Volume 55, Issue 3 p. 1814-1832
Research Article
Free Access

Improving Permafrost Modeling by Assimilating Remotely Sensed Soil Moisture

S. Zwieback

Corresponding Author

S. Zwieback

Department of Geography, University of Guelph, Guelph, Ontario, Canada

Correspondence to: S. Zwieback,

[email protected]

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S. Westermann

S. Westermann

Department of Geosciences, University of Oslo, Oslo, Norway

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M. Langer

M. Langer

Periglacial Research, Alfred Wegener Institute Helmholtz Centre for Polar and Marine Research, Potsdam, Germany

Geography Department, Humboldt University, Berlin, Germany

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J. Boike

J. Boike

Periglacial Research, Alfred Wegener Institute Helmholtz Centre for Polar and Marine Research, Potsdam, Germany

Geography Department, Humboldt University, Berlin, Germany

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P. Marsh

P. Marsh

Department of Geography, Wilfrid Laurier University, Waterloo, Ontario, Canada

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A. Berg

A. Berg

Department of Geography, University of Guelph, Guelph, Ontario, Canada

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First published: 12 February 2019
Citations: 23

Abstract

Knowledge of soil moisture conditions is important for modeling soil temperatures, as soil moisture influences the thermal dynamics in multiple ways. However, in permafrost regions, soil moisture is highly heterogeneous and difficult to model. Satellite soil moisture data may fill this gap, but the degree to which they can improve permafrost modeling is unknown. To explore their added value for modeling soil temperatures, we assimilate fine-scale satellite surface soil moisture into the CryoGrid-3 permafrost model, which accounts for the soil moisture's influence on the soil thermal properties and the surface energy balance. At our study site in the Canadian Arctic, the assimilation improves the estimates of deeper (>10 cm) soil temperatures during summer but not consistently those of the near-surface temperatures. The improvements in the deeper temperatures are strongly contingent on soil type: They are largest for porous organic soils (30%), smaller for thin organic soil covers (20%), and they essentially vanish for mineral soils (only synthetic data available). That the improvements are greatest over organic soils reflects the strong coupling between soil moisture and deeper temperatures. The coupling arises largely from the diminishing soil thermal conductivity with increasing desiccation thanks to which the deeper soil is kept cool. It is this association of dry organic soils being cool at depth that lets the assimilation revise the simulated soil temperatures toward the actually measured ones. In the future, the increasing availability of satellite soil moisture data holds promise for the operational monitoring of soil temperatures, hydrology, and biogeochemistry.

Key Points

  • Satellite soil moisture was assimilated into a permafrost model to constrain temperature profiles
  • Temperature estimates improved most for porous organic soils, mediated by the strong moisture control on thermal conductivity
  • Improvements were larger for deeper temperatures than for surface temperatures

Plain Language Summary

We explore whether soil moisture data improve the accuracy with which we can predict the soil temperature profile in cold regions. Knowledge of the temperature conditions is important for monitoring the stability of the terrain, for understanding the response of vegetation and microorganisms, and many other applications. Soil moisture data may be useful in this context because soil moisture influences the thermal dynamics of the soil, but so far, such data have been in short supply. Using novel satellite soil moisture data, we show that soil moisture information does indeed help to improve the estimates of deeper temperatures, at least in organic soils. In the future, the increasing availability of satellite soil moisture data holds promise for the operational monitoring of soil temperatures, hydrology, and biogeochemistry.

1 Introduction

Soil moisture can have a strong impact on the soil thermal dynamics, as it modifies the surface energy balance and the subsurface thermal properties (Göckede et al., 2017; Liljedahl et al., 2011). It is hence crucial to permafrost modeling, and yet its dynamic changes are often neglected in transient permafrost modeling exercises (Jafarov et al., 2012; Westermann et al., 2016). The neglect partially arises because the spatiotemporal patterns of soil moisture in the Arctic are poorly constrained by observations (Wrona et al., 2017a). Also, soil moisture is difficult to model, owing largely to the coupled nature of the water fluxes and the evolution of the permafrost table (Wright et al., 2009). These difficulties are compounded by the presence of organic soils that are often highly heterogeneous in periglacial environments (Quinton & Marsh, 1999). Consequently, the uncertainties in the thermal and moisture conditions remain large. The knowledge gap poses a limitation for permafrost temperature modeling and, more generally, for geomorphological, ecological, and biogeochemical studies (Koven et al., 2015; Watts et al., 2014; Westermann et al., 2016).

In summer, soil moisture influences the thermal dynamics largely through the surface energy balance and conductive heat transfer (Liljedahl et al., 2011; Wright et al., 2009). The two processes impart a complex control of soil moisture on the soil temperature evolution, as their effects are somewhat opposite in nature. As the soil dries, evaporation becomes an increasingly negligible component of the energy balance, resulting in increased soil temperatures (Liljedahl et al., 2011). Conversely, the thermal conductivity decreases, and this decrease is especially pronounced in organic soils (Beringer et al., 2001; O'Donnell et al., 2009). While a dry organic soil's surface heats up, the insulative effect keeps the deeper soil layers cool (Porada et al., 2016). Observationally, the insulative effect upon drying has been often inferred to dominate in organic soils. For instance, active layer thicknesses were observed to be lower during dry years in Alaska (Shiklomanov et al., 2010). Spatially, drier patches often have lower subsurface temperatures and smaller thaw depths, in both experiments (Göckede et al., 2017; Shiklomanov et al., 2010) and under natural conditions (Kane et al., 2001; Wright et al., 2009). However, the opposite relation has also been observed at intermediate soil moisture conditions (Boike et al., 2008; Rouse et al., 1992). The cooling influence of a dry surface occurs to a lesser degree, or may even be reversed, in mineral soils (Santanello & Friedl, 2003; Shur & Jorgenson, 2007). Thus, it is over organic soils that we would expect permafrost modeling to benefit most from large-scale soil moisture measurements.

Satellite remote sensing can provide spatially extensive information on soil moisture. Satellite remote sensing products exist at a range of spatial scales, but currently, there is no operational product available at any scale that is reliable at high latitudes. At the coarse-scale end of the spectrum, the accuracy of the Soil Moisture Active Passive passive product (∼40-km resolution), commonly considered to be the most reliable global product, has been found insufficient at the Trail Valley Creek (TVC) site in the Low Arctic tundra of the Northwest Territories, Canada (Wrona et al., 2017a). At the other end of the spectrum, fine-scale synthetic aperture radar data can be used to retrieve soil moisture. There have been a small number of promising studies across high-latitude ecosystems (Bourgeau-Chavez et al., 2013; Jacome et al., 2013). Most recently, C-band Radarsat-2 retrievals (100-m resolution) achieved relatively high accuracies of around 0.04 m3/m3 at the TVC site (Zwieback & Berg, 2019). In summary, tailor-made fine-scale products hold the greatest promise for permafrost applications, while dedicated circum-Arctic coarse-scale products have yet to become available.

To improve permafrost modeling using satellite soil moisture retrievals, the time-variable and partially opposing effects of soil moisture on the thermal dynamics have to be accounted for. In such complex systems, the most expedient way to harness indirect observations (surface soil moisture) to estimate unobserved quantities (soil temperature profile) is data assimilation (Tippett et al., 2003). By incorporating observations into a model that captures the relevant processes, the unobserved quantities can be updated in an optimal way that accounts for the uncertainties in both observations and model predictions (Whitaker & Hamill, 2002). The shortage of satellite soil moisture observations at higher latitudes has precluded the assimilation of soil moisture into permafrost models, even though this approach is widely used to improve the representation of the water and energy budget in temperate and subtropical regions (Dunne & Entekhabi, 2006; Renzullo et al., 2014). There, the Ensemble Kalman Filter (EnKF) is the state of the art data assimilation tool (Chen et al., 2011; Renzullo et al., 2014). It uses an ensemble of model runs to represent the uncertainty in, for example, the atmospheric forcing and the model parameters.

The variability of the model simulations across the ensemble is crucial for the success of soil moisture data assimilation. In order for the EnKF to revise the modeled soil temperatures, the modeled moisture content and temperatures must be correlated in the ensemble. Otherwise, the assimilation provides no additional information on soil temperatures. The correlation quantifies the coupling between soil moisture and the soil temperature profile, and it summarizes the manifold interactions between soil moisture and temperatures accumulated through time. Despite its importance for permafrost modeling, the magnitude, variability, and depth dependence of the ensemble coupling have not been explored.

The value of data assimilation is also strongly dependent on the uncertainty of the soil moisture data (De Lannoy et al., 2007). The higher the uncertainty, the less information the data provide on soil moisture and thus soil temperatures (even when the ensemble coupling is sufficient). In light of these complex influences, dedicated analyses are required to quantify the usefulness of data assimilation as a function of soil type and accuracy of the soil moisture retrievals.

To understand where and how the assimilation of satellite soil moisture can improve permafrost modeling, we pursue three objectives:
  • characterize the modeled relation and ensemble coupling between surface soil moisture and temperature profiles;
  • assess the theoretical feasibility by assimilating synthetic soil moisture data using an EnKF; and
  • assimilate Radarsat-2 soil moisture data to quantify the real-world potential.

To meet these three objectives, we rely on the Cryogrid3 model, a state-of-the-art permafrost scheme based on an energy-balance boundary condition. To capture the most important controls of soil moisture on the thermal regime, we extended it by a simple lumped soil hydrology model (Westermann et al., 2016). Our analyses focus on the Low Arctic tundra at TVC in the Northwest Territories Canada, taking advantage of the considerable variability in soil properties and moisture conditions. We concentrate on the summertime, as we lack distributed wintertime observations. To mimic operational conditions for permafrost modeling, we use globally available reanalysis data (Modern-Era Retrospective Analysis for Research Applications, version 2 [Merra-2]) as forcing, despite their lower accuracy compared to in situ data (Gelaro et al., 2017).

To characterize the coupling (objective 1), we use an ensemble approach, whereby uncertainties in the forcing and the soil properties are considered. The synthetic twin experiment also allows us to provide a first quantitative estimate of the potential improvement due to data assimilation across a range of soil types and accuracies of the soil moisture retrievals (objective 2). The assessment is likely optimistic, as all sources of uncertainty are precisely known in this idealized experiment. A more realistic setting is provided by the real-world experiments in objective 3.

2 Data and Study Site

2.1 Study Area

The TVC study site is located in the uplands to the east of the Mackenzie Delta, in the Northwest Territories, Canada (Wrona et al., 2017a). This morainal landscape is characterized by rolling topography interspersed with numerous lakes and drained lake basins (Quinton & Marsh, 1999). The area is underlain by continuous permafrost that has been observed to be warming rapidly (Kokelj et al., 2017). The permafrost temperatures are closely related to the vegetation cover, which encompasses sparse tundra (dominated by mosses, lichens, graminoids, and herbaceous shrubs), erect dwarf shrub tundra (<40-cm height), and tall shrub tundra (up to 2-m height). The soils beneath shrubs remain warmer during winter due to the insulative effect of the deeper snow that accumulates there (Lantz et al., 2013). Here, however, we focus on sparse tundra sites, as our in situ measurements only covered this land cover, which is dominant on the uplands.

The tundra is covered by organic cryosoils, except in disturbed areas such as those affected by thaw slumping. The soil properties vary greatly on small spatial scales, as they are closely linked to the microtopography (Quinton & Marsh, 1999). Mineral earth hummocks protrude 5–40 cm above the surrounding interhummocks. The hummocks consist of a mineral fine-grained soil core that is overlain by a thin layer of organic soil. The thickness of the organic soil veneer ranges from <5 to 15 cm, and the surface is predominantly covered by lichen communities. Conversely, the interhummocks are characterized by a thick ( urn:x-wiley:wrcr:media:wrcr23837:wrcr23837-math-000125 cm), highly porous moss and peat cover that is often colonized by graminoids or herbaceous shrubs (Quinton & Marsh, 1999). As the water table in the interhummocks is predominantly well below the surface, the thick organic cover can provide effective insulation during the summer, depending on its moisture content, so that the active layer depths (25–60 cm) are smaller than beneath the adjacent hummocks (50–100 cm). The large spatial differences indicate the comparatively small importance of lateral heat fluxes, which, nevertheless, will tend to smooth the frost table topography.

2.2 In Situ Data

Distributed soil moisture and temperature observations were acquired at two open tundra plots (Trail Valley Main Met [TMM] and Trail Valley Upper Plateau [TUP]) in 2014 (24 July to 25 August) and 2016 (05 June to 24 August; Wrona et al., 2017b; Zwieback, Westermann, et al., 2018). Each plot consisted of multiple sites within a radius of 100 m to capture the spatial variability in soil conditions. The location of the sites differed between the two study years; in total, we studied 14 sites, equally partitioned between hummocks and interhummocks. Soil moisture was measured at 5 cm and at 10- or 20-cm depth in 2014 and 2016, respectively, using Stevens Hydraprobe sensors. The measured dielectric constants were converted to volumetric soil moisture estimates using location-specific calibration equations (Wrona et al., 2017a). The near-surface soil moisture dynamics at 12 of the 19 sites were largely decoupled from precipitation events, as indicated by a low dynamic range of <0.1 m3/m3. In contrast to the limited temporal variability, there was large spatial variability in soil moisture conditions, as average values of adjacent locations within plots differed by ∼0.3 m3/m3, even for comparable microtopographical positions. The large spatial and subdued temporal variability is not uncommon in the tundra (Engstrom et al., 2005).

Temperature measurements were colocated with the soil moisture observations as the Stevens Hydraprobe sensors recorded soil temperatures with 0.3-K accuracy. The observed temperatures at 10/20 cm reflect the variability in soil types and moisture conditions: The organic soils at interhummocks tend to be warmer at wet locations than at adjacent dry ones in summer, whereas the differences are smaller at hummocks with thin organic soils (Figure 1d). The summertime soil temperature measurements were complemented by all-year measurements from 2015 onward at the TMM site at 4- and 20-cm depth (not colocated with any soil moisture measurements). Finally, meteorological data, such as precipitation and incoming shortwave and longwave radiation, were recorded at the TMM site. We used them to check the performance of the reanalysis-based model forcing.

Details are in the caption following the image
The Trail Valley Creek study area in the Northwest Territories, Canada, consists of two subsites, TMM and TUP. The analyses and in situ measurements are restricted to the sparse tundra (a), which is characterized by hummocky microtopography (b). The hummocks consist of a mineral core overlain by a thin organic TO soil; the adjacent interhummocks are characterized by porous organic O surface soils (c). (d) The porous organic soils act as thermal insulators: The deeper soil temperatures are the lowest at dry interhummocks. The lower panels show the air temperature (dark line: daily mean; shaded area: diel variability) and precipitation observed at TMM. TUP = Trail Valley Upper Plateau; TMM = Trail Valley Main Met.

2.3 Forcing Data

The atmospheric forcing was taken from the Merra-2 data set (Global Modeling and Assimilation Office, 2017). This global reanalysis product is based on the retrospective assimilation of a wide range of observations (e.g., in situ, satellite; temperatures, precipitation) into the Goddard Earth Observing Model (Gelaro et al., 2017). Merra-2 provides internally consistent and comparatively accurate estimates of land surface conditions. Here we use the air temperature, humidity, wind speed, incoming shortwave and longwave radiation, and precipitation at an hourly resolution.

To ingest the data into the model, we had to bias correct the incoming shortwave radiation. Initially, we had planned to ingest the (interpolated) data as provided, so as to mimic operational conditions and to keep the forcing internally consistent. However, the incoming radiation was too high by ∼15% in summer 2016 compared to the in situ measurements at TMM, causing the soil to heat up unrealistically. The bias was accounted for by scaling the incoming radiation by a constant factor, which however cannot be applied to larger scales. The other forcing variable that showed large biases was the precipitation (30% too low), but we did not bias correct it owing to its indirect influence on the temperature regime. However, we did account for the large uncertainty in the precipitation and the other forcing variables in the ensemble generation for data assimilation (section 4.2).

2.4 Remote Sensing Data

The assimilated satellite soil moisture time series were based on fine-scale Radarsat-2 stripmap mode acquisitions (Zwieback, Westermann, et al., 2018). The acquisitions were made from different orbits at an approximately biweekly repeat interval. The underlying retrieval approach was developed for the hummocky tundra at TVC by Zwieback and Berg (2019). It is based on the VV backscatter amplitude, which is postulated to increase linearly with soil moisture content. This empirical model was found to perform better than physically based approaches, presumably owing to limitations of the scattering models associated with the organic soils (subsurface scattering and dielectric mixing model) and the microtopography. The observed logarithmic backscatter did not exhibit strong deviations from linearity with either incidence angle or soil moisture, in contrast to predictions by the physically based models, but in line with the linear one. The applicability of the linear model was enhanced by the low dynamic range in soil moisture. The retrieval approach inverts the linear relationship in a Bayesian hierarchical framework that adaptively pools information from adjacent pixels to increase the precision of the soil moisture estimates while maintaining their 100-m resolution. The retrievals were found by Zwieback and Berg (2019) to provide reasonable estimates of the surface soil moisture (Root Mean Square Error [RMSE] upon calibration: ∼0.04 m3/m3, correlations with in situ data: ∼0.4). The mediocre correlations but good calibrated RMSE values reflect the relatively low dynamic range observed in the study area in both years 2014 (between 25 July and 23 August; 13/9 acquisitions at TMM/TUP) and 2016 (between 03 July and 21 August; 16/9 acquisitions at TMM/TUP).

The satellite retrievals were calibrated to the individual in situ probe data, using least-squares regression to account for the arbitrary offset and scaling of the synthetic aperture radar data (Zwieback & Berg, 2019). Ideally, such a calibration would not be necessary, and the data requirements render this approach infeasible for operational monitoring.

3 Cryogrid-3 Model

3.1 Model Description

Cryogrid-3 is a 1-D land surface scheme for permafrost regions (Westermann et al., 2016). Its main output is an estimate of the soil temperature profile, whose evolution is governed by the two key components of the model: the subsurface thermal dynamics (conductive heat transfer and phase change) and the surface energy balance. Both components depend on soil moisture Θ. The inclusion of a surface energy balance boundary condition is essential for our purposes, because of the soil moisture dependence of evaporation, and one of the main advantages of CryoGrid-3 over simpler permafrost models that have different boundary conditions based on, for example, empirical n-factors (Jafarov et al., 2012; Westermann et al., 2013).

The model neglects the advection of heat by water and vapor fluxes, which are often considered of minor importance in summer (Kane et al., 2001; Roth & Boike, 2001; Wright et al., 2009). The use of an intermediate-complexity model like Cryogrid-3 for exploring the potential of soil moisture assimilation seems warranted for first analyses, as it captures the key influences of Θ on the soil thermal regime. However, more complex three-dimensional models for permafrost environments like GEOtop (Endrizzi et al., 2011, 2014) or the semidistributed Cold Regions Hydrological Model (Pomeroy et al., 2007) will be required whenever advection is important. Devising appropriate schemes that are computationally tractable and easily parameterized on large scales, especially when they must represent fine-scale phenomena like microtopography, remains one of the greatest challenges for permafrost modeling.

In previous versions of the model, the water content was prescribed, but here we use an extended model with a simple dynamic soil moisture scheme (Figure 2a). It is a lumped hydrological model with only two layers. This simple representation of the soil moisture profile mimics the way static soil moisture was prescribed in many transient modeling studies (Jafarov et al., 2012; Westermann et al., 2013, 2017). The near-surface layer governs evaporation in the tundra due to the paucity of vascular plants (Liljedahl et al., 2011), and its often dynamic moisture content exerts a dominant control on the ground heat flux due to the high porosity and thus air content of the surficial organic cover (Beringer et al., 2001). The lower part of the active layer often decouples from the surface (Boike et al., 2008; Quinton & Marsh, 1999). The two-layer model is intended to capture these key influences of soil moisture on the thermal dynamics while keeping the model complexity and parameterization as simple as possible (Cherkauer et al., 2003). However, the coarse discretization cannot capture complex soil moisture profiles, for example, after precipitation events, and it further introduces artificial jumps in the soil thermal properties. Going forward, a finer soil moisture discretization appears propitious for soil moisture assimilation and long-term modeling alike. General-purpose land surface models appear particularly appropriate, as they are becoming increasingly apt at modeling permafrost temperatures and coupled biogeochemical processes (Beringer et al., 2001; Ekici et al., 2015; Lawrence et al., 2008).

Details are in the caption following the image
In the Cryogrid-3 model, the soil thermal dynamics and properties are coupled to soil moisture. (a) The model consists of (i) a lumped two-layer scheme with simple parameterizations of the fluxes (arrows; meaning of terms described in the text) and (ii) a thermal dynamics scheme based on conductive heat transfer, with a much finer discretization (temperature nodes shown as blue dots). Soil moisture influences the thermal dynamics via the energy balance (in particular through evapotranspiration E) and via its control on the soil thermal properties: (b) heat capacity of thawed organic and mineral soils and (c) thermal conductivity of thawed organic and mineral soils. The degree of saturation Θ is the volumetric moisture content divided by the porosity.

3.1.1 Thermal Dynamics

The subsurface thermal dynamics are governed by conductive heat transfer and phase changes
urn:x-wiley:wrcr:media:wrcr23837:wrcr23837-math-0002(1)

The change in temperature T depends on the soil's thermal properties, which in turn are parameterized as a function of the water content, ice content, and the soil matrix. The effective heat capacity ce accounts for the phase change of water, whose temperature dependence is described by a freezing characteristic curve. For a thawed soil, the heat capacity increases with soil moisture (Figure 2b). Also, the thermal conductivity k increases with water and even more so with ice content, and this increase is particularly pronounced for porous organic soils (Figure 2c). To numerically solve the equation, the soil is finely discretized in space and time. The time step is chosen adaptively (typical value: 10 min) to ensure stability.

The surface energy balance constitutes the upper boundary condition (Westermann et al., 2016). The temperature of the uppermost soil layer Tu changes according to the balance of the radiation fluxes (shortwave Snet and longwave Lnet), turbulent exchange (latent λE and sensible heat H), and the conductive ground heat flux into the deeper layers G. The turbulent fluxes are computed using the bulk similarity approach (Westermann et al., 2016). The latent heat flux, or evapotranspiration E, depends on soil moisture Θ, as it is lower than the potential evaporation Ep when the soil is dry. A simple β approach is used (Lee & Pielke, 1992): E = βEp, where β generally decreases with soil moisture. The dependence is a function of the depth of the frost table and the partitioning into evaporation and transpiration (see Appendix Appendix A for details). In winter, the upper boundary condition is modified to account for snow cover. The upper boundary condition is complemented by a lower boundary condition, which is given by a prescribed heat flux.

3.1.2 Soil Hydrology

The soil moisture dynamics are approximated by a simple two-layer lumped model. It is very similar to the Variable Infiltration Capacity (VIC) or Arno models in that it combines the water balance of each layer with simple semiempirical parameterizations of the water fluxes (Cherkauer et al., 2003; Todini, 1996). Changes in the near-surface soil moisture reflect the balance of inflows (precipitation P minus runoff R) and outflows (evapotranspiration E, drainage D, and percolation C), all of which are approximated by simple power-law-type functions. The general idea is that wetter soils lose more water than dry ones, with magnitude and moisture dependence being described by characteristic time scales τ and degrees of saturation Θ, respectively. The detailed formulas of all the fluxes can be found in Appendix Appendix A. The lower layer is replenished by percolation C and loses water due to baseflow B and evapotranspiration E. Being a 1-D model, lateral fluxes cannot be represented, even though they constitute a major component of the water balance, especially on sub-kilometer scales. Also, the dynamics below the lower layer are neglected, that is, the moisture is assumed static.

The dynamic soil moisture in the two layers entails changing thermal properties ce and k. This requires interpolation, as the grid used for the thermal computations is finer than the layers of the lumped model (Figure 2a). To bridge this gap, which also exists in the VIC model, we use simple nearest neighbor interpolation (Cherkauer et al., 2003).

3.2 Predicted Influence of Soil Moisture on the Soil Thermal Regime

To better characterize the relation between soil moisture and temperatures (part of objective 1), we ran a suite of model simulations. We estimated the model-predicted impact of soil moisture on the thermal regime by artificially fixing the soil moisture content during a dry and warm spell in early July 2016. It is during such warm conditions that the largest heat fluxes toward the permafrost table can occur, and hence it is also then that soil moisture can have the largest impact. To separate the moisture-mediated role of evaporative cooling from its impact on the soil thermal properties, we also ran simulations with evapotranspiration artificially set to zero.

4 Data Assimilation Approach and Experiments

4.1 EnKF

EnKFs provide estimates of the modeled states (here soil moisture and temperature) and their uncertainties (Tippett et al., 2003), given the assimilated observations. They differ from nonensemble based methods in that the covariance matrices that quantify the uncertainties are derived from an ensemble of states, rather than being propagated explicitly. The use of an ensemble to represent the covariances allows the filter to more flexibly deal with model nonlinearities, and it reduces the computational burden.

The EnKF alternates two steps: the forecast and analysis step. In the forecast step, the ensemble is propagated to the next time instance an observation is available. To this end, the Cryogrid-3 model is run for each of the N ensemble members with its member-specific parameterization and perturbed forcing, using the previous post-assimilation estimate as initial condition. Once the j = 1…N ensemble states xf,j have been simulated, the mean urn:x-wiley:wrcr:media:wrcr23837:wrcr23837-math-0003 and covariance Cf of the predicted pre-assimilation state are given, respectively, by
urn:x-wiley:wrcr:media:wrcr23837:wrcr23837-math-0004(2)
In the analysis or assimilation step, the observations are ingested to update the state. In our case the observation y is a scalar (one satellite surface soil moisture measurement). It provides insight into the state via the innovation, the discrepancy between y and its predicted value urn:x-wiley:wrcr:media:wrcr23837:wrcr23837-math-0005. H is the observation operator that maps the state to the observables (De Lannoy et al., 2007); for instance, it could link the soil moisture to the observed backscatter or inferred dielectric constant. As we assimilate soil moisture directly, its matrix representation consists of a single column whose only nonzero value corresponds to the surface soil moisture in the state vector. The innovation is central to updating the ensemble mean (forecast urn:x-wiley:wrcr:media:wrcr23837:wrcr23837-math-0006 to assimilation urn:x-wiley:wrcr:media:wrcr23837:wrcr23837-math-0007 in the notation of Tippett et al., 2003)
urn:x-wiley:wrcr:media:wrcr23837:wrcr23837-math-0008(3)
Here K, the Kalman gain matrix, governs the update. It in turn depends on the covariance matrix of the observations R (a scalar in our case, assumed known) and that of the model forecast Cf:
urn:x-wiley:wrcr:media:wrcr23837:wrcr23837-math-0009(4)

The equation for the Kalman gain matrix provides insight into the assimilation procedure. In our case, K consists of a single column that contains the forecast covariances of the state x with the surface soil moisture (up to a constant). Consequently, if the covariance of the temperature at a given layer vanishes (zero coupling), the assimilation of the soil moisture observation will not affect the updated temperature estimate (Chen et al., 2011).

To compute the post-assimilation covariance matrix Ca, we used the deterministic Ensemble Square Root Filter scheme proposed by Whitaker and Hamill (2002). Ca is given implicitly by the updated ensemble, which in turn is computed by applying a modified Kalman update to the deviation of ensemble member j, xa,j, from the mean.

4.2 Synthetic Experiment

The synthetic experiment provides idealized conditions for studying the efficacy of soil moisture assimilation. The basis of a synthetic twin experiment is the simulation of the “truth,” to which the ensemble results with and without assimilation (open loop) can be compared (Chen et al., 2011). Contrary to the truth run, the ensemble simulations are subject to model and forcing uncertainties. The availability of a true reference solution facilitates the assessment of different aspects of the assimilation procedure. We focused on three such aspects: the temperature-moisture coupling as a function of soil type, the achievable improvements in the soil temperature, and the accuracy requirements on the soil moisture data.

Our synthetic-twin experiments consisted of a series of truth runs. To capture a range of soil conditions, we focused on interhummocks with porous organic soils, on hummocks with a thin organic soil cover, and a mineral loam soil (Table 1). The total soil depth was set to 10 m (Table 1), with the soil layer thicknesses increasing from 1 cm near the surface to 1 m at the bottom (Westermann et al., 2017). The thermal evolution during one summer season at TVC was simulated during 3 years (2014–2016, after 4 years of spin up). For each year, we also conducted three additional runs with perturbed forcing in the truth simulation, applying the same forcing perturbation as in the ensemble. In total, this yielded 12 replicates per soil type, which allowed us to robustly assess the assimilation approach.

Table 1. Model Parameters for the Three Soil Types: O (Organic Soil in Interhummocks), TO (Thin Organic Soil on Hummocks), and M (a Loamy Mineral Soil), Based Mainly on Quinton and Marsh (1999), Wrona (2016), and Anders (2017)
Soil type
Parameter O TO M
Surface parameters
a Snow-free surface albedo (−) 0.18 0.2 0.16
ε Snow-free surface emissivity (−) 0.98 0.98 0.98
z0 Snow-free aerodynamic roughness length (m) 0.015 0.015 0.015
Qb Geothermal heat flux (W/m2) 0.05 0.05 0.05
ρs Snow density (kg/m3) 200 200 200
ηs Snow redistribution multiplier (−) 0.8 0.5 0.2
Subsurface parameters
di Soil layer thicknesses (m) [0.13, 0.20, 9.67] [0.04, 0.13, 9.87] [10.00]
ϕi Soil layer porosities (−) [0.90, 0.75, 0.40] [0.65, 0.45, 0.40] [0.40]
oi Matrix organic content, volumetric (%) [100, 100, 0] [100, 64, 0] [0]
Hydrological parameters
γ Transpiration contribution (−) 0.2 0.2 0.2
RWC Residual water content (m3/m3) 0.05 0.05 0.05
FC Field capacity (m3/m3) 0.70 0.25 0.25
αR Runoff shape parameter (−) 3.5 3.5 3.5
αD Drainage shape parameter (−) 2.0 2.0 2.0
ΘD,w Wet drainage DOS (−) 0.8 0.9 0.8
ΘD,d Dry drainage DOS (−) 0.5 0.7 0.5
ΘC Percolation DOS (−) 0.2 0.2 0.2
ΘB,d Baseflow DOS (−) 0.9 0.9 0.9
τD,w Wet drainage time scale (days) 3 15 15
τD,d Dry drainage time scale (days) 60 300 300
τC Percolation time scale (days) 7 35 35
τB Baseflow time scale (days) 180 900 900
  • Note. DOS = degrees of saturation.

In the synthetic truth runs, the physical parameters such as the porosity were adopted from previous studies (Anders, 2017; Quinton & Marsh, 1999; Wrona, 2016) for the hummocks and interhummocks (Table 1). One notable exception is the roughness length, whose ensemble mean we set to 1.5 cm according to literature values (McFadden et al., 2003). The hydrological parameters were set to plausible values based on the observed snow depth (snow distribution multiplier) and soil moisture (time scales and characteristic degrees of saturation). To account for the associated uncertainties, we perturbed these parameters in the ensemble generation.

The ensemble for the open-loop and assimilation runs consisted of N = 25 members that deviated from the respective truth run by perturbed meteorological forcing and model parameters. The forcing perturbations, that is, their size and whether they were additive or multiplicative, mimicked general practice in land-surface data assimilation studies based on reanalysis data (Dunne & Entekhabi, 2006; Renzullo et al., 2014). To reflect the larger forcing uncertainties at high latitudes, we generally followed a conservative approach by applying perturbations that were as large or larger than in the literature (Table 2). The air temperature was perturbed with additive noise with a temporal correlation length of 6 hr and a standard deviation of 3 K (compared to 2 K in Renzullo et al., 2014). The precipitation was perturbed by multiplicative noise with a magnitude of 100% (compared to 60% in Renzullo et al., 2014, and Dunne & Entekhabi, 2006). The radiative terms were perturbed multiplicatively by 20% based on Urraca et al. (2018).

Table 2. The Perturbation of Model Parameters and Forcing Can Be Either Additive (Zero-Mean Gaussian Noise) or Multiplicative (Lognormal Noise With Mean 1) in Nature
Parameter Perturbation type Magnitude Autocorrelation (hr)
Soil parameters
a Snow-free surface albedo Multiplicative 10%
z0 Snow-free aerodynamic roughness length Multiplicative 10%
ρs Snow density Multiplicative 10%
FC Field capacity Multiplicative 20%
ΘD,w Wet drainage DOS Multiplicative 20%
ΘD,d Dry drainage DOS Multiplicative 20%
ΘC Percolation DOS Multiplicative 20%
ΘB,d Baseflow DOS Multiplicative 20%
τD,w Wet drainage time scale Multiplicative 100%
τD,d Dry drainage time scale Multiplicative 100%
τC Percolation time scale Multiplicative 100%
τB Baseflow time scale multiplicative 100%
Forcing
P Precipitation Multiplicative 100% 24
Ta Air temperature Additive 3 K 6
Li Incoming longwave Multiplicative 20% 6
Si Incoming shortwave Multiplicative 20% 6
  • Note. The magnitude represents the standard deviation or the coefficient of variation. Time series of perturbations applied to forcing parameters are autocorrelated.

The parameter perturbations were chosen to reflect the nature of the model components. The thermal model component largely consists of physical parameters that can be measured directly. The most critical spatially variable parameters for a given soil type are the surface albedo, the aerodynamic roughness length, and the snow density, and they were perturbed by 10%. The perturbations applied to the soil hydrology parameters are much larger (20% for the degree of saturation thresholds and 100% for the time scales of the flux parameterizations), reflecting their semiempirical nature and the large spatial variability in moisture conditions. These large perturbations ensured a sufficiently wide ensemble spread of the soil moisture (standard deviation of the degree of saturation of 15–20%). Note that the soil type, such as the organic matter content, was assumed known with sufficient accuracy (Westermann et al., 2016).

The open loop run served as basis for the moisture-temperature coupling analysis. The metric was computed as the Pearson correlation coefficient between surface soil moisture and temperatures at different depths.

The synthetic soil moisture observations were realistic in terms of their repeat period and accuracy. The repeat period was taken to be 5 days, similar to the Radarsat-2 measurement interval at our study site, but also to globally available data like Soil Moisture Active Passive or Sentinel-1. The assumed accuracy of the soil moisture observations also mirrored that of the Radarsat-2 retrievals (0.05 m3 m3, white noise). To explore the impact of variable accuracies on the assimilation results, we also ran the experiments with four times and half that accuracy.

The synthetic assimilation employed the EnKF (equations 2-4). The prescribed observational uncertainty R was set to its actual value. To quantify the improvement of the simulated thermal regime upon assimilation, we computed RMSE values for both the open loop and the assimilation runs and subsequently compared them. The RMSEs were computed for the mean daily temperature, the diel temperature amplitude (difference between maximum and minimum), and the end-of-season thaw depth (computed via interpolation as the depth where T = 0 °C), assumed to be the active layer thickness. We only computed these values on days when no soil moisture observations were made, as the assimilation introduced discontinuities, thus distorting diagnostic quantities such as the diel amplitude. The RMSEs of these diagnostic quantities were complemented by those of the instantaneous T measurements.

4.3 Real Data Experiment

The real-data experiments for the summers of 2014 and 2016 mirrored the synthetic experiments in their setup. The ensemble perturbations were identical. We recall that these were large chosen to mimic operational conditions. In particular, the sizable prescribed uncertainties for the hydrological parameters, which were not calibrated, reflect the large spatial variability and associated uncertainties in the hydrologic regime.

The evaluation was based on the same RMSE metrics, this time computed with respect to the in situ observations (individual sites within the two plots; the first day of in situ measurements was discarded to allow for equilibration of the temperature measurements). To account for the uncertainties in the in situ observations σT = 0.3 K, we additionally normalized the instantaneous RMSE by σT to yield urn:x-wiley:wrcr:media:wrcr23837:wrcr23837-math-0010.

5 Results

5.1 Coupling Between Surface Soil Moisture and Soil Temperatures

To understand the coupling, we first analyze the simulations where soil moisture was held constant. The predicted influence of soil moisture on the thermal regime strongly varies with soil type, as it modulates the importance of the two competing processes, evaporation and changing soil thermal properties. Four days into the dry spell, the simulated ground heat flux G decreases by one order of magnitude for organic soils for dry compared to wet conditions (Figure 3a), in agreement with observations by Liljedahl et al. (2011) and the assumed dominant effect of the greatly variable soil thermal conductivity. Conversely, in mineral soils, the simulated G increases slightly as the soil gets drier, in line with Santanello and Friedl (2003). This small increase is driven by the lack of evaporative cooling at the surface, as G is seen in Figure 3a to decrease with soil moisture when evapotranspiration is suppressed.

Details are in the caption following the image
Soil moisture control on the simulated thermal regime, 4 days into a hypothetical dry spell in early July. The soil thermal regime of organic soils (dark blue) differs from that of mineral soils (gray), both for normal conditions (thick solid lines) and when evapotranspiration (ET) is artificially suppressed (β = 0, thin dashed lines). Soil moisture exerts a strong, texture-dependent control on the ground heat flux (a), the temperature gradient (b), daily average near-surface soil temperature (c), and near-surface diel temperature amplitudes (d). The model parameters are identical to those in section 4.

Concomitantly, organic soils can maintain steeper temperature gradients in the model when they are dry, mainly due to the low k (Figure 3b). The simulated temperature difference between the warm surface and the cooler subsurface is twice as large for dry as it is for wet organic soils. In mineral soils, by contrast, evaporative cooling and the (much lower) decrease in k with drying largely cancel another out in the Cryogrid3 model, so that the simulated temperature gradients are small and insensitive to soil moisture (Figure 3b).

In contrast to deeper soil temperatures, the daily near-surface temperatures urn:x-wiley:wrcr:media:wrcr23837:wrcr23837-math-0011 are predicted to increase as the soil dries. Declining evaporation leads to surface warming, whereas the soil thermal properties have a limited influence (simulated urn:x-wiley:wrcr:media:wrcr23837:wrcr23837-math-0012 is almost constant with soil moisture when evapotranspiration is suppressed; Figure 3c). This trend applies to both mineral and organic soils. The simulated diel amplitude ΔT also shows a similar soil moisture dependence in both soil types, as it greatly increases as the soil dries (Figure 3d).

The coupling observed in our model runs with variable soil moisture strongly depends on the soil type. In porous organic soils O, the moisture-temperature correlation is predominantly positive (∼0.1–0.4; Figure 4a) below 10 cm, consistent with a dominant control of the thermal conductivity on temperatures. It is weaker at hummocks with thin organic covers TO (∼0.1–0.2; Figure 4b) and essentially disappears at mineral soils M (∼0.0; Figure 4c). At 20-cm depth, this coupling remains almost constant throughout the day (Figure 4d). Conversely, for shallow temperatures, the coupling is negative during the day (evaporative cooling) and positive during the night (Figure 4d).

Details are in the caption following the image
Coupling between surface soil moisture Θu and the soil temperature profile across the synthetic experiments is expressed by the ensemble correlation coefficient ρ. Over the entire summer season, the median value (line) and the 5–95% spread (shaded region) vary with soil type: Wet porous organic soils O (a) are associated with warmer soils at depth, that is, ρ > 0. This relationship is weaker for the hummocks, characterized by dense and thin organic TO soils (b), and disappears for mineral soils M (c). The ρ in (a)–(c) apply to 9 pm local time, whereas (d) shows the diel variation in organic soils O on 24 June.

5.2 Synthetic Twin Experiment: Improvement in Temperature Estimates

The synthetic data assimilation experiment illustrates the potential improvement in the soil temperature profile estimates under realistic conditions. The observed improvements reflect the moisture-temperature coupling in that they are strongly dependent on the soil type.

In organic soils O, the improvements are on the order of 50% along the entire profile (Figure 5a). The RMSE of 20-cm average soil temperatures is improved by ∼50%, down to 0.8 K, due to the assimilation of soil moisture. There is a concomitant improvement in the active layer thickness, from 0.20 to 0.07 m. Nearer the surface, the daily averages (from 2.2 to 1.2 K) also improve markedly and so do the instantaneous values, in contrast to the diel temperature amplitude.

Details are in the caption following the image
Assimilation of synthetic surface soil moisture observations improves soil temperature estimates, depending on the soil type. (a–c) For the three soil types, the RMSE with respect to the truth runs (12 replicates) for the experiments with assimilation (EnKF, 0.05 m3/m3 noise level) is compared to those without (open loop), for the ALT, the daily average temperature at 20 and 5 cm ( urn:x-wiley:wrcr:media:wrcr23837:wrcr23837-math-0013 and urn:x-wiley:wrcr:media:wrcr23837:wrcr23837-math-0014), the diel amplitude at 5 cm (ΔT5), and the instantaneous measurements at 20 and 5 cm (T20, T5). (d) Dependence on the noise level of the assimilated soil moisture observations, relative to the open loop RMSE. ALT = active layer thickness; EnKF = Ensemble Kalman Filter.

The effect of soil moisture assimilation on the modeled temperature profiles is illustrated in Figure 6a. Without data assimilation, the organic interhummock soil is too dry, and the 20-cm soil temperatures are too low by ∼2 °C. Once the first soil moisture observation is assimilated on 05 July, the soil moisture is corrected upward and so is the 20-cm soil temperature. The lower temperatures are updated owing to the positive coupling that reflects the time-integrated effect of soil moisture on the lower soil temperatures. The 5-cm near-surface temperatures, with much less coupling, do not profit as much from assimilation.

Details are in the caption following the image
Example time series of the impact of assimilation in the synthetic experiment for organic (interhummock) and thin organic (hummock) soils. The time series were averaged within 24-hr windows. The assimilation and open loop runs are represented by the ensemble mean; the assimilation run is further characterized by its ensemble spread (shaded: 10–90% ensemble interval). The days when observations (black circles) are assimilated are shown by blue markers on top of the smoothed assimilated time series.

Permafrost modeling of thin organic soils (TO; hummocks) does not benefit as much from assimilation (Figure 5b). The improvements of the 5- and 20-cm daily average temperatures and of the active layer depth are on the order of 10%. The improvements are also visible in the example time series of Figure 6b, where soil moisture assimilation revises 20-cm temperatures upward by ∼1 °C to account for the wet bias in the open-loop simulation.

In mineral soils, the temperature estimates do not improve noticeably when surface soil moisture observations are assimilated (Figure 5c). The lack of improvement throughout the soil profile reflects the very low coupling between soil temperature and moisture content.

The improvements in the soil temperature estimates depend on the accuracy of the soil moisture observations (Figure 5d). The synthetic experiments with more accurate observations (0.025 instead of 0.05 m3/m3; organic soil) suggest that the associated improvements in the soil moisture are only small (<10% compared to the standard assimilation experiment). Conversely, the soil temperature estimates deteriorate when the soil moisture retrievals are much less accurate (0.2 instead of 0.05 m3/m3): The deterioration is largest close to the surface (5 cm).

5.3 Satellite Soil Moisture Assimilation: Improvement in Temperature Estimates

The assimilation of real soil moisture observations improves the estimates of the daily average temperature at 10 and 20 cm (Figure 7). Despite a similar improvement in the instantaneous temperatures, the obtained χ≈4 indicate that the modeling error continues to dominate over that of the reference in situ observations. Averaged over the entire summer season, the improvements in the deeper soil temperatures are larger for interhummocks with organic soils (0.5 °C or 30%, n = 7 for 2014 and 2016 combined), than they are for the hummocks with thin organic covers (0.3 °C or 20%, n = 7). In contrast to the deeper temperatures, assimilation makes little difference to 5-cm temperatures.

Details are in the caption following the image
Assimilation of Radarsat-2 surface soil moisture observations improves estimates of 10/20-cm soil temperatures. The RMSE with respect to the in situ data is compared for runs with assimilation (EnKF) to those without (open loop): the daily average temperature at 20, 10, and 5 cm ( urn:x-wiley:wrcr:media:wrcr23837:wrcr23837-math-0015, and urn:x-wiley:wrcr:media:wrcr23837:wrcr23837-math-0016), the instantaneous temperature (T20, T10, and T5), and the diel amplitude at 5 cm (ΔT5). For the instantaneous temperatures, the scale of the normalized quantity χ is indicated by a gray bar. (a and b) Interhummocks with porous organic soil in 2014 and 2016, respectively. (c and d) Hummocks with thin organic soil in 2014 and 2016, respectively. EnKF = Ensemble Kalman Filter.

The improvements in deeper soil temperatures are illustrated by comparison of two adjacent organic interhummocks (Figures 8a and 8b), one dry and one moist. Without assimilation (open loop), the predictions are identical. With ingestion of the first soil moisture observation, the modeled soil moisture is revised downward for the dry interhummock. The impact of this first ingestion on the spatial errors is shown in Figure 9a for all three instrumented interhummocks: The Θ error decreases for all three. A negative Θ increment implies that the 20-cm soil temperature and thus its error are also revised downward (positive coupling). At the moist interhummock (the lowest in Figure 9a), little adjustment takes place because the pre-assimilation soil moisture was accurate. The modeled soil temperature remains ∼1.5 °C too low. Later assimilation steps have a smaller impact on the temperature estimates (Figure 9b).

Details are in the caption following the image
Effect of Radarsat-2 soil moisture assimilation on temperature estimates illustrated for sites with organic (interhummock, a and b and d and e) and thin organic (hummock, c and f) soils; the sites overlap with Figure 1. The time series were averaged within 24-hr windows. The assimilation and open loop runs are represented by the ensemble mean; the assimilation run also by the 10–90% ensemble interval; the days when observations are assimilated are shown by blue markers on top of the smoothed assimilated time series. Note the disparity in spatial scales (<10 cm for in situ and implicitly for the assimilated Θ [black circles] vs. ∼50 km for the forcing data).
Details are in the caption following the image
The impact of assimilation on the T and Θ errors (relative to the in situ data) compared for nearby stations. The light blue ellipse shows the 90% ensemble interval of the T error (vertical) and Θ error (horizontal) prior to assimilation for each station. The black arrow shows the increment (change in state) due to assimilation, giving rise to the post-assimilation interval in darker blue. (a and b) The three organic interhummocks in 2014, (c and d) three hummocks (thin organic) in 2016. (a) and (c) correspond to the first seasonal ingestion of soil moisture, commonly associated with large temperature increments.

The impact of assimilation is shown for another pair of interhummocks in Figures 8d and 8e. The assimilation essentially removes the temperature bias at 10 cm (1–3 °C), whereas the 5-cm temperatures barely change. The difference between 5- and 10-cm temperatures is also evident in the zoomed-in plot of Figure 10. The assimilation mainly shifts the 10-cm temperatures, so the long-term average matches that of the in situ data more closely. Conversely, the 5-cm temperatures barely change upon assimilation, and the diel course remains overestimated.

Details are in the caption following the image
Time series of temperature and soil moisture (m3/m3) during 10 days in July for the wet organic soil example from Figure 8. The instantaneous temperatures reveal deviations between the in situ and the modeled temperatures. The assimilated Radarsat-2 observations are shown as black circles with the associated 90% uncertainty range.

The soil temperature improvements are somewhat smaller at the two hummocks shown in Figures 8c and 8f. The deeper temperatures are improved by ∼1 °C, as the assimilation can successfully account for the colder (warmer) conditions at the dry (wet) hummock. However, the temperature errors remain larger than they are for the interhummocks, and larger spatial offsets remain (Figures 9c and 9d). In contrast to the deeper temperatures, the near-surface temperatures actually deteriorate by up to 1 °C.

Finally, these examples illustrate that the soil moisture estimates improve. At the end of the assimilation period, the modeled mean soil moisture is within one standard deviation of the contemporaneous satellite observation in all examples in Figure 8. However, the subdued temporal dynamics in, for example, Figure 8c remain difficult to capture.

6 Discussion

6.1 Contribution of Soil Moisture Observations to Permafrost Modeling

Surface soil moisture observations can improve estimates of subsurface soil temperatures, as indicated by our synthetic and real-data assimilation experiments. The degree of improvement is strongly contingent on the soil type, and it also varies with depth. Soil moisture assimilation was most successful at organic soils. When dry, they act as insulators: The deeper soil remains cool. This association is commonly observed (Göckede et al., 2017, e.g.). In the model, it was represented by a positive ensemble correlation, or coupling, between surface soil moisture and deeper temperatures (Figure 4). It is this coupling that allowed the EnKF to correctly revise the 10- and 20-cm soil temperature given a surface soil moisture observation (e.g., Figure 5e). Conversely, the coupling between surface soil moisture and shallower (5 cm) temperatures was weak, and data assimilation provided little improvement. For thin organic soil covers, the same associations were observed, but they were weaker (Figure 4). The temperature estimates consequently improved less. Finally, surface soil moisture observations provide little information on soil temperatures in mineral soils (only synthetic data), associated with the limited insulative protection dry mineral soils afford (e.g., Figure 5).

Soil moisture can be a major source of uncertainty in permafrost modeling. In the Low Arctic and Subarctic, where organic soils are prevalent, accurate soil moisture information can be crucial for capturing spatial and interannual variability in active layer temperatures. But how does it compare to other sources of uncertainty like soil type and snow cover? These are known to exert a dominant control on the thermal regime, and their accurate representation remains a challenge (Ekici et al., 2015; Lawrence et al., 2008). We assumed accurate knowledge of the essentially time-independent soil properties like porosity, which constitutes a major limitation for operational monitoring, as we discuss in the next section. Snow also remains a limiting factor, which we implicitly acknowledged by large ensemble uncertainties (section 4.2). However, its influence on the surface and near-surface (top 30 cm) temperatures during summer, which we focused on, is small; in contrast to that of soil moisture.

6.2 Open Questions and Limitations

We could only make a first step toward establishing soil moisture assimilation as part of operational permafrost modeling. The increasing availability of in situ and remotely sensed soil moisture data will make it easier to overcome one major limitation of our study, namely, its restriction to a single site and season. Not only was the geographical extent limited, but there were also limitations in terms of the spatial scale and calibration. The 100-m resolution was too coarse to resolve the spatial variability in soil properties associated with the microtopography (Endrizzi et al., 2011; Engstrom et al., 2005), but we did not explicitly address the spatial scale gap between the Radarsat-2 data and the in situ observations. The representativeness error was implicitly included in the lumped observational error, which was estimated by direct comparison of the radar retrievals with the in situ observation. Contrary to the assumption of the assimilation system, the observation error likely also included systematic time-variable components, in part due to the representativeness error (Zwieback, Colliander, et al., 2018). The appropriate treatment of scale differences remains an open question, in particular also if coarse-scale soil moisture products (∼40 km) are to be assimilated.

The calibration of the soil moisture retrievals also remains an open issue, as our referencing with respect to in situ data is infeasible under operational conditions. Longer time series, absolute soil moisture estimation approaches (e.g., for polarimetric low-frequency data), and bias-aware assimilation procedures will help to solve the calibration issue (De Lannoy et al., 2007; Zwieback & Berg, 2019). However, the limited temporal variability in the examples of Figure 8 highlights its difficulty. Multiannual time series will also be required to address open questions to do with thermal processes during winter, such as the length of the zero-curtain period (Riseborough et al., 2008).

Improvements to the coupled permafrost model are needed as well. Also in this context, calibration and scale are two important issues. We did not perform a dedicated calibration against in situ data but prescribed very large parameter uncertainties to capture the sizable spatial variability in moisture regimes observed in our study region (Figure 8). The idea was to let the soil moisture observations constrain the model soil moisture (Dunne & Entekhabi, 2006). In the future, however, these observations could also constrain the model parameters (De Lannoy et al., 2007). Finally, both the hydrological and the thermal model components had limitations in representing processes such as evaporation (simple β approach that cannot account for stomatal regulation or transfer-limited conditions; e.g., Liljedahl et al., 2011), advection (neglected altogether), infiltration, and water redistribution (simple two-layer scheme). An explicit representation of the microtopography is also necessary for bridging the scale gap to the satellite observations. More complex models, such as 3-D models or general-purpose land surface schemes that have become increasingly adept at modeling permafrost temperatures, could thus improve the estimation accuracy, albeit at increased computational costs and parameterization complexity (Chadburn et al., 2017; Endrizzi et al., 2011).

The interactions between surface soil moisture and soil temperatures raise the question of how remotely sensed surface temperature may be used to better represent the thermal and hydrological conditions (Langer et al., 2010). While surface temperature observations are widely employed to constrain soil moisture in temperate regions, in permafrost regions, they have been used as an upper boundary condition for soil temperatures, holding the soil moisture content constant (Langer et al., 2013). This latter use could have counterproductive effects if the soil moisture content is far off. For instance, if an organic soil was wrongly assumed to be wet, the imposition of the observed warm daytime surface temperature would induce a spurious warming of the deeper soil. Data assimilation could be an elegant solution to the complex, diurnally changing covariability, provided the soil moisture uncertainty is appropriate. The complementarity of surface temperature and soil moisture observations for improving permafrost modeling (e.g., for model calibration) should hence be explored (Westermann et al., 2017).

Soil moisture assimilation may become valuable for biogeochemical and ecological studies in permafrost regions. Both moisture and temperature exert a dominant control on processes such as respiration or methane production (Chadburn et al., 2017; Sturtevant et al., 2012). As ingesting satellite soil moisture into dedicated models can improve their soil moisture and temperature profiles, these improvements may, in turn, enhance the quality of the predicted carbon stocks, fluxes, and related variables (Watts et al., 2014). The value of soil moisture assimilation in biogeochemical applications is one of the exciting questions our study raises.

7 Conclusions

We assimilated soil moisture data, synthetic and satellite-derived, into a permafrost model using an EnKF. Our overall aim was to assess to what extent surface soil moisture observations can improve permafrost modeling, in particular the representation of the active-layer temperatures during summer. Based on these synthetic and real-data assimilation experiments, we draw the following conclusions:
  1. Surface soil moisture information has the potential to improve permafrost modeling because soil moisture exerts a strong control on the soil thermal properties and the surface energy balance.
  2. The model-based coupling between surface soil moisture and soil temperatures, a necessary condition for improving soil temperatures by soil moisture assimilation, strongly depends on soil type. In organic soils, drying induces a pronounced insulative effect that keeps the ground heat flux and deeper soil temperatures low, even though the diminishing importance of evaporative cooling contributes to high surface temperatures. Conversely, in mineral soils, the coupling is weak because the two opposing effects largely cancel out.
  3. Assimilating surface soil moisture into a permafrost model like CryoGrid-3 using an EnKF can exploit the complex interrelation between moisture and soil temperatures. Also, it accounts for uncertainties in atmospheric forcing, the model parameters, and the observations. However, owing to the strong dependence of the thermal regime on soil type, we made the strong assumption that the soil properties were known.
  4. In organic soils, assimilating surface soil moisture can improve soil temperature profiles according to our synthetic and real-data experiments. The improvement is larger for deeper temperatures, which also have a much larger memory and persistence. In mineral soils, the improvements in temperature and active layer depth estimates were negligible.

In summary, our findings highlight the importance of soil hydrology observations for modeling permafrost and active layer conditions. Novel observational and model capabilities also hold promise for improving biogeochemical monitoring, for detecting incipient thermokarst and more generally for understanding and predicting land surface changes in the Arctic.

Acknowledgments

The authors are grateful to Beth Wrona, William Woodley, Justin Adams, Branden Walker, Tracy Rowlandson, and Rachel Humphrey for their efforts in collecting field data. They acknowledge funding by the Canadian Space Agency, ArcticNet, and NSERC (Discovery Grants Program; Changing Cold Regions Network). Simon Zwieback was supported by the Swiss National Science Foundation (P2EZP2_168789) and Moritz Langer by the Federal Ministry of Education and Research (BMBF; grant 01LN1709A). The in situ soil moisture and temperature data, as well as the colocated calibrated Radarsat-2 retrievals, are freely available from the URLs provided in the references (registration required) and so are the reanalysis data.

    Appendix A: Lumped Hydrological Model

    The lumped hydrological model developed for this study consists of two layers. Their depths are prespecified but can be dynamically adjusted if the layers are partially frozen (negative soil temperatures). If the frost table is located inside the layer at a given time step, the layer's lower boundary is taken to be the thermal node just above the frost table. Conversely, the layer's soil moisture is held constant whenever the upper boundary is frozen. Owing to these simplifications, the model cannot account for liquid water flow below the freezing point.

    The soil moisture change within each layer reflects the balance of fluxes into and out of the layer according to the water balance equations. The semiempirical parameterizations of the fluxes follow those of similar lumped schemes like ARNO or VIC (Cherkauer et al., 2003; Todini, 1996). To facilitate the interpretation and perturbation of the parameters, the fluxes are parameterized in terms of time scales τ and unitless characteristic degrees of saturation Θ·. To simplify the formulas for the fluxes, we express the storage as both the total water content w and the degree of saturation urn:x-wiley:wrcr:media:wrcr23837:wrcr23837-math-0017.

    The upper layer gains water by that part of the net precipitation (reduced by evapotranspiration, P − E) that does not run off immediately. The runoff R increases with the upper layer's degree of saturation Θu, compare Todini (1996)
    urn:x-wiley:wrcr:media:wrcr23837:wrcr23837-math-0018(A1)
    where r = 0.3 is a dimensionless maximum runoff fraction which we added to account for the limited overland flow in organic soils, ΘR is a characteristic runoff degree of saturation and αR is a shape parameter. Whenever the storage capacity is exceeded, the excessive water is lost immediately. Otherwise, the losses are the lateral drainage D, the percolation to the lower layer P, and the evapotranspiration E. Drainage is zero below a critical degree of saturation ΘD,d and increases rapidly above ΘD,w, as in the ARNO model (Todini, 1996)
    urn:x-wiley:wrcr:media:wrcr23837:wrcr23837-math-0019(A2)
    The percolation C depends on the moisture content in the upper and lower layers Θu and Θl
    urn:x-wiley:wrcr:media:wrcr23837:wrcr23837-math-0020(A3)
    The evapotranspiration E = (1 − γ)EE + γET consists of evaporation EE and transpiration from vascular plants ET, weighted by γ. Each component is parameterized by a β approach, according to which the flux drops below its potential rate (computed using bulk similarity, assuming 100% relative humidity at the surface) when it is moisture limited: E· = β·Epot. More precisely, the upper and lower layers contribute to the overall flux with their own moisture-dependent β·, according to (Lee & Pielke, 1992)
    urn:x-wiley:wrcr:media:wrcr23837:wrcr23837-math-0021(A4)

    The characteristic degree of saturation Θ·,r below which β < 1 corresponds to the field capacity in case of transpiration and to the residual moisture content for evaporation. The contributions from the upper and lower layers are weighted by an exponential decay with depth urn:x-wiley:wrcr:media:wrcr23837:wrcr23837-math-0022. z is a characteristic length scale corresponding to the rooting depth (8 cm) for transpiration and the depth of the surface layer (3 cm) for evaporation. With this parameterization, the contribution can be adjusted dynamically to the position of the frost table. The evapotranspiration is set to zero for frozen soil.

    The lower layer gains water through percolation and loses water through evapotranspiration and baseflow, or deep drainage, B. As in the ARNO model (Todini, 1996), B is zero unless the lower-level moisture exceeds a characteristic degree of saturation ΘB (and provided that the soil underneath is thawed):
    urn:x-wiley:wrcr:media:wrcr23837:wrcr23837-math-0023(A5)