Flood risk assessment for informal settlements

Abstract

The urban informal settlements are particularly vulnerable to flooding events, due to both their generally poor quality of construction and high population density. An integrated approach to the analysis of flooding risk of informal settlements should take into account, and propagate, the many sources of uncertainty affecting the problem, ranging from the characterization of rainfall curve and flooding hazard to the characterization of the vulnerability of the portfolio of buildings. This paper proposes a probabilistic and modular approach for calculating the flooding risk in terms of the mean annual frequency of exceeding a specific limit state for each building within the informal settlement and the expected number of people affected (if the area is not evacuated). The flooding risk in this approach is calculated by the convolution of flooding hazard and flooding fragility for a specified limit state for each structure within the portfolio of buildings. This is achieved by employing the flooding height as an intermediate variable bridging over the fragility and hazard calculations. The focus of this paper is on an ultimate limit state where the life of slum dwellers is endangered by flooding. The fragility is calculated by using a logic tree procedure where several possible combinations of building features/construction details, and their eventual outcome in terms of the necessity to perform structural analysis or the application of nominal threshold flood heights, are taken into account. The logic tree branch probabilities are characterized based on both the orthophoto recognition and the sample in situ building survey. The application of the methodology is presented for Suna, a sub-ward of Dar es Salaam City (Tanzania) in the Msimbazi River basin having a high concentration of informal settlements.

Appendices

Appendix 1: Estimating the parameters of the intensity–duration–frequency (IDF) curves

The IDF curves can be characterized by two or three parameters, as shown in the following expressions:

$$ h_{r} \left( {d,T_{R} } \right) = a\left( {T_{R} } \right) \cdot d^{n} $$

(12)

$$ h_{r} \left( {d,T_{R} } \right) = \frac{{a\left( {T_{R} } \right) \cdot d}}{{\left( {b + d} \right)^{c} }} $$

(13)

in which T _R is the return period and a(T _R ), b, c, and n are the parameters that have to be estimated through a probabilistic approach. In the present study, the power-law curves expressed in (12) have been used. Herein, a Gumbel probability distribution (belonging to the GEV family of distributions) has employed, considering only the extreme events on a block fixed window (Maione and Moisello 1993) to fit the extreme rainfall data:

$$ P\left( {h_{r} } \right) = \exp \left\{ { - \exp \left[ { - u\left( {h_{r} - v} \right)} \right]} \right\} $$

(14)

where P(h _r ) is cumulative distribution function (CDF) for h _r . The parameters of the Gumbel distribution are related to the sample mean μ and sample standard deviation σ through the following equations:

$$ u = 1.28/\sigma $$

(15)

$$ v = \mu - 0.45 \cdot \sigma $$

(16)

The inverse of CDF (14) can be calculated by calculating h in terms of P(h _r ) and duration d:

$$ h_{r} \left( {d,P} \right) = v - \ln \left[ { - \ln \left( P \right)} \right]/u $$

(17)

Substituting (15) and (16) and introducing the variation coefficient CV equal to μ/σ:

$$ h_{r} \left( {d,P} \right) = \mu \left( d \right) \cdot \left\{ {1 - CV\left( d \right) \cdot \left[ {0.45 + \frac{1}{1.28} \cdot \ln \left[ { - \ln \left( P \right)} \right]} \right]} \right\} $$

(18)

Since the probability P is related to the return period T _R , h can be expressed in terms of the return period:

$$ h_{r} \left( {d,T_{R} } \right) = \mu \left( d \right) \cdot \left[ {1 + CV\left( d \right) \cdot K} \right] $$

(19)

where⁶

$$ K = - \left\{ {0.45 + \frac{1}{1.28} \cdot \ln \left[ { - \ln \left( {1 - \frac{1}{{T_{R} }}} \right)} \right]} \right\} $$

(20)

The experimental evidence also shows that extreme precipitations have a physical property, known as scale invariance, such that holds the following relation:

$$ h_{r} \left( {T_{R} ,sf \cdot d} \right)/h_{r} \left( {T_{R} ,d} \right) = (sf)^{n} $$

(21)

in which sf is a scale factor and n is a parameter function of the location. It can be shown that this scale invariance implies the statistical self-similarity between the probability distribution of h _r (d) and h _r (sf·d). Applying the scale invariance by means of the bound method, an equal value of n can be imposed for any return period T _R (Chow et al. 1988). As a result of the statistical self-similarity, μ(d) = a _μ ·d ⁿ, in which μ(d) is the mean value for the Gumbel distribution. Substituting the expression for μ(d) in Eq. (19), one obtains the flood height as function of duration d and return period T _R :

$$ h_{r} \left( {d,T_{R} } \right) = a_{\mu } \cdot d^{n} \cdot \left( {1 + CV_{m} \cdot K} \right) $$

(22)

Taking into account the general expression (12), the above equation can be written as:

$$ h_{r} \left( {d,T_{R} } \right) = a\left( {T_{R} } \right) \cdot d^{n} $$

where a(T _R ) can be calculated as:

$$ a\left( {T_{R} } \right) = a_{\mu } \cdot K_{{T_{R} }} $$

(23)

where $K_{{T_{R} }} = \left( {1 + CV_{m} \cdot K} \right)$. $K_{{T_{R} }}$ is generally known as the growing factor (with T _R ). CV _m denotes the mean CV over different durations d. For a variation coefficient slightly variable with the duration d, the mean value CV _m can be evaluated by the following expression:

$$ CV_{m} = \frac{1}{k} \cdot \sum\limits_{i = 1}^{k} {CV_{i} } $$

(24)

in which k is the considered duration, generally equal to 5, (e.g., refers to d = 1, 3, 6, 12, and 24 h) in our study k is equal to 7 (refers to d = 10′, 30′,1 h, 3 h, 6 h, 12 h, 24 h).

Appendix 2: The sample field survey sheet

A typical survey sheet filled during the phase of data acquisition in the field, Suna sub-ward, Dar Es Salaam (See Sect. 5.5).

Appendix 3: Logic tree

The detailed logic tree used in a simulation-based procedure for constructing the fragility curve (see Sect. 3.2).