Microtopographic features, such as polygonal ground, are
characteristic sources of landscape heterogeneity in the Alaskan
Arctic coastal plain. Here, we analyze the hypothesis that
microtopography is a dominant controller of soil moisture in
polygonal landscapes. We perform multi-year surface–subsurface
isothermal flow simulations using the PFLOTRAN model for summer
months at six spatial resolutions (0.25–8 m, in increments
of a factor of 2). Simulations are performed for four study sites
near Barrow, Alaska that are part of the NGEE-Arctic
project. Results indicate a non-linear scaling relationship for
statistical moments of soil moisture. Mean soil moisture for all
study sites is accurately captured in coarser resolution
simulations, but soil moisture variance is significantly
under-estimated in coarser resolution simulations. The decrease in
soil moisture variance in coarser resolution simulations is greater
than the decrease in soil moisture variance obtained by coarsening
out the fine resolution simulations. We also develop relationships
to estimate the fine-resolution soil moisture probability
distribution function (PDF) using coarse resolution simulations and
topography. Although the estimated soil moisture PDF is
underestimated during very wet conditions, the moments computed from
the inferred soil moisture PDF had good agreement with the full
model solutions (bias
Northern permafrost soil currently contains approximately 1700 billion
metric tons of frozen organic carbon (Tarnocai et al., 2009). Global
climate is warming (Stocker et al., 2013), and “Arctic
amplification” is predicted to cause disproportionately larger
temperature increases at high latitudes (Holland and Bitz, 2003). This
warming will cause permafrost thaw and decomposition, leading to
Soil moisture,
Large portions of the Arctic are characterized by polygonal ground
features, which are formed due to thermal expansion and contraction of
ice wedges within the soil (Hinkel et al., 2005). Polygons are
classified as “low-centered” or “high-centered” based on the
relationship between their central and mean elevations. Polygonal
ground features are dynamic components of the Arctic landscape in
which ice-wedge thaw under low-centered polygon rims leads to
subsidence and eventually (
The recognition that soil moisture dynamics occur across a wide range
of spatial scales (i.e., soil pore, Childs, 1940 to continental,
Brocca et al., 2010; Li and Rodell, 2013) has motivated a large
literature attempting to integrate relationships of soil moisture
heterogeneity with topographic, biological, and forcing
controls. Numerous studies have identified statistical self-similarity
of soil moisture across a range of spatiotemporal scales via field
observations and numerical experiments. A soil moisture field is
self-similar if (Dubayah et al., 1997):
Numerical studies have investigated the importance of including spatial variability on model predictions. Sivapalan and Woods (1995) showed that subgrid variability of rainfall and soil moisture can have significant impact on land surface fluxes. Choi et al. (2007) demonstrated that subgrid variability impacts mean soil moisture predictions under relatively dry conditions. Jana and Mohanty (2012a) found that power-law scaling of soil hydraulic parameters allowed accurate prediction of subgrid topographic effects for four different hillslope configurations. However, there remains limited understanding of sub-meter scale soil moisture heterogeneity arising due to polygonal ground features in Arctic ecosystems (Chapin III et al., 2002).
Given the importance of soil moisture spatial heterogeneity on hydrological and biogechemical dynamics, watershed to global-scale models have integrated several approaches to account for the relevant processes, including: (1) using a non-spatially explicit tiling approach (Oleson, 2013), (2) employing effective parameters at coarse resolution (Jana and Mohanty, 2012b), and (3) modifying the governing equations to explicitly include terms related to soil moisture variance (Choi et al., 2007; Kumar, 2004). We note that the third approach could also include terms related to higher-order moments, but we are not aware of such efforts in the literature.
We analyzed here another approach to represent subgrid hydrological
heterogeneity in models; i.e., developing relationships (i.e., reduced
order models (ROMs)) between the mean properties (which could be
estimated with a coarser-resolution model) and either the statistical
(Riley and Shen, 2014) or spatially explicit (Pau et al., 2014)
properties of the field of interest (here
This study had three primary objectives: (1) characterize spatial scaling of soil moisture heterogeneity in the presence of polygonal ground features for an Arctic ecosystem, (2) develop reduced order models that allow prediction of higher-order statistical moments of soil moisture given coarse-resolution model simulations, and (3) identify controlling properties of the relationships between spatial heterogeneity and spatial resolution of predicted soil moisture fields as a first step toward representing spatial soil moisture heterogeneity in a coarser-resolution model. To address these objectives we performed multi-year surface–subsurface isothermal flow simulations using the PFLOTRAN model for summer months at multiple spatial resolutions. Descriptions of the study site, climate forcing, and model setup are presented in Sect. 2. Results of our spatial scaling analysis are presented in Sect. 3. We conclude with discussion, limitations of our approach, and observations and model structures required to overcome those shortcomings in the future.
In order to reduce uncertainty regarding impacts of climate change in
high-latitude ecosystems, a long term Department of Energy (DOE)
Next-Generation Ecosystem Experiment (NGEE-Arctic) project was
initiated with sites located near Barrow, Alaska (71.3
In this study we used the PFLOTRAN model, an open-source subsurface flow and reactive transport model (Hammond et al., 2012), which we modified to include surface flow. Subsurface reactive flows and transport processes in PFLOTRAN are solved using implicit time integration and finite volume spatial discretization. PFLOTRAN uses the Portable Extensible Toolkit for Scientific Computation (PETSc) libraries (Balay et al., 2013) for parallelization and domain decomposition.
We sequentially coupled a 2-D diffusion-wave overland flow model with
PFLOTRAN:
Polygonal ground regions in Arctic ecosystems are also characterized
by fine-scale variation in soil texture across the polygon centers,
rims, and troughs (Quinton and Marsh, 1998). Troughs and centers of
low-center polygons allow for preferential infiltration during the
thaw season, which in turn leads to zonation of vegetation types
across polygonal features (Minke et al., 2009). Apart from horizontal
variability in soils due to surface features, cryoturbation leads to
vertical heterogeneity in Arctic soils. Cryoturbation is a physical
process of mixing soil material due to freeze–thaw cycles of ice
wedges, which causes near surface soil to move downwards and deeper
soil to move upwards with a time scale of hundreds of years (Bockheim,
2007). Koven et al. (2009) have shown inclusion of cryoturbative
mixing within a terrestrial carbon cycle model leads to a better
agreement between model predictions and observations of bulk soil
organic matter and
The following van Genuchten (1980) relationship was used to
approximate observations reported in Hinzman et al. (1991) of
capillary pressure and hydraulic conductivity as a function of water
saturation given by,
Boundary conditions (BCs) for the surface domain included precipitation and snowmelt while evapotranspiration (ET) was applied as a sink term for the subsurface domain. BCs for PFLOTRAN were obtained by running an offline Community Land Model (CLM4.5) simulation using meteorological data (1998–2002) from the Ameriflux station in Barrow, AK (shown in Fig. 3). A 3000 years CLM4.5 simulation was performed to allow for subsurface biogeochemistry in the model to reach equilibrium and then hourly output was saved for PFLOTRAN simulations. The ET sink was distributed vertically within the PFLOTRAN subsurface domain using the same exponential rooting profile applied in CLM4.5 for Arctic shrubs (Oleson, 2013). Because of a lack of observations, no horizontal heterogeneity in vegetation type was accounted for in this study.
We performed 5 year multi-resolution PFLOTRAN surface–subsurface
simulations to characterize soil moisture scaling for our four
NGEE-Arctic study sites. The finest resolution PFLOTRAN meshes for all
four sites were created starting with 0.25
We perform several analyses of the simulation outputs: (1) characterize the relationships between soil moisture moments and spatial resolution of the simulations, (2) investigate how these relationships changed when coarser-resolution simulations are used instead of spatially averaging the finest-resolution simulation (3) develop analytical approximations to relate 2nd, 3rd, and 4th statistical moments with the mean moisture, (4) investigate the topographic controls on the soil moisture probability density function, and (5) develop a method to combine the coarse-resolution simulation predictions and the fine-resolution topographic information to dynamically estimate the fine-resolution soil moisture probability distribution function.
Across the four sites and five years of simulation, the coarse-resolution PFLOTRAN simulations show that soil moisture in sites A and B are comparable and relatively drier, site C is intermediate, and site D is the wettest (Fig. 5. Time series of simulated mean soil moisture for the four NGEE-Arctic study sites.) Predicted soil moisture decreased in the first half of each year except 2000, corresponding to a net loss associated with evapotranspiration. All sites became wetter starting in mid July (2001) and mid August (1998, 1999, 2000, and 2002) corresponding to increasing precipitation inputs (Fig. 3). The relatively smaller drydown period in 2000 following initial saturation occurred because of much higher precipitation in the beginning of the summer season.
The coarse-resolution simulations are able to capture the mean of the
fine-resolution soil moisture (
We analyzed the loss of variance due to coarsening of the DEM using
information theory (Shannon and Weaver, 1949). The information
content,
We aggregated the simulated
Ivanov et al. (2010) reported hysteresis between
Next we examine relationships between simulated soil moisture variance
and spatial resolution at all sites for the entire simulation
period. To illustrate the patterns that emerged, we discuss these
relationships at Site A for the driest (
In this polygonal tundra system the soil moisture distribution is
strongly controlled by topography, exhibiting a strong inverse
relationship between saturation and elevation (Fig. 12). We therefore
investigated an approach to estimate both the full probability
distribution function (PDF) of fine-resolution soil moisture (with
We next compared the first four central moments from the estimated
(Eq. 10) and simulated PDFs (e.g., Fig. 14 for Site A). The bias and
correlation of the first four central moments across all four sites
are
The approach presented in the previous section estimated statistical
properties of the soil moisture distribution at finer spatial
resolution from coarse resolution simulations without explicitly
retrieving
The maximum and mean
With the demonstrated success of
Even though both downscaling approaches can accurately capture spatial
distributions of soil moisture at the finest resolution (with mean
error
The results presented in previous Sects. 3.1–3.4 assumed no
heterogeneity in vegetation cover and applied a horizontally
homogenous evapotranspiration sink within the subsurface domain of
PFLOTRAN model. As reported by Gangodagamage et al. (2014), our study
site has varying vegetation types that are associated polygonal
landscape features: mosses and sedges are mostly present in wetter
parts of the domain (troughs and centers of low-centered polygons);
while lichen and shrubs mainly cover drier areas (rims of low-centered
polygons and centers of high-centered polygons). As a first step to
account for vegetation heterogeneity, we spatially varied the
evapotranspiration sink based on the vegetation distribution. Based on
the scaling factor (Sect. 3.3; Fig. 15), the evapotranspiration sink
was increased (decreased) by 50 % for regions with
In this study, we analyzed multi-year surface–subsurface isothermal flow simulations during summer months for four polygonal ground study sites near Barrow, AK. PFLOTRAN simulations are performed at six different spatial resolutions for each of the four study sites. We analyzed simulation results to characterize spatial scaling of statistical moments for soil moisture and developed relationships to predict those statistical moments at fine-resolution from coarse-resolution simulations. Although coarse-resolution simulations are able to accurately represent mean soil moisture, soil moisture variance is significantly under estimated in coarser-resolution simulations. Soil moisture variance decreased at coarser resolution due to loss of information content of slope and curvature of the underlying DEM. However, the observed decrease in soil moisture variance in coarser-resolution simulations is greater than the decrease in soil moisture variance obtained by coarsening out the fine-resolution simulation.
A concave relationship between soil moisture mean and variance without a hysteresis effect is predicted. The PDF of topography and soil moisture are strongly inversely correlated and a method to obtain the fine-resolution soil moisture PDF from coarse-resolution simulations is developed and tested. The inferred soil moisture PDF accurately represented the fine-resolution simulated PDF. The moments computed from the inferred soil moisture PDF were in very good agreement when compared to moments derived from fine-resolution simulations.
Several important caveats need to be acknowledged regarding our results. Our simulations assumed a static active layer depth corresponding approximately to the maximum seasonal value seen at the NGEE-Arctic sites. Although we included a first-order estimate of vertical heterogeneity in soil types, horizontal heterogeneity and vertical heterogeneity associated with cryoturbative mixing were neglected. The evapotranspiration flux is prescribed from an offline CLM simulation, implying that we were unable to account for soil moisture-ET feedbacks and horizontal heterogeneity in vegetation type. Although we believe that our basic conclusions regarding polygonal tundra soil moisture spatial structure and topographic controls are valid, future work should characterize the impacts of these simplifications on our conclusions.
Finally, though the method to estimate the soil moisture probability
density function from coarse-resolution simulations is accurate, that
method is unable to retrieve the spatially explicit dynamic
fine-resolution soil moisture field. We therefore presented two
methods to map simulated coarse resolution soil moisture data onto
fine resolution grid using downscaling factors. The first downscaling
approach, based on fine- and coarse-resolution simulations, is able to
capture mean and variance of soil moisture at fine resolution. The
second downscaling approach, which relied only on DEMs at the two
resolutions, is able to capture spatial pattern
This research is conducted under the Next-Generation Ecosystem Experiments (NGEE Arctic) project supported by the Office of Biological and Environmental Research in the DOE Office of Science, through Contract No. DE-AC02-05CH11231 between Lawrence Berkeley National Laboratory and the US Department of Energy.
Characteristics of NGEE-Arctic study sites.
van Genuchten model parameters used to fit data reported in Hinzman et al. (1991).
Bias and correlation (
Bias and correlation (
Maximum and mean absolute error between simulated soil moisture field
at 0.25
LIDAR DEM for the four NGEE-Arctic study sites.
Fitted van Genuchten model (in red) to data (in blue) reported in Hinzman et al. (1991).
Time series of meteorological forcing dataset for summer
months (June–September) of 1998–2002 used for PFLOTRAN
simulations:
DEM for Site B (top row) and Site C (bottom row) at 0.25, 1,
and 8
Time series of simulated mean soil moisture for the four NGEE-Arctic study sites.
Time series of simulated soil moisture variance at site A for
1999 with PFLOTRAN mesh at the following resolutions: 0.25
Information content vs. grid resolution for
Soil moisture mean vs. variance at all four sites using finest resolution simulation for entire study period.
Simulated soil moisture variance vs. elevation variance at different mean soil moisture levels.
Slope of linear relationship between soil moisture variance – topography variance (computed from data presented in Fig. 9) vs. mean soil moisture bin.
Soil moisture variance vs. scale factor for simulated soil
moisture at Site-A for driest (blue) and wettest (red) day in
1999. A dashed line shows results obtained by performing PFLOTRAN at
different spatial resolutions, while a solid line shows results
obtained by aggregating 0.25
PDF for soil moisture at Site A for 1999 based on
0.25
Comparison of soil moisture moments computed from estimated PDF and fine-scale simulations for Site A.
Mean downscaling factor for the four NGEE-Arctic sites.
Linear relationship between downscaling factors for elevation
(
Simulated soil moisture for driest day (
Comparison of simulated soil moisture variance obtained for DEM at 0.25 [m] with estimated soil moisture fields at finest resolution via two downscaling approaches.
Soil moisture variance vs. scale factor for simulated soil
moisture at Site A for the driest in 1999. Results are shown for (i)
PFLOTRAN simulation at different spatial resolutions, (ii)
aggregation of 0.25
Comparison of simulated soil variance with and without vegetation heterogeneity for simulations performed at 0.25 [m].