ECONOMIC OPTIMISATION AS A BASIS FOR THE CHOICE OF FLOOD PROTECTION STRATEGIES IN THE NETHERLANDS

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1 THEME B: Floods 19 ECONOMIC OPTIMISATION AS A BASIS FOR THE CHOICE OF FLOOD PROTECTION STRATEGIES IN THE NETHERLANDS Jonkman S.N. 1,2, Kok M. 1,2,3 and Vrijling J.K. 1 1 Delt University o Technology, Faculty o Civil engineering, Section o Hydraulic Engineering, Stevinweg 1, 26 GA Delt, the Netherlands, tel , ax Road and Hydraulic Engineering division, Ministry o Transort, Public Works and Water Management, the Netherlands, 3 HKV Consultants, Lelystad Abstract: At the beginning o the new century several strategies are roosed that aim at increasing the level o lood rotection in the Netherlands. In this aer an economic method or the analysis o these strategies and their eectiveness is suggested. The method o economic otimisation takes into account the exenditure or a saer system and the exected (value o the) economic damage. In the economically otimal situation the total costs in the system, the sum o investments and exected economic damage, are minimised. The results ollowing rom the economic otimisation should be considered as a technical advice to olicy makers. Several lood rotection strategies alied or considered in the Netherlands, such as dike heightening, Room or rivers and lood insurance, have been schematised in the economic otimisation. The aer also shows how uture develoments, such as climate change and economic growth, can be taken into account in the method. From these schematisations criteria have been derived which can be alied or cost beneit analysis o alternatives. Keywords: lood risk, lood rotection, economic otimisation, cost beneit analysis Figure 1: The Netherlands without lood rotection (the dark area would be looded due to sea and river loods) 1. INTRODUCTION Large arts o the Netherlands are located below sea level and/ or are threatened by river loods. Without the rotection o dunes, dikes and hydraulic structures more than hal o the country would be almost ermanently looded as is shown in igure 1. The Netherlands has a long history o loods. The last disastrous lood occurred in A storm surge rom the North Sea inundated large arts o the Southwest o the country. Aart rom immense economic damage, 1835 ersons drowned during this disaster. Ater the 1953 lood the Delta Committee was installed to investigate the ossibilities or a new saety aroach. Based on this work lood rotection levels have been derived or the lood rone areas in the Netherlands. Since the work o the Delta Committee, erormed in the late 195 s, some

2 2 XXX IAHR Congress AUTh, Thessaloniki, Greece develoments have resulted in an increased awareness o lood risks. Firstly, the economic value o the country has increased raidly. It can be questioned i the rotection standards as derived by the Delta Committee still rovide enough rotection when the current economic value is considered. Moreover, in 1993 and 1995 extremely high river discharges occurred, which made large-scale evacuations necessary. In the uture climate change, the associated sea level rise and higher river discharges and soil subsidence will lead to an increase o lood hazards or the Netherlands. This overview o develoments illustrates the necessity o re-consideration o the level o lood rotection in the Netherlands, in which the necessary investments and the increase o the values to be rotected will have to be taken into consideration. At the beginning o the new century new strategies have been roosed in the Netherlands, which mainly aim at increasing the level o lood rotection, without raising the dikes in the river system. The discussion on the level o lood rotection lacks a general ramework or rational evaluation and comarison o alternative solutions. Aim o this aer is to contribute to the debate rom a technical oint o view by suggesting an economic method or the analysis o lood rotection strategies and their eectiveness, based on the concet o lood risk. The aroach will limit itsel to economic actors, although it is realised that many other asects are o imortance in the inal decision on lood rotection, such as the ecological and social asects. The ideas brought orward in this aer can thus be considered as advice to the decision makers rom a technical/ economical oint o view. The aer is structured as ollows. Section 2 will introduce the concet o lood risk and give a brie overview o some lood rotection strategies. Section 3 shows how these strategies can alied in a ramework or economic decision making, with the use o the methods o economic otimisation and cost beneit analysis. The conclusions rom this study are summarized in section FLOOD RISK APPROACH AND FLOOD PROTECTION STRATEGIES 2.1. FLOOD RISK The concet o lood risk in the Netherlands was already introduced by the Delta Committee, which was installed ater the 1953 disaster to investigate the ossibilities or a new aroach o lood rotection [van Danzig, 1956]. The Delta Committee decided that the level o rotection o a lood rone area should be deendent on the robability o occurrence o a lood, the damage that it could cause and the amount o investments required to achieve a certain level o rotection. In a risk based aroach the robabilities and consequences o looding have to be considered together and in coherence. (Flood) risk is generally deined as the roduct o robabilities and consequences. Due to limitations in knowledge and comuting ower a simliied aroach o lood rotection has been adoted by the Delta Committee in the 196 s, in which dikes are dimensioned based on a design water level with a certain robability o exceedance. In the last decade o the 2 th century methods have been develoed to determine the robability o looding and the consequences o a lood, which orm the basis or the risk based aroach o lood rotection. It introduces the ossibility to comare dierent measures or their eectiveness and to include costs and beneits in the analysis. Furthermore a comarison with risk levels in other sectors o society is ossible FLOOD RISK REDUCTION APPROACHES In this section an overview is given o measures, which reduce the economic lood risk. Flood risk mitigation in the Netherlands traditionally aimed at reduction o lood hazards through imroved dike construction by heightening and / or strengthening o the dikes along the

3 THEME B: Floods 21 rivers. Nowadays the concet o reventing looding without raising the dikes is generally adoted. For examle by giving more Room or rivers with riverbed widening and deeening and the lanning o additional green rivers. Recently the otion o creation o socalled emergency storage areas in the river system has been investigated. An emergency storage area situated ustream will be looded intentionally in case o extreme river discharges. Part o the extreme discharge will be stored in the emergency storage area and thus looding o the area with large economic value, which is situated downstream, can be revented. Furthermore strategies that aim at reduction o damage when a lood occurs are distinguished. As art o the satial lanning olicy imortant economic values in lood rone areas can be moved to higher grounds. Secondary water deences, dikes that sto the lood roagation ater breach o the main dike, can revent looding o valuable areas. Guidelines or the construction o buildings can limit the vulnerability o buildings or looding conditions and thereore reduce economic damage. As a mitigating measure the occurred economic damage can be comensated, either by government or by an insurance comany. These two otions mean in act a inancial reallocation o the lood damage. Based on the concet o lood risk as outlined in section 2.1 the measures described above can be classiied as is shown in table 1. Table 1: Overview o measures to economic lood risk Flood risk reduction Reduction o looding robabilities Mitigation o lood damages Dike strengthening and heightening Satial lanning Room or rivers: riverbed widening and Secondary water deences deeening, green rivers Emergency storage areas Building restrains Flood insurance Comensation by government 3. ECONOMIC OPTIMISATION AND COST BENEFIT ANALYSIS The method o economic otimisation is resented as a ramework or the derivation o an economically otimal level o risk in section 3.1 or the measures shown in table 1. This method is closely related to the cost beneit analysis, as is shown in section ECONOMIC OPTIMISATION The derivation o the (economically) accetable level o risk can be ormulated as an economic decision roblem. According to the method o economic otimisation, the total costs in a system (C tot ) are determined by the sum o the exenditure or a saer system (I) and the exected value o the economic damage (E(D)). In the otimal economic situation the total costs in the system are minimised: min( C tot ) = min( I + E( D)) (1) The alication o the economic otimisation or the measures mentioned in table 1 will be shown in some simliied examles in section It will also be shown how uture develoments can be taken into account in Basic case: dike heightening and river widening The method o economic otimisation was originally alied by van Danzig [1956] to determine the otimal level o lood rotection (i.e. dike height) or Central Holland (this area orms the economic centre o the Netherlands). An exonentially distributed looding

4 22 XXX IAHR Congress AUTh, Thessaloniki, Greece robability (P ) was assumed, which deends on the lood level h and the arameters A and B o the exonential distribution: P = e h A B The total investments in raising the dikes (I tot ) are determined by the initial costs (I h ) and the variable costs (I h ). The dike is raised X metres, the dierence between the new dike height (h) and the current dike height (h ). I = I + I X and X = h h (3) tot h h In this study a more general ormulation has been chosen between investments and lood rotection level (denoted by looding robability). Based on van Danzig a linear relation between the two has been adoted, but or more ractical alications another relation can be chosen. The investment unction is reormulated by substitution as a linear unction o the negative logarithm o the looding robability with arameters constant I and steeness I and ormula 4 is obtained: I tot = I + I' ln( P )) (4) The total costs are the sum o investments and the exected value o the economic damage. This exected damage has to be discounted to resent value with reduced interest rate (r ), which is the dierence between real interest rate (r) and economic growth rate (g): r = r-g. The economic otimum is ound by minimising the total costs. The derivative o the total costs and the looding robability results in the economically otimal looding robability (P,ot ), rom which the otimal dike height can be derived: C = I + I' ln( P )) + P D / r' (5) tot dc / dp = P = I' r' / D (6) tot, ot The relation between (decreasing) looding robability and investments, risk and total costs is shown in igure 2. (2) costs (Dl) 1.4E+9 1.2E+9 1.E+9 8.E+8 6.E+8 4.E+8 2.E+8 otimum Investments Risk Total Costs.E ln(p) decreasing looding robability increasing rotection level Parameters (based on [van Danzig, 1956]: I = (Dl) I = (Dl) D = (Dl) r =.15 (/yr) Results: P,ot = (/yr) - ln (P,ot ) = 11.8 Figure 2: Relation between total costs and decreasing ailure robability, or the examle and corresonding variables analysed in [van Danzig, 1956] This case shows the alication o the economic otimisation or the measure o dike heightening. I a linear relation between (the negative logarithm o) looding robability and investments is assumed or river widening measures, then this case will also be alicable or that situation.

5 THEME B: Floods Economic otimisation o other measures Emergency Storage areas In order to revent looding o an area with large economic value it can be considered to create an emergency storage area ustream which will be looded intentionally in case o extreme river discharges. The area will be designed to revent a large lood with robability o exceedance (P ). This requires a certain investment (or examle the construction o hydraulic structures to allow or a controlled lood) and the accetance o a certain damage in the emergency storage area (which is also considered as an investment). These investments will have a steeness o I NOG. The robability o a lood in the economically valuable area will be reduced with a certain raction α. This raction can be considered as the residual risk, or the cases that the use o the storage area ails or when it does not revent looding o the large area. The total costs and the otimum can now be written as is shown in ormula 7: (1 + α ) P D I r' NOG C = I + I ( ln( P )) + P = (7) tot, NOG NOG, ot, NOG r' (1 + α) D Flood damage mitigation by satial lanning or secondary water deences Investments can be done to revent damage in case o a lood. Economically valuable areas can be moved to higher grounds due to satial lanning and the construction o secondary water deences can revent looding o valuable areas. It is assumed that the investment will deend on the level o lood rotection with steeness I DAM. The investments will lead to a reduction o lood damage with a raction δ. For satial lanning measures it could be assumed that these will limit economic growth (g), and that thus the value or reduced interest rate (r ) has to be adjusted. Total cost or (C tot,dam ) can now be written as: P δ D I dam r' C = I + I ln( P )) + P = (8) dam (, ot, DAM tot, DAM r' δ D Flood insurance and comensation by government Another ossible measure is the insurance o lood damage by a rivate insurer, see or examle [Kok, 22]. Flood damage will (artly) be comensated, but this requires an additional investment in the orm o insurance remiums to be aid in advance. The remium will amount the exected value o the damage multilied by a actor β to account or roit and income o the insurer (assume β 2). It can be considered to combine insurance and dike strengthening. All damage will be comensated and the total costs equal the sum o investments and insurance remium, see ormula 9: β P D I ' r' C tot, INS = I + I ' ln( P )) + P, ot, INS = (9) r' β D Insurance (β > 1) will lead to a lower otimal robability and thus to higher rotection levels. Note that or β = 1 (i government comensates all damage) this equation equals the basis case Future develoments in economic otimisation Based on revious work [Vrijling, 198] and [van Danzig, 1956] it will be shown how sea level rise and economic growth can be modelled in the economic otimisation. The examles above assume a constant ailure robability. Develoments, such as sea level rise and increasing river discharges (or the degradation o the water deences over time), can lead to an increase o looding robability. This can be modelled by assuming an exonentially distributed looding robability (with arameters A and B) that will increase over time (t in years) due to sea level rise, as is shown in ormula 1: h ηt A B P ( t) = e = P, e η t B (1)

6 24 XXX IAHR Congress AUTh, Thessaloniki, Greece Where: P, looding robability chosen at t= η sea level rise (m/year) Furthermore (otential) economic damage in the area will increase over time due to economic growth (g). Economic damage at time D(t) can now be written as a unction o the economic damage at t= (D ): g t D( t) = D e (11) The exected economic value can now be ound over lanning eriod T, by discounting to the resent value with the real interest rate r. (1) and ormula 12 is obtained: T T D P r ' t t, T E( D) = P ( t) D( t) e dt = P D e dt = (1 e ) (12), Where: = r g - η / B When a linear relation is assumed between investments and the (negative logarithm o the) initial looding robability the total costs can be ormulated as ollows. It can be shown by a similar substitution as given or the case o dike heightening that a time deendent variable (2) investment is introduced, which has a steeness o I t D P, T C = I + I' ln( P )) + I t + (1 e ) (13) tot, t The level o rotection that should be chosen at t = can be derived as a unction o lanning eriod T (in years) with ormula 14: I' Ctot / dp, = P, ot, o ( T ) = (14) T D (1 e ) Note that or the situation o a very long lanning eriod (T = ) and no sea level rise (η =, thus = r g = r ), the otimum ollowing rom ormula 14 is equal to the otimum derived or the basic case o dike heightening o ormula 6. With this equation it can be shown that a lower otimal looding robability and thus a higher rotection level will be ound when uture develoments are taken into account. For the original examle o van Danzig (see igure 2 or arameters) the otimal looding robability is shown as a unction o the lanning eriod or dierent number o sea level rise in igure 3. otimal looding robability (P,) 1.E E-5 1.E-6 lanning eriod (T) m/yr.5 m/yr.1 m/yr Figure 3: Otimal looding robability as a unction o lanning eriod and sea level rise 1 t r ' t This can be modelled as a negative exonential unction, since: 1/(1 + r') e 2 Following the substitution or the basic case o dike heightening it can be shown that I t = I h η

7 THEME B: Floods 25 Economic otimisation and the value o human lie It is ossible to take the value o human lie into the economic otimisation [Vrijling, 2]. Assume that a certain scenario will result in N atalities and that every erson has an economic value l. The economic otimum can again be ound by minimising the total costs, which has been shown here or the basic case o dike heightening: C = I + I ln( P )) + P ( D + N l) / r' P = I' r' /( D + N ) (15) tot ', ot l The valuation o human lie may raise numerous ethical and moral questions, because some eole consider lie invaluable. From the equation it can be seen that not taking into account the economic value o human lie in the economic otimisation will lead to lower exected damages and thus to lower otimal saety levels. Exerience shows that the inluence o loss o lie is relatively limited in an economic analysis. In this section the ossible alication o the method o economic otimisation or dierent cases has been shown. O course, this oers the ossibility to combine some o the ormulations shown: or examle economic otimisation or dike heightening, including the value o human lie and uture develoments COST BENEFIT ANALYSIS The basic rincile o cost beneit analysis requires that a roject results in an increase o economic welare, i.e. the beneits generated by the roject should exceed the costs o it. The economic otimisation merely takes into account the cost side o the lood rotection roblem, and does not consider the otential economic beneits o an imroved lood rotection o the area. It has been shown by Voortman [22] how economic beneits can be taken into account in the ramework resented above. This shows that the economic otimisation as resented above is a secial (limited) case o this ull cost beneit analysis. In a simliied cost beneit analysis, as or examle alied in [Parker, 1987], the cost beneit criterion is ormulated as ollows. The risk reduction (i.e. the beneits) or a certain roject should exceed the costs o (or investments in) this alternative. This corresonds with the condition that should be checked in addition to the economic otimisation: total costs in the initial situation should exceed the total costs ater comletion o the roject. In the table 2 the investments or the measures described above and the risk reductions achieved are summarized, using the given ormulation. Also the derived economic otima are shown. Table 2: Overview o measures, derived economic otima, and cost beneit criteria, (P - looding robability ater comletion o the roject, P, robability in the initial state) Measure Investments Beneits Economic otimum (i.e. Risk reduction) dike heightening / I + I' ln( P )) ( P P ) D / r' P, ot = I' r' / D, river widening emergency storage I ( ln( )) + I NOG P P, D / r' (1 + α) P D / r' I NOG r' area P, ot, NOG = (1 + α) D damage reduction I I ( ln( )) + DAM P P D / r' P D / r', δ I r' dam P =, ot, DAM δ D lood insurance and I + I' ln( P )) P D / r' I' r', P dike heightening ot INS =,, β D + β P D / r' Secial cases, which include T sea level rise and I + I' ln( P )) + I t t 1 1 e I' economic growth P D ( ) P,, ot, o( T ) = T r' D (1 e ) valuation o human I + I' ln( P )) P ( D N l) / r', + P ' ' /( ), ot = I r D + N l lie P ( D + N l) / r'

8 26 XXX IAHR Congress AUTh, Thessaloniki, Greece From the table it can be seen that the roitability o a measure will deend on the ratio between investments and risk or damage reduction. Based on the table an analysis o cost eectiveness can be carried out. Decision makers may choose the most cost eective strategy, i.e. the roject that achieves the largest risk reduction with the smallest investments. This is the roject or which the highest rotection level is ound (i.e. the smallest otimal ailure robability) at lowest cost. However, it should be noted that based on other values, such as ecological, social and olitical considerations, an alternative could be chosen that would not be the most avourable when merely economic asects are considered. 4. CONCLUSIONS In this aer an economic ramework or analysis o lood rotection strategies and their eectiveness has been suggested in the orm o the method o economic otimisation. According to the method o economic otimisation, the total costs in a system are determined by the sum o the exenditure or a saer system and the exected value o the economic damage. In the otimal economic situation the total costs in the system are minimised. The results ollowing rom the economic otimisation should be considered as a technical advice to olicy makers. Several lood rotection strategies alied or studied in the Netherlands have been schematised in the economic otimisation. It should be noted that this aer considers individual measures, the economic otimisation o a combination o measures should be urther investigated. The method o economic otimisation is closely related to the cost beneit analysis. For these schematisations criteria have been derived which can be alied or cost beneit analysis o alternatives. Generally the roitability o a measure will deend on the ratio between investments and risk or damage reduction. Summarizing: when carrying out an economic analysis or rojects that aim at imroving saety levels it should irst be investigated whether the roject is beneicial to society, whether the beneits exceed the costs. In addition the otimal level o rotection can be ound with the economic otimisation. From an economic oint o view decision makers may choose the lood rotection strategy that achieves the largest risk reduction at lowest costs. The inal decision on a desired lood rotection level should not only consider economic asects, but it should involve a comarison o all relevant alternatives. The economic otimisation and the cost beneit analysis can rovide imortant rational inormation in this decision-making rocess. REFERENCES Danzig D. van, Economic decision roblems or lood revention, Econometrica 24, , 1956 Kok M., Vrijling J.K., van Gelder P.H.A.J.M., Vogelsang M.P., Risk o looding and insurance in the Netherlands, in: Proc. o the Int. Symosium o Flood Deence, Beijing, 22 Parker, Dennis J.; Green, Collin.H.; Thomson, Paul M.; Urban lood rotection beneits; Gower Technical Press; 1987 J.K. Vrijling, J.A. van Beurden, Sealevel rise: a robabilistic design roblem, Proceedings o the International Conerence on Coastal Engineering Delt , 199 Vrijling, J.K.; Gelder, P.H.A.J.M. van, An analysis o the valuation o a human lie In: M.P. Cottam, D.W. Harvey, R.P. Pae, & J.Tait (eds.) ESREL 2 - "Foresight and recaution", Volume 1,.197-2, Edinburgh, Scotland, UK, 2 Voortman H., Risk-based design o large-scale lood deence systems, Delt University, ISBN , 23

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