The economic importance of the Arctic has been increasingly recognized. Various governmental and commercial projects have been initiated internationally to develop the socio-economic infrastructure in the Arctic. Among others, there are projects for oil and gas fields in Mackenzie Valley, Canada (Mackenzie, 2017), in Prudhoe Bay, USA (Petrowiki, 2017), as well as in the Pechora and Yamal regions, Russia (Gazprom, 2017). To design hydraulic constructions, such as dams, bridges, roads, and pipelines, and to estimate the costs and risks of flood damage during the infrastructure's lifetime, information is needed on dangerous river discharges. These values are calculated from the upper-tails of probability density functions (PDFs) for the maximal river runoff. The PDFs are usually constructed with three parametric distributions (e.g. Pearson type III or log Pearson type III) using the mean value, the coefficient of variation, and coefficient of skewness (Guideline SP33-101-2003, 2004; Bulletin 17-B, 1982). These parameters are calculated from observations with an assumption of stationarity in the climate and hydrological regimes (Thomas, 1985). It means that the values of the PDF parameters and runoff extremes do not change in the future or during the period of building construction.

A great number of weather anomalies and detrimental flood events have been observed during the last decade. Climate change has especially been recorded in the polar regions. Climate models predict a robust increase in precipitation over the Arctic and sub-Arctic (Collins et al., 2013; Laine et al., 2014). From October to March, precipitation in the Arctic is expected to increase by 35 and 60 %, under medium and high greenhouse gas (GHG) concentration pathways, respectively (RCP4.5 and 8.5), relative to the period 1986–2005 (IPCC, 2013). The projected precipitation increases from April to September under the same GHG pathways are 15 and 30 %, respectively. Due to climate warming and increased rainfall, annual-mean snowfall is projected to decrease over northern Europe and mid-latitude Asia, and to increase in northern Siberia, especially in winter (Krasting et al., 2013). Further, precipitation extremes are projected to increase, the climate model results being robust particularly for northern Eurasia in winter (Kharin et al., 2013; Toreti et al., 2013; Sillman et al., 2013). In Siberia these increases in precipitation will be accompanied by a decrease in the number of consecutive dry days (Sillman et al., 2013). Over northern Eurasia, the net precipitation (precipitation minus evapotranspiration) is also projected to increase during winter. The projected changes discussed above are likely with a high confidence (Collins et al., 2013), and therefore point to an urgent need to better evaluate the response of other components of the Arctic freshwater system, including terrestrial hydrology (Prowse et al., 2015).

There are two opposing opinions about climate change effects on the hydrological regime, in answer to the question: “is it necessary for managers and stakeholders to take account of climate change?” According to Milly et al. (2008) climate change effects are already substantial, and should be taken into account by planners and water managers. The opposing view projects doubts on climate change, and suggests one pay attention to the uncertainties due to the short observed time series (Lins and Cohn, 2011; Montanari and Koutsoyiannis, 2014; Serinaldi and Kilsby, 2015). We propose accounting for the future climate change effects on environmental risks even in the event that uncertainties can not be fully evaluated or are unknown. It is better to prevent disasters than to deal with their consequences, which may be more expensive than the initial investment. We consider that the changes in meteorological variables would remain noticeable in runoff, which is an element of general water balance. From a practical point of view, methods to evaluate the extreme flood events are required irrespective of the debates about the extent or reality of the climate change (Madsen et al., 2013).

In flood estimation two main approaches are usually applied. The deterministic approach is based on the combined use of a regional climate model (RCM) and a physically based rainfall–runoff hydrological model (Fig. 1). RCMs provide the future meteorological forcing variables with a high temporal resolution to drive a hydrological model that describes complex physical processes, such as infiltration, snow melting, and evapotranspiration. This allows for generating synthetic time series for river runoff (discharges) for individual watersheds, so that flood events with the required exceedance probability are then estimated from the simulated time series. Successful applications of this approach have been achieved in numerous studies (Veijalainen et al., 2010; Lawrence and Haddeland, 2011; Archeimer and Lindström, 2015). The large-scale rainfall–runoff models have also been used to assess changes in the future flood frequency by Lehner et al. (2006) for the European Arctic. The shortcoming of these studies is that the results are sensitive to algorithms calculating a pseudo-daily precipitation input from projected climatology provided by global circulation models (Verzano, 2009). The second approach to evaluating the hydrological response to the expected climate change is stochastic. Weather generators are used to simulate time series of meteorological forcing for physically based hydrological models (Kuchment and Gelfan, 2011). Thus, estimates of extreme hydrological events (floods or droughts) with the required exceedance probability are obtained for a climate scenario by producing the meteorological signal with the Monte Carlo method. Both approaches are usually applied for a single catchment. In regional-scale analysis, the runoff should be simulated for a set of watersheds. It makes the calculations extremely costly computationally, especially in the case of climate ensembles.

The approach presented in this paper could be named probabilistic (to distinguish from the stochastic modelling described above). This approach allows us to skip the generation of the runoff time series, since only PDF parameters are directly calculated from the meteorological statistics for the projected periods of 20–30 years (Fig. 1). These simulated PDF parameters are further used to evaluate the future runoff values with the required exceedance probability using theoretical distributions from the Pearson system (Elderton and Johnson, 1969). Since the probabilistic model simulates only three to four PDF parameters, this approach allows for a regional-scale assessment of detrimental hydrological events in the future to be easily performed, and to define the regions where the risks of damage for infrastructure increase.

The probabilistic approach used in this study combines statistical methods with elements of the theory of Markov processes. Both have been traditionally applied in hydrological engineering calculations to evaluate design floods (Kite, 1977; Benson, 1968; Kritsky and Menkel, 1946). The traditional frequency analysis of flood and drought requires the hydrological time series to estimate the PDF parameters and to calculate the runoff of the required exceedance probability. However, the PDF parameters can also be estimated from the meteorological variable statistics. The idea of performing the direct simulation of the PDF parameters from the climate projections (without the simulation of time series) is proposed by Kovalenko (1993). Kovalenko et al. (2010) simplified the basic probabilistic model for engineering hydrology, and Viktorova and Gromova (2008) applied this approach to produce a regional-scale assessment of the future drought extremes for the European part of Russia.

The main idea of the simplified method is the “quasi-stationarity” of the changing climate and hydrological regime for periods of 20–30 years. This idea allows us to represent the multi-year runoff statistically with a set of PDF parameters for the particular time window; the set is different for the past (or reference period) and the future (or projected period) climatology. Thus, climate change could be accounted for in the calculations of the runoff-tailed values, which are usually required for the assessment of risks in water management. The IPCC recommends climate projections are represented as multi-year means of the meteorological values for a period of 20–30 years (Pachauri and Reisinger, 2007), i.e. under the same quasi-stationarity assumption.

The probabilistic model provides a more economical way to produce the hydrological projections for the extremes on a regional scale. This is because of (i) a low number of forcing and simulated variables (only three to four statistics for climate and hydrological variables are needed), (ii) a low number of parameters (physical processes are described integrally by a lumped hydrological model), and (iii) relative simplicity in the regionally oriented parameterization. Furthermore, the probabilistic model does not require large spatially distributed datasets and may be applied to regions with poor data coverage, such as the Arctic.

The aim of this study is to perform a regional-scale assessment of the future extreme floods based on climate projections for the Russian Arctic. The novelty of the study includes two aspects. First, we present the method to assess the frequency and magnitude of extreme floods in a changing climate, adapted in this case to the Arctic territories. It could also be applied to other territories, as the regionally oriented parameterization is relatively simple. Second, the paper provides the projected changes in the mean values and coefficients of variation (CVs) of the flood spring depth of runoff under four climate scenarios for the Russian Arctic. The regional-scale assessments are based on the Special Report on Emissions Scenarios (SRES) and representative concentration pathway (RCP) scenarios. The regions are delineated, where the frequency and magnitude of floods are expected to change substantially. Maps include a warning for those regions where engineering calculations on extreme maximal discharges should be corrected to account for climate change. An example of the engineering calculation of a maximal discharge of 1 % exceedance probability for the Nadym River at Nadym is provided using the outputs of three climate models for the period 2010–2039.

The idea of the method used in this study is (i) to simulate the future PDF parameters of the multi-year peak runoff using the projected mean values for precipitation and air temperature, (ii) to construct the PDF with simulated parameters and a previously defined theoretical distribution (Pearson type III), and finally (iii) to calculate the maximal runoff with the required exceedance probability. This idea was used to perform the regional-scale assessment of the maximal runoff for the northern territories of Russia, where the peaks occur during the spring. On these territories, the peak runoff is usually formed by seasonal snow melting and may be expressed as the spring flood depth of runoff (h, mm/(time period)), which is the volume of spring flood runoff (m3) from a drainage basin divided by its area (m2). The spring flood depth of runoff was chosen instead of the maximal discharge because this allows for mapping the spatial distribution of maximal runoff. Thus, the spring flood depth of runoff can be used to define regions for which the design maximal discharges should be corrected according to climate change scenarios. After such regions were delineated, the correction of the maximal discharge with the required probability of exceedance can be done using climate projections. From the spring flood depth of runoff, the river discharge with a required exceedance probability (Qp, m3 s-1) is calculated according to the method proposed in Guideline SP33-101-2003 (2004): Qp=k0μhpδδ1δ2F/(F+b)n, where k0 is the flood coincidence factor, which reflects a simultaneousness of precipitation/melting water input, i.e. depends on the shape of the hydrograph; μ is the factor of inequality of the depth of runoff and maximal discharge statistics; hp is the spring flood depth of runoff (mm; time period) with chosen probability p (0.1, 0.05, 0.01) estimated from the exceedance probability curve (or PDF); δ, δ1, δ2 are the watershed fractions for lake, forest, and swamp respectively; F is the watershed area (km2); b is the additional area that adjusts for the reduction of runoff (km2); and n is the degree of runoff reduction. For the ungauged basin the value k0 is estimated from observations on a neighbouring gauge located on the same type of landscape (Guideline SP33-101-2003, 2004). In our study, the value k0 was considered to be constant for the reference and projected periods. The values of μ, δ, δ1, δ2, b, and n may be obtained from look-up tables (Guideline SP33-101-2003, 2004) or from global datasets representing land cover (e.g. Bartholomé and Belward, 2005).

The analysis of the expected climate change in Russia and particularly over the Arctic is provided by Govorkova et al. (2008) and Meleshko et al. (2008). These studies considered the territories of the Russian Federation as a whole. In our study, we provide the estimates for the geographical domain of the Russian Arctic, which was outlined according to the hydrological principles as suggested by Ivanov and Yankina (1991) and further used by Nikanorov et al. (2007). The projected climatology averaged over the Russian Arctic is presented in Table 4 for the SRES and RCP scenarios. Generally, an increase in annual precipitation of over 20 mm (6 %) and warming of over 2.1 ∘C were predicted according to the SRES scenarios. For the RCP scenarios, the changes were more pronounced, with the precipitation mean values expected to increase by more than 40 mm (12 %), accompanied by a warming of 3.3 ∘C. The strongest increase (over 60 mm or 16 %) in precipitation with the highest warming (over 3.9 ∘C) was predicted by CaESM2 for the RCP2.6 scenario (Table 5).

The future means and CVs of the spring flood depth of runoff were assessed from the projected climatology using the method described above. For the entire territory of the Russian Arctic an increase of over 27 mm (17 %) in the mean values and a slight decrease in CVs were predicted according to the SRES scenarios (Table 4). Using the scenarios of the Fifth Assessment Report, the changes in the statistics of the spring flood depth of runoff were more notable; based on the RCP2.6 scenario, an increase of over 38 mm (23 %) in the mean values and a decrease of over 0.03 (16 %) in the CVs were expected. The strongest increase (over 45 mm or 27 %) in the means with the lowest decrease in the CVs (over 0.06 or 17 %) was predicted by CaESM2 for the RCP2.6 scenario.

According to all scenarios considered, the highest increase in the future means of the spring flood depth of runoff (of 30–35 %) was predicted for Arkhangelsk Oblast and the Komi Republic (Fig. 5b). Moderate changes in the mean values (of 10–18 %) are also predicted for Siberia (Fig. 5c and d), mostly according to the RCP scenarios. For the SRES scenarios, an increase of 10–18 % in the mean values was predicted for the Kola Peninsula and Karelia (Fig. 5a), accompanied by a decrease in CVs.

We can not compare our results with other studies directly because we address different flooding characteristics. Only an indirect comparison is possible. For the comparison, we assume that for the Pearson type III distribution, an increase in the means and CVs leads to an increase in upper-tail values. Subsequently, present 100-year floods will occur more frequently (Fig. 6). Also, a decrease in the means and CVs leads to a decrease in the upper-tail values. In this case, we can expect that the number of events of 100-year floods decreases. We compared our results with the studies by Hirabayashi et al. (2008, 2013), Lehner et al. (2006), and Dankers and Feyen (2008) using this assumption. For the eastern part of the Arctic, an increase in the historical 100-year maximum discharges is predicted by Hirabayashi et al. (2008, 2013) under the SRES:A1B scenario for the period 2001–2030. This is in accordance with our results; we also expect an increase in the upper-tail runoff values since the mean values and CVs were estimated to increase in general for this region. For the north-east European Arctic, we expect a significant increase in the frequency of present 100-year flood events. This is in contrast to Hirabayashi et al. (2013). The flood frequency decreases in many regions of northern and eastern Europe according to Hirabayashi et al. (2013). The feasible reason for such disagreement is that the model used by Hirabayashi et al. (2013) is very coarse; it was calibrated using observations from watersheds larger than 100 000 km2. In our study, the probabilistic model was calibrated using observations for watersheds of medium range. Lehner et al. (2006) used the WaterGAP model with climate projections derived from the HadCM3 and ECHAM4/OPYC3 GCMs. The results suggest that present 100-year flood events will occur more frequently in the north-eastern European Arctic in the 2020s, which is in accordance with our results.

For the Kola Peninsula and Karelia, we predicted a decrease in the mean values with a slight increase in the CVs according to the SRES:A1B and SRES:B1 scenarios. Dankers and Feyen (2008) suggested a strong decrease in present 100-year floods for north-eastern Europe (i.e. Finland, northern Russia, and part of the Baltic States) under the SRES:A2 and SRES:B2 scenarios, which is generally in agreement with our results. A similar tendency of decreasing maximal discharges was predicted for northern Finland (Veijalainen et al., 2010).

There are several sources of uncertainties in the method described above: (1) from the assumed (given a priori) type of distribution (Pearson type III); (2) from the limited length of hydrological time series that were used to evaluate the parameters of the distribution for the reference period; (3) from the limited length of meteorological time series to evaluate the climatology for the model parameterization; (4) from the uncertainties in future climatology provided by climate models (forcing); (5) from the mapping errors due to interpolation techniques; and (6) from the errors due to the calculation of the maximal discharges from the spring flood depth of runoff (Eq. 1). The uncertainties inherent in the simulated PDF parameters include items 1–5 from the list above. These uncertainties are evaluated by Kovalenko (1993) for the maps of means/CVs provided by Rogdestvenskiy (1986) and Vodogretskiy (1986) with the assumption that the errors in the future and past climatology are the same. The average percentage errors in the projected means/CVs are equal to 15/25 %; thus, it suggests considering the changes in the PDF parameters to be substantial if they exceed the reference values for more than these thresholds. The regions with substantial changes in the means and CVs of the spring flood flow depth are shown in Fig. 7.

In these regions, the frequency and magnitude of floods were predicted to differ substantially from the historical (reference) period. The changes in the mean values and coefficients of variation were predicted according to the outputs of the climate models of the Max Planck Institute for Meteorology: MPIM:ECHAM5 for the SRES:B1 scenario and MPI-ESM-LR for the RCP2.6 scenario. A substantial increase in the mean values is expected for Arkhangelsk Oblast, Komi Republic, and eastern Siberia (see Fig. 8 for the boundary of the regions). These are warning regions where the flood-related risks for hydraulic constructions in the future may be different from the past. In these regions, calculations of the maximal discharges should be corrected in line with the expected climate change.

As an example, the climate-based correction for the Nadym River at Nadym, according to climate model outputs for the RCP2.6 scenario, is given below. A new bridge over the Nadym River was constructed in 2015 and repaired after the spring flood in 2016. The maximal discharge of rare occurrence (e.g. 1 % exceedance probability) is required to assess the bridge height and cost. The watershed of the Nadym River is located in the region, where the increase in the mean spring flood depth of runoff was predicted under RCP2.6 scenario (Fig. 7, right, upper panel). Thus, the climate change impacted upper-tail maximal discharge may be considerably larger than the value estimated from the observed time series. Hydrological observations for the Nadym River are available at Nadym (gauge number 11805, the watershed area is 48 000 km2; see the bottom panel of Fig. 8). The statistics of the spring flood depth of runoff for this gauge were calculated from observations in the period 1954–1980, which was considered as the reference in this case (Table 6). The reference climatology was calculated by averaging the observations from the regular meteorological sites for the Nadym River catchment area for the same period. Then, the projected climatology with delta correction for the period 2010–2039 under the RCP2.6 scenario was obtained from the CMIP5 dataset. The parameter GÑ was estimated according to the observed climatology and the parameter c‾ was calculated from the projected climatology according to Shevnina (2012). These values were used to predict the first and second initial statistical moments, and the coefficient of variation (m1, m2 and CV) of the spring flood depth of runoff. The projected CS was estimated from the given ratio of CS / CV. The projected PDF was obtained from these values together with the spring flood depth of runoff 1 % exceedance probability (h1%, mm) (Table 6). The confidence intervals for the reference values of h1% were calculated using the formulas suggested by Ashkar and Bobée (1988) with the assumption that the given distribution is Pearson type III. The 90 % confidence interval for the reference h1% equal to ±64.5 mm, which is about 23 % of the quantile value. The projected values of h1% are within these uncertainties for all considering climate scenarios (Table 6); thus, due to the short time series we can not prove that the future changes in h1% are statistically insignificant. However, we suggest taking it into account for the projected climatology when calculating hydrological risks due to practical reasons; it is better to prevent a disaster rather than to deal with its consequences, which may be more expensive than the initial investment (Räisänen and Palmer, 2001). Finally, the maximal discharge with 1 % exceedance probability (Q1%, m3 s-1) was estimated from h1% according to Eq. (1). The values of the parameters in Eq. (1) were taken from the look-up tables (Guideline to estimate hydrological characteristics, 1984). The value of k0 was considered to be constant for the reference and projected periods and set to be equal to 1 in our example, for the sake of simplicity; μ is equal to 1.0; δ, δ1, δ2 are equal to 0.84, 0.06, and 0.08 correspondingly; b  equals 1.0 (km2), and n equals 0.17.

For the period 2010–2039, the maximal discharge of 1 % exceedance probability, which was calculated with averaging of the multi-model output, is 570 m3 s-1 larger than the discharge of the same probability of exceedance, which was calculated from the observations. The largest increase in the maximal discharge was predicted according to the CanESM2 model (over 7 % larger than the historical value). The maximal discharge of 8572 m3 s-1 changed the probability of exceedance from 1 % (calculated from the observations) to 2.5 % (calculated according to the averaged climate projections).

A probabilistic approach was applied in estimating the impact of climate change on the frequency and magnitude of extreme floods in the Russian Arctic. The projected meteorological mean values for periods of 20–30 years were used to estimate the future means, CVs and CSs of the spring flood depth of runoff, and to model the PDFs with a Pearson type III distribution. The future frequency and magnitude of extreme floods with a required exceedance probability were then evaluated from the simulated PDFs.

In this study, to perform the model cross-validation, the runoff data were extracted from the official issues of Roshydromet; however, in calculating multi-year time series of spring flood depth of runoff (and maximal discharge), the global and regional runoff databases may also be used. The examples of the datasets are (i) the Global Runoff Data Centre, Germany; (ii) the Environmental Information System (HERTTA), Finnish Environment Institute; and the Vattenwebb by the Swedish Meteorological and Hydrological Institute. To perform the assessments for other regions, the steps are as follows: (i) to choose the middle size watersheds with a catchment area from 1000 to 50 000 km2; (ii) to calculate the multi-year time series of runoff (yearly maximal discharges or spring flood depth of runoff) from the daily runoff time series; (iii) to select the time period without statistically significant trends (reference period); (iv) to estimate the mean values, CVs, and CSs from the observed time series of runoff or to evaluate them from the regional maps (i.e. Spence and Burke, 2008) and the statistics of the precipitation and air temperature; (v) to perform the model parameterization using general (Kovalenko et al., 2010) or regional-oriented schemes (Shevnina, 2012); (vi) to assess the mean values of the precipitation and air temperature from the results of the GCM/RCM models for the future; and (vii) to evaluate the future means, CVs, and CSs of multi-year runoff with Eq. (4). To perform the model cross-validation and to develop the regional-oriented parameterization scheme, the multi-year time series of runoff with periods of statistically significant shifts in the mean values and CVs are required.

The probabilistic model was further applied for a regional-scale assessment of extreme flood events for the Russian Arctic. The regional-oriented parameterization by Shevnina (2012) allows for a successful prediction of 67–83 % of the PDFs (see Sect. 2.2). The projected mean values, CVs, and CSs of the spring flood depth of runoff for the period 2010–2039 were estimated under the SRES:A1B, SRES:B1, RCP2.6, and RCP4.5 climate scenarios with outputs of three climate models. For the region studied, an increase of 17–23 % in the mean values of spring flood depth of runoff and a decrease of 5–16 % in the CVs were predicted depending on the scenarios considered. For the north-west Russian Arctic, an increase in the means and a decrease in the CVs were predicted. The regions with substantial changes in the mean values (over 15 %) and CVs (over 25 %) were defined for 2010–2039. For territories where the means and CVs increased substantially, extreme floods are predicted to occur more frequently and the risk of flooding is increased. We suggest correcting the hydrological engineering calculations and accounting for the projected climatology. This might reduce the risk of a potential hazard for hydraulic construction, the oil and gas industry, transport infrastructure, and population located in these threatened regions.

The model presented in this study provides an affordable method to produce forecasts of extreme flood events (in the form of PDF or as maximal discharge with a required exceedance probability) under the projected climate change scenarios. This is possible due to the low numbers of simulated variables and parameters. The regionally oriented parameterization of the model is also relatively simple and may be improved by involving a variance of precipitation, which could be obtained from the projected climatology (Meehl and Bony, 2011). However, due to various simplifications, the model presented in this study does not allow for an estimation of possible changes in spring flood timing or changes of intra-seasonal runoff variability for a particular watershed. On a regional scale, however, the method provides an explicit advantage in estimating extreme hydrological events under altered climate, especially for regions with insufficient observational data. It could be useful for a broad-scale assessment to define the threatened regions where a crucial increase/decrease in the extreme flood events is expected. When the warning regions are defined, a catchment-scale rainfall–runoff model could be applied to further distinguish details not anticipated by the method described in this study. Such models also allow for evaluating the value of the spring flood coincidence factor k0 (Eq. 1) for the projected periods (which was constant in our calculations). The evaluation and inter-comparison of the presented model and rainfall–runoff models is of high interest.

Another weak point of the method is the use of look-up tables for physiographic parameters. In our study, to calculate the extreme discharges of the Nadym River we used look-up tables for the territory of the former Soviet Union from Guideline to estimate basic hydrological characteristics (1984). For other regions worldwide, these physiographic parameters may be derived from spatially distributed datasets, e.g. according to Bartholomé and Belward (2005). Also, an issue to be studied is the effect of the spatial resolution of projected climatology on the ability of this model to estimate the frequency/magnitude of extreme floods for watersheds of different sizes.

The method described in this study was simplified for the use of engineering calculations, as the projected climatology for periods of 20–30 years as recommended by the IPCC (Pachauri and Reisinger, 2007) assumes a quasi-stationary climate. In general, the quasi-stationarity assumption may be eliminated and a non-stationary regime could be considered. In this case, the PDFs could be evaluated based on the full form of the Fokker–Planck–Kolmogorov equation (Domínguez and Rivera, 2010) with the multi-model climate ensemble approach (Tebaldi and Knutti, 2007).