1 Introduction

Floods are one of the most frequently occurring and destructive natural hazards around the world (Pinter 2005). About 800 million people (more than 11% of the world population) now live in areas prone to flooding. Seventy million people (1% of the population) suffer from the effects of floods every year (Kundzewicz et al. 2013). Flood risk management is a major challenge for many countries, and the importance of resolving the problem increases because of climate change and population growth (APFM 2009). All known types of floods can occur in Russia because of the differences of geographical and climatic conditions. Most common are floods from melting snow (in the European part of Russia and Siberia), ice jams (on the rivers that flow from south to north), heavy rain (in the South of Russia and in the Russian Far East) (Dobrovol’skii and Istomina 2009). During August and September 2013, Eastern Russia and Northeastern China were stricken by catastrophic flooding (Semenov et al. 2014). In China, as a result, 85 people died, more than 60,000 buildings were destroyed, and more than 787,000 hectares of farmland in the heavily agricultural region have been damaged (Duan et al. 2016). In Russia, more than 13,000 houses have been flooded (Bolgov et al. 2015; Danilov-Danilyan et al. 2014).

Flood protection in Russia is produced mainly by the construction of dams and dikes. Nonstructural measures for flood risk management are declared, but they are hardly used. This is because of the liberal practice of state aid delivery. After floods in the Amur basin in 2013, about 200,000 people received one-time payment from the state; about 4500 houses and apartments were built or purchased for the affected population. Some citizens, who have received new houses, have proved their rights to damaged houses by the court. Therefore, in Russia, economic measures of flood risk reduction do not work, and almost all costs for compensation are borne by the state (Simonov et al. 2016).

Russia lags far behind the USA (FEMA 2015; Michel-Kerjan and Kunreuther 2011) and the European Union (Directive 2007) in the development of legislation on the flood risk management. Only one article of the Water Code of the Russian Federation (Water Code 2006) is devoted to the prevention of floods and provides for the establishment of the boundaries of flooding and the total prohibition on the new construction.

Therefore, the development of flood risk management acts is an important task for Russia. It should take into account the significant differences between Russia and other countries in the number of gauging stations, land use patterns within the floodplains, the mentality of the population, etc.

In recent years, it has developed two main approaches to risk assessment in the world. The first approach is based on an understanding that risk can be defined as the combination of hazard and vulnerability (Apel et al. 2009; IPCC 2014; UNISDR 2009). Another approach relies on priority conception (Slovic 1987; Vojinovic and Abbott 2012; Vojinovic et al. 2015), according to which the qualitative methods of flood risk assessment are used.

The aim of this paper is to present different approaches to flood risk assessment in Russia. In addition to quantitative methods, we propose to use a hybrid approach to establish flood risk zones. Under this approach, qualitative gradation of the risk is established depending on quantitative factors such as annual probability of river flooding, flow depth and its velocity. The proposed gradations reflect our perception of risk assessment. Other authors may also propose other ways to criteria determination for risk zoning, which may be a matter of debate.

2 Flood hazard assessment

The terms “flood risk” and “flood hazard” are often used synonymously (Shrubsole et al. 2003). The standard (ISO 2009) defines a hazard as a source of potential harm, i.e., “situation or thing that has the potential to harm a person.” At the same time in Russia, the “flood hazard” means a certain scale of flood that has happened (small, dangerous, very dangerous and catastrophic). This approach makes it possible to compare and categorize the flood without detailed post-disaster evaluations and assessments.

The peculiarity of hydrological monitoring in Russia is a very low density of gauging stations (Voskresenskii 2011); therefore, the development of flood hazard maps is a promising objective (Franci et al. 2016; Di Baldassarre et al. 2009a; Liu et al. 2016). For this purpose, after each flood it is necessary to identify flooded areas using ground-based or remote sensing data (Zhao et al. 2014; Merkuryeva et al. 2015; Horritt 2006; Di Baldassarre et al. 2009b). This would prohibit the construction of buildings and structures before the development of flood risk maps and reduce state expenditures for aid after floods. Figure 1 provides the boundary of flooding, which is set according to a survey of residents.

Fig. 1
figure 1

Flood hazard map with the boundary of flooding that was set according to a survey of residents

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3 The evaluation of flood risk as the probability of flooding

In Russia, the creation of inundation maps with the boundaries of flood zones is the most widely used approach for the flood risk assessment. In this case, the risk is the probability of flooding the considered point on the ground.

In the European Union, the USA and certain other countries is only allocated a boundary of 100-year flood based on the forecast of climate change (Milly et al. 2002; Arnell and Gosling 2016; Kundzewicz et al. 2010). In some cases, the boundaries of 200- and 1000-year flood are defined.

The Government Resolution of the Russian Federation No. 360 of April 18, 2014 (Government RF 2014), established the necessity of the 2-, 4-, 20-, 33- and 100-year flood boundaries identification. However, the need of identification of such a large number of flood boundaries is not justified, while the Water Code (2006) prohibits any construction within any of them. At the same time, for many rivers the 2- and 4-year flood boundaries are located inside permanent riverbed. Another problem is the use of maps with low-accuracy topographic imaging. It leads to a significant reduction of precision for flood boundaries delineation. However, the main problem of flood risk maps development is using indirect methods for calculating the frequency of water levels occurrence in the absence of gauging stations.

When considering the flood on the Amur River in 2013, it should be taken into account that water flows at border parts of the rivers Amur, Ussuri, Argun were not measured for about 50 years. This circumstance makes it impossible to use the hydrodynamic models for forecasting. Another disadvantage of the probabilistic approach to flood risk assessment is disregarding the other risk factors such as flow depth, flow velocity and duration of flooding.

The approach to the flood risk assessment based on the probability of flooding is also used in other aspects in Russia. For example, the assessment of flood probability throughout the entire territory based on hydrological data from single gauging station is widely used. This method gives satisfactory results on the rivers with floods due to snow melting, but with local heavy rains, it does not allow to estimate possible losses from floods.

4 The evaluation of flood risk as maximum damage magnitude

In Russia, the maximum possible damage is a major indicator of man-made flood risk. This approach is used in the development of safety declarations for dams and dikes (Shchedrin and Kosichenko 2011). In some cases, the maximum damage is calculated for a 100-year flood. The maximum damage can be defined in physical terms such as population, housing area, the length of roads, etc., as well as in economic terms. Due to lack of initial data, it is allowed to produce an assessment based on the region-averaged data. This simplification gives high error in mountainous regions where the population density in the valleys of the rivers is much higher than the average density throughout the region.

5 The calculation of risk based on long-term average of the actual damage

The average long-term damage is widely used as a measure of natural disasters. On the basis of this, it is convenient to carry out large-scale flood risk zoning by continents, countries, major river basins.

The first disadvantage of this approach is the instability of estimates, because after each catastrophic flood the average annual damage changes dramatically. For example, the material losses from the three largest floods have made more than 40% of damage for 30 years all over the world (Brakenridge 2015). The catastrophic flooding in the Amur River basin in 2013 has led to an increase in average long-term damage in Russia by three times.

Secondly, the damage incurred in different years is very difficult to bring to a certain single equivalent level. This problem is especially acute for the Russian Federation, where all aspects of the flood damage formation have changed dramatically over the past 25 years.

In this regard, it is worth highlighting three basic aspects:

  1. a.

    The difficulty of bringing the amount of damage in different years to a common price level.

  2. b.

    Change in land use patterns within the floodplains.

  3. c.

    Change in the methods of damage calculation.

Let us consider each of these aspects separately.

The problem of bringing the amount of damage in different years to a common price level is solved, as a rule, with the use of deflators. In the Russian context, there are no justified deflators, because inflation rates vary significantly in different sectors of the economy. Some researchers have made the damage calculation in dollars. However, this approach provides even higher error, because the rate of inflation in Russia has never corresponded to a change in the US dollar rate. Up to 1990s, the exchange rate between the ruble and the dollar was significantly undervalued, and in the further, it did not always reflect the real inflation (Fig. 2).

Fig. 2
figure 2

Exchange rate between the ruble and the dollar, adjusted for inflation

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Over the past 25 years, the structure of flood damage in Russia has changed dramatically. It is caused by changing land use patterns within the floodplains. As a result, there is a persistent increase in the proportion of damage to the population and the decline in the share of damage to agriculture. As a result, an increase in the proportion of damage to the population and the decline in the share of damage to agriculture have been observed everywhere. Other components of the damage have also changed, but in different ways in various river basins. The difficulty of floodplains usage trends estimation is the necessity of using only expert assessments.

In Russia, a very low proportion of buildings and property is insured against floods. Therefore, insurers hardly participate in the definition of flood damage. The state methods of damage determination have been repeatedly modified, and it led to changes in the results of damage calculation.

For example, to calculate the damage caused by the floods in the Amur River basin in 2013 the special method has been developed. According to some experts, the calculation results obtained using this method may be between five to ten times above the actual damage.

Thus, the long-term average damage can be used as a measure of risk only on a limited basis. In order to do so, the damages for different years should be recalculated to an equivalent level with using the coefficients, which take into account all the above aspects.

6 The calculation of risk by scoring system

This approach is based on the definition of risk-level quality gradation depending on several factors of flood hazard. It takes into account various combinations of factors. At the same time, the computation of the parameter, the value of which determines level of risk, can be performed.

The one of the best known examples of this group of methods is the calculation of “magnitude,” according to the duration of floods, affected areas of the region and the severity class (Brakenridge 2015). The greatest magnitude of 8.49 for the period of 1984–2015 has a flood in China in 1995. At the top part of the flood rating composed in terms of magnitude, there are no floods with the greatest number of human victims and the maximum economic damage. For example, flood caused by Hurricane Katrina ranks 720th in the rating with a magnitude of 6.35.

In Russia, there are several approaches to the evaluation of flood risk in scores. The first approach is based on the calculation for certain regions the several indicators characterizing the vulnerability of the territory to floods (Gladkevich et al. 2012; Frolova et al. 2014). Then, using a multivariate analysis for each region a risk level in scores is calculated. It should be noted that the results of the federal subjects of Russia scoring for the flood risk are significantly different by various authors. That could be explained by the use of various particular indicators and methods of generalization.

Some authors have proposed to estimate the risk depending on the maximum gauge excess over the bankfull stage and repeatability of this exceedance. In most cases, there are combinations of accounted hazards in which the results are contrary to the meaning of the phenomena. For example, the widespread formula proposed by Buzin (2008; Tersky and Frolova 2011) is as follows:

$$A = \left( {H_{\hbox{max} } - H_{\text{f}} } \right)\left( {1 - p} \right),$$
(1)

where A denotes the score of danger, H max denotes the highest observed water level at gauging station, H f denotes the bankfull stage, and p denotes repeatability of the flooding (expressed as a decimal).

The formula shows that the risk in a river section with an annual floodplain flooding is absent. At the same time, Russia has many rivers with an annual flooding of the floodplain, which are marked with a significant flood damage.

Though the calculation of risk by scoring system has a number of shortcomings, the development of new approaches is promising. This is because the scoring system allows to visualize the information about floods on small-scale maps.

7 Flood risk assessment, based on the mathematical expectation of harm

Currently, the system of Russian and international standards for risk management defines risk as a combination of the probability of an event and its negative consequences (UNISDR 2009). Therefore, the term “flood risk” should be understood to mean the mathematical expectation of harm. This approach is increasingly used in the assessment of flood risk in many countries.

In Russia, a risk assessment based on the expectation of damage is almost never used. It is caused by the following circumstances:

  1. a.

    A significant part of the buildings has not cadastral registration, and in some rural areas this proportion is about 90% or more;

  2. b.

    Cadaster of real estate does not include market value of buildings;

  3. c.

    Property insurance against floods is not developed.

In this context, it is difficult to apply an approach based on the calculation of the risk for each building or structure. For example, the use of HAZUS-MH software requires identification of each structure (Scawthorn et al. 2006).

Therefore, we proposed a method based on the calculation of the mathematical expectation of the vulnerability of some reference object, expressed as a fraction of its value or percentage (Fig. 3) (Shalikovskiy 2006, 2009, 2012).

Fig. 3
figure 3

Standard depth–damage function

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The zoning of floodplains in economic terms of risk is the calculation of the mathematical expectation of damage to reference object at different points of the area. The calculation can be made by Monte Carlo method or by the formula:

$$E\left( D \right) = \sum\limits_{i = 1}^{n - 1} {\frac{{\left( {D_{i}^{{}} + D_{i + 1}^{{}} } \right)}}{2} \cdot \frac{{\left| {p_{i} - p_{i + 1} } \right|}}{100\% }} ,$$
(2)

where E(D) denotes mathematical expectation of damage, and D i and D i+1 denote flood damage with probability p i and p i+1.

This made possible building a risk map for the reference object (Fig. 4). These maps have a relative constancy because during their creation the nature and intensity of land use are not considered. At the same time, they are easy to use by nonprofessionals. For this purpose, special correction coefficients taking into account the differences in the level of vulnerability of the considered and reference object have been developed. For example, in buildings three correction coefficients (K 1 , K 2 and K 3 ) are used. The first coefficient depends on qualitative characteristics of building, its state, wall material, etc. We have developed a classification of buildings, which provides for their division into six classes according to their resistance to flooding depending on their design and materials of walls, ceilings and foundations. Building conditions can be found through inspection by using special tables (Tables 1, 2). A similar method has been used by Papathoma-Köhle et al. (2015) with respect to torrential flooding in the European Alps. Thus, we have developed a scale for the correction coefficient to the vulnerability of buildings (Table 3).

Fig. 4
figure 4

Example of risk map of mathematical expectation of damage to reference object

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Table 1 Classification of buildings according to their resistance to flooding
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Table 2 Qualitative conditions of buildings through inspection
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Table 3 Correction coefficient to the vulnerability of buildings (К 1)
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The second correction coefficient is calculated according to excess of the ground floor height of the building over the ground:

$$K_{2} = \left\{ {\begin{array}{*{20}l} {0.45 + \left( {1.4 - d} \right)^{2.7},} & {{\text{if}}\quad d < 1.4\;{\text{m}},} \\ {0.45,} & {{\text{otherwise}} .} \\ \end{array} } \right.$$
(3)

where K 2 denotes the second correction coefficient and d denotes the excess of the ground floor height of the building over the ground.

The third correction coefficient takes into account the number of floors of a building:

$$K_{3} = \frac{1}{0.4 + 0.6 \cdot n}$$
(4)

where K 3 denotes the third correction coefficient and n denotes the number of floors of a building.

We have developed the expectation of damage maps to more than 50 communities in different regions of Russia. For insurance agent, it takes only a few minutes to determine the vulnerability of corrections based on the building inspection and to establish insurance rates according to the map. However, these maps are not currently demanded, as Russia has not developed property insurance. This is because state aid delivery is guaranteed in eliminating the consequences of natural disasters.

Thus, the proposed approach makes it possible to assess the risk of the individual real estate directly from both the GIS model and a zoning map, which is particularly important for development of insurance. In the future, it may be used for risk assessment within the individual territories. This will be possible when the real estate cadaster will be filled with information and the transition to a market value of real estate will happen. The mathematical expectation of damage is also useful in the analysis of information about actual damage. However, the same problems, which have been in the calculation of the average annual damage, are retained, but at the same time, expectation calculation can be made on the basis of the shorter period of observations. In addition, the value of mathematical expectation of damage is more stable over time. It is caused by the fact that the damage from the catastrophic flood is adjusted for its probability. For example, after the disastrous flood in the Amur River basin in 2013, the average annual flood damage in Russia has increased by 80% and its mathematical expectation increased only by 15%.

8 The combined approach to the flood risk assessment

The main aspect of the flood risk management is setting the permissible usage types of hazardous territories. In the EU countries, flood risk maps are used for such purposes. On these maps, the flood risk zones are represented depending on the probability of flooding. For example, in the UK three flood risk zones have been set for floods on the rivers (Table 4).

Table 4 Definition of flood zones in UK (DCLG 2014)
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In Russia, the necessity of the 2-, 4-, 20-, 33- and 100-year flood boundaries identification has been established (Government RF 2014).

In our view, the establishment of zones for flood risk management should take into account not only the probability of flooding, but other factors. This is due to the fact that in the area of 100-year flood can be located buildings and facilities, to which to the specific requirements for their adaptation to the level of risk (for example, in operation or reconstruction) should be applied. Uniform requirements to the entire area of 100-year flood are not enough for effectively managing the risk of flooding. The identification of a large number of flood boundaries is not adequately justified and has technical difficulties. For example, if for one river the difference in level between 20-year flood and 100-year flood may be less than 0.3 m, then for another river it can be several meters. Obviously, in the first instance, certain types of land use at the 20-year flood border may be accepted, but in the second case, any activity is unacceptable.

In delineation of the boundaries for the flood risk zones, the most appropriate option is the establishment of zones with four risk gradations:

  1. (1)

    “Very High Flood Risk” means a high probability of victims, the possibility of damage, the high economic damage in the implementation of any kind of economic activity. Very High Flood Risk zone should be used for recreation and activities that could not be carried out in other areas.

  2. (2)

    “High Flood Risk” implies the mean frequency of flooding, significant economic damage and the possibility of victims in the catastrophic floods. The territory may be used for certain types of economic activity.

  3. (3)

    “Medium Flood Risk” means a zone with a rare flood; probable damage could be fully insured at reasonable rates. The territory may be used for most types of economic activity and for the limited residence of the population under certain conditions;

  4. (4)

    “Low Flood Risk” is an area with low probability of flooding and may be used for all kinds of activities.

The proposed risk zones for river flooding are shown in Table 5.

Table 5 Definition of zones for flood risk management
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For each of the flood risk zones, we have developed proposals for acceptable use of territories, which include requirements for buildings and infrastructure (Shalikovskiy 2006). Figure 5 shows an example of risk maps. We have developed such maps for settlements in different regions of Russia.

Fig. 5
figure 5

Example of risk map

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9 Discussion and conclusions

The purpose of this study was to analyze the approaches to flood hazard and risk assessment in Russia. At the present time, this issue has a number of specific features in Russia:

  1. (1)

    Sparse network of gauging stations;

  2. (2)

    Small amount of real estate have cadastral registration;

  3. (3)

    Inconsistency of cadastral and market value of buildings;

  4. (4)

    A significant change in the direction and intensity of using floodplains in the last 25 years.

For these reasons, it should be a phased approach to the implementation of full-fledged mechanisms for flood risk assessment and management. The approach to floodplain zoning used in the USA under the National Flood Insurance Program (NFIP) is the most developed, but it is time-consuming and very expensive. In the EU countries, a simplified approach is used. It is based on establishing two or three flood risk boundaries depending on the frequency of flood occurrence (DCLG 2014). However, there are no reasons for the establishment of regulations of allowable changes of the real estate within flood boundaries.

Therefore, for the conditions of Russia, we propose a phased procedure for flood hazard and risk assessment:

  1. (1)

    According to satellite images, a survey of residents and other available methods and approximate border of flooding in the actual flood is established. The area within these boundaries is declared as preliminary flood hazard area with the establishment of the prohibition for building until the more detailed maps will be developed.

  2. (2)

    The distribution of the water depth and velocity is determined by modeling at different values of the annual probability of river flooding.

  3. (3)

    By results of modeling, the border areas of Low, Medium, High and Very High Flood Risk zones are delineated. For selected areas, the relevant regulations of economic activity are set.

  4. (4)

    According to the modeling the compilation of risk map in terms of mathematical expectation of damage is also made. The maps create the conditions for efficient tariff-setting for the purpose of flood insurance.

This approach can be used only in areas with a real threat of flooding. At the same time, there are areas of land with the potential and the imaginary risk of flooding.

Potentially dangerous areas include areas protected against floods by constructions of insufficient reliability; areas of land, which can be flooded during the forced discharges from reservoirs; areas with difficult conditions of runoff, etc. For these territories, it is advisable to use the approaches based on the calculation of maximum damage.

Territories with imaginary dangers of flooding are areas that could be flooded for the unfavorable combination of several natural and anthropogenic factors, each of which individually cannot be identified as dangerous. In respect of such areas, methods of scenario analysis should be used.