3.1 Multispectral imagery

3.2 Radar altimetry data

3.3 In situ water levels and discharges

The altimetry-based water level time series derived from radar altimetry were compared to gauge records from in situ stations for validation purpose. Data from 10 gauge stations were found in close vicinity to altimetry virtual stations (VSs; at a distance of less than 20 km along the streams). Virtual stations are built at intersections between an orbit ground rack and a water body (lake, river and floodplain) (Crétaux et al., 2017). Besides, surface water storage variations were compared to the river flow entering the delta, summing the records from three gauge stations located in upstream part of the delta. Daily data of water level and discharge were downloaded for free from the Canadian government website (http://wateroffice.ec.gc.ca).

4.1 Quantification of surface water extent

Multispectral imagery is commonly used for delineating flood extent using spectral indices (e.g. Frappart et al., 2006b; Sakamoto et al., 2007; Crétaux et al., 2011b; Verpoorter et al., 2014; Ogilvie et al., 2015; Pekel et al., 2016). As we do not have any external information to perform a supervised classification using the current state-of-the-art machine learning techniques (Pekel et al., 2016; Tulbure et al., 2016; Klein et al., 2017), we used the approach proposed by Sakamoto et al. (2007) to monitor the water surface area extent in the Mackenzie Delta (Fig. 2). This approach is based on the application of thresholds on the enhanced vegetation index (EVI), the land surface water index (LSWI) and the difference value between EVI and LSWI (DVEL = EVI − LSWI) to determine the status (non-flooded, mixed, flooded and permanent water body) of any pixel in an 8-day MODIS composite image of surface reflectance. As the spectral response of the near infrared (NIR) and shortwave infrared bands is highly dependent on the Earth surface nature, in particular water versus soil–vegetation surfaces, their complement was used to define LSWI. For instance, the surface reflectance presents low values (a few percentage points) over non-turbid water bodies and high values (a few tens of percentage points) over vegetation feature in the NIR spectral bands. The spectral response in the SWIR is mainly dominated by strong water absorption bands, which is directly sensitive to moisture content in the soil and the vegetation. For water surface area, the signal in the SWIR is assumed to be zero even in turbid waters (Wang and Shi, 2005). Thus, LSWI is expected to get values close to 1 for water surface areas and lower values for non-water surface areas.

The two indices, used in this approach, are defined as follows (Huete et al., 1997; Xiao et al., 2005):

where for MODIS, ρ_blue is the surface reflectance value in the blue (459–479 nm, band 3), ρ_red is the surface reflectance value in the red (621–670 nm, band 1), ρ_NIR is the surface reflectance value in the NIR (841–875 nm, band 2), and ρ_SWIR is the surface reflectance in the SWIR (1628–1652 nm, band 6). For OLI, ρ_blue, ρ_red, ρ_NIR, and ρ_SWIR are associated with channel 2 (452–512 nm), channel 4 (636–673 nm), channel 5 (851–879 nm), and channel 6 (1570–1650 nm), respectively. The constants $a,b,c$ and d are equal to 2.5, 6, 7.5 and 1, respectively, for both MODIS and OLI (USGS, product guide).

Figure 2Flow chart of the method (adapted from Sakamoto et al., 2007) used to classify each pixel of the multispectral images acquired over the Mackenzie Delta in four categories (non-flooded, mixed, flooded and permanent water bodies) for each year from 2000 to 2015 using MODIS 8-day composite data from the day of the year (DOY) 169 to 257.

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To process multispectral images, the first step consists of removing the cloud-contaminated pixels by applying a cloud masking based on a threshold of the surface reflectance in the blue band (ρ_blue≥ 0.2). Then, spectral indices are computed. Note that, contrary to Sakamoto et al. (2007), no smoothing was applied on spectral index time series. In a second step, the identification of the status of each pixel is performed by applying thresholds on EVI, LSWI and their differences (Fig. 2), which reduce the noise component. Thresholds determined by Sakamoto et al. (2007) were validated for our study site using OLI images acquired on 1 July and 2 August 2013 and compared to MODIS (Fig. S1 in the Supplement). Histograms show a similar bi-modal distribution for both EVI, LSWI and EVI-LSWI between MODIS and OLI 500 m (Figs. S1 and S2). For EVI, pixels with a value lower than 0.1 are clearly associated with water land surfaces, while pixels with a value higher than 0.3 are associated with soil and vegetation features. Other pixels, with an EVI value between 0.1 and 0.3, are identified as mixed surface types. For LSWI, pixels with a value higher than 0.5 are clearly associated with water land surfaces, while pixels with a value lower than 0.3 are associated with vegetation features or soil land surfaces when LSWI values are negative. Other pixels, with an LSWI value between 0.3 and 0.5, are identified as mixed surface types. Contrary to what was found by Sakamoto et al. (2007) in the Mekong Basin, no negative values of LSWI were observed over our study area. This threshold was not applied in this study. For EVI–LSWI, pixels with a value lower than −0.05 represent water land surface and values between −0.05 and 0.1 are associated with mixed pixels. Other pixels, with values higher than 0.1 are represented vegetation features or soil land surfaces (Fig. S2). Each pixel was then classified in two main categories: non-flooded (EVI > 0.3 or EVI ≤ 0.3 but EVI − LSWI > 0.05) and water-influenced (EVI ≤ 0.3 and EVI − LSWI ≤ 0.05 or EVI ≤ 0.05) (Fig. 2). The second category was divided into three sub-classes: mixed pixels (0.1 < EVI ≤ 0.3), flooded pixels (EVI ≤ 0.1) and permanent water bodies (e.g. lake, river and sea), the latter denoting when the total duration of a pixel classified as flooded is longer than 70 days out of 105 days for the study period. This annual duration for our study corresponds roughly to two-thirds of the study period, as proposed by Sakamoto et al. (2007). The spatio-temporal variations of floods have been characterized for the months between June and September over the 2000–2015 period.

Hereafter, in this paper we define water surface area as permanent water bodies with flooded areas, although inundated surfaces include only inundated areas.

4.2 Validation of MODIS retrievals using OLI

Evaluation of the performance of the water surface area detection from MODIS is based on the comparison between land surface water estimated from MODIS at a 500 m resolution, OLI at a 30 m resolution, and OLI re-sampled at 500 m resolution. For validation purposes, MODIS and OLI images are selected when (1) the time difference between the acquisitions of two satellite images is lower than 3 days and (2) the presence of cloud over the area is lower than 5 %. Following these criteria, only two cloud-free OLI composites were selected between 1 July and 2 August 2013.

4.3 Satellite-derived water level time series in the Mackenzie Delta

The concept of radar altimetry is explained below. The radar emits an electromagnetic (EM) wave towards the surface and measures the round-trip time (Δt) of the EM wave. Taking into account propagation corrections caused by delays due to the interactions of electromagnetic waves in the atmosphere, and geophysical corrections, the height of the reflecting surface (h) with reference to an ellipsoid can be estimated as follows (Crétaux et al., 2017):

where H is the satellite centre of mass height above the ellipsoid, R is the nadir altimeter range from the satellite centre of mass to the surface (taking into account instrument corrections; $R=c\mathrm{\Delta }t/\mathrm{2}$, where c is the light velocity in the vacuum), and ∑ΔR_propagation is the sum of the geophysical and environmental corrections applied to the range.

where ΔR_ion is the atmospheric refraction range delay due to the free electron content associated with the dielectric properties of the ionosphere, ΔR_dry is the atmospheric refraction range delay due to the dry gas component of the troposphere, and ΔR_wet is the atmospheric refraction range delay due to the water vapour and the cloud liquid water content of the troposphere.

where ΔR_{solid Earth} and ΔR pole are the corrections respectively accounting for crustal vertical motions due to the solid Earth and pole tides. The propagation corrections applied to the range are derived from model outputs: the global ionospheric maps (GIMs) and Era-Interim datasets from the European Centre for Medium-Range Weather Forecasts (ECMWF) for the ionosphere and the dry and wet troposphere range delays respectively. The changes in the altimeter height h over the hydrological cycles are related to variations in water level. Here, the Multi-mission Altimetry Processing Software (MAPS) was used to precisely select valid altimetry data at every virtual station location (see Sect. 3.3) series in the Mackenzie Delta. Data processing consisted of four steps (Frappart et al., 2015b):

• the rough delineation of the river–lake cross sections with overlaying altimeter tracks using Google Earth (distances of ±5 km from the river banks are generally considered);

• the loading of the altimetry over the study area and the computation of the altimeter heights from the raw data contained in the GDRs;

• the selection of valid altimetry data through a refined process that consists of eliminating outliers and measurements over non-water surface areas based on visual inspection (the shape of the altimeter along-track profiles permit identification of the river that is generally materialized as a shape of “V” or “U”, with the lower elevations corresponding to the water surface area; see Santos da Silva et al., 2010 and Baup et al., 2014 for more details);

• the computation of the time series of water level.

4.4 Surface water volume storage

The approach used to estimate the anomalies of surface water volume is based on the combination of the surface water extent derived from MODIS images with altimetry-based water levels estimated at virtual stations distributed all over the delta (Fig. 5). Surface water level maps were computed from the interpolation of water levels over the water surface areas using an inverse-distance weighting spatial interpolation technique following Frappart et al. (2012). Hence, water level maps were produced every 8 days from 2000 to 2015. For each water pixel, the minimal height of water during 2000–2015 is estimated. As ERS-2, ENVISAT and SARAL had a repeat cycle of 35 days, water levels are linearly interpolated every 8 days to be combined with the MODIS composite images.

Surface water volume time series are estimated over the Mackenzie Delta following Frappart et al. (2012):

where V is the anomaly of surface water volume (km³), S is the surface of the Mackenzie Delta (km²), h (λj, φj) the water level, h_min (λ_j,φ_j) the minimal water level for the pixel of coordinates (λ_j,φ_j) inside the Mackenzie Delta, δ_j equals 1 if the jth pixel is associated with permanent water body/inundated and 0 if not and ΔS the pixel surface (0.25 km²).

Figure 3Maps of surface water extent duration for (a) annual average from 2000 to 2015, (b) annual standard deviation from 2000 to 2015, (c) error average from 2000 to 2015, (d) standard deviation from 2000 to 2015, difference between annual average water surface area duration from 2000 to 2015 and water surface area duration during (e) 2006, the period associated with the highest flood event, and (f) 2010, the period associated with the lowest flood event recorded over the period.

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5.1 MODIS-based land water extent and their validation

Following the method of Sakamoto et al. (2007), all pixels of 8-day image have been classified into four groups: class 0 corresponding to vegetation, class 1 to permanent water, class 2 to inundation, and class 3 to a mixture of land and water. A map of annual average of water surface area, composed of inundated and permanent water bodies (classes 1 and 2), was obtained at spatial and temporal resolutions of 500 m and 8 days respectively from June to September over the 2000–2015 period (Fig. 3a). A map of annual average of water surface area duration along with associated standard deviation over 2000–2015 during an ice-free period of 3.5 months (105 days) is presented in Fig. 3b. Permanent water bodies (i.e. identified as water surface area more than 70 days annually) are located along the Mackenzie River main channel, its tributaries (Reindeer, Peel, Middle and East channels) and major lakes of the Delta. The longer water areas (i.e. identified as flooded between 30 and 70 days annually) are surrounding permanent water bodies. Other areas of the delta are annually inundated up to 30 days (Fig. 3a). The map of standard deviation of the annual flood duration shows ranges from a few days over the areas affected by floods during a short time span to 15 days close to permanent water bodies (Fig. 3b).

Maps of errors made on water surface area duration with associated standard deviation are shown in Fig. 3c and d over 2000–2015. Mixed pixels have been used to calculate the error for each pixel on water surface area duration, corresponding to the class 3 “mixed” of Sakamoto et al. (2007) classification. Standard deviation is presented in Fig. 3d. Maximal error and standard deviation is obtained for pixels of potential flooding area in the delta. If short differences – lower than 20 ± 12 days – can be observed in the downstream part of the delta (over 69^∘ N), longer differences (30 to 50 ± 15 to 20 days) are present in the upstream part. They can be attributed to the presence of small permanent lakes in this area. Important inter-annual differences can be observed between wetter (Fig. 3e) and dryer (Fig. 3f) years.

Table 1Validation of surface water extents (km²) determined using OLI 30 m, OLI 500 m, and MODIS 500 m images with the results of Emmerton et al. (2007).

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Surface water extent (the sum of permanent bodies and inundated areas) were also estimated by applying the approach described in Sect. 3.1 for OLI images at 30 m of spatial resolution, and resampled at 500 m of spatial resolution. They were compared to MODIS-based surface water extent for the closest date (Table 1). Figure S3a, b and c present the maps of the surface water extent determined using MODIS, OLI 500 m and OLI 30 m respectively, acquired in July 2013. Medium and large-scale (with a minimal size of 300 m) land water features are well detected, as displayed in the enlarged part of the images. Figure S3c presents an enlarged image of surface water extent using OLI 30 m with permanent and inundated bodies. Surface water extent from OLI 500 m and MODIS are similar for both dates, with differences lower than 20 % (Table 1). For example in July 2013, water surface area is about 4499 km² for OLI 500 and 3798 km² for MODIS (Table 1). Percentages of common detection of surface water were estimated for the pixels detected as water surface area in the pair of satellite images. These percentages are 73 and 74 % for July and August 2013, respectively. Areas detected as water by both sensors correspond to the main channels and connected floodplains. Differences appear on the boundaries of areas commonly detected as inundated and on small scales and can be attributed to the difference of acquisition dates between MODIS and OLI (Fig. S4). These results highlight the robustness of the method of Sakamoto et al. (2007) for accurate water surface area retrievals. These surface water extents have been compared with surface water extents (channels and wetlands) determined by Emmerton et al. (2007) in Table 1. For MODIS, differences are lower than 15 % and for OLI 500 differences are about 25 % (Table 1).

However, the comparison between surface water extent estimated from OLI 30 m and MODIS 500 m shows important differences. In July 2013, surface water extent is about 3798 km² from MODIS and 7685 km² from OLI 30. The surface extents are higher for OLI 30 by a factor of 2 (Table 1). According to Emmerton et al. (2007), the Mackenzie Delta is composed of 49 000 lakes with a mean area of 0.0068 km² and 40 % of the total number of lakes have an area inferior to 0.25 km². The pixel sizes of OLI 30 m and MODIS 500 m are approximately 0.0009 and 0.25 km², respectively. Thus, the high difference between the water surface areas detected using OLI 30 m and MODIS is probably associated with a spatial sample bias. Small-scale water features detected from OLI cannot be detected from MODIS due to a lower spatial resolution.

Surface water extents determined using OLI 30 have been compared to Emmerton et al. (2007) surface water extents (including channels, wetlands and lakes). Emmerton et al. (2007) classified the Mackenzie Delta habitat in lakes, channels, wetlands and dry floodplains using information from topographic maps derived from aerial photographs taken during the 1950s for low-water periods. Differences between surface water extent of OLI 30 and Emmerton et al. (2007) are lower than 15 % (Table 1).

Table 2Satellite validation of surface water extent using OLI 30, OLI 500 and MODIS 500 m.

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In order to investigate the assumption of spatial sample bias associated with MODIS 500 m, a satellite validation of surface water extent is performed (Table 2). Permanent water and inundated surfaces have been calculated for MODIS, OLI 500 and OLI 30. For OLI 30 and OLI 500, pixels identified as surface water for the two dates are considered as permanent waters (Table 2). In July 2013, inundated surfaces are nearly equal, about 577 km² for MODIS, 690 km² for OLI 500 and 627 km² for OLI 30 (Table 2). In August, inundated surfaces are equal to 250 km² and are 2.5 times more important than OLI 30 (98 km²), if we consider OLI 30 as truth.

Time series of surface water extent in the Mackenzie Delta were derived from the 8-day maps of surface water extent (Fig. 4). Surface extent water varies from 1500 to 14 284 km² between 2000 and 2015 along the hydrological cycle. Each year, water surface area extent is at its maximum in June in response to the spring ice break-up and snow melt that occurred in May (between day of year, DOY, 110 and 130 on average) in the Delta and decreases to reach a minimum in September, as previously observed by Goulding et al. (2009a, b). On average, during the study period, maximum surface water extent is ∼ 9600 km² . The largest water surface area extent was reached in June 2006 with an inundated area of 14 284 km², which represents ∼ 85 % of the delta total surface (Fig. 4). Large surface water extents (∼ 12 500 km²) were also detected in 2011 and 2013 in accordance with high discharge peaks reported for these years (http://wateroffice.ec.gc.ca/) and the historic inundation that occurred in Aklavik in 2006 (Beltaos and Carter, 2009).

Figure 4Time series of surface water extent from 2000 to 2015, between June and September, derived from the MODIS images.

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5.2 Altimetry-based water levels and their validation

The Mackenzie Delta is densely covered with altimetry tracks from the ERS-2, ENVISAT and SARAL missions that were all on the same nominal orbit. A total of 22, 27 and 24 altimetry virtual stations were built at the cross section of an altimetry track with a water body for these three missions respectively (see Fig. 5 for their locations). A water level temporal series is obtained for each virtual station.

Table 3Statistic parameters obtained between altimetry-based water levels from altimetry multi-mission and in situ water levels.

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The quality of altimetry-based water levels was evaluated using in situ gauge records. Only 6 virtual stations are located near in situ stations (with a distance lower than 20 km) for ERS-2 data, with 10 for ENVISAT and 8 for SARAL data. Characteristics of these virtual stations are given in Table 3. For ERS-2 and SARAL comparisons, the correlation r is low at the station 0114-c, i.e. −0.38 and 0.15 respectively (Table 3).

Figure 5Locations of virtual stations (VSs) in the Mackenzie Delta for ERS-2 (yellow dots), Envisat (green dots) and SARAL (purple dots) altimetry missions. Altimetry tracks appear in grey. In situ stations are represented using red triangles.

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Figure 6Altimetry-based water levels from 1995 to 2015 compared with in situ water levels for the station 0744-a, located in the downstream part in the Mackenzie Delta, using (a) the ERS-2 mission and (b) a water level anomaly with statistic parameters, (c) the ENVISAT mission and (d) a water level anomaly with statistic parameters, and (e) using SARAL mission.

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For ERS-2, quite high correlation coefficients are obtained for four virtual stations out of six, with r ≥ 0.69 and RMS ≤ 1 m (Table 3). For the two other stations, no correlation is observed (−0.38 and 0.08 for ERS-2-0114c and ERS-2-0200-d respectively with a RMS ≥ 1 m) (Table 3).

For ENVISAT, 8 out of 10 stations have a correlation coefficient ranging between 0.66 and 0.93 (Table 3). Except for ENV-0572-a, which is located 22 km away from the nearest in situ station, higher correlations were found when the river is larger at the VS (Table 3). For example, ENV-0114-b exhibits a negative correlation (r= −0.27) where the cross section was only 150 m wide (Table 3). This station is also located near the city of Inuvik. The presence of the town in the altimeter footprint could exert a strong impact on the radar echo and explain this low correlation.

For SARAL, five out of six virtual stations have a good correlation r coefficient higher than 0.76 with a low RMS (Table 3) due to its narrower footprint with an increase in the along-track sampling.

Figure 7Altimetry-based water levels from 1995 to 2015 compared with in situ water levels for the station 0439-a located in the centre of the Mackenzie Delta using (a) the ERS-2 mission and (b) a water level anomaly with statistic parameters, (c) the ENVISAT mission and (d) a water level anomaly with statistic parameters, and (e) the SARAL mission and (f) a water level anomaly with statistic parameters.

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Comparisons between water levels derived from altimetry and in situ are shown for two stations for ERS-2 (called ERS-2-0744-a and ERS-2-0439-a; Figs. 6a and 7a), three for ENVISAT (ENV-0744-a, ENV-0439-a and ENV-0028-a; in Figs. 6b, 7b and 8) and two for SARAL (SARAL-0744-a and SARAL-0439-a; Figs. 6c and 7c). Virtual station 0744-a is located in the downstream part of the delta, 0439-a in the centre and 0028-a in the upstream part (Fig. 5). For each station, water levels obtained by altimetry and water levels obtained by in situ gauges are superposed (Figs. 6, 7 and 8). Then, water level anomalies, which are computed as the average water level minus the water level, have been calculated for altimetry and in situ data.

Figure 8Altimetry-based water levels from 2002 to 2010 compared to in situ water levels for the station 0439-a located in the centre of the Mackenzie Delta (a) using ENVISAT mission and (b) water level anomaly with statistic parameters.

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The virtual station 0744-a is located in the north of the Mackenzie Delta (Fig. 5). Water level time series have been processed between 1995 and 2015 and compared to in situ data of the station 10MC010 for each mission ERS-2, ENVISAT and SARAL (Fig. 6). In situ data are not continuous since the river is frozen from October to April. With regard to altimetry, data have been acquired throughout the year, but during frozen periods water levels are unrealistic due to the presence of river ice. Thus, the processing is done only from the beginning of June to the end of September for multispectral imagery treatment. The correlation r between altimetry water levels and in situ levels is 0.88 for ERS-2, 0.93 for ENVISAT and 0.99 for SARAL (Table 3). For the three missions, RMS is weak, lower than 0.15 m (Table 3). At this station, the variation of water level is about 2 m on average with an important water level in June that decreases to September (Fig. 7a, c and e).

The virtual station ERS-2-0439-a is in the centre of the Mackenzie Delta and water level time series have been recorded between 1995 and 2015 and compared to in situ data of the station 10MC008 for the three missions ERS-2, ENVISAT and SARAL (Fig. 7). The correlation between altimetry water levels and water levels from in situ gauges is about 0.76 for ERS-2, 0.89 for ENVISAT and 0.96 for SARAL (Table 3). RMS is included between 0.35 and 0.5 m for the three missions. On average at this station, water levels variations are about 4 m, with a maximal water level in June that decreases to reach a minimal value in September (Fig. 7a, c and e).

Water level time series between 2002 and 2010 at the virtual station ENV-0028-a, located upstream of the Mackenzie Delta, have been compared to in situ data of the station 10LC014 (Fig. 8). A good correlation was found for this station too, with a coefficient correlation r of 0.83 and a RMS of 1.84 m (Table 3). For this station, variations of water levels are much higher, with 9 m on average, but reach 12 m during the 2006 extreme event (Fig. 8a). Water level time series were constructed only for ENVISAT mission since for the two others (ERS-2 and SARAL), altimetry water levels were not consistent, exhibiting values around 70 m. Therefore, water levels determined by altimetry and water levels from in situ gauges have a difference, which is probably explained by the distance between virtual stations and in situ gauges (16.31 km) since the slope is about −0.02 m km⁻¹ in the Delta (Hill et al., 2001). Moreover, the seasonal cyclic thawing and freezing of the active layer causes cyclic settlement and heave at decimetre levels, estimated to 20 cm (Szostak-Chrzanowski, 2013).

Figure 9Water level maps in the Mackenzie Delta in 2006 (historic flood) obtained by combining inundated surfaces determined using MODIS images with altimetry-derived water levels (a) in June, (b) in July, (c) in August and (d) in September.

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5.3 Time series of surface water storage anomalies in the Mackenzie Delta

The minimum water level of each inundated pixel was determined over the observation period. Maps of 8-day surface water levels were created after subtracting the minimum water level to water level at time t, using MODIS-based flood extent and altimetry-derived water levels in the entire delta from June to September. Example of water level maps are presented for 2006 at 4 different dates (in June, July, August and September), characterized as an historic flood (Fig. 9).

Over the study period, water level maps show a realistic spatial pattern with a gradient of water level from south to north, consistent with flow direction in the delta. In Fig. 9a, in June 2006, for example, water levels are higher (about 5 m) upstream than downstream (about 0.5 m). The surface water storage reaches its maximal extent in June (Fig. 9a) and then decreases during the following months, reaching 1 m in September in the entire delta (Fig. 9b, c and d).

The time series of surface water volume variations was estimated from 2000 to 2010 and then from 2013 to 2015, between June and September, following a similar approach to that in Frappart et al., 2012 (Fig. 10). Surface water storage was estimated from 2000 to 2003 using ERS-2 data, from 2003 to 2010 using ENVISAT data and from 2013 to 2015 using SARAL. Between 2010 and 2013, surface water storage could not be estimated due to lack of RA data over the delta. The impact of the presence of a virtual station located in the upstream part of the delta and the inclusion of ERS-2 data on our satellite-based surface water volume estimation were assessed. For ERS-2 and SARAL data, no virtual station was created in the upstream part due to unreliable water levels in the upstream part of the delta. During the SARAL observation period, in situ water levels from 10LC014 station were used. One curve corresponds to surface water volume with virtual stations in the upstream part of the delta (2002–2015; red) and another one without virtual stations in the upstream part of the delta (2000–2015; green). Correlations between river discharges and surface water volumes with and without (2002–2015) upstream virtual stations are the same (0.66). In the presence of a virtual station in the upstream part of the Mackenzie, the water volume decreases by ∼ 0.3 km³ on average (Fig. 10). The correlation is lower (0.63) when ERS-2 data are included in the analysis (2000–2015). The integration of ERS-2 data has a lower accuracy and slightly decreases the correlation between water storage and flux.

Figure 10Surface water volume from 2000 to 2015, determined by combining inundated surfaces from MODIS with altimetry data; 167 red points correspond to surface water volume obtained with a virtual station located in the upstream part of the Delta, green points to surface water volume without a virtual station located in the upstream part of the Delta. The Mackenzie River Delta discharges at 10LC014 gauge station appear in blue.

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Figure 11Temporal and spatial variations of surface water levels (in metres) in the Mackenzie Delta. (a) Location of virtual stations used to analyse spatial variations; green dots are corresponding to latitudinal variations along the Mackenzie River (from number 1 to 8) and red triangles are corresponding to longitudinal variations at three different latitudes (letters from A to I). (b) Surface water level time series along the Mackenzie River at different latitudes. Panels (c–e) show surface water levels time series at three different latitudes with three virtual stations at each latitude to analyse longitudinal spatial variations.

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In terms of temporal variability, a clear seasonal cycle is visible, with a yearly maximum of water surface area volume occurring in June (about 9.7 km³ on average), followed by a decrease until September (Fig. 10). The peak generally corresponds to the presence of the extensive flood covering the delta in June, and during summer the volume decreases to reach its minimal in September (∼ 0.2 km³). The largest surface water volume occurred in 2006 with a volume of 14.4 km³ (Fig. 10), known as an historic flood (Beltaos and Carter, 2009). These results showed that the satellite-based surface water volume estimation is consistent with the Mackenzie River discharge, which is the main driver of the delta flooding.

6.1 Spatio-temporal dynamics of surface water extent

Maps of surface water extent duration for annual average from 2000 to 2015 exhibit important spatio-temporal variations along the Mackenzie Delta (Fig. 3a). Areas with open water present during the whole study period are located along the Mackenzie River and its tributaries. On the contrary, areas covered with open water for a duration lower than 30 days in the study period of 120 days are mostly located in the western upstream and eastern downstream parts of the delta but also in some locations in the western downstream part and along the Mackenzie mainstream (Fig. 3a). They correspond to regions only inundated in June during the floods caused by spring ice break-up and snow melt occurring in May (see Fig. 9 for the temporality of the flood extent). The central part of the Mackenzie is inundated between 40 and 70 days per year (Fig. 3a). As can be seen in Fig. 9, this area is not continuously inundated except for during two flood events in June in response to snowmelt and in August and September in response to an increase in river discharges of the Mackenzie River. This secondary peak ranges from 3000 to 5000 km² in comparison with the earlier one that ranges from 4000 to 10 000 km² (Fig. 4). Maps of difference between the duration of extreme surface water surface area and the average water surface area duration from 2000 to 2015 were estimated for the large historic flood that occurred in 2006 (Fig. 3e) and for the minimal flood that occurred in 2010 (Fig. 3f). The whole Mackenzie Delta was practically covered in water in 2006, whereas large areas, especially in the downstream part of the delta, were not inundated in 2010 (Fig. 3f).

6.2 Spatio-temporal dynamics of surface water levels in the Mackenzie delta

For all stations and RA missions, a strong seasonal cycle can be seen, with a maximum water level reached in June after the spring ice break-up and snow melt that decreases to reach a minimal value in September, in good accordance with the hydrological cycle of the Mackenzie Delta. The delta is frozen from October to May, and during spring–early summer the freshwater meets an ice dam that was formed in winter, which provokes river discharge variations from 5000 m³ to 25 000 m³ on average (http://wateroffice.ec.gc.ca/, Fig. 1b). Then, these important variations provoke water level increases and significant floods each year in the delta. However, water level variations as revealed from RA are not equal over the delta. In the upstream part, variations are 9 m on average, 4 m in the centre and 3 m in the downstream part of the Mackenzie Delta.

Water level time series from data acquired by the ENVISAT mission between June and September, averaged over 2002–2010, are presented in Fig. 11. Each time series has been shifted manually and errors are not shown here for clarity purposes. Virtual stations used to discuss the spatio-temporal variations were chosen along the Mackenzie River from upstream to downstream and at similar latitudes on the Mackenzie River and its tributaries. They are represented using green dots for variations along the Mackenzie River and red triangles for latitudinal variations (Fig. 11a). Time series from Fig. 11b are located along the Mackenzie River, number 1 corresponding to the upstream part and number 8 to the downstream part. Logically, a stronger seasonal cycle is observed upstream than downstream. If the primary peak of flooding that occurs in June clearly appears for all the stations, the secondary peak of August–September is not well marked for all the stations. This could be due to either local differences in the hydrodynamics of the river or due to the low temporal frequency of acquisition of the altimeters that is not sufficient to fully capture all specificities of the hydrological cycle (see Biancamaria et al., 2017 for instance). Latitudinal differences can also be noticed (Fig. 11c). Larger annual amplitudes of water levels can be observed in the Mackenzie River than over its tributaries. The second flood event occurs earlier in the central part (August) than in the western and eastern parts (September).

6.3 Spatio-temporal dynamics of surface water storage

The spatio-temporal dynamics of surface water storage is presented in Fig. 9 for 2006. A strong upstream–downstream gradient of water levels can be observed in June with water levels ranging 0 to 5 m from north to south (Fig. 9a). It strongly decreases in July (0 to 1.5 m in Fig. 9b) and does not appear in August (Fig. 9c) and September (Fig. 9d). For these two later months, differences in water levels are more homogeneous of the whole delta (except in a region located around 135^∘ W and between 68^∘ N and 68^∘30^′ N in August). Our results were compared to the ones estimated by Emmerton et al. (2007) under the assumption of a storage change as a rectangular water layer added to the average low-water volume for a stage variation from 1.231 m above sea level during a low-water period and 5.636 m above sea level during peak flooding. Using this approach, Emmerton et al. (2007) found an increase in water volume of 14.14 km³ over the floodplains and 7.68 km³ over the channels. With our method, maximal water volume is around 9.6 km³ on average and can reach 14 km³. As can be seen in Fig. 11, water levels present a strong decreasing gradient of amplitude over the delta towards the mouth and are, on average, lower than 5.636 m from Emmerton et al. (2007). The difference of approaches is likely to account for such discrepancy. The comparison between storage and flux (discharge) exhibits quite a good correlation (R= 0.66 with no time-lag) between these two quantities. Several studies demonstrated that there are no linear relationships among surface water extent, surface water volume and river discharge due to the presence of floodplains non-connected to the river (e.g. Frappart et al., 2005; Heimhuber et al., 2017). Due to the small area of the non-connected lakes present in the Mackenzie delta, they are detected in our approach based on the use of MODIS images at 500 m of spatial resolution, as mixture areas (except during the June flood event where almost all the delta is inundated and all the flooded areas are connected to the river). Only the floodplains connected to river are considered in this study.