Quantification of active layer depth at multiple scales in Interior Alaska permafrost

Much of Interior Alaska is underlain by permafrost that has been thawing at an unprecedented rate. Top-down expansion of the seasonally thawed ‘active layer’ and development of thermokarst features are increasing across the landscape. This can be attributed primarily due to a warming climate and disturbances like wildfires which have accelerated summer season permafrost thaw. Quantification of active-layer thickness (ALT) is critical to understanding the response of permafrost terrains to these disturbances. ALT measurements are time consuming, and point based. As a result, there are large uncertainties in ALT estimates at regional/global scales (100 km2 or larger) using field scale (1 m2) measurements as direct inputs for calibrating/validating large scale process-based or statistical/empirical models. Here we developed a framework to link field scale ALT measurements with satellite observations to a regional scale (100 km2) via an intermediary upscaling of field scale ALT to the local scale (1 km2) with fine-resolution airborne hyperspectral and light detection and ranging data, thus leading to a characterization of ALT across space and time at multiple scales. We applied an object-based machine learning ensemble approach to upscale field scale (1 m2) measurements to the local (1 km2) and regional scale (100 km2) and achieved encouraging results across three permafrost experimental sites in Interior Alaska that represent a variety of terrain types. Our study demonstrates that generating local scale data products is an effective approach to bridge the gap with field scale measurements and regional scale estimations as it seeks to reduce upscaling uncertainty.


Introduction
Permafrost thaw depth contains critical information to understand a variety of phenomena in cold regions such as hydrologic change and positive climate warming feedbacks associated with CO 2 and CH 4 emissions (Streletskiy et al 2015, Hrbác ˇek et al 2020, Clayton et al 2021).A significant measurement for tracking top-down and lateral thaw of permafrost is the activelayer thickness (ALT), which is the maximum thaw depth at the end of the summer thaw season (Yi et al 2007).ALT has a crucial role in permafrostaffected areas by buffering the reach of many biological and hydrological drivers in the subsurface that may contribute to increased environmental changes (Shiklomanov et al 2013).ALT is vulnerable due to top-down thaw or disturbances, though vegetation cover and soil can guard it against summer thaw (Douglas et al 2020).ALT quantification is essential to understanding the response of permafrost terrains to these disturbances.However, collecting ALT measurements in the field is financially, logistically, and physically challenging (Hall 1982, Zwieback et al 2019).These field measurements are typically found along convenient and key locations, such as near settlements, major roads, infrastructure, or near key environmental features and landmarks (Zhang et al 2014, Zou et al 2017).
Due to the challenges associated with collecting sufficient yearly ALT field data over difficult terrain, upscaling can be employed to estimate ALT at various spatial and temporal scales to aid in identifying trends related to permafrost thaw.Permafrost thaw depth measurements have been linked to both local and regional scales at various geographic locations, across spatial scales, and representing numerous timespans with remote sensing and machine learning techniques (Yi et al 2018, Michaelides et al 2019, Zorigt et al 2020, Zhang et al 2021).Airborne and spaceborne remote sensors can easily cover broad areas (Romanovsky et al 2010, Hu et al 2021).Machine learning models can assist in predicting ALT and other related features from specific measurement locations in cold regions across a wider area ( Nonetheless, such large-scale process-based models and empirical models are vulnerable to increased uncertainty when relying on field scale measurements to upscale to a regional scale (Ramirez-Villegas et al 2017, Dressler et al 2022).This is relevant to ALT estimations as there are considerable uncertainties for ALT predictions with field scale (1 m 2 ) measurements as inputs for calibrating/validating large scale processbased or statistical/empirical models at regional/global scales of 100 km 2 or larger (Yi et al 2018, Jiang et al 2020).Given this, there exists a need to bridge the gap with field scale and regional scale estimations by developing local scale products.The contribution of this study was to bridge the gap between field measurements and large-scale thaw depth modeling methods, which includes empirical models/machine learning models and process-based based analytical models.We developed an object-based machine learning ensemble framework to connect field scale ALT measurements with spaceborne imagery for regional scale ALT estimations.This was realized by generating local scale (1 km 2 ) ALT products by first utilizing fine-resolution airborne hyperspectral and LiDAR data, thus leading to a characterization of ALT across multiple spatial and temporal scales.

Study area
The general study area is just north of Fairbanks, Alaska.It is ∼190 km south of the Arctic Circle, experiences frequent snowfall, and contains widespread permafrost that is undergoing widespread thaw degradation (Douglas et al 2016, Jorgenson et al 2020).Two factors contributing to this degradation are widespread formation of taliks and thermokarst.Taliks are unfrozen zones above the active layer or within permafrost, and thermokarst are hollows that stem from ground subsidence caused by the thawing of ice-rich permafrost (Douglas et al 2021, Farquharson et al 2022).These form due to increases in air temperature, precipitation, fire events, and/or landcover change (Jones et al 2015, Devoie et al 2019).Such features are found in our study areas, which includes three 1 km 2 local scale sites alongside a 100 km 2 regional scale site that fully encompasses the local scale sites (figure 1).Both study areas are in the boreal biome but include some areas with tundra ecotypes.These contain deciduous and evergreen forests, shrubs, tussock tundra, wetlands, and water bodies, along with some disturbed and developed land.The local scale sites are referred to as Creamer's Field, Farmer's Loop, and Tunnel.The regional scale area (100 km 2 ) envelopes the three smaller study areas (∼1 km 2 ).
Creamer's Field, part of the Creamer's Field Migratory Waterfowl Refuge, is dominated by fen and shrubland ecotypes in the north and center, while the south is dominated by deciduous and evergreen forests along with wetlands.The low gradient site exhibits a minimal change in elevation (∼7 m km −1 ).Farmer's Loop, on both sides of Farmer's Loop Road, is dominated by deciduous and evergreen forests, fens, and shrubs.It has an increase in elevation east of Farmer's Loop Road resulting in a moderate gradient (∼20 m km −1 ).Lastly, Tunnel is south of the Steese Highway, and is heavily dominated by deciduous and evergreen forests, with shrubs also present.It contains a higher and steeper elevation gradient (∼107 m km −1 ).Though the region has experienced multiple major fire disturbances in the past 20 years (Zhang et al 2023) none of our study sites have evidence of major fires or floods within the last ∼50 years that would have impacted vegetation, soil, or permafrost, and necessitate the need for annual, updated images.

Data description
ALT measurements have been made along 400 m transects at 4 m intervals from 2016 to 2021 and served as inputs to estimate ALT at the local scale and were obtained by the same trained team of individuals.2016 had an anomalously high rainfall summer and was associated with an increase in thaw over previous years that has since not fully recovered.LiDAR imagery was acquired in June 2017 by Quantum Spatial and was utilized at all scales.The horizontal resolution was 1.5 m, nonvegetated vertical accuracy was ⩽19.6 cm, and vegetated vertical accuracy was ⩽29.4 cm.These data were further separated into a digital terrain model

Methodology
We combined ALT field measurements with image objects from airborne hyperspectral imagery, NDVI, and LiDAR data to predict ALT at the local scale, before then utilizing the estimated local scale ALT outputs with spaceborne multispectral imagery, NDVI, and LiDAR data to predict ALT at the regional scale (figure 2).With the airborne hyperspectral imagery, we utilized minimum noise fraction, which computes the normalized linear combinations of the original bands that then create output channel images with steadily increasing noise levels, and thus steadily decreasing image quality (Luo et al 2016).
• Field data was averaged and spatially matched to image objects from airborne hyperspectral imagery via image segmentation alongside NDVI and LiDAR data to develop random forest (RF), support vector machine (SVM), k-nearest neighbor (k-NN), and multiple linear regression (MLR) upscaling models.• Combined model outputs were used to generate a final prediction of ALT at the local scale utilizing ensemble analysis (EA), a weighted average algorithm, alongside generating accuracy statistics.• At the regional scale, local scale ALT predictions were averaged and spatially matched to image objects derived from spaceborne multispectral imagery, alongside NDVI and LiDAR data to develop RF, SVM, k-NN, and MLR upscaling models.• Model outputs were combined to create a final prediction of ALT at the regional scale using EA, alongside generating accuracy statistics.

Object-based data processing
An object-based image analysis (OBIA) technique was utilized with the airborne hyperspectral imagery from ProSpecTIR-VS and AVIRIS-NG, alongside spaceborne multispectral imagery from WV-2 and Landsat 8.In OBIA, a homogeneous group of pixels, also known as image objects, are the subject of analysis.OBIA was chosen as it proved itself to provide better overall accuracy and results over the traditional pixel-based method EA refers to the combination of RF, SVM, k-NN, and MLR algorithms used in this research into one overall, weighted output.The rationale is that each of these algorithms have their pros and cons, and thus an EA of multiple model outputs can create a more robust model with more accurate predictions (Zhang et al 2022).An average weighting scheme was employed whereby a model with a larger r, known as the Pearson's Correlation Coefficient, would obtain a higher weight, with the sum of the weights being 1.0 (Zhang et al 2018).The r can measure the goodness-of-fit of the models (Moreno-Martínez et al 2018).Thus, algorithms that produced worse r outputs would be minimized, while those that provided better r outputs would have a stronger influence.The formula for the correlation coefficient can be seen below: where n is the number of matched samples, p i is the model prediction, o i is the observed in-situ data, pi is the mean of the predicted values, and ōi is the mean of the observed in-situ data values.Mean absolute error (MAE) and root mean square error (RMSE) were also utilized.MAE is the average absolute error between the actual and the predicted values.RMSE is the square root of the mean squared error between the actual and predicted values and is more sensitive to outliers.The larger the difference between the MAE and the RMSE, the greater variance of the individual errors within the test sample.The formulas for MAE and RMSE can be seen below: All five models were first run at the 1 km 2 local scale sites.These would be based off the segments that contained field ALT data as inputs to train the models.Once outputs were created for the 1 km 2 areas, they served as inputs to further upscale ALT estimations to the 100 km 2 regional scale with the same models.However, given that EA produced the overall best results at the local scale areas, it was decided to utilize only the predicted local scale ALT values from EA as the inputs for the further upscaling procedure to the regional scale.Thus, local scale EA outputs were utilized as the inputs for the five models at the regional scale.

Field scale ALT quantification
Results for the ALT transects at the field scale can be found in figure 3.At transect AB in Creamer's Field there was a slight decrease in ALT between thick, generally deciduous-dominated forest, represented by a high DSM, to more open tussock tundra, represented by a low DSM.From 2016 to 2021, ALT became relatively deeper in the forested area, with limited thawing or even a slight reversal in the canopy-free areas that were dominated by fen and shrubland.This was similar at transects CD and EF, which were both located at Farmer's Loop.Transect GH in Tunnel had widespread increase in ALT regardless of elevation or ecotype, which was largely evergreen forest and shrubland.Transect AB contained relatively shallow ALT values normally within 100 cm.Other transects contained ALT that easily exceeded 100 cm and were even able to exceed 200 cm.Most ALT values greater than 100 cm represented areas where taliks or thermokarst features formed as they typically experience a winter freeze deeper than 100 cm (Douglas et al 2021).
ALT was relatively stable at Creamer's Field and more varied at Farmer's Loop and Tunnel.This is supported with table 1, which shows mean and standard deviation of ALT per ecotype at the field scale.In 2016 and 2021, the highest mean ALT in Creamer's Field was at evergreen forest (82.3/76.7)and fen (80.1/77.1),while the lowest mean ALT was in deciduous forest (68.6/69.0)and shrubland (74.3/65.8).At Farmer's Loop it was deciduous forest (105.7/120.6)and herbaceous (105.9/117.1)that had the highest mean ALT, while evergreen forest (69.1/72.7)and fen (73.7/68.9)contained the lowest.The highest mean ALT in Tunnel was in shrubland (86.7/110.5),with the lowest at herbaceous (52.7/68.7).Standard deviation tended to increase between both years, which was expected given the increased depth of ALT in 2021.In general, standard deviation was low in Creamer's Field (<20.0) and high in both Farmer's Loop (<66.0) and Tunnel (<44.0).

Local scale ALT quantification
Table 2 highlights  In both years for Farmer's Loop, EA created the best r (0.67/0.69) and RMSE (20.16/29.66)and produced the best MAE for 2021 (19.95).At Tunnel, it produced the best r for both years (0.65/0.79).Excluding MLR, the rMAE was similar between all models in Creamer's Field and Farmer's Loop, however at Tunnel there was even greater variation.RF, SVM, and k-NN produced acceptable results at all sites.MLR tended to have the poorest values.A comparison between the field measurements and local scale ALT estimates based on EA from table 2 can be seen in figure 4, which demonstrates an encouraging agreement between them.The combined model uncertainty is represented as the standard deviation to ensemble prediction (STDE; Zhang et al 2023).
ALT estimations at the local scale in 2016 and 2021, difference in ALT, ecotypes, and STDE for Creamer's Field, Farmer's Loop, and Tunnel can be found in figures 5-7, respectively.In Creamer's   The lowest values at Farmer's Loop were in fen (73.9/70.9).Deciduous forest contained high mean ALT at both Farmer's Loop (103.4/120.2) and Tunnel (89.3/111.1).Creamer's Field had the lowest standard deviation (<10.0) in both years, while Farmer's Loop contained the highest standard deviation (<22.0) for all ecotypes except deciduous forest.

Regional scale ALT quantification
For both years at the regional scale, there was a notable change in r, RMSE, and MAE produced by the five models as seen in  8, which contains a scatter plot and linear regression for 2016 and 2021, reveals a promising agreement between local scale ALT estimations produced with EA and estimated ALT at the regional scale with EA.ALT estimations at the regional scale with WV-2 in 2016 and 2021, difference in ALT, ecotypes, and STDE can be found in figure 9. Deep ALT values occurred in deciduous and evergreen forest.Shallow ALT estimations were at bog and fen.ALT at lower elevations and within valleys tended to be at least 20 cm shallower than in areas at higher elevations or hilltops.STDE was consistent between both years, thus indicating similar areas that were easier or challenging for models to agree.Table 5 shows the mean ALT per ecotype at the regional scale.High mean ALT was recorded in 2016 and 2021 with Landsat 8 and WV-2 at evergreen forest (85.4/103.7 cm, 89.2/105.9cm) and deciduous forest (86.7/108.0cm, 93.4/111.2cm).Low mean ALT was found at bog (73.9/71.3cm, 78.2/78.3cm) and fen (76.6/88.0cm, 79.1/88.9cm).Landsat 8 and WV-2 had similar patterns, yet WV-2 contained deeper mean ALT values.At all three scales, areas that contained a deeper active layer were associated with the deciduous forest ecotype.This is expected as trees found in this ecotype were typically taller, more densely spaced, and contained deeper root systems while trees in the evergreen forest ecotype were generally less densely spaced.Conversely the fen ecotype contained shallower ALT at all scales, which was anticipated as the plants in this ecotype are smaller and contained shallower root systems.In addition, there is increased soil moisture content that can help to reduce the rate of thaw during summer, which would also be evident with the bog ecotype.Herbaceous and shrubland vegetation contained shallow root systems with shallow ALT, however some areas may have included land that was formerly dominated by deep rooted trees, and therefore contained deeper ALT.Lastly, permafrost found in sparsely vegetated areas would have had minimal root penetration yet be more susceptible to higher temperatures in summer.

Discussion
The framework in this study can contribute to the quantification of permafrost thaw at multiple temporal and spatial scales.It also has potential to be applied to other permafrost-rich regions of the world outside of Interior Alaska.Studies have directly focused on local scale upscaling of field measurements (Siewert et al 2021, Zhang et al 2021).Numerous studies have also separately applied upscaling techniques to a regional/global scale (Obu et al 2019, Jiang et al 2020, Ran et al 2022, Peng et al 2023).Particularly at the regional/global scale, there was greater uncertainty with permafrost thaw measurements.We have shown it is possible to generate local scale data products to bridge the gap with field    measurements and regional scale estimations; thus, reducing uncertainty.In terms of limitations, it should be noted this procedure would perform best in areas where the field scale, local scale, and regional scale sites contain relatively similar makeup of terrain and vegetation.If significant changes in elevation and land cover are not properly addressed, there is potential for increased uncertainty with estimating ALT at all scales (Yi et al 2018).Model accuracies and errors were also found to be more positive with regional scale estimates than with local scale estimates.A possible explanation for this is that local scale estimates were more sensitive to minor topographical and ecological changes that would be challenging to represent at a regional scale.At the regional scale, the same minor topographical and ecological factors would be prone to being agglomerated with nearby pixels used to create image objects which were focused on more substantial changes.This possibility may also explain why model uncertainties tended to be greater with local scale estimates than with regional scale estimates.This framework did not address underground features such as soil composition or soil moisture, which would have likely enhanced ALT estimations.We were also unable to quantify ALT in water bodies and developed land containing structures and roads.This technique was utilized in areas that contained discontinuous permafrost (Douglas et al 2020).It should not be presumed that this procedure can reveal and differentiate between permafrost and non-permafrost zones, which may pose added complications if permafrost vanishes from previously mapped areas.Newly initiated thermokarst features were present in the region over the studied timespan, however they were not accounted for due to being localized and difficult to properly interpret from remote sensing imagery.This can be remedied with continuous monitoring of the features to better account for these disturbances.Clearly with ongoing and future projected climate warming in the area thermokarst features will become more common and thus will need to be accounted for in future efforts.
This approach can likely be improved with the inclusion of other relevant datasets, particularly where permafrost soil and ice contents vary or where a broader variety of ecotypes are represented.Accessible data such as temperature, precipitation, index measure.Soil data was available; however, it was at a significantly coarser resolution than the acquired imageries and would thus be of questionable benefit.It is conceivable that if such variables were connected to this upscaling technique for ALT estimation enhanced results would be accomplished.There also exists vast potential for this approach to be applied to predict other variables at multiple scales such as greenhouse gas emissions (e.g.CO 2 and CH 4 ), snow depth, and soil moisture.

Conclusions
Our study established that generating local scale data products provided a compelling approach to bridge the gap with field scale measurements and regional scale predictions.We developed a framework that successfully quantified ALT at multiple spatial and temporal scales with the use of an object-based machine learning ensemble approach in a permafrost-rich region of the world.Field ALT measurements were upscaled to three 1 km 2 local scale sites with airborne hyperspectral sensors and LiDAR.From there we further upscaled the predicted 1 km 2 local scale ALT estimations to a regional scale at approximately 100 km 2 by utilizing spaceborne multispectral sensors and LiDAR.At the local scale, both 1 m ProSpecTIR-VS and 5.2 m AVIRIS-NG provided effective and consistent ALT results.Here, all algorithms were able to produce similar outcomes with EA producing the best results.There were similar positive results at the regional scale between the 2 m WV-2 and 30 m Landsat 8 imageries for the further upscaling procedure, with the former resulting in enhanced results.Here, the k-NN and MLR algorithms struggled, while RF and SVM provided more respectable outcomes, with EA again providing the best results.Deep ALT was associated with the deciduous forest ecotype, which also experienced an increase in ALT between 2016 and 2021.Shallow ALT was associated with the fen ecotype, which experienced relative stability or even a reversal in thaw over the same time period.

Figure 1 .
Figure 1.Locations of the three local scale study areas at 1 km 2 and the regional scale study area at 100 km 2 near the city of Fairbanks in Interior Alaska.

Figure 2 .
Figure 2. Methodology framework to upscale field scale ALT measurements to the regional scale by developing local scale ALT products.Yellow indicates the field-to-local scale framework and green indicates the local-to-regional scale framework.
the r, RMSE, MAE, and relative MAE (rMAE) in 2016 and 2021 for the local scale sites produced by RF, SVM, k-NN, MLR, and EA that utilized airborne hyperspectral 1 m ProSpecTIR-VS imagery (Farmer's Loop) and 5.2 m AVIRIS-NG imagery (Creamer's Field and Tunnel).The values generated by EA tended to be the most positive or second best.At Creamer's Field, EA produced the best r for both 2016 (0.72) and 2021 (0.69), alongside in 2021 the best RMSE (11.54) and MAE (9.34).

Figure 4 .
Figure 4. Scatter plot and linear regression between field ALT measurements and the estimated local scale ALT (cm) from EA at Creamer's Field, Farmer's Loop, and Tunnel in 2016 and 2021.Error bars represent STDE.

Figure 5 .
Figure 5. Field ALT (cm) and predicted ALT (cm) at the 1 km 2 local scale at Creamer's Field using EA in (a) 2016 and (b) 2021, (c) change in predicted ALT between 2016 and 2021, (d) ecotype map using RF, and STDE in (e) 2016 and (f) 2021.

Figure 6 .
Figure 6.Field ALT (cm) and predicted ALT (cm) at the 1 km 2 local scale at Farmer's Loop using EA in (a) 2016 and (b) 2021, (c) change in predicted ALT between 2016 and 2021, (d) ecotype map using RF, and STDE in (e) 2016 and (f) 2021.

Figure 7 .
Figure 7. Field ALT (cm) and predicted ALT (cm) at the 1 km 2 local scale at Tunnel using EA in (a) 2016 and (b) 2021, (c) change in predicted ALT between 2016 and 2021, (d) ecotype map using RF, and STDE in (e) 2016 and (f) 2021.

Figure 8 .
Figure 8. Scatter plot and linear regression between local scale ALT estimations produced from EA and the estimated regional scale ALT (cm) from EA with WV-2 in 2016 and 2021.Error bars represent STDE.

Table 1 .
Mean and standard deviation (in parentheses)for ALT estimations per ecotype produced at the field scale.Ecotypes with no ALT measurements in the model database are denoted with '-' .

Table 2 .
Predicted ALT statistics for the local scale sites with RF, SVM, k-NN, MLR, and EA.
depth between the two years from roughly −10 cm to +30 cm, while at Creamer's Field it was from −10 cm to +15 cm.Tunnel almost exclusively had an increase in ALT, particularly at the shrubland ecotype in the center, where ALT increase exceeded +40 cm, indicating rapid thaw.The 5.2 m imagery at Creamer's Field and Tunnel did not separate trails cm: Farmer's Loop experienced consistent trends in both years.Table 3 shows the mean and standard deviation of ALT per ecotype at the local scale for 2016 and 2021.At Creamer's Field the highest mean values in both years were at fen (76.8/76.2) and herbaceous (77.9/73.7),while the lowest were at bog (73.7/56.3)and deciduous forest (69.3/73.6).

Table 3 .
Mean and standard deviation (in parentheses)for ALT estimations per ecotype produced from EA at the local scale.Ecotypes with no ALT measurements in the model database are denoted with '−' .

Table 4 .
Predicted ALT statistics at the regional scale with RF, SVM, k-NN, MLR, and EA that were derived from local scale EA outputs.

Table 5 .
Mean ALT estimations per ecotype produced from EA at the regional scale.
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