The study area covers the entire land area of Denmark, which corresponds to approx. 43 000 km2. In order to restrict the domain for the data analysis and modeling to an area where WTD-driven GHG upscaling may be of relevance, we calculated the union of two map layers that include a river valley bottom delineation (Sechu et al., 2021) and a map of wetlands (Greve et al., 2014). The two map layers correspond to approx. 775 000 ha and approx. 904 000 ha, respectively, and their union, which marks our model domain, amounts to approx. 1 162 000 ha, roughly one-fourth of the total land area of Denmark (Fig. 1). For the final analysis, the domain was further constrained to the carbon-rich lowland soils. The total area of peat soils with organic content (OC) greater than 12 % constitutes approx. 129 000 ha, of which approx. 74 000 are cultivated, either extensively as permanent grassland (35 %) or intensively for a variety of crop types (65 %) (Greve et al., 2019; Levin, 2019). Peat extraction is still taking place sporadically in Denmark. The Danish climate is characterized as temperate with evenly distributed precipitation over the year. The Danish Meteorological Institute states the mean annual temperature as 8.7 ∘C and the mean annual precipitation as 759 mm.

A total of 24 492 WTD observations were assembled from various sources in order to compile a comprehensive training dataset that reflects long-term average summer conditions. WTD observations recorded between the months of May and September in the period of 2000 to 2021 were used as training data. Figure 1 depicts the locations of the WTD observations, and Table 1 provides an overview of the different sources and WTD statistics. Data from the Danish well database JUPITER (Hansen and Pjetursson, 2011) were processed by first constraining the well location to a 200 m buffer around the lowland soils. Second, only wells with a maximum filter depth of 5 m below ground were selected. The median WTD was used in cases where a well had multiple observations within the specified period. This resulted in 5716 WTD observations. The wells are primarily located in the fringe areas and only 132 wells coincide with the OC > 12 % class. Moreover, 4796 WTD observations were obtained from two soil auger campaigns (2010 and 2021) that specifically targeted lowland soils with high organic content (Greve et al., 2014). A total of 653 out of the 4796 locations sampled in summer 2010 were revisited in summer 2021, and for the double-sampled locations, the mean WTD was used in the final training dataset. The mean and not the median WTD was calculated for the resampled auger sites because only two measurements were available. The soil auguring equipment was limited to a maximum depth of 1.21 m, and in cases where the water table was not detected by the auger, information could only be derived for the minimum WTD at the given location. In general, the auger and well observations are in fair agreement with each other and show an average deviation of 0.1 m for sampling locations with a difference of less than 100 m. Further, 9980 groundwater-dependent lakes with a surface area greater than 100 m2 and located within a 200 m buffer around the peatland soils were used as proxy WTD observations. Since lake water level observations were missing, values were drawn from a normal distribution with an assumed mean of -0.25 m, i.e., above terrain, and a standard deviation of 0.05 m. Additional dummy points for saturated conditions were placed along the coastline and the river network. Here, 1000 points for each category were placed randomly and assigned a WTD of 0 m. Lastly, dummy points for drained conditions were generated along drain ditches and within drained forest. Here, 1000 points for each category were placed randomly and sampled from a normal distribution with a mean WTD of 1.21 m and standard deviation of 0.2 m. Under Danish conditions, ditches drain the agricultural land year-round in most cases. Figure 2 depicts the WTD variability of the training dataset differentiated for the data sources. The WTD data derived from the national well database were the only source that contained deep WTD observations. The data originating from the soil coring campaigns provided mostly shallow data; however, 3110 samples had a WTD of 1.21 m and thereby solely indicated a minimum WTD. The WTD of lakes is entirely above terrain, i.e., negative WTD values, whereas coast and rivers were assigned a WTD of 0 m. We created a training dataset for summer conditions because the WTD observations from the soil auger campaigns are primarily from summer months and the WTD data from this source represent the primary information on the shallow WTD, i.e., the top meter below terrain. Based on the WTD observations from the national well database, the median WTD for summer is 2.0 m, whereas the median WTD for winter is 1.75 m based on the same processing as was applied for the summer data but for the months from October to March. The difference of 0.25 m can be understood as an overall annual amplitude.

Based on a data synthesis by Tiemeyer et al. (2020), the WTD-driven GHG response functions of CO2 and CH4 emissions from organic soils exhibit a nonlinear relationship with the most distinct sensitivity in the depth interval of 0 to 0.5 m. In consequence, we aim at modeling WTD with the highest possible accuracy for this GHG-sensitive WTD interval. With the same motivation, Bechtold et al. (2014) presented a WTD transformation function that resulted in a pseudo-linearity between WTD and GHG. For our purpose, the transformation function presented by Bechtold et al. (2014) was adapted to 1WTDt=e3⋅WTD-1WTD<01-e-3⋅WTDWTD≥0, where WTDt is the transformed WTD. As shown in Fig. 2, WTDt varies between -1 and 1 and reaches its upper asymptote at a WTD of approximately 1 m. The applied WTD transformation also allows us to incorporate the 1.21 m WTD data that represent a minimum observation since the WTDt variability above 1 m is minimal.

A set of 27 covariates was curated to gather national-scale map layers that are deemed relevant to explain the WTD variability in the training dataset (Table 2). The individual maps were resampled from their native resolutions to the defined output resolution of 10 m. The covariates encompassed high-resolution data on topography, water body proximity, lithology, land use and hydrology. The water body proximity was expressed as both the vertical and horizontal distance to the nearest water body, which contained rivers, lakes and the coastline. Additionally, the vertical and horizontal distance to the nearest ditch was calculated to capture the effect of drainage on WTD in lowland soils. Using the historical crop type records, a six-class ranked map indicating wetness of agricultural fields was created. The wetness rank represents a qualitative analysis based on agricultural expert judgment based on the Danish Agricultural Land Parcel Information System for approx. 600 000 fields for the years 2016 to 2020. Moreover, high-resolution data relevant to discriminate saturation conditions of the soil were obtained from Landsat and Sentinel-1 satellite systems, such as land surface temperature (LST), which serves as a valuable proxy for water-saturated soil conditions.

We applied the CatBoost implementation of the well-established gradient-boosting decision tree (GBDT) algorithm (Dorogush et al., 2018; Prokhorenkova et al., 2018). In an additive training process, GBDT builds a prediction model based on an ensemble of weak learners, i.e., decision trees. For a pre-defined number of iterations, GBDT attempts to correct itself by adding a decision tree trained against the residuals of the ensemble sum of its predecessors. CatBoost is favorable over similar ML algorithms, such as random forest algorithms, support vector machines, or other GBDT implementations (e.g., XGboost or LightGBM), with respect to computational time and memory usage, while achieving a competitive accuracy (Hancock and Khoshgoftaar, 2020; Huang et al., 2019). The model is set up to predict WTD at a resolution of 10 m. Given the areal extent of the domain, over 116 million grid cells are simulated by the GBDT model. The cost function used in training the model was set to the root-mean-square error (RMSE) and key hyper parameters were tuned via a randomized search. The following CatBoost hyper parameters were included in a simple randomized search with 2000 iterations: learning_rate, depth, subsample, rsm (random subspace method), l2_leaf_reg, min_data_in_leaf. The selected hyper parameters affect the overall architecture of individual trees and limit the effect of overfitting. The best performing model with respect to a 25 % holdout validation was selected for subsequent final training. The final GBDT model was trained over 1000 iterations where 10 % of the data were used as validation data to initiate early stopping once the validation cost function did not improve over 10 iterations. CatBoost allows for assigning weights to the individual training data, which are used to calculate the cost function. In order to emphasize the GHG-sensitive depth interval 0 to 0.5 m in the model training, a weight of 2 was assigned to shallow WTD observations.

The Shapley additive explanations (SHAP) approach (Lundberg and Lee, 2017) was implemented to investigate the covariate importance of the trained GBDT model. SHAP builds upon game theory principles to explain the output of any ML model by quantifying marginal contributions of the applied covariates. SHAP values represent the contribution of each covariate to the final prediction and thereby provide valuable insights into trained ML models. The magnitude and sign of the SHAP values indicate the importance of a covariate and the direction of impact on the prediction, respectively. We calculated SHAP values (i) for the training dataset to get insights into the trained GBDT model and (ii) for the prediction dataset to generate maps showing the relationships between covariates and WTD.

The first measurements of CO2 fluxes from cultivated peat soils in Denmark were performed in the 1970s using an in situ alkaline CO2 trap method (Petersen et al., 1976), but it was not until 2008–2009 that a national monitoring campaign was accomplished, where net fluxes of CO2, CH4 and N2O were measured at eight sites using closed chamber techniques (Elsgaard et al., 2012; Petersen et al., 2012). Data on net ecosystem carbon balance from this campaign (Elsgaard et al., 2012) are used as the current Tier 2 emission factors (EFs) for organic soils with > 12 % OC in Denmark's National GHG Inventory report submitted under the United Nations Framework Convention on Climate Change and the Kyoto Protocol (Nielsen et al., 2021). National campaigns have not been repeated, but a number of research projects have generated additional data on annual emissions of GHGs from Danish organic soils. A synthesis of these studies was performed in the present study (Tables S1 and S2 in the Supplement), and the data were used to derive response functions for GHG emissions in relation to WTD at mean annual conditions.

For analyzing CO2 emissions, we employed a nonlinear Gompertz function according to Tiemeyer et al. (2020): 2CO2-C(WTD)=CO2-Cmin+CO2-Cdiff⋅e-a⋅eb⋅WTD, where CO2-Cmin is the lower asymptote, CO2-Cdiff is the difference between upper and lower asymptote, a controls the displacement along the WTD axis and b defines the gradient. Indirect CO2 emissions from leaching of dissolved organic carbon (CO2-CDOC) were added to Eq. (2) based on standard EFs of 0.31 MgCha-1 for drained soils and 0.24 MgCha-1 for rewetted soils (IPCC, 2014).

For analyzing CH4 emissions, we fitted an exponential WTD response function according to Tiemeyer et al. (2020) and Evans et al. (2021): 3CH4(WTD)=CH4min+c⋅e-d⋅WTD, where CH4min is the lower asymptote while c and d control the shape of the exponential function (Tiemeyer et al., 2020). The Danish sites for which CH4 emission data were available represented drained and restored cropland and grassland, including sites where the water level at least under experimental conditions was close to surface. Methane emission from ditches (CH4ditch) was estimated by considering a fraction of the land, i.e., 10 %, where drainage ditches are located. As opposed to Tiemeyer et al. (2020), who applied a ditch fraction parameter for all grids, we only included grids that are actually containing a ditch. The location of the ditches was derived based on publicly available datasets. Given the applied grid size of 10 m, this corresponds to an averaged drainage ditch dimension of 1 m, which can be considered very suitable for Danish conditions. The applied EFs for CH4ditch were 1165 kgCH4ha-1yr-1 for cropland and 948 kgCH4ha-1yr-1 for grassland (IPCC, 2014), where the latter represents the weighted average of IPCC's shallow (34 %) and deep (66 %) drained grassland EFs, as applied in Tiemeyer at al. (2020).

Data for N2O emissions showed no systematic WTD dependence, and as a consequence land-use-specific EFs were applied. We applied the EFs from Wilson et al. (2016) as updated from the IPCC (2014) wetlands supplement: 13.0 kgN2O-Nha-1yr-1 for cropland, 4.7 kgN2O-Nha-1yr-1 as average for grassland (deep or shallow drained, nutrient rich or poor) and 0.1 kgN2O-Nha-1yr-1 for rewetted organic soils.

All GHGs were converted to CO2-eq using their global warming potential (GWP) over a 100-year period according to the sixth IPCC assessment report (Forster et al., 2021) where 1 kgCH4 = 27 kgCO2 and 1 kgN2O = 273 kgCO2. For applying the land-use-specific EFs and WTD response functions, we used a 2020 land use classification for Denmark (Levin and Gyldenkærne, 2022). Based on the available WTD observations, the WTD map captures a long-term average summertime condition. Since the applied GHG upscaling method is based on annual mean WTD, a scaling parameter is subtracted from the summertime WTD map to obtain an annual average. As described in Sect. 2.2, the annual variability is estimated to be 0.25 m. In order to correct for seasonality, 0.125 m was subtracted from the summer WTD map. Negative values were set to zero.

The hyperparameter tuning of the GBDT model resulted in the following results: depth = 10, learning_rate = 0.05, subsample = 0.8, rsm = 0.8, min_data_in_leaf = 1 and l2_leaf_reg = 5. The GBDT model was trained against WTDt, but throughout the paper results and analyses are based on the back-transformed variable WTD. Figure 3 depicts the final simulated WTD map that represents a long-time average summertime condition for the period of 2000 to 2021 for Åmosen, which is one of the largest peatlands in Denmark. For the visual assessment, a color scheme that emphasizes the depth interval of 0 to 1 m has been selected. Even though WTD is simulated for a larger domain (lowland soils and river valleys), only grid cells with OC > 12 % are shown since the applied GHG upscaling method is only valid for such conditions. The WTD map discloses a distinct spatial heterogeneity with fully saturated conditions laying in very close vicinity to well-drained conditions.

We applied SHAP to investigate feature importance of the trained GBDT model for the well and auger WTD observations, i.e., excluding the dummy points (Fig. 4). The six most important covariates were, ordered in high to low importance: horizontal distance to water bodies, horizontal distance to ditches, vertical distance to water bodies, wetness rank based on cropping history, clay content of the deepest soil horizon and land surface temperature (LST). Negative SHAP values are associated to negative impact, i.e., more shallow WTD and positive SHAP values are linked to a deeper water table. Locations close to water bodies exclusively possess negative SHAP values whereas locations with a large horizontal distance to the closest water body have both negative and positive SHAP values. The SHAP values for the horizontal distance to drain ditches are separated with positive values (producing a deeper WTD) for low distances, which clearly reveals the functioning of the added dummy points representing well-drained conditions along the drain ditches. The interpretation of the SHAP values for the vertical distance to water bodies is that WTD does not follow small-scale topographical variation and instead the water table has a smoother variation than topography, which results in a deeper WTD (positive SHAP value) for areas with a high vertical distance to the nearest water body. The wetness classes based on the cropping classes show a clear WTD sensitivity, where the low ranks, which are linked to crops that favor well-drained conditions possess positive SHAP values, and the wet classes relate to a negative impact on the simulated WTD. A high clay percentage produces a positive impact on the prediction, i.e., deeper WTD. LST also shows a clear link to WTD, with higher values yielding a deeper WTD and lower LST, resulting in more water-saturated conditions.

Figure 3 exemplifies three of the seven listed covariates (i.e., LST, wetness rank and vertical distance to nearest water body) to elucidate key connections between model input and output. For LST (Fig. 3b), there is a direct relationship, with lower LST in areas of high saturation caused by either evaporative cooling of the land surface due to high water availability or enhanced heat conductance towards deeper layers for wet soils, whereas deeper water tables, i.e., drier conditions, are collocated with higher LST. Further, we observe a good agreement between WTD and the wetness rank, derived from the cropping history from 2016 to 2020 (Fig. 3c). Fields with crops associated with a wet rank, i.e., permanent poor grassland with low nitrogen application rates, are associated with a low WTD, while crops that require drainage, e.g., winter wheat, potatoes or sugar beet, are found at fields with a deeper WTD. The agronomic requirements reflected by the ranked wetness map are characterized by plausible mean WTD, which show consistent differences between each other. For the entire domain, the mean WTD values for the three wettest categories are below 0.4 m, whereas the three dry categories have a WTD of 0.65 m and deeper. LST and wetness rank are to some degree connected to each other, with a lower LST for crops with a higher wetness rank. However, exceptions are found for drained forests that are associated with a low LST and a low wetness rank. Topographical variability is generally low in peatlands. Nevertheless, the vertical distance to the closest waterbody reveals small-scale topographical features that effect the simulated WTD (Fig. 3d).

Figure 5 depicts the spatial distribution of SHAP values for the same three covariates substantiates previous findings (Fig. 4). High LST has a positive impact on the prediction, resulting in deep WTD, and low LST has a negative impact on the prediction. In the case of drained forest, which has a low LST, the negative impact of LST is overruled by the positive impact of the crop-based wetness rank. The latter shows a very clear separation of negative impact for the wet ranks and positive impact for the dry ranks. The negative impact of the vertical distance to the nearest waterbody is predominately limited to locations that are actually river or lake grids. A distinct positive impact is found for locations with a high vertical distance.

In order to assess the overall accuracy of the WTD map, we conducted a 5-fold cross-validation experiment. For this, five GBDT models were trained using 80 % of the data for training, and 20 % of the data were held back for validation. The five validation datasets were sampled so each WTD observation served exactly once as validation data. Figure 6 presents the scatter density plot of both observed and simulated WTD for the five validation datasets, with Fig. 6a including the dummy points and Fig. 6b excluding them. The effect of the WTD transformation and the weighting scheme of WTD data in the depth interval of 0 to 0.5 m becomes apparent. The model shows the best accuracy for the shallow water table interval, whereas the performance deteriorates below a WTD of 1 m. The poor performance of WTD below 1 m can be explained by the transfer function which hinders the GBDT model to discriminate WTD variability below a WTD of 1 m. In the case of WTD-driven GHG upscaling, this is acceptable since the applied WTD response functions are not sensitive to changes in WTD deeper than approx. 0.5 m. The scatter plot reveals that the dummy points with zero and negative WTD, i.e., above terrain, are generally represented quite well by the GBDT model. Taking only the well and auger WTD observations into consideration, a slight bias for the shallow WTD observations becomes evident.

Table 3 quantifies the performance of the GBDT model for the 5-fold cross-validation test both including and excluding the dummy points. The performance for the well and auger observations for the top 0.5 interval shows a bias of -0.2 m. Also taking dummy points into consideration, the bias of the top 0.5 m interval and the 0.5 to 1 m interval was -0.05 and 0.08 m, respectively. We consider the validation excluding the dummy points as the more relevant performance quantification for the given application. For the deeper intervals the metric scores are comparable for the entire training dataset and the subset exclusively based on well and auger data. WTD values deeper than 1 m perform worst of all stated metrics, which underpins the visual assessment of Fig. 6.

For the entire model domain, the GBDT model predicts a WTD interval sensitive to GHG variability, i.e., 0–0.5 m, for 36 % of the area. For the delineated peat soils, with OC > 12 %, this area amounts to 54 %. After correcting from summer to annual conditions, i.e., subtracting 0.125 m (half the mean annual amplitude), these area estimates increase to 45 % and 64 %, respectively. For agricultural areas with OC > 12 %, the mean WTD is 0.49 m with a standard deviation of 0.35 m, which underpins the distinct WTD variability in peatlands, and this is also partly overlapping with the range of WTD associated with high sensitivity of the resulting emissions of CO2, CH4 and N2O.

The parametrization of the fitted WTD-driven response functions for CO2 and CH4 emissions (Fig. 7) showed a systematic relationship where CO2 emissions increased with increasing WTD between 0 and 0.4–0.5 m before reaching an asymptotic level of 10 MgCO2-Cha-1yr-1. The fitted parameters are as follows: CO2-Cmin = 1.132 Mg CO2-C ha1- yr-1, CO2-Cdiff = 10.903 Mg CO2-C ha1- yr-1, a = 6.415 and b = 14.183 m-1. CH4 emissions were consistently negligible at WTD depths below 0.2–0.3 m, but they increased at higher WTD to emissions of up to 0.8 MgCha-1yr-1. However, it is clear that a shallow WTD does not necessarily cause high CH4 emissions, but it instead provides a window of opportunity for methane fluxes to the atmosphere. The fitted parameters are as follows: CH4min = -21.48 kg C ha-1 yr-1, c = 258.83 and d = -5.16 m-1. N2O emissions were not modeled, but average values for observations at WTD > 0.3 m (n = 19) and < 0.3 m (n = 6) were 13.3 and 3.8 kgNha-1yr-1, respectively, thus representing a value similar to IPCC EFs for drained soil but a value somewhat higher for rewetted soils (Wilson et al., 2016).

Upscaling GHG emissions can be estimated based on the following elements: (1) the GHG upscaling method presented in Sect. 2.5, (2) the long-term annual average WTD map, (3) a land use map and (4) a map delineating the drainage ditches. With a spatial resolution of 10 m, the WTD maps open the possibility to estimate GHG at equally high resolution. However, given the apparent uncertainties in the WTD map and the WTD response functions, GHG values are aggregated to national scale.

For the approximately 74 000 ha with OC > 12 %, the total emission of the three gases CO2, N2O and CH4 amounts to 2.6 MtCO2-eq. Figure 8 depicts the relationship between WTD and the estimated GHG emissions, expressed as emission factor converted to CO2-eq. Emissions of CO2 dominate the GHG budget at WTD deeper than approx. 0.1 m, whereas methane emissions become dominant at WTD closer to the soil surface. The contribution from CH4 emissions is apparent, starting from a WTD of approx. 0.3 m, whereas low CH4 emissions for deeper WTD are related to the minor CH4ditch component, which is not WTD dependent and takes place throughout the lowland soils. N2O emissions have no WTD response function, and thus emissions are rather constant across the WTD variability. Spatial heterogeneity of N2O emissions is based on the applied land-use-specific emissions factors that are indirectly linked to WTD variability, which results in a slight decrease in N2O emissions with decreasing WTD. Based on the minimum of total GHG emissions shown in Fig. 8, a WTD of approx. 0.04 m can be identified as the optimal WTD for minimal GHG emissions, i.e., 5.6 Mg CO2-eqha-1yr-1. Yet, the exact numbers should be viewed as indicative, since for example the possibility of negative CO2 emissions at low WTD depends on the presence of wetland vegetation. Nevertheless, even in the absence of negative CO2 emissions, the data indicates that an optimal rewetting strategy should aim for a WTD in a range between 0 and 0.1 m to balance the trade-off between CO2 and CH4 emissions.

Table 4 states the emission factors for the three considered land use classes. The emission factors for N2O are in direct agreement with the ones stated in Sect. 2.5, whereas the emission factors for CO2 and CH4 are affected by the modeled WTD variability. In total, based on both area and emission factor, cropland dominates the GHG emissions of peatlands in Denmark. As expected, emission factors from rewetted peat soils are lowest.

The combination of a high-resolution WTD map and WTD response functions of GHG emissions allows us to evaluate the effects of alternative rewetting scenarios. For this, it is assumed that the WTD of an agricultural field can be changed to the optimal WTD, allowing a reduction in total GHG emissions to 5.6 Mg CO2-eqha-1yr-1 (Fig. 8). Figure 9 shows the results of three rewetting scenarios and a theoretical baseline as functions of the peatland area that is rewetted with a maximum of 74 000 ha. The baseline expresses the theoretical maximum emission reduction with the assumption that all agricultural fields are originally well drained and thus having a uniform reduction of 36.8 Mg CO2-eqha-1yr-1, which expresses the reduction from the maximum asymptote to the minimum of the total GHG curve in Fig. 8. In the three rewetting scenarios, the reference emissions are derived from the WTD response functions, and thus many agricultural fields have a lower reference emission than the baseline, which will result in a decreased emission reduction with respect to the baseline. The first scenario prioritizes wet fields in the restoration; i.e., the agricultural fields with the most shallow mean WTD are prioritized in the rewetting strategy. This scenario can be regarded as pessimistic with respect to the expected GHG emission reduction. The second scenario prioritizes the dry fields with the deepest mean WTD, which in turn can be considered an optimistic scenario. The third scenario selects fields in a random order and lies in between the optimistic and the pessimistic scenarios. The prioritization order is based on over 79 000 digitized fields, and the WTD of an entire field is set to 0.04 m for calculating the reduction in GHG emissions. In cases where the entire peatland area is rewetted, the reduction in GHG emissions is estimated to be 2.0 Mt CO2-eqyr-1 by all three scenarios. However, we observe large discrepancies between the restoration scenarios if only a fraction of the total peat area is rewetted. Prioritizing dryer fields already provides a high reduction starting with the first rewetted fields, whereas prioritizing wet fields shows little reduction. In fact, the reduction potential in the wet scenarios is just 30 % of the dry scenario for the first 10 000 ha. A deviation of 50 % between wet and dry scenarios is first exceeded for a rewetting area of above 20 000 ha. The random scenario lies in between the optimistic and pessimistic scenarios, with a linear emission reduction of 26.1 MgCO2-eqha-1yr-1. The linear emission reduction of the random scenario is 10.7 MgCO2-eqha-1yr-1 lower than the baseline scenario. This relates to the WTD map that introduces spatial variability in the random scenario opposed to the fully drained conditions assumed in the baseline scenario.