Spatial scale-dependent land-atmospheric methane exchange in the northern high latitudes from 1993 to 2004

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Introduction
The importance of natural methane (CH 4 ) emissions from terrestrial ecosystems in the northern high latitudes in greenhouse gas radiative forcing has drawn a great attention in the past decades (e.g.Koven et al., 2011;Gao et al., 2013;Zhu et al., 2013a).The regional CH 4 budget and its temporal dynamics have been widely studied using "topdown" (e.g.Chen and Prinn, 2006;Kim et al., 2011) and "bottom-up" (e.g.Walter et al., 2001;Glagolev et al., 2011;Zhu et al., 2013b) approaches.However, it is still a challenge to have an accurate quantification given the high spatial and temporal variability of CH 4 emissions from this region (Solomon et al., 2007).Laboratory and field studies Figures indicate that the dynamics of CH 4 fluxes are mainly determined by variations in water table, temperature, pH, and microbial substrate availability (Whalen and Reeburgh, 1996;MacDonald et al., 1998;Christensen et al., 2003;Wagner et al., 2005).As an effective "bottom-up" approach, process-based biogeochemical models are often used to study the effects of these environmental factors on CH 4 fluxes by considering the effects of soil hydrological and thermal dynamics on CH 4 production and consumption (e.g.Zhuang et al., 2004;Wania et al., 2010).Among these abiotic and biotic environmental controlling factors, the dynamics of the water table depth (WTD) is one of the most important factors in field observation (e.g.Nykänen et al., 1998;Heikkinen et al., 2002) and model-based (e.g.Petrescu et al., 2008;Bohn and Lettenmaier, 2010) studies.
Since the measurements of water table are only available at limited sites over the Earth's surface, most process-based biogeochemical models, operated at large grid cells (e.g.0.5 • ), simply treat WTD as spatially uniform within each grid cell, without considering the sub-grid spatial heterogeneity of water table position (e.g.Walter et al., 2001;Zhuang et al., 2004Zhuang et al., , 2007)).This simple representation of WTD may bias gridcell-mean CH 4 fluxes, therefore regional CH 4 emissions.A recent model experiment that focused on a single model grid cell (100 km) (Bohn and Lettenmaier, 2010) indicated that the model-estimated CH 4 emissions without considering the sub-grid spatial heterogeneity of water table were biased by factors ranging from 0.5 to 2. Further, assuming different sub-grid spatial variability of WTD, simulated daily CH 4 fluxes were found to be biased low and high as the water table fell and rose, respectively.However, seasonal variability of WTD, which is greatly influenced by climate conditions, may obscure the impact of WTD on the bias of CH 4 emissions at a longer time scale.To date, it is still not clear how annual CH 4 budgets will be affected in their both direction and magnitude when the sub-grid spatial heterogeneity of WTD is taken into account.
To our knowledge, there is no such study on the effects of spatial scaledependent WTD on CH 4 dynamics at large scales.Here we use a coupled hydrologybiogeochemistry model framework, incorporating sub-grid spatial variations in the WTD Figures

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Full to assess CH 4 emissions from pan-Arctic terrestrial ecosystems with three objectives: (1) to quantify pan-Arctic land-atmospheric CH 4 exchanges at a fine spatial resolution by considering sub-grid spatial variability of WTD; (2) to analyze the spatial and temporal dynamics of CH 4 emissions; and (3) to examine the difference in the magnitude and temporal variability of CH 4 emissions with and without considering sub-grid spatial variability of WTD.

Overview
A macro-scale hydrological model (Variable Infiltration Capacity, VIC; Liang et al., 1994) and a biogeochemical model (Terrestrial Ecosystem Model, TEM; Zhuang et al., 2004) were coupled (Fig. 1) to make estimates of daily CH 4 exchange between terrestrial ecosystems and the atmosphere over the pan-Arctic, which is defined as the land area within the watersheds of major rivers that drain into the Arctic Ocean, excluding icedominated Greenland and Iceland (Lammers et al., 2001).To consider the effects of sub-grid spatial variability of WTD on estimated CH 4 emissions, the grid-cell-mean WTD simulated by VIC at a coarser spatial resolution was downscaled into a finer resolution at a sub-grid level using a TOPMODEL-based parameterization.The VIC-TEM-TOPMODEL framework was initially developed by Lu and Zhuang (2012) to estimate land-atmospheric CH 4 exchanges in the Alaskan Yukon basin.Here, the same coupled framework but with a new TOPMODEL-based parameterization scheme was used to assimilate satellite-based inundation data to improve the parameterization of TOPMODEL-based WTD redistribution.

Models and data
The TEM model explicitly simulates carbon and nitrogen dynamics of vegetation and soils, and has been used to examine terrestrial CH 4 dynamics in northern high latitudes Introduction

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Full  (Zhuang et al., 2004;McGuire et al., 2010;Zhu et al., 2011).TEM has its hydrological module (Zhuang et al., 2002) to simulate water dynamics of terrestrial ecosystems.However, like many existing biogeochemistry models, the hydrological module is formulated as a simple "single-bucket".To improve the estimates of soil moisture profile, a key controlling factor for biogeochemical processes of CH 4 , more sophisticated hydrological models, like VIC, are needed (e.g.Bohn and Lettenmaier, 2010;Lu and Zhuang, 2012).The VIC model used physically-based formulations to calculate energy fluxes and soil water movement and runoff (Liang et al., 1994).The explicit representation of the frozen soil/permafrost algorithm (Cherkauer et al., 2003) improved the capacity of the VIC model for cold region studies (Su et al., 2005(Su et al., , 2006)).In the VIC-TEM-TOPMODEL framework (Fig. 1), the VIC model was first used to solve daily moisture and energy balances.The simulated soil temperature profile, freeze/thaw fronts, and soil ice profile were directly fed into TEM, while the simulated soil moisture profile was converted into WTD based on the soil moisture deficit method (Bohn et al., 2007) and then fed into TEM after redistributing WTD based on a TOPMODEL parameterization scheme.Finally, TEM was run to simulate daily CH 4 emissions and consumption over the pan-Arctic.
The process-based TEM model explicitly simulates CH 4 production, oxidation, and transport (diffusion, ebullition, and plant-aided transport) processes in the soil, with the following governing equation (Zhuang et al., 2004): where ∂C M is soil CH 4 concentration at a given depth (1 cm depth step) and a given time (1 h time step); ∂(D(∂C M /∂z))/∂z is CH 4 diffusion and D is the CH 4 diffusivity in soil column; P , Q, E , and R represent the CH 4 production, oxidation, ebullition, and plant-aided transport rate, respectively; Z wt is WTD and Z soil is the lower boundary of the soil column.These CH 4 -related processes were formulated as functions of climate, vegetation, and soil conditions for major terrestrial ecosystems in the northern high latitudes (Zhuang et al., 2004).Introduction

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Full To run the VIC and TEM models within the VIC-TEM-TOPMODEL framework, the spatial data of climate, vegetation, and soil from a variety of sources were used (Fig. 1).Gridded daily meteorological forcing data was acquired from NCEP/NCAR Reanalysis Datasets (http://www.esrl.noaa.gov/psd/data/gridded/data.ncep.reanalysis.surfaceflux.html).For VIC, precipitation, maximum/minimum air temperature and wind speed, were used.For TEM, precipitation, mean air temperature and downward solar shortwave radiation were required, except for those forcing from VIC simulations (soil temperature/moisture profiles and freezing/thawing fronts).For both VIC and TEM, gridded vegetation type information was derived from MODIS/MCD12C1 product with UMD vegetation classification scheme (https: //lpdaac.usgs.gov/products/modis_products_table/mcd12c1),and gridded soil physical properties (e.g.soil texture, porosity) were taken from the World Inventory of Soil Emission Potentials (ISRIC-WISE) spatial soil database (Batjes, 2006).For the VIC model parameterization, vegetation-specific parameters (e.g.minimum stomatal resistance, rooting depths) were obtained from VIC model website (http://www.hydro.washington.edu/Lettenmaier/Models/VIC/), and typical calibration parameters that control soil water infiltration processes were taken from previous studies (Nijssen et al., 2001a, b, c).For the TEM model parameterization, key parameters that control methanogenesis and methanotrophy processes were taken from Zhuang et al. (2004).

TOPMODEL parameterization
In the VIC-TEM-TOPMODEL framework, the redistribution of WTD was made by applying topography-based watershed-scale TOPMODEL to represent spatial variability of local WTD.By assuming uniform soil hydraulic properties within each watershed and that local transmissivity decreases exponentially with depth (Beven and Kirkby, 1979), the relationship between local WTD (Z wt i ) and watershed-mean water table (Z wt ) was expressed as: where s is local terrain slope; f T is a temperature piecewise function used to represent the effect of frozen soil on soil drainage depth, in which T is mean surface air temperature in January; and α is a calibration parameter.
For each month of the period of 1993-2004, a three-step calibration procedure was used to best match the monthly TOPMODEL-based spatially-averaged fraction of inundated area to the monthly satellite-based inundation fraction over the pan-Arctic: (1) the spatially-averaged fraction of inundated area (A i ) in a month was first calculated from equal-area satellite-based inundation fraction data (Prigent et al., 2007;Papa et al., 2010); (2) the parameter α was calibrated to find an optimal value for that month to generate monthly Z wt i having a probability of P (Z wt i ≤ 0) = A i ; and then (3) the optimal α was applied to each day in that month to calculate daily Z wt i .The daily Z wt i was set as zero whenever it was negative (above the soil surface) in the simulation of CH 4 Introduction

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Full emissions.An illustration of TOPMODEL parameterization, description of topographyrelated spatial data, and calibration results were provided in the Supplement.

Simulation protocol
In this study, two sets of model simulations, with (referred to as VIC-TEM-TOPMODEL simulation) and without (referred to as VIC-TEM simulation) considering sub-grid spatial variability of WTD, were conducted to estimate daily CH 4 emissions.In the first set of simulations, we used the VIC-TEM-TOPMODEL framework to simulate daily CH 4 fluxes: VIC and TEM were operated at a spatial resolution of 100 km and 5 km, respectively, and the simulated 100 km grid-cell-mean WTD was redistributed into 5 km WTD at a sub-grid level via a TOPMODEL-based parameterization scheme.The choice of 5 km here was a special case of a finer spatial resolution for the VIC-TEM-TOPMODEL simulations, but the choice of any finer spatial resolution did not affect our simulations when the TOPMODEL-based parameterization scheme was applied.The probability distributions of 100 km and 5 km WTD over the region shared same mean value but with distinct variances.The variance of WTD increased after the redistribution of WTD, and the degree of the increase was determined by the parameter calibration (m in Eq. 2) with a target of best matching the simulated monthly inundated area fraction to the monthly satellite-based inundation fraction.Thus, the variance of WTD at a finer spatial resolution was only determined by satellite-based saturated area fraction; and the probability distribution of WTD at a finer scale did not change no matter what finer resolution was used.In the second set of simulations, only VIC and TEM models were used.In this case, both VIC and TEM were operated at the same spatial resolution (100 km) and no redistribution of WTD was applied.

Spatial patterns of methane fluxes
The VIC-TEM-TOPMODEL simulations indicated there is a large spatial variability of land-atmospheric CH 4 fluxes, simulated at a 5 km spatial resolution over the pan-Arctic (Fig. 2c).The highest emissions of CH 4 occurred in the West Siberian Lowlands (WSL, Fig. 2b) and the Hudson Bay Lowlands (HBL), where extensive wetlands exist, with a source of atmospheric CH 4 up to 400 mg CH 4 m −2 d −1 during the growing season (May-September).The sinks of atmospheric CH 4 occurred in the southern parts of Canada and Siberia, where drier ecosystems with higher soil temperatures favor CH 4 consumption, with a sink up to 1.To analyze the relationship between 5 km CH 4 fluxes and major environmental controls, the WSL sub-region was further analyzed.The spatial patterns of CH 4 emissions and consumption were dominated by the distribution of WTD, although the spatial patterns were also affected by soil temperatures with a southward increasing trend (Fig. 2d and e).As expected, at a 5 km spatial resolution, shallower water table position corresponded to higher CH 4 emissions, while deeper water table position corresponded to lower CH 4 emissions and favored CH 4 consumption.In addition, positive CH 4 fluxes (i.e.net CH 4 emissions) generally occurred when the WTD was less than 0.5 m, beyond which soils generally acted as a sink of CH 4 (Fig. 2d and e).
Given the importance of water table in estimating CH 4 emissions, it was also worthwhile to evaluate the accuracy of the simulated WTD.The estimated WTD was compared with a dataset of water table observations, compiled by Fan et al. (2013).The comparison was limited to those well sites with shallow water table (< 2 m below the land surface) where soil moisture is coupled to water table (Fan et al., 2007), and around 5000 observations across southern Canada were available for the comparison (Supplement Fig. S7).Overall, the simulated WTD were comparable to the observations at well sites, although our estimates of water table were generally shallower as indicated by the histogram of WTD.The deeper water table at these well sites might be due to human activities including pumping, irrigation and drainage that were not represented in our model.In addition, the spatial pattern of WTD was generally consistent with an existing cartography-based 30-arc wetland map (GLWD-3, Lehner and Döll, 2004), although inconsistences existed in the southern part of the WSL (Fig. 2e and f).
The depth of 0.5 m might have been used as a WTD threshold to determine the spatial distribution of wetlands in the WSL, although this WTD threshold was slightly deeper than those thresholds (0.2-0.4 m) suggested by Fan and Miguez-Macho (2011).

Temporal variability of methane fluxes
Driven with 12 yr climate data, 5 km CH 4 emissions from the VIC-TEM-TOPMODEL simulations showed that the inter-annual variability of CH 4 fluxes from terres-Introduction

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Full trial ecosystems over the pan-Arctic ranged from 38.1 Tg CH 4 yr −1 in 2000 to 55.4 Tg CH 4 yr −1 in 1994 (Fig. 3a).The estimated annual CH 4 emissions were within the range of previous measurements and model-based estimates, ranging from 20 to157 Tg CH 4 yr −1 , with the minimum and maximum values reported by Christensen et al. (1996) and Petrescu et al. (2010), respectively.There was a significant declining trend of annual net CH 4 emissions from 1993 to 2004, with an annual decreasing rate of 0.83 Tg CH 4 yr −2 .Correlation analysis indicated that annual 5 km CH 4 emissions were inversely correlated with WTD (statistically significant) and soil temperature (statistically insignificant), both of which had an increasing trend during the 12 yr period (Fig. 3a, Table 1).The high correlation coefficient (r = −0.66,at a significance level of p < 0.05) between annual 5 km CH 4 emissions and WTD highlights the importance of WTD in determining CH 4 fluxes.
To examine the seasonal variability of daily CH 4 emissions, we took the year 1994, having maximum 5 km CH 4 emissions from 1993 to 2004, as an example year for analysis (Fig. 3b).Most of emissions occurred from May to September, with the highest fluxes in July.Low CH 4 emissions were estimated in winter due to low soil temperature, while high CH 4 emissions occurred in summer due to high soil temperature and a shallow water table.Although both WTD and soil temperature influenced CH 4 emissions, the temporal dynamics of daily CH 4 fluxes are correlated better with WTD than soil temperature.Daily CH 4 emissions and WTD had a consistent seasonal variability with concurrent increases, peaks and decreases.The trough of CH 4 fluxes occurring in early August was caused by an abrupt drop-down of the water table, which could be attributed to the sudden decrease of precipitation but still high evapotranspiration (indicated by air temperature) in August (Supplement Fig. S6).

Differences due to spatial scales
There were large differences in both magnitude and temporal variability of methane emissions between 5 km VIC-TEM-TOPMODEL and 100 km VIC-TEM simulations.

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Full from 1993 to 2004 were 42 % larger than those simulated at a 100 km resolution (32.2 Tg CH 4 yr −1 ) (Fig. 3a).The 100 km CH 4 emissions tended to increase from 1993 to 2004 (statistically insignificant), which is contrary to the 5 km CH 4 emissions (Fig. 3a, Table 1).The inter-annual variability of the 100 km CH 4 emissions was positively correlated with soil temperature (r = 0.84, at a significance level of p < 0.01).Similarly, the 100 km daily CH 4 emissions had a consistent temporal variability with daily soil temperature (Fig. 3b).The 100 km CH 4 emissions were more dependent on soil temperature than on WTD.In contrast, WTD was more important in determining the 5 km CH 4 emissions.
The difference in the magnitude of annual net CH 4 emissions between 100 km and 5 km resolutions was due to changing emitting area and flux density.The fraction of CH 4 emitting area at a 5 km resolution was higher than that at a 100 km resolution due to the enhanced variance of 5 km WTD after WTD redistribution (19 % vs. 12 % over WSL, Fig. 4), although mean regional WTD was same.Mean flux density of 5 km resolution simulations over all emitting grid cells was larger than that of 100 km resolution due to the nonlinear dependence of CH 4 emissions on WTD (Fig. 4).The increases in both emitting area and CH 4 flux density resulted in a 42 % increase of annual net CH 4 emissions over the study region.The differences in CH 4 emissions at these two scales vary across the region and the annual total CH 4 budget over the study region at a 5 km resolution was consistently larger during the period of 1993-2004.Positive bias of CH 4 emissions (higher at a 5 km resolution) between the two scales tended to occur in those grid cells with deeper water table, while negative bias tended to occur in those with shallower water table (Fig. 5).This is consistent with the findings in Bohn and Lettenmaier (2010) that the simulated daily CH 4 fluxes without considering the sub-grid spatial heterogeneity of WTD (100 km simulation in our case) had biased high (low) under shallower (deeper) water table conditions.
In TEM, the emission rates of CH 4 have a positive temperature response and a negative WTD response (higher CH 4 emissions at shallower water table) (Zhuang et al., Introduction Conclusions References Tables Figures

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Full  Full Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Due to the limited availability of satellite-based inundation data used for TOPMODEL-based parameterization scheme, these two sets of model simulations were run from 1993 to 2004.The VIC-TEM-TOPMODEL simulations at a 5 km spatial resolution were used to analyze the spatial and temporal dynamics of CH 4 emissions over the pan-Arctic.The effects of spatial scale-dependent WTD on CH 4 emissions were examined by comparing the Discussion Paper | Discussion Paper | Discussion Paper | 100 km and 5 km CH 4 simulations with VIC-TEM-TOPMODEL and VIC-TEM models, respectively.
5 mg CH 4 m −2 d −1 .Given the extremely high spatio-temporal variations of field CH 4 fluxes even under similar environmental conditions (e.g.Van Huissteden et al., 2005), a general evaluation of the magnitude and variability of simulated CH 4 fluxes was conducted here.In comparison with field CH 4 measurements, the estimated daily CH 4 fluxes during the growing season, −1.5 ∼ 400 mg CH 4 m −2 d −1 , were within the range of reported CH 4 fluxes within the study region (Supplement Table S1), −9 ∼ 471 mg CH 4 m −2 d −1 .The mean positive CH 4 flux (68.2 mg CH 4 m −2 d −1 ), during the growing season, of all CH 4 emitting grid cells over the study region was closer to the mean value of site measurements of CH 4 emissions (60.1 mg CH 4 m −2 d −1 ).In comparison with extensive field CH 4 measurements in WSL during the growing season (∼ 1500 instantaneous measurements across representative mire landscapes) (Glagolev et al., 2011), the probability distributions of the modeled and observed daily CH 4 emissions had similar mean and median fluxes, although the model was unable to simulate extremely high CH 4 fluxes (> 370 mg CH 4 m −2 d −1 ) (Supplement Fig. S5).Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Mean annual net CH 4 emissions simulated at a 5 km resolution (45.8 Tg CH 4 yr −1 ) Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper |

Fig. 1 .
Fig. 1.Conceptual framework of coupled models to estimate net methane emissions.Shown are external spatial inputs (blue) for driving or calibrating models, internal information exchange (yellow) between models, and final model outputs (green).Arrows indicate the direction of information exchange among all components.See text and auxiliary materials for more details.

Fig. 4 .
Fig. 4. Probability distributions of mean water table depth during the growing season (May-September) at 100 km (a) and 5 km (b) spatial resolutions across West Siberian Lowlands.The colored and grey bars indicate methane emitting and non-emitting zones, respectively; darker colored bars correspond to higher methane emitting rates.
Fan and Miguez-Macho (2011)l topographic wetness index, and TWI represents watershed-mean TWI.The watershed-mean water table (Z wt ) was calculated as an area-weighted mean WTD of intersected VIC grid cells (Supplement Figs.S1 and S2).m is a decay parameter controlling the exponential decline of transmissivity with depth, and a larger m corresponds to deeper soil (slower declining rate of transmissivity with depth) and therefore stronger spatial variance of the local WTD (Z wt i ) within a watershed.The magnitude of m is determined by the local sediment-bedrock profile, which is controlled by climate and geology/topography.FollowingFan and Miguez-Macho (2011), the following equation was used to represent the effects of climate and topography on the parameter m over the pan-Arctic: Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper |

Table 1 .
Pearson correlations between annual CH 4 emissions (at 5 km and 100 km resolutions) and spatially-averaged water table depth and top-layer (0-5 cm) soil temperature during the growing season (May-September) over the pan-Arctic during the period of 1993-2004.The annual changing rate of each variable is given in corresponding bracket.
a p value less than 0.05.b p value less than 0.01.Introduction