/h)
 L
Overland flow length (m)
 N
Manning’s roughness coefficient
 Q_{f}
Infiltration capacity (m^{3}/h)
 S
Slope
 T
Return period (year)
 t_{c}
Time of concentration (min)
 T_{e}
Emptying time (day)
 U
Moderation factor
 V
Stormwater runoff volume (m^{3})
 σ_{24}
Standard deviation of annual maximum daily rainfall intensity
 λ
Duration of rainfall for statistical analysis (h)
 μ_{24}
Mean of annual maximum daily rainfall intensity (mm/h)
 τ
Time base of design storm runoff hydrograph (min)
Introduction
The existing drainage system in Dhaka, Bangladesh focuses on collecting the stormwater as completely and as quickly as possible and discharging it directly to local waterways. This system has proven unsatisfactory and it leads severe flooding in lowlying areas. With an increased urbanization, fraction of pervious area is reduced resulting in low stormwater recharge into the aquifer. Although the city had an excellent natural drainage system consisting of 24 natural canals and a large retention wetland pond before 1940 (Haq 2006), with the rapid and unplanned urbanization, most of the canals have been illegally occupied by real estate companies and this has resulted reduced carrying capacity of stormwater of the city. About 85 % of the city is now drained through 40 (lined) channels to the surrounding rivers (Tawhid 2004). The annual average rainfall of the city is 2,076 mm (Ahammed and Hewa 2011). The total rainy days of Dhaka vary from 95 to 144 days; however, the mean value is 120 days with standard deviation as 11. The mean frequency of daily rainfall intensity equal or greater than 100 mm/day in a year is 2 (SD = 1.5).
Type of Infrastructure  Description 

Open channel  Number = 22 Width = 10 to 30 m Length = approx. 80 km 
Underground pipe  Length = 265 km Diameter = 45 to 300 cm 
Box culvert  Length = 10.5 km Size = 2.5 m × 3.4 m to 4.1 m × 6.0 m 
Permanent pumping station  Number = 3 Capacity = 9.6 m^{3}/s at Narinda, 10.0 m^{3}/s at Kallyanpur, 22 m^{3}/s at confluence of Buriganga River and Dholai Channel 
The existing drainage system has failed to reduce flood frequency in Dhaka and the utilization of stormwater has been ignored (Barua and Ast 2011; Ahammed and Hewa 2012). Moreover, the continual construction of stormwater/sewerage systems, water storages and water distribution networks aimed at providing water security is no longer a sustainable solution, because of financial and environmental impacts (Brown et al. 2009). Therefore, some forms of decentralized stormwater management tools, like water sensitive urban design (WSUD—the Australian version of sustainable urban water cycle management) or low impact development (LID—the corresponding strategy in North America) may provide sustainable solution to stormwater management problems in Dhaka, Bangladesh.

Development of design specifications required in the design process of WSUD technologies,

Hydraulic design of leakywells,

Investigation of the site conditions for consideration of installation feasibility of leakywells in Dhaka City.
Materials and methods
Study area
Rainfall intensity duration and frequency relationships in Dhaka
It is always important to carry out some forms of validation on the produced IDF relationship. Lumbroso et al. (2011) applied disaggregation model for cross checking of produced IDF curves in Caribbean Region. They performed frequency analysis of disaggregated data to establish IDF curves for 2, 5, 10, 25 and 50 years return periods and found that 95 % confidence interval boundaries of the generalized extreme values (GEV) fit 6 h observed IDF data. BenZvi (2009) derived IDF curves from large partial duration series (PDS) at four stations of Israel meteorological service. For instance, he found that annual maxima series (AMS) were the best described by generalized Pareto distribution (GP) and GEV, while Gumbel and lognormal distributions were capable of describing both PDS and AMS.
Time of concentration
Estimation of time of concentration for Banani, Dhaka
Method  Formula  Time of concentration, t_{c} (min)  Considered t_{c} (min) 

Rational method (Pilgrim 2001)  t_{c} = 0.76 A^{0.38}  82  86 
Bransby Williams equation  \( t_{\text{c}} = \frac{FL}{{A^{0.1} S^{0.2} }} \)  123  
Kirpich method  \( t_{\text{c}} = 0.0078\left( {\frac{{L^{0.77} }}{{S^{0.385} }}} \right) \)  78  
National resources conservation service (NRCS)  \( t_{c} = \frac{L}{60V} \) or \( t_{\text{c}} = \frac{{25.2 \left( {n.L} \right)^{0.8} }}{{P^{0.5} S^{0.4} }} \)  71  
Kinematic wave formula  \( t_{\text{c}} = \frac{{0.94 n^{0.6} L^{0.6} }}{{i^{0.4} S^{0.3} }} \)  109  
Kerby equation  \( t_{\text{c}} = \left( {\frac{0.67 n L}{{S^{0.5} }}} \right)^{0.467} \)  51 
Six different methods were applied to Banani catchment to get an appropriate value. As we observed in the Table 2, resulting t_{c} values from six methods were not equal. It was furthered noticed that three methods produced reasonably closer values (82, 78, 71 min) and hence, it was rational to take t_{c} for Banani as 82 min, the highest of these three values. However, the arithmetic mean of all estimations provided the value as 86 min, which represented all methods and we considered it in the design process of leakywells. It was clear from the work that getting an appropriate t_{c} value for the catchment was hard and could be subjective.
Regime in balance strategy
Critical stormwater runoff volume
The weighted average runoff coefficient of composite developed area (roof and pavement) was calculated as 0.9. The estimated value was multiplied by frequency conversion factor (F_{y} = 1.2 for 100 years recurrence interval). However, runoff coefficient of green fields of Dhaka was considered as 0.20 (Ahmed and Rahman 2010).
Estimation of stormwater volume using Eq. 2 for designing hydraulic structures is idealised; it does not represents the peak quantity. Usually, in practice, the declining limb of a hydrograph is 2–4 times longer than the rising limb. To consider the worst scenario of stormwater quantity control in Dhaka City, we also estimated stormwater volume assuming the declining limb of hydrograph is three times longer than the rising one. This awful situation doubles the stormwater volume computed by the Eq. 2.
Diameter of leakywell and emptying time
Interim relationship between ARI and emptying time
Recurrence interval of storm (years)  1  2  5  10  20  50  100 
Emptying time (days)  0.5  1.0  1.5  2.0  2.5  3.0  3.5 
Results and discussions
 Basic design specification

Critical storm duration = 86 min

Site time of concentration = 15 min

Time base of design storm runoff hydrograph = 101 min

Recurrence interval = 100 years

Rainfall intensity (100 years and 86 min storm) = 117 mm/h

Effective runoff coefficient = 1.0

Soil hydraulic conductivity = 1.53 × 10^{−5} m/s

Moderation factor = 1.0

 Stormwater runoff volume in 500 m^{2} allotment

Peak stormwater runoff volume (from roofs and pavements) = 51.43 m^{3}

Runoff volume beyond the capacity of existing drainage = 30.86 m^{3}

Runoff volume for green field sites = 16.73 m^{3}

Runoff volume in regime in balance strategy = 14.13 m^{3}

Critical runoff volume for each leakywell (total two) = 7.07 m^{3}

 Dimensions of leakywell and emptying time

Assumed depth of leakywell = 2.0 m

Diameter of leakywell = 2.0 m

Emptying time = 1.25 days

(for 1 m < D < 10 m) where, Q_{f} infiltration capacity, K_{o} observed soil hydraulic conductivity, a = 6.244D + 2.853, b = 0.93D^{2} + 1.606D − 0.773.
The above results have been discussed based on an idealized situation. For an awful circumstances, where the estimated stormwater volume may be double due to longer declining limb of hydrograph, four leakywells each with diameter D = 2.5 m and depth H = 2.0 m in 500 m^{2} residential allotment may be necessary to control the stormwater quantity. Installations of hydraulic structures considering this situation will be expensive and hence, idealized circumstances can be adopted for installations of leakywells in Dhaka City.
Conclusions
This paper has explained a recent approach for urban stormwater management in residential areas of Dhaka City. Some basic design specifications were prepared for applying WSUD principles. We applied scaling theory to 57 years (1953–2009) daily rainfall data to develop IDF relationship. It was prepared based on daily rainfall data, which is the only source of precipitation in Bangladesh. Validity of IDF was checked comparing the corresponding values to Darwin, Australia. Prepared IDF of Dhaka has significant practical implication, as it is one of the major hydrological tools for designing drainage structures. We applied six different methods for estimation of time of concentration, another important design specification and took the arithmetic mean value of all methods. We considered regime in balance strategy, i.e. stormwater runoff volume ‘after–before’ of urbanization was considered in the design process.
Introducing of leakywell will be first kind of work in Bangladesh. Using regime in balance strategy for recurrence interval of 100 years, we assumed that around 60 % stormwater runoff volume in Banani area is beyond the capacity of existing drainage system and is responsible for flooding, which can be managed by installing two leakywells, each with diameter D = 2.0 m and depth H = 2.0 m in 500 m^{2} allotment. We considered emptying time, groundwater table, topographic slope and soil hydraulic conductivity and found that these scenarios would support for installation of leakywells. Hence, the approach explained in this paper can be an effective solution of everyday problems of stormwater quantity control in residential areas of Dhaka City. This approach can also be applicable to other countries with similar geoenvironmental conditions.
Notes
Acknowledgments
This study was supported by Australian Government’s Endeavour Award. The first author of this paper is the recipient of Endeavour Award Scholarship 2010 for conducting his PhD study at the University of South Australia. Comments by two anonymous reviewers and Professor Nesar Ahmed from Bangladesh Agricultural University significantly improved the quality of this paper. The authors are also sincerely grateful to Bangladesh Meteorological Department for providing the daily rainfall data of Dhaka.
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