University of Leeds Public empowerment in ood mitigationobokhove/fdsleeds2018.pdf · ood gauge data, yielding a clearcost-e ectivenessanalysis. I Using gauge data of UK/French oods;

University of Leeds

Public empowerment in flood mitigation

University of Leeds


Using “Flood-Excess Volume” to quantify &communicate flood-mitigation schemes

Onno Bokhovewith thanks to M. Kelmanson1, T. Kent1, G. Piton1 and J.-M.

Tacnet1, & . . .

(1) School of Maths, University of Leeds,(2) Universite Grenoble Alpes, IRSTEA, France

School of Mathematics, Leeds 22nd November 2018

University of Leeds


Motivation: Wetropolis

I interactive model of extreme rainfall and river flooding in an urban environmentI conceptualises many important aspects of the science of flooding and extreme

events in a way that is accessible to and directly engages the public

I provides a scientific testing environment for flood modelling, control andmitigation, and data assimilation, and has inspired numerous discussions withflood practitioners and policy makers . . .

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/users/amtob/dropbox/Camera Uploads/2016083016207.mov

Motivation: public empowerment and diagnostic

I I will introduce the well-known concept of flood-excess volume (FEV), as thevolume of water that caused the flood damage, to discuss flood-alleviation plans,plans which aim to protect us against floods.

I The objective is to give interested citizens, including decision makers, tools toeffectively assess/improve such plans. I will use easy-to-understand arithmetic,taking divisions/using percentages, as well as graphical tools.

I Moreover, what we developed is a straightforward diagnostic for simulations &flood gauge data, yielding a clear cost-effectiveness analysis.

I Using gauge data of UK/French floods; Boxing Day 2015 Apperley Bridge:

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1. Flood-Alleviation-II+ River Aire analysis

Figure: Armley gauge dataaround the Boxing Day 2015floods. Bottom left: waterlevel time series (raw data);top left: rating curve(stage–discharge relationship);top right: resulting dischargetime series. “Novel”: errors

Well-known Flood-excessvolume (FEV):

Ve ≈Nm∑k=1

(Q(hk)−QT )

)∆t

... is the volume of floodwater one wishes to mitigate(i.e., reduce to zero) by thecumulative effect of variousflood-mitigation measures.

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FEV: square lake representation

GOAL: to quantify and communicate the efficacy of various flood–mitigationmeasures in a straightforward and concise manner.

IDEA: calculate the FEV for a flood event of interest and express as the capacity of a2m-deep square ‘flood-excess lake’ with side-lengths O(1km).

OUTCOME: a graphical tool that (i) contextualises the magnitude of the floodrelative to the river and its valley/catchment and (ii) facilitates quick and directassessment of the contribution and value of various mitigation measures.

For the River Aire case: the FEVis represented as a 2m-deep‘flood-excess lake’ of side-length2.15km

Ve ≈ (9.34± 0.51)Mm3 ≈(21502 × 2)m3.

Given the size of the lake as well as the geography of the river valley concerned, onecan make an estimate of the contribution and effectiveness of flood-plain enhancementfor flood storage and other flood-mitigation measures.

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Ve ≈ (9.34± 0.51)Mm3 ≈(21502 × 2)m3.


University of Leeds







Ve ≈ (9.34± 0.51)Mm3 ≈(21502 × 2)m3.


University of Leeds


Leeds Flood Alleviation Scheme II+

FEV of Boxing Day 2015 flood (1 : 200+yr flood) allows for first-order analysis ofFASII (online Leeds CC/Executive Board report Dec 2017):

I Planned protection against 1 : 200yr flood, EA’s data!I 4 Scenarios in Table: higher flood walls in Leeds, Calverley (1Mm3)/Rodley

(2.2Mm3) /both potential flood-water storage sitesI Natural Flood Management hailed (e.g. tree planting 7%→ 15% coverage

Upper Aire) but 0% coverage in basic scheme? No quantification?I Cost quantification minimal: £123M (Calverley & Rodley) and £109M (only

Calverley)? Other measures . . . no costs/no detail?

Scenarios, does something not add up? Is available flood-storage volume used?

Leeds location Walls only +Rodley +Calverley +Rodley&CalverleyWhitehall Rd to 1.74 1.53 1.6 1.5Wellington Br - 12.07% 8.05% 13.79%Viaduct Rd to 2.27 2.0 2.09 1.96

Cardigan Fields - 11.89% 7.93% 13.66%

% of FEV 100% 2.29.34→ 23.55% 1

9.34→ 10.71% 34.26%

Table : Given height defence walls along 2 different river stretches. Wall-heightreduction given as a percentage for each location and compared against extraflood-storage reduction percentage wrt FEV of Ve = 9.34Mm3.

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Q: what fraction of the FEV is reduced, and at what cost, by a suite of mitigationmeasures?

Given a calculation (or estimate) of potential flood-storage volume and associatedcost of each mitigation measure, the ‘flood-excess lake’ can be partitioned accordinglyand overlaid with a cost per 1% of FEV mitigated. Scenarios S1 & S2 from thehypothetical Leeds’ Flood Alleviation Scheme II (FASII+):

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Q: what fraction of the FEV is reduced, and at what cost, by a suite of mitigationmeasures?

Inconsistency? FASII rejects storage further upstream and close to Leeds but not NFM(yet very far upstream)? Big storage closest to Leeds rejected: nature reserve, even ifonly needed 1 : 100yr. Scenarios S3 & S4 (rejected massive sites further upstream)from hypothetical Leeds’ Flood Alleviation Scheme II (FASII+):

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Q: what are optimal flood-storage sites? Flood control? Right spot?

I Options: Rodley (1Mm3 at 5mi), Calverley (0.75Mm3 at 7mi), Holden Park(∼ 2.355Mm3 at ∼ 20mi), Cononley Washlands (∼ 2.355Mm3 at ∼ 30mi).

I Leeds CC Executive Board report 04-12-2017.

I BBC news item https://www.bbc.co.uk/news/uk-england-leeds-44568909:

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https://www.bbc.co.uk/news/uk-england-leeds-44568909

Q: Flood control?

Options: Rodley (1Mm3 at 5mi), Calverley (0.75Mm3 at 7mi), Holden Park(∼ 2.355Mm3 at ∼ 20mi), Cononley Washlands (∼ 2.355Mm3 at ∼ 30mi).

I Scenarios S0 (walls only) and S4 (Cononley Washlands & Holden Park storage)win in FASII+.

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2. Reservoirs & NBS: River Calder data analysis

Figure: River Calder gaugedata at Mytholmroyd aroundthe Boxing day floods.Bottom left: water stage timeseries; top left: rating curve(stage–discharge relationship);top right: resulting dischargetime series.

Error bars in stageshighlighted.

Q: what fraction of the FEVVe = (1.65± 0.22)Mm3 isreduced, and at what cost, byparticular flood-mitigationmeasures?

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NBS assessment: River Calder

Exploratory flood-alleviationscheme comprising (i)temporary storage in reservoirs,(ii) upscaled ‘leaky’ debris dams(50yrs), and (iii) tree planting.

I takes into accountuncertainty in storagecapacity;

I draw-down and control ofreservoirs has greatpotential;

I major upscaling of leakydams can have areasonable andcost-effective impact;

I mean FEV mitigated is50%: more measures (e.g.,flood walls) required tooffer full protection.

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3. GRR international: River Brague, France

Introducing‘giving-room-to-the-river’bed widening: increases theriver width in order to increasethe discharge capacity for asimilar water depth.

Figure: River Braguereconstructed flow dataaround the 2015 flash floods.Bottom left: water stage timeseries; top left: rating curve;top right: resulting dischargetime series and FEV. New‘GRR’ rating curve reducesFEV for same hT .

Q: what fraction of the FEVis reduced, and at what cost,by particular flood-mitigationmeasures?

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FEV assessment: River Brague

An alternative to raising flood walls: giving-room-to-the-river (GRR) increases theriver width in order to increase the discharge capacity for a similar water depth.

1.5 m

20 m

5 m

a) Current transverse profile

b) Giving-room-to-the-river transverse profile

b 1

I New ‘GRR’ rating curve reduces FEV for same hT .

I GRR is assessed favourably alongside flood walls and retention measures in anexploratory flood-mitigation analysis for the River Brague.

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FEV assessment: River Brague

Exploratory flood-alleviationscheme comprising (i) storagein reservoirs (retention), (ii)flood walls, and (iii) GRR.

I Ve =(0.488± 0.311)Mm3 isrepresented by a2m-deep square lake ofside 494m

I lighter colour = bettervalue

I nearly 2/3 of the18.4Me scheme isrelated to the retentionmeasures even thoughthey manage only 25%of the problem

I most cost-effectivemeasure is GRR.

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4. NBS: beaver dams as flood mitigation extreme floods?

I Statement on site BBC: “Beavers should be re-introduced to England to improvewater supplies, prevent floods and tackle soil loss, a researcher says”.

I Claim Puttock et al. (2017): “this research forms a solid base, from which todevelop an understanding of how beavers may form a ‘nature based solution’ tothe land management, water resource and flooding problems faced by society”.

I Really? Now also in Yorkshire.

River flood date(s) Ve hT Ve/Vb 0.5Ve/Vb 0.1Ve/Vb

- - Mm3 m - - -Aire 26-12-2015 9.34± 0.51 3.9 8490 4246 849

Calder 26-12-2015 1.65± 0.22 4.5 1500 750 150Don 25/26-06-2007 3.00± 0.24 2.9 2727 1363 272

Tamar 23-12-2012 1.96± 0.20 2.95 1780 890 178Tamar 24-12-2013 3.65± 0.36 2.95 3317 1658 321

Table : 5 FEVs Ve are given for threshold levels hT indicated. Gauge data usedto calculate FEVs located at Armley, Mytholmroyd, Sheffield Hadfields &Gunnislake resp. 4 floods: Boxing Day flood of 2015 for Rivers Aire & Calder,2007 flood River Don, & Dec 2012/2013 floods River Tamar. Extra storagevolume obtained behind beaver dams of 1 beaver colony in Devon, on tributary,Vb ≈ 1100m3 behind 13 beavers dams over ∼ 200m.

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https://www.bbc.co.uk/news/uk-england-york-north-yorkshire-45708504

NBS: beaver dams as flood mitigation extreme floods?

River flood date(s) Ve hT Ve/Vb 0.5Ve/Vb 0.1Ve/Vb

- - Mm3 m - - -Aire 26-12-2015 9.34± 0.51 3.9 8490 4246 849

Calder 26-12-2015 1.65± 0.22 4.5 1500 750 150Don 25/26-06-2007 3.00± 0.24 2.9 2727 1363 272

Tamar 23-12-2012 1.96± 0.20 2.95 1780 890 178Tamar 24-12-2013 3.65± 0.36 2.95 3317 1658 321

Table : Added columns with estimates of the number of (equal-size) beavercolonies required in each respective catchment that would offer 100%, 50% or10% flood mitigation (i.e. rest covered otherwise) via floodwater storage behind(a potentially huge number of) beaver dams, with the relevant FEV Ve beingnormalised with respect to Vb, i.e., Ve/Vb, 0.5Ve/Vb and 0.1Ve/Vb. With thenumber of beaver colonies required ranging from 100s (last column) to 1000s(fifth column), the clear and inescapable conclusion is that flood mitigation byfloodwater storage behind beaver dams is not a viable option to protect againstextreme flood events. Notwithstanding . . . infiltration/reservoir act (p24)?

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Conclusions

The details are in some sense of secondary importance here; the take-home messageis that the FEV-based cost-effectivess analyses offer: (i) a complementary way ofclassifying flood events; and (ii) a protocol to optimise the assessment of mitigationschemes, in a comprehensible way.

Further comments:

I this analysis does not replace the need for performing detailed hydrodynamicmodelling and should be used either prior to or in tandem with the modelling. Itdoes, however, as an important practical alternative, partly replace suchcalculations in cases where insufficient computational resources are available

I FEV enables one to quantify the contribution of NBS/NFM measures – this israrely done in policy/literature! – and highlights the issue of NFM scalability

I the square-lake representation encourages evidence-based decision-making forassessing flood-mitigation schemes

I FEV and cost-effectiveness analysis revealed lack of clarity in Leeds’ FloodAlleviation Scheme Phase II?

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Thanks very much for your attention ...

References, articles all rejected, with bizarly contradictory reviews, controversial:

1 Bokhove, O., Kent, T., Zweers, W. (2017): ‘Wetropolis’ flood demonstrator.Outreach project report, Maths Foresees.Available at: http://www1.maths.leeds.ac.uk/mathsforesees/projects.html

2 O. Bokhove, M. Kelmanson, T. Kent (2018a): On using flood-excess volume inflood mitigation, exemplified for the River Aire Boxing Day Flood of 2015.Rej. evidence-synthesis article: Proc. Roy. Soc. A.See also: https://eartharxiv.org/stc7r/

3 O. Bokhove, M. Kelmanson, T. Kent, G. Piton, J.-M. Tacnet (2018b):Communicating nature-based solutions using flood-excess volume for threeUK and French river floods. Rej. evidence-synthesis article: Proc. Roy. Soc. A.See also the preliminary version on: https://eartharxiv.org/87z6w/

4 O. Bokhove, M. Kelmanson, T. Kent (2018c): Using flood-excess volume inflood mitigation to show that upscaling beaver dams for protection againstextreme floods proves unrealistic. Rej. evidence-synthesis article: Proc. Roy.Soc. A.See also: https://eartharxiv.org/w9evx/

I Rej. 3 proposals on a.o. flood control (EPSRC program grant & NERC Cases)

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http://www1.maths.leeds.ac.uk/mathsforesees/projects.html

https://eartharxiv.org/stc7r/

https://eartharxiv.org/87z6w/

https://eartharxiv.org/w9evx/

Open questions: Leeds’ Flood Alleviation Scheme II

Accessible analysis based on FEV, wall heights stated & local estimates revealed that:I Now: Level/hydrograph comparisons of simulated (?) scenarios, also with

level/hydrograph of Boxing Day 2015 flood, are missing?I Now: Has giving-room-to-the-river, GRR, combined with wetland creation, been

sufficiently explored around Kirkstall & Armley areas in Leeds?I Now: Flood alleviation by NFM, cq. tree planting, not at all quantified?I Implicitly tree planting is quantified at 0% flood mitigation (too low!) at a cost

of £10M to £32.3M (i.e. £∞M/1% = wrong)? Now: Better quantificationpossible, but likely with large uncertainty.

I Rodley, closest (to Leeds) large flood-storage site dismissed because it is anature reserve and a weir would be visually disturbing, but LCC allowed newhousing development where the weir, to be used ∼ 1 : 100yr only, should be?Compensate nature reserve ∼ 1 : 100yr? Q: > 2015: new buildings in floodplain at 3 or 4 critical spots?

I Quoted flood volumes Calverley (1Mm3) & Rodley (2.2Mm3) seem too highgiven the wall heights LCC stated? Given these wall heights & the FEVcalculated, estimates of the available flood-storage volumes are 0.75Mm3 &1.1Mm3. Q: Flood control? Unexplored/uncertified; for future.

I Future: Largest potential flood-storage sites around Kildwick dismissed becausetoo far away to store heavy rainfall near Leeds but NFM measures are furtheraway? Provide protection upsteam of Leeds?

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5. Reservoirs & spatial rainfall: River Don data analysis

June 2007 floods...flood-excess volume (FEV) isdefined as volume of floodwater one wishes to mitigate(i.e., reduce to zero) bycumulative effect of variousflood-mitigation measures.

Right: River Don gauge dataJune 207 floods. Bottom left:water stage time series; topleft: rating curve(stage–discharge relationship);top right: discharge timeseries.

Q: what fraction of FEVVe = (3.00± 0.24)Mm3 isreduced, and at what cost, byparticular flood-mitigationmeasures?

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Rainfall scenarios: River Don

Partioning in three subcatchments, Reservoir, Sheaf and upper Donhttps://www.sheffield.ac.uk/doncatchment/about:

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https://www.sheffield.ac.uk/doncatchment/about


The ‘FEV–scenarios’ framework is straightforward yet elegant: information covering arange of rainfall scenarios, mitigation measures, and geographical areas of a rivercatchment is encapsulated in a single graphic. Moreover, it is highly flexible and canincorporate any number of scenarios, rainfall distributions, and locations.

“Rainfall fraction” ProbabilityScenario Reservoir Sheaf Upper Don Winter Summer

S1 13

13

13

12

14

S2(a) 12

12

0 18

112

S2(b) 0 12

12

18

112

S2(c) 12

0 12

0 112

S3(a) 1 0 0 112

16

S3(b) 0 1 0 112

16

S3(c) 0 0 1 112

16

Table : Summary of seven (hypothetical) precipitation scenarios, with therainfall fraction for the three locations, and seasonal probabilities.

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Three roughly equal-size subcatchments, Reservoir, Sheaf and upper Don . . . :I Rainfall matrix over rainfall scenarios; note that . . . :

Arf =

13

13

13

12

12

0

0 12

12

12

0 12

1 0 00 1 00 0 1

and Ar = VeArf =

1 1 11.5 1.5 00 1.5 1.5

1.5 0 1.53 0 00 3 00 0 3

Mm3.

(1)

I Storage matrix, reservoirs in Reservoir and leaky dams in upper Don:

As =

Vr 0 Vd

Vr 0 Vd

Vr 0 Vd

Vr 0 Vd

Vr 0 Vd

Vr 0 Vd

Vr 0 Vd

=

2.8 0 0.5672.8 0 0.5672.8 0 0.5672.8 0 0.5672.8 0 0.5672.8 0 0.5672.8 0 0.567

Mm3. (2)

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I Possible storage in each area, given the seven rainfall scenarios:

Am = min(As, Ar) =

1 0 0.5671.5 0 00 0 0.567

1.5 0 0.5672.8 0 00 0 00 0 0.567

Mm3. (3)

I Storage vector is sum thereof:

rv = (1.567, 1.5, 0.567, 2.067, 2.8, 0.0, 0.567)T Mm3 and (4a)

rrf = rv/Ve = (0.5223, 0.5, 0.189, 0.689, 0.933, 0, 0.189)T (4b)

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Three roughly equal-size subcatchments, Reservoir, Sheaf and upper Don . . . :

I Probability distribution assigned to the seven scenarios across the summer andwinter:

vw = ( 12, 18, 18, 0, 1

12, 112

, 112

)T and (5a)

vs = ( 14, 112

, 112

, 112

, 16, 16, 16

)T , (5b)

I Means flood-mitigation measures for winter and summer is inner product of theabove two vectors:

m1 = rrf · vw = 0.4408± · · · = (44.08± 17.51)%

andm2 = rrf · vs = 0.4325± · · · = (43.25± 16.38)%

respectively.

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Graphical overview of fractionof FEV captured by variousmeasures in Don catchmentfor 7 summer-rainfallscenarios. Stacked verticallyare the respective probabilitydistributions, relative to theassociated FEV, which is fixedfor all scenarios. The blueshaded areas to the left of thethick, stepped, solid linedenote the fractions of theFEV mitigated per scenario,to be read horizontally (e.g.,93.3% for (S3a)). The meanFEV (43.25%) over all 7scenarios and standarddeviation (16.38%) areindicated by thick and thinvertical dashed linesrespectively.

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University of Leeds


University of Leeds


Documents

University of Leeds Public empowerment in ood mitigationobokhove/fdsleeds2018.pdf · ood gauge data, yielding a clearcost-e ectivenessanalysis. I Using gauge data of UK/French oods;