*4.2. Flood Extent and Frequency for Winter 2019/2020 in Estonian Floodplains*

In Figure 5, open water and water under vegetation mapped from S1 data for winter 2019/2020 at our test sites are presented. The winter of 2019/2020 was extremely warm in Estonia. The monthly average temperatures from November 2019 to March 2020 were above zero (Figure 6). Climatological averages for December, January, February, and March have been negative in Estonia in the past (Figure 6). Due to positive air temperatures in the 2019/2020 winter, the soils did not freeze, there was no permanent ice cover on inland waters, and the precipitation was mostly rain. Due to the environmental conditions of winter 2019/2020, open water could be mapped throughout the winter. The flooded area (in hectares—ha) was estimated as the extent of water-covered area outside the official shoreline within the region of interest shown in Figure 1.

**Figure 5.** *Cont*.

(**e**) (**f**)

**Figure 5.** Floods mapped at test sites; (**a**) Open water frequency (%) at Alam-Pedja, (**b**) Frequency of water under vegetation (%) at Alam-Pedja, (**c**) Extent of open-water flood (ha) and water level (cm) at Alam-Pedja, (**d**) Extent of flood under vegetation (ha) and water level (cm) at Alam-Pedja, (**e**) Open water frequency (%) at Soomaa, (**f**) Frequency of water under vegetation (%) at Soomaa, (**g**) Extent of open-water flood (ha) and water level (cm) at Soomaa, (**h**) Extent of flood under vegetation (ha) and water level (cm) at Soomaa, (**i**) Open water frequency (%) at Matsalu, (**j**) Frequency of water under vegetation (%) at Matsalu, (**k**) Extent of open-water flood (ha) and water level (cm) at Matsalu, (**l**) Extent of flood under vegetation (ha) and water level (cm) at Matsalu.

**Figure 6.** Meteorological data: monthly average air temperature (black) and corresponding climatological average (blue).

At the Alam-Pedja test site, open-water floods occurred near the Emajõgi river. The frequency of flood in pixel varied mainly between 5 and 25%; however, in some areas it reached over 50% (Figure 5a). Figure 5c also shows the water level measured at the Tartu hydrological station on the Emajõgi river and the estimated open-water flood extent. From mid-February, the water covered area repeatedly exceeds the shoreline, and the maximum open-water flood extent (>1000 ha) lasted from February 29 until 15 March 2020 (Figure 5c). In Figure 5, the flood frequency (Figure 5b) and extent (Figure 5d) under the vegetation at the Alam-Pedja test site are also shown. The extent of the flooded area under the vegetation was about three times larger than that of the open-water flood, reaching up to 3500 ha on 13 March 2020 (Figure 5d). However, the frequency of FUV was lower than that of the open-water flood, between 5 and 25%.

At the Soomaa floodplain, the largest flood extent was detected at the beginning of the study period on 7 November 2019, when the open-water flood reached up to 230 ha and the flooded area under the vegetation was 4400 ha (Figure 5g,h). Starting from mid-November, the open-water flood decreased, and the following flood events occurred in mid-December and mid-January. The last flood event lasted from mid-February until mid-March (Figure 5g). The maximal water level measured at the Riisa hydrological station corresponds well to the maximal open-water flood events (Figure 5g). The frequency of open-water flooding remained below 50% in Soomaa. The flood extent analysis revealed that floods detected under the vegetated area lasted through the winter. In the forested area at the Soomaa test site, the floods were absent only during the second half of November (Figure 5h). The flood frequency map presented in Figure 5f indicates the forested areas (dark blue denotes flood frequency >75%) where floods occurred throughout almost the whole duration of the winter.

At the Matsalu test site, large open-water floods outside the official shoreline (ETD) could be detected throughout almost the whole duration of the winter (Figure 5k). The maximum open-water flood extent was detected in March, reaching up to 3000 ha (Figure 5k). In Figure 5i, there is a highlighted area (red rectangle) where open-water floods were observed most frequently (on more than 70% of images). The Matsalu test site has fewer forested areas than the Alam-Pedja and Soomaa test sites. However, there are large areas covered with coastal reed at this test site. The largest floods under the vegetation at this test site are related to an area with coastal reeds (Figure 5j, red rectangle). At the Matsalu test site, the floods under the vegetated area were smaller at 1300 ha (Figure 5k), compared to the open area floods at 3000 ha (Figure 5l).

#### *4.3. Causation Analysis between Flood Extent and Water Level Measured at Hydrological Stations*

An analysis was performed with the aim of defining the critical water level at the closest hydrological station that indicates the start of a flooding event (shoreline excess), and to find site specific relationships between the measured water level and flood extent. At the Alam-Pedja test site, a polynomial relationship between the flooded area extent and water level measured at the Tartu hydrological station (HS) was observed (Figure 7). The correlation (r2) with water level was most significant (0.94) for the open-water flood extent estimated from IW VH data; the correlation (r2) for EW HV was 0.85 (Figure 7). The r2 between the flooded area extent under vegetation and the water level measured at the Tartu HS was 0.51 (Figure 7). Our analysis indicated that open-water floodings at the Alam-Pedja floodplain occur when the water level at the Tartu HS increases above 120 cm (Figure 7, red line). Additionally, there was a significant correlation (0.51) between the extent of the flooded area under vegetation and the water level measured at the Tartu HS. It was not possible to define the precise critical water level for the Tartu HS at which flooding under vegetation starts (Figure 7).

**Figure 7.** Correlation between flooded area and water level at the closest hydrological station. FA: flooded area extent; WL: water level. Red line denotes the critical water level at which coastline excess occurs and flooding starts.

The relationship between the water level at the Riisa HS and the flooded area extent at Soomaa was polynomial (Figure 7). The correlation coefficient (r2) between the Soomaa open-water flood extent and the water level measured at the Riisa hydrological station was 0.62 for EW HV data and 0.57 for IW VH data (Figure 7). The correlation (r2) between the water level measured at the Riisa hydrological station and the flooded area extent under vegetation was 0.29 (Figure 7). Our analysis showed that open-water floodings occur when the water level at the Riisa HS increases above 160 cm (Figure 7, red line).

While the relationship between the water level and the extent of the flooded area was polynomial at the Alam-Pedja and Soomaa test sites, the relationship was linear at the Matsalu test site. The r2 between the open-water flood extent at the Matsalu site and the water level measured at the Kasari hydrological station was 0.34 for IW VH data and 0.38 for EW HV data (Figure 7). There was no correlation between the water under vegetation and the water level measured at the Kasari HS (Figure 7). At the Matsalu test site, floods occurred throughout the winter, and it was not possible to define a precise critical water level at the Kasari HS that could be related to the beginning of flooding.

#### **5. Discussion**

Previous studies have shown the advantages of incidence angle dependent thresholding in the case of TerraSAR-X and Envisat ASAR datasets [18,54]. Our operational setup for flood mapping from S1 data for Estonian floodplains integrates incident angle dependent water thresholding and post-processing using auxiliary information from the Estonian Topographic Database. Post-processing using information from the ETD enables the elimination of water lookalikes. We evaluated the open water mapping accuracy for IW mode VH polarization at our test sites. There was good agreement between the water mapped from IW VH data and the S2 MNDWI index, with an accuracy as high as 96.70% and a kappa hat of 0.86 (Table 6). The accuracy of flood mapping using S1 VH polarization has also been evaluated by Twele et al. [23], who obtained a kappa hat coefficient of 0.88 and an accuracy of 94%. While their operational methodology applied for flood mapping differs from that used in our study, the overall accuracy of the flood mapping is comparable. In the study conducted by Twele et al. [23], the split based thresholding for water mapping was used together with the HAND index in the post-processing step.

During the winter season, the default imaging mode of S1 over the Baltic Sea region is the EW regime. To delineate the information about flooded areas in Estonia, an algorithm for open water mapping for the EW regime was established and applied. The open water mapping accuracy from EW HV polarization data was 97.8%. By including the information from EW data, we could delineate the flood maps approximately using 55 images from each test site. Combining the information from IW and EW regimes, we analyzed 83 images from the Alam-Pedja test site, 93 from the Soomaa test site, and 64 from the Matsalu test site for open water mapping for the period of 1 November 2019–31 March 2020 (Figure 5). Thus, the proposed flood mapping method was tested on a large and diverse dataset. The method developed and proposed in the current study has potential for operational mapping of floods in Estonia and neighboring countries (e.g., Latvia).

The winter of 2019/2020 was extremely mild in Estonia, and there was no permanent ice on the rivers, nor was there snow cover. The monthly averaged air temperature was above 0 ◦C at all meteorological stations. Our analysis of flood duration and extent showed that in the winter of 2019/2020, floods were observed almost through the whole period of winter. However, the dynamics of the floods differed between the test sites. The maximum flooding observed at Alam-Pedja occurred in March, while at Soomaa and Matsalu several flood events were detected during the winter of 2019/2020. Analysis of the open-water flood extent and water level measured at the closest hydrological station confirmed the correlation between these variables. The correlation was more significant (r2 < 0.6) for the inland riverside floodplains of Alam-Pedja and Soomaa. For the coastal floodplain at Matsalu, the correlation was 0.34, indicating that the river gauge data cannot be used as proxy for flood extent as the coastal flood was significantly influenced by marine processes (not only by riverine hydrology and precipitation). The analysis also revealed that at Alam-Pedja, floods occur when the water level rises above 120 cm at the Tartu HS. At the Soomaa test site, floods occur when the water level rises above 170 cm at the Riisa HS. At the Matsalu test site, open water outside the official coastline could be observed throughout the winter, and we could not define the precise water level at the Kasari HS that results in a flooding at the floodplain. The Matsalu floodplain is located at the outflow to the Baltic Sea; therefore, it is also influenced by the water level in the sea.

Defining the water level at the closest hydrological station from which the floods start (shoreline excess occurs) can provide information for risk mitigation. Hydraulic modelling is a common tool used in flood risk estimation [57]. However, for hydraulic and hydrological modelling, detailed information about riverbed topography, a digital elevation model of the landscape, and a flow rate are needed. These datasets are not always available; therefore, analysis of remote sensing information in combination with standard gauge data can give valuable information from a single source. S1 time series analysis with local gauge data has been used to determine the positional accuracy of riverside embankments [58]. A study conducted by Wood et al. [58] also pointed out the possibility of determining the positional accuracy of embankments using only a sequence of S1 imagery and gauge data without using topographic data.

In the winter of 2019/2020, several floods in forested areas that harmed economic activities were also reported in the Estonian press [41]. However, the economic loss caused by wintertime flooding in Estonia is unknown. The current study indicated that at the inland riverside floodplains of Soomaa and Alam-Pedja, the flooded areas under vegetation reached up to 4500 ha and were about three times larger than open-water floods at these test sites. Voormasik et al. [30] analyzed the flood extent at Alam-Pedja from TerraSAR-X imagery and estimated the area of flooded forest to be about three times larger than the extent of the open-water flood. Studies indicate that an evaluation of the extent of flooded forest near inland riverbank floodplains is necessary for the estimation of the total flood extent and its economic consequences. Our analysis also revealed that in the case of the inland water floodplains of Alam-Pedja and Soomaa, flood under vegetation could be correlated with the water levels measured at the closest hydrological station.

#### **6. Conclusions**

The current paper presents an automatic water mapping method for S1 EW and IW modes by compiling local incident angle thresholding and the application of ancillary information from the Estonian Topographic Database in a post-processing scheme. The proposed method was used to analyze the flood duration and extent in Estonian floodplains during the extremely mild winter of 2019/2020. Our analysis revealed the areas that are most frequently inundated in Estonian floodplains. The observed flood maps allowed us to evaluate the connections between the extent of the flooded area and the water level measured at the closest hydrological station. The study enabled us to determine the water level at which floods occur at the floodplains and to provide valuable information for risk mitigation purposes (standard water level readings from automatic stations are available with a ten-minute interval). The analysis of the extent and frequency of wintertime floods can form the basis for various economic analyses, evaluations of revenue foregone in the forest industry due to mild winters, and evaluations of stress to northern boreal alluvial meadows. The analysis also contributes to the implementation of flood risk assessment and management directive in Estonia [59]. Moreover, the proposed method can be implemented for operational flood mapping in Estonia and neighboring countries.

**Author Contributions:** Conceptualization, L.S.; methodology, L.S. and A.A.; software, L.S. and A.A.; formal analysis, L.S. and A.A.; writing—original draft preparation, L.S.; writing—review and editing, L.S., A.A. and R.U.; visualization, L.S. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the European Regional Development Fund within the National Programme for Addressing Socio-Economic Challenges through R&D (RITA1/02-52-04) and by Estonian Environment Agency project "Development and implementation of flood monitoring service from satellite remote sensing data" (LLMAE21069).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not Applicable.

**Data Availability Statement:** The data supporting the conclusions of this article will be made available by the authors, without undue reservation.

**Acknowledgments:** We would like to thank the Estonian Environment Agency for its cooperation.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

