Remote Sensing of Environment 141 (2014) 105–115
Contents lists available at ScienceDirect
Remote Sensing of Environment
journal homepage: www.elsevier.com/locate/rse
Quantifying spatial distribution of snow depth errors from LiDAR using
Random Forest
Wade T. Tinkham a,⁎, Alistair M.S. Smith a, Hans-Peter Marshall b, Timothy E. Link a,
Michael J. Falkowski c, Adam H. Winstral d
a
Department of Forest, Rangeland, and Fire Sciences, College of Natural Resources, University of Idaho, 975 W. 6th St., Moscow, ID 83844-1133, USA
Center for Geophysical Investigation of the Shallow Subsurface, Boise State University, Boise, ID 83725, USA
Department of Forest Resources, University of Minnesota, St. Paul, MN 55108, USA
d
Northwest Watershed Research Center, Agricultural Research Service, Boise, ID 83712, USA
b
c
a r t i c l e
i n f o
Article history:
Received 20 November 2012
Received in revised form 29 October 2013
Accepted 30 October 2013
Available online 23 November 2013
Keywords:
LiDAR
Snow
Snow depth
Snow volume
Random Forest
a b s t r a c t
There is increasing need to characterize the distribution of snow in complex terrain using remote sensing
approaches, especially in isolated mountainous regions that are often water-limited, the principal source of
terrestrial freshwater, and sensitive to climatic shifts and variations. We apply intensive topographic surveys,
multi-temporal LiDAR, and Random Forest modeling to quantify snow volume and characterize associated errors
across seven land cover types in a semi-arid mountainous catchment at a 1 and 4 m spatial resolution. The LiDARbased estimates of both snow-off surface topology and snow depths were validated against ground-based
measurements across the catchment. LiDAR-derived snow depths estimates were most accurate in areas of
low lying vegetation such as meadow and shrub vegetation (RMSE = 0.14 m) as compared to areas consisting
of tree cover (RMSE = 0.20–0.35 m). The highest errors were found along the edge of conifer forests
(RMSE = 0.35 m), however a second conifer transect outside the catchment had much lower errors
(RMSE = 0.21 m). This difference is attributed to the wind exposure of the first site that led to highly variable
snow depths at short spatial distances. The Random Forest modeled errors deviated from the field measured
errors with a RMSE of 0.09–0.34 m across the different cover types. The modeling was used to calculate a
theoretical lower and upper bound of catchment snow volume error of 21–30%. Results show that snow drifts,
which are important for maintaining spring and summer stream flows and establishing and sustaining waterlimited plant species, contained 30 ± 5–6% of the snow volume while only occupying 10% of the catchment
area similar to findings by prior physically-based modeling approaches. This study demonstrates the potential
utility of combining multi-temporal LiDAR with Random Forest modeling to quantify the distribution of snow
depth with a reasonable degree of accuracy.
© 2013 Elsevier Inc. All rights reserved.
1. Introduction
A direct result of climate warming in mountainous regions of North
America has been an accelerated arrival of spring temperatures and an
approximate one-third reduction in mountain snowpack water storage
that directly reduces summer downstream water availability (Cayan,
Kammerdiener, Dettinger, Caprio, & Peterson, 2001; Mote, Hamlet,
Clark, & Lettenmaier, 2005). As a result, predicted future shifts in the
timing of spring thaw or precipitation phase (i.e. snow vs. rain) have
important implications for water and land management (Elsner et al.,
2010). Spatial and temporal heterogeneity of snow and specifically the
variability in snow depth and density have been identified as key
variables to determine hydrologic budgets and regimes (NRC, 2010);
especially in complex terrain that is the source of many of the world's
rivers. However, snow depth and snow water equivalent (SWE) have
⁎ Corresponding author. Tel.: +1 208 885 6327.
E-mail address: [email protected] (W.T. Tinkham).
0034-4257/$ – see front matter © 2013 Elsevier Inc. All rights reserved.
http://dx.doi.org/10.1016/j.rse.2013.10.021
proven to be two of the most difficult variables to accurately quantify
at scales larger than in situ measurement points (b 1 m2) (Anderton,
White, & Alvera, 2004; Molotch & Bales, 2005), but are frequently
needed at larger scales (e.g. Meromy, Molotch, Link, Fassnacht, & Rice,
2013). Active remote sensing has demonstrated the potential to characterize these properties over extended spatial (N km2) and temporal
scales (e.g., Dozier, Green, Nolin, & Painter, 2009; Hopkinson, Collins,
Anderson, Pomeroy, & Spooner, 2012; Nolin, Dozier, & Mertes, 1993;
and others), however limited research has investigated the accuracies
and sources of uncertainty with using these methods. An equal
challenge is the creation of reference datasets for testing the accuracy
of derived products and datasets (Tinkham et al., 2013).
The use of both active and passive remote sensing to characterize
and quantify the spatial heterogeneity of snow properties has been
widespread since the 1980s (Carsey, 1992; Dozier et al., 2009;
Hopkinson et al., 2012; Nolin et al., 1993; Painter, Dozier, Roberts,
Davis, & Green, 2003; Pietroniro & Leconte, 2005; Trujillo, Ramirez, &
Elder, 2007). Passive hyperspectral platforms and satellite sensors
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W.T. Tinkham et al. / Remote Sensing of Environment 141 (2014) 105–115
such as Landsat and MODIS have been used to map snow surface
properties such as snow cover and grain size (Dozier, 1989; Painter
et al., 2003). However, studies characterizing three-dimensional
properties of the snow pack have been limited, with several studies
highlighting the need for higher spatial resolution data to accurately
represent the complex spatial patterns of snow (Blöschl & Sivapalan,
1995; Dozier et al., 2009; Nolin et al., 1993; Painter et al., 2003). Active
remote sensing platforms such as Light Detection and Ranging (LiDAR)
and Synthetic Aperture Radar (SAR) are being explored and tested for
their ability to estimate snow depth and SWE (Deems & Painter, 2006;
Hopkinson, Pomeroy, Debeer, Ellis, & Anderson, 2010; Rango, 1993). A
challenge that has been widely noted in both the scaling up from
point observations and the remote sensing of snow properties is the
ability to relate measurements of snow depth to SWE, which is informative but is less frequently measured due to the effort required (Liston &
Elder, 2006; Sturm et al., 2010). This can be particularly difficult in
heterogeneous landscapes where terrain, vegetation, and hydrometeorological variability can cause large variations in the relationship
between snow depth and density across short temporal and spatial
scales (Winstral and Marks, unpublished data). The preferential deposition and redistribution of snow through interactions with wind and
topography (Liston et al., 2008; Pomeroy et al., 1998; Winstral, Elder,
& Davis, 2002), and forest canopies (Pomeroy et al., 1998; Storck et al.,
2002) can lead to heterogeneous patterns of snow depth. However, airborne LiDAR has been demonstrated as a useful tool to provide
spatially-explicit snow depth and volume distribution information
(Dadic, Mott, Lehning, & Burlando, 2010; Deems, Fassnacht, & Elder,
2006; Hopkinson et al., 2001) and to quantify snow depth within catchments (Cavalieri et al., 2012; Cline et al., 2009; Hopkinson, Sitar,
Chasmer, & Treitz, 2004; Hopkinson et al., 2010). Recently these
approaches have been reaffirmed by the use of Terrestrial Laser
Scanning (TLS) systems for understanding fine spatial and temporal
scale process variability such as snow ablation and depth (Egli, Jonas,
Grunewald, Schirmer, & Burlando, 2012; Grünewald, Schirmer, Mott,
& Lehning, 2010; Grünewald et al., 2013; Schirmer, Wirz, Clifton, &
Lehning, 2011).
Paired multi-temporal airborne LiDAR acquisitions collected near
peak snow accumulation and during snow-free conditions have the
potential to provide sub-meter resolution estimates of snow depth at
catchment-wide scales and has been used to infer catchment level
snow volume and snow water equivalent (Hopkinson et al., 2010;
Nolin, 2010). One of the inherent benefits of LiDAR data is that it is
a-spatial, meaning that the spatial resolution of LiDAR-derived products
is arbitrary and dependent on the density of data collected and accuracy
of interpolation methods. This resolution is also controlled by the
computational limitation that can be encountered when producing
fine resolution products (1 m or less) that require multiple inputs.
The application of multi-temporal LiDAR for the purpose of estimating
snow depths at landscape scales is not a new concept (Dadic et al.,
2010; Hopkinson et al., 2001, 2012). Studies have coupled snow-on
LiDAR acquisition with other geospatial data to estimate snow depth
on sea ice (Leuschen et al., 2008; Varbai & Cahalan, 2007). Dadic et al.
(2010) used helicopter-based LiDAR to map snow depths of the Haut
Glacier d' Arolla glacier basin to compare against snow redistribution
models. The latter study used identical acquisition and processing
procedures and took advantage of modern LiDARs capability to be interpolated at any spatial resolution (c.f. Evans, Hudak, Faux, & Smith, 2009;
Hudak, Evans, & Smith, 2009), the data was used to produce 10 m snow
depth contours for validating snow models (Dadic et al., 2010). The
NASA Cold Land Processes Experiment (CLPX 2002/03) acquired
LiDAR datasets for estimating snow depth at high resolution, and several
studies used these data to quantify and study snow distribution and
variability in six different 1 km2 regions in Colorado (Cline et al., 2009;
Deems et al., 2006; Deems, Fassnacht, & Elder, 2008; Fassnacht &
Deems, 2006; Trujillo et al., 2007, 2009). The recent development of
the JPL Airborne Snow Observatory which has just completed the
first year of a three-year demonstration mission utilized scanning
LiDAR to map weekly snow depth over two mountain watersheds
in California and Colorado (http://www.jpl.nasa.gov/news/news.
php?release=2013-154).
Several of these studies had to overcome limitations including
inconsistent LiDAR acquisition parameters or processing methods
between two acquisitions (Hopkinson et al., 2001, 2004), limited
snow depth validation data (Fassnacht & Deems, 2006), and multitemporal datasets that do not share 100% coincident coverage (Banos,
Garcia, & Alavedra, 2011; Hopkinson et al., 2012). To overcome these
sub-sampling challenges, Banos et al. (2011) used LiDAR and aerial
photography in a catchment in the Eastern Pyrenees in an attempt to
estimate snow depth. However, the two LiDAR acquisitions only overlapped by 15% and used distributed snow modeling to simulate the
depths across the rest of the catchment. Similarly, Hopkinson et al.
(2012) utilized strips of snow-on LiDAR data that were partially coincident with a prior LiDAR snow-off acquisition to model land surface
classes and derive an estimate of catchment SWE. One of the greatest
challenges highlighted in past studies is the need to accurately
georeference the snow-on and snow-off LiDAR surfaces as small errors
in referencing can potentially lead to significant snow depth errors,
especially in areas of high slope (Hopkinson et al., 2001, 2012).
Fig. 1. Interaction of surface features (topography/vegetation) and LiDAR surface errors (±e) with errors in snow depth (d). (A) Snow-laden canopies limit LiDAR pulse penetration leading to elevated surfaces. (B) Tree-well depressions are difficult to detect or interpolate leading to overestimates of snow volume. (C) Total surface error greater in shallow (b0.25 m) snow
depths: small snow filled depressions may not be recorded if snow depth is within error of combined surface. (D) Matted vegetation layers can prevent surface returns, creating an
elevated false snow-off ground surface with associated upper bound error. In some vegetation types, this matted vegetation form can in-fill with snow. (E) Rocky outcrops with large
sudden drop-offs (N1 m) can (i) interact with wind to produce drifts and (ii) exhibit considerable snow-off interpolation errors.
W.T. Tinkham et al. / Remote Sensing of Environment 141 (2014) 105–115
107
vegetation (e.g. ceanothus; Fig. 2D). This matted vegetation type can
form an expansive dense vegetative mat, causing LiDAR surface errors
as very few pulses penetrate the matted layer to produce actual ground
returns (Gould, Glenn, Sankey, McNamara, & Spaete, 2013; Hopkinson
et al., 2004; Tinkham et al., 2011). A final potential source is related to
surface interpolation errors around rocky outcrops, which can lead to
high LiDAR surface errors masking buildups of snow on leeward sides
(Fig. 1e). Each of these potential sources of error can be magnified,
especially on steep slopes, if careful attention is not paid to ensuring
adequate co-registration of the two surfaces.
The objectives of this study are to: (i) Assess the utility of multitemporal LiDAR acquisitions to quantify the spatial distribution of
snow depth within a heterogeneous landscape, and (ii) Use these data
alongside the Random Forest algorithm (Breiman, 2001) to further
understand the controls of vegetation and topographic features
on errors in LiDAR estimated snow volume at catchment scales
(10–100 ha). Coincident field snow survey data collected on the same
date as the snow-on LiDAR data acquisition were used to validate the
depth derived from the multi-temporal LiDAR data. Snow-on, snow-off,
and error surfaces were produced at both 1 and 4 m resolution to
evaluate the tradeoff in resolution with computational strain.
2. Methodology
2.1. Study site
Fig. 2. Reynolds Creek Mountain East study area map showing (A) seven cover types
spatially distributed across the catchment, (B) NAIP aerial photography with location of
99 high-precision ground survey plots, and (C) LiDAR-derived digital elevation map and
contour map showing the variability of terrain form.
Past investigations have both observed and speculated that several
sources of error unique to snow covered landscapes can arise through
the interaction of the LiDAR pulses with topography and vegetation
(Fig. 1). These represent sources of error that are independent of the
sensor acquisition parameters. Although not an issue in the present
study, snow-laden conifer canopies can often present challenges in the
classification of LiDAR point returns by preventing pulses from reaching
the surface (Fig. 1A). Tree-wells in conifer systems (Fig. 1B), which are
deep snow surface depressions (typically on the order of 1–2 m) caused
by snow interception and longwave radiation emission from tree boles
and which sometimes extend to the ground surface, pose an additional
problem in the interpolation of LiDAR points. This is because pulses are
less likely to penetrate to the base of some of the denser conifer crowns.
Along with the influence that tree canopy interception can have,
redistribution of snow released from tree canopies can lead to large
variations in snow depth over short (1–2 m) distances (Hardy et al.,
1997). Attenuated snow depth errors (±d) are apparent due to surface
co-registration problems that can arise on scour locations and steep
slopes that contain little or no snow at the time of both acquisitions
(Fig. 1C). These problems occur within surface depressions and other
features that contain small amounts of snow, but where the observed
depth is less than the combined LiDAR surface error. Another potential
source of error is in areas comprised of low-lying densely matted
This study was conducted in the Reynolds Mountain East (RME)
catchment, which is a 38 ha catchment, located at latitude 43° 5′ N,
longitude 116° 45′W. The catchment is part of the greater Reynolds
Creek Experimental Watershed, which is maintained as a hydrometeorological research site by the USDA Agricultural Research Service,
Northwest Watershed Research Center. The catchment has a general
northerly aspect, with a mean slope of 8° (σ = 4.5) but reaching 30°
in isolated locations and elevations ranging from 2023 to 2142 m
(Fig. 2). The landscape mosaic is dominated by a shrub-steppe cover
type (mountain big sagebrush, Artimesia tridentata Nutt. ssp. vaseyana
and mountain snowberry, Symphoricarpos oreophilus Gray) but with
large patches of meadow (Lupinus ssp., Carex ssp., and Poa ssp.) and
bare-ground, and homogenous coniferous and deciduous tree stands
(Douglas-fir, Pseudotsuga menziesii, quaking aspen, Populus tremuloides)
occurring in topographically sheltered portions of the catchment. The
creek side is lined by Salix spp. and there are small patches of ceanothus
(Ceanothus prostrates Benth.; Fig. 2). The diverse mix of cover types,
radiation regimes, and topographic sheltering within a relatively small
area makes this site a perfect location to evaluate the performance of
remote sensing methods across a variety of vegetation classes.
2.2. LiDAR acquisitions
Two airborne discrete return LiDAR acquisitions were obtained from
the same vendor, with the same instrumentation and acquisition
parameters. The data were acquired by the same vendor, with postprocessed using the same methods and parameters on both datasets
(as outlined below). This consistency of methods is not only a fundamental requirement of multi-temporal remote sensing but was essential to minimize the influence of both sensor acquisition and
processing parameters on the understanding of the subsequent uncertainties within the produced multi-temporal datasets. The snow-off
dataset was acquired in mid-November 2007 and the snow-on dataset
was acquired on March 19, 2009 to approximately coincide with the
historic peak snow pack accumulations given the obvious logistical
constraints. Each acquisition used a Leica ALS50 Phase II Laser, operating
at 1064 nm with up to 4 returns per pulse recorded and was flown at
approximately 900 m above ground level (agl). The data was acquired
with a 50% flight line overlap and had a nominal pulse density of
6 pulses m − 2 , with an off nadir scan angle of ± 15°. The vendor
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W.T. Tinkham et al. / Remote Sensing of Environment 141 (2014) 105–115
Table 1
Comparison of DTM vertical accuracy utilizing both a surface produced from a single primary filtering and a surface produced following a secondary filtering. These are further
compared to the surface accuracies reported by Tinkham et al. (2011).
RMSE (m)
RMSE (m) from Tinkham
et al. (2011)
Cover type
Primary filtering
Secondary filtering
Cover type
BCAL
MCC
Aspen
Ceonothus
Conifer
Forb
Bare ground
Shrub
Overall
0.210
0.317
0.366
0.140
0.470
0.296
0.297
0.188
0.328
0.259
0.124
0.452
0.261
0.264
Aspen
Ceanothus
Conifer
Forb
Bare ground
Shrub
Overall
0.190
0.126
0.249
0.130
0.507
0.268
0.273
0.193
0.412
0.292
0.131
0.467
0.268
0.280
performed flight line calibration and tiling of the raw LiDAR data using
the TerraScan and TerraMatch software, respectively (Terrasolid Ltd.,
Jyväskylä, Finland). Absolute vertical accuracy for the snow-off and
snow-on acquisitions was reported by the vendor as 3.3 and 3.7 cm
root mean square error (RMSE) respectively, these were based on
1002 and 323 real time kinematic (RTK) global positioning system
(GPS) points surveyed on gravel road surfaces at the lower elevations
of the watershed. This represents the RMSE of the point elevations
within the point cloud. The low vertical accuracy of the acquisition is
attributed to GPS base stations being installed on a ridgeline at the
southern end and valley bottom at the northern end of the study
site during the acquisition. Along with the xyz coordinates, GPS time,
intensity, and scan angle were also recorded for each return. Data
were projected into the horizontal datum and projection of NAD83
UTM Zone 11 North and the vertical datum of NAVD88.
For each acquisition, the Multi-scale Curvature Classification LiDAR
algorithm (MCC: Evans & Hudak, 2007) was used to classify the raw
LiDAR point cloud into ground and non-ground returns using parameters from a prior study (Tinkham et al., 2011). This prior study within
the catchment cross-compared two commonly applied LiDAR surface
generation algorithms (MCC and the BCAL algorithm; Streutker &
Glenn, 2006) and demonstrated that minimal difference in accuracy
was observed between each approach. Overall, for the cover types
found within our study area the MCC approach indicated a marginal improvement within the dominant cover types and thus was selected
(Tinkham et al., 2011, 2013). To further improve on the MCC accuracy
we explored the use of both optimized MCC scale and curvature parameters and a secondary filtering, where the MCC algorithm is reapplied to
solely the ground points identified by the initial MCC application
(Tinkham et al., 2012). This refinement of the MCC parameters and
the additional step of the processing led to marginal improvements in
accuracy within all catchment cover types (Table 1).
Across the entire catchment, the LiDAR derived DEM had a mean
vertical RMSE of 29 cm, but this error varied by cover type and topographic features (Tinkham et al., 2011). This error is partially attributed
to the acquisition measurement and subsequent classification and interpolation errors. The snow-on and snow-off point clouds were interpolated with a thin-plate spline to produce both 1 and 4 m surfaces that
were then differenced to create spatially explicit snow depth maps
(Fig. 3). The surfaces were assessed for co-location errors by verifying
the vertical and horizontal position of a weather station and support
cabin at opposite sides of the catchment, this process revealed horizontal
and vertical differences less than 4 cm. With the level of co-registration
error being less than the combined point cloud absolute error provided
by the vendor, the surfaces were not adjusted. In order to correct for
classification and interpolation induced errors, negative snow depths
(0.00–0.10 cm), which typically occurred on a windswept ridge that
was observed to be snow free on the date of the acquisition and only
accounted for approximately 0.1% of the catchment, were corrected
manually to a depth of 0.00 cm. Further, for snow depths b0.10 cm
and for isolated outlier snow depths N4 m (of which there were b30
cells), the average of the surrounding cells was assigned. From these
spatially explicit maps, snow volume was computed by multiplying the
snow depth by the grid cell dimensions.
2.3. Error accounting
In the summer of 2009, a total of 99 high-precision ground survey
plots (0.5 m point spacing on a square grid: Tinkham et al., 2011)
Fig. 3. (A) LiDAR-derived snow depth map with locations of manual snow depth transects, illustrating the heterogeneous nature of snow distribution within the catchment, and (B)
Random Forest regression predictions of spatially explicit LiDAR DEM vertical error. 1 m LiDAR-derived maps are on the left, with 4 m maps on the right.
W.T. Tinkham et al. / Remote Sensing of Environment 141 (2014) 105–115
Table 2
List of variable derived from LiDAR point cloud at 1 and 4 m resolution for use in Random
Forest modeling. The five variables identified as important in the final 1 m model are
identified with ‡, while the four important variable in the final 4 m model are identified
with ⁎.
Variable
Metric name
Metric description
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
MinHeight
MaxHeight
RangeHeight
MeanHeight
ModeHeight
StDevHeight
VarHeight
CVHeight
InterQuartHeight
KurtosisHeight
SkewnessHeight
ADDHeight
#1Returns
#2Returns
#3Returns
#4Returns
TotalReturns
‡
PCT1
PCTothers
PCT1AB0.1
PCTothersAB0.1
‡
PCTABMean
PCTABMode
PCT5Height
⁎ PCT10Height
⁎ PCT25Height
⁎ PCT50Height
PCT75Height
PCT90Height
PCT95Height
NormAspect
‡⁎
PlanCurve
‡
ProCurve
‡
Slope
Minimum Return Height
Maximum Return Height
Range of Heights
Mean of Heights
Mode of Heights
Standard Deviation of Heights
Variance of Heights
Coeficient of Variation of Heights
Inter-Quartile Range of Heights
Kurtosis of Heights
Skewness of Heights
Mean Absolute Deviation Height
Number of 1st Returns
Number of 2nd Returns
Number of 3rd Returns
Number of 4th Returns
Total Returns
Percentage 1st Returns
Percentage not 1st Returns
Percentage 1st above 0.10 m
Percentage not 1st above 0.10 m
Percentage Returns Above Mean
Percentage Returns Above Mode
5th Percentile of Heights
10th Percentile of Heights
25th Percentile of Heights
50th Percentile of Heights
75th Percentile of Heights
90th Percentile of Heights
95th Percentile of Heights
Normalized aspect
Curvature Perpendicular to Slope
Curvature Parallel to Slope
Slope in Degrees
109
predicted the LiDAR error across the bare ground DEM. Optimal subsets
of variables were selected for use in the prediction of vertical DEM error,
to produce the most parsimonious and accurate model. Subsets were
derived by iteratively running the RF algorithm and selecting the
model that provided the highest accuracy but used the fewest predictor
variables as identified by a Model Improvement Ratio (MIR) (Falkowski,
Evans, Martinuzzi, Gessler, & Hudak, 2009; Murphy, Evans, & Storfer,
2009). The MIR procedure takes the mean decrease in the MSE,
standardized from zero to one to indicate variable importance. From
predefined threshold levels, model variables are then selected, with all
variables above the threshold retained in each iterative model. From
these candidate models the final model was determined based on
the smallest mean square error of prediction and largest percentage
variation explained.
Before running the model selection procedure, a screening process
based upon Gram-Schmidt QR-Decomposition was used to remove
multi-collinear predictor variables (Gentle, Hardle, & Mori, 2005;
Golub & Van Loan, 1996). The regression models came from 5000 bootstrap replicates of the calculated plot level MSE training dataset
(n = 99) with replacement using a 36% data-withhold sample. With
each of the bootstrap replicates producing an individual tree against
which the data-withhold sample is then used in the calculation of the
mean squared error (MSE) at each node and within the tree. Overall
error and accuracy of the model was calculated by averaging error
rates across all trees in the forest; this is similar to estimating error
and accuracy through a cross-validation procedure (Cutler et al., 2007).
From the final RF models, spatially explicit predictions of LiDARderived DEM vertical MSE were generated across the catchment using
the AsciiGridPredict function of the yaImpute package within the R
statistical software program (Crookston & Finley, 2008). These spatial
maps of predicted LiDAR vertical errors were then converted to RMSE,
as this is the more common statistic used when reporting LiDAR
accuracy (Fig. 3).
2.4. Snow depth and volume validation
were stratified by cover and terrain type to capture the variability that
topography and vegetation have on the accuracy of LiDAR derived
surface (Fig. 2). The 0.5 m survey point spacing was selected to produce
a validation dataset of higher point spacing and precision then the
LiDAR dataset. Each survey plot was conducted over a 16 m2 area and
was then sampled to correspond to a 1 × 1 m and 4 × 4 m grid spacing,
with 9 points/m2, allowing the LiDAR to be assessed at two resolutions.
Each plot was surveyed using a Topcon GTS-236w laser total station that
had been georefenced using both a Topcon Hyper-pro real-time kinematic (RTK) global positioning system (Topcon Corp., Livermore, CA,
USA) and USGS monuments. Vertical and horizontal precision of the
RTK was 15 and 10 mm, respectively, with the survey points estimated
to be within 2–3 cm horizontally and vertically. For each plot, all survey
points were differenced from the snow-off LiDAR-derived DEM to
determine error, the errors were squared and all points were averaged
to determine the mean squared error (MSE) of the plot. Although less
commonly applied, MSE is the appropriate statistic to use in this case
as it can be estimated without bias using the point data. In order to
account for the error associated with the LiDAR-derived estimates of
snow depth, a spatially explicit map of LiDAR DEM vertical error was
developed using the survey plot MSEs (n = 99) at both a 1 and 4 m
grid scale, along with thirty-four variables derived from the snow-off
LiDAR point cloud (Table 2) within a regression using the Random
Forest algorithm (Breiman, 2001). Random Forest is an ensemble
regression that consists of multiple decision trees, outputting the
unweighted average over the forest. This was performed by running a
model selection procedure in the R statistical software package (Liaw
& Wiener, 2002) to develop a Random Forest (RF) regression tree that
The spatially explicit predicted errors of the snow-off DEM were
propagated through to the snow depth maps to determine the range
of possible snow depths within each grid cell following Eq. (1), where
the snow depths come from the differenced LiDAR DEMs and the
predicted errors come from the RF regression predictions of vertical
error. The range of possible snow volume within a grid cell was
Table 3
Comparison of individual manual snow survey measures with LiDAR-derived snow
depths. Performed with both 1 m and 4 m processing. The comparison highlights the conservative nature of the predicted error derived from the decision tree modeling, showing
that accuracy assessment can be conducted in a spatially explicit manner.
LiDAR-survey (m)
Mean RF model
RMSE (m)
Cover type
n
Mean
StDev
RMSE
1 m processing
Shrub
Willow
Deciduous
Conifer edge
Conifer outside
Overall
105
183
102
154
94
544
−0.08
0.09
0.06
0.08
−0.04
0.05
0.13
0.2
0.13
0.36
0.21
0.24
0.15
0.21
0.14
0.37
0.21
0.25
0.37
0.28
0.26
0.18
–
0.27
4 m processing
Shrub
Willow
Deciduous
Conifer edge
Conifer outside
Overall
105
183
102
154
94
544
−0.06
0.11
0.09
0.1
0.15
0.07
0.15
0.21
0.14
0.37
0.23
0.26
0.16
0.24
0.17
0.38
0.28
0.27
0.28
0.34
0.3
0.27
–
0.3
110
W.T. Tinkham et al. / Remote Sensing of Environment 141 (2014) 105–115
Fig. 4. Comparison of coincident manual and LiDAR estimated snow depths by cover types. In all cases the given regression functions performed slightly better than a linear function. The
RMSE are arrived at by differencing the individual point level measures with the LiDAR estimated depths. Across all of the cover types the RMSE is 0.25 and 0.28 m for the 1 and 4 m
surfaces respectively. The linear lines represent a 1:1 line.
performed in a similar manner, but the depth values were first
multiplied by the area of a single grid cell.
Range of Snow Depth ¼ Snow Depth
r
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2
Predicted Erroroff þ ðPredicted Erroron Þ2
ð1Þ
Due to the simplified terrain and surface roughness in snow covered
landscapes, a conservative estimate of the snow-on LiDAR DEM error is
assumed to equal the snow-off LiDAR DEM error. In this case, Eq. (1)
simplifies to √(Predicted Error2 × 2). We acknowledge that the snowon surface would be expected to exhibit lower LiDAR DEM errors due
to the high reflectivity and simplicity of the snow-on surface (Deems
& Painter, 2006) and that this conservative assumption may produce
inflated estimates of the total error. The most optimistic scenario,
although unrealistic, of snow volume error can be considered by assuming no snow-on LiDAR DEM error, which simplifies Eq. (1) to √(Predicted
Error2). Calculation of the error by both routes effectively produces an
upper and lower bound estimate of the error.
The catchment was stratified by both redistribution terrain classes
and cover types for assessment of distributed snow depth and volume.
For this analysis, redistribution classes were defined as high, moderate,
and low snow depth zones. High and low zones are classified as snow
depths ± 1 standard deviation of the mean catchment snow depth
(114 ± 93 cm for both 1 and 4 m grid). The seven catchment cover
types ranging from bare-ground to mature trees is shown in Fig. 2A.
A coincident snow survey was designed to be temporally coincident
with the snow-on LiDAR acquisition to serve as a manual validation
of LiDAR-derived snow depth map. The coincident snow survey
was georeferenced using differentially corrected high precision GPS
W.T. Tinkham et al. / Remote Sensing of Environment 141 (2014) 105–115
111
snow-on surfaces at small spatial extents. This 1 m data will be
more beneficial in understanding fine-scale topographically-driven
hydrological processes that occur over short spatial scales, such as
flow pathways in ephemeral water courses, and for the validation of
distributed snow modeling in heterogeneous landscapes. However, for
regional-scale assessments of snow cover the gain in precision in
using the 1 m grid scale should be considered against the computational
benefits of using the 4 m grid scale. The analysis also highlights the
cover type dependent accuracy that has been noted in past studies
(Hopkinson et al., 2004).
3.2. Random Forest predicted error
Fig. 5. Comparison of coincident manual and LiDAR estimated snow depths for the Conifer
Outside transect at the 1 and 4 m scales. The linear lines represent a 1:1 line.
locations (±0.5 m), containing 545 snow probe depth measurements,
stratified by 4 of the investigated cover types (Fig. 3). The snow survey
was used to both assess the mean depth measurements with the coincident 1 and 4 m LiDAR grid cells and to evaluate the predicted accuracy
of the snow depth within each cover type.
3. Results and discussion
3.1. Snow depth validation
Table 3 shows that when comparing LiDAR-derived snow depths to
ground-based snow depth surveys, the LiDAR based estimates at the
1 m and 4 m cell sizes were most accurate in the deciduous and shrub
transects (RMSE = 0.14–0.17 m), compared to the conifer edge
transect (RMSE = 0.37–0.38 m). However, a second transect within
another conifer stand (conifer outside transect) located just outside
the catchment produced RMSE of 0.21 and 0.28 m for the 1 and 4 m
surfaces respectively (Fig. 5). The discrepancy between observed errors
within different cover types is attributed to the simplified nature of the
snow surface within the shrub and meadow cover types, supporting the
simplified snow surface error proposed by Deems and Painter (2006);
as compared to the LiDAR filtering challenge introduced by the complex
vertical structure of the snow covered tree cover types. The results show
contradictory results to Hopkinson et al. (2004), who showed conifer
cover types with little understory vegetation to produce smaller errors
than other treed cover types. When comparing these results with a
second conifer transect with similar understory conditions located just
outside the catchment, errors are found that are similar to the prior
study (Fig. 5, Table 2). The high errors exhibited for the conifer edge
transect within the catchment are attributed to the location which is
near the edge of a snow drift, where several stinger drifts (~3 m long
and 0.5 m wide) extending into the conifer stand were observed by
the field sampling crew. Across all transects, it is believed that coregistration errors between the manual snow survey and LiDAR surfaces
may be leading to inflated snow depth error observations.
Overall the 1 m grid size provides similar or better snow depth
accuracies in all cover types when compared to the 4 m grid size
(Table 2 and Fig. 4). We attribute this improvement to the ability
of the 1 m grid size to capture variability in both the ground and
The final models produced a RMSE of prediction for the random forest
trees of 0.24 and 0.21 m at the 1 and 4 m grid sizes, respectively, with
correlation coefficients of 0.59 and 0.78 (p b 0.0001) between the
observed and predicted DEM errors at the 1 and 4 m resolutions,
respectively. Although Table 2 shows that at coincident snow probe
locations the 1 m surface provided more accurate representations
of terrain, modeling these accuracies at the fine scale includes more
variability leading to a need for more training data as scales decrease
to capture the increase heterogeneity. The comparison of the RF
predicted RMSE and the observed survey grid plot level RMSE led to
an overall RMSD of 0.14 m (range of 0.07–0.28 m) across all 99 plots
(Tinkham et al., 2013), providing a conservative estimate for the errors
commonly associated with different vegetation and terrain features
(Tinkham et al., 2013). This conservative modeling of errors is evident
in comparing the LiDAR snow depth with the manual snow measurements (Table 3). This shows that the in situ and LiDAR estimated
snow depths are similar between cover types, but also highlights that
the predicted errors at both the 1 and 4 m grid size are approximately
10% greater than the observed error from the ground surveys (Table 3,
Tinkham et al., 2013). When comparing the snow survey calculated
depth errors against the Random Forest modeled error there is a
RMSE ranging from 0.09 to 0.34 m, with the 1 m surface producing
predicted errors more closely representing the field calculated errors
(Fig. 6).
A possible source of error that could arise in the Random Forest
modeling may come from the training data that was used to train the
predictive model of LiDAR surface error. The model is limited by the
training data's ability to fully represent the range of conditions; this
may have led to errors in the current study as survey plots were not
sampled on roads, stream beds, or within the willow cover type. The
linear high error features that are evident within the 4 m predicted
error map are coincident with roads and stream beds within the catchment (Fig. 3). Without sampling these catchment features, the regression
tree was not able to distinguish them as unique cover types and was
forced to produce uncertain predictions of error. Differences seen
between the two resolutions (Fig. 3) are attributed to the training data's
ability to represent the catchment level textural heterogeneity, when
scaling up by a factor of sixteen from 1 to 4 m grid size, remotes sensing
theory says variability will be reduced (Moody & Woodcock, 1995). This
means that both resolutions will capture different features within the
landscape, leading to them representing the error structure differently
when modeled. Within the 1 m error prediction map the same features
seem to be more reasonably represented, while areas within the bare
ground cover type were predicted to have excessively high errors
(Fig. 3). These excessive errors are attributed to training plots that were
located upon rocky outcroppings, which were shown to cause DEM
vertical RMSE of up to 1.75 m (Tinkham et al., 2011) and although this
type of feature occupies a small area, they are an important component
of the variability within the catchment. Within the bare ground cover
type these outcroppings raised the average plot level RMSE to 0.44 m
while the median was only 0.21 m. However, given the RF model uses
the individual plot data and not the cover type mean or median values
the snow volume errors should not be overly influenced by individual
112
W.T. Tinkham et al. / Remote Sensing of Environment 141 (2014) 105–115
Fig. 6. Comparison of Random Forest modeled errors against LiDAR-derived snow depth errors from snow depth transects within the catchment at the 1 and 4 m scales. Across all transects
within the catchment the difference between individual observed and predicted errors for the 1 and 4 m surfaces was a RMSE of 0.22 and 0.24 m, respectively. The linear lines represent a
1:1 line. Overall, observed and predicted upper bound snow depth errors demonstrated correlations of 0.24 and 0.22 (p b 0.001) at the 1 and 4 m scales, respectively, with similar values
for the lower bound errors.
outliers (Tinkham et al., 2013). Studies attempting a similar analysis
should be careful to capture a representative sample of the variability
seen within cover types; improved field surveying (e.g. installing a greater
number of plots with smaller spatial extents) may have provided an even
stronger representation of the surface errors. The limited agreement
between the predicted and observed snow depth errors is in part attributed to co-registration errors of the manual snow measurements and fine
scale fluctuations of snow depth within the catchment (Fig. 6).
3.3. Catchment level snow volume
At the catchment level the total snow volume error at both grid scales
was estimated to have an upper and lower bound of approximately 30
and 22%, respectively, with the bare ground and ceanothus cover
types exhibiting the greatest errors (Tables 4, 5). With a mean snow
depth of 0.16 m within the bare ground cover type, the modeled surface
errors quickly mask the snow signal and quickly lead to these high
errors. However, together these two cover types account for less than
5% of the catchment snow volume.
Both the low and high redistribution zones only occupied approximately 10% of the catchment area but exhibited contrasting snow volume
error levels. Although the low snow depth zone error magnitude appears
excessive, these exposed rocky areas only exhibited a mean snow depth
of 5 cm and thus represent a very small fraction (~2%) of the
catchment-wide snow volume. In contrast, high (drift) zones account
for approximately 30% (±5 and 6% at the 1 and 4 m scales, respectively)
W.T. Tinkham et al. / Remote Sensing of Environment 141 (2014) 105–115
113
Table 4
Distribution and quantification of snow depth and volume across the catchment, stratified by redistribution zones. Upper and lower bound error assessment performed with 1 m sampling
and 4 m sampling.
Snow volume (m3)
Snow depth (m)
Catchment area
Distribution regime
Mean
Min
Max
StDev
Minimum
Maximum
% Error
Hectares
%
Upper 1 m distribution
High
Moderate
Low
Total
3.29
1
0.05
1.14
1.05
0
0
0
6.64
3.09
1.33
6.64
0.97
0.46
0.07
0.94
114,528
193,799
1
308,328
142,061
407,911
21,317
571,289
10.7%
35.6%
100%
29.9%
3.9
30
3.7
37.6
10.4%
79.7%
9.9%
100%
Upper 4 m distribution
High
Moderate
Low
Total
3.29
1
0.05
1.14
2.08
0.21
0
0
6.15
2.07
0.2
6.15
0.97
0.46
0.07
0.94
111,999
192,870
9
304,877
142,863
409,875
13,242
565,979
12.1%
36.0%
99.9%
30.0%
3.9
29.9
3.7
37.5
10.3%
79.7%
9.9%
100%
Lower 1 m distribution
High
Moderate
Low
Total
3.29
1
0.05
1.14
1.35
0
0
0
6.45
2.79
1
6.45
0.97
0.46
0.07
0.94
118,560
222,888
17
341,465
138,029
375,967
15,649
529,646
7.6%
25.6%
99.8%
21.6%
3.9
30
3.7
37.6
10.4%
79.7%
9.9%
100%
Lower 4 m distribution
High
Moderate
Low
Total
3.29
1
0.05
1.14
1.08
0
0
0
6.15
2.07
0.2
6.15
0.97
0.46
0.07
0.94
116,519
219,796
32
336,348
138,343
377,296
9935
525,575
8.6%
26.4%
99.3%
22.0%
3.9
29.9
3.7
37.5
10.3%
79.7%
9.9%
100%
Table 5
Distribution and quantification of snow depth and volume across the catchment, stratified
by cover type. Upper and lower bound error assessment performed with 1 m sampling
and 4 m sampling.
Snow volume (m3)
Snow depth (m)
Cover type
Min
Max
StDev
Minimum
Maximum
% Error
Upper bound 1
Bare-ground
Ceanothus
Conifer
Deciduous
Meadow
Shrub
Willow
Total
m
0.16
0.97
1.43
1.25
1.91
1.1
1.32
1.14
Mean
0
0
0
0
0
0
0
0
3.14
3.52
4.75
6.15
6.64
5.71
4.26
6.64
0.26
0.43
0.41
1.25
1.31
0.66
0.34
0.94
1653
2608
16,732
59,024
67,361
135,856
25,096
308,328
29,111
5188
27,231
99,118
98,239
267,869
44,532
571,289
89.3%
33.1%
23.9%
25.4%
18.6%
32.7%
27.9%
29.9%
Upper bound 4
Bare-Ground
Ceanothus
Conifer
Deciduous
Meadow
Shrub
Willow
Total
m
0.16
0.96
1.43
1.91
1.25
1.1
1.32
1.14
0
0
0
0.16
0
0
0
0
1.92
2.73
3.18
6.15
5.51
5.34
3.82
6.15
0.26
0.43
0.4
1.32
1.25
0.66
0.34
0.94
1900
1377
15,739
65,335
59,859
139,907
20,760
304,877
20,993
6695
28,211
99,834
97,732
263,214
49,301
565,979
83.4%
65.9%
28.4%
20.9%
24.0%
30.6%
40.7%
30.0%
Lower bound 1
Bare-ground
Ceanothus
Conifer
Deciduous
Meadow
Shrub
Willow
Total
m
0.16
0.97
1.43
1.25
1.91
1.1
1.32
1.14
0
0
0
0
0
0
0
0
2.85
3.44
4.64
5.98
6.45
5.6
4.19
6.45
0.26
0.43
0.41
1.25
1.31
0.66
0.34
0.94
2362
2947
18,259
64,190
71,846
153,929
27,933
341,465
22,558
4796
25,691
93,033
93,709
248,176
41,673
529,646
81.0%
23.9%
16.9%
18.3%
13.2%
23.4%
19.7%
21.6%
Lower bound 4
Bare-Ground
Ceanothus
Conifer
Deciduous
Meadow
Shrub
Willow
Total
m
0.16
0.96
1.43
1.91
1.25
1.1
1.32
1.14
0
0
0
0.16
0
0
0
0
2.43
3.04
3.52
7.15
6.05
6.15
4.39
7.15
0.26
0.43
0.4
1.32
1.25
0.66
0.34
0.94
2511
1868
17,518
70,130
64,529
155,240
24,550
336,348
16,823
5852
26,377
94,748
92,014
244,673
45,088
525,575
74.0%
51.6%
20.2%
14.9%
17.6%
22.4%
29.5%
22.0%
of the total snow volume (Table 4). This result is similar to that found
previously by Marks, Winstral, and Seyfried (2002), who showed that
drifts contained 25% of the SWE in only 10% of the catchment area
based on physically-based snowpack modeling results. The consistency
between the two approaches confirms the utility of multi-temporal
LiDAR for the assessment and validation of catchment scale snow volume
distributions.
This is of particular significance given that drifts act as water sources
late into the growing season and allow for pockets of water limited species (e.g. aspen and fir trees) to be established or sustained. This results
in a heterogeneous vegetation structure across the landscape that in
turn influences the radiative and hydrometerological regime and
creates biological “hotspots” (Baumeister & Callaway, 2006; Campbell
& Bartos, 2001; Reba, Marks, Winstral, Link, & Kumar, 2011). Relatively
high snow densities in the drift zones could potentially amplify the
importance of this observed high snow volume by providing more
water per unit snow depth than observed in shallower snow that has
not been condensed through redistribution processes (Sturm et al.,
2010). Although the effect of rocky outcroppings is potentially significant, as large quantities of snow could potentially accumulate over
time, these features are limited in extent within Reynolds Mountain
East (b1% of area), rarely accumulate snow depths N10 cm and can be
seen as isolated patches of high error values along the northeast side
of the catchment.
4. Conclusions
This study presented a robust and comprehensive evaluation of the
efficacy of multi-temporal LiDAR to quantify snow depths and the use
of Random Forest to estimate the associated accuracies across seven
different vegetative cover classes. The utility of Random Forest for the
assessment of accuracies was well demonstrated both in the present
study and in related works (Tinkham et al., 2013). Given the relatively
fast analysis of multi-temporal LiDAR produced results of snow volume
distribution that agreed with a prior intensive 8 year field measurement
and modeling study (Marks et al., 2002) the potential of multi-temporal
LiDAR for this application has been re-affirmed. While it is apparent that
challenges remain in quantifying snow volume from multi-temporal
LiDAR (Nolin, 2010), advances in the acquisition and processing of
114
W.T. Tinkham et al. / Remote Sensing of Environment 141 (2014) 105–115
LiDAR are making these surmountable. However, the contrasting errors
found between the two manually measured snow depth transects within the conifer cover type highlight how difficult it can be to validate
snow depth in areas were depth varies at very small spatial scales.
The current study determined a theoretical upper bound of 30%
error in catchment wide snow volume through Random Forest modeling, highlighting the range of accuracies within different cover types
and snow redistribution zones. Although the lower bound error of
21.6% represents a considerable improvement, clear strategies are
apparent that could further reduce this lower bound. For example, the
adoption of cover specific classification algorithms may allow the errors
to be lowered in heterogeneous landscapes, or enhanced understanding
of how pulse intensity can be used to penetrate dense vegetation.
Ultimately, even with improved LiDAR processing for DEM creation
the snow volume error will always be dominated by the LiDAR DEM
error in the underlying snow-off surface, which in the current study
represents the 21.6%. These estimates could be enhanced by building
off studies applying high precision Terrestrial LiDAR Systems (TLS) or
ground based topological surveys from total stations to validate aerial
LiDAR estimates of snow depth (Grünewald et al., 2010; Prokop, 2008;
Schirmer et al., 2011). It is likely that this would result in very small
errors of snow volume. Under such a schema, robust validation of the
error in the snow-on surface would be required, perhaps through a
snow-on high precision topographical survey referenced to monument
controls.
Clearly, the complexity of the surfaces at this site and the shallow
snow depths represent an effective worst-case scenario to test the
utility of multi-temporal LiDAR and Random Forest for snow volume
assessments. Through performing similar analysis of landscapes with
either more continuous or simpler cover types, it is likely that this
lower bound error of 21.6% could be greatly diminished. The magnitude
of the upper and lower bound errors in this study are driven by the
LiDAR DEM error; a high percentage when compared to the shallow
snow depths at our site. Clearly, repeating this application on sites
with snow packs an order of magnitude deeper than what we observed
(e.g., 5–6 m as observed in the Sierra Nevada and Cascade Ranges)
would make the LiDAR DEM errors a small percentage of the total
depth, likely reducing the upper and lower error bounds by a similar
degree.
The ability to perform this type of analysis at extended spatial scales
will help to advance understanding of the importance of snow distribution on water resources, surface energy balance, and vegetation dynamics.
The application of these techniques is of potentially high importance in
semiarid regions that rely on shallow snow packs for annual water supply.
The next step in investigating the spatial distribution of snow at landscape
levels will require the incorporation of snow density and/or SWE to
improve the estimation of water storage in complex terrain.
Acknowledgments
We would like to thank Dr. Andrew Robinson for his guidance and
review of the statistical methodologies utilized in this work.
This project was funded by the UMAC and the Idaho Space Grant
Consortium, which are both in turn funded by NASA. Additional
funding and support was provided through the Agricultural Research
Service Northwest Watershed Research Center. Funding support was
provided by Idaho NSF EPSCoR and under awards NSF EPS-0814387,
NSF EPS-0701898, NSF CBET-0854553, and a NASA New Investigator
Award NNX10AO02G.
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