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Published online 29 March 2006
Published in Soil Sci Soc Am J 70:753-762 (2006)
DOI: 10.2136/sssaj2005.0214
© 2006 Soil Science Society of America
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Soil Biology & Biochemistry

Probability Distribution and Spatial Dependence of Nitrous Oxide Emission

Temporal Change in Hummocky Terrain

T. T. Yates*, B. C. Si, R. E. Farrell and D. J. Pennock

Dep. of Soil Science, Univ. of Saskatchewan, Agriculture Bldg., 51 Campus Dr., Saskatoon, SK, S7N 5A8 Canada

* Corresponding author (Yates{at}sask.usask.ca)


   ABSTRACT
TOP
 ABSTRACT
INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 CONCLUSIONS
 REFERENCES
 
Climate controls soil N2O emissions via its effects on soil properties such as water-filled pore space. Changes in climate should produce changes in the probability distribution and spatial dependency of soil N2O data. Knowing the extent of the changes in the distribution of this data is important for validating model predictions. The objectives of this study were to describe the probability distributions and estimate the spatial dependency of soil N2O emission data. On a hummocky, agricultural landscape in Saskatchewan, N2O emission data and related soil variables were taken from a 128-point transect 15 times over 2 yr. Probability distributions were compared using a Chi-square test. The range in spatial correlation was determined using the indicator semivariogram with a nested model fit approach. The mean N2O flux ranged from 25.3 to –0.2 ng N2O–N m–2 s–1. Probability distributions ranged in shape from reverse J-shape through log normal to symmetrical. The majority of distributions were statistically different from each other, showing a lack of temporal stability. Mean N2O flux and distribution shape followed an event-based/background emission pattern. High flux events had statistically similar, reverse J-shaped distributions. As mean N2O flux decreased to a background level distribution, shape changed to log normal and symmetrical forms. A high nugget/sill ratio characterized the majority of sampling dates, although spatial dependency was generally moderate. Flux values in the fourth quartile tended to have a spatial dependency of 15 m, probably reflecting a topographic control at a landform element scale.

Abbreviations: MDCD, minimum detectable concentration difference • WFPS, water-filled pore space


   INTRODUCTION
TOP
 ABSTRACT
 INTRODUCTION
MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 CONCLUSIONS
 REFERENCES
 
NITROUS OXIDE (N2O) is a greenhouse gas with a 100-yr global warming potential of approximately 296 times that of CO2. The level of atmospheric N2O is estimated to be increasing at a rate of 0.8 (± 0.2) ppb yr–1 (IPCC, 2001). It is estimated that up to 70% of anthropogenic emissions come from agricultural activities (Agriculture and Agri-Food Canada, 1998), with the soil identified as the chief source (FAO and IFA, 2001).

Respiratory denitrification is considered the dominant source of soil N2O emissions (Tiedje, 1988). However, soil N2O emissions are also produced as a byproduct of nitrification (Skiba et al., 1993). The availability of O2, C, and N are important process level controls on the production of N2O in the soil (Robertson, 1989). Oxygen has a major influence on the synthesis and activity of reductive enzymes (Tiedje, 1988), and denitrification occurs in anaerobic soil microsites or hotspots (Parkin, 1987). Anaerobic conditions depend on the rates of O2 diffusion versus consumption (Tiedje, 1988). The diffusion of O2 is slowed by the presence of water in soil pores and as films on soil aggregates (Renault and Stengel, 1994), and denitrification becomes the dominant process producing N2O when the water-filled pore space (WFPS) exceeds approximately 60% (Lemke et al., 1998; Davidson and Verchot, 2000). Beyond a WFPS of 80%, production of N2O drops as denitrification consumes N2O and produces N2 (Veldkamp et al., 1998). Below a WFPS of 60%, increased diffusion of O2 limits denitrification, and N2O production is attributed to nitrification (Robertson and Tiedje, 1987).

The probability distribution of soil N2O data is commonly described as approximately log normal or highly skewed (Parkin, 1987; Corre et al., 1996). Parkin (1987) attributes this to the patchy distribution of denitrification in anaerobic microsites. High values of N2O flux occur only when all conditions are nonlimiting. Hence, measurements of N2O emissions from the soil are typically characterized by high degrees of spatial and temporal variability (Groffman et al., 2000). The large uncertainty associated with soil N2O emission data makes the definition of predictive relationships between N2O flux and controlling variables difficult (Corre et al., 1996). In turn, upscaled measurements and model predictions of soil N2O flux are highly uncertain (Derwent et al., 1999). Validation of model estimates of soil N2O flux should include reproduction of the probability distribution of measured soil N2O data. Parkin (1987) modeled denitrification activity and produced a highly skewed data set of denitrification rates with a similar probability distribution as the original denitrification measurements. He speculated that the probability distribution of soil denitrification data would change temporally as controlling factors, such as soil moisture, changed. However, little information is available on how the probability distribution of soil N2O data changes with time as state variables such as soil moisture and temperature change.

The probability distribution can give us information about the variability in N2O emission data but cannot tell us anything about the spatial dependency of the data. Information is available on the spatial dependence of N2O emissions at a moment in time (Ambus and Christensen, 1994), but there is little information on how spatial dependency changes over time. Our first objective was to examine the shape and temporal stability of the probability distribution for successive samplings of soil N2O flux data collected from the same set of locations across two growing seasons. The second objective was to estimate the range of spatial dependence for each of these data sets and to assess its change over time.


   MATERIALS AND METHODS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
RESULTS
 DISCUSSION
 CONCLUSIONS
 REFERENCES
 
Field Site and Sampling Design
The research site was located in the St. Denis National Wildlife Area (52°12' N, 106°5' W), approximately 40 km east of Saskatoon, Saskatchewan, Canada. The site was on a hummocky, till terrain. Slopes were 10 to 15%, and the parent material was a combination of unsorted calcareous till and glacio-lacustrine sediments. The glacio-lacustrine sediments blanket the till in a thin mantle, leaving the till very close to the surface or exposed on topographically high positions and some convergent areas that lead into lower slope positions. Soil types range from thin Typic Calciborolls on the tops of knolls through the thicker Typic Haploborolls in the mid-slope and toe-slope positions, to Albic Argiborolls and Argic Cryaquolls in depressional positions. Haplic Calciborolls were found in shoulder and back-slope positions and in some foot-slope positions. Overall, soil textures range from a loam at topographically high positions to a silt loam in depressions. The hydrologic pattern on the site is depression focused where the bulk of infiltrating water moves laterally through the depression margins, where it is recycled through evaporative and transpiration processes (Hayashi et al., 1998).

A detailed topographic survey of the site was completed using a Sokkisha Set 5 Electronic Total Station (Sokkisha Co. Ltd., Tokyo, Japan) and a Trimble Pro XRS Global Positioning System (Trimble Navigation, Sunnyvale, CA). In June 2003, a 128-point, linear transect was established at the site on cultivated land that had been fallow since 2002. The previous crop was Hordeum vulgare. Locations were evenly spaced (4.5 m) and represented numerous landform cycles including three vegetated depressions (Fig. 1 ). In May 2004, the east side of the site, including the transect area, was seeded to grass by Ducks Unlimited Canada. The mix consisted of Agropyron elongatum, Agropyron intermedium, Bromus biebersteinii, Elymus dauricus, Festuca rubra, Onobrychis viciifolia, Elymus canadensis, Agropyron trachycaulum, and Medicago sativa.


Figure 1
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  		Fig. 1. Profile of relative elevation (m) along the sample transect at the St. Denis Site. Tree symbol denotes location of vegetated depression.

 
Soil Nitrous Oxide Flux Measurements
At each location along the 128-point transect soil N2O flux was measured using a two-piece, closed, vented chamber (International Atomic Energy Agency, 1992) consisting of a polyvinyl chloride ring base and vented cap with sampling port similar to Hutchinson and Mosier (1981). The chamber, when placed for sample collection, had a head space of 2.25 L and covered a soil surface area of 0.02 m2. Before the start of data collection, the bases were pressed into the soil and secured using 20-cm spikes, where they remained for the duration of the field season. At each sampling event, the chamber was placed onto the base and sealed by a rubber ring within the cap. Samples of the headspace gas were drawn from the chamber with a 20-mL syringe and injected into 12-mL evacuated tubes for transport back to the laboratory. Samples of the headspace gas were drawn at three equally spaced time intervals of 8 min. In 2003, the N2O concentration in ambient air was used as the initial (time zero [t0]) concentration after Anthony et al. (1995). In 2004, individual t0 samples were collected from each chamber. Sampling of the 128 points was executed by four people each sampling a complete time interval and moving from location to location every 45 s. This allowed for a complete transect sampling in less than 2 h. Gas sampling was timed to begin at midday. Samples were returned to the lab, placed in cold storage, and analyzed within 1 to 2 wk.

Nitrous oxide concentrations were determined using a Varian CP3800 GC (Varian Canada Inc., Mississauga, ON) equipped with dual electron capture detectors. Operating conditions for the GC were as follows: injector temperature = 100°C, column temperature = 35°C, detector temperature = 370°C; separations were performed using Poraplot Q columns (12.5 by 0.32mm i.d. fused silica capillary column, DF [film thickness] = 8 µm; includes a 2.5-m particle trap) with ultra-high purity He (14.4 mL min–1) as the carrier gas and P5 (95:5 v/v Ar:CH4 mix) as the make-up gas (12.0 mL min–1). Samples (300 µL) were introduced using a CombiPAL auto-sampler (CTC Analytics AG, Switzerland) with on-column injection and a split ratio of 10:1. The system was calibrated using standard gases (N2O in N2) obtained from PraxAir (Mississauga, ON). Data processing was performed using the Varian Star Chromatography Workstation (ver. 6.2) software. Internal calibration curves were obtained by applying linear least squares regression to the gas concentration (ppbV N2O) versus peak area data; N2O concentrations in the headspace samples were then calculated automatically from the regression equations.

Ambient air samples were included as reference samples in each analytical run to check the within-run precision, calculate the minimum detectable concentration difference (MDCD), and correct for detector drift. The MDCD was calculated by (i) analyzing matched pairs of the reference gas samples at regular intervals during each analytical run, (ii) calculating the average difference between sample pairs (µpair diff) and the standard deviation ({sigma}pair diff) and (iii) calculating the MDCD using Eq. [1].

Formula 1[1]

The MDCD was used to filter the raw data when calculating the actual N2O flux (i.e., concentration differences between t0 and each subsequent time step that were < MDCD were not considered to be significantly different from the t0 concentration). Anthony et al. (1995) arbitrarily chose to use an MDCD that was twice the mean absolute difference between pairs of ambient air samples. The form of MDCD presented in this study has a statistical basis in that it is a value that is within the upper bound of the 95% confidence interval for the mean paired difference. The variability in our data is such that the method used here to calculate the MDCD is slightly more rigorous than that used by Anthony et al. (1995).

Although some studies assume that the change in N2O concentration within the chamber over time is linear (Lemke et al., 1999), it has been demonstrated that the concentration (ng L–1) versus time (min) relationship is not linear due to the decreasing concentration gradient between the chamber air and the soil air (Hutchinson and Mosier, 1981). Measuring N2O concentration at t0 and for each of the three 8-min time intervals produces four points for the concentration versus time curve and allows its description using a polynomial relationship. The vertical flux of N2O at the soil–atmosphere interface (ng N2O-N m–2 s–1) was calculated as the slope of the line tangent to the concentration versus time curve at t0. That is, the flux at t0 was calculated as the first derivative of the second-order polynomial equation (y = ax2 + bx + c) used to describe the concentration versus time relationship. The flux (ng N L–1 min–1) was converted to an area-second basis by multiplying by 1.87 L min m–2 s–1 (i.e., the chamber volume ÷ [surface area x 60 s min–1]). In cases where "rogue" data points prevented the use of the second-order polynomial model (i.e., only three points available instead of four), the flux was calculated as the slope of the linear model that best described the concentration versus time relationship (Hutchinson and Mosier, 1981) (Eq. [2]).

Formula 2[2]
where FN2O is the flux at t0, V = chamber volume (L), A = cross-sectional area of soil covered by the chamber (m2), kt = time constant (60 s min–1), and m = slope of the linear regression equation (ng L–1 min–1).

Measurement of Soil Moisture, Soil Temperature, and Climate Data
At each location, volumetric soil moisture over a 15-cm depth was measured at the time of gas sampling using time domain reflectometry after Topp and Ferre (2002). Readings were obtained manually from a Tektronix 1502 B cable tester (Tektronix, Wilsonville, OR). Also at each location, soil temperature was measured at 5- and 20-cm depths using buried type T thermocouples constructed of twisted copper and constantan (45% Ni and 55% Cu) wire pairs and read using a Barnant DuaLogR thermocouple reader (Barnant Company, Barrington, IL). A meteorologic station on site recorded hourly averages of precipitation, air temperature, and wind speed.

Statistical Analysis
Summary statistics and histograms were generated using MINITAB Release 14 (Minitab Inc. 2003). Probability distributions of soil N2O emission data sets were assessed by making individual, pairwise comparisons of the shape and peak locations of their histograms using the Chi-square test (Eq. [3]). The histogram is a common exploratory tool for data analysis and the Chi-square test is based on, and looks at, the actual shape of the histogram. A common criticism of the use of the Chi-square test is the subjectivity associated with the binning of data (Press et al., 1992). However, by using 15 bins (15–20 is recommended) and keeping the number of bins consistent between histograms (a requirement of the Chi-square test), we minimize the subjectivity. Si (2002) used this technique to compare histograms of soil water flux. Alternative methods for comparison of distributions include the K-S test and its variants. The K-S test has no subjectivity because it is based on the cumulative probability distribution. However, it is generally considered not sensitive, especially when the median values of the distributions being compared are similar (Press et al., 1992). Our data sets have large numbers of zero values, and as a result the majority of median values are at or near zero. Furthermore, the K-S test and its variants are not sensitive because of presence of "notches" in the data (Press et al., 1992). Notches are a lack of data points at certain probabilities. The K-S test and its variants require many data points at all probabilities, a feature absent in some of our data sets. For these reasons we chose the Chi-square test.

Histograms were consistently constructed using 15 bins or frequency classes.

Formula 3[3]
where NB is the number of bins, Ri is the frequency of N2O values that fall within a specific ith bin for data from a specific sampling day, and Si is the frequency of N2O values that fall within a specific ith bin for data from another sampling day. The null hypothesis that there is no significant difference between probability distributions of data sets for any two sampling days was rejected if the Chi statistic was greater than the critical value (23.68) determined using a preselected significance level of 95% and 14 degrees of freedom (N-1). Conversely, if the Chi statistic was less than the critical value, the null hypothesis was not rejected and the two distributions were said to be similar. Chi-square determinations and comparisons between data sets from different sampling days were made using Mathcad 11 (Mathsoft Engineering and Education Inc., 2002).

To present and organize the histograms of the N2O flux data, a visual classification was used that grouped each of the 15 distributions into one of four classes: reverse J-shaped, semi-reverse J-shaped, log normal, and symmetrical. The reverse J-shaped distribution is described in Williams (1984) and represents an extremely skewed data set. The semi-reverse J-shaped class was created for the purpose of describing highly skewed distributions that did not fit the definition of the reverse J-shaped distribution and seemed transitional to the log normal shaped distributions. The symmetrical distribution class recognized that, although exhibiting some skew, there were distributions that were very close in shape to a normal distribution.

Trangmar et al. (1985) provide a comprehensive explanation of spatial dependence and its application to soil properties. Briefly, the range of spatial dependence is the maximum separation distance between two locations over which these locations can be said to be spatially related with regard to the soil property of interest. Locations separated by distances greater than this maximum are spatially independent. The range is derived by determining the change in semivariance of the soil property as distance between measurement locations increase. Spatial independence is achieved when the semivariance no longer increases and is constant (sill). The distance required to reach the sill is the range. Theoretically, when the separation distance is zero, the sill should be zero. This is often not the case, and the level of semivariance when the separation distance is zero is called the nugget variance or nugget. The nugget is a measure of unexplained variability. A high nugget/sill ratio indicates large variation over short distances or little spatial correlation.

The spatial dependence for the N2O flux on each sampling day was determined using the indicator semivariogram and a nested semivariogram model (Goovaerts, 1997). The semivariogram is sensitive to extreme values that are common in N2O flux data. Preliminary data analysis indicated that a robust estimator such as Cressie (1993) was insufficient to overcome the effect of extreme values and that a transformation of the data was required. The indicator transform or semivariogram is the use of the semivariogram on data that has been characterized by cutoff or threshold values. The thresholds can be chosen based on cumulative probability levels. The first, second, and third quartile of the distribution of N2O flux measurements for each sampling date were chosen as threshold values for this analysis. For the data from each sampling date, each of the 128 values was coded as an indicator datum, i(u{alpha};zk), of 1 or 0 depending on whether the flux value (u{alpha}) was less than or equal to or greater than the threshold value (zk), respectively (Goovaerts, 1997). In this way only the position of the data point in relation to the threshold value is considered. By using more than one threshold value, one can look at the spatial pattern of small values separate from large values and vice versa. This allows spatial patterns to emerge that might have been masked by the extreme values. Following Goovaerts (1997) (Eq. [4]), the indicator semivariogram was written as

Formula 4[4]
where zk is the threshold value, h is the distance between sample locations, N is number of sample locations, and i(u{alpha}; zk) and i(u{alpha} + h; zk) are indicator data separated by h. This is the regular semivariogram applied to the indicator data. The semivariogram was calculated over a lag spacing of 4.5 m and a distance of 288 m, which is half the total lag distance.

Visual inspection of the empiric semivariogram (Fig. 2 ) indicated that more than one basic model may be necessary to fit the semivariogram rather than a blind fit with a single spherical model. After Goovaerts (1997), a linear combination of four models was nested and fitted to the semivariograms produced for each threshold value on each sampling date. A nugget model and three spherical models, each representing a different range of spatial dependency, were used. These ranges of spatial dependency were 15, 50, and 125 m. The nested model was designed to fit these three ranges and the nugget model to each semivariogram and to indicate which spatial scale was dominant on each date and at what threshold value. The nested model (Eq. [5]) was written as

Formula 5[5]
where a, b, c, and d are parameters representing the relative contribution of each model to the total semivariance or sill. The nugget model was represented by g(h) = 0 if h = 0, otherwise 1 and the spherical model for each range of spatial dependence (Eq. [6]) was

Formula 6[6]
with {tau} as the range of spatial dependence. The estimates of parameters a, b, c, and d were used in an iterative function, which minimized the sums of squared error and gave the best fit to the curve and best estimates of the parameters (Eq. [7]) (Cressie, 1985).

Formula 7[7]
where m is the number of lags, gSP(hi,a,b,c,d) is the model semivariogram, and {gamma}I(h;zk) is the sample semivariogram. The model fit was weighted toward the initial values in the curve by dividing N(h) by the model semivariogram.


Figure 2
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  		Fig. 2. Semivariogram for three sampling dates at St. Denis site. High nugget effect and range of spatial dependency of approximately 125 m for 7 Aug. 2003. Range of approximately 50 m for 30 Mar. 2004. Range of approximately 15 and 125 m for 7 Oct. 2004.

 

   RESULTS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
DISCUSSION
 CONCLUSIONS
 REFERENCES
 
Precipitation and Air Temperature
Daily precipitation for the 2003 and 2004 field seasons is shown in Fig. 3 . The collection of rainfall and air temperature data for the St. Denis site began on 18 June 2003. During the period of sample collection in 2003 (19 June to 15 October), cumulative precipitation totaled 164 mm. The mean daily air temperature for this period was 15°C, with a mean daily peak of 26°C (16 August) and a mean daily low of –2°C (15 October) (data not shown). In 2004, the cumulative rainfall during the period of sample collection (30 March to 7 October) was 270 mm. The mean air temperature for this period was 13°C, with a mean daily peak of 22°C (18 July) and a mean daily low of 0°C (1 October) (data not shown).


Figure 3
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  		Fig. 3. Daily precipitation (mm) at the St. Denis site for the 2003 and 2004 field seasons. Nitrous oxide flux measurements occurred on italicized sampling dates.

 
Rainfall recorded at the Saskatoon Airport for the period from 30 Mar. 2003 to 18 June 2003 was 61 mm (Environment Canada, 2005a). Thus, the total rainfall recorded in 2003 for a period equivalent to the 2004 field season was 225 mm. In 2003, 61% of precipitation fell between 20 June and 13 July and 28 August and 9 September (Fig. 3), whereas the majority of precipitation in 2004 was more evenly distributed over a much longer period, between approximately 12 May and 24 August (Fig. 3). Rainfall from April 2003 to September 2003, inclusive, was below the 30-yr average of 250 mm for the Saskatoon Airport (Environment Canada, 2005b), whereas rainfall in 2004 was above average. Mean air temperature reported for this same 30-yr period was 13°C.

Soil Moisture and Soil Temperature
The soil moisture data for each sampling day is presented as mean WFPS (%) ranked according to mean N2O flux (Fig. 4 ). The mean WFPS in 2003 was at or near 60% on seven dates including the four dates on which the mean flux was highest and the date on which the lowest mean flux was recorded. There is no value for 30 March because the soil was frozen at the time of sampling and the time domain reflectometry could not be used. Mean soil temperature for sampling dates in March, April, and October was < 10°C and on most dates was < 5°C (Fig. 4). Mean soil temperature on all other sampling dates was consistently > 10°C.


Figure 4
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  		Fig. 4. Mean WFPS (0–15 cm) and soil temperature (0–20 cm) at the St. Denis site for 2003 and 2004. Error bars indicate 95% confidence interval. Water-filled pore space absent for 30 March due to frozen soil. Data are presented in order of decreasing mean N2O flux.

 
Nitrous Oxide Flux
The N2O flux data had a range of mean values and standard deviations with the largest fluxes also having the largest ranges and standard deviations. On three dates, the mean flux was < 15 ng N2O–N m–2 s–1. Fluxes on the remaining dates were < 9.0 ng N2O–N m–2 s–1, with fluxes < 1.0 ng N2O–N m–2 s–1 on four sampling dates (Table 1). The lowest mean flux dates were also associated with the lowest range in values and standard deviation. On only one date (23 June 2004) was the mean flux negative.


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  		Table 1. Mean N2O flux, standard deviation, range (ng N2O-N m–2 s–1), skewness, kurtosis, zero bin frequency, and distribution shape for the 15 sampling dates at the St. Denis transect during 2003 and 2004. Data are in order of decreasing mean N2O flux (n = 128).

 
Probability Distributions and Chi Square Comparison
Probability distributions for the N2O data from the 15 sampling days in 2003 and 2004 (Fig. 5 ) all exhibited some degree of skewness and kurtosis (Table 1) and ranged in shape from symmetrical through log normal to reverse J-shaped (Williams, 1984). The majority of dates had skewness values < 5, although the four dates with the largest mean fluxes exhibited skewness values > 5 and the highest values of kurtosis. High frequency in the bin centered on zero (Table 1) is associated with reverse J-shaped and symmetrical distributions. On 19 June 2003 (Fig. 5) and 10 Sep. 2003, there were what seemed to be reverse J-shaped distributions except for a single, very low-frequency bin to the left of the peak; the distributions for these two dates have been called semi-reverse J-shaped.


Figure 5
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  		Fig. 5. Histograms of N2O data from the St. Denis transect. Each histogram has 15 bins. Data are in order of decreasing mean N2O flux.

 
Results of the Chi-square testing demonstrate that the majority of distributions were significantly different from each other (Fig. 6 ). That is, of 105 possible comparisons, only eight pairs of distributions did not show a significant difference. In 2003 and 2004, consecutive sampling dates were similar in distribution shape, specifically the two dates in July of 2003 and the two dates in April of 2004.


Figure 6
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  		Fig. 6. Results of a Chi square test of similarity between probability distributions for N2O flux measurements at the St. Denis transect for the 15 sampling dates in 2003 and 2004. Black cells indicate distributions that were not significantly different from each other at a 0.05 probability level. Data are in order of decreasing mean N2O flux.

 
Spatial Dependence of Nitrous Oxide Flux
Table 2 shows the results of the nested model fit to the indicator semivariogram for the 25, 50, and 75% quartiles of the cumulative probability distribution for the N2O flux data. The data are presented in ranked order according to mean N2O flux. For each sampling date and each quartile, the contribution of semivariance to the total semivariance or sill is shown for the nugget model and the 15-, 50-, and 125-m range of spatial dependence. On four dates in 2003, the number of zero values in the data set was such that the threshold level was zero at the first and second quartiles; hence, the results of the model fit are given only for the second quartile. On 19 June 2003 and three dates in 2004, the threshold values were zero for all three quartiles, indicating that at least 75% of the values on those days were zero. A complete cross-date comparison of parameters of spatial dependence is only possible for the third quartile. However, it is clear that as mean flux decreases the number of zero values in the data increases.


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  		Table 2. Semivariance expressed as a fraction of total semivariance for a nugget model and spherical models for three ranges of spatial dependence (15, 50, and 125 m) nested in indicator semivariogram for the N2O data from 15 sampling times at the St. Denis transect in 2003 and 2004. Threshold values for indicator semivariogram represent the 25, 50, or 75% quartiles of the distribution of N2O flux measurements. Data are in order of decreasing mean N2O flux.

 
In the third quartile, the nugget semivariance as a fraction of the total variance was > 0.7 on seven dates and between 0.3 and 0.7 (inclusive) on the eight remaining sampling dates. The 15-m range of spatial dependence contributes to the total semivariance on nine dates, whereas the 50-m range of spatial dependence contributes to the total semivariance on three dates. The 125-m range of spatial dependence contributes on 10 dates; however, on 29 April 2004 there was a strong trend in the data (not shown), and the estimate of the contribution of that range to the total semivariance is not reliable. This was the only date for which the indicator semivariogram could not overcome a trend in the data. Contribution to total semivariance by the 125-m range on the other nine dates is smaller than that contributed by the 15-m range.


   DISCUSSION
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
CONCLUSIONS
 REFERENCES
 
Soil N2O flux measurements from hummocky, agricultural landscapes in the Canadian Prairie region are not common. However, Corre et al. (1996) reported a median value of 1050 µg N2O–N m–2 d–1 (12.2 ng N2O–N m–2 s–1) for spring N2O flux measurements from unfertilized, fallow, agricultural land in the Black soil zone of Saskatchewan. Lemke et al. (1998) recorded mean N2O flux values as high as 350 µg N2O–N m–2 h–1 (97.2 ng N2O–N m–2 s–1) from the Parkland region of Alberta. Hence, the highest mean value of N2O flux obtained from the St. Denis site (25.3 ng N2O–N m–2 s–1) is within the range of previously published data.

Skewed probability distributions for N2O flux data are common (Parkin, 1987; Ambus and Christensen, 1994; Corre et al., 1996). Parkin (1987) described a probability distribution for a denitrification rate measured from intact soil cores as approximately log normal. However, this distribution may be more appropriately described as a reverse J-shaped (i.e., strongly skewed with the peak at the left end at or near zero) (Williams, 1984). Many of the probability distributions for the data from the St. Denis National Wildlife Area are reverse J-shaped or semireverse J-shaped. In general, however, the probability distributions for the St. Denis data represent a range of distribution shapes (Fig. 5). The symmetrical distributions represent shapes transitional between normal and log normal distributions. The semireverse J-shape represents a transition between log normal and the reverse J-shape distributions.

The data presented in Table 1 show a clear relationship between the magnitude of the mean N2O flux and the distribution shape. The reverse J-shape distributions are generally associated with a range in values that is an order of magnitude greater than that associated with the other distributions—the only exception occurring on 25 June 2003. As the mean flux declines, the distribution decreases in skewness and evolves into shapes that are log normal and, finally, symmetrical. This relationship is also evident in the results of the Chi-square tests (Fig. 6), where the dates with the highest mean fluxes and reverse J-shape distributions are statistically similar to each other.

The relationship between mean N2O flux and the distribution shape can be explained by grouping the 15 sets of flux measurements into event-based and background emission patterns as proposed by Brumme et al. (1999) or as transitional between the two patterns. Brumme et al. (1999) proposed that N2O emissions rise and fall seasonally over and above a low level (background) emission pattern that is occasionally interrupted by extreme peak emissions due to a climatic event (event-based). Such events may be rewetting of the soil following a dry period or frost/thaw events, which could be considered analogous to high precipitation events and spring snow melt that occur at the St. Denis site.

The July 2003 and April 2004 flux measurements represent event-based emission patterns. The triggering event in each case is an increase in WFPS (Fig. 4) to a value approaching or exceeding the 60% threshold needed to restrict oxygen diffusion to microsites of activity and trigger denitrification. In April 2004, the event is spring snow melt, and in July 2003 the event is an intense precipitation event that occurred just before the 7 July sampling date (Fig. 3). Although soil temperature was low in April 2004, it did not prevent peak emissions from occurring. It can be assumed that available N was not limiting in April 2004 because it has been found that in the spring, labile N from the previous growing seasons is available for mineralization (Boone, 1994). This would be in addition to N made available due to the flush of mineralization on rewetting of the soil (Cabrera, 1993) during snow melt and freeze/thaw effects (van Bochove et al., 2000). The July precipitation event followed a long dry period (Fig. 3), and a flush of mineralization on rewetting of the soil may have provided the N necessary for the N2O emission event.

The event-based emission patterns in July 2003 and April 2004 have similar reverse J-shape distributions and high mean N2O fluxes that reflect the inclusion of a small number of extreme flux values. As the effects of the event diminish (i.e., as WFPS and probably available N decline), the frequency of extreme flux values decreases. This is first observed in the measurements made immediately after the peak emissions (16 July 2003 and 29 Apr. 2004). On these 2 d, the frequency of values in the zero bin increased (Table 1) at the expense of high and extreme values (Fig. 5) even though the mean N2O flux was still relatively high (Table 1). This occurs because of a decline in denitrification as hot spots of activity shut down. As this trend continues, the flux distribution transitions toward a background emission pattern, represented by small mean N2O flux, which is probably a reflection of continued nitrification. In 2003, this background pattern had become established by 7 August but was interrupted by a precipitation event on 9 September (Fig. 3) that saw an increase in mean N2O flux and a movement of the distribution pattern back to the reverse J-shape on 10 September (Table 1). After the September event, the pattern again became symmetrical during the early fall (i.e., by 15 October).

In 2004, the transition from a spring event-based emission pattern to the background emission pattern (i.e., the transition from a reverse J-shape distribution to a symmetrical distribution) included a period when the distributions were log normal. This may reflect the more even distribution of precipitation that occurred during 2004 (Fig. 3), which, in turn, may have slowed the transition. During 2004, precipitation events did not have the dramatic effect they had in 2003 perhaps because the soil did not go through extended dry periods as it did during 2003 (Fig. 3) and because establishment of the grass cover may have reduced the amount of N available for denitrification. The precipitation event before 23 June failed to produce any large emission of N2O (Table 1).

The transition toward the background emission pattern and the background emission pattern itself were related to specific distribution shapes, but there was little statistical similarity in these shapes (Fig. 6). Exceptions to this occurred on 19 June 2003 and 10 Sep. 2003 and again on 30 Mar. 2004 and 3 June 2004 (Fig. 4 and 5). In both sets of comparisons, the probability distributions were similar despite differing soil conditions (Fig. 6). However, the mean N2O flux was similar on 30 Mar. 2004 and 3 June 2004, suggesting that different limiting factors may result in the same pattern of emission. The low soil temperature on 30 March (Fig. 4) may have restricted microbial activity, thus reducing oxygen demand and preventing anaerobic microsites from fully developing even during a period when the soil was wet and N availability should be nonlimiting. On 3 June, the WFPS was > 60%, but by this time much of the labile N from spring thaw may have been used up during the burst of activity that occurred in April. It seems that multiple controls on N2O production during the year can result in combinations of flux values that produce a distinctive distribution shape. Thus, enhanced knowledge of how process-level factors change across a season are needed to predict distribution shapes and the magnitude of mean N2O fluxes.

Cambardella et al. (1994) suggested that strong spatial dependency existed if the nugget semivariance of a variable expressed as a fraction of the total semivariance was < 25%, moderately spatially dependent if it was 25 to 75%, and weakly spatially dependent if the ratio was > 75%. The spatial dependency for the soil N2O emissions could be clearly described as moderate to weak based on the nugget variance in Table 2. However, there is a trend for the nugget model fraction of the total semivariance to increase with decreasing mean N2O flux. Overall, the ratio is lowest on the first five dates shown, which are associated with the event-based emission pattern. The highest overall ratios are associated with the last five dates when fluxes were lowest and activity exhibited the background emission pattern. Lowering of the mean N2O flux probably magnifies measurement error, reducing our ability to estimate the spatial dependency.

Although it is difficult to make an across-date comparison for each quartile of the indicator semivariogram, we can observe that the range of spatial dependency, as determined using the nested model approach, is not stable over time. As a fraction of the total semivariance, each chosen range varies in its importance to the spatial dependency from date to date. For the third quartile, where a complete across date comparison can be made, the 15-m range seems to account for the most semivariance. This is likely a reflection of the range of the slope class or subunits of the catenas along the transect. Overall, the catena sequences (upper to lower slope) (Fig. 1) were represented by the 50-m range and did not have much influence on the spatial dependency of N2O emission. The 125-m range contributed to the total semivariance on several days and probably reflects the broad geomorphologic structure of the site, which seems to host a broad ring of vegetated depressions in the center of the site that is crossed by the transect.

Corre et al. (1996) observed a topographic control to the distribution of hot spots, finding that hot spots of denitrification were concentrated in positions of low relief. The extreme values in the St. Denis data tended to be associated with footslope and certain depressional positions in the cultivated area of the transect (data not shown). In contrast, vegetated depressions produced low, undetectable, or negative fluxes and, as a consequence, had little impact on the distribution of the data. This suggests that extreme values are an important characteristic of this landscape (i.e., combined agricultural and nonagricultural land use in a hummocky terrain) that cannot be rejected but may be location specific. The indicator semivariogram and the nested model approach provided insight into the spatial scales of the N2O emissions at the site. There was only one date (29 April 2004) when the indicator semivariogram was unable to remove the strong trend in the data. As well, an across date comparison was not possible with the indicator semivariogram due to the large number of zero flux values in several of the data sets. It might be useful to apply methods of analysis that do not require the assumption of stationarity and can provide local (point-by-point) information on scale and variance, as opposed to globally, over the entire transect. In this way, we can examine extreme values and their temporal variation directly so we may better understand the implications for modeling and prediction of soil N2O emissions. Models must be validated through their ability to reproduce the range of distributions associated with the pattern of emissions that occur in these landscapes.


   CONCLUSIONS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 CONCLUSIONS
REFERENCES
 
The objectives of this study were to describe the shape and temporal stability of the probability distribution for soil N2O emission data and to estimate and assess the temporal stability of the spatial dependence of these data. The shape of the probability distributions for soil N2O emission data at the St. Denis site had poor temporal stability. The shape of the distribution ranged from symmetrical through log normal to a reverse J-shape. The reverse J-shaped probability distribution was associated with the highest mean N2O flux and short-term temporal stability in distribution shape at times when controlling factors to N2O production were nonlimiting.

The pattern of emission can be grouped into event-based, transitional, and background emission patterns. The event-based pattern is a result of a triggering event, such as high water-filled pore space that coincides with nonlimiting conditions of soil temperature and available N. As soil moisture declines or available N is used up, these microsites shut down, mean flux decreases, and the probability distributions change toward symmetrical as the emission pattern changes to a background level.

Spatial dependency was characterized by high nugget/sill ratio on most sampling days. The nugget/sill ratio decreased on days when soil conditions were most conducive to denitrification and hot spot activity was highest. The indicator semivariogram was able to overcome the influence of extreme values on most days; however, a strong trend was present on at least 1 d and proper spatial analysis for data of that nature will require alternative methods not sensitive to stationarity. Due to the high number of zero fluxes in several data sets, an across-date comparison over all threshold values was not possible. Extreme values are important to these data sets, and an understanding of their influence on variability and scale is necessary for improvement and validation of models designed to predict N2O emission in these landscapes.


   ACKNOWLEDGMENTS
 
Financial support of study was provided by the Biological Greenhouse Gas Sources and Sinks program administered by Agriculture and Agri-Food Canada and Ducks Unlimited Canada. Additional support in the form of in kind contributions and site access was provided by the Canadian Wildlife Service. We would like to individually recognize Glenn Padbury of AAFC and the technical assistance of Jeff Braidek and Angela Taylor. The cooperation of the producer Mike Starosta was also much appreciated.

Received for publication July 5, 2005.


   REFERENCES
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 CONCLUSIONS
 REFERENCES
 




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