Modelling of growing season methane fluxes in a high-Arctic wet tundra ecosystem 1997–2010 using in situ and high-resolution satellite data

Figures & data

Fig. 1 The Zackenberg valley and the investigation area surrounding the research station (ZERO). The field inventory map of the dominant plant communities estimated in the Rylekærene study site is superimposed over the area. The vegetation map is the studied area referred to as Rylekærene throughout the text. The red dot on the Greenland map is the location of Zackenberg. The Footprint areas are the average 80% cumulative flux distances of the two towers.

Fig. 2 Average (±1 SD) normalised NDWI based on MODIS surface reflectance data 2000–2010. Data was averaged for each 8-d period after DOY of snowmelt and it was normalised against the seasonal average NDWI. The dotted lines show the time window used for choosing high-resolution Landsat data day 38–55 after DOY of snowmelt.

Table 1 The different sensors recording the Landsat images that were used in the analysis

Year	Satellite sensor	DOY of Landsat image	DOY with 10 cm snow depth
1997	Landsat 5 TM	222	170^a
2000	Landsat 7 ETM+	204	165
2002	Landsat 7 ETM+	214	171
2007	Landsat 7 ETM+^c	210	159
2008	Landsat 7 ETM+^c	222	175
2009	Landsat 7 ETM+^c	199	152^b
2010	Landsat 7 ETM+^c	219	167

Day of year (DOY) when the images were obtained is also included. The DOY of 10 cm snow depth for the different years, which was used as start of the growing season, is also given.

^aDOY of 10 cm snow depth based on snow coverage by Buus-Hinkler et al. (2006).

^bIn 2009, the snow depth was by far the shallowest on record and peaked at 17 cm. It was therefore below 10 cm already DOY 136 according to snow depth measurements at C1. In the central parts of the fen, it was visually seen to melt DOY 152.

^cImages taken when the Scan Line Corrector on Landsat 7 was broken.

Fig. 3 Workflow for the model development and the model evaluation. The white boxes are steps in the work process of the model development or the model evaluation. The grey boxes are input data or equations going into the models. The thick arrows indicate steps in the work process, whereas thin arrows indicate input. The final results of the model evaluation were the root mean square error, the model-in situ ratio and the goodness-of-fit given by a linear regression equation.

Table 2 Monitored environmental variables used in the modelling of CH₄ fluxes

Year	T 10	WtD	AL
1997	M1^a	–	T1997
2000	M2^b	M2	M2
2002	M1^a	–	M1^c
2007	M1^d	M1	M1
2008	M1	M1	M1
2009	M1	M1	M1
2010	M1	–	M1

T ₁₀ is the soil temperature at 10 cm depth, WtD is the water table depth and AL is the active layer thickness. Gaps in the data series were filled by linear interpolation. The ‘–’ either means that no measurements were done, or that they were not necessary in the modelling process. M1 is the monitoring site 1, M2 is the monitoring site 2 and T1997 is the Tower site 1997 (Fig. 1).

^a T ₁₀ modelled with a linear regression fitted between T ₁₀ at monitoring site 1 d 1–57 of the growing seasons 2007, 2008 and 2009 and T ₁₀ at C1 (R ²=0.47, n=4147).

^b T ₁₀ was measured from the 8 July 2000. At the start of the growing season, a linear regression fitted between hourly averaged T ₁₀ at monitoring site 2 in 2000 and hourly T ₁₀ at C1 (R ²=0.89, n=1062) was used.

^cAL modelled with a linear regression fitted between AL at monitoring site 1 of the growing seasons 2007, 2008 and 2009 and AL at ZEROCALM1 (Jensen and Rasch, 2011) (R ²=0.96, n=23).

^d T ₁₀ was measured from the 4 July 2007. At the start of the growing season, a linear regression fitted between hourly values of T ₁₀ at monitoring site 1 and C1 (R ²=0.80, n=1531) for the growing season 2007, was used.

Table 3 Average (±1 SD) CH₄ fluxes and environmental variables measured between 10 a.m. and 6 p.m. in the period 30 June–4 August 2007, for the different plant communities

Plant communities	T 10 (°C)	WtD (cm)	ALmax (cm)	CH4 flux (mg CH4 m^−2 h^−1)	Sample size
Continuous fen	7.4±1.3	−3.4±3.6	49±3	9.1±5.3	154
Hummocky fen	7.4±1.3	−8.2±4.2	47±4	3.6±2.5	108
Grassland	6.0±1.3	–	56±8	0.1±0.4	110
Salix snowbed	8.2±2.1	–	78±3	−0.04±0.04	51
Vaccinium Heath	7.6±2.3	–	69±5	−0.02±0.04	54
Cassiope heath	7.7±1.6	–	74±6	−0.03±0.03	54
Dryas heath	8.9±2.1	–	75±5	−0.03±0.03	54

The T ₁₀ is the average soil temperature at 10 cm depth and WtD is the average water table depth (centimetres below moss surface) measured 21 June–4 August 2007. AL_max is the average active layer thickness (centimetres below moss surface) from the 4 August 2007, when the thickest AL was measured.

Fig. 4 The relationship between temporal variation in CH₄ fluxes to (a) averaged soil temperature at 10 cm depth and (b) averaged water table depth. Equation (3) is given in the text.

Table 4 Parameters for the models relating temporal variation in CH₄ fluxes and temporal variation in environmental variables

Plant communities	Equation	Environmental variables	a	b	c	d	R ^2
Continuous fen	Linear	WtD	11.11±0.47	0.41±0.07	–	–	0.81
Hummocky fen	Linear	WtD	4.10±0.35	0.10±0.05	–	–	0.34
Continuous fen	Eq. (3)	T 10	4.50±0.63	–	0.13±0.02	–	0.79
Hummocky fen	Eq. (3)	T 10	2.14±0.45	–	0.10±0.04	–	0.47
Continuous fen	Eq. (4)	T 10, AL	4.41±0.59	–	0.13±0.02	0.17±0.15	0.76
Hummocky fen	Eq. (4)	T 10, AL	1.97±0.36	–	0.11±0.03	0.17±0.15	0.54
Continuous fen	Eq. (5)	WtD, T 10	7.38±2.54	0.17±0.15	0.06±0.05	–	0.85
Hummocky fen	Eq. (5)	WtD, T 10	2.31±0.98	0.01±0.06	0.10±0.05	–	0.47
Continuous fen	Eq. (6)	WtD, T 10, AL	7.38±2.54	0.17±0.15	0.06±0.05	0.17±0.15	0.85
Hummocky fen	Eq. (6)	WtD, T 10, AL	2.31±0.98	0.01±0.06	0.10±0.05	0.17±0.15	0.47

Linear means a linear regression. Equations (3)–(6) are given in the text. a, b and c are fitted parameters, d was parameterised by Friborg et al. (2000), and R ² is the coefficient of determination.

Fig. 5 Plot-averaged CH₄ fluxes against spatial variation in water table depth at the DOY of the satellite image 2007 (DOY 210).

Fig. 6 Categorised water table depth (WtD_cat) against Landsat-based NDWI averaged for each WtD_cat category. None of the satellite pixels had an average water table above the soil surface, and there is hereby no zero WtD_cat.

Fig. 7 (a) In situ and modelled CH₄ flux and (b) input variables against day after day of year (DOY) of snowmelt. The in situ CH₄ flux is the average±1 SD averaged for each day after DOY of snowmelt 1997, 2000, 2007 and 2008. The modelled CH₄ flux is the average flux modelled by Model_sat 2 for each day after DOY of snowmelt 1997, 2000, 2007 and 2008. Model_sat 2 was chosen as it was the best model according the model evaluation. The model range is the minimum and the maximum of the eight models averaged for each day after DOY of snowmelt 1997, 2000, 2007 and 2008. The water table depth range is the minimum and maximum of the measured values for each day after DOY of snowmelt 1997, 2000, 2007 and 2008. Active layer thickness and soil temperature at 10 cm depth is the average for each day after DOY of snowmelt 1997, 2000, 2007 and 2008.

Fig. 8 Modelled CH₄ fluxes against in situ CH₄ fluxes. (a) Average of modelled CH₄ fluxes for all Model_nosat and Model_sat to show the difference between models with and without satellite-based NDWI; (b) Model_sat 2 and Model_sat 4 against in situ CH₄ fluxes to illustrate the difference between models including and excluding the temporal variation in WtD; (c) Model_sat 1 and Model_sat 2 against in situ CH₄ fluxes to illustrate the difference between models including or excluding the effect of AL; and (d) Modelled CH₄ fluxes modelled with Model_sat 2 for the different years against in situ CH₄ fluxes.

Table 5 Ratios of modelled CH₄ fluxes to in situ CH₄ fluxes for the different years and the different models

Model	Equation	1997	2000	2008	2009	Mean all years	RMSE
1nosat	(3)	0.88	1.59	0.83	1.32	1.16±0.36	1.64
2nosat	(4)	0.83	1.48	0.78	1.17	1.07±0.33	1.58
3nosat	(5)		1.63	0.85	1.43	1.31±0.40	2.10
4nosat	(6)		1.52	0.80	1.25	1.19±0.36	1.84
Mean allnosat		0.86	1.55	0.82	1.30	1.18±0.36	1.67
1sat	(9_3)	1.09	0.87	1.20	1.15	1.08±0.15	1.61
2sat	(9_4)	1.03	0.78	1.13	1.03	0.99±0.15	1.50
3sat	(9_5)		0.96	1.24	1.25	1.15±0.16	1.94
4sat	(9_6)		0.87	1.15	1.09	1.04±0.15	1.62
Mean allsat		1.06	0.87	1.18	1.13	1.07±0.14	1.56

Root mean square errors (RMSE) in mg CH₄ m⁻² h⁻¹ for the different models are also included.

Fig. 9 CH₄ fluxes modelled by Model_sat 2, averaged for the Rylekærene area, and accumulated over the first 57 d of the growing seasons 1997–2010.

Fig. 10 (a) Accumulated modelled CH₄ fluxes day 1–57 of the growing season for Rylekærene; (b) maximum MODIS-based NDWI for the NDWI peak period of the growing seasons in Rylekærene 1997–2010; and (c) and average soil temperature at 10 cm soil depth at C1 day 1–57 of the growing season. The gap in the soil temperature 2005 was caused by broken soil temperature sensors.

Table 6 Average (± 1 model SE) modelled CH₄ fluxes for the entire Rylekærene area for the first 57 d of the growing season

Year	CH4 fluxes (mg CH4 m^−2 h^−1)
1997	1.5±1.2
2000	2.3±1.1
2002	2.9±3.7
2007	1.6±1.0
2008	3.0±5.3
2009	1.4±0.8
2010	1.5±0.6

The model used for these estimates was the Model_sat2. The variation in CH₄ fluxes due to heterogeneity in the modelled area is not included in the model SEs and it is strictly an estimate of the model uncertainty.

Table A Abbreviations, symbols and their descriptions

Abbreviation or symbol	Description
a, b, c and d	Model parameters in Equations (3)–(6)
AL	Active layer thickness
ALmax	Peak active layer thickness measured during the growing season
C1	Climate station (Fig. 1)
DOY	Day of year
	Methane flux
	Average chamber-measured methane fluxes from all plots
	Plot-averaged chamber measured methane fluxes
	Fraction of CH4 flux of an individual plot in relation to the average CH4 flux from all plots
k	Intercept of exponential regression between and WtDcat [eq. (8)]
l	Growth constant of exponential regression between and WtDcat [eq. (8)]
M1	Monitoring site 1
M2	Monitoring site 2
Modelnosat	Model data that do not include remote sensing data
Modelsat	Model data that do include remote sensing data
MODIS	Moderate resolution imaging spectroradiometer
NDWI	Normalized difference water index
NIR	Near-infrared wavelengths (780–900 nm)
RMSE	Root mean square errors
	Model standard deviation
	Standard deviation of a model parameter
	Standard deviation of a model parameter
SWIR	Short-wave infrared wavelengths (1000–3000 nm)
SD	Standard deviation
SE	Standard error
T 10	Soil temperature at 10 cm depth
T1997	Tower site 1997
u	Intercept of linear regression between WtDcat and NDWI [eq. (2)]
w	Slope of linear regression between WtDcat and NDWI [eq. (2)]
WtD	Water table depth
WtDcat	Categorized water table depth
y	Year

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