The trend analysis was performed using the selected hydroclimate indices for each of ten Polish and eight Norwegian catchments in the projection period (1971–2100). Additionally to 130-year-long time series, we used three 30-year-long subperiods, the reference period (1971–2000), the near-future period (2021–2050) and the far-future period (2071–2100) and we estimated the relative changes of hydroclimatic extremes in the future with respect to the reference period. The latter approach is commonly used in the climate change impact studies instead of a long-term trend analysis on the grounds that in this way the nonstationarity of time series can be neglected. The main drawback of that approach lies in the dependence of the results on the time horizon used (Alfieri et al. 2016).
In the analysis we used an ensemble of climate model outputs. Following the discussion presented by Knutti et al. (2010), there is no recommended approach to model averaging. The decision whether model averaging should be performed and which method should be used for averaging depends on the specific application. Therefore, in the present study both combined and individual ensembles are applied. A part of the analysis related to the comparison of different trend estimation approaches using 130-year-long time series is based on a combined ensemble model output. We combine seven projected hydroclimatic variables from seven GCMs/RCMs using a simplified form of the total variation approach (Sain and Furrer 2010). This combining strategy has an advantage of considering the variance and correlation among the climate model output.
The comparison of changes of extreme indices within the 30-year windows for the near-future and far-future periods in relation to the reference period, is performed using individual climate ensembles which are equally weighted. The examples are taken from a case study of the ten Polish and eight Norwegian catchments. We illustrate the results using two catchments, one from Poland and one from Norway. The choice of the catchments was dictated by their typical for each country behaviour, but otherwise was arbitrary.
Hydrological modelling: calibration and validation stages
The results of calibration range from 0.48 to 0.79 of NS for the Polish catchments and from 0.56 to 0.85 for the Norwegian catchments. This shows a very good agreement between the observed and estimated flows. Table 4 shows the results of calibration and validation of the Polish catchments. The acceptable value of Nash–Sutcliffe criterion—based on daily flow in lowland and mountainous catchments—may vary because of the error square value in the formulation. Therefore, in lowland area (e.g. Łasica catchment) a NS of ≥0.4 is generally accepted to reflect a reasonable model performance for various purposes (ecological, water resource management, impact analysis, irrigation).
As an illustration, the hydrographs of the observed and modelled flow data for the validation period in 2005 for one Polish (Narewka) and one Norwegian (Ardal) catchments are presented in Fig. 4. Narewka and Ardal results are shown on the left and right panels, respectively. The figure shows a good agreement, except for base flow which is not always well represented. This may originate from the fact that the NS criterion used for the calibration puts more focus on medium to high flows (Gupta et al. 2009). Altogether, the validation results for the GR4J model are of the same accuracy as the results for the HBV model presented in Romanowicz et al. (2016), where the same catchments from Poland and Norway were analysed.
Projected hydroclimatic indices
The multi-model climate projections are used to simulate streamflow projections for the selected catchments using the calibrated GR4J model. The simulated annual maximum and mean daily flows during the period 1971–2100 for seven climate projections under the RCP4.5 emission scenarios are shown in Fig. 5. The Narewka flows are presented in the left panel, and the Ardal flows are shown in the right panel. Shaded areas present ensemble spreads: light red—for the reference period 1971–2000; light green—for the future period 2001–2100; blue lines show ensemble means of annual maximum daily flow (AmaxDF) and annual mean daily flow (AmeanDF). The yellow line shows a 10-year moving average. The catchment response to an external forcing depends on the catchment flood regime, the elevation, land cover and its spatial location. Narewka has a snow-dominated flood regime and is a lowland catchment. Ardal is rainfall-dominated. The shaded area reflects the flow variability related to the climate model ensemble, but it gives only a qualitative description of the trends in projections. The visual inspection gives an impression of decreasing annual maximum flows in Narewka and increasing trends in Ardal. The statistical tests presented in the following part of the section will tell us whether the visual impressions are quantitatively justified.
Projected changes in the selected indices of temperature, precipitation and flow in two future periods (2021–2050 and 2071–2100)
The aim of this section is an illustration of the influence of climate model variability on changes of extreme indices within a 30-year window. In order to compare differences in the hydroclimatic variables between the baseline condition and future conditions (reference period 1971–2000, near-future 2021–2050 and far-future 2071–2100), the annual maximum, minimum and mean precipitation in a relative format (%), temperature in absolute change (°C) and flow in a relative format (%) are compared. Figure 6a–c describes changes derived for the Polish catchments, and Fig. 7a–c shows the results for the Norwegian catchments. The figures present the box plots showing the median and 0.25 and 0.75 quantiles from the seven GCM/RCM climate projections listed in Table 2. In this section all the ensembles are treated as equally likely. According to the projected changes in the different climate indices, climate change has the potential to modify future flow characteristics remarkably across the country in near- (2021–2050) and far (2071–2100)-future periods (Figs. 8, 9).
The changes of precipitation show much higher variability than temperature changes (Figs. 6a, b). Increases of annual maximum, mean and minimum air temperature were observed for all studied catchments, with median annual mean increases from 1.2 to 3.0 °C, which is consistent with the results presented by Romanowicz et al. (2016).
The mean changes of annual maximum precipitation show even up to 250% decrease either in near- or in far-future periods. On the average, the mean changes of annual mean precipitation in Polish catchments have varying sign in the near future and 20–30% increase of mean precipitation in the far future (Fig. 6b).
Relative flow changes for annual maximum and mean flows are shown in Fig. 6c. As expected, the changes of annual maximum flows have the largest spread, reaching up to 700–800% for the Łasica and the Nysa catchments. Myśla is also characterized by large relative changes of maximum flow values, in particular for the far-future period.
Figure 7a–c presents the results of analysis of relative trend changes for the Norwegian catchments. Whereas the changes in temperature have similar positive trends in the near and far future, the variability among the catchments is more uniform in the Polish than in the Norwegian catchments. The largest annual maximum temperature changes (upper panel of Fig. 7a) are projected in Fustvatn catchment (over 10 °C for one of the ensemble members of climate projections). On the other hand, the largest changes of mean annual temperature (middle panel of Fig. 7a) are projected for the Polmak catchment. Also projected annual minimum temperature changes (lower panel of Fig. 7a) are the largest in Polmak and are in the range between −5 and 15 °C.
Presented in Fig. 7b, upper panel, annual maximum precipitation indices show the largest variability for the Fustvatn catchment for the near future. In the far future the decrease of annual maximum and mean precipitation is predicted in the Fustvatn and Viksvatn catchments.
Annual maximum and mean flow changes shown in Fig. 7c vary between catchments and periods. As mentioned before, those changes are probably related to changing flood regimes in the catchments caused by rising temperatures. Most of the Norwegian catchments show increased annual maximum flow in the near- and far-future periods except in the Polmak, where it decreases. Most notably catchments like Ardal, Eggedal, Krinsvatn, Myglevatn and Atnasjo exhibit small to moderate increases in annual maximum flow. Fustvatn shows large increase of annual maximum flow in the near future and no change/decrease in the far future. This behaviour is consistent with large variability of precipitation projections in this catchment shown in Fig. 7b. The annual mean flows show smaller changes, in particular in comparison with the changes projected in Polish catchments.
Autocorrelation and seasonality in the selected projected hydroclimatic indices
In this study, the autocorrelation of each hydroclimatic time series was examined and correlograms were produced. Autocorrelation coefficients are commonly used to examine whether time series exhibit nonrandom characteristics. If a serial correlation exists in a time series, it increases the likelihood of rejecting the null hypothesis of no trend, when in fact the null hypothesis should be accepted in the original Mann–Kendall test. This is because the variance of the Mann–Kendall test statistics is underestimated. In Table 5, the letter N denotes time series without serial correlation and the letter Y represents time series with a significant serial correlation.
Temporal trends in the projected hydroclimatic variables
Four trend detection methods (MK, MMK, DWT, DHR) have been applied to estimate trends of future hydroclimatic extreme indices for the 1971–2100 period. The results for two catchments, one Polish catchment Narewka and one Norwegian catchment Ardal, are presented for graphical illustration of projected annual maximum/mean flow, sum/maximum precipitation and maximum temperature.
The results of the DHR-based trend estimation illustrated in Figs. 8a, b show differences in projected trends for the extreme and mean annual flows for the Narewka and Ardal catchments. The differences are due, among other reasons, to different flow regimes in both catchments, snow melt dominated in the Narewka and rainfall-dominated in the Ardal catchment. With increasing maximum and mean rainfall and decreasing snow-fall following increasing temperatures, the flow regimes change in those catchments which were previously snow-dominated. These changes may result in changes of dominant modes of catchment behaviour and may cause the nonstationarity of model parameters (i.e. the parameters selected in different from modelled flow conditions may not be adequate in future climatic conditions).
Figures 9a, b show trends of the projected time series using the discrete wavelet components for the Polish and Norwegian catchments. The trend, wavelet details and original data of the wavelet components are shown by blue continuous lines, light blue continuous lines and red dots, respectively. The DWT results confirm the DHR results that the annual maximum daily flows increase in the Narewka catchment (Fig. 9a), whilst the temporal slope change is more clearly visible for the DHR than the DWT. In Fig. 9b, the results of the DWT analysis for the Ardal catchment are presented. Here we can also see the consistency between the results of trend analysis using both approaches.
The annual maximum precipitation, annual sums of precipitation and annual daily maximum temperatures show similar trends under DWT and DHR approaches for both catchments. The annual mean flow for Narewka shows larger “visual” trend in the DWT approach than the DHR. The main difference consists of the presence of uncertainty estimates of the time-variable mean (so-called trend) for the DHR approach. This difference has very important implications in detecting the existence of trend using statistical tools of hypothesis testing. Namely, the DHR-based low-frequency nonparametric component is derived together with its error estimates, which have the form of a zero-mean white noise (Young et al. 1999). This enables the application of the normal test to find the significance of changes in mean values of that component taking into account their variance. Taking into account the uncertainty of trend estimates explains why the DHR-based trend estimates are the most conservative of all the other techniques applied.
Trend test in the selected variables
Tables 6 and 7 show the results of trend analyses of all selected indices using four techniques, DHR, DWT and either Mann–Kendall or modified Mann–Kendall, for the Polish and Norwegian catchments. Trends in selected indices of precipitation, temperature and flow projections are estimated for the whole period 1971–2100. Results of the DHR analysis of annual maximum flows for Polish and Norwegian catchments are presented in the supplementary material. Tables 6 and 7 indicate that there are differences in the results for the individual hydroclimatic variables and that there are differences in the results for different catchments.
The results of the four applied trend detection methods, MK, MMK, DHR and DWT, are consistent in most cases. All methods show positive trend for annual mean temperature and annual sums of precipitation for both Polish and Norwegian catchments. Annual maximum precipitation shows positive trend for DWT and MK, MMK, but DHR shows no trend for that index in Dunajec and five other Norwegian catchments (Ardal, Fustvatn, Myglevatn, Viksvatn and Atnasjo).
The DHR shows no statistically significant trend in annual maximum flows in Polish catchments, except for Myśla, where it is positive. The other methods are less restrictive and show mostly positive trend in that index in Polish catchments with the exception of Wisla and Biala, where the negative trend is shown by those two approaches. Of the Norwegian catchments, Polmak has shown the negative trend in annual maximum flow by all techniques tested. The explanation for a negative trend may lie in a changing flow regime, as already mentioned. That catchment has snow-melt-driven flood regime, and similar changes were observed already by Madsen et al. (2014). However, according to the DHR and DWT, the snow-melt-based Atnasjo shows a positive trend detected in this catchment by all approaches tested. The other catchment that shows no or negative trend in the annual maximum flow is Eggedal, with a mixed flow regime. Therefore, more research is required to explain the annual maximum flow changes in those particular catchments.
Annual mean flows were included for the comparison with the extreme flows. All the methods show that Nysa and Flinta have no trend in annual mean flow and the rest of the catchments have positive trends. Therefore, some Polish catchments show no statistically significant positive trend in annual maximum flow values, whilst the mean flows are increasing. These are Narewka according to all three methods tested and the rest of the Polish catchments that have negative trend according to the DWT and MMK, with except of Myśla.
The seasonal maximum temperature, flow and precipitation indices are more variable, which is not surprising and indicates interannual changes in climatic patterns. All winter annual maximum flow trends are positive for the Norwegian catchments. Trends are also positive for the Dunajec, Nysa and Myśla, but negative for the Guber. Annual maximum summer flows have mostly positive trends for Polish catchments, but the trends are mixed for the Norwegian catchments. They are positive only for Krinsvatn, Myglevatn and Atnasjo for all the methods applied, and they are nonpositive (zero or negative) for the rest of the catchments. The seasonal precipitation patterns are not always consistent with the flow patterns. Namely, winter maximum precipitation and flow trends have opposite direction in Wisła, Narewka, Flinta and Guber catchments in Poland. On the other hand, summer maximum precipitation trends have opposite directions in Wisła and Nysa in Poland and Eggedal and Viksvatn in Norway. In a summary, there is a visible tendency for the change of flood regime from winter to summer period, which can be explained by the rising air temperatures.
In this study, the DWT and DHR approaches have clearly demonstrated how timescale information can be extracted from the data. By and large, the DHR method is more discriminating, which shows in the larger amount of “0”, i.e. “no trend” results. The possible changes of flood regime require further analysis of the mechanisms of those changes.
Meresa et al. (2016) concluded that climate change is likely to have a widespread impact on future flow and precipitation in Poland. In our study, highest impacts can be found in the north-west part of Poland (Myśla, Flinta), which is likely to suffer from increased annual maximum flow. Interestingly, the annual maximum flow trends do not necessarily coincide with the changes of annual mean flows. Increases in annual precipitation indices were observed in most catchments in this study, but they are not necessarily statistically significant. In the Norwegian catchments, large changes are expected in the north and north-west parts of the country, with the north getting wetter but with decreasing annual maximum flows and the north-west, becoming more prone to floods.