InSAR surface motion time series were calculated at a pixel resolution of 80 m × 90 m across the study site. To calculate the surface motion, we used 410 Sentinel-1A and -1B synthetic aperture radar images (descending orbit 125) gathered every 6 to 12 d between 12 March 2015 and 1 July 2019 from the European Space Agency Copernicus Open Access Hub (https://scihub.copernicus.eu, last access: 18 March 2022). Satellite interferometry was applied using these images with the APSIS technique (Sowter et al., 2013). The APSIS technique contains an adapted version of the established SBAS Differential InSAR time series algorithm (Bateson et al., 2015; Cigna and Sowter, 2017). It was designed to improve the density and spatial distribution of survey points to return measurements in vegetated areas, where Differential InSAR processing algorithms habitually struggle due to incoherence (Osmanoğlu et al., 2016; Gong et al., 2016). The APSIS algorithm was implemented using Terra Motion Limited's in-house Punnet software, which covers all aspects of processing from the co-registration of SLC (Single Look Complex) data to the generation of time series (Sowter et al., 2016). Standard interferometry image thresholds were as follows: a maximum horizontal baseline no more than 250 m, a maximum temporal separation of 1 year between image pairs using a coherence threshold of 0.25, and a minimum multi-look point acceptance threshold of 360 to a resolution of 80 m by 90 m. Motion was measured relative to a stable reference point, a building on glacial till, at Wick Airport (58.4533∘ N, 3.0879∘ W). Phase unwrapping was implemented using an in-house implementation of the Statistical-cost, Network-flow Algorithm for Phase Unwrapping (SNAPHU; Chen and Zebker, 2001). Two products were produced for each georeferenced pixel location, the multi-annual average velocity (m yr-1) of the time series calculated from the radar line of sight, and the 6–12 d time series of surface motion that detects the seasonal expansion and contraction (or bog breathing) as annual oscillations in relative height (Alshammari, et al., 2018). Each motion time series was then processed as follows.

First, using the R programming environment (R Core Team, 2013), the time series was sub-sampled into equal time intervals of 12 d, to match the longest overpass interval of Sentinel-1 images since Sentinel-1B, which reduces overpass times to 6 d, was not operational until 2016. Outliers were re-estimated using the R “tsclean” function (Box and Cox, 1964), from the R package “Forecast” (Hyndman et al., 2019). Gaps were filled with a linear interpolation using the R “approx” function (Becker et al., 1988) from the R “stats” package (R Core Team, 2020) after “spline” interpolation methods were found to produce contradictory results with adjacent time series across the largest gaps. The “detrend” R function aligned and reset each time series around zero by subtracting the mean.

Second, multichannel singular spectrum analysis (MSSA) using the SSA-MTM toolkit (Ghil et al., 2002; SPECTRA, 2021) was applied to isolate the cyclical, annual seasonal component of the time series from regional climate trends. The MSSA procedure initially calculates covariance after channel reduction with principal component analysis (PCA); then, using moving windows of 2–12 months, long enough to capture annual cycles, we recovered 80% of the signal variance in the first 20 empirical orthogonal functions (EOFs), which included the seasonal cycles in the time series. In the first instance, surface motion time series were reconstructed using EOFs 1–6. This reconstruction captured the seasonal cycles but also included longer-term climate trends, notably 3 wetter years leading to the 2018 European-wide drought (Buras et al., 2020). This climate trend causes merging and shouldering of peaks that compromised the detection of the seasonal cycles, particularly in the west of the study area, where it is wetter. To overcome this difficulty, we used a surface motion time series reconstruction using EOFs 5 and 6 (Fig. 2; Sect 1.1 and Fig. S1 in the Supplement) which extracted only the seasonal cycles. The final MSSA reconstruction provides a signal of relative movement, not absolute surface height, where a rise in the bog surface is an increase in displacement values and a fall is a decrease (Fig. 2).

Third, the MSSA reconstructions were then analysed for two of three surface motion metrics used to represent the condition of the peatland within each pixel for each motion year using the R “pracma” peak-find function (R Core Team, 2013). Metric one is the date of the annual peak “swelling” in the seasonal cycle (peak timing) of the MSSA reconstruction within 12 months from mid-May (Fig. 2). This has been shown to relate to peatland ecohydrology (Alshammari, et al., 2020; Tampuu et al., 2020). Metric two is the annual maximum amplitude (m) in the surface motion signal (amplitude) measured from the previous minimum of the MSSA reconstruction (Fig. 2). This is an indicator of the elastic response of the peat to changes in water storage (Roulet, 1991; Waddington et al., 2010). Metric three is the multi-annual average velocity (m yr-1) of the peatland surface calculated directly and previously described from the APSIS processing. This is a measure of vertical peatland growth (greater positive value) or subsidence (greater negative value) calculated over a fixed section of the time series (Sowter et al., 2013).

As the 2018 drought caused severe and widespread subsidence, it was found to have subdued the multi-annual average velocity and for this reason, we concentrated our analysis between 10 May 2015 and 9 May 2018, discarding the drought period. Multi-annual average velocity was recalculated accordingly. While the impacts of climate anomalies on the time series were noticeable and interesting, the first step is to gain an understanding of how InSAR data can be used to characterise peatland condition, and we focus on this aspect. We also screened time series with multiple peaks per annum or years where peaks were not discernible, and these pixels were classed as having irregular cycles. Irregular time series made up 8.4 % of the data set and are commonly associated with water courses and damaged bog (including agriculture and some forested pixels). Exclusion of these irregular time series does not affect our conclusions. Additionally, for the first year in the time series (2015 to 2016) many surface motion time series are truncated preventing the accurate calculation of amplitude or peak timing. In that year the mapping is incomplete, so for clarity we show results for a complete motion year from the mid-section of the concentrated analysis (2016 to 2017). To understand the relationships between the three metrics with respect to peatland condition we visualised the metrics in a three-axis plot (Fig. 3).

The training bed of the sub-sites SS1 to SS5 was divided manually into 130 smaller polygons (hereafter, sub-site polygons). Polygons ranged from (0.3 to 0.6 km2), a practical size (a) for reliable field and map-based validation and (b) to be appropriate for capturing key features of the landscape (e.g. pool systems, forestry or restoration blocks, streams and banks). To find boundaries between the polygons, one of the authors without specialist peatland knowledge searched for distinct contrasts in the landscape structure (e.g. topographic setting, natural drainage, evidence of drainage ditches and where these features would influence hydrology, forestry plantation, restoration, land management and the likely range, consistency or inconsistency in peak timing). This was possible using Google Earth, maps and the InSAR data (Supplement 1.2, Fig. S2). An additional set of 125 polygons was randomly selected across the whole study area using the Esri ArcMap “random point” tool (hereafter, random polygons). The immediate area close to the point were similarly assessed for features in the landscape, to define the polygon boundaries (most between 0.2–0.5 km2). While the sub-sites included the continuum of conditions and features adjacent to each other, the random polygons ensured that there was an improved capture of the ecohydrological states across the whole study area, reducing the likelihood that the sub-sites may have excluded a particular ecohydrological state. Summary statistics of the three surface motion metrics were calculated for each polygon. Average altitude, slope and aspect for all InSAR points in each polygon were also calculated from the Shuttle Radar Topography Mission Digital Elevation Model (Jarvis et al., 2008) to provide measures of topography (Supplement 1.3).

The full set of polygons (sub-sites and random polygons) was then passed to one of the authors with specialist peatland knowledge and based locally for a “blind” (i.e. without prior knowledge of or information about InSAR metrics within the polygons) ground-based ecohydrological classification. For each polygon, the cover of plant functional types (PFTs; Sphagnum, other mosses, shrub, sedges, grasses, rushes, and conifer trees) and the presence of hydrological features (pools, streams, drains, erosion gullies, slope) were recorded using a semi-quantitative scale (0: not present or scarce; 1: present; 2: co-dominant; 3: dominant). Current management (conservation, drainage for agriculture and peat cutting, forestry, restoration by forest-to-bog, restoration by drain blocking, and wind-farm construction) and historical management (e.g. burning, land-use conversion including wind-farm development, and restoration) were also documented for each polygon. The author responsible for classification visited and surveyed all the sub-site polygons and 86 of the random polygons (i.e. 85 % of all polygons) by walking across the area within the mapped polygon. For the random polygons where access was not permitted, shared local knowledge from stakeholders (land managers, project officers on the ground, wardens, and gamekeepers) was used instead of a field visit. In all cases, this was complemented with a combination of existing data, 1:50000 UK Ordnance Survey maps, NatureScot National Vegetation Classification maps (SNH, 2019), and Google Earth imagery.

Using the semi-quantitative scores, the PFT and hydrology polygon attributes were clustered by similarity using a hierarchical cluster analysis (HCA; Supplement 1.4, Fig. S3). To avoid an overly split hierarchical tree with only one or two members per cluster requiring complex explanation, it was deemed more informative to analyse the PFTs, hydrology, and the topography categories separately from each other. For the PFTs, once the clustering was complete, the average score of the semi-quantitative scale of each PFT in the cluster was ranked. The top three PFTs were used to characterise and name the plant functional group composition (Tables S1–S4 in the Supplement). For data visualisation of the results, clusters were further grouped based on the dominant PFT, resulting in five plant functional groups: Sphagnum, shrub, grass, bare peat (where low or absent vegetation was dominant), and forestry (Table 2). The four polygons that were dominated by rushes (R) had shrub as a co-dominant vegetation, so they were incorporated into the shrub group. While sedges (Sg) were co-dominant in many Sphagnum and shrub polygons, they were not the dominant PFT in any cluster and therefore did not form a separate group.

We also categorised topography into equal altitude belts (0–150, 151–300, and 301–450 m) and split slope face direction into four quadrants (north, east, south, and west facing) and ran the HCA. Except for the highest most eroded SS3 site, altitude and aspect did not show any meaningful cluster groups and played no further part in the analysis. The lack of topographic relationships is largely due to the gentle relief of the Flow Country, which has few sheltered slopes and deep valleys. Instead, we used average gradient (degrees) in the polygon and found a natural breakpoint at 1.5∘ that split the data set equally between flat (<1.5∘) and slope (>1.5∘).

Within the three-axis plot, we then chose a point with a winter peak timing, a high amplitude, and extreme positive velocity, normally associated with “soft”, wet Sphagnum peat and mapped the whole study area relative to that point. The actual reference point was selected by isolating the points that peaked in the winter and then stepping down through the percentiles of the metrics distributions until the case with the most frequent timing (e.g. February), highest positive velocity (e.g. 0.006 m yr-1), and highest amplitude (e.g. 0.008 m) was identified. For the condition mapping, data for all other points in the three-axis plot were then paired with this reference point and the Euclidian distance between them in three-dimensional (Cartesian) space was calculated. Based on the subsequently observed bimodal distributions (Sect. 4; Fig. 3), if the paired point was on the opposite side of the bimodal distribution to the reference point, the Euclidian distance was mapped as a “V”-shaped path via zero velocity and zero amplitude at the mid-date, 10 November, between the earlier and later timed clusters in the distribution. Prior to calculation, the positions of the outer portions of the three-axis plot were adjusted. This is because if the paired point is before (left of) the earlier peak and after (right of) the later peak the difference between the peak timing and the origin would be overestimated. To mitigate this, these cases were folded inwards along the axis of the peak of their distributions (effectively turning the upturned “W” shape of the bimodal distribution into an “M” shape). Using the natural breaks (Jenks) classification in Esri ArcGIS as a guide, thresholds were used to classify distance from the soft, wet Sphagnum point. These values were then mapped to produce an ecohydrological classification across the whole study site.

To further validate our ecohydrological classification map, we remotely identified and marked the central locations of all the pool systems within the study area (328 in total) using Google Earth images and determined if these markers corresponded to the soft, wet Sphagnum state. Although soft, wet areas in which Sphagnum is dominant do not necessarily contain pool systems, pool systems in this area almost always contain soft, wet peat. Furthermore, in the study area, pool systems provide a spatially distributed, abundant, and easily identifiable sample of this part of the peatland system. They also correspond to the part of peatland systems most unequivocally associated with the “near-natural” ecohydrological condition in this type of upland blanket bog. As the position of each pool marker did not take into account that pool systems often display complex morphology and varying geometries (and sometimes variable condition) related to local hydrological conditions (Goode, 1973; Lindsay, 2018), there was a need to tolerate a level of spatial uncertainty. To capture this, a wider area of 150 m (using the buffer function in Esri ArcMap) was calculated around the marker. This buffer area contained at least three pixels by three pixels of the ecohydrological map. We then calculated the percentage of pixels identified in the ecohydrological classification as soft in the buffer. Pixels classed as irregular were not included in the count (Table S5). We acknowledge that we focus on one particular state of peat, which does not account for the presence of drier, thin, or damaged peat conditions. Indeed, stiffer, thin, and damaged peat cannot readily be associated with a single, well-defined and remotely identifiable feature distributed across the whole study area in the same way. For instance, whilst drains can be observed from Google Earth, their age, maintenance, and the extent of their impact on the peat would require further evidence beyond the scope of this study.

The HCA revealed ecological groups relating to dominant plant functional types that were comparable between the sub-site and random polygons (Table 2) as well as hydrological groups separating polygons with pool systems and polygons with streams from all other polygons (Fig. S3). When the HCA classifications and topographic information (slope) were compared to the surface motion metrics, we determined the following consistent relationships for the sub-site and random-site polygons.

The observed relationship between surface motion metrics and ecohydrology is readily interpreted in the context of reported field measurements of peat surface motion (Howie and Hebda, 2018; Morton and Heinemeyer, 2019). Flatter sites under near-natural conditions are poorly drained, wetter, and dominated by Sphagnum spp. In turn, Sphagnum spp. have a considerable capacity for water storage as a direct result of their physiology (Kellner and Halldin, 2002), resulting in peak water storage and seasonal swelling of the surface later in the year. Drier sites with compacted peat have less capacity to store water and reach water holding capacity earlier in the autumn (Price, 2003). Furthermore, the more degraded peat at these sites is less elastic and therefore exhibits a lower-amplitude response to changes in water storage (Holden et al., 2004; Lui and Lennartz, 2019). As the seasonal water balance shifts, drier, better drained sites lose water first followed by the Sphagnum sites, which may continue to swell on account of hysteresis during the first stages of water loss (Howie and Hebda, 2018). Synthesising Sect. 4.2 (Figs. 4–7) the bimodal distribution of peatland surface motion timing within our landscape may be interpreted as reflecting two dominant components of the landscape. Wetter, flatter sites, typically dominated by Sphagnum and sedges, are soft peats; they tend to reach peak surface heights later in the year (December to February window) and have higher amplitudes and more positive velocities. Drier shrub- and grass-dominated sites are “stiff” peats; they tend to reach peak surface heights earlier in the year (August to October window), with slightly (but not exclusively) lower-amplitude oscillations and more negative velocities. Additionally, in the three-axis plot there are points characterised by both low amplitudes, negative velocities, and peak timings that can also fall outside the window of the soft and stiff class. These subtle variations in the metrics identified a third broad ecohydrological class which reflects thin peats, the most degraded and drained grass-dominated sites, or sites under restoration that are in transition to either a soft or stiff state.

Mapping and applying thresholds to the Euclidian distance calculations into these three broad peatland classes relative to the soft peat condition generated the peatland condition map (Fig. 8a). The classification produced a patchwork of conditions in the Flow Country, and the map evidences the widespread occurrence of the stiff peat condition associated with both naturally drier areas on the slopes and wet, soft peat margins but also areas made drier by a land-use history of burning and drainage. The impact of restoration activities, following the felling of forestry on deep peat in the last 25 years, can also be seen: recent forest-to-bog clearance is displayed as “thin/modified” peat, whilst areas well on their way to recovery are showing as either the soft or stiff condition (Fig. 8b and c). In polygons where forest is planted on peat, the signal is much more mixed with a greater proportion of the irregular class. This mixture is a result of the poorer SAR response over trees and the variable conditions encountered within forest stands. For example, in these forestry plantations, fire breaks, gaps between blocks (termed “rides”) and riparian areas that were never planted can still be wet, soft, and Sphagnum-rich in contrast with the planted blocks themselves. Furthermore, plantations may enclose areas of deep peat with pools and may display variable wetness and dryness depending on site and topography.

Using the criteria for the remote validation that pool systems should always include a pixel of the soft peat category within the 150 m buffer, 97.9 % (321/328) of the pool systems were identified as having at least one pixel of that class in the surrounding buffer (Table S5). A detailed inspection of the remaining 2.1 % (7/328) of pool system markers without a soft classified pixel within the 150 m buffer reveals that these pool systems all showed evidence of localised erosion or drainage causing degradation of their natural hydrology. While not validated in the same way, further inspection of our classification combined with specialist knowledge of the area indicates that the thin/modified class corresponds to areas under restoration, notably areas recently felled for forest-to-bog restoration, areas subject to intensive grazing, and thin peat soils on steeper higher ground and in valley bottoms (e.g. Fig. 8b and c). The abundance of the thin/modified class is striking in the east of the study area, and we note that this corresponds to long-term historical usage of the land for agriculture and associated cutting of peat for fuel (Andersen et al., 2018; Minasny et al., 2019).

Within the area, our method identifies approximately 254 km2 (27.3 % of the area) as soft, wet Sphagnum-dominated peat, 481 km2 (51.7 %) as stiff shrub-dominated peat, 117 km2 (12.8 %) as the thin/modified peat class, and 78 km2 (8.4 %) as irregular time series. This classification therefore provides an overall measure of the current state of this blanket bog landscape, to which future regional change, on account of climate change or restoration, may be compared.