## Abstract

The frequency of flood loss events is increasing, both regionally and globally, due to the rising population and subsequent development of flood-prone areas, and as a result of environmental and climatic changes. This observation is not universally true for the time series of the losses themselves, at least not in the past one or two decades. One explanation for this is the improvement in flood control and flood protection in certain countries, both for floods that originate in the sea (storm surges) and for inland floods. While the qualitative effect of protection measures – reducing losses – is undisputed, quantitative examples are rare. Performance, or efficiency, needs to be calculated by comparing the costs of investment and maintenance against the losses prevented after a measure was put in place. In this article, a quantitative analysis of the performance of flood control measures is presented for four cases: the storm surge protection of the city of Hamburg, the Mississippi River and Tributary project, the activities of the Tennessee Valley Authority and the Sylvenstein Reservoir in Bavaria. In each case, a significant benefit has been observed in the past decades, proving that flood protection pays off many times over.

## Introduction

In almost all articles and publications dealing with floods and their consequences, the statement, ‘Flood losses are increasing’, is found. While there is no doubt that absolute loss figures from extreme events tend to reach higher values today than in the past, the statement must be rendered more precisely.

Losses are determined by three components: the intensity of an extreme event, the values exposed to the hazard, and their vulnerability to it. Each of the components may drive losses alone or together with the two others. But they may also counteract each other partly or fully. As losses are realizations of risk, the only difference between loss and risk is that the latter adds probabilities to the individual events to form the general hazard.

The flood hazard is influenced in many ways, both by natural and man-made causes. Climate variabilities (natural) from seasonal to decadal time scales and climate change (mostly man-made) lead to changes in the meteo-hydrological patterns. In the context of losses, we first have to consider various aspects to make the above statement meaningful, such as ‘Have flood peak discharges increased?’ – ‘Has the flood duration/volume increased?’ – ‘Has the frequency of extreme flows increased?’ Next, we must consider how human actions have influenced the hydrological cycle and generation of run-off and flood waves in the region considered. Environmental changes (land use, river training, water management, etc.) have changed the situation practically everywhere in the world over the last century.

In the same way, we have to specify what we mean by ‘increase in losses’. Are we looking at the frequency of losses? Or at their annual aggregate? In which geographic region? In original or inflation-adjusted values? Or even in normalized figures to account for growth of values-at-risk over time? Do we take into account the changed number of people (size of population) by specifying per capita losses? Do we consider the economic power of the region considered by, for instance, normalizing via GDP changes or other quantities?

A loss can only happen at locations where the property is destroyed, damaged or otherwise adversely affected. The value of the property, the number of human structures and the quantity of belongings are growing steadily in all countries. In addition to more and higher-value items, their susceptibility to water, in particular, has increased. In the past, many things that got wet during a flood could be dried and used as before. Today, electronic components are found everywhere, which once under water often produce a total loss of the device to which they belong.

While the vulnerability is rising due to higher susceptibility, it can be lowered by preparedness, prevention and protective measures. In the context of such a multi-method approach, forecasts and warnings have improved considerably with modern observation, computation and communication techniques, and flood management (retention, diversion) and defense (dikes, levees) have been established in many places. The downside of this is that a false feeling of security is created in the people concerned, who rely – sometimes too much – on the effectiveness of these measures and fail to behave properly in the face of the given hazard.

## How to make losses comparable

We certainly agree that comparing absolute loss figures, even if they are adjusted to inflation, is not a sufficiently suitable method. Comparing two loss events at the same location at different times and loss events in different countries requires more than just considering pure values in dollars.

For a detailed analysis, we have to identify the causes of a trend in the observed series of loss data. This may be due to the changing number of buildings in the flood-affected areas (increased values-at-risk), the increase in repair/replacement costs (vulnerability) and – in the context of insured losses – the larger portion of insured people/businesses (increased insurance penetration).

For the insurance sector, and even more for the reinsurance sector, it is crucial to identify a trend. As premiums are usually calculated as a percentage of the sum insured (corresponding to the value of an insured object), a change in the value of an insured object is automatically accounted for in the premium. However, external factors, for instance, environmental factors such as climate change, are not subject to such automatic adjustments. Unrevealed trends lead to a bias in the calculation. Hence, if there is a trend introduced by climate change, we need to know how strong it is.

There are studies that found that losses do not increase at all after certain normalization procedures and conclude that climate change is not an influencing quantity (Barredo, 2009). However, the justification for that conclusion is questionable. Why? Because improvements in flood control and flood management are not quantified. But they certainly have a large effect on losses. One needs to be careful as to whether this effect is positive or negative. Flood control does reduce or even eliminate frequent losses. But it may not be effective at all during extreme events that far exceed the design criteria. However, while ostensibly offering safety, flood control measures also lull residents and businesses into a feeling of security, with the consequence that values-at-risk (exposure) increase in the protected area. The risk, defined as the integral over all possible flood events and their probabilities combined with the respective losses, may thus increase, or even mushroom. The portion of risk from highly frequent floods that is eliminated is outweighed by low-probability, high-consequence flood losses, hence introducing a much higher risk contribution.

It is very difficult though to account for the effects of flood prevention. Only in some cases, is there a definite point in time when they become effective (see the example of the Sylvenstein Reservoir below). Usually, the process is dynamic, and the protection level is improved by many small steps over several decades so that the resulting effect is often not attributable to certain measures. The larger the spatial scale, the more difficult it is to quantify the influence.

While it is often clear that flood protection reduces some of the losses, the extent of the reduction is not always obvious and therefore it remains open as to whether they actually pay off (= reduction of losses is larger than investment plus maintenance) and to what extent they pay off.

In this article, a number of examples are presented in which the effect of flood protection and/or flood control is shown in quantified terms. We look at floods which originate in the sea (storm surges) and floods as a result of precipitation and/or snowmelt. Four cases from Germany and the United States are analyzed ranging from the storm surge protection of a coastal city (Hamburg) and managing a large watershed (Mississippi) to two single rivers (Tennessee, Isar).

Practically, all investment decisions to establish protection are made after large losses. Many, both large-scale and – and even more so – small-scale initiatives, were preceded by a catastrophic event, such as in the case of the 1927 Mississippi flood, the 1998 Yangtze flood, and the Holland (1953), Hamburg (1962) and New Orleans (2005) storm surge disasters. These events make populations and decision-makers ready and willing to spend funds – and sometimes even abandon long-established policies.

## Storm surge protection of Hamburg

### The 1962 flood and the storm surge protection program

Hamburg is located on the estuary of the Elbe River some 100 km upstream of the river's mouth at the North Sea. It is, after Rotterdam and Antwerp, Europe's third largest port (in terms of tonnage) and Germany's second largest city. In February 1962, a storm surge catastrophe flooded roughly one-sixth of the city causing losses of three-quarters of a billion (109) German Marks (equivalent to €385 m) and claiming 318 lives.

After the disaster, the storm surge prevention strategy in Germany changed from reactive (defense during a flood) to proactive protection (measures in place before a flood). To prevent further disasters of this kind, Hamburg invested huge funds in flood protection in the years and decades that followed (Kron & Müller, 2014). The flood protection line was straightened in some areas and dikes were built or reinforced according to modern engineering standards. Work on the defenses along the Lower Elbe was also expedited. Today, storm surges in Hamburg reach greater levels than they did 50 years ago. This is due to the construction of various hydraulic structures and other measures (such as dredging). Furthermore, climate change and the associated rise in sea levels have also contributed to higher storm surges. This needed to be taken into account as well. Nowadays, the physics of storm surges is better understood than 20 years ago. In fact, storm surge protection is a permanent and continuously ongoing task.

Altogether, Hamburg now has a continuous flood protection line that is 103 km long and with a crest at least 7.50 m above normal sea level (5.70 m until 1962). (Note: in the following, all water levels and height figures are given in meters above normal sea level.) This line comprises 78 km of dikes and 25 km of flood defense walls – especially in the city center – made up of 79 individual structures such as locks, barrages, sluice gates, pumping stations and barrage gates. The dikes have grown from their pre-1962 width of 12 m to a width of 69 m and a height of 8.90 m. In 2012, the Hamburg Senate decided to raise the new storm surge high-water protection design level – based on the St. Pauli gauge – from 7.30 m to 8.10 m (Müller & Gönnert, 2014). The protection for Hamburg's port, however, remains somewhat lower. Without flood protection, a massive storm surge with a height reflecting the design flood would inundate around 342 km2 or 45% of the city area, affecting around 325,000 inhabitants and 165,000 jobs.

Since the 1962 flood, which reached a peak water level of 5.70 m at Hamburg's St. Pauli gauge, nine subsequent storm surges have surpassed this level (see Table 1). The highest storm surge of 6.45 m occurred in 1976, while the second highest at 6.08 m was recorded on 6 December 2013 during winter storm Xaver. On three other occasions, the water reached at least 5.95 m. At no time, however, did the floods cause any noteworthy losses in the city. Yet Hamburg's port area did not escape so lightly: in 1976, many firms there sustained damage, including the Airbus aircraft plant.

Table 1.

Highest storm surge water levels in Hamburg since 1962.

 17 February 1962 5.70 m 3 January 1976 6.45 m 24 November 1981 5.81 m 28 February 1990 5.75 m 23 January 1993 5.76 m 28 January 1994 6.02 m 10 January 1995 6.02 m 5 February 1999 5.74 m 3 December 1999 5.95 m 6 December 2013 6.08 m
 17 February 1962 5.70 m 3 January 1976 6.45 m 24 November 1981 5.81 m 28 February 1990 5.75 m 23 January 1993 5.76 m 28 January 1994 6.02 m 10 January 1995 6.02 m 5 February 1999 5.74 m 3 December 1999 5.95 m 6 December 2013 6.08 m

### Cost of flood protection in Hamburg

The expansion of flood protection in Hamburg since 1962 can be subdivided – from a financial perspective – into three phases. The costs listed below do not include the measures taken in the port area. The reconstruction of damaged dikes and construction of new dikes between 1962 and 1979 cost about €415 m (in original values). Assuming that expenditure in the first year was three times as high as in 1979 and declined linearly during this period, this yields an inflation-adjusted total (based on 2018 figures) of around €1.4 bn (€1.4 × 109) for this first phase (Figure 1).

Fig. 1.

The investment in flood control for the city of Hamburg was carried out in three stages: (a) 1962–1979: Total investment €415 m (€20181,400 m), a linear decrease of annual costs assumed. (b) 1980–1992: About €10 m annually; the total of €130 m relates to roughly €2018230 m). (c) 1993–2018: Known annual costs of the storm surge protection program (sum: €2018975 m). Data basis: Agency of Roads, Bridges and Waters of the Free and Hanseatic City of Hamburg. All the figures in the graph are given in euros.

Fig. 1.

The investment in flood control for the city of Hamburg was carried out in three stages: (a) 1962–1979: Total investment €415 m (€20181,400 m), a linear decrease of annual costs assumed. (b) 1980–1992: About €10 m annually; the total of €130 m relates to roughly €2018230 m). (c) 1993–2018: Known annual costs of the storm surge protection program (sum: €2018975 m). Data basis: Agency of Roads, Bridges and Waters of the Free and Hanseatic City of Hamburg. All the figures in the graph are given in euros.

From 1980 to 1992, around €10 m was invested in protective measures each year, amounting to a total of €130 m, mainly to raise dikes that were too low. After adjustment for inflation, this is equivalent to around €230 m (2018 values). In addition, the height of the dikes was increased in 1991 so that a water level of 7.30 m could still be contained at the St. Pauli gauge. For the third phase starting in 1993 and ending in 2018, the investment totaled around €975 m (inflation-adjusted to 2018). This means that altogether around €2.6 bn has been invested to date to improve flood protection in Hamburg. The third phase of the storm surge protection program was completed in 2018, but a new program is already being prepared to take account of the amended high-water protection levels. The costs of this follow-up program are estimated at €670 m. After completion, the nominal future design is for storm surges with a return period corresponding at present to about 7,200 years.

### Cost–benefit analysis

A precise analysis of the costs and benefits associated with flood protection is virtually impossible. However, the costs spent on protective structures can be compared to the losses prevented as a result of this work. A number of assumptions must be made here.

The loss in 1962 totaled €1.6 bn at present-day values. If the catastrophe of 1962 were to happen today, the total loss would be significantly greater in view of the much higher value of assets in the area, and their presumably greater vulnerability to water. It is, therefore, advisable to consider several scenarios when comparing costs and benefits in a sample calculation. For the sake of simplicity, it is assumed that the five events of 1976, 1994, 1995, December 1999 and 2013 (bold in Table 1), where water levels reached at least 5.95 m, would have flooded the same areas as in 1962 if defenses had remained at the same level.

The four other storm surges – 1981, 1990, 1993 and February 1999 – with maximum water levels between 5.74 m and 5.81 m, exceeding only slightly the 1962 mark, are not considered here. It can be assumed that these events would not have been catastrophic as sufficient technical possibilities of defending dikes have been available since the 1980s.

The first version of this analysis (see Figure 2) is based on the assumption that, in the case of flooding, the losses incurred in the affected city area would not be greater than the €1.6 bn (inflation-adjusted figure) of 1962 representing the minimum assumption. This consequently yields a minimum ‘net gain’ from flood protection of around €5.4 bn (losses prevented: five times €1.6 bn minus costs of €2.6 bn equals €5.4 bn).

Fig. 2.

Net benefit curves of Hamburg's flood protection measures from 1962 to 2018 based on three scenarios of increasing values. Even a highly conservative estimate of the losses prevented yields a ‘net gain’ of €5.4 bn (2018 value) as a result of the defenses built by the city since 1962. The figure rises to €15.1 bn when the increase in asset values in recent decades is taken into account, and to €18.4 bn when additionally the higher flood levels are accounted for. Note: Storm surges are not associated with calendar years but with winters. The winter (the storm surge year) begins on 1 October of a year, with the last three months of a year belonging to the following storm surge year. Therefore, the storm surges of winter storms Anatol in December 1999 and Xaver in December 2013 belong to the years 2000 and 2014, respectively. Data basis: Agency of Roads, Bridges and Waters of the Free and Hanseatic City of Hamburg.

Fig. 2.

Net benefit curves of Hamburg's flood protection measures from 1962 to 2018 based on three scenarios of increasing values. Even a highly conservative estimate of the losses prevented yields a ‘net gain’ of €5.4 bn (2018 value) as a result of the defenses built by the city since 1962. The figure rises to €15.1 bn when the increase in asset values in recent decades is taken into account, and to €18.4 bn when additionally the higher flood levels are accounted for. Note: Storm surges are not associated with calendar years but with winters. The winter (the storm surge year) begins on 1 October of a year, with the last three months of a year belonging to the following storm surge year. Therefore, the storm surges of winter storms Anatol in December 1999 and Xaver in December 2013 belong to the years 2000 and 2014, respectively. Data basis: Agency of Roads, Bridges and Waters of the Free and Hanseatic City of Hamburg.

For a more realistic view, however, it is necessary to include the increase in concentration of asset values over the years. The growth in the local gross domestic product of Hamburg is used as a proxy factor for the extrapolation in the second version. In this case, the costs saved would total €15.1 bn, with roughly €4.2 bn alone being saved in losses that would have been attributable to winter storm Xaver in December 2013.

For the third version, it is additionally assumed that the area flooded – and hence the total loss – would increase with higher water levels. If we choose to assume that the loss increases by 1% for every 2 cm that the water rises above the peak 1962 level of 5.70 m, the ‘net gain’ from flood protection is €18.4 bn. In this case, Xaver would have caused a loss of €5.0 bn. If the assumption is changed to 1% per 1 cm increase in water level, the resulting figures are €21.8 bn and €5.7 bn, respectively.

In all versions, the costs-to-benefits ratio would improve considerably if, in addition to the five events considered, the four storm surges with the next highest water levels of between 5.74 m and 5.81 m had been included in the analysis, which were all above the 1962 level.

No event has so far breached the high-water protection level of 7.30 m which applied until 2012, let alone the new high-water protection level of 8.10 m. The cost–benefit comparison shows that investing in flood protection has yielded a high return on investment for the city of Hamburg. Although the analysis must be based on certain assumptions and the figures are merely rough approximations, a ‘gain’ equal to around 10 times the costs does appear realistic. This gain will increase further with every future storm surge that passes without causing major losses.

## Mississippi River and Tributaries (MR&T) project

### Background and main features of the MR&T project

The Mississippi River watershed is the largest catchment in North America. Together with some large tributaries (Missouri, Ohio, Tennessee, and Arkansas), the river forms the main artery system in the heartland of the United States (Figure 3). After the great flood on the Mississippi in 1927, which produced losses in the order of one-third of the US budget at the time, the Flood Control Act was passed and the MR&T project was established (Camillo, 2013). An amount of US$325 m (original values) was appropriated to build, repair and reinforce levees, dams, pumping stations, detention systems and flood bypasses on the Mississippi and its tributaries. The U.S. Army Corps of Engineers (USACE) was given the task of implementing the measures. Fig. 3. Mississippi watershed. Source: MRC (2019). Fig. 3. Mississippi watershed. Source: MRC (2019). More than 3,500 km of levees have been established since 1928, and floodwaters can be stored in numerous reservoirs. The six great reservoirs on Upper Missouri alone can hold 90 billion cubic meters of water. Approximately, four million people are protected against frequent flooding. Besides flood control, structures for securing minimum depth for navigation and facilities for hydropower generation, irrigation and recreation are also a major focus of the project. Today, the MR&T project is around 90% complete regarding physical components. It has cost more than US$15 bn so far (in original values). The damage prevented by these measures is estimated by the Mississippi River Commission at US$823 bn – 54 times as much as the cost (MRC, 2017). Additionally, there are benefits from using the rivers as waterways, amounting to almost 3 billion dollars each year. Since 1940, the volume of goods shipped on the Mississippi has increased from 30 to 500 million (metric) tons, which yields US$2.9 bn annually in transportation benefits. During the 1988, 1999 and 2012 droughts, the Mississippi River remained open to traffic. This ability to keep the river open is a further valuable benefit of the MR&T project.

### Cost–benefit considerations for past time periods

For every fiscal year (October 1 to September 30), the USACE, together with the U.S. National Weather Service, compares the damage costs from flood events with the costs prevented by flood control measures. For the years 2004–2013, this comparison is shown in Figure 4. Storm surge damage on coasts, e.g. from hurricanes Katrina and Rita in 2005, are not included.

Fig. 4.

Potential losses, incurred losses, and losses prevented by USACE measures in the period 2004–2013 (different forms of display for better readability). Data source: USACE (S. Durden, personal communication, 2014). (a) Incurred and prevented losses in the United States. (b) As in (a) with bar for 2011 in full size. (c) Potential losses without flood control. (d) Prevented losses. (e) Incurred losses. (f) Sums in the period 2004–2013.

Fig. 4.

Potential losses, incurred losses, and losses prevented by USACE measures in the period 2004–2013 (different forms of display for better readability). Data source: USACE (S. Durden, personal communication, 2014). (a) Incurred and prevented losses in the United States. (b) As in (a) with bar for 2011 in full size. (c) Potential losses without flood control. (d) Prevented losses. (e) Incurred losses. (f) Sums in the period 2004–2013.

Levees and reservoirs prevent losses during small and moderate floods every year. However, protective and control structures show their greatest worth during an extreme event. In order to avoid uncontrolled breaching at an unforeseen location, emergency outlets are provided. They may consist of lateral discharge weirs but are also created by blasting a levee, as was carried out near Cairo, Illinois in 2011. Large floods occurred in 1973 and 1993, but it was not until 2011 that a flood reached the same order of magnitude as that in 1927. Along the Mississippi River alone, losses prevented in 2011 amounted to far in excess of US$200 bn (see Table 2) (MRC, 2017). Table 2. Effectiveness of the MR&T project (in values of 2012). Without MR&T project With MR&T project Effectiveness of MR&T project Total losses Incurred losses Prevented losses Loss reduction Actual state (as occurred in 2011) US$237.2 bn US$2.9 bn US$234.3 bn 98.8%
Only reservoirs, without levees (as if) US$237.2 bn US$225.3 bn US$11.9 bn 5% Without MR&T project With MR&T project Effectiveness of MR&T project Total losses Incurred losses Prevented losses Loss reduction Actual state (as occurred in 2011) US$237.2 bn US$2.9 bn US$234.3 bn 98.8%
Only reservoirs, without levees (as if) US$237.2 bn US$225.3 bn US$11.9 bn 5% Source: USACE (2012). Table 3. Highest discharges in the Isar (m3/s) at Munich for four large floods since 1960 in comparison to the hypothetical situation without the Sylvenstein dam. Date Maximum reservoir inflow (m3/s) Discharge in Munich (m3/s) Without reservoir With reservoir May 1999 920 1,550 800 August 2002 530 970 470 August 2005 1,100 1,800 1,040 June 2013 675 1,300 770 Date Maximum reservoir inflow (m3/s) Discharge in Munich (m3/s) Without reservoir With reservoir May 1999 920 1,550 800 August 2002 530 970 470 August 2005 1,100 1,800 1,040 June 2013 675 1,300 770 A total of US$45.84 bn (in 2012 dollars) in flood losses was registered in the 10 years from 2004 to 2013 in the areas under the control of USACE. At the same time, an estimated US$485 bn of losses were prevented there, a more than 10-fold amount. Of the total loss potential of about US$530 bn, only around 8.5% was realized and a massive 91.5% prevented (Figure 4(f)). Figures for the total costs invested in flood protection in the United States by the USACE since the Corps' existence is not available. In this context, other benefits, in particular, inland navigation, play a considerable role as well. Many measures bring benefits in different ways, and individual aspects cannot be considered in isolation.

Looking at a longer period (from 1927 to 2012, Figure 5) also shows a strongly diverging course of the accumulated expenditure (curve C) and accumulated prevented losses (curve B). It becomes evident that starting in the year 1972, curve B ascends about four-fold compared to before 1972 (this can also be seen from curve A – the individual annual benefits – that assumes often higher values from 1972 onwards). This may be due, on the one hand, to inconsistencies in the assessment of gains (there is no known reason whether this is so); on the other hand, curve B would rise if the exposure protected by flood control had started to increase. In this case, a gradual increase can be expected rather than a sudden leap. In fact, the slope suddenly becomes four-fold, at least until the mid-1990s where it then increases even further.

Fig. 5.

Accumulative curves of costs (for construction, repair and maintenance) and annual monetary benefits (damage prevented) for flood control measures by the USACE in the period 1927–2012. Cost index based on the year 2000. Source: USACE (2014). Green line: Annual benefits (A). Blue line: Accumulated benefits (B). Red line: Accumulated costs (C). Slopes 1, 2, 3 and 4: line 1 represents the average increase in benefits for the period up to 1972; lines 2, 3 and 4 describe the double, triple and quadruple of this increase. It can be seen that – after a short steep increase in 1974–1975 – the increase from about 1975 is about four times as much (the ‘Accumulative benefits’ curve runs parallel to line 4), and from the mid-1990s the increase is even higher (about six-fold slope). Please refer to the online version of this paper to see this figure in color: http://dx.doi.org/10.2166/wp.2019.023.

Fig. 5.

Accumulative curves of costs (for construction, repair and maintenance) and annual monetary benefits (damage prevented) for flood control measures by the USACE in the period 1927–2012. Cost index based on the year 2000. Source: USACE (2014). Green line: Annual benefits (A). Blue line: Accumulated benefits (B). Red line: Accumulated costs (C). Slopes 1, 2, 3 and 4: line 1 represents the average increase in benefits for the period up to 1972; lines 2, 3 and 4 describe the double, triple and quadruple of this increase. It can be seen that – after a short steep increase in 1974–1975 – the increase from about 1975 is about four times as much (the ‘Accumulative benefits’ curve runs parallel to line 4), and from the mid-1990s the increase is even higher (about six-fold slope). Please refer to the online version of this paper to see this figure in color: http://dx.doi.org/10.2166/wp.2019.023.

Fig. 6.

Isar flood in Munich 1899 at the Bavarian State Parliament. Source: Lang (2009).

Fig. 6.

Isar flood in Munich 1899 at the Bavarian State Parliament. Source: Lang (2009).

Fig. 7.

Catchment area of the Isar in Southern Bavaria. Source: LfU (2011).

Fig. 7.

Catchment area of the Isar in Southern Bavaria. Source: LfU (2011).

The statement in the graph (Figure 5) that for every dollar invested about 8 dollars in benefits are generated is valid for the whole period shown (1927–2012). If only the last 40 years are regarded, this figure is much higher. The accumulative curve of benefits increases about 14 times as much in the period 1972–2012 and even 20 times as much since 1992 compared to the accumulative expenditures, which comprise – besides investment costs – maintenance and repair.

### The Mississippi River flood of 2011

The 2011 flood was the largest event on the middle and lower Mississippi since 1927 (USACE, 2012). While it did cause a considerable amount of losses, it did not enter folklore as a disaster – although it had the size to become one. The reason why it was forgotten so soon by most was the highly effective management of the flood waters, which was possible because of the decades-long efforts that had been put into the MR&T. While 68,000 km2 (16.8 million acres) had been flooded in 1927, the even-larger 2011 flood inundated only 26,000 km2 (6.4 million acres).

The areas potentially affected by the flood, roughly 90,000 km2 of the MR&T project area along the lower Mississippi, are home to four million people. Here, 1.46 million homes and commercial buildings are found. All but 21,000 are protected by the MR&T project.

According to calculations by the USACE, US$237 bn losses (in 2012 dollars) would have been incurred during the 2011 Mississippi flood without the flood control measures accomplished in the past decades. The actual loss figure was only US$2.9 bn. This equates to 98.8% prevented losses. In 2011 alone, more than US$234 bn in losses were thus prevented (Table 2), most of it by levees. The reservoirs contributed only about US$12 bn.

When dealing with these calculations, one must keep in mind that the establishment of flood control involves significant interactive effects. If there was no flood control, the values-at-risk (exposure) in flood plains and in areas near rivers that could ultimately be developed only because of the previous protection works would not have increased in the way they did. It is impossible to isolate this development and it can only be taken into account in a speculative manner.

As a minimum assumption, one could take the losses from the 1927 event, which flooded an area almost the size of Ireland – mainly in Louisiana, Arkansas and Mississippi. More than 250 people lost their lives and 650,000 had to be evacuated. The losses were US$230 m in original values, which translates to some US$3.3 bn in today's values (inflated on the basis of the U.S. Consumer Price Index for 2018 in relation to the one for 1927).

However, in addition to the 2011 flood, large floods such as the 1973 spring flood or the ‘Great Flood of 1993’ and dozens of moderate and small flood events have occurred in the past 87 years which did not cause any noteworthy inundation and did not generate losses. Not only did the accumulation of losses prevented in these events contribute to the benefit, but also the fact that public life and economic activities were not interrupted or disrupted, i.e. indirect costs were avoided. The Mississippi River example provides more clear evidence that even high investments in flood control pay off – in multiple ways. The MR&T project is known as ‘among the most successful and cost-effective public works projects in the history of the United States’ (Feinstein, 2011).

## The Tennessee Valley Authority

The city of Chattanooga (Tennessee) is located immediately upstream of a Tennessee River Gorge. This narrow gorge generates backwater during high flows, which used to lead to flooding in the city on average once a year. In March 1867, the flood stage of 17.70 m was reached and the whole city was inundated.

In 1933, the Tennessee Valley Authority (TVA) was founded as a non-profit organization owned by the governments of seven southeastern US states (Leuchtenburg, 1952). Today, TVA is the largest power supplier in the United States. Reducing the Chattanooga flood risk was among the highest priorities when the TVA reservoir system was designed. Today, it remains the main objective in the control strategy of the system, whose total flood detention capacity comprises 13.5 billion cubic meters of storage, with 6.2 billion cubic meters alone (seven reservoirs) for the protection of Chattanooga. The record flood level since completion of the TVA reservoir system occurred in 1973. The flood level rose to 11.25 m in Chattanooga; without control management, it would have reached 16.00 m.

TVA began to report the positive influences of their dams on flood losses in a detailed way in 1936. Each object in the 500-year flood zone worth at least US$200 bn was registered with its characteristics (e.g., private home, two-story, basement, wood construction, first-floor level, etc.) and a value figure assigned. Until today, losses of US$6.7 bn (in original values) have been prevented in the TVA operation area during 64 flood events since 1936. Chattanooga contributed US$5.6 bn to this total, the remainder (US$1.1 bn) came from the lower Ohio River and Mississippi River watersheds (Saint, 2015). The total also includes – although probably to a very limited extent – indirect costs caused by downtimes, service interruption, etc.

TVA's aim was not only flood prevention but also power generation, improvement of navigation on the Tennessee River and advancement of agricultural and industrial development in the region. Therefore, the cost-effectiveness of flood prevention cannot be isolated and stated clearly in this example. In 2014 alone, TVA had revenues of US\$11 bn, primarily – but not only – from selling electricity. In addition, there is a high (but not easily expressible in monetary values) recreational value of the dams and the benefits for navigation (guarantee of a minimum navigable water depth in the river). This means the asset side of the system not only includes prevented losses but also these other benefits.

## The Sylvenstein Reservoir on the Isar River, Germany

### Background and construction

The Isar River, which has its headwaters in the northern Alps and flows through the heart of Munich, has posed a hazard to the city and its people for centuries. Great floods washed away bridges in 1813 and 1899, causing more than 100 deaths in the former case (Figure 6). After three large floods had occurred on the upper Isar in 1954, 1955 and 1956, the idea to construct a reservoir started to take shape (Lang, 2009).

In 1959, the Sylvenstein Reservoir went into operation (Figure 7). Since then, all flood peaks were successfully reduced and major losses avoided. The reservoir not only helps to protect Munich but also numerous other communities up- and downstream of the Bavarian capital. The structure is a 48 m high and 180 m long earthen dam with an impervious core (slurry wall) (Lang & Overhoff, 2015). The flood storage was designed for a specific flood volume of 50,000 m3 per km2 of catchment area (corresponding to an effective rainfall depth of 50 mm), which is quite a high figure. From 1994 to 2001, the dam's crest was increased by 3 m and a new spillway was built. These works increased the flood storage from 59 million m3 to 85 million m3 (and thus the specific flood storage to 70,000 m3). The total storage volume became 124 million m3.

Original construction costs amounted to €31 m, including about €2.5 m for power generation installations. The measures taken in the late 1990s cost another €19 m, and the reinforcement measures (installation of a slurry wall) in 2015 cost €24 m. In total, some €180 m (in 2015 euros) has been invested in the dam. Additionally, there are costs for regular maintenance but they can be assumed to be more or less compensated for by the income from power generation of about 20 GWh (20 million KWh) annually.

### Flood control and loss prevention history

The effectiveness of the reservoir in preventing floods can be seen in Figures 8 and 9. The series of annual discharge maxima at the Isar gauge in Munich clearly shows the different behavior from 1960 onwards, after the Sylvenstein Reservoir was completed. From the time records began in 1898 until operation started in 1959, there were six occasions when a discharge above the critical value of 900 m3/s was observed above which damage would have occurred. (Note: after some training measures on the Isar in Munich this critical discharge is 1,100 m3/s nowadays.) This means the damage threshold was exceeded six times in 61 years (an average of once every 10 years). In addition, the threshold was very nearly reached on a further three occasions.

Fig. 8.

Annual peak discharges at the Munich/Isar gauge. Peak discharges before () and after () completion of Sylvenstein Reservoir. Data source: Bavarian State Agency for Environment.

Fig. 8.

Annual peak discharges at the Munich/Isar gauge. Peak discharges before () and after () completion of Sylvenstein Reservoir. Data source: Bavarian State Agency for Environment.

Fig. 9.

Maximum discharges >800 m3/s at the Munich/Isar gauge. The upper (unfilled) portions of the 1999, 2002, 2005 and 2013 bars indicate the (theoretical) peak discharge without the effect of the reservoir. The horizontal line (- - -) reflects the discharge threshold for significant damage (900 m3/s); this threshold was elevated to 1,100 m3/s in 2010 when the Isar was restored within the city limits of Munich. Note: Vertical axis starts at 800 m3/s. Data source: Bavarian State Agency for Environment.

Fig. 9.

Maximum discharges >800 m3/s at the Munich/Isar gauge. The upper (unfilled) portions of the 1999, 2002, 2005 and 2013 bars indicate the (theoretical) peak discharge without the effect of the reservoir. The horizontal line (- - -) reflects the discharge threshold for significant damage (900 m3/s); this threshold was elevated to 1,100 m3/s in 2010 when the Isar was restored within the city limits of Munich. Note: Vertical axis starts at 800 m3/s. Data source: Bavarian State Agency for Environment.

After 1959, the 900 m3/s discharge value was only exceeded once, in 2005 at 1,040 m3/s. But the 2005 flood value was successfully reduced from 1,800 m3/s with the help of the reservoir. The theoretical discharges of the four flood events of 1999, 2002, 2005 and 2013 in Munich, simulated for a flood without the reservoir, are shown in Figure 9. They would very likely have caused losses in the order of several hundred million euros.

### The 2005 flood

The August 2005 flood event became the acid test for the Sylvenstein Reservoir. On 23 August, the flow in the Isar downstream of the dam increased to about 400 m3/s. The water came – apart from the minimum release of a mere 5 m3/s from the reservoir – exclusively from the intermediate catchment. At the same time, the reservoir received 905 m3/s inflow and, due to the measured rainfall intensities of up to 21 mm per hour and continuing, inflows of more than 900 m3/s for a period of nine hours were to be expected. The inflows eventually even peaked at 1,100 m3/s (Figure 10).

Fig. 10.

Modification of the flood wave by the Sylvenstein Reservoir during the August 2005 flood. Source: Strobl et al. (2007).

Fig. 10.

Modification of the flood wave by the Sylvenstein Reservoir during the August 2005 flood. Source: Strobl et al. (2007).

In order to prevent overflowing of the dam via the spillway, the release rate from the dam was increased gradually to 350 m³/s. Thanks to this measure, the surcharge volume and discharge over the spillway could be kept as low as possible. In the end, the dam was just about filled to the top with only little spillway discharge.

The discharge in Munich was successfully reduced to 1,040 m3/s. Apart from some minor damage (e.g. embankment erosion and flooded basements), Munich escaped without losses. Without the reservoir, 1,800 m3/s would have arrived, the highest value since records began in 1898. Figure 11 shows the areas that would have been inundated in Munich in this case. These areas would have comprised a considerable part of the center of the city.

Fig. 11.

Theoretical inundation area along the Isar River in Munich for the August flood 2005 (1,800 m3/s) without the Sylvenstein Reservoir. The old city (center) is within the dashed line. Source: LfU (2006).

Fig. 11.

Theoretical inundation area along the Isar River in Munich for the August flood 2005 (1,800 m3/s) without the Sylvenstein Reservoir. The old city (center) is within the dashed line. Source: LfU (2006).

The flood hazard in Munich (and some other cities along the Isar River) has been largely reduced by the Sylvenstein Reservoir (Table 3). This can also be seen from the official flood return periods for Munich: With the reservoir, the theoretical 100-year flood is 1,050 m3/s (without reservoir: 1,500 m3/s) and the 1,000-year flood is 1,250 m3/s (without reservoir: 2,100 m3/s). The full discharge capacity of the Isar in Munich exhausting all safety margins is around 1,400–1,500 m3/s. This means that, if protection measures do not fail, the city is safe against an event that is significantly rarer than an average of once every 1,000 years.

Official estimates for loss potential in the city are not available, but own estimates based on the flooded area in Figure 11 and assumptions for average flood losses per unit area, distributed according to main land-use classes (city center, urban housing area, commercial/industrial area, urban park area), yields a loss figure in the order of €1.8 bn for the theoretical 2005 event without the dam (1,800 m3/s). These losses do not include indirect losses and costs for defense measures.

Even though the assumptions made have a high degree of uncertainty, the result is striking: prevented losses of about 10 times the overall (inflation-adjusted) construction costs in just one event.

## Conclusions

The above examples show that investment in flood control and flood protection ultimately pays off – even many times over. The benefit of such investments will, however, not always be evident right away. Sometimes, it may take decades before the balance of prevented losses (plus other benefits) minus costs becomes a positive value. Among the examples of systems that have not yet experienced their ‘Big One’ are the huge coastal flood protection works in the Netherlands (Delta Project) and the Thames Barrier in London. But when (not if!) it happens, the positive effect is immediately very substantial.

Apart from the investment costs, maintenance costs have to be included too, although these are often more than compensated for by other usages such as freshwater storage, low-flow augmentation, power generation, recreation, navigation, etc.

While most flood control measures are effective or helpful for high-frequency events (return periods of up to 20 years), they become vitally important if the magnitude of the design flood (e.g. 100 years) is approached. In certain cases, measures are aimed exclusively at extreme events and are only deployed in such cases (some flood polders, spillways, etc.). It would be absurd to abandon a facility, redesign it for some other purpose or let it rot just because a serious event has not happened over a period of several decades.

On the other hand, if an extreme event (significantly) exceeds the design criteria, a flood protection measure may suddenly and completely lose its effect. It can even have a major negative impact, in particular, if the values-at-risk in a supposedly ‘completely protected area’ have increased solely on the strength of that flood control measure. Generally, one should monitor or even control the impact that protection measures have on values-at-risk and, therefore, on the exposure to flooding. While controlling development is very difficult, recording and checking against the situation for which the design was made should at least be ensured.

There is a further limitation to investing in control and protection works: not everything is worth protecting in the same way and with the same effort. Nevertheless, some measures are planned and implemented out of political considerations (for instance because the people concerned demand it, although the measures cannot be justified purely from an economic point of view).

A fairly recent example of a questionable investment is the protection of agricultural areas in Somerset in the United Kingdom, which experienced large-scale flooding in February 2014. However, only some 150 houses were affected, a rather small figure compared to the 6,000 to 10,000 during the entire event. Experts believe that the furious protests by concerned farmers so exaggerated the importance of the issue that politicians promptly reacted with a raft of measures. A flood protection program (dikes, dredging, and improvement of infrastructure) costing over £20 m (about €28 m) was enacted by the British government (Gov-UK, 2014). This move was regarded with some skepticism. Not every house needs to be protected at huge expense and effort. Nominally, in this case, we are talking about a figure of almost €190,000 investment per house (€28 m/150 houses) (Harrabin, 2014).

In the vast majority of cases, investing in precautionary measures, be they technical, organizational or behavioral, leads to an enormous reduction of expenditures in the medium and long term. The difficulty in initiating and enforcing flood protection measures lies in the fact that investments have to be made to prepare for events with very little probability. At the same time, there are already other demands for funds, and those involve certainty, not a probability of considerably less than 100%.

Measures against flood losses are normally much more efficient than those against windstorms and earthquakes. Losses from the latter phenomena can normally only be reduced (prevented) by reinforcing the objects concerned, i.e. make them more loss resistant. The increase in loss resistance will drag on for several generations of buildings as improvements are made building by building. For floods, in contrast, the loss probability for a certain area changes the moment a measure is completed and in effect. In fact, the flood hazard can theoretically almost be ‘switched off’ for a given location (e.g. through a dam large enough to control even extreme flows). The accumulation of these measures, each starting to contribute at a different point in time, eventually leads to a negative loss trend.

The cases presented show beyond doubt that flood protection measures eventually pay off. The quantification of a typical or representative benefits-to-costs factor is not advisable though. First, this factor is specific for each case regarded, varies over a wide range and cannot be generalized. Second, even for a certain case, it varies over time, as, in particular, the Hamburg example shows. Thus, we do not think that it is useful to quantify a typical benefits-to-costs factor. It is sufficient to know that the factor is greater than one in the long run.

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