Combining a climate-permafrost model with fine resolution remote sensor products to quantify active-layer thickness at local scales

Active-layer thickness (ALT), defined as the maximum depth of seasonally thawed soil overlying permafrost, has been identified as an essential climate variable by the World Meteorological Organization (Michaelides et al 2019), and has been the focus of the Circumpolar Active Layer Monitoring (CALM) program (Shiklomanov et al 2012). Effective quantification and monitoring of ALT are critical to understand the impacts of wildfires and climate warming on permafrost degradation and recognize the response of terrain conditions to the disturbances. Efforts for ALT mapping have focused on developing or applying large-scale process-based or statistical-empirical models at regional/global scales (1000 km² or larger) with a coarse resolution (1 km or larger) (e.g. Anisimov et al 1997, Riseborough et al 2008, Dankers et al 2011, Koven et al 2011, Park et al 2016, Qin et al 2017, Yi et al 2018, Peng et al 2023) or moderate spatial resolution (30–100 m) (Pastick et al 2013, 2015, Mishra and Riley 2014). Radar remote sensing or geospatial techniques have also been explored for estimating ALT at regional scales with varying degree of success (e.g. Nelson et al 1997, Liu et al 2012, Schaefer et al 2015, Chen et al 2019, Michaelides et al 2019). Local application of such type of ALT products is constrained by their coarse spatial resolution, and large uncertainty caused by ineffective model parameterization, limited process understanding, sparse field calibration/validation in terms of mapping areas (Yi et al 2018), and unreliable assessment caused by the severe scale difference between model grids and field observations (Pastick et al 2015).

ALT mapping with fine resolutions (5 m or smaller) is particularly significant for directly assessing vulnerability of local habitats, infrastructure, engineering features, and supporting mobility activities in cold regions. Presently, local (fine scale) ALT information is mainly available from in-situ point based measurements. Direct application of climate-permafrost models to estimate ALT at fine spatial resolutions is challenging because these models require inputs of climatic variables accounting for environmental heterogeneity at regional/global scales, but climatic conditions can be homogeneous within a landscape at local scales (10 km² or smaller). Local ALT spatial variation is controlled by vegetation composition, topography, hydrology, and soil properties with great complexity while interannual variation is mainly influenced by air temperature, precipitation, and snow characteristics (Loranty et al 2018). A link of homogeneous climate variables with terrain biophysical characteristics that can account for the heterogeneity of soil conditions may have the potential to quantify spatial and temporal variation of ALT at local scales where there are currently few options.

The simplest climate-permafrost model was developed based on the Stefan solution to relate climate to the thermal regime of the active layer of permafrost (Nelson and Outcalt 1987, Hinkel and Nelson 2003):

$$\begin{align}Z = \sqrt {\frac{{2{k_t}{n_t}}}{{{\rho _b}WL}}} \times \sqrt {{\text{DD}}{{\text{T}}_a}} \end{align} \tag{ 1 }$$

where Z is the ALT in meters; k_t is the thermal conductivity of thawed soil; n_t is the thawing n-factor, a ratio of the seasonal degree-days sum at the soil surface to that in the air to parameterize the temperature regime at the ground surface; ρ_b is the soil bulk density; W is soil water content; L is the latent heat of fusion; and DDT_a is the annual thawing index which is defined as the cumulative number of degree-days above 0˚C over a year. Calculation of ALT based on equation (1) requires inputs of soil parameters and n-factor which usually are unknown for most regions; thus, a catchall scaling parameter E was defined (Nelson and Outcalt 1987):

$$\begin{align}E = \sqrt {\frac{{2{k_t}{n_t}}}{{{\rho _b}WL}}} \end{align} \tag{ 2 }$$

where E is called 'edaphic factor' to summarize the response of soil to climatic forcing and can vary across space if soil conditions are different. Equations (1) and (2) are then combined as:

$$\begin{align}Z = E \times \sqrt {{\text{DD}}{{\text{T}}_a}} .\end{align} \tag{ 3 }$$

By rearranging equation (3), E has been estimated for different land cover types by using measured ALT and annual thawing index data assuming E was constant within each land cover type to map ALT at regional scales (Zhang et al 2005, Park et al 2016). Peng et al (2018) explored geostatistical methods for estimating E in the Northern Hemisphere. At local scales, E can change widely within and across land cover types, topographic position, or parent material. Among these control factors of E, vegetation is an obvious indicator to inform soil conditions, particularly in areas where 'ecosystem protection' promotes permafrost stability (Shur and Jorgenson 2007). Vegetation type and canopy structure, along with surface soil organic layer and depth, modulate the soil surface thermal balance through insulation which governs the rate of seasonal thaw (Fisher et al 2016). The coupling of surface vegetation and subsurface soil allows application of high-resolution sensor products to indirectly quantify E across space to account for the heterogeneity of soil conditions, and thus consequently estimate ALT using equation (3) by accounting for climatic forcing down to local scales.

In this study, we developed an approach to generating fine-resolution ALT products at local scales by integrating a modified climate-permafrost model with high-resolution remote sensor products and contemporary machine learning solutions. The U.S. Army Corps of Engineers Cold Regions Research and Engineering Laboratory (CRREL) has been collecting end-of-season ALT data at two lowland permafrost experiment stations in Interior Alaska since 2014. These two sites represent much of the permafrost and variety of ecotypes in Interior Alaska.

Up to 2022, we have made a total of 3177 field measurements at these two field sites which encompass common boreal ecoregion land cover classes (Evergreen and Deciduous Forest, Mixed Forest, Shrubland, Grassland, and Wetland), cumulatively representing 74% of the boreal and taiga biome (Latifovic et al 2017). Meanwhile, the National Aeronautics and Space Administration (NASA)'s Arctic-Boreal Vulnerability Experiment (ABoVE; Miller et al 2019) and our aerial campaigns collected Airborne Visible InfraRed Imaging Spectrometer—Next Generation (AVIRIS–NG) hyperspectral imagery and light detection and ranging (lidar) elevation data at the sites. Fine resolution satellite imagery collected by WorldView-2 is also available. This rich dataset provides a unique opportunity to map the edaphic factor E at a fine spatial resolution, leading to a projection of ALT at local scales using a single climatic variable, the annual thawing index. This has potential to largely reduce the intensive field measurements in the future, to project how, when, and where the local permafrost terrains respond to global climate warming, and assist with decision making, especially over U.S. Army training sites in Interior Alaska.

NASA's ABoVE collects and distributes airborne hyperspectral imagery products with rich radiometric contents at a spatial resolution of 5 m or larger, while spaceborne WorldView-2 provides 0.5 m pansharpened multispectral imagery products. Airborne lidar offers elevation information complimentary to optical sensor products. We integrated these three data sources in our developed approach with an expectation to better predict the edaphic factor E indirectly, because it is evidenced that a fusion of them can improve vegetation characterization across heterogeneous landscapes (Zhang et al 2016). This work is a further effort of Zhang et al (2021) for mapping ALT at local scales using fine resolution remote sensor products. Zhang et al (2021) linked annual field measurements with remote sensor datasets to spatially extrapolate ALT at local scales. A constraint of the previous method is that it cannot be applied to map ALT for a specific year if field measurements are not available for that specific year. For example, to map ALT in 2024, field measurements must be conducted for 2024 to calibrate a remote sensor model to be used to estimate ALT for areas without measurements. The aim of this work was to improve the previous method so that ALT could be spatially and temporally extrapolated by including the climatic forcing in the procedure to reduce/eliminate the intensive field work.

2.1. Study area

Our study area is located at two of CRREL's long term permafrost experiment stations: Farmer's Loop, and the Creamer's Field Migratory Wildfowl Refuge (Creamer's Field), near Fairbanks in Interior Alaska (figure 1). The region is characterized by a cold continental climate with dry winters. This area is underlain by discontinuous permafrost up to 60 m thick primarily located along north facing slopes or in lowlands where vegetative cover or soils offer thermal protection (Jorgenson et al 2008, Douglas et al 2014). The area is part of the boreal biome and represents typical discontinuous permafrost terrain with varying ALT. Both sites are lowlands comprised of undifferentiated perennially frozen silt deposits (Péwé et al 1966) that range from peaty-silty abandoned floodplain deposits with small Holocene ice wedges at Creamer's Field to thicker deposits of eolian silt at Farmer's Loop likely of late Pleistocene age. The Pleistocene permafrost over this area consists of syngenetic ice-rich windblown loess and organic matter representing high carbon 'yedoma' permafrost vulnerable to thawing (Douglas and Zhang 2021, Zhang et al 2021). Massive ice wedges and ice cemented silt are also common over this area (Douglas et al 2021). The study site had more than 160 d per year with air temperature below 0 °C during 2014–2022 based upon records from the station at the Fairbanks International Airport.

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2.2. Data

We developed an ALT estimation protocol to integrate years of field ALT measurements with remote sensor data and linked a climate-permafrost analytical model based upon Stefan's solution with machine learning techniques. There are two major components in the protocol: (1) estimation of the edaphic factor E over field ALT measurement spots using a modified climate-permafrost model based on Stefan's solution; and (2) projection of E and ALT across the entire study area using an object-based machine learning upscaling solution and remote sensor data. These are described below.

3.1. Estimating edaphic factor E using a modified Stefan solution

We first modified the Stefan based climate-permafrost model by including spatial and temporal information in the model. ALT for a specific spot and a specific year is estimated as:

$$\begin{align}Z\left[ {S,T} \right] = E\left[ {S,\,1} \right] \times \sqrt {{\text{DDT}_a}} \left[ {1,\,T} \right]\end{align} \tag{ 4 }$$

where S refers to Space for a specific location; and T refers to Time for a specific year. This can be also considered as a matrix with dimensions S and T. For local scale modeling, E barely changes across time if no severe disturbances occur but varies across space. This is reflected in E[S, 1]. The annual thawing index DDT_a is homogeneous for a local landscape for a specific year but varies across years, which is reflected in $\sqrt {{\text{DDT}_a}} \left[ {1,\,T} \right]$. Therefore, the end of season ALT for a specific S and T is a combination of climatic forcing in year T and site-specific soil condition at location S.

For our study area, we had nine years of ALT measurements at 353-point locations, and the annual thawing index for each year could be derived from the daily air temperature measurements from nearby weather stations. By rearranging equation (4) using matrix calculation functions, E across space can be estimated as:

$$\begin{align}E\left[ {S,\,1} \right] = \frac{{Z\left[ {S,T} \right] \times \sqrt {{\text{DDT}_a}} {{\left[ {1,\,T} \right]}^t}}}{{\sqrt {{\text{DDT}_a}} \left[ {1,\,T} \right] \times \sqrt {{\text{DDT}_a}} {{\left[ {1,\,T} \right]}^t}}}\,\end{align} \tag{ 5 }$$

where t refers to the transpose of the matrix $\sqrt {{\text{DDT}_a}} \left[ {1,\,T} \right]$. The estimated E across space can be used to calibrate and validate a remote sensor-based model to project E for the entire study area.

3.2. Object-based machine learning estimation of E and ALT

Due to the coupling effects of soil features, land surface characteristics, and terrain conditions, which is reflected in optical sensors and lidar elevation information, linking the estimated E with remote sensor data to develop a model and project E across the entire study area offers the key to further recognize the spatial and temporal variation of ALT. The relationship between E and remote sensor variables can be quantified below:

$$\begin{align}E\left[ {S,\,1} \right] = f\left( {B_i}\left[ S,1\right] {,\,{\text{DEM}}\,} \left[S,1\right] {,\,{\text{CHM}}\,} \left[S,1 \right],\, \ldots \right).\end{align} \tag{ 6 }$$

Therefore, E can be estimated from sensor derived indicators such as surface reflectance B_i (i refers to different bands), topographic information reflected in DEM, vegetation information reflected in CHM, as well as other variables. Note that these variables should have a comparable spatial resolution to the field scale to reduce the uncertainty in the model development. The relationship between soil conditions reflected in E and surface indicators reflected in remote sensor data is complicated, thus sophisticated machine learning solutions are preferred to catch the nonlinear characteristics among them. For this study, we selected the support vector machine (SVM) regression approach because it requires less training samples to generalize a model. The SVM algorithm looks for a hyperplane in higher dimensions to fit the data with the aim of minimizing the coefficients. It has been frequently used in remote sensing, as reviewed by Mountrakis et al (2011).

To estimate E and ALT, we applied an object-based modeling and mapping procedure which has proven more effective and accurate when high resolution imagery products are used (Douglas and Zhang 2021, Zhang et al 2021). We generated objects from the WorldView-2 imagery using the multiresolution image segmentation approach in eCognition Developer 10 (Trimble 2020). A total of 5283 objects were created with varying sizes from 0.06 m² to 9144 m². We then extracted corresponding spectral and spatial features including the mean and standard deviation values for each object. To integrate hyperspectral data in the protocol, we first reduced the high dimensionality of hyperspectral imagery using the minimum noise fraction (MNF) algorithm, a commonly used feature selection approach for preprocessing hyperspectral imagery; we then calculated the spatial mean MNF value of each of the selected MNF layers for each object. Lidar statistical descriptors of DTM and CHM including mean and standard deviation were also determined for each object and merged with WorldView-2 and AVIRIS-NG imagery derived features, leading to a fused remote sensor dataset. We spatially matched E estimated from equation (5) with the fused remote sensor dataset, resulting in a reference dataset with E as the dependent variable and remote sensor data (WorldView-2 surface reflectance, AVIRIS-NG selected MNF layers, lidar derived DEM and CHM) as the independent variables to develop an upscaling model. If multiple E values were within an object, an average E was determined for this object, leading to a reduced number of reference objects (792). We applied the k-fold cross validation approach to avoid over-fitting issues if the same dataset was used in both training and testing procedures. The k-fold cross validation is a state-of-art technique in machine learning calibration and validation. This method randomly splits the reference samples into k equal groups, and then iterates the model k times. In each iteration, one group is used to assess the model, and the remaining groups are used to train the model. Here, we set k to 5 rather than the commonly used 10 because we had a relatively small number of reference samples (Anguita et al 2012). If the model is acceptable, E can be projected for the entire study area using the fused sensor dataset. Consequently, ALT can be estimated for any past years or future to model the response of ALT to different climate warming scenarios using equation (4). In this work, we mapped the ALT for our study area using the developed protocol for 2015 (the shallowest ALT) and 2019 (the deepest ALT) and calculated the statistical metrics including R², mean absolute error (MAE), and root mean squared error (RMSE) in terms of field measured ALT to evaluate the performance of the developed protocol.

Areas covered by other land cover types including urban impervious area and water were masked out as non-region of interests (ROIs) because we did not have field data over these land cover types. We conducted an object-based SVM classification following Zhang et al (2020) and generated an ecotype map to constrain the estimation of E and ALT to ROIs only. An overall accuracy of 95% was obtained in classifying six land cover types (Mixed Forest, Moss Spruce, Tussock Tundra, Wetland, Water, and Others) based upon a total of 378 reference objects identified in the field and interpreted from the WV-2 imagery.

4.1. Annual thawing index and field measured ALT

Figure 2 displays the annual thawing index (degree-days) calculated from the daily air temperature data and the average of field measured ALT (cm) across four major ecotypes (Mixed Forest, Moss Spruce, Tussock Tundra, and Wetland) in the study area. The thawing index varied across years with 2015 as the lowest and 2019 as the highest (figure 2(a)), leading to the shallowest and deepest ALT observed in the field correspondingly (figure 2(b)). This shows that climatic forcing is a major factor impacting thaw depth. ALT varied nearly two-fold across ecotypes, with the deepest found in the Wetland ecotype (101.5 cm), and shallowest in Moss Spruce (58.6 cm). Mixed Forest (86.5 cm) and Tussock Tundra (70.1 cm) have an intermediate depth with the same climatic forcing. We attributed the lower ALT in Moss Spruce and Tussock Tundra to greater moss cover and structural characteristics of overstory vegetation while higher ALT in Wetland was likely due to the frequent presence of surface water. This indicates a strong coupling of ALT with surface ecotypes, and their varying responses to climatic forcing. Correlation analyses of ALT and DDT_a across ecotypes showed that Tussock Tundra had the highest correlation coefficient of 0.77 while Mixed Forest had the lowest correlation coefficient of 0.33. The inconsistence of ALT and DDT_a was also observed across time, indicating other climatic forcing factors such as rainfall and snow cover but were not considered in the climate-permafrost model.

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4.2. Estimation of edaphic factor E using remote sensor data

The scatter plot of estimated E from remote sensor data and equation (5) is displayed in figure 3. In general, estimation from remote sensor data had a good agreement with the derivation of E from equation (5), indicating sensor derived surface reflectance and elevation data could explain 72% of the variance of E derived from the modified Stefan solution. Further application of the edaphic factor model to estimate E for the study area is displayed in figure 4(a). A joint observation of figure 4(a) and the ecotype map figure 4(b) revealed the variation of E within an ecotype, as well as across ecotypes. Higher E values appeared within Mixed Forest while lower values occurred in Moss Spruce and Tussock Tundra. This was expected because the E model was constrained by the field measured ALT to catch its spatial variation so that it could account for the spatial heterogeneity of soil conditions reflected in the remote sensor observations. The coverage of Wetland with a high E value was small in the study area.

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4.3. Estimation of ALT in 2015 and 2019

Based upon equation (4), we estimated the shallowest ALT in 2015 and the deepest ALT in 2019 to assess the performance of the developed protocol. The corresponding statistical metrics for accuracy assessment are listed in table 1, and the scatter plots and regressions between the estimated and measured ALT are provided in figure 5. Based on the estimated E using equation (4), the developed protocol could explain 62.0% of the variance of 2015 field measured ALT, and 69.8% of the variance of 2019 field measured ALT. A larger RMSE of 17.35 cm in 2019 was observed than in 2015 (11.81 cm) due to the deepest ALT in that year. The results were encouraging and improved compared to the estimations using an ensemble machine learning approach to link field measured ALT with fine resolution hyperspectral imagery products directly, which produced a R² of 0.52 in 2015 and R² of 0.49 in 2019 in terms of the same field dataset (Zhang et al 2021). The scatter plots of estimated ALT in terms of field measured ALT confirmed the general agreement between two datasets evidenced by the lower ALT in 2015 (figure 5(a)) and higher ALT in 2019 (figure 5(b)). We also estimated ALT for other years with varying explained variance from 60.7% for 2017 to 70.4% for 2021, suggesting the changing role of air temperature in controlling ALT across years.

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Table 1. Model performance for estimating ALT in 2015 and 2019.

	2015	2019
R2	0.620	0.698
MAE	11.81	11.01
RMSE	15.71	17.35

Similarly, by linking the estimated map of E (figure 4(a)) and the annual thawing indices of 2015 and 2019, we produced the ALT maps for these two years (figure 6). As expected, the high/low ALT pattern for a specific year would be consistent with the map of E to reflect the coupling of soil conditions and ALT, but the variation between years would reflect the climatic forcing, thus it was able to project the response of ALT to future climate warming scenarios indicated in the annual thawing index. The spatial variation of ALT revealed the varying degree of thawing protection from different ecotypes, indicating the heterogeneous local response to homogeneous climatic forcing.

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Our 9 year field measurements and coincident airborne and spaceborne fine resolution sensor products provided an opportunity to link a simple climate-permafrost model with machine learning solutions to quantify a heterogeneous terrain response to a climatic forcing that is homogeneous over the landscape. Our developed protocol could not only document the spatial and temporal variation of ALT in history, but also project the response of ALT to different future climate warming scenarios. The testing results over our study area were encouraging with a R² larger than 0.6 for ALT prediction, indicating that air temperature reflected in the annual thawing index is the principal driver of ALT change across time.

Precipitation and snow cover are also important climatic factors controlling ALT (Loranty et al 2018, Douglas et al 2020). A study using a portion of the field ALT dataset (2014–2019) found that the ALT variation from 2014 to 2017 had a strong relationship to anomalously high summer rainfall amounts in 2014 and 2016, leading to greater ALT than in 2015. This suggests a wetter summer would contribute to a deeper ALT at the end of summer, but the rain-induced thaw varied across ecotypes with Wetland as the most responsive and Tussock Tundra, Mixed Forest, and Moss Spruce less sensitive to rainfall (Douglas et al 2020). We also analyzed the precipitation data during 2014–2022 and our ALT field measurements (results were not shown in this study). The wettest summer was found in 2021 with the highest accumulated rainfall among the 9 year time period, but the deepest ALT was not revealed in 2021 (figure 2), indicating the compound effects of climatic factors on ALT. Snow cover is reported as another important factor. The influence of snow cover on the ground thermal region depends on the timing, duration, accumulation, and melting processes of seasonal snow cover; density, structure, and thickness of seasonal snow cover; and the interactions of snow cover with the physical conditions of the landscapes (Zhang 2005). In the seasonally frozen regions like our study area, a deeper snow depth can substantially increase the summer ALT because a deep snowpack will insulate the soil from the cold atmosphere, leading to warmer soil and higher ALT. We also explored the relationship between field measured ALT and snow depth data recorded in Fairbanks (results were not shown). We found a positive relationship between ALT and snow depth, but an inclusion of the annual accumulated snow depth data similar to the calculation of the annual thawing index in the climate-permafrost model did not improve the performance of the designed procedure. This indicates the timing of the snow cover is also important and should be considered. The air temperature, rainfall, and snow cover have a complicated effect on ALT and these factors also interact. For example, air temperature impacts snow melting which can change soil moisture content; the greater winter/spring snow depth is often associated with high air temperature, and both appear to have contributed to the degradation of permafrost in Interior Alaska (Jorgenson et al 2001). Methods to effectively integrate these external drivers with internal physical controls, such as vegetation cover and topography in the modeling procedure need further investigation. A potential solution might be the copulas method, which was effective at describing the effects of temperature and snow depth on the cycles in landscape freeze-thaw in cold regions (Hatami and Nazemi 2022). The exclusion of rainfall and snow cover in the model was identified as the predominant source of error in the developed protocol.

The limited field measurements and constraints in data processing also contribute to uncertainties in estimating ALT. We collected field data along three transects representing major ecotypes and vegetation structure in our study domain. Theoretically a stratified sampling scheme should be used but practically collecting field data across a large area is challenging, especially over harsh environments in cold regions. For better local-scale ALT estimation, the vegetation structure, composition, topography, and hydrology information should be considered to identify optimal transects or number of field measurements and their locations. A better sampling design would make the ALT map more robust. Errors from data processing were also inevitable such as parameter setting in machine learning and image segmentation. We applied trial-and-error procedures to identify optimal parameters for data processing. The setting of these parameters can be data or site-specific. It is beyond this study to examine the effects of each parameter on ALT estimation, but it is identified as an area of future research need.

Although there are constraints in the modeling procedure, the inclusion of fine resolution remote sensor products in the protocol to characterize the varying response of local terrains to the homogeneous climate control is valuable. NASA has been regularly collecting airborne hyperspectral imagery using AVIRIS-NG in support of ABoVE, but the 5 m spatial resolution products may constrain its application for a finer ALT mapping and bring in uncertainties if such products are directly matched with 1 m field scale measurements for upscaling. The difference in scale between field measurements and large-scale process-based models has been reported as a major concern in calibrating and validating the process-based models (Pastick et al 2015). The finer resolution pansharpened WorldView-2 imagery products could mitigate this while taking advantage of the finer spectral resolution of AVIRIS-NG products. The integration of two optical sensor products and lidar elevation information in the procedure successfully detected the spatial variation of the edaphic factor E and ALT. The local-scale ALT map products can be used as an independent permafrost dataset to calibrate and validate the large-scale processed-based models to reduce the uncertainties in scale difference between field scale and model grid. There is also potential to further upscale the ALT to regional scales by linking the local-scale ALT products with moderate resolution satellite products such as 30 m Landsat and spaceborne topographic datasets, by slightly modifying the protocol to generate a regional-scale edaphic factor E map. Similarly, large-scale E and ALT maps can be also generated using the developed procedure by integrating observed ALT at the long-term CALM sites with sensor data products such as Landsat and Sentinel and climatic data in the modeling procedure. Once we quantify the relationship between E and remote sensor observations, E can be extrapolated to large areas such as pan-Arctic regions as long as the samples can represent the landscapes of interests. Consequently, we can generate ALT maps for regions without measurements but covered by satellite observations. This can be used as an alternative to the process-based models for larger scale ALT estimations to project the response of seasonally frozen terrain to climate warming.

We measured ALT at three transects during 2014–2022 in Interior Alaska and developed a protocol to upscale the measurements across space and time by linking a climate-permafrost model with machine learning solutions. We draw the following conclusions from this study.

• (1)  
  The model was effective at differentiating the heterogeneity of ALT within and across ecotypes by using fine remote sensor data products to characterize the internal physical conditions of a landscape reflected in the edaphic factor E across space.
• (2)  
  The model has the capacity to project ALT across time by integrating the external climatic forcing as a mechanism in the procedure. This expands the value of the developed protocol in projecting response of the local seasonally thawed permafrost terrain to long-term climate warming, and thus enhance decision-making for land management and human activities.
• (3)  
  The rationality of the protocol can be extended to larger scale ALT estimations by integrating CALM observations and moderate resolution remote sensor products such as Landsat to estimate a regional/global-scale edaphic factor E.
• (4)  
  The developed procedure promotes the mission of NASA's ABoVE by linking field measurements with geospatial data products derived from airborne AVIRIS-NG and spaceborne WorldView-2 sensors to better understand the coupling of permafrost ecosystems and climate change.

The data that support the findings of this study are openly available at the following URL/DOI: https://daac.ornl.gov/ABOVE/guides/Active_Layer_Thaw_Depths.html. Data will be available from 31 December 2024.

This research was funded by the Strategic Environmental Research and Development Program (Project RC18-1170), the Environmental Security Technology Demonstration Program (Project RC22- 7408), and the U.S. Army Engineer Research and Development Center Army Direct Program (Ground Advanced Technology).