Response of a Sedum Green-roof to Individual Rain Events

8/10/2019 Response of a Sedum Green-roof to Individual Rain Events

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Ecological Engineering 25 (2005) 17

Response of aSedumgreen-roof to individual rain events

Edgar L. Villarreal , Lars Bengtsson

Department of Water Resources Engineering, Lund University, Box 118, SE-221 00 Lund, Sweden

Received 10 July 2004; received in revised form 4 November 2004; accepted 16 November 2004

Abstract

Precipitation and runoff data from several controlled experiments (with dry and wet initial conditions) on a Sedum album

green-roof have been analysed by means of linear programming in order to estimate a unit hydrograph (UH). The obtained UH

was able to accurately predict peak flows and runoff volumes for any rain input. Results from the experiments indicated that

roof slope had no effect on the direct runoff hydrograph, i.e., on peak flows and stormwater volumes. Whether conditions were

dry or wet affected the retention capacity of the green-roof; for dry conditions, between 6 and 12 mm of rain were required to

initiate runoff, while for wet conditions the response was almost straight.

2004 Elsevier B.V. All rights reserved.

Keywords: Sedum album; Green-roof; Stormwater; Unit hydrograph; Linear programming

1. Introduction

Green-roofs are increasingly being used as a source-

control measure for urban stormwater management

as they detain and slowly release rainwater. Their

implementation is also recognised as having other

benefits, including: habitat creation for birds and

insects (Scholz-Barth, 2001); filtering of aerosols;

energy conservation by providing thermal insulation

(Eumorfopoulou and Avarantinos, 1998; Kohler et al.,2002; Wong et al., 2003); improvement of local micro-

climate through evaporation; reduction of rooftop tem-

peratures (Kohler et al., 2002).The last three effects of

Corresponding author. Tel.: +46 46 222 4477;

fax: +46 46 222 4435.

E-mail address: [email protected] (E.L. Villarreal).

green-roofs are related and can mitigate the urban heat

island effect. Some authors (e.g.,Scholz-Barth, 2001)

claim that green-roofs have the potential to control

nutrients; however, the effect of green-roofs on nutrient

reduction is still under investigation. It should be noted

that the benefits of green-roofs are site specific.

From an aesthetic point of view, green-roofs help to

maintain a pleasant living environment and to maintain

a balance between vegetation and urban infrastructure.

Compared to other local stormwater management solu-tions, green-roofs have the advantage of requiring no

additional space, as land can be at a premium in urban

areas. Conversely, they have the potential to transform

between 40 and 50% of the total impervious areas of

cities into usable space. An additional advantage is that

they require little maintenance apart from initial water-

ing to establish plants (although this is only necessary

0925-8574/$ see front matter 2004 Elsevier B.V. All rights reserved.

doi:10.1016/j.ecoleng.2004.11.008


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2 E.L. Villarreal, L. Bengtsson / Ecological Engineering 25 (2005) 17

if natural precipitation is insufficient) and occasional

fertilization.

From the point of view of stormwater management,

it is of interest to know how green-roofs perform sea-sonally over the long term.Bengtsson (2002)used the

water balance approach to study the hydrology of a

Sedum green-roof in Augustenborg, a residential areain

Malmo, southern Sweden. Sedum is commonly used in

Sweden as this genus has modest soil requirements and

is resistant to drought and high exposure to wind and

sun. For the Sedum green-roofs at Augustenborg, it was

found that annual runoff can be reduced by up to 50%

due to evapotranspiration. Studies carried out in other

countries have demonstrated similar results. Accord-

ing toKohler et al. (2002), evaporation from green-

roofs in Germany (5 and 12 cm thick) can account for

6079% of the annual precipitation. Basedon examples

from cities such as Chicago, Philadelphia and Portland,

Scholz-Barth (2001)claimed that, on average, 75% of

rainwater was retained by extensive green-roofs in the

United States. The variation between reported results

is due to different thicknesses of the soil layers and

contrasting types of vegetation.

As stated above, green-roofs can offer improved

urban climate and stormwater management; however,

the studies cited, with the exception ofZimmer and

Geiger (1997), have not looked at their response toindividual rain events, which is an important param-

eter for design of these systems. The objective of this

paper is to describe the response of green-roofs to indi-

vidual rain events. To this end, controlled experiments

on a Sedum albumgreen-roof plot were carried out in

Lund, southern Sweden, and linear programming was

used to analyse the results of these experiments. The

aim was to produce a unit hydrograph (UH) by which

the response of the system could be predicted. Differ-

entroof slopesand initial conditions (wet and dry) were

tested.

2. Materials and methods

2.1. Green-roof plot and rain events

A section ofSedum album green-roof (henceforth

referred to as the plot) was placed in the car-park of the

Department of Water Resources Engineering at Lund

University. The plot (0.80 m 1.93 m, W/L = 0.41) had

a soil-vegetation layer of 4 cm and an underlying geo-

textile layer. The soil was composed of 5% crushed

limestone, 43% crushed brick, 37% sand, 5% clay

and 10% organic material. When dry, the total weightof the green-roof was 35 kg/m2 and the soil poros-

ity was 70%. The plot was placed on an impervious

raised frame, which allowed for runoff collection. Arti-

ficial rains which mimicked both real and synthetic

(i.e., design) rain events were applied over the plot

by means of a sprinkler; then runoff volumes were

measured at 1 min intervals using beakers. The exper-

iments were carried out for different slopes (2, 5,

8 and 14) under both dry (7 summer days with-

out precipitation between experiments, during July

August 2003) and wet initial conditions (i.e., at field

capacity).

The temporal distribution of the three rain events

used for the wet-condition experiments are shown in

Fig. 1. Rain events (a) and (b) replicate real storms reg-

istered at the weather station Turbinen in Malmo which

is located about 25 km from Lund;Fig. 1(c) shows the

2-year designrain for Lund (Niemczynowicz, 1984). In

addition to these rain events, several experiments with

constant rainfall intensity (0.4, 0.8 and 1.3 mm/min)

and dry initial conditions were carried out to ascer-

tain the amount of rainwater required to initiate runoff.

Design rains were used for the experiments becausedesign of urban stormwater structures is based on those

events.

2.2. Mathematical model

The relationship between Q (direct runoff) and R

(effective precipitation) can be written as (Singh, 1976)

Qj= U1Rj+U2Rj1 + +UiRji+1 (1)

in which j = 1, 2, . . ., n (n being the total number of

intervals, or positive Q ordinates spaced at t); i = 1,2,. . .,m;m being the total number of unit hydrograph

ordinates; and i =j for jm and i = m for j > m. The

parametersU1,U2,. . .,Umare the ordinates of a unit

hydrograph oftduration (forthe experiments withthe

green-roof:t= 1 min). These ordinates are subject to

the linear constraint:

t

m

i=1

Ui = 1 (2)


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E.L. Villarreal, L. Bengtsson / Ecological Engineering 25 (2005) 17 3

Fig. 1. Rain events used for the experiments: (a) 2 August 2002, Malmo; (b) 22 July 2001, Malmo; (c)Tr= 2-year for Lund.Pindicates the total

amount of precipitation.

An additional constraint can be set to obtain only pos-

itive values:

Ui 0 (3)

Eq.(1)and the linear constraints Eqs.(2) and (3)rep-

resent the derivation of the unit hydrograph that can

be obtained by linear programming. In addition, lin-

ear programming requires specification of an objectivefunction which must also be linear. The rationale of this

function is to produce a unit hydrograph that minimises

the difference between the observed runoff hydrograph

ordinates,Q, and the reconstituted hydrographs ordi-

nates, Q, computed from U- and R-values. This is

accomplished by minimising the sum of absolute dif-

ferences betweenQ and Q:

Qj Qj= j (4)

Thus, Eq.(1)can be rewritten as

Qj= U1Rj+U2Rj1 + +UiRji+1 + j (5)

in whichis the difference betweenQand Qand may

be positive, zero, or negative; yet, linear programming

requires that must not be negative. This problem is

solved by introducing two slack variables as proposed

byDeininger (1969):

j= uj vj (6)

In which uj and vj are the two non-negative slack

variables that account for positive, zero, or negative

differences. Thus, the objective is to minimise the sum

of these variables:

Z = min

n

j=1

(uj+ vj) (7)

whereZis the objective function.


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Fig. 2. Rain necessary to start runoff, abstractions, effective precipitation and direct runoff.

The differences in peak flow and volume values for

an experiment with a given rainfall event with different

slopes (Table 1),are solely due to continuing abstrac-

tion () which in turn depends on the initial moisture

content of the soil. The continuing abstraction for the

experiments is a fraction of the total precipitation (P);

this fraction ofP was detained in the soil but eventually

ran off.Fig. 4(a)(d) illustrates both the experimental

and deduced direct runoff hydrographs for the experi-

ments for comparison.

2.4. Retention capacity

The experiments with even precipitation were car-

ried out at weekly intervals in order to ensure dry initial

conditions. A summary of the results is presented in

Fig. 3. Average unit hydrograph (1 mm) deduced from uniform rainfall inputs.


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6 E.L. Villarreal, L. Bengtsson / Ecological Engineering 25 (2005) 17

Fig. 4. Simulated (dashed line) and experimental (continuous line) direct runoff hydrographs.

Table 2.Between 6 and 12 mm of precipitation were

required before runoff appeared. Retention depended

to a great extent on rainfall intensity and the slope of

the green-roof; the lower the intensity and slope, the

greater the retention. For a horizontal green-roof under

exceptionally dryinitial conditions, up to 15 mm of rain

can be retained. The maximum retention for a sloped

roof is 10 mm.

Table 2

Retained precipitation dry initial conditions (values in parentheses are % with respect to P)

Rain (mm/min) Duration (min) Total precipitation,P(mm) Rain to start runoff (mm) Total runoff Retention (mm)

Slope 2

0.4 60 24 12 9.2 (38%) 14.8 (62%)

0.8 30 24 10 11.0 (46%) 13.0 (54%)

1.3 30 39 9 31.0 (79%) 8.0 (21%)

Slope 8

0.4 50 20 8 11.4 (57%) 8.6 (43%)

0.8 30 24 7 16.7 (70%) 7.3 (30%)

Slope 14

0.4 60 24 8 14.6 (61%) 9.4 (39%)

0.8 60 48 7 38.0 (79%) 10.0 (21%)

1.3 60 78 6 70.0 (90%) 8.0 (10%)


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3. Discussion and conclusions

The experiments presented here suggest that slope

does not influence the shape of the direct runoff hydro-graph. Indeed, an average UH prepared from uniform

rainfall intensities can accurately simulate the response

hydrograph for any slope and rain event. The greatest

differences between estimated and observed peak flow

values were for the lowest slope: the estimated values

were 716% greater than the observed values. For the

other slopes, most of the estimated values were lower

than the observed values, but the difference was not

more than 10% for any slope. The greatest difference

between observed and estimated values of direct runoff

hydrograph volumes was 5%.

The experiments suggest that slope does influence

retention volumes for dry initial conditions. For a rain-

fall with an intensity of 0.4 mm/min, 62, 43, and 39%

of the total precipitation were retained in the green-

roof having slopes of 2, 8, and 14, respectively. The

corresponding retentions for an 0.8 mm/min rainfall

were 54, 30, and 21%; and for a 1.3 mm/min rain, 21

and 10% were retained for 2 and 14 slopes. Thus,

for a specific rainfall, retention diminishes as slope

increases, and for a specific slope, retention is greatest

for low intensity events. On the whole, the results indi-

cate that under dry initial conditions water can be bothretained and detained, whereas with initial wet condi-

tions only detention is possible. From the experiments

with dry initial conditions and uniform rain intensity,

it was found that between 6 and 12 mm of rain were

necessary to initiate runoff. These values are roughly

comparable to the 10 mm found byBengtsson (2002)

forSedumgreen-roofs in Malmo.

TheestimatedUHcanbeapplieddirectlytoestimate

the response ofSedum album green-roofs having the

same characteristics of the one employed in the exper-

iments. For other types of green-roofs, the approach

used here can be employed to estimate their response

providing that coincident records of precipitation and

runoff data are available.

Acknowledgements

Edgar Villarreal received financial support from the

Swedish Association of Graduate Engineers (Civilin-

genjorsforbundet) through the Environmental Fund

(Miljofond).

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Response of a Sedum Green-roof to Individual Rain Events