Time series of streamflow observations, which constitute the basis for all hydrological analyses, are generally characterized by a relatively short record period, typically ranging from several years to several decades. In fact, the average length of 6945 daily streamflow series collected by the Global Runoff Data Centre, and available worldwide, is 44 years . The information extracted by hydrologists from these time series (in the form of statistical indices, calibration of model parameters, etc.) is generally used for water resource management, for instance for hydropower generation mid- to long-term planning. The short record period is a major issue for hydrologists since it may be insufficient to capture and provide a clear understanding of the decadal variability in hydrological processes. For example, after studying a 90-year-long daily streamflow series of the Po River (Italy), and highlighting significant natural variability at the decadal scale, stated that “more research efforts are needed to improve the interpretation of such long-term fluctuations”. Studying natural variability requires long instrumental records (typically longer than 100 years), but such long time series are non-existent in remote regions such as northern Québec (Canada). The length (number of years) of 221 observed streamflow time series from Québec – extracted from the (cQ)2 (Impact des Changements Climatiques sur l'hydrologie (Q) au Québec) database – is shown in Fig. b and c, emphasizing that very few series have more than 50 years of data. Hydrological decadal variability is crucial in this region, since it is home to some of the largest hydropower systems in the world; as well, significant interannual inflow variability has been recorded in several Québec catchments (e.g., ; ). The few decades of observations available for this region are not sufficient to allow a robust analysis of multi-decadal hydrological variability and thus raise the issue of the reconstruction of past hydrology, i.e., occurring before the systematic recording of streamflows.

Over the past decades, different methods have been used by hydrologists to reconstruct natural flows on catchments of interest, depending on available data. These methods may be classified into two groups, according to the temporal resolution of the reconstructed series.

The first group brings together the methods based on long and continuous hydro-climatic series constructed with daily or sub-daily observations and consequently allows the reconstruction of streamflow time series at a fine temporal scale (e.g., daily resolution). When long streamflow series are available for other catchments close to the one under study, classical statistical regressions or other regionalization methods could be applied for the reconstruction e.g.,. The paired catchment approach – consisting of calibrating and then using a streamflow–streamflow model – could also be used e.g.,. When long climatic series (typically covering precipitation and temperature) are available in the studied region, the reconstruction could be done by using a rainfall–runoff model in order to transform the climatic series into streamflow series (e.g., simulation of 124 years of streamflow for the Thames River (UK) by ).

The second method is based on continuous or discrete series of paleo-indicators, generally producing reconstructed series at seasonal or annual resolutions . The most natural proxies used for hydrological reconstructions are sediment stratigraphy e.g., and tree ring series (see reviews by ). This latter proxy for streamflow reconstruction, referenced as dendrohydrology , is analyzed in a bid to reconstruct past hydro-climatological variations in a given catchment by studying tree ring width variations among different trees sampled in the same region. Reconstructed streamflow series are obtained by applying either direct or indirect methods. The direct methods aim to link tree ring series with streamflow series through statistical models calibrated over an observation period (e.g., in Tasmania (Australia) by , and in the southeastern United States by ). The indirect methods aim firstly to reconstruct climatic series, such as temperature or precipitation, and secondly to transform these climatic series into streamflow series through rainfall–runoff models (e.g., in the western US by ). These methods allow the continuous reconstruction of the annual or seasonal water balance of a given region, over long time periods. Additionally, other information could be extracted following tree ring analysis and used to reconstruct discrete chronologies of extreme hydrological events. For example, used anatomical tree ring signatures to reconstruct paleofloods of the Red River in Manitoba (Canada).

Recently, dendrohydrological methods have been successfully applied in boreal environments, characterized by a rarity of long hydro-climatological series. For example, used tree ring multi-proxies (tree ring widths, tree ring densities and tree ring stable isotope ratios) to produce spring, summer, and annual flow series of the Caniapiscau Reservoir in northern Québec (Canada) for the 1800–2000 period. On the same catchment, used both continuous series (tree ring minimal density measurements) and discrete series (with ice scars due to ice abrasion during floods) to produce spring flood series for the 1850–1980 period. These two reconstructions revealed significant flow variability in this region, in terms of both annual flows and flood frequency. It should be noted that the Caniapiscau Reservoir is the most upstream and one of the largest reservoirs of the La Grande complex, which is one of the biggest hydropower generation complexes in the world, with a total installed generating capacity of 17 418 MW. Decadal hydro-climatological variability in this region thus provides important information concerning the long-term planning of hydropower generation.

Although the above-mentioned hydrological reconstructions were associated with good verification statistics on the calibration period, the lack of observed streamflow data did not allow a rigorous independent verification of those reconstructions. An alternative solution involved carrying out new reconstructions based on different proxies and different methods and then, as an additional verification step, analyzing the consistency between the different reconstructions. Comparisons of streamflow reconstruction methods are rare in the literature, and the Caniapiscau Reservoir catchment offers an interesting case study since various tree ring reconstructions have been performed there. Thus, our objective is to apply a new reconstruction method on the Caniapiscau Reservoir in order to compare the obtained streamflow series with series obtained by dendrohydrology and to study the observed streamflow variability over the 1881–2011 period. This new reconstruction is based not on natural proxies but on a historical reanalysis of geopotential height fields. A climatic ensemble was reconstructed at daily resolution using the ANATEM methodology , a resampling method based on synoptic situation similarities between days (found by looking at the geopotential height reanalysis), with a sampling of observed climatic series for a given time period (the observation period) over a longer time period (the reconstruction period). Then, a rainfall–runoff model – previously calibrated on the observed period – was used to transform this climatic ensemble into a streamflow ensemble. The performances of the hydro-climatic reconstructions and of the rainfall–runoff model calibration were firstly evaluated over the observed period by comparing the reconstructions and the simulations with the observations. Secondly, the tree rings based on the ANATEM centennial reconstructions were compared and, finally, the long-term hydrological variability in the Caniapiscau Reservoir was discussed.

In Québec, 99 % of the produced electricity comes from hydropower generation systems. The La Grande water resources system, located in northern Québec and operated by Hydro-Québec (HQ), is one of the most important hydropower systems in the world, with an installed capacity of 17 418 MW (the Three Gorges Dam is the most important hydropower system in the world with a total installed capacity of around 22 000 MW). This system produces 50 % of the total energy generated by HQ. The Caniapiscau hydroelectric reservoir catchment is the first dam of the La Grande operational chain (the Brisay power plant installed at the outlet of the Caniapiscau Reservoir is ranked as the ninth with an installed capacity of around 500 MW) and is a 37 328 km2 snowmelt-dominated catchment. Figure  illustrates the hydro-climatic context of the Caniapiscau Reservoir catchment. The catchment elevation (SRTM data; ) ranges from around 500 to 900 m a.s.l., with the highest elevation areas located in the southern parts of the catchment. The daily streamflow series (Fig. 2a) and the monthly regimes (Fig. 2c) show the strong snow-dominated signature of the catchment, with an annual flood observed due to snowmelt during the month June. On average, the mean annual precipitation and runoff are around 800 mm (with around 300 mm falling as snow) and 650 mm, respectively, on the Caniapiscau Reservoir, and the mean annual temperature is around -3.6 ∘C. Catchment climatic data used in this study consist of daily series of minimum, mean, and maximum air temperature and of total precipitation, available for the 1950 to 2011 period. This dataset was produced by HQ, using kriging methods . Daily streamflow series are available from 1962 to 2011. Note that only the 1962–1979 period was considered for the rainfall–runoff model calibration here, since the Caniapiscau Dam was built during the 1980–1982 period, and streamflow series available for 1982 to 2011 are naturalized flows produced by HQ. Nevertheless, this second period (1982–2011, mean annual values are plotted in grey in Fig. b) will be used as a validation period for the reconstruction.

Two yearly time series of Caniapiscau Reservoir flows have been used here for comparison at the centennial scale: (i) the series of annual flows proposed by for the 1800–2000 period and (ii) the series of spring floods proposed by for the 1850–1980 period. The first yearly time series was processed from continuous tree ring series derived from 20 black spruce (Picea mariana (Mill.) BSP) sites located within 200 km around the Caniapiscau Reservoir. Two reconstruction methods were used (partial least-squares (PLS) regression and best analogue methods), and the reconstructions obtained were combined in a single composite reconstruction. The second yearly time series was processed from ice-scar time series derived from a small lake located next to the Caniapiscau Reservoir and using tree ring densities obtained from 12 black spruce sites. A new transfer model technique based on generalized additive model (GAM) theory was used to process spring flood reconstructions.

The general methodology consists of the reconstruction of an ensemble of daily climatic time series (with the ANATEM method) and of the transformation of this daily climatic ensemble into a daily streamflow ensemble, using a rainfall–runoff model. The ANATEM method is built on the combination of two approaches: (i) the ANA (which stands for “ANAlogue”) approach, which aims to find, for a given day, a given number of analogue days, based on the similarity of synoptic circulation , and (ii) the TEM (which stands for “TEMoin”, the French word for “witness”) approach, which is a basic regression model that uses a continuous and long-term reference (the witness) climatic series to reconstruct past climate. The ANATEM method thus allows the reconstruction of the climate of the past by combining synoptic information (ANA approach) with local climatic observations (TEM approach). Finally, this method allows the production of an ensemble of daily climatic time series by the selection of several analogues for any given day. For a complete description of the ANATEM method and an evaluation of its performance at the regional scale (French Alps), see . The rainfall–runoff transformation is done here with GR4J , a daily lumped continuous rainfall–runoff model, and its snowmelt routine, CemaNeige . GR4J and CemaNeige have four and two free parameters to calibrate, respectively, using the observed streamflow data available on the studied catchment. The whole streamflow reconstruction methodology – performed in the R-project environment (, http://www.r-project.org/) – is carried out in four steps (see Fig. ):

Step 1: calibration of the rainfall–runoff (R-R) model. The rainfall–runoff model is calibrated on the observed streamflow data.

The GR4J rainfall–runoff model was used to transform the climatic ensemble into ensembles of streamflow time series. GR4J is an efficient and parsimonious (only four free parameters to be calibrated) daily lumped and continuous model, which, when it is combined with its snow accumulation and melt routine, CemaNeige , is well suited for the hydrological modelling of snow-dominated catchments. GR4J and CemaNeige (model pair hereafter denoted CemaNeigeGR4J) were recently evaluated over several catchments located in Québec e.g., and showed good modelling performances. The structure of the CemaNeigeGR4J model is presented in Fig. . GR4J is based on two nonlinear stores (production and routing stores) and a unit-hydrograph, while CemaNeige is a degree-day snow accounting routine, which divides the studied catchment into five elevation bands. CemaNeigeGR4J uses as inputs daily series of precipitation, minimal and maximal air temperatures, and a daily potential evapotranspiration series, calculated using formula, designed for rainfall–runoff modelling. CemaNeigeGR4J produces daily streamflow series. GR4J and CemaNeige have four and two free parameters to calibrate, respectively. These six parameters – highlighted in Fig.  and described in Table  – were calibrated conjointly over the same calibration period using a local gradient search procedure, applied in combination with pre-screening of the parameter space . The Kling and Gupta efficiency criterion (, hereafter denoted KGE) was used as objective function. The KGE criterion ranges between -∞ and 1 (perfect simulation) and is estimated as follows: KGE=1-(β-1)2+(α-1)2+(r-1)2,

where β is the ratio between the means of the simulated and observed streamflow time series – this quantifies the simulation bias and ranges between 0 and +∞ (values > 1 indicate a model overestimation); α is the ratio between the standard deviations of the simulated and observed streamflow time series – this quantifies the ability of the simulation to reproduce the variability in the considered variable and ranges between 0 and +∞ (values > 1 indicate a model overdispersion); and r is the coefficient of correlation between the simulated and the observed streamflow time series – this quantifies the ability of the simulation to reproduce the observed temporal variations in the considered variable and ranges between -1 and 1 (perfect correlation).

Using KGE limits the biases of both water balance and variability, while keeping a good temporal correlation. Note that, for each model simulation, the first simulated year was used as an initialization period and was not considered for the final performance evaluation. All the rainfall–runoff model outputs presented in the paper have been produced at the daily resolution by using both GR4J rainfall–runoff model and its snowmelt routine CemaNeige.

The ANA approach is a resampling method based on synoptic circulation similarities between days, with a sampling of observed climatic series for a given time period (here, 1950–2011, the observation period) over a longer time period (here, the 1880–2011 period, the reconstruction period). The synoptic information considered for the analogy is geopotential height fields. Here, each day is described by four geopotential height fields: (i) 1000 hPa at 0 h, (ii) 1000 hPa at 24 h, (iii) 500 hPa at 0 h, and (iv) 500 hPa at 24 h. The geopotential height fields are extracted over a large domain covering the studied area (see Sect.  and Appendix A). The metric used to rank the days in terms of analogy is the distance (see Appendix B), which highlights similarities in terms of geopotential field shapes and has been shown to provide better outcomes than what is obtained by using classical Euclidean distances in this framework . Note that a seasonal constraint is imposed for the identification of analogue days: the potential analogue days of a given day are the ones included in a 60-day period centred on the calendar studied day. Thus, analogues of a winter day are themselves winter days: for example, the potential analogue days for 1 January 1880 are all of the available days within the 1 December to 30 January period of the observation period (here, 1950–2011). Another constraint is also imposed for the identification of analogues in which no analogue can be selected if they are closer than 15 days from the chosen date. For example, the potential analogue days for 1 January 2000 are all of the available days within the 1 December to 30 January period of the observation period except the 15 December 1999 to 15 January 2000 period. The ranking of analogue days is based on the Teweles and Wobus distance (see Appendix B). For each studied day, a given number of n analogues days is considered, thus generating a climatic ensemble of n time series. Here, the 20 nearest analogue days were selected for each studied day and each 20CR member considered (n=20). Table  illustrates the generation of this climatic ensemble by giving several analogue days obtained for three particular dates (1 and 2 January 1880 and 30 December 2011). For example, when considering member 1 of the 20CR (M1), the first analogue day of 1 January 1880 is 23 January 1984, the second analogue day is 12 December 1991, and the 20th analogue  day is 16 January 1988. Finally, 20×5 (5 members of the 20CR considered) daily climatic series were generated over the 1880–2011 period.

Using ANA outputs, ANATEM aims to exploit the available long-term reference time series (hereafter denoted TEM) to improve the climatic reconstruction by applying a classical regression between ANA outputs and the reference series. In this study, the ANA approach was directly applied for the precipitation reconstruction (since no precipitation “witness” series was available), while the ANATEM approach was applied for the reconstruction of daily temperature (using the BEST daily temperature series). As in , the local regression model (hereafter denoted LM), applied here for the temperature reconstruction, is based on an additive correction, modelled by a daily harmonic function. The parameters of this regression function were estimated over the observation period (here, 1950–2011) on the interannual mean monthly residuals of the differences between the catchment temperature series and the TEM series. The regression function has the following expression: T^LM(d)=TTEM(d)+β(d)+ϵ(d), where T^LM(d) is the estimate of the air temperature for the day d; TTEM(d) is the value of the witness series temperature for the same day; β(d) is the correction, depending on the calendar day of the year; and ϵ(d) is a residual assumed to have zero mean.

The ANATEM method was applied at the daily resolution over the 1880–2011 period. The ensemble of temperature values reconstructed for the day d has the following expression: [T^ANATEMk(d)]k=1,…,n=T^LM(d)+[T(dk)-T^LM(dk)]k=1,…,n, where [T^ANATEMk(d)]k=1,…,n is the ensemble of n reconstructed temperature values for the target day d, T^LM(d) is the air temperature estimate obtained with the regression model for the day d, dk is the kth analogue day selected for the day d, T(dk) is the observed temperature value for the kth analogue day, T^LM(dk) is the air temperature estimate obtained with the regression model for the kth analogue day, and n is the total number of analogue days (here n=20; see Sect. ).

The final climatic ensemble is built with 100 precipitation (ANA outputs) and air temperature (ANATEM outputs) daily series over the 1880–2011 period. For each day, the 100 climatic values are obtained based on the 20 “closest” analogue days for each of the five 20CR members considered.

Using the rainfall–runoff model parameter set obtained after calibration (step 1), the reconstructed climatic ensemble is finally transformed into one streamflow ensemble, available over the 1881–2011 period (1880 being used as an initialization period) at the daily temporal resolution. The final streamflow ensemble thus consists of 100 daily streamflow series over the 1881–2011 period.

In order to compare the reconstructed streamflow time series against observations, the reconstructed ensembles were first aggregated: a daily series was generated for each of the five 20CR members considered by averaging the 20 daily series constituting each ensemble. The five daily mean series are denoted ANA‾ or ANATEM‾, depending on the method used to produce them. The evaluation of the reconstruction performances was based on the three KGE components and its final values. For the reconstructed climatic time series, the computation of these four scores was carried out over the 1950–2011 period, at the daily timescale but also at the monthly timescale, in order to evaluate the intra-annual reconstruction performances, and at the yearly timescale, in order to evaluate interannual reconstruction performances. For the reconstructed streamflow ensemble, these scores were computed over mean annual flow values and mean May flow values over two time periods, 1963–1979 (rainfall–runoff model calibration period) and 1982 to 2011 (naturalized flows).

Over the 1963–1979 calibration period, the CemaNeigeGR4J model performs very well with a KGE value of 0.93 (rainfall–runoff simulations with KGE > 0.8 are generally considered good). The values of the six calibrated parameters are detailed in Table . Figure  presents the performance of the CemaNeigeGR4J rainfall–runoff model over the calibration period (1963–1979). Simulated and observed quantiles of monthly streamflow show a strong correlation (Fig. a), with a limited overestimation of the lowest values by the rainfall–runoff model observed during the winter months (from January to April, Fig. b). The timing of the simulated regime is similar to the observed one. However, systematic limited biases are found, with an overestimation of the winter streamflow values (January to April) and of the spring flood values (June) and an underestimation of the streamflow values during the snowmelt period (July to October). The model is also able to simulate the general interannual variability in mean annual streamflow (Fig. c), with higher values for the 1964–1969 period and lower values for the 1970–1976 period, for example. Nevertheless, non-systematic biases are found for several years, with both underestimations (e.g., years 1964 and 1969) and overestimations (e.g., years 1972 and 1975) of mean annual streamflow values. Finally, the observed and modelled distributions of annual streamflow values are similar (Fig. d), with an overestimation of the lowest mean annual streamflow values.

In this section, the results of the climatic reconstruction are presented, first in terms of performance estimated over the observed period (1950–2011) and then in terms of centennial mean annual series (1880–2011).

In this section, the results of the streamflow reconstructions are presented, first in terms of performance estimated over two time periods and then in terms of centennial series (annual mean flows and spring flood values).