The inventory map (scale 1:2 000 000) and the Cadastre of aufeis of the North-east USSR (Simakov and Shilnikovskaya, 1958b), hereinafter referred to as the Cadastral map and the Cadastre, became the first summarizing quantitative work on aufeis within the territory. The effort was carried out in the framework of the Central complex thematic expedition of the North-East Geological Survey of the USSR.

The Cadastre contains data on 7448 aufeis fields of different size and over 2000 boolgunyakhs (frost mounds). Of the total number of aufeis fields, 7006 are plotted based on air-photo interpretation data and another 442 based on geological reports from field data. It should be noted that aufeis was identified based on geomorphologic features, meaning that in some cases only the areas or river valleys with aufeis were identified but not aufeis itself.

In the Cadastre (1958) and our digitalization, the following characteristics of the aufeis are presented: location (the name of the river, the distance from the mouth or source), size (maximum length, average width and area) and the dates of ice recording in aerial images (ranging from 8 June 1944 to 27 September 1945). Areas of the aufeis were evaluated via planimetry.

Only very large aufeis fields (>3.3 km2) were plotted on the Cadastral map (1958), while others are shown as point locations. Each aufeis field on the Cadastral map (1958) has its corresponding number, whose identifier and corresponding information can be found in the Cadastre (1958). As noted by Simakov and Shilnikovskaya (1958a), some very small aufeis fields (<0.01 km2) could have been missed due to their indecipherability on aerial images, or they might have already melted at the time of the aerial photograph. The example of the Cadastral map's sheet (1958) for the Indigirka River upper reaches is presented in Fig. 2.

Here, we developed the GIS database of aufeis in the Indigirka River basin up to the cross section at the Vorontsovo gauging station based on the Cadastre (1958) and topographic maps. Our compilation contains data on 896 aufeis fields. The aufeis fields are presented as point objects in our database. The areas are specified for only 808 aufeis fields. The total area of all the aufeis fields within the specified area accounts for 2063.6 km2 and the areas of individual aufeis fields vary from 0.01 to 82 km2.

In the Cadastre, the dates of ice recording for 592 aufeis fields (66 %) are presented, based on aerial images within the study area. The average seasonal date of recording is 2 August, ranging from 8 June to 27 September. The dates of ice recording for the remaining 34 % of the aufeis were not described, meaning that aufeis detection could be carried out based not on the visible ice presence at the aerial images but on geomorphological features of river valleys. Therefore, the Cadastre might contain data on old aufeis glades, where the aufeis itself was absent.

Spatial positioning of the Cadastral map of aufeis was conducted using the location description by Russian topographic maps with the scale of 1:200 000. Grosse and Jones (2011) used the same set of maps for compiling the dataset of pingos (frost mounds) in northern Asia and described those maps in details therein. The maps at 1:200 000 scale were based on more detailed maps of 1:50 000 and 1:100 000 scale, which were derived from aerial photography acquired in the 1970–1980s. The use of the 1:200 000 scale guarantees the position assessment precision to within 100 m. Each map sheet was visually searched for aufeis, and identified aufeis was marked with an area polygon in a GIS layer. The locations of 330 aufeis fields (area 358 km2) were determined based on topographic maps. When digitized, a point was plotted in the middle of aufeis on a topographic map.

The locations of the remaining aufeis were determined with the spatially positioned map of the Cadastre. Additionally, 11 aufeis fields were found which were absent in the Cadastre but present in the topographic maps. Aufeis areas were estimated using digitalization of the maps. Areas of the remaining aufeis were estimated with the Cadastre. It was not possible to estimate the area of 88 aufeis fields, as they were not drawn on the topographic maps, and only their location, but not area, was stated in the Cadastre.

Aufeis location and area are relatively easy to determine using Landsat and/or Sentinel-2 images, received immediately after snow cover melt. Snow and ice are known to be characterized by relatively high reflectance in the visible and near-infrared spectral bands and its significant decrease in the mid-infrared band. The Normalized Difference Snow Index (NDSI) is based on this pattern and is calculated according to the formula (Hall et al., 1995): NDSI=(GREEN-SWIR1)/(GREEN+SWIR1), where SWIR1 is reflectance in the mid-infrared band (1.56–1.66 µm for the Landsat-8 images), and GREEN is reflectance in the green band (0.525–0.6 µm for the Landsat-8 images). Following Hall et al. (1995), the threshold value for snow and ice is set at 0.4. Apart from using NDSI, other indices have been suggested to detect aufeis using Landsat images (but not used here). These are the Normalized Difference Glacier Index (NDGI) and the Maximum Difference Ice Index (MDII). Their advantages and disadvantages are discussed by Morse and Wolfe (2015).

Landsat-based detection of aufeis required some additional data to exclude other surface types with similar spectral characteristics, such as snow-covered areas and turbid water. It is problematic to separate floodplain lakes from aufeis using late spring satellite images because many of these lakes are still ice-covered in May–June. Morse and Wolfe (2015) recommended creating a mask of water surface using midsummer images (when all water bodies are not already covered by ice), to exclude them from further analysis.

Aufeis detection in the Indigirka River basin was carried out based on the Landsat-8 OLI satellite images, from 2013 to 2017, downloaded from the United States Geological Survey web-service (https://earthexplorer.usgs.gov, last access: 26 February 2019). We used Landsat 8 Collection 1 Level 1 terrain-corrected product (L1T) with radiometric and geometric corrections. In total, 33 images completely covering the Indigirka River basin were processed. We selected late spring images (between 15 May and 18 June) to detect the maximum possible number of aufeis fields, since in June they melt intensively. There was between 1 % and 20 % of cloudiness in some images.

Preprocessing of the images was performed with the use of the Semi-Automatic Classification Plugin module (QGIS 2.18). It includes the calculation of surface reflectance and atmospheric correction using the Dark Object Subtraction (DOS1) image-based algorithm described by Chavez (1996).

The Aufeis detection algorithm was realized in ArcGIS with the help of the ModelBuilder application. Apart from the Landsat images, the digital terrain model GMTED2010 (Danielson and Gesch, 2011) with a spatial resolution of 250 m was used to build a network of thalwegs within the study basin. This is essential for semi-automated separation of the aufeis from snow-covered areas in late spring Landsat images. Indeed, almost all aufeis is located either at streams or thalwegs, or in immediate proximity to them. On the contrary, snow cover in late spring mainly remains on mountain ridges and other elevated locations, i.e. relatively far from thalwegs. Based on the preliminary analysis of aufeis location in relation to the network of thalwegs created, we found that a 1.5 km wide buffer zone around the thalwegs covers almost all aufeis. So, snow- and ice-covered areas, which are located outside this buffer, are excluded from further analysis.

The process of aufeis detection using Landsat images consisted of the following steps:

detection of snow-ice bodies with a NDSI threshold of 0.4;

Morse and Wolfe (2015) suggested a new spectral index, MDII, for automatically distinguishing snow bodies from ice ones. However, here some of the high-elevation aufeis fields were partially covered with snow at the image acquisition time. Instead of automatic processing, the outlining of high elevation aufeis was conducted manually when snow cover was present, with separation of aufeis from adjacent snow-covered areas.

Further, during melt season, the aufeis often divides into several neighbouring areas. When assessing the number of aufeis fields with satellite data, it is therefore necessary to aggregate the areas into one aufeis field if they are located at a distance <150 m (or five Landsat pixels) from each other and within one aufeis glade.

As a result of semi-automated processing of Landsat images, aufeis with a total area of 1253.9 km2 was detected. During the subsequent comparison with the Cadastre data (see Sect. 3.3 for more details), over 100 aufeis fields, with a total area of 33.5 km2, were delineated manually. The gaps were mainly due to the presence of snow cover and/or cloud coverage in the images. To reduce the number of gaps, two to three images from the same area were used. The total number of aufeis fields, identified with the Landsat images in the Indigirka River basin, was 1213, and their total area was 1287.4 km2. Therefore, an omission error of automatic aufeis detection can be estimated as 2.7 % of their total area.

The structure of the GIS dataset of aufeis according to Landsat images is presented in Table 2.

Cross-verification of aufeis data collection using the Cadastre (1958) and satellite imagery was performed in two steps. In the first step, we found the closest aufeis field in the Landsat-derived dataset for each aufeis field from the Cadastre data if the distance between them was less than 5000 m. The determination of search radius was based on a preliminary analysis of the aufeis locations by the Cadastre in relation to the Landsat-based dataset. As a result, the cross index (identifier of the closest aufeis in the Landsat-derived dataset) and minimum distance (m) to the closest aufeis were determined for aufeis from the Cadastre. For the Landsat-based dataset, the cross index is the key field for the reference to the dataset from the Cadastre.

In the second step, a full manual verification was performed to find the mistakenly interrelated aufeis. For example, if the closest aufeis fields from the Cadastre and from the Landsat-based dataset were at a distance of less than 5000 m but in different thalwegs, they were considered to be different (unrelated) aufeis fields.

In total, 260 aufeis fields from the Cadastre were not verified by Landsat images. For them, the NoData value (-9999) was set in the CrossIndex and Distance_m fields of the attributive table (see Table 1 for the structure of the GIS dataset from Cadastre).

The results of the comparison are presented in Table 3. In total, 634 aufeis fields from the Cadastre were found by the Landsat images. They correspond to 611 aufeis fields identified with the images, meaning that in 23 cases, one aufeis field in an image corresponds to two aufeis fields in the Cadastre. But 262 aufeis fields from the Cadastre were not detected by the satellite images. Those are mainly small aufeis fields, which melt by the middle of June. However, among them there are also 43 large aufeis fields over 1 km2 (Fig. 3a). It is likely that since the mid-20th century, when the field observations were conducted and the Cadastre of aufeis was compiled, some aufeis could have disappeared.

A little over half of the aufeis detected by Landsat images is included in the Cadastre: a total of 602 aufeis fields detected (the total area of 250.4 km2) are not included in the Cadastre (Fig. 3b). Such a significant difference can be caused for the following reasons:

In some cases a single aufeis field, according to the Cadastre, corresponds to two or more aufeis fields in a satellite image.

Aufeis area distribution according to the Cadastre and satellite data is shown as Lorenz curves (Fig. 4). In both cases, the shape of the curves signifies a high degree of irregularity which is similar: 10 % of the largest aufeis fields make up 61 % and 57 % of their total area according to the Landsat and the Cadastre data, respectively.

The cross-verification of the Cadastre and satellite data shows that almost 60 % of aufeis fields that are unconfirmed in the Landsat imagery and that are therefore only present in the Cadastre have an individual aufeis area of less than 0.25 km2 (Fig. 5a). The confirmed aufeis accounts for about 20 % of the area stated in the Cadastre. Thus, it was mainly small aufeis fields that were not confirmed in the Landsat images. Conversely, Fig. 5b shows that almost 60 % of the aufeis fields detected in the Landsat images but not listed in the Cadastre have an area of less than 0.25 km2 each.

In general, aufeis distributions by elevation as assessed using the Cadastre and Landsat data are quite similar, although there are some differences that are elevation-specific (Fig. 6). Most aufeis is located in the elevation band of 1000–1200 m. At lower elevations (up to 800 m) the number of aufeis fields according to Landsat data is higher than stated in the Cadastre. At the elevations of 1400–2000 m, more aufeis is identified in the Cadastre data than in the satellite images. This can be explained by the fact that many aufeis fields located at high altitudes often have a small area, so they could have been missed during the analysis of the satellite data. Further, they could have been covered with snow at the image acquisition time, which would increase the possibility of them being missed.

The elevation band of 200–300 m is characterized by the location of large aufeis fields. Though less than 2.5 % and 5.0 % of aufeis fields by the Cadastre and Landsat images are situated here, they represent about 11 % and 13 % of aufeis area from the datasets respectively (Fig. 7).

In the Indigirka River basin, there are several zones with a high density of aufeis: in the southern part (the Suntar and Kuidusun River basins) as well as in the central part (Chersky Range slopes) (Fig. 8). The largest aufeis fields identified by satellite images are located in the Syuryuktyakh River basin on the north-east slopes of the Chersky Range. Meanwhile, aufeis is almost absent in the northernmost (lowland) part of the Indigirka basin.

We analysed the aufeis coverage for six river basins with available streamflow data. The headwater part of the Indigirka River, with the gauge near the Yurty village (area 51 100 km2), is the basin with the largest aufeis coverage (Table 4). Correlation between average elevation of the basins and their aufeis coverage (expressed as a percentage) is statistically significant. Among six basins, the Spearman rank correlation coefficients between the basin average elevation and aufeis percentage are 0.71 and 0.77 by the Cadastre and satellite data, respectively.

The assessment of aufeis area interannual variability was conducted in two areas: for the Bolshaya Momskaya aufeis, which is located in the Moma River channel (area in the Cadastre is 82 km2), and for a group of large aufeis (total area in the Cadastre is 287.8 km2) in the Syuryuktyakh River basin, which is the left-bank tributary of the Indigirka River.

Cloudless images from Landsat-5 (TM), Landsat 7 (ETM+) and Landsat-8 (OLI) were used with the acquisition dates between 1 May and 30 June. In the USGS archives, there are no Landsat-5 images for the study area for the 1984–2007 period. This limits the duration of satellite observations on aufeis to the period since 1999 (when the Landsat-7 satellite was launched). Also, the clouds complicate the acquisition of representative data. The list of the acquisition dates and assessed aufeis area values is presented in Table 5.

Both areas are located at low elevations (Bolshaya Momskaya 430 to 500 m and Syuryuktyakh 200 to 500 m), which contributes to the relatively early and intensive aufeis melt in spring. The aufeis fields reach their maximum area by the beginning of May. Using the available satellite images it is impossible to make a reliable conclusion on aufeis area increase or decline because the acquisition dates vary significantly from year to year. However, it is possible to make some conclusions based on the available data, detailed below.

In 2002–2017 the Bolshaya Momskaya aufeis did not reach the maximum area stated in the Cadastre (82 km2), even though the satellite image was acquired during the first week of May (2005) when aufeis melting had not yet started. Comparing two images, taken in similar conditions (8 May 2005 and 15 May 2013), it was found that aufeis area in 2013 was smaller than in 2005 by 18.1 km2. Accordingly, the Bolshaya Momskaya aufeis may have seen a decreasing trend over time in its maximum coverage.

The area of the largest aufeis field in the Syuryuktyakh River basin in May 2014 was 78.0 km2, which is 8 km2 larger than stated in the Cadastre. One may note also that the maximum aufeis areas in the Syuryuktyakh River basin were detected by the images received at the end of the period (2014–2017), including mid-June (18 June 2015). Therefore, it can be suggested that the aufeis areas within the Syuryuktyakh River basin have not decreased since 2002.