Knowledge about water surface velocities on rivers supports the understanding of a wide range of processes. In cold regions, river-ice freeze-up, and in particular break-up, and the associated transport of and action by ice debris is often the most important hydrological event of the year; this transport produces flood levels typically exceeding those of other periods (Fig. 1) and associated dramatic consequences for river ecology and infrastructure (e.g. Prowse et al., 2007; Kääb and Prowse, 2011; Rokaya et al., 2018a). River discharge measurements are complicated during freeze-up and break-up due to the physical impact of ice on instrumentation, and the determination of water surface speeds from tracking river ice floes can aid with estimating discharge (Beltaos and Kääb, 2014). This possibility is of particular importance for the major Arctic rivers of North America and Siberia, which transport large amounts of freshwater into the Arctic Ocean; however, the discharge of these rivers is least known for the ice break-up period – notably the period during which annual discharge peaks (Zakharova et al., 2019).

In addition to in situ measurements and ground-based remote sensing (e.g. Lin et al., 2019), water surface velocities are mainly retrieved using airborne or space-borne radar interferometry (Romeiser et al., 2007). During periods when rivers carry ice floes, or other visible surface objects, water velocities can be measured using near-simultaneous satellite (or airborne) images, optimally with time separations of the order of minutes (Kääb and Leprince, 2014). Such near-simultaneous imaging of the Earth surface is provided by satellite stereo sensors, where two or more stereo image partners are, by necessity, temporally separated by approximately 1–2 min (Kääb and Leprince, 2014). Ice floes (or other floating objects) are then tracked over this time lag to estimate water surface velocities during the image acquisition period. Satellite stereo imaging that is useful for this purpose stems from either fixed stereo or agile stereo. (In principle, satellite video could also be used to track ice floes but has to our knowledge not been demonstrated for this purpose yet; d'Angelo et al., 2014, 2016.) Fixed stereo is provided by two or more fixed cameras with different along-track viewing angles, e.g. the ASTER or ALOS PRISM sensors. Agile stereo is provided by one single camera that is rotated during overflight to point repeatedly to the same ground target, e.g. the WorldView or Pleiades satellites. Kääb and Prowse (2011) demonstrated the method deriving river-ice and water velocities over reaches of a few tens of kilometres of the Mackenzie and St. Lawrence rivers in Canada, using both types of satellite stereo images. Kääb et al. (2013) used ASTER fixed satellite stereo to measure and analyse river-ice flux and water velocities over a 600 km long reach of the Lena River in Siberia. Finally, Beltaos and Kääb (2014) demonstrated how water surface velocity fields derived in this way can be used to estimate river discharge. While Kääb and Leprince (2014) may have indicated other seasons and satellite constellations to track river ice floes over short time spans, all of the above studies have the following in common: (i) they use images during ice break-up for the most part, (ii) they use dedicated stereo systems, and (iii) they mostly use rare and opportunistic acquisitions. Point (i) limits the application of the method to one short time period of the year, and (ii) and in particular (iii) prevent the method from being applied operationally and systematically over large reaches of many rivers. The PlanetScope cubesat constellation offers the new, currently unexplored possibility of performing systematic worldwide observations of river-ice velocities and the water velocities indicated by them. The primary aim of the present study is to demonstrate and explore these possibilities, and the secondary aim is to evaluate the estimation of water velocities during river freeze-up, instead of during break-up. As the main focus of this study is a methodological one, we do not study the selected hydrological, hydraulic, or geomorphological applications that seem possible in detail.

The PlanetScope optical cubesat constellation scans the Earth surface systematically and daily (Figs. 2 and 3) involving the overlap of consecutive acquisitions with a time lag of around 1.5 min. A time lag of this order is perfectly suited to track floating matter, in particular river ice floes. Thus, PlanetScope offers the possibility of systematic daily measurement of water surface velocities, as long as ice floes are present on the water and sky conditions are clear. In this study, we first introduce the PlanetScope cubesat constellation in more detail. After a description of the methods used to track ice floes over minute-scale time lags, we demonstrate and discuss the typical ice-floe conditions suitable for tracking, and derive velocities over a 60 km long reach of the Amur River, Siberia, and a 200 km long reach of the Yukon River, Alaska. We also discuss the error budget of the measurements in detail. Finally, we draw conclusions regarding the potential for systematically measuring river-ice and water velocities from the PlanetScope constellation and briefly sketch out the possible fields for the application of this method.

The following descriptions of the PlanetScope constellation and data, and the methods used, are an update and specification of the descriptions given by Kääb et al. (2017). The Planet cubesat constellation, referred to as PlanetScope, consists of small 10 cm × 10 cm × 30 cm satellites. Their main components are a telescope and CCD area array sensor. One half of the 6600 pixel ×4400 pixel CCD array acquires red–green–blue (RGB) data and the other half acquires near-infrared (NIR), both in 12 bit radiometric resolution. At the time of writing, the majority of the PlanetScope satellites provides images of about 3.7 m spatial resolution at an altitude of 475 km (delivered as resampled to 3 m; Fig. 1), and an individual scene size of roughly 25–30 km × 8–10 km (Planet Application Program Interface, 2019). While most other optical Earth observation instruments in space acquire in push-broom geometry (i.e. 1-D sensor arrays scanning in orbit direction), the data from the Planet satellites are 2-D frame images. Each complete image is taken at one single point in time, and has one single acquisition position and one single bundle of projection rays. For comparison, push-broom sensors integrate an image over a time interval of a few seconds so that acquisition time, position, and attitude angles vary throughout an image (Nuth and Kääb, 2011; Kääb et al., 2013; Girod et al., 2015).

Currently, the Planet cubesat constellation consists of around 150 cubesats following each other on two near-polar orbits of roughly 8 and 98∘ inclination respectively, and at an altitude of approximately 475 km (Fig. 2), imaging the Earth at local morning from both an ascending and descending orbit. The distance along the orbit between the cubesats is constructed such that the longitudinal progression between them over the rotating Earth leads to a void-less scan of the surface. Thus, the full constellation provides sun-synchronous coverage of the entire Earth (except the polar hole) with daily resolution (Fig. 2 in this paper ;Foster et al., 2015; Kääb et al., 2017). To guarantee this void-less surface imaging at all latitudes as well as when satellite positions and pointing angles are not exactly nominal, the swaths of subsequent cubesats overlap in the across-track direction by some kilometres (Figs. 2, 3). Within these swath-overlaps Earth surface targets are imaged twice (sometimes even more) with a time lag of roughly 1.5 min. This time lag is exploited in the present study and constitutes its core principle. The PlanetScope constellation also involves other time lags; however, these are not considered here (e.g. less than 1 s between RGB and NIR acquisitions; or a few hours, depending on the latitude, between acquisitions from ascending and descending orbits).

During the PlanetScope constellation's technological demonstration phase, the cubesats were mostly launched from the International Space Station into an orbit with a 52∘ inclination and an approximate 375 km height (Fig. 2 in this paper; Kääb et al., 2017). Data from these satellites form the majority of Planet's cubesat data archive holding for 2016 and into early 2017, before acquisitions from the near-polar sun-synchronous orbits took over. The build-up of the PlanetScope constellation and frequent replacement of its cubesats enables, among others, fast technological turnover and improvement of the image sensors. As a result, images from the more recent cubesat generations used in this study typically have better radiometric contrast than images from earlier generations.

Within the swath overlaps and over the corresponding approximate 1.5 min time lag we track river ice floes using standard image matching techniques. For image matching purposes, the geometric characteristics of repeat imagery are of particular interest. PlanetScope images are available at different processing levels, and here we use “analytic” data. Analytic data are radiometrically processed and orthorectified. We do not apply “unrectified” data, another processing level available, which comes with minimal radiometric processing and in the original central projection. The image orientation from on-board measurements is refined by Planet by matching the scenes onto a global reference mosaic (at the time of writing from Landsat, ALOS, and Open Street Map layers) and the images are orthoprojected using a digital elevation model (DEM). As for all orthoprojected satellite data, vertical errors in the orthorectification DEM cause lateral distortions in the resulting PlanetScope orthoimages. The size of these offsets is proportional to the DEM error and the off-nadir viewing angle (Kääb et al., 2016, 2017; Altena and Kääb, 2017). In a worst-case scenario for PlanetScope data (Kääb et al., 2017), a DEM error of 10 m results in orthorectification offsets of around 30 cm in the scene centre and 65 cm at the outer scene margin. For repeat river observations, the differential effect of these offsets can be reduced by co-registering the near-simultaneous images using stable points along shorelines. Over the limited width of rivers (a few kilometres at most), water surface topography is approximately planar. This means that a first-order polynomial co-registration model is sufficient to bring repeat unrectified frame images into overlap. This co-registration procedure will also greatly reduce offsets between the orthorectified analytic images used here, as the same DEM is used for both near-simultaneous images (Kääb et al., 2017). Errors in the DEMs used for orthorectifying PlanetScope images are a composite of (i) DEM elevation errors with respect to the real topography at the time of DEM acquisition, and of (ii) real-world elevation changes between the elevations at DEM acquisition and the elevations at satellite image acquisition. Orthorectification DEMs are, by necessity, outdated (although generally with limited consequences) unless acquired simultaneously with image acquisition. For river surfaces, the latter elevation deviations will primarily stem from water level variations between the DEM acquisition and the image acquisition dates. However, the small field of view of PlanetScope cubesats and the resulting low sensitivity to orthorectification DEM errors, the frame geometry of the PlanetScope cameras, and the accessibility of unrectified images, if needed, all contribute to minimize topographic distortions.

Bright ice floes on a dark water surface constitute features of strong visual contrast and tracking them over short time intervals is a particularly easy task for image matching algorithms. Thus, for matching the repeat PlanetScope data, we use a standard method – normalized cross-correlation (NCC) – solving the cross-correlation in the spatial domain and reaching sub-pixel accuracy by interpolation of the image (Kääb and Vollmer, 2000; Debella-Gilo and Kääb, 2011b; Kääb, 2014). NCC solves for translations between corresponding image elements. We apply the Correlation Image Analysis software (Kääb, 2014), but established scripts or routines for normalized cross-correlation between images exist for many programming languages. As the tracking of ice floes over short time intervals represents little challenge for image matching, we expect that other image matching methods (Heid and Kääb, 2012; Lin et al., 2019) would not provide a substantial advantage. However, over longer time intervals or strong horizontal water turbulence conditions, such as backwaters, ice-floe rotation over time would become significant; therefore, in these cases, image matching methods that are able to model feature rotation in addition to translation could be advantageous (Debella-Gilo and Kääb, 2012). The matching window sizes used in this study for the PlanetScope data are 30 pixels × 30 pixels (90 m × 90 m) as was found to be roughly optimal from a few tests. However, tests with different window sizes are not the focus of this study (Debella-Gilo and Kääb, 2011a). Measurements with a correlation coefficient smaller than 0.7 are removed and no other post-processing is applied (Kääb et al., 2017).

For comparing and supplementing our results based on Planet cubesats, we also use data from other satellites. A Landsat 8 scene from 16 September 2013 (i.e. ice-free conditions) is employed to automatically delineate the river water surface over the Yukon River study reach used in this work. Indexes used for the purpose of mapping water areas from multispectral satellite data are typically based on the reflectance contrast of water between blue (high reflectance) and near-infrared wavelengths (low reflectance) (McFeeters, 1996; Pekel et al., 2016). However, for our study site and conditions, we find that the contrast between the blue and thermal infrared Landsat bands is larger than the blue vs. infrared contrast due to a high suspended sediment concentration that increases the near-infrared reflectance and, thus, reduces the contrast to reflectance at blue wavelengths. To increase index sensitivity compared with the commonly used normalized difference indexes (McFeeters, 1996), we apply a band ratio. Thus, river outlines were obtained from a raster-to-vector conversion of a noise-filtered (3×3 median filter) and thresholded band ratio image (Paul et al., 2002) between the blue and thermal infrared bands of Landsat 8. The Landsat 8 blue band has 30 m spatial resolution, and the thermal infrared bands are also provided at a 30 m resolution, although they were originally taken at 60 m resolution.

For one of our Planet cubesat acquisition pairs over the Yukon River, a Sentinel-2 scene exists that was taken with a 1 h time difference. Sentinel-2 multispectral data have a spatial resolution of up to 10 m (Drusch et al., 2012; Kääb et al., 2016). We visually identified the position of a number of large ice floes corresponding between the Planet and Sentinel-2 images and measured the associated displacement along the river to estimate average velocities over the 1 h time period.

In order to compare the velocity retrieval from Planet cubesat data to a method used earlier for the same purpose we also measure short-term ice-floe displacements over the Yukon River reach from an Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) stereo strip. The ASTER fixed satellite stereo, taken at a 15 m spatial resolution and in near-infrared, implies a time lag of around 55 s between the two images of a stereo pair that can be exploited to track ice floes in a very similar fashion to the Planet cubesat images. The exact procedures, performance, and accuracies are presented in Kääb et al. (2013). As a speciality, satellite vibrations (so-called jitter) were modelled and corrected for when using the ASTER data. The results presented here for the Yukon River are based on a specially tasked ASTER acquisition, and have not been published before.

The river flow results of this study are presented as simple maps of measured velocity vectors or magnitudes, or as longitudinal profiles of water flow speed and derived parameters. For the latter we have to average the velocity vectors along the river reach. For that purpose, we move a running window, which is 4 km long in the reach direction and has infinite width, in 100 m steps along the mean direction of a study reach. The window length of 4 km and the step size of 100 m are experimentally chosen for our study sites to smooth the measurements substantially but at the same time leave enough detail.

At each window position, the number of measurement grid points within the river mask from Landsat 8 data as well as the average (or median) speeds and directions for the velocity measurements within the correlation threshold are computed. Dividing the number of grid elements within the river mask by the window length then gives an approximate river width for each step. This river width is then corrected for the deviation between the mean flow direction per window step against the overall mean direction of the river reach studied, essentially rotating the window at each step to align with the actual flow direction. (Note that other procedures exist that are more specialized for estimating river width when the flow vectors are not available; Allen and Pavelsky, 2018.) The surface area flux is then the multiplication of the average river speed and (corrected) width for each window step.

In this study, we exploit the fact that the cross-track overlaps of the swaths of subsequent PlanetScope cubesats (Figs. 2 and 3) produce near-simultaneous optical acquisitions, separated by approximately 90 s. Over this time lag we track river ice floes and use them as indicators for water surface velocities. Planet cubesats scan the entire land surface of the Earth at daily repeat and with an approximate 3 m spatial image resolution. Our study shows that these data substantially extend the possibilities to measure river-ice and water surface flow from near-simultaneous optical satellite data. Over many rivers that carry river ice, ice floes can be tracked during freeze-up and/or break-up with accuracies of the order of ±0.01 m s-1. Freeze-up conditions appear to be particularly well suited for this work due to the longer time periods over which ice floes are present, and the more favourable types and densities of ice floes.

We find three main obstacles when applying the method. By constellation design, the PlanetScope cross-track overlaps (never intended for measuring minute-scale changes and motions!) do not cover the entire Earth surface but only parts of it, depending on latitude, for instance two-thirds of a cubesat swath at 65∘ N (Fig. 3). Second, cloud cover seems rather typical for the river freeze-up and break-up seasons, and considerably complicates the acquisition of suitable Planet cubesat data – as for any optical satellite instrument. Third, freeze-up for some of the northernmost rivers or river reaches seems to occur during sun angles that are too low to acquire suitable images. As a very rough guess from our Planet cubesat archive searches, we estimate that there is a 50 % chance of getting a least one cubesat image per year with drifting ice visible for a given river location. The chances that the river location is then included in the swath overlap from a subsequent cubesat is lower, and the chances are considerably lower again when considering river locations that are covered several times (per year or in total) by overlaps that enable tracking. However, despite these limitations, the tracking of river ice in near-simultaneous Planet cubesat data substantially increases the possibilities for deriving surface velocities on cold-region rivers compared with the very few occasional optical stereo acquisitions suitable for the same purpose.

The strong visual contrast provided by the bright ice floes on the dark water surface, in combination with the short time lag of around 1 min exploited here, lead to few other motion components apart from translation and represent quite optimal conditions for image matching. Therefore, as our study is focused on evaluating the potential of the Planet cubesat constellation, not on the image matching algorithm, we used standard normalized cross-correlation (NCC) as the tracking method. Future work could test if other tracking methods have advantages over NCC for tracking ice floes in near-simultaneous satellite images. In particular for sea-ice tracking, other matching procedures are used that are optimized to work on sequences of low-resolution satellite data with time lags of hours to days (e.g. Lavergne et al., 2010; Petrou and Tian, 2017). An overview and assessment of state-of-the-art image-based tracking approaches for water flow measurements, in which some are certainly relevant for near-simultaneous Planet cubesat data, is given in Lin et al. (2019).

The parameters provisionally chosen for the moving windows to compute longitudinal flow averages (4 km length, 100 m step width) could easily be adjusted. Our visualizations turn out to be little sensitive to the exact choice of window parameter values. For the long river reaches studied here, the mean river direction defining the initial window orientations is almost identical to the orbit azimuth. Thus, the image matches on the floodplain outside the rivers can easily be transformed into their satellite along-track and cross-track components, which is a preferred coordinate system for analysing the geometric performance and errors in satellite data (Kääb et al., 2013). In the present study we do not find geometric errors of concern, such as satellite jitter, which Kääb et al. (2013) found and corrected in a similar study based on another satellite data type.

As we only use our longitudinal averaging procedure for visualization purposes, it is not optimized for specific applications such as estimating river width, discharge, or parameters of river morphology and flow. In particular, larger voids in the measured velocity field, due to low correlation coefficients, will bias the flow averages per window step. This effect seems strongly reduced for freeze-up conditions as the coverage by ice floes during these conditions typically appears to be much more complete compared with break-up conditions (see Sect. 4.1). River areas without ice floes only lead to voids in the measurements if they are larger than the matching window size (here 30 pixels ×30 pixels; 90 m × 90 m) in at least one dimension, as the matching algorithm used (NCC) is not sensitive to where the matched features are located in the window. A first measure to indicate problems from voids in the velocity field in the profiles is to plot the percentage of void pixels per window position (Fig. 10c). Smaller voids can be filled, whereby the measured velocities enable the application of a directional interpolator, or the matching window sizes can be automatically adapted to the distribution of ice floes – small windows for dense ice floes and larger ones for sparse ice floes (Debella-Gilo and Kääb, 2011a). The effect of voids on derived parameters can be tested by simulating voids for a rather complete data set (e.g. the Yukon River 4 November 2018) from actual voids in another data set (e.g. the Yukon River 16 May 2017) (McNabb et al., 2019).

Another effect to be taken into account is the influence of river branching on the averages. Again, treatment of this effect depends much on application and parameters of interest. For instance, the mean flow speed and surface area flux that we compute are not affected, whereas making connections between our surface flow measurements and river discharge would require taking branching into account. An initial simple procedure for that purpose would be to intersect the moving window at each step with the river outlines and to compute the flow averages for each intersection area separately.

Although not exploited further in this study, we would like to note the existence of a Sentinel-2 scene of 4 November 2018, taken about 1 h after the Planet scenes over Yukon River. Due to this large time lag between the Planet and Sentinel-2 scenes and the related large displacements and deformations/rotations of river-ice features, traditional image matching methods that solve only for translations are complicated, but manual tracking of distinct floes is still clearly possible. Tests show good agreement between the speeds derived over 1 h and those over 171 s. Thus, the fact that most Planet cubesats, Sentinel-2A and 2B, and Landsat 7 and 8 are on similar orbits can create additional opportunities for tracking river-ice movement, for investigating short-term changes in river-ice cover and speed, and for additional or combined multispectral mapping and analysis in combination with the Planet cubesats.

As demonstrated here for a 200 km long reach of the Yukon River, remotely-sensed water velocities over long reaches might offer improved insights into river morphology. For instance, we find a variation in water speeds of approximately 20–21 km wavelength for the Yukon River (and the Lena River; Kääb et al., 2013) that could be compared to according wavelengths found from laboratory experiments and models on bar formation (Lanzoni, 2000a, b).

A major purpose of satellite-based river observations is to estimate discharge in order to spatially or temporally complement the sparse in situ measurements available from gauging stations (Beltaos and Kääb, 2014; Bjerklie et al., 2018; Zakharova et al., 2019; and many others, see references in the cited ones). River velocities from the approach demonstrated here can offer an additional type of input measurement (or a possibility for independent comparison) when linking satellite-based measurements of river height and slope from altimetry data, and measurement of river surface from optical (Allen and Pavelsky, 2018) or radar images, to standard discharge equations (Bjerklie et al., 2018; Zakharova et al., 2019). Such satellite data are available over large regions (Allen and Pavelsky, 2018) and consequently fit well to the river velocities as derived by our approach. Satellite-altimetric river heights will even improve in the (near) future due to the new Sentinel-3 and high-resolution ICESat-2 missions (Brown, 2019), and the upcoming SWOT mission (Durand et al., 2010). Moreover, Landsat 8 and Sentinel-2 combined offer sub-weekly repeat to measure parameters such as river width.

In summary, the water mapping opportunities from the daily repeat Planet data (Cooley et al., 2017) and opportunities to measure ice velocities from them, as demonstrated here, could aid in detecting ice jams and related flooding (Fig. 1), as well as providing a better understanding of the mechanisms involved in ice jam formation. The damages from ice jam floods cause annual economic losses of the order of several hundred million EUR per year in North America and Siberia (Prowse et al., 2007; Rokaya et al., 2018a, b). Finally, while substantially fewer in number, we speculate that near-simultaneous overpasses of tropical and temperate rivers could similarly be exploited, tracking sediment or floating matter in place of ice (Kääb and Leprince, 2014).