Monitoring Surface Water Dynamics in the Prairie Pothole Region Using Dual-Polarised Sentinel-1 SAR Time Series

The North American Prairie Pothole Region (PPR) represents a large system of wetlands with great importance for biodiversity, water storage and flood management. Knowledge of seasonal and inter-annual surface water dynamics in the PPR is important for understanding the functionality of these wetland ecosystems and the changing degree of hydrologic connectivity between them. Optical sensors have been widely used to calibrate and validate hydrological models of wetland dynamics. Yet, they are often limited by their temporal resolution and cloud cover, especially in the case of flood events. 5 Synthetic aperture radar (SAR) sensors, such as the ones on board the Copernicus Sentinel-1 mission, can potentially overcome such limitations. However, water extent retrieval from SAR data is often affected by environmental factors, such as wind on water surfaces. Hence, for reliably monitoring water extent over longer time periods robust retrieval methods are required. The aim of this study was to develop a robust approach for classifying open water extent dynamics in the PPR and to analyse the obtained time series covering the entire available Sentinel-1 observation period from 2015 to 2020 in the light of ancillary 10 data. Open water in prairie potholes was classified by fusing dual-polarised Sentinel-1 data and high-resolution topographical information using a Bayesian framework. The approach was tested for a study area in North Dakota. The resulting surface water maps were validated using high-resolution airborne optical imagery. For the observation period, the total water area, the number of water bodies and the median area per water body were computed. The validation of the retrieved water maps yielded producer’s accuracies between 84% and 95% for calm days and between 74% and 88% on windy days. User’s accuracies were 15 above 98% in all cases, indicating a very low occurrence of false positives due to the constraints introduced by topographical information. Surface water dynamics showed strong intra-annual dynamics especially in the case of small water bodies (< 1 ha). Water area and number of small water bodies decreased from spring throughout summer when evaporation rates in the PPR are typically high. Larger water bodies showed a more stable behaviour during most years. During the extremely wet period 20 between the autumn of 2019 and mid-2020, however, the dynamics of both small and large water bodies changed markedly. While a larger number of small water bodies was encountered, which remained stable throughout the wet period, also the area of larger water bodies increased, partly due to merging of smaller adjacent water bodies. However, the area covered by small water bodies was more stable than the area covered by large water bodies. This suggests that large potholes released water faster via the drainage network, while small potholes released water mainly to the atmosphere via evaporation. The results 25 1 https://doi.org/10.5194/hess-2021-330 Preprint. Discussion started: 8 July 2021 c © Author(s) 2021. CC BY 4.0 License.

variations in total water surface area of ca. 50% within a catchment. Although they analysed only a relatively small number of images, their results highlight the dynamic nature of surface water extent in the PPR. The use of Landsat imagery for monitoring surface water extent in the PPR is limited by its temporal resolution, which is additionally degraded by cloud cover, and its relatively coarse spatial resolution of 30 m (Rover and Mushet, 2015). In this context, Vanderhoof and Lane (2019) assessed the Landsat-based Global Surface Water (GSW) dataset (Pekel et al., 2016) for mapping the distribution of wetland 70 sizes in the PPR and characterising their interactions. The authors concluded that analysis of the Landsat-based product alone would suggest that the landscape in the PPR is dominated by wetlands of sizes 0.2 ha to 8.0 ha. Using a dataset based on HR imagery that was pan-sharpened to 0.5 m spatial resolution, however, resulted in smaller wetlands dominating the distribution of wetland sizes. Based on this product they also detected narrow interactions between wetlands in the form of channels and locations where adjacent wetlands merged during wet periods (Vanderhoof and Lane, 2019). 75 However, HR satellite or airborne imagery are typically not available at the very short time intervals necessary to resolve intra-annual variations in water body sizes. Moreover, the flood mitigation potential of the wetlands in the PPR is a function of the water volume existing at the beginning of a flood event (Huang et al., 2011b). While cloud cover additionally limits the temporal resolution of optical data, SAR sensors could provide a more continuous monitoring of surface water extent. SAR data have been successfully used for wetlands mapping (e.g. Reschke et al., 2012;Schlaffer et al., 2016;White 80 et al., 2015). In addition to the ability of microwave radiation to penetrate clouds, SAR sensors are not only highly sensitive to the occurrence of open water surfaces (Richards, 2009) but also to flooding beneath vegetation (Tsyganskaya et al., 2018).
Recent missions, such as Sentinel-1, also offer data at spatial resolutions comparable to or higher than Landsat and temporal sampling intervals in the order of several days. Open water surfaces act as specular reflectors and, as a result, appear dark in the resulting imagery (Giustarini et al., 2016). Factors, such as wind  or vegetation protruding through 85 the water surface, however, lead to an increase in the energy amount scattered back to the sensor and, hence, increase false negative rates in the classification. Dry, sandy areas , wet snow  or tarmac can be confused with open water during SAR image classification. In recent years, several studies have aimed at mapping and monitoring surface water dynamics in the PPR from SAR data. In particular, the analysis of multi-polarised data has received attention, as co and cross-polarised data respond differently to scattering mechanisms like surface and volume scattering.  Montgomery et al. (2018) analysed time series acquired by Radarsat-2 for classifying prairie wetlands according to their hydroperiod, i.e., the number of days per year that a wetland is covered by water.
Strong fluctuations in water extent in accordance with precipitation inputs were reported especially for the more hydrologically disconnected study sites. The rather long revisit cycle of Radarsat-2 of 24 days was mentioned as a major limiting factor for 95 characterising surface water dynamics. In a study by Huang et al. (2018), data acquired by Sentinel-1, which has a temporal resolution of 12 days over most of the PPR, have been used to classify open water in the PPR of North Dakota. A set of polarised indices was created from the dual-polarised imagery and used together with backscatter coefficients as features in a random forest classifier trained on reference surface water products, such as the aforementioned GSW dataset. The authors noted that limitations of their approach relate to omission of water-covered areas due to inundated vegetation and the spatial 100 resolution of the sensor as well as commission errors due to smooth surfaces resembling open water in SAR imagery (Huang et al., 2018).
Such limitations, along with the short observation periods available yet for most SAR missions, in comparison to, e.g., Landsat, pose the greatest hindrances for a wider uptake of SAR data for a long-term monitoring of wetland dynamics. In contrast to most SAR missions up to date, the two-satellite Sentinel-1 constellation focuses on providing consistent data over 105 longer time periods (Torres et al., 2012), which is ensured by the launch of Sentinel-1 C/D planned from 2022 onwards (ESA CEOS EO Handbook, 2021). Therefore, there is a need for novel algorithms making use of the capabilities of Sentinel-1, such as dual polarisations and its high spatial temporal resolutions, while addressing the abovementioned limitations, such as misclassification due to water surfaces roughened by wind or land surfaces resembling open water. In the field of flood mapping, the inclusion of ancillary topographic information has been used to minimise the influence of these factors. Such ancillary 110 information can be integrated into the classification workflow either by masking during post-processing (e.g. Westerhoff et al., 2013;Schlaffer et al., 2015) or by probabilistic data fusion of SAR and topographic data (e.g. D'Addabbo et al., 2016).
Here, a retrieval algorithm for open water bodies in the PPR based on dual-polarisation Sentinel-1 data is proposed. We use a probabilistic approach combining SAR backscatter and information derived from a LiDAR-based digital elevation model in order to minimise the occurrence of false positives caused by bare areas, tarmac or wet snow, which has been identified as a 115 limiting factor in the aforementioned study (Huang et al., 2018). The method is applied to the full time series of Sentinel-1 imagery available for the snow-free months between 2015 and 2020. We hypothesise that a time series of water extent maps at sub-monthly intervals will facilitate the analysis of both intra-annual and inter-annual variations in the distribution of water body sizes. As mentioned earlier, modelling studies, such as Liu and Schwartz (2011), have demonstrated the sensitivity of small water bodies to intra-annual variations, whereas larger water bodies were only affected by deluge or drought periods at 120 larger time scales. Our focus is both on inter-annual surface water dynamics as well as on the impacts of short, intense rainfall or snowmelt events on the number of water bodies and the area covered by them. To our knowledge, this is the first time that inter-annual wetland dynamics in the PPR are studied using the entire length of the Sentinel-1 time series. Furthermore, this study represents the first analysis of wetland dynamics during the flood events of 2019, which caused large areas in the Midwest to be inundated (Yin et al., 2020). 2 Material and methods

Study area
The study area comprises the Pipestem Creek catchment in North Dakota (ND), USA (Fig. 1). The catchment has an area of ca. 2,770 km 2 and forms part of the PPR, which covers a large part of the Great Plains in the Northern USA and Southern Canada. Climate is continental with cold, dry winters (Wu and Lane, 2017) and a long-term average annual precipitation 130 of approximately 440 mm (Huang et al., 2011a), most of which occurs during the summer months (Fig. 2a). Inter-annual precipitation variability is high: during the study period from 2015 to 2020, annual precipitation measured at Jamestown blizzards in mid-October led to the declaration of a state-wide flood emergency (Umphlett, 2019). Between 2015 and 2018, the Palmer Drought Severity Index (PDSI), which was derived from GRIDMET data (Abatzoglou, 2013) and averaged over the study area, oscillated between -2 and +2 indicating normal to slightly dry and slightly wet conditions, respectively. In the last two years of the observation period, however, PDSI increased until reaching values > 5 in late autumn of 2019, indicating extremely wet conditions which persisted until summer of 2020. The occurrence of discharge peaks in 2017, 2019 and 2020 145 coincided with periods of positive PDSI (Fig. 2b). operating at a wavelength of ca. 5.6 cm. The ground-range detected (GRD) product has a spatial resolution of ca. 20 m (Torres et al., 2012). Data for the study area is available from March 2015 onwards. Since wet snow and ice cover on lakes can alter backscatter behaviour, the study was limited to the months May to October, which we assumed to be mostly snow-free. A total number of 74 scenes acquired between May 2015 and October 2020 was downloaded from the Copernicus Open Access Hub.

Data
From 2016, data were available at an interval of 12 days with a few exceptions (Fig. 2b). All the scenes used in this study were acquired from the same relative orbit (number 34) and available in both vertical send -vertical receive (VV) and vertical send -horizontal receive (VH) polarisations. The downloaded GRD scenes were filtered using a Gamma-MAP speckle filter (Lopes et al., 1993) with a window size of 3 × 3 pixels and radiometrically calibrated to obtain the backscattering coefficient σ 0 . Terrain correction was carried out using the Range-Doppler approach and the digital elevation model from the Shuttle Radar Topography Mission (Farr et al., 2007). The scenes were resampled to a common grid with a pixel spacing of 10 m 160 in the Universal Transverse Mercator (UTM Zone 14 North) projection. The SAR data were pre-processed using the Sentinel Application Platform (SNAP version 7), provided by the European Space Agency (ESA). Sentinel-1 data, the DTM and the water bodies were aggregated to the 10 m grid mentioned above. The water body polygons were aggregated by retaining pixels as water pixels if they were covered by a water polygon by more than 50%. Then, the Height Above Nearest Drainage (HAND), z HAND , was computed from the DTM. HAND consists of the relative elevation of a DTM pixel above the nearest pixel pertaining to the drainage network (Rennó et al., 2008) and has been used in flood remote 170 sensing for masking areas that are not prone to floods (Westerhoff et al., 2013;Schlaffer et al., 2015;Twele et al., 2016). In order to take the special environmental conditions encountered in the PPR into account, we used both the identified potholes as well as the drainage network obtained from the DTM after filling the pothole sinks as drainage pixels. The drainage network was extracted using the r.watershed tool in GRASS GIS (GRASS Development Team, 2017).

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As a source of information on land use/land cover, the US Department of Agriculture (USDA) NASS CDL for North Dakota was downloaded (henceforth referred to as CDL). The CDL for 2015 is based on data from Landsat 8, DEIMOS-1 and UK2 that were acquired during that year. The CDL has a spatial resolution of 30 m and is provided under a Creative Commons licence (US Department of Agriculture, 2016). The CDL was resampled to the same grid as the Sentinel-1 data using nearest neighbour resampling.

Validation data
The surface water extents were validated for three different dates in 2016, 2017 and 2019 using aerial imagery from the National Agriculture Imagery Program (NAIP). These years were selected to have a representation of dry and wet years. False-colour composites of the images are shown in Appendix A (Fig. A1). NAIP imagery has a spatial resolution of 1 m and comprises four bands in the visible and near-infrared (NIR) portions of the electromagnetic spectrum. For validating the water extents derived from Sentinel-1, we sampled points across the extent of the NAIP images and classified them manually into water and non-water classes. Although wetlands occur frequently in the study area, a random sample would likely underrepresent surface water. To account for this class imbalance, a stratified random sampling approach was applied. With the help of the DTM-derived potholes, 200 pixels per class were randomly sampled from potholes and upland areas throughout each of the three NAIP footprints, resulting in 400 reference points for each reference image (shown in Fig. A1). The NIR band was 190 especially useful in identifying areas where vegetation was emerging from water surfaces. We assumed that such conditions would fundamentally impact radar backscatter from these areas. Whenever vegetation was protruding through the water surface around a sampling point, the respective point was classified as non-water as the proposed approach applies only to open water surfaces.

Water extent delineation 195
Calm, open water surfaces typically cause specular reflection of incident microwave radiation. In SAR scenes with an approximately balanced mix of open water and land classes this phenomenon leads to bimodal grey-value histograms. However, these classes rarely occur at similar proportions within a scene and, as a result, bimodality of the histogram is not commonly observed. Efforts have been made to balance water and non-water classes by subsampling areas from SAR images where water and land pixels are equally represented (Martinis et al., 2009;Schlaffer et al., 2016;Chini et al., 2017). An example of such an 200 effort are split-based approaches (Martinis et al., 2009;Chini et al., 2017), where image subsets showing a bimodal grey-value distribution are automatically selected from a SAR scene based on a set of pre-defined criteria. This approach is especially useful if the approximate locations of the water bodies or flooded areas are not known a priori.
The locations of prairie potholes are governed by the landscape features of the PPR and have been reported to be relatively stable over longer time periods (Bolanos et al., 2016). Therefore, we chose to treat the potholes as the baseline of the study.

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The pothole locations were determined based on the water bodies product contained in the 2011 LiDAR data. We assumed that this dataset contained more water bodies than what could be classified from satellite data due to the higher spatial resolution and the fact that the data had been acquired during extremely wet conditions (Wu and Lane, 2017). Therefore, it was regarded as a suitable baseline dataset for monitoring surface water dynamics in as many potholes as possible.
An overview of the water classification workflow is shown in Fig. 3. In contrast to other studies on remote sensing-based 210 water retrieval, which treat a scene uniformly, i.e., by estimating the statistical distributions of water and non-water classes along with classification thresholds across the entire image, the class-specific backscatter distributions were estimated locally, i.e., for each of the known pothole locations. The reasoning behind this approach is that backscatter values may vary considerably over large regions over both water and land surfaces due to wind or semi-submerged vegetation, on the one hand, and variations in soil moisture, wet snow cover or vegetation structure and moisture, on the other.

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In order to estimate the backscatter distribution to be expected for open water an independent reference layer is required (Schlaffer et al., 2017), e.g., derived from optical data. Here, we chose the CDL for 2015 as reference layer. Backscatter values for open water bodies delineated in the CDL were extracted for the months May to October, henceforth denoted σ 0 w,p for each of the two polarisations p ∈ {V V, V H}. Pixels along the borders of water areas in the CDL were excluded to minimise border Pothole-specific threshold retrieval Water probability estimation VV/VH combination

HAND
Open water extent effects. The mean of σ 0 w,p isσ 0 w,p . For each of the previously delineated potholes, we checked if at least 10 pixels had σ 0 p values 220 lower thanσ 0 w,p . If this condition was not fulfilled it was assumed that no open water was present in the respective pothole. Otherwise, we proceeded to check the bimodality of the σ 0 distribution within the pothole. We followed the approach by Chini et al. (2017) for this. As a first guess, the histogram was automatically split using Otsu's approach (Otsu, 1979). The bimodality was then assessed using Ashman's D (Ashman et al., 1994), which is defined as

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where µ 1 , µ 2 are the means of the two histogram portions and σ 2 1 , σ 2 2 their variances. A value of D > 3 was assumed to be an indication of a bimodal histogram. If this condition was not fulfilled, the region around the pothole was extended to include neighbouring pixels in order to include a higher number of non-water pixels and checked again for bimodality. For each pothole, the sampling region around the pothole was further extended by including neighbouring pixels up to a maximum number of 10 iterations. If a bimodal histogram was encountered before reaching this number of iterations the final Otsu threshold for the 230 respective pothole was saved. In the following, the threshold value derived for σ 0 p is denoted τ p . The parameters of the water and land distributions for each pothole were estimated as and respectively, where σ 0 w,p are all σ 0 p ≤ τ p , σ 0 l,p are all σ 0 p > τ p . N w,p and N l,p are the number of σ 0 w,p and σ 0 l,p values, respectively. The probability of a pixel belonging to the water distribution given a certain value of σ 0 p was computed as p(σ 0 p |W ) and p(σ 0 p |L) are the probability density functions (PDFs) p(W ) in Eq. 4 denotes the prior probability of a pixel being land or water. If no information is available, p(W ) = 0.5 can be used giving equal prior probability to the land and water distributions (Giustarini et al., 2016). However, as the location of the open water surfaces was known to be mainly confined by the topography of the potholes, which changes little over time 245 (Bolanos et al., 2016), we chose to incorporate this knowledge. Bayes' theorem has been used as an efficient framework to fuse information from different sources, e.g., for obtaining SAR-based flood delineation maps (e.g. Frey et al., 2012;D'Addabbo et al., 2016;Li et al., 2019). Here, p(W ) was modelled using logistic regression with z HAND as predictor: where b 0 , b 1 are regression parameters which were estimated using 20 samples, each consisting of 5000 land and 5000 water 250 pixels identified from the CDL. An additional sample of 4985 land and 4668 water pixels not containing any of the pixels used for training was set aside for testing. When sampling the training and testing data, pixels in a buffer region along the border between land and water were excluded to obtain a pure sample of each class. Pixels that are identified as land in the CDL may still be prone to the occurrence of wetlands. For example, they may be located in depressions that have been drained or may have been not covered by water when the imagery used for the CDL has been acquired. In order to account for potential 255 sampling biases Eq. (7) was fitted to each of the 20 training samples separately and the average of the estimated parameters b 0,i , b 1,i , 0 < i ≤ 20 was used to estimate p(W ).
The estimated p(W |σ 0 p ) values were classified into water and non-water classes taking into account the spatial relationship between areas with high p(W |σ 0 p ), which changes over time, and the static pothole extents derived from the DTM. This approach served to minimise the occurrence of isolated clusters of water pixels far from potholes which may occur due to 260 speckle or dry land surfaces appearing as dark areas in the SAR image. This condition was implemented using a region growing approach, using the DTM-based pothole area as seed. The region growing was limited to a maximum of 10 iterations to prevent "spilling" of positive pixels into large portions of the scene. The idea is illustrated in Fig. 4. Two potholes are separated in the

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In addition, the final water area should take into account the information from both VV and VH polarisations. The respective water probabilities, p(W |σ 0 V V )and p(W |σ 0 V H ), were combined based on their values. We opted for a rather conservative approach for combining the two datasets to minimise the occurrence of false positives. In summary, we applied the following conditions for classifying dynamic open water from water probability: where ∨ is a logical OR and ∧ is a For validation, producer's and user's accuracies were computed for the water class using the combined product against the reference data described in Section 2.2.4. Each of the three reference datasets was compared to the Sentinel-1-derived water 275 bodies closest in time to the date of the respective NAIP acquisition. In order to estimate the impact of using VV or VH polarisation, accuracies were also computed for each polarisation separately using a threshold of p(W |σ 0 p ) > 0.5.

Analysis of surface water dynamics
Prairie wetlands can merge over time with neighbouring wetlands or split into separate water bodies. Hence, monitoring the area of individual water bodies is challenging. To track surface water dynamics across the study area, we computed the total 280 water area, areas covered by individual water bodies and the number of discrete water bodies for each of the observation dates.
We were furthermore interested in the inter and intra-annual dynamics of wetlands of different sizes. For this purpose, water bodies were divided in four different size bins and the contribution of each bin to the total water extent was tracked along the observation period. The metrics were computed using the R package landscapemetrics (Hesselbarth et al., 2019). In accordance with the spatial resolution of the Sentinel-1 sensor, before deriving the metrics we applied a minimum mapping unit of 0.04 ha, equal to the area of four pixels, to remove small clusters of water pixels from the result. Such small clusters are often the result of noise.
3 Results and Discussion

Open water classification
The obtained p(W ) values are shown in Fig. 5. It can be seen that high p(W ) predominantly occur in potholes and along 290 rivers and streams, whereas most of the upland areas are assigned values close to zero. We validated the estimated p(W ) using an independent test sample with labels assigned from the LiDAR-based water map. Calculating an overall accuracy for the test sample would not take into account the unknown occurrence of potential wetlands in the CDL land class. Therefore, we computed the sensitivity of our approach as s = T P/(T P +F N ), where T P denotes true positives and F N false negative test values, after classifying the predicted p(W ) into binary values using a threshold of p(W ) = 0.5. The sensitivity quantifies the 295 capability of the classifier to correctly identify existing water bodies and was calculated as 0.985.
Open water maps were produced for the months May to October from 2015 to 2020 (Fig. 6c,d). In Fig. 6c), most of the water bodies were identified in both VV and VH polarisations. However, the subset also shows several wetlands only detected in VV, visible as light-blue areas in the RGB composite. VH backscatter over land areas is mainly related to volume scattering. In areas with sparse vegetation density, this may lead to a low contrast between water and non-water in the VH band of the image. In 300 such cases, no suitable threshold could be determined. The subset shown in Fig. 6d) contains several wetlands only classified in the VH data (pink colour). Comparison with the corresponding backscatter image (Fig. 6b) reveals that VV backscatter seems to be increased over these water bodies as indicated by the reddish colours. This, in turn, again leads to lower contrast between water and surrounding non-water classes. In some cases, water bodies could not be detected in either polarisation, e.g., the large water body in the centre of Fig. 6d,f). This is often the case when, on the one hand, ice cover is present or the 305 water surface is roughened by wind and, on the other hand, when the surrounding land surface appears dark, as in the centre of Figure 6b). Such darker areas are often related to grassland and sparsely vegetated areas, which can be distinguished in the false-colour images in Fig. 6e,f) by their paler appearance from vegetated fields visible in bright red colour. Agricultural fields tend to appear brighter in the SAR imagery (Fig. 6a,b) owing to high soil moisture and vegetation influencing both VV and VH-polarised backscatter.

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Comparison with independent NAIP data, which was carried out for three dates, resulted in high producer's accuracies (> 84%) for two dates and very high user's accuracies for all three dates (> 98%), suggesting some underestimation of the water extent (Table 1). The high user's accuracies are the result of a very low number of false positives. The underestimation of the water extent is to be expected due to the difference in spatial resolution between Sentinel-1 (ca. 20 m) and the reference data (1 m). In such cases, validation points located close to the edges of objects may coincide with mixed pixels in the lower 315 resolution imagery. In the case of the validation carried out for July 2016, producer's accuracies were lower, especially for VV, possibly due to wind roughening the water surface. Such effects are visible in the NAIP imagery and may have occurred also on the following day when the Sentinel-1 scene was acquired. The extent of the NAIP image acquired in 2019 is located in the upper Pipestem catchment and dominated by a high number of small water bodies which were sometimes not detected by our approach, leading to somewhat lower producer's accuracies below 90%.

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The accuracies reported here are similar to the ones reported by Huang et al. (2018) who compared open water extent derived from dual-pol Sentinel-1 data against reference extents derived from NAIP imagery over the Pipestem Basin. The authors of that study also used the scene acquired on 5 July 2016 for validation. For the water class, they obtained producer's accuracies between 64% and 92%, and user's accuracies between 87% and 99%. For the wind-affected scene of July 2016, a producer's accuracy of 64% was reported, while here, 87.8% were obtained with the combination of VV and VH polarisations.

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The inclusion of topographic information may have helped to mitigate the effect of the backscatter increase due to the windroughened water surface. This interpretation is supported by the relatively high producer's accuracy for VV of 74.5% on that day. In comparison to Huang et al. (2018), user's accuracies reported here were consistently higher, suggesting a lower overestimation of water extent. We attribute this to the integration of HAND in the Bayesian framework, which helped to constrain water extent retrieval even in image areas where the contrast between water and non-water pixels was low. Such low contrast 330 areas often lead to a "spilling" into non-water areas during the region-growing process.  Wind is an important environmental factor in the prairies and has been shown to affect SAR water extent retrieval by causing scattering from roughened water surfaces . As a result, the contrast between water and non-water areas may be decreased to the point that no distinction is possible also by visual means. Such a case can be observed in Fig. 7a), where hardly any open water surfaces could be detected by the algorithm. The scene was acquired on a windy day during 335 which average wind speed measured at nearby Jamestown Regional Airport exceeded the 99% quantile of the recorded daily averages since 1990 (source: GSOD). Especially larger water bodies are not visible in the co-polarised backscatter image due to the low contrast. The water body delineation based on VH-polarised data, however, did not display the same issues. While the backscatter from larger open water bodies still shows some influence of water surface roughening, this fact inhibited water extent delineation to a far lower degree (Fig. 7b).

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The effect of wind on SAR backscatter from water surfaces was a frequently encountered problem in this study, especially for VV-polarised imagery. VH data were shown to be less affected by this problem, which is in line with our expectations and findings available in literature (Henry et al., 2006). However, as the cross-polarised signal is dominated by volume scattering (Richards, 2009), areas with sparse vegetation often resemble water surfaces in the resulting imagery (Twele et al., 2016).
Hence, its full potential lies in the complementary use together with co-polarised data as it was demonstrated here. to incorporate a-priori information on the probability of an area becoming flooded during an inundation event. The authors note 350 that, when using the ancillary information, both false and missed alarms were reduced with respect to the use of SAR intensity data only.

Surface water dynamics
Throughout the study period the number of potholes with open water surfaces strongly varied between ca. 2,300 and more than 5,000. In general, the number of water bodies, the total water area and the median area per water body were relatively stable 355 between 2015 and 2019, whereas 2020 differed considerably from the rest of the observation period (Fig. 8a). A number of outliers occur in the time series. For example, the image acquired on 12 October 2019, when heavy winds influenced the water retrieval (Fig. 7) has a lower number of water bodies and total water area and higher average water area per detected water body indicating that only larger objects could be detected. In addition, e.g., in October of the years 2015, 2017, 2018 and 2020, the number of water bodies and their median area showed sudden changes due to wind on the water surface or emerging ice 360 cover which limited the algorithm's capability to accurately delineate the surface water extent. As a result, large water bodies were only partially classified as water and, therefore, higher numbers of small water bodies were erroneously identified. In the following discussion, the results for these dates will not be taken into account.
Between 2015 and 2019, the number of water bodies displayed a seasonal behaviour with highest numbers in spring, then reaching an annual minimum in late summer and increasing again during September and October (Fig. 8a). During the same 365 period, the total water area varied between ca. 14,000 ha and 16,000 ha. In the first half of the study period, total water area declined from ca. 16,000 ha in 2015 to 15,000 ha in 2017. Seasonal water dynamics were also pronounced. In most years, total water area declined from spring throughout summer until autumn. This is especially noticeable in 2017, when water area declined from ca. 15,400 ha in May to ca. 13,180 ha in October. The subsequent two wetter years again differ from each other in terms of intra-annual dynamics of water area. In 2018, total water area remained relatively stable throughout the snow-free 370 period while 2019 started with higher values which then declined until mid-September by ca. 1,500 ha. This was followed by a steep increase until water area reached its maximum of the study period up to that point at ca. 16,500 ha (Fig. 8b). This behaviour coincides with the exceptional spring floods of that year and the wet October leading to widespread flooding along the James River and other regions of ND (Umphlett, 2019). The median area per water body (Fig. 8c) was similar to the inverse of the number of water bodies. Potholes tended to have larger water areas in summer than in spring and autumn. In combination 375 with the seasonal decrease in water area and number of water bodies this suggests that smaller water bodies dry out during summer. In addition to the strong increase in total water area at the end of 2019, which is not found in other years, we can also observe a decrease in median water area per pothole and a larger number of water bodies, suggesting that a large number of small potholes filled due to the intense storm event. The year 2020 differs from the rest of the study period in all three indicators. The number of water bodies and the total water area are consistently higher than in all previous years, with both 380 indicators surpassing the maximum values of those years during all the observed months in 2020. At the same time, the median area per water body was smaller in 2020 than in previous years, indicating a much larger abundance of small water bodies. The decrease of both total water area and the median area along with the stable or even increasing number of water bodies suggests that small water bodies remained present throughout 2020.
The persistence of small water bodies throughout 2020 becomes obvious when looking at the contributions of water bodies 385 of different sizes to the total water area. Fig. 9 shows the total water area of water bodies from four different size classes. In the following, water bodies > 1 ha will be referred to as large water bodies, water bodies < 1 ha as small water bodies. Large water bodies accounted for most of the total water area in the Pipestem Basin. The water area in these size classes (1 to 8 ha, > 8 ha), with the exception of the aforementioned dates affected by wind and ice cover, was rather stable until 2018 and showed little seasonal variability ( Fig. 9a and b). The water area accounted for by small water bodies, however, showed a clear seasonal 390 pattern with a decrease in water area from spring throughout summer ( Fig. 9c and d). In 2019, water area was higher in spring than in summer also in the two larger size classes. During the storm event of October 2019, water area increased in all four size classes. Large water bodies accounted for 88.7% of the total increase in water area of almost 2,000 ha between 18 September and 24 October 2019. During the wet year 2020, water area of large water bodies showed an adverse behaviour from small water bodies. While the water area in the larger two size classes declined between May and July, the total area of small water 395 bodies stayed relatively stable and increased in autumn.
The strong increase in water area and the emergence of small wetlands in October 2019 with respect to an earlier year can also be seen in the water extent maps in Fig. 10. In 2016 (Fig. 10a), a decrease in the extent of water bodies is visible from early summer (green colour) towards August (dark blue and yellow). The decreased water extent leads to a disconnection of some water bodies into several smaller ones. Between August and October, water extent only increases by a small amount, which August and October (orange and red colour, respectively) water extent increases and, especially in October, many wetlands are beginning to merge (Fig. 10b). This disconnecting and merging behaviour illustrates that an increase in overall water area not necessarily translates into an increase in the number of small water bodies and vice-versa. This may explain some of the seemingly non-corresponding temporal patterns seen in total water area, number of water bodies and median water body size 405 in Fig. 8.
Using the time series of water extent maps derived from Sentinel-1 imagery it was possible to track changes in total water area, number of water bodies and median water body area. In general, the temporal patterns found in these variables followed the expected seasonality. In a modelling study, Liu and Schwartz (2011) Liu and Schwartz [9] reported intra-annual dynamics with the number of small water bodies declining from spring throughout summer, whereas the number of larger water bodies remained stable throughout the year. Our results covering a period of six years corroborate these findings. In most years, the contribution of small water bodies to total water extent declined from May towards the end of summer and then increased again until the end of October. The area of larger water bodies, however, remained stable. Along with the typically declining number of water bodies and the increase in median water body size, this suggests that a large number of small water bodies falls dry during the summer months when evaporation rates are high. In the following year, these small potholes typically re-fill after 415 spring rains and snowmelt.  To our knowledge, this study is the first time that surface water dynamics in the PPR have been monitored using Sentinel-1 over a longer period covering both dry and wet years. This enables us to also support findings from previous studies (e.g. Liu and Schwartz, 2011) on inter-annual differences in wetland extent. While intra-annual changes in water extent have been found mainly for small water bodies, larger wetlands should only change on an inter-annual time scale. Our results demonstrate 420 that the contribution of wetlands both larger and smaller than 1 ha to the total water extent is in line with what would be expected from meteorological indices indicating water availability, such as PDSI (Fig. 2). During the extremely wet period in late 2019/early 2020, large water bodies showed significantly higher water extent values than during the rest of the time period. It is noteworthy that these increased water extents in larger wetlands decreased again relatively quickly along with the decrease in PDSI during 2020, whereas the extent of small water bodies remained relatively stable. This may suggest that larger 425 wetlands can act as a water storage during wet periods but then return to their formerly stable extent by releasing water to the drainage network. Small potholes, however, tend to be more geographically isolated, i.e., do not have well-defined inlets or outlets and their water balance is mainly controlled by vertical fluxes, such as rainfall, evaporation and drainage to the sub-soil (Cohen et al., 2016). They may persist as long as meteorological conditions are wet enough to support them. During most of 2020, PDSI was above 2 in the study region, which indicates such conditions. Furthermore, the snowpack during the winter 430 of 2019/2020 was thicker than normal (Umphlett, 2019) and the water released after melting fed many of the smaller potholes leading also to a higher number of smaller water bodies.
The time series of water extent and number of water bodies also reveal differences between the 2019 flood events reported in the literature (Umphlett, 2019). At the time of writing, we could not find an analysis of the effects of these extreme events on wetland extents in the literature. While extensive floods have been reported for spring 2019 across the Midwest (Umphlett,435 2019; NOAA, 2019) (Umphlett, 2019;NOAA, 2019), which are visible as peaks in the discharge time series, the autumn event led to much higher flood peaks in the Pipestem Creek (Fig. 2). During the spring event, the extent of large water bodies showed a lower increase with respect to the summer months than during the autumn event. The extent of small water bodies also increased during the second event, however, not as much as in spring. The results reported here show merging of smaller into larger wetlands, which may contribute to this behaviour. This finding, which is somewhat in contrast to our expectation 440 that small potholes replenish more quickly than larger ones, may also suggest that larger water bodies contributed more to floodwater runoff than small water bodies. Inter-annual changes in prairie wetland extent have been tracked using Landsat data (Vanderhoof et al., 2016;Krapu et al., 2018;Rover et al., 2011) and high-resolution aerial imagery (Wu and Lane, 2017;Wu et al., 2019), however, the limitations due to cloud cover and the long intervals between acquisition of NAIP data typically do not allow to reproduce extreme events. The analysis of SAR time series unaffected by cloud cover and with high temporal 445 resolution may help to understand the complex threshold behaviour which characterises catchments in the PPR (Shaw et al., 2013).
A major limitation encountered in this study for the monitoring of wetland dynamics during extreme events is the rather low temporal resolution of Sentinel-1 over the study area. Imagery over the study area currently is only acquired by one of the two satellites of the Sentinel-1 constellation and only along ascending passes. This limits the acquisition interval of the 450 entire catchment to the revisit time of 12 days. Additionally, imagery was not acquired during every overpass, further reducing temporal resolution. Obviously, this time span is too large to resolve flood events caused by storm or rain-on-snow events.
The combination of Sentinel-1 data with other SAR sensors, such the Radarsat Constellation Mission or the future NASA-ISRO SAR (Kumar et al., 2016) mission, may help to mitigate this problem in the future. In the present study, only water extent, which is directly observable by satellite imaging systems was analysed. However, for many applications, such as water 455 availability assessment or flood management, also surface water storage would be of interest. Pothole bathymetry data only exist at very limited scales (e.g. Mushet et al., 2017). While empirical relationships between water surface and stored volume exist for prairie potholes of different size classes (Gleason et al., 2007) validating such estimates is difficult due to missing reference data. The planned Surface Water Ocean Topography (SWOT) mission (Biancamaria et al., 2016) may help to provide such information in the future.
In this study, a novel approach for retrieving dynamic open water extent in prairie pothole wetlands from dual-pol Sentinel-1 SAR data was presented. Using a Bayesian framework, topographic information was integrated in the retrieval processed via HAND. The results demonstrate that the approach was successful in mapping changes in water extent in prairie potholes when their location was known a priori. The inclusion of topographic information, at least in some cases, helped to mitigate the 465 adverse effects of non-water areas resembling water surfaces due to low backscatter and of wind roughening the water surface.
The impact of the latter factor was further decreased by the combination of co-polarised and cross-polarised SAR data as the However, the value of Sentinel-1 for this application will further increase with the time period covered by this long-term Earth observation programme.