Being dynamic in time and space, seasonal snow represents a difficult target
for ongoing in situ measurement and characterisation. Improved understanding
and modelling of the seasonal snowpack requires mapping snow depth at fine
spatial resolution. The potential of remotely piloted aircraft system (RPAS)
photogrammetry to resolve spatial variability of snow depth is evaluated
within an alpine catchment of the Pisa Range, New Zealand. Digital surface
models (DSMs) at 0.15 m spatial resolution in autumn (snow-free reference)
winter (2 August 2016) and spring (10 September 2016) allowed mapping of snow
depth via DSM differencing. The consistency and accuracy of the RPAS-derived
surface was assessed by the propagation of check point residuals from the
aero-triangulation of constituent DSMs and via comparison of snow-free
regions of the spring and autumn DSMs. The accuracy of RPAS-derived snow
depth was validated with in situ snow probe measurements. Results for
snow-free areas between DSMs acquired in autumn and spring demonstrate
repeatability yet also reveal that elevation errors follow a distribution
that substantially departs from a normal distribution, symptomatic of the
influence of DSM co-registration and terrain characteristics on vertical
uncertainty. Error propagation saw snow depth mapped with an accuracy of
Seasonal snow provides a globally important water resource (Mankin et al., 2015; Sturm et al., 2017), which is highly variable in space and time (Clark et al., 2011). Difficulties associated with collecting field observations limit the characterisation and understanding of spatial variability in snow depth and, in turn, our ability to improve spatially distributed modelling of seasonal snow. While insight can be gained via modelling on moderate to large scales (Winstral et al., 2013), resolving the fine-scale variability and its controlling processes remains limited by the ability to capture such variability in the field (Clark et al., 2011). Since water storage within a snowpack is a function of snow depth and density, and the former exhibits higher spatial variability than the latter, advances in measuring snow depth at high spatial resolution offer promise for improved estimates of snow water equivalent (SWE) (Harder et al., 2016).
Historically, studies of seasonal snow processes have relied on in situ observations. With biweekly temporal resolution, Anderson et al. (2014) gained substantial insights into physical controls on seasonal snow processes, albeit with a dependence on statistical scaling to relate transect-scale observations to basin-scale processes. Alternatively, the nature of automated snow measurement instrumentation often precludes continuous in situ measurement across networks sufficiently dense to characterise fine-scale spatial variability. Kinar and Pomeroy (2015) provide a comprehensive review of instrumentation and techniques for measuring snow depth and characterising snowpacks. In summary, while instrumentation and methodologies exist for obtaining accurate and temporally continuous, measurements of snow depth and related snowpack properties at point locations, adequately resolving the high spatial variability of snow depth remains a challenge. This is exacerbated by local field conditions, such as exposure to wind or the complexity of the topography and vegetation further increasing the spatial variability in snow depth (Clark et al., 2011; Kerr et al., 2013; Winstral and Marks, 2014).
Remote sensing has provided substantial advances in quantification of seasonal snow variability, with imaging sensors supporting spatial and temporal resolutions that allow a range of scales to be explored. Space-borne satellite imagers provide a synoptic view and accompanying step-change capability in capturing properties of snow-covered areas, although trade-offs exist between competing spatial, spectral and temporal resolutions (Dozier, 1989; Nolin and Dozier, 1993; Hall et al., 2002, 2015; Sirguey et al., 2009; Malenovský et al., 2012; Rittger et al., 2013; Roy et al., 2014; Bessho et al., 2016). Passive and active microwave sensors offer the capacity to retrieve estimates of snow water equivalent directly from space-borne platforms but also suffer substantial limitations, including coarse spatial resolution in the case of passive microwave sensors and complexities in successfully processing snow signals and accounting for complex terrain in the case of both passive and active sensors (Lemmetyinen et al., 2018). Despite the progress in remotely mapping snow, reliable determination of snow depth, particularly in complex terrain, remains challenging. Modern, very high-resolution stereo-capable imagers show promise for retrieving snow depth over large areas from space, although the influence of topography on uncertainties and complications introduced by shadows in alpine terrain demand attention (Marti et al., 2016).
Advances in light detection and ranging (lidar) technologies have become increasingly relevant for measurement of snow depth, firstly from air (Deems et al., 2013; Painter et al., 2016) and more recently from space-borne platforms (Treichler and Kääb, 2017). Of the three modes of lidar data capture, terrestrial laser scanning (TLS) (e.g. Revuelto et al., 2016) offers the best performance in terms of precision and accuracy. TLS can resolve snow depth on a fine scale across relatively large areas but remains limited by view-obstruction and logistical challenges of placing equipment in situ in complex terrain. Airborne lidar provides a balance of spatial resolution and accurate surface elevation measurement and, combined with density estimates, can provide SWE estimates on the catchment scale across substantial areas of hundreds of square kilometres (Painter et al., 2016). High financial costs and logistical challenges, however, preclude regular airborne lidar data capture in many regions globally. Treichler and Kääb (2017) assessed ICESat lidar data, which is designed primarily for measuring surface elevation over polar regions to characterise seasonal snow depth in subpolar southern Norway. Despite reasonable estimates of snow depth, measurements were accompanied by relatively large errors for most temperate locations. ICESat measurements are also limited by their punctual nature and footprint, yielding a relatively sparse and coarse spatial distribution, in turn complicating inferences about spatial variability.
Location and hypsometry of the study catchment within the Pisa Range, New Zealand.
Recent technological advances, including the miniaturisation of imaging and positioning sensors, as well as improvements in battery power and autonomous navigation have significantly lowered the barriers associated with a remotely piloted aircraft system (RPAS, also known as unmanned aerial systems, UAS, and unmanned aerial vehicles) operation (Watts et al., 2012). This, combined with ever-increasing computing power and significant improvements in machine-vision for dense photogrammetric reconstruction (Hirschmuller, 2008; Lindeberg, 2015), provides new opportunities to map small areas photogrammetrically at very high resolution in a temporally flexible, on-demand, fashion. Examples of RPAS use related to mapping snow depth are promising but tend to apply to sub-catchment scales and to not fully characterise the uncertainty associated with photogrammetric modelling (Vander Jagt et al., 2015; Bühler et al., 2016; De Michele et al., 2016; Harder et al., 2016, Cimoli et al., 2017; Avanzi et al., 2018). Furthermore, most RPAS studies of snow depth to date have mapped terrain of relatively low complexity (e.g. Avanzi et al., 2018; Fernandes et al., 2018). Additionally, with a few exceptions (e.g. Harder et al., 2016; Bühler et al., 2017; Marti et al., 2016), previous studies have often relied on multirotor platforms despite their relatively short endurance and reduced spatial coverage relative to fixed-wing alternatives. Merit remains in characterising fine-scale variability in snow depth distribution across an entire catchment, a scale that fixed-wing RPAS can more easily capture. However, increased terrain complexity and the magnitude of the image block can, in turn, challenge photogrammetric modelling. Determination of snow depth via RPAS photogrammetry relies first on the reconstruction of three-dimensional scenes from a set of overlapping images and then on the principal of differencing between temporally subsequent surfaces, provided by point clouds or digital surface models (DSMs) (Vander Jagt et al., 2015; Harder et al., 2016). A snow-free surface provides a reference data set for absolute snow depth, while changes in snow distribution through winter can be assessed by comparing surfaces obtained while snow cover is present in the catchment. Because changes in snow depth through time, either through processes of accumulation, ablation or redistribution, may be subtle, the repeatability and vertical accuracy achieved by photogrammetric modelling is paramount. The aim of this paper is to test a methodology for retrieving snow depth across an entire catchment via RPAS photogrammetry from a fixed-wing platform. We seek to evaluate the performance, limitations and usefulness of this approach and assess how well snow depth can be resolved on the catchment scale. Associated challenges include minimising spatial uncertainties sufficiently to reliably detect changes in snow depth over time, with a decimetre level of vertical accuracy targeted, while also reducing the need and complication of extensive in situ collection of ground control points (GCPs). This approach was assessed during a campaign of winter RPAS-based photogrammetric surveys of an alpine catchment in the Pisa Range, New Zealand, was undertaken.
Timing details for RPAS flights during 2016. All flights were completed between noon and early afternoon.
The paper describes the field site, field and photogrammetric methods, as well as the quality and accuracy assessment. Results are considered in terms of the validation and repeatability of the method, as well as considering the spatial distribution of snow within the catchment. The discussion addresses the performance of RPAS photogrammetry in this context, sources and nature of the associated uncertainty as well as pitfalls and limitations that were encountered, before demonstrating the insight that RPAS-derived data can provide for the study of seasonal snow. While primarily exploring and assessing the potential of RPAS photogrammetry for measuring seasonal snowpack, this study has broader implications for the wider field of modern close-range photogrammetry, as typically implemented from low-cost (relative to manned systems) unmanned systems. While considered here in terms of seasonal snow, the characterisation of RPAS photogrammetry performance presented also applies to other applications involving three-dimensional surface and/or volume change analysis.
The study catchment (Fig. 1), a tributary of the Leopold Burn located in the
Pisa Range of the Southern Alps/Kā Tiritiri-o-te-Moana of New Zealand
(44.882
We used the Trimble UX5 Unmanned Aircraft System, a fixed-wing RPAS manufactured by Trimble Navigation for photogrammetric applications. A single two-blade propeller, driven by a 700 W electric motor, propels the platform. Power is supplied from a 14.8 V, 6000 mAh lithium-polymer battery allowing a flight endurance of 50 min. Autonomous navigation is supported by a single-channel GPS receiver, which also provides approximate coordinates for each photo centre, while an accelerometer logs orientation data.
Imagery is captured by a large-sensor (APS-C) Sony NEX 5R mirrorless reflex
digital camera providing a maximum imaging resolution of 4912 pixels by
3264 pixels or about 0.04 m GSD at 400 ft (122 m) a.g.l. The camera is
fitted with a Voigtlander Super Wide-Heliar 15 mm
Typical flight path for the mapping of the study catchment using the Trimble UX5, GCP network established for each flight mission, and reference snow depth locations. Flight log is from the spring flight mission. The configuration of the ground control point (GCP) and check point (CP) assignment for the triangulation of each flight is shown in the panels on the right-hand side.
Three RPAS missions were undertaken with identical planning and differing
states of snow cover in the catchment (Table 1). Flight planning was carried
out using the Trimble Aerial Imaging software. All flights imaged 15 strips,
aligned along the major axis of the study catchment (Fig. 2). The study area
was imaged with 90/80 % forward/sideward overlap with respect to the
lowest elevation to ensure that sufficient overlap was maintained when
mapping rising ground. Exposure locations are determined automatically by the
software to achieve the desired overlap, with the camera being triggered
accordingly during flight using on-board Global Navigation Satellite System (GNSS) navigation. The duration of
each flight was
Achieving a robust constraint of exterior orientation parameters during
aero-triangulation (AT) depends on the availability of a set of high-quality
ground control points (GCPs). This is particularly true if the imaging
platform lacks a precise-point-positioning capability (e.g. it carries
only single-frequency GPS and is not capable of determining differentially
corrected positions). Such code-only GPS navigation is accompanied by
uncertainties 2 orders of magnitude greater than the expected accuracy of
the models. Ground control networks were established for each RPAS flight
mission using real-time kinematic (RTK)
GNSS surveying with a Trimble R7 base station and R6 rover units. GCP
locations were measured with accuracy of the order of
It is well established that photogrammetric control is best achieved within the bounds of the GCP network (Linder, 2016), while the uncertainty associated with the geolocation of resected points increases beyond the control network. To constrain the area within the study catchment for photogrammetric processing, the GCP network was distributed around the catchment perimeter, as well as through the central area of the catchment. Additionally, the placement of GCPs on the valley floor and at mid-elevation within the catchment ensured that the network also sampled the elevation range of the catchment. An extensive GCP network was established for the first flight with no snow on the ground, which permitted the robustness of AT to be tested under different GCP scenarios, as discussed further in Sect. 3.2.1. This allowed the network to be refined and reduced in size for subsequent missions, a matter of practical importance when working in alpine areas during the winter. Control point networks for each mission are illustrated in Fig. 2. A new GCP network was established for each survey campaign due to the inability to establish permanent markers (e.g. on poles) due to the conservation status of the study area. Although the layout of the network was similar for each mission, there were no common GCPs shared between different flights, with the only common setting being the set-up of the base station for each RTK survey.
To assess the quality of snow depth data derived from RPAS photogrammetry, independent measurements were collected by manual snow probing on 10 September 2016, the same day as the spring RPAS mission. This approach has been established as standard practice in similar studies (e.g. Nolan et al., 2015; De Michele et al., 2016). Aluminium avalanche probes with 0.01 m graduations, providing a nominal precision of 0.01 m, were used. The sampling strategy involved the measurement of snow depth every 50 m along three elevation contours within the study catchment, namely 1460, 1500 and 1540 m (Fig. 2). This strategy ensured that snow depth was measured across a representative sample of slope aspect and elevation, while optimizing navigation across the catchment. Snow depths were measured at each location by probing 5 times within arm's reach, and the location of the central measurement was surveyed with RTK GNSS, under the same protocol and achieving the same level of accuracy as the GCP survey. This provided 430 measurements of snow depth, with the mean snow depth at each of the 86 locations providing a sample for comparisons with RPAS-derived snow depth.
The goal of aero-triangulation (AT) in photogrammetry is to transform a set
of images into a scene in which geometrically accurate measurements can be
made in three-dimensional, often geographic, space. This georeferencing
process requires a transformation from the inherent coordinate system of the
device capturing imagery (a camera) to an appropriate geographic coordinate
system (Vander Jagt et al., 2015; Linder, 2016). While traditional
photogrammetry has long relied on metric (calibrated) cameras, the use of
off-the-shelf non-metric cameras requires the simultaneous solving of both
interior orientation (the camera model) and exterior orientation. This
process, known as self-calibration, applies a bundle-block adjustment to
solve the camera model describing the precise focal length (
Summary results of alternative ground control point (GCP) and check point (CP) scenarios tested for aero-triangulation within UAS Master.
Initially, AT was carried out using the photogrammetry module of Trimble Business Center, v3.40 (TBC), which relies on a simplified implementation of the adjustment process from Inpho UAS Master. Deliverables produced using TBC, however, suffered from severe elevation artefacts which limited their usefulness for further analysis. This is discussed further in Sect. 5.3.
Following the identification of shortfalls in TBC, AT was carried out using
Trimble Inpho UAS Master® v8.0 (UAS Master). UAS Master is a
feature-rich photogrammetry package that is targeted to RPAS applications
(Trimble, 2015, 2016) and is a comprehensive alternative to
software often used in similar studies such as Pix4D or Agisoft Photoscan.
The AT solution is initialised by the positional parameters (
The robustness of photogrammetric modelling was assessed by testing several
alternate control scenarios, based on the autumn mission when 23 GCPs were
placed and measured in the field. The following scenarios were evaluated:
all 23 control points as horizontal and vertical GCPs, 14 control points as horizontal and vertical GCPs, 6 control points as horizontal and vertical GCPs.
In each scenario, the balance of the control points was provided as check
points (CPs). In retaining GCPs, we ensured that the perimeter of the study
catchment remained fully constrained within the network. As the number of
GCPs decreased, the root mean square error (RMSE) for CPs provided an
indication of AT robustness. It was found that as few as 14 GCPs provided an
acceptable triangulation across the study area, with some degradation
apparent when only six GCPs were used, primarily in terms of
Standard deliverables from the photogrammetric modelling included a dense point cloud; a digital surface model, interpolated to 0.15 m spatial resolution; and an ortho-mosaic, resampled to 0.05 m spatial resolution. The DSM and the ortho-mosaic are the principal products for further analysis. Each DSM provides the basis for determining snow depth, while the ortho-mosaics allow for assessment of the snow-covered area, and for snow-free areas to be identified when assessing the quality and repeatability of DSMs between flight missions.
Summary statistics for each of the triangulations used to produce DSMs and ortho-mosaics from each of the three flight missions for ground control points (GCPs) and check points (CPs).
Snow depth was derived by differencing DSM of flights 2 and 3 from the
baseline obtained during flight 1 (ref) as follows:
Summary statistics, typically based on the rms error of GCPs and CPs from the AT, indicate the expected accuracy of deliverables. Since snow depth is determined by differencing two DSMs, error propagation can provide an assessment of uncertainty associated with the dDSM. The overall accuracy of the DSM differencing approach should also be validated against independent reference data (e.g. snow depth measured in situ), temporally coincident with RPAS measurements. Areas of snow-free terrain during Flight 3 further supplement snow depth observations by providing an extensive source of samples with which to assess the repeatability of the photogrammetric modelling process.
Previous studies have considered the accuracy of RPAS-derived snow depth by comparison with reference data from in situ snow depth alone (Bühler et al., 2016; De Michele et al., 2016; Harder et al., 2016) while ignoring the uncertainty inherent to each photogrammetric model and their propagation into the dDSM. Here, the accuracy of photogrammetrically derived snow depth is assessed by exploring both approaches. Relating photogrammetric model quality, as inferred from GCPs and CPs, to observed uncertainties in the determination of snow depth provides the basis for realistically informing uncertainties in snow depth from ongoing RPAS measurements. This in turn allows rigorous inferences about the evolution of snow depth to be made, without the need for further campaigns of in situ validation. While high-resolution reference elevation data, such as lidar-derived elevation or surface models would provide a useful benchmark for assessing RPAS DSM quality, no such data were available for the study area.
Since snow depth is determined via DSM differencing as a linear combination
of two independently measured variables (Eq. 6), the uncertainty
associated with snow depth (SD), measured in the vertical dimension, for
each measurement date (
In reality, perfect co-registration between constituent DSMs and the Gaussian assumption are unwarranted. Subsequently, inferences associated with the evolution of snow depth may be compromised due to confidence intervals being conservative or immoderate. Therefore, we use dDSM for snow-free areas to characterise the experimental distribution of errors and assess the validity of the Gaussian assumption in this context.
The approach above provides a means to determine the expected accuracy of
snow depth derived from RPAS photogrammetric surveys. In order to validate
this estimate, a reference data set of in situ observations was sampled in the
field using snow probes, with a nominal precision of
Here, 430 measurements of snow depth provided 86 mean reference values, with the standard deviation of each set of five measurements providing 95 % confidence intervals. The aim of this sampling strategy was to assess and account for co-location uncertainty and spatial variability between the RPAS and reference snow depth data sets. Reference snow depths were compared with those from the spatially coincident pixels from the map of RPAS-derived snow depth. RPAS-derived snow depth quality was assessed in terms of residuals and weighted linear regression between reference and RPAS-derived snow depths.
Emergence of snow-free areas at the time of the spring flight facilitated comparison between autumn and spring DSMs on those areas. As the same terrain surface mapped from two independent flights should yield identical DSMs, the residual between them provides a means to characterise the distribution of errors in the photogrammetric processing, which can be readily compared to the assessment made from CPs.
Snow-covered and snow-free areas were segmented using an unsupervised classification of the spring ortho-image using the Iso Cluster classification tool in ArcGIS v10.3. With five output classes, this approach enabled discrimination between illuminated snow pixels, shaded snow pixels, and vegetation and soil-dominated snow-free pixels. Snow-free pixel classes were then grouped to provide a mask within which the distribution of spring dDSM values could be characterized. While this approach relies on the characterisation of repeatability for snow areas, good image contrast and the high overall density of TPs generated across the image block, regardless of the presence or absence of snow, indicates that photogrammetric reconstruction performance should be comparable for both snow-free and snow-covered areas. This is a product of the camera properties, which maintain high dynamic range across scenes of mixed land cover and extensive snow cover. Therefore, this residual represents a measure of the repeatability of the technique for measuring surface height change, including derivation of snow depth.
Processed ortho-mosaics for autumn
A primary motivation for exploring the use of RPAS photogrammetry for mapping
a snowpack is the ability to resolve fine-scale spatial variability in snow
depth. This capability was assessed by computing and comparing the
semi-variograms of reference and RPAS-derived snow depths from the autumn
flight. While the sample size for reference snow depths remained fixed
(
Since GCPs are used to solve the photogrammetric model, they do not provide
an independent assessment of accuracy. Such an assessment is provided by the
CPs, the RMSE of which was of the order of centimetres for all flights
(Table 3). Planimetric RMSE (i.e.
While the RMSE of CPs increased for the winter and spring flights, possibly
due to a less constrained model, the level of accuracy achieved is compatible
with expectations for the determination of snow depth. Additionally, the more
tightly constrained first AT reduced the error for the baseline model, in
turn contributing a reduced uncertainty in derived snow depths, despite the
reduced control for subsequent ATs. For all flight missions, the
photogrammetric processing performed well in the correlation of images and
the construction of the image block, as indicated in Table 3. Tie point (TP)
generation relies on the successful match of unique targets across multiple
images, which was achieved despite the complicated contrast over snow. For
all flights
Residuals between snow depths measured by RPAS photogrammetry and
probing for all probe locations (“all”, blue) and non-tussock probe
locations (“n-t”, red)
Map
Snow depth was found to be highly variable across the study catchment for both winter and spring (Fig. 3). The midwinter flight mapped near-complete snow cover across the study catchment, while large snow-free areas developed by the spring flight, where snow-covered area was reduced by about one-third (Fig. 3a and b). Where snow was present, depths ranged from less than 0.10 m, typically on exposed ridgelines and broad elevated slopes, to 2 m or more where cornices formed along ridgelines, as well as in gullies. Average snow depth was greater for winter, although maximum depths were comparable between winter and spring. Between winter and spring, considerable ablation was observed. Areas of deepest snow were spatially coincident between winter and spring, with the greatest retention of snow in cornices and gullies. Where shallow snow was present on ridgelines in winter, it was largely lost by spring.
Propagation of errors under the Gaussian assumption, based on the RMSE from
each AT, yielded vertical uncertainties for snow depths at the 90 %
confidence level of
Comparison of RPAS-derived and reference snow depth yielded a mean residual
of
Good agreement between data sets is further demonstrated in Fig. 4b.
Relatively large horizontal error bars accompanying the reference
measurements (Fig. 4b) reflect the substantial spatial variability in snow
depth measured by probing, even within arm's reach. Substantial departure
occurs for reference snow depths between 0.20 and 0.60 m which tend to
exceed RPAS measurements. Negative depths in the RPAS-derived data set is a
product of co-registration uncertainty, particularly in areas where the
surface model represents large vegetation or is influenced by rock outcrops,
as well as spurious values from the constituent DSMs. Agreement between
reference and RPAS-derived data sets improved with the removal of reference
measurements made above tussocks. This filtering saw the
Parameters of weighted regression between reference and RPAS-derived snow depths.
The emergence of snow-free areas for the September flight permitted a
comparison of height derived on snow-free surfaces between the pre-winter and
spring flights (Fig. 5). The small magnitude of the residuals, compatible
with errors consistent with the uncertainty of the triangulation CPs,
demonstrates the repeatability in the derivation of snow-free surfaces.
Furthermore, the absence of any spatially structured trend in the
distribution of the residual indicates robust photogrammetric modelling from
the RPAS platform. At 0.15 m resolution, the snow-free pixels from the
spring mission provided a large sample (
Mean,
The set of residuals departed substantially from the Gaussian distribution
and was better represented by the Student's
Observed (calculated under Gaussian assumption) and fitted normal
and
Comparison of histograms and accompanying descriptive statistics for
the residual between DSMs for slopes between 5 and 10
Semi-variograms for snow depth, based on measurements provided by probing (86 samples), and two random samples drawn from RPAS-derived snow depth of 1000 and 5000 observations.
The non-Gaussian nature of the residual distribution deserves further
scrutiny. Similar distributions have been identified for comparable
repeatability assessments of photogrammetric dDSMs used for mapping snow
depth (Nolan et al., 2015), but have not been explored in detail. Analysing
the variability of the mean and standard deviation of the residual for discrete classes of slope, as well
as the kurtosis of the residual distribution,
provided insight into the role of terrain. For classes of slope up to
65
The observed pattern in the mean and standard deviation of the residual
indicates that larger and more variable errors are associated with steeper
slopes. Reduced kurtosis accompanying the error distribution on larger slopes
(Fig. 6) reveals a tendency towards a Gaussian distribution of residuals as
mean slope increases. Here, for slopes
Observed (calculated under Gaussian assumption) and fitted normal
and
The semi-variograms for RPAS-derived snow depth, compared to that from the reference measurements, are shown Fig. 8. They exemplify the new insight that high-resolution mapping provides into the spatial variability of snow depth. Both the 1000 and 5000 random point samples captured a comparable structure of spatial auto-correlation with a range of ca. 40 m. The 5000-point sample improved the resolution of the semi-variogram, with an improved signal-to-noise ratio. In contrast, the reference data, despite being demanding in fieldwork, performed poorly at capturing the spatial variability, as most measurements were separated by a minimum distance of 50 m. A lack of spatial auto-correlation in the reference data confirms a posteriori that probing samples could be assumed to be independent of each other, which is desirable for the accuracy assessment. Additionally, it also reveals that probing failed to capture most of the spatial structure of the snow depth field, thus stressing a limitation of this classical method to characterise the snowpack.
Overall, RPAS photogrammetry is found to be suitable for determining snow
depth via DSM differencing. Primarily, the achievement of uncertainties
Mapping snow depth continuously at 0.15 m resolution, across an entire hydrological catchment, represents a new contribution to the quantification and characterisation of spatial variability in snow depth on this scale, which is up to 2 orders of magnitude greater than many similar studies to date. Before considering the broader implications of this in terms of snow processes, uncertainty, limitations and pitfalls of the approach are considered.
Vegetation contributes to uncertainty, particularly when validating RPAS-derived snow depths against reference snow depths. As described in Sect. 4.2.2, the agreement between RPAS-derived and probed snow depths improved substantially when areas of large tussock vegetation were excluded. It is likely that the presence of tussock introduces a bias into the snow depth measurement, whereby a probe may penetrate the tussock foliage, and possibly also a sub-vegetation void, before striking the ground surface. This is similar to the cavity effect highlighted for airborne lidar measurement of snow (Painter et al., 2016), and similar challenges have been documented by Vander Jagt et al. (2015). High-resolution dDSMs, on the other hand, resolve the vegetation surface, and so vegetation height is inherently better accounted for.
As identified by Nolan et al. (2015), photogrammetrically derived snow depths may also be affected by the compaction of vegetation below the snowpack, which may introduce an anomalous signal of surface height change, to the point of returning false negative snow depths. Correcting observed surface height change would not be straightforward, and is not possible with the data acquired within this study. The effects of vegetation compaction are likely to be greatest in the early winter. As grass typically does not rebound until after the complete removal of the winter snowpack, ongoing subsidence of vegetation below the snowpack through midwinter and spring is expected to be minimal. Ongoing future measurement of snow depth via surface differencing (regardless of the source of DSMs) will benefit from the development and incorporation of vegetation compaction and cavity models.
Ultimately, this study suggests that, for areas dominated by tussock vegetation, RPAS photogrammetry may provide a more reliable means of measurement than probing. A lack of knowledge regarding the specific location of sub-snow vegetation when making measurements by probing is likely to provide a systematic overestimation of snow depth (Fig. 4). In the New Zealand context, almost all seasonal snow occurs above the treeline, so the inability of photogrammetry to penetrate the forest canopy is a lesser concern than for the Northern Hemisphere.
The vertical residual between two elevation profiles, extracted from
the same DSM, along a common transect and offset horizontally by
0.5 m
In mapping snow depth across a catchment with relatively complex terrain, we
have been able to characterise the influence of terrain on dDSM uncertainty.
The assumption that error associated with physical measurements is normally
distributed and often underpins subsequent statistical inferences. As
demonstrated in Sect. 4.2.3, the error associated with the bias between
independently acquired DSMs significantly departed from normal and was
better approximated by the Student's
Consistent with Kääb (2005), the vertical error introduced by a
uniform, one-dimensional (e.g. horizontal) offset, is given by the following:
Complicating this effect is the fact that co-registration uncertainty exists in two dimensions. Subsequently, it will become dependent on aspect as well as slope (Nuth and Kääb, 2011), with neither possessing a uniform spatial distribution. This effect is expected to be more pronounced with very high-resolution (i.e. sub-metre) surface models due to a greater frequency and magnitude of breaks in surface slope being resolved compared to coarser models. The modification of surface slope for constituent DSMs (e.g. through the addition of snow) further convolves the propagation of vertical uncertainty. Despite this, the leptokurtic observed error distribution indicates that the reliance on statistics that assume a Gaussian distribution of errors will provide an overestimated characterisation of the expected accuracy. Overestimation of uncertainties may in turn affect statistical inferences and the computation of uncertainties on derived parameters.
The convolution of vertical and planimetric accuracy stresses the importance of ensuring a robust AT and the benefits of utilising high-quality ground control. With new photogrammetric platforms leveraging non-metric cameras and resulting image blocks prone to suboptimal photogrammetric modelling (Sirguey et al., 2016), there is a need to be wary of systematic bias or spatial structure in the distribution of errors, which may not be revealed readily by residuals from the AT alone. These considerations are especially important where a relatively high level of precision is required, and the signal-to-noise ratio may be low when assessing relatively subtle surface height and/or volume changes from dDSMs. Utilising independent ATs as the control of co-registration quality, rather than explicitly co-registering DSMs, has the further advantage of simplifying the processing chain from data acquisition to change detection, mitigating against the risk of introducing gross error when co-registering DSMs and avoiding the need for snow-free (or stable) reference areas within the analysis region.
Initial processing using the photogrammetry module of Trimble Business Center (v3.40) produced strong striping artefacts in the dDSM. Striping involved a periodic bias in surface height change, aligned with the 15 image strips. This was readily revealed because identical flight plans between successive surveys made constructive errors obvious, rather than convoluted with terrain variability. This systematic error was severe and problematic, particularly when considering the surface change resulting from the addition of snow cover to the ground. Extensive snow cover concealed stable references, precluding characterisation of the error and its empirical removal from the real signal of surface height change (e.g. Albani and Klinkenberg, 2003; Berthier et al., 2007). Products derived using UAS Master (v8.0) did not exhibit such artefacts, allowing the potential source of error associated with AT from TBC to be investigated.
The absence of systematic bias in dDSMs derived using UAS Master indicates a more reliable AT. Thus, the UAS Master triangulation provided a reference surface for further exploration of the nature of the bias propagated in the TBC triangulation. Comparisons from the winter flight are presented here. The nature of the photogrammetric problem described in Sect. 3.2.1 dictates that small errors in the interior orientation and/or the rotational components of the exterior orientation can result in large, spatially structured errors in the adjusted image block (Sirguey et al., 2016).
Cimoli et al. (2017) reported an improved performance in mapping snow depth with the application of a radial lens distortion correction. In our case, no significant difference was detected between the distortion models provided for each of the two software calibrations of the same camera, for the same flight. (Fig. 11a). Minimal divergence in lens distortion was observed beyond 10 mm radius, reaching 1 % at 14.5 mm. Agreement between lens distortion models indicated that differing interior orientation solutions between TBC and UAS Master were not the source of the artefacts seen in products of the TBC triangulation.
Since the observed artefact was propagated along the flight lines, the roll
parameter (
The impact of bias in
The observed propagation reinforces the need for vigilance when working with such data sets, particularly those delivered from “off the shelf” photogrammetry packages, which are becoming increasingly popular. Artefacts such as the striping identified here, and evidence of non-optimal AT, are likely to be less obvious as the complexity of the mapped terrain increases. As RTK GPS-equipped RPAS become more common, increased precision of initial AT parameters may mitigate the risk of error introduced by spurious solutions for refined parameters. Currently, however, RTK systems have an increased power demand, which can substantially reduce the flight time.
Map of the systematic artefacts in surface height change (dh)
(expected to represent snow depth), propagated when differencing digital
surface models (DSMs) resulting from aerial-triangulation in TBC v3.40
Comparison of lens distortion characterised by individual
triangulations of data from the same flight carried out in two different
software packages, TBC and UAS Master
Figure 8 demonstrates the new insight that RPAS photogrammetry can provide over probing for resolving spatial variability in snow depth, particularly on fine scales. Therefore, RPAS photogrammetry can provide a basis for improving spatially distributed snowpack models. In turn, this contribution will further improve understanding of seasonal snow processes, where there has been a dependency on point-based observations over glaciers to characterise atmospheric controls on seasonal snow (e.g. Cullen and Conway, 2015). While knowledge of the atmospheric controls on ablation processes has improved (Conway and Cullen, 2016), our understanding of the redistribution of snow and preferential accumulation have not kept pace. RPAS photogrammetry represents a valuable avenue for determining how these processes are represented in existing and new snow and glacier models, which will enable short-term hydrological forecasts and climate projections in snow-covered areas to be improved. Such data can also facilitate the use of geostatistical approaches for examining controls on spatial distribution of snow, such as that applied to the Brewster Glacier, New Zealand (Cullen et al., 2017). In this case, the density of measurements provides insights into spatial variability on scales that would allow consideration of terrain and meteorological controls on snow distribution on micro-scales, extending understanding beyond the spatial co-variance between snow depth and elevation.
The ability to resolve fine-scale variability reliably from continuous raster snow maps lessens the dependence on interpolation through areas of sparse data for interpreting controls on spatial distribution of snow. While previous studies have been able to correlate between snow and terrain properties (e.g. Anderson et al., 2014), such studies rely on the inference of catchment-scale processes from transect-scale observations. The ability to produce spatially continuous maps of snow depth across an entire catchment at a resolution of 0.15 m bridges this gap and reduces the reliance on inferences when scaling up from point- or transect-based in situ observations to catchment-scale processes. Such data sets provide an opportunity to build on previous work in understanding the relationships between snow redistribution, preferential accumulation and ablation, terrain and meteorology (Winstral et al., 2002, 2013; Webster et al., 2015; Revuelto et al., 2016). While RPAS photogrammetry is severely limited in spatial scale compared to airborne lidar, resolving snow depth in this way across an entire catchment facilitates robust integration into hydrological models, enhanced by validation against catchment discharge (e.g. from streamflow data).
Schematic of the relationship between height (
The mapping of snow depth effectively provides a volumetric view of the
snowpack across the catchment (i.e. depth
This study has demonstrated that RPAS photogrammetry provides a suitable, repeatable means of reliably determining snow depth in an alpine catchment of low relief that possesses some terrain complexity. Achieving decimetre-level accuracy for measuring snow depth provides a basis for monitoring seasonal snowpacks and associated processes, especially considering the capacity to provide very high-resolution, spatially continuous measurements across an entire hydrological catchment. This ability to characterise the seasonal snowpack will provide an important stepping stone for improved modelling of seasonal snow and associated processes, especially through accurate mapping of an entire hydrological catchment.
Challenges encountered through this deployment provide important points for consideration in this and other applications of close-range photogrammetry, especially from RPAS platforms, for surface and volume change analysis. Specifically, a small but persistent bias in photogrammetric solutions for the roll parameter exemplifies the possibility of suboptimal solutions in processing software. Such a bias can introduce substantial systematic errors which may be difficult to correct and can compromise further analysis.
We show that uncertainty analysis from the AT only, based on a limited number of check points, may underestimate the uncertainty. Alternatively, an assessment of repeatability of photogrammetric modelling on stable ground can support a more detailed uncertainty analysis. It reveals, however, that the statistical distribution of the error of differentiated surface models is more complex than normal and governed by terrain parameters. The leptokurtic residual distribution demonstrates that an assumption of Gaussian law can substantially overestimate confidence intervals, in turn compromising inferences. This result has important practical applications for the computation of uncertainties in studies that characterise volume change from repeated surface modelling.
Finally, there is scope to further refine the characterisation of uncertainty associated with RPAS photogrammetry in order to ensure that all potential sources of error are captured, and that statistical analysis is appropriate to the distributions within underlying data. Existing methods for mitigating the impact of co-registration uncertainty of coarser products may permit modelling and correction of such errors in the very high-resolution products that are now available.
The data used in this research are available on request from Todd A. N. Redpath.
TR and PS designed the study and collected the data. TR processed and analysed the data and wrote the manuscript with input from PS and NC. PS and NC supervised the research.
The authors declare that they have no conflict of interest.
The authors are grateful to those who provided assistance in the field: Julien Boeuf, Kelly Gragg, Mike Denham, Craig MacDonell, Aubrey Miller, Sam West, Thomas Ibbotson and Alia Khan. Sean Fitzsimons provided helpful feedback on the draft manuscript. This research was carried out under the Department of Conservation Research & Collection Authorisation 53609-GEO. This research was funded by a University of Otago Doctoral Scholarship with support from the Department of Geography and an internal grant of the National School of Surveying, as well as a fieldwork grant from the New Zealand Hydrological Society. The authors thank the editor, Martin Schneebeli, and two anonymous reviewers, whose thorough and thoughtful comments improved this manuscript. Edited by: Martin Schneebeli Reviewed by: two anonymous referees