Climate warming has been more acute in the Arctic than at lower latitudes and this tendency is expected to continue. This generates major challenges for economic activity in the region. Among other issues is the long-term planning and development of socio-economic infrastructure (dams, bridges, roads, etc.), which require climate-based forecasts of the frequency and magnitude of detrimental flood events. To estimate the cost of the infrastructure and operational risk, a probabilistic form of long-term forecasting is preferable. In this study, a probabilistic model to simulate the parameters of the probability density function (PDF) for multi-year runoff based on a projected climatology is applied to evaluate changes in extreme floods for the territory of the Russian Arctic. The model is validated by cross-comparison of the modelled and empirical PDFs using observations from 23 sites located in northern Russia. The mean values and coefficients of variation (CVs) of the spring flood depth of runoff are evaluated under four climate scenarios, using simulations of six climate models for the period 2010–2039. Regions with substantial expected changes in the means and CVs of spring flood depth of runoff are outlined. For the sites located within such regions, it is suggested to account for the future climate change in calculating the maximal discharges of rare occurrence. An example of engineering calculations for maximal discharges with 1 % exceedance probability is provided for the Nadym River at Nadym.

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.

Three approaches to evaluate a hydrological response to the expected climate change.

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 (

The core of the probabilistic hydrological model is a linear differential
equation with stochastic components having solutions statistically
equivalent to the solutions of the Fokker–Planck–Kolmogorov (FPK) equation
(Pugachev et al., 1974). It allows the evaluation of the probability density
function of a random hydrological variable with parameters dependent on
climate variables. Under a quasi-stationary assumption of climate change,
the FPK equation is approximated by a system of algebraic equations to simulate
initial statistical moments of multi-year runoff (Kovalenko, 1993, 2014)
(see Appendix for details). These moments are further used to calculate the
PDF parameters and to model them using the theoretical formulations
(e.g. Pearson type III). In our study, the simple model suggested in Kovalenko et
al. (2010) was used to model the statistical moments of the spring flood depth of runoff:

The system of Eq. (2) allows for evaluating the multi-year runoff statistical moments for the projected time period based on the climatology and multi-year runoff statistics for the reference (historical) period. The climate and runoff regime are steady within both the reference and projected periods (the assumption of quasi-stationarity). The “steady” aspect is defined statistically; i.e. there are no significant trends and changes in the mean values of the meteorological and hydrological characteristics within the periods. However, the basic statistics (mean, CV, and coefficient of skewness – CS – values) are significantly different for the reference and projected periods.

The system of Eq. (2) was applied as follows:

The initial statistical moments from the observed hydrological and
meteorological time series for the chosen reference (

The model parameters for the reference period were assessed:

The future (

The future mean value and CV were obtained. The future CS was
calculated from the given ratio of CS

Rainfall–runoff models are usually validated against observed time series
(Lehner et al., 2006; Arheimer and Lindström, 2015). The system of Eq. (2)
allows for simulating the PDF parameters for the multi-year runoff
without producing time series. The predicted PDF parameters for the single
time period are based on the PDF parameters calculated for the other period.
Two time periods should have different parameter values and the difference
should be statistically significant (Kovalenko et al., 2010). Such kinds of
periods were found in the observed time series, enabling us to perform the
probabilistic model validation using a cross-validation procedure. In the
simplest cross-validation procedure, the observational dataset is separated
into two sub-sets, called the training set and the testing/control set. From
the training set the model parameters are evaluated and then used to nominally predict
the parameters of the control PDFs (Kovalenko, 1993). In our case,
the nominally predicted PDF was compared with the empirical distribution for
the testing/control period using the Pearson

The partition of the observed time series of the spring flood depth of
runoff

The whole period of observations was divided into the sub-periods with the
statistically significant difference (shift) in the mean values. Dividing
into the subsamples was done according to the Student's

The initial first and second statistical moments of the flood spring depth of
runoff for each sub-period were calculated according to Bowman and Shenton (1998).
The third moment was estimated from the entire time series, and the
ratio of CS

The nominally predicted exceedance probability curves compared with
the empirical exceedance probability (ECDF) for the sub-periods with
statistically significant shift in the mean value for the Yana River at
Verkhoyansk:

For the cross-validation, we (i) considered the first sub-period as the
training and calculated the reference values of the model parameters, and
(ii) predicted nominally (“in the past”) the first and second moments for the
second sub-period (which was considered as a control). The same procedure
was applied backwards. We validated two versions of the model: (i) with the
basic parameters setting as proposed by Kovalenko et al. (2010) and
(ii) with the regional-oriented parameterization as suggested by Shevnina (2012).
The empirical and nominally predicted PDFs were compared for each sub-period
and the goodness-of-fit between them was estimated using the Pearson

The model cross-validation was performed with observations collected during
the period from the 1930s to the 2000s. The observed data were extracted
from the official edition of the multi-year/year books of the State Water
Cadastre of the Russian Federation (see e.g. Kuznetsov, 1966). The spring
flood depth of runoff time series at 76 gauges for medium size catchments
(1000–50 000 km

The example of the cross-validation for the Yana River at Verkhoyansk
gauge is shown in Fig. 2. In partitioning the time series into two
sub-periods, the time series (Fig. 2, top panel) was first divided at the point

The sub-periods with a statistically significant shift in the mean values for the spring flood depth of runoff were selected for the 23 time series (Table 1), which constitutes 30 % of the data considered. For the corresponding watersheds, the average values of the annual precipitation and the mean air temperature were calculated using observations from 37 meteorological stations (approximately two stations per watershed) for each sub-period (Table 1). The observed meteorological time series were obtained from Razuvaev et al. (1993), Radionov and Fetterer (2003), N. Bryazgin (personal communication, 2008) and the multi-year catalogs on climatology (e.g. Catalogue of Climatology of USSR, 1989).

Sub-periods with the statistically significant shift in the mean values of the spring flood depth of runoff with the multi-year statistics and climatology.

Continued.

Notations:

For each gauge and sub-period, the statistical moments were nominally
predicted using Eq. (4) for the two versions of the model parameter settings
(Table 2). We also compared these predictions with the case where the
nominally predicted PDF for one sub-period was modelled using the
statistical values calculated from the observed data of the other sub-period
(“no model” case). The “no model” case illustrates the “stationary climate”
scenario in which climate change is not taken into account, and thus the
PDFs' parameters are not modified for the period of nominal prediction. This case
reflects the situation as considered in the guidelines for engineering
hydrology (Guideline SP33-101-2003, 2004; Bulletin 17-B, 1982), when only the
observed runoff time series were used to evaluate the PDF parameters. The
percentage of nominally predicted PDFs that matched successfully to the
empirical PDFs according to the Pearson

The model with the constant parameters gives a more conforming result than
the “no model” case: the percentage of successfully matched PDFs is
5–10 percentage points higher. Using the regional parameterization algorithm to
calculate the parameter

In performing the long-term assessment of the extreme flood events in the Russian Arctic, the period from 1930 to 1980 was chosen as the reference period, while the projected period was from 2010 to 2039. The following datasets were used: (i) the climatology for the reference period (Fig. 4a and b), (ii) the mean values and CVs of the spring flood depth of runoff for the reference period (Fig. 4c and d), and (iii) the climatology for the projected period (Fig. 4e and f). The reference climatology was obtained from the climatology catalogs and the archives of the Arctic and Antarctic Research Institute, covering 209 meteorological stations (Radionov and Fetterer, 2003; Catalogue of Climatology of USSR, 1989). The climatology was interpolated into the model grid nodes using the algorithm by Hofierka et al. (2002). For the precipitation, we use annual values, although the spring floods are formed only by snow cover and spring rainfall. However, in the Arctic the relationship between spring flood depth of runoff and both annual and winter–spring sums of precipitation are strong (Shevnina, 2011).

The climatology for the projected period is provided by the climate models (Pachauri and Reisinger, 2007; Taylor et al., 2012). In this study, the projections of two emissions scenarios (SRES: A1B and B1) and two representative concentration pathways (RCPs: 2.6 and 4.5) scenarios were extracted from CMIP3 and CMIP5 datasets. Results of climate models of the Max Planck Institute for Meteorology MPIM:ECHAM5 (Roeckner et al., 2003), the Max Planck Institute Earth System Model MPI-ESM (Giorgetta et al., 2013), the Hadley Center for Climate Prediction and Research HadCM3 (Johns et al., 2003), HadGEM2-A (Collins et al., 2008), the Geophysical Fluid Dynamics Laboratory GFDL:CM2 (Delworth et al., 2006), and the Canadian Center for Climate Modelling Earth System Model CanESM2 (von Salzen et al., 2013) were used. These global climate models (GCMs) produce approximately similar climate projections. This allows one to testify that the hydrological modelling results do not vary much under slightly different climate forcing factors. To obtain the climate forcing, the projected mean values of air temperature and precipitation were corrected using the delta changes method (Fowler et al., 2007). For that, the relative changes in the variables (in degrees for the temperature and in % for precipitation) were first calculated based on the historical simulations and observed climatology for the reference period. Then these changes were added to/multiplied to the projected climatology. The corrected mean values of the annual precipitation and annual average air temperature were estimated for the nodes of the corresponding climate model grids.

The data used in the study:

The model parameters and the nominally predicted multi-year statistics of the spring flood depth of runoff for the catchments selected for the cross-validation.

Continued.

Notations:

The means and CVs of the spring flood depth of runoff were extracted from
the maps of Rogdestvenskiy (1986) and Vodogretskiy (1986) by scanning the paper maps, image georeferencing, digitizing the data,
and interpolating onto the grid nodes of the particular GCM. These maps were
designed based on the observations for the period from the early 1930s up
to 1980 (Rogdestvenskiy, 1988). In producing these maps, the observations on
catchments of medium size (from 1000 to 50 000 km

The values of

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

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.

The observed and projected the mean values (bars) and coefficients of
variation (squares) of the spring flood depth of runoff expected for the regions
of the Russian Arctic for the period 2010–2039:

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.

The percentage of successful fits between the nominally predicted and empirical PDFs according to the goodness-of-fit tests for 0.05 level of statistical significance.

The reference (1930–1980) and projected climatology (2010–2039) and statistics of the spring flood depth of runoff averaged for the entire territory of the Russian Arctic.

Schematic explanation of the changes in the upper-tail values due to
changes in the parameters of the exceedance probability curve:

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 km

Projected (2010–2039) climatology and statistics of the spring flood depth of runoff averaged for the entire territory of the Russian Arctic according to the results of different climate models.

Notations:

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.

Climatology and the statistics of the extreme flood runoff for the Nadym River at Nadym evaluated from the observations and under the climate projection RCP2.6 for the period 2010–2039.

Notations:

The regions with substantial changes in the mean values

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 km

For the period 2010–2039, the maximal discharge of 1 % exceedance
probability, which was calculated with averaging of the multi-model output,
is 570 m

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 km

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

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).

Our study is based on third party data. The citations to the datasets have been included in the reference list.

The concept of probabilistic modelling to obtain a hydrological response to
an expected climate change was proposed by Kovalenko (1993), it is presented
further as provided in Kovalenko et al. (2010). This approach considers
multi-year runoff time series (annual, maximal, and minimal) as realizations
of a stochastic process of the Markov chain type (Rogdestvenskiy, 1988).
Then, a first-order ordinary differential equation is used as a lumped
hydrological model for the multi-year flow time series:

The solution of Eq. (A2) is statistically equivalent to the solution of the
Fokker–Planck–Kolmogorov equation (Pugachev et al., 1974):

In engineering hydrological applications and flood frequency analysis, only
three parametric probability density functions are used (Bulletin 17-B,
1982). Then Eq. (A3) may be simplified to a system of ordinary differential
equations for three statistical moments

The authors declare that they have no conflict of interest.

This study was funded through the Ministry of Education and Science of the Russian Federation (project 1413) and supported by the Academy of Finland (contract 283101). The article processing charges for this open-access publication were covered by the Academy of Finland. The authors are very thankful to the reviewers of BER and HESS, who provided very useful comments and suggestions for improving the manuscript. Our special thanks to Lynn. Edited by: C. De Michele Reviewed by: F. Serinaldi, I. Fedorova, and one anonymous referee