SCOPE 35 - Scales and Global Change

ABSTRACT

A key problem in the measurement of N gas fluxes from terrestrial ecosystems is their typically high degree of spatial and temporal heterogeneity. Gas fluxes vary at both fine and coarse scales of resolution. In this paper we review several studies of spatial variability in N gas fluxes. In the first example, fine-scale variation in N₂O production was examined using geostatistical techniques. A significant amount of the variation in N₂O production could be explained by spatial autocorrelation and by correlation with soil water. In the second example, seasonal and edaphic variations in N₂O production from the shortgrass steppe were measured. The results were incorporated into a simulation model which related N₂O production from nitrification and denitrification to soil moisture, temperature, and NH₄⁺and NO₃^- production. A simplified version of this model was developed to calculate annual N₂O production from a heterogeneous landscape. Spatial variations in NH₃⁰ production from cattle urine were determined at the same site. NH₃⁰ production is controlled by the joint spatial distributions of cattle urine deposition and of soil properties which control NH₃⁰ evolution rate. The effect of N transport by cattle is to reduce mean NH₃⁰ volatilization rates below maximal rates. A common technique to all of these studies was to relate hard-to-measure gas flux rates to more readily measured soil and landscape properties.

INTRODUCTION 

Nitrogen gases play significant roles in atmospheric biogeochemistry at local and global scales (Crutzen, 1983). Nitrogen gases influence the climate as greenhouse gases, participate in the formation and destruction of O₃, influence atmospheric acidity, and are significant vectors for loss and gain of nitrogen from terrestrial ecosystems (Lacis et al., 1981; Crutzen, 1983; Bolin et al., 1983). Biogenic sources of N gases are currently significant, and may become more so with changes in climate and land use. Despite the importance of N gases in the atmosphere, fluxes in and out of terrestrial ecosystems are not well known. Data are particularly scanty for N species and from ecosystems whose emissions are not significant to N budgets. Such data may be important in defining global balances.

Although there are many problems with measurement of N gas fluxes, a key difficulty is the high degree of spatial and temporal variability characteristic of N gas fluxes. High variability is found at small scales, within experimental units and between sites which vary in vegetation, soil properties, or water balance. Folorunso and Rolston (1984) reported extreme small scale variability, with coefficients of variation for N₂O flux from 3 x 36 m plots of 161 to 508%. Mosier et al. (submitted) reported coarser-scale differences in N₂O flux from 80 to 160 g N ha^-1y^-l between a slope and an adjacent swale. Similar variations in NH₃⁰ flux from the same pair of sites were reported Schimel et al. (1986). Accurate calculation of flux rates requires techniques for reducing random variation within experimental units, and knowledge of the factors that result in systematic variation between ecosystems. Considerable progress must be made in the measurement and modelling of fluxes in order to calculate fluxes over large areas and to predict how those will change with climate and land-use changes.

In this chapter we present three examples where gas flux rates were calculated for areas of considerable heterogeneity. The first example is of a study of within-site heterogeneity and demonstrates a class of techniques for minimizing experimental error in spatially variable data. The second example is of a study of systematic variation in gas flux rates within a landscape. The third study considers the impact of spatial variability mediated by transport processes. In these examples, gas flux rates, which are hard to measure, are related to other, more readily measured variables using statistical or modelling techniques. Our intent in this paper is not to present definitive numbers for specific ecosystems but, rather, to demonstrate that spatial heterogeneity is tractable and that its inclusion into experimental designs can improve both the accuracy of flux estimates and contribute to knowledge of rate controls.

GEOSTATISTICAL ANALYSIS OF WITHIN-PLOT VARIATION

Two approaches to the explanation of some of the small-scale variability associated with denitrification measurements are examined in this section.

First, the possibility is examined that a portion of the variability of denitrification rates may be spatially autocorrelated. Autocorrelation would permit improved estimation of the rates through the use of techniques from regionalized variable theory, such as kriging and cokriging (Journel and Huijbregts, 1978). Second, the dependence of denitrification rates in the field on soil water contents is examined. Estimates of denitrification rates over large areas would be greatly improved if a strong relationship were found with a variable such as soil moisture whose spatial distribution can be easily measured in the field, sensed remotely, or modelled more readily than denitrification.

The example used in this paper consists of denitrification rates measured in 31 groups of four soil cores taken at 2 m intervals along a 60 m transect at an agricultural field site in central Sweden. The cores in each group of four were taken at 8 cm intervals. Details of sampling and denitrification measurement are presented in Svensson et al. (1985). The measured denitrification rates varied widely about the mean rate (6.4 ng h^-1 g^-l  D. W.of soil) with a coefficient of variation of 146%.

A sample semivariogram (Webster , 1985) was calculated to obtain a quantitative expression of the relationship between the expected variance of two measurements and the distance separating the locations where the measurements were made (Figure 10.1). The lowest semivariance was found for measurements made at the closest spacing (2 m) between sampling points (Figure 10.1). The expected variance for two samples appeared to vary

Figure 10.1 Semivariogram for logarithmically transformed denitrification rates. The theoretical model shown by the smooth curve was fit by nonlinear regression. The vertical axis is unitless

periodically with distance (Figure 10.1); measurements taken 12 m and 24 m apart tended to be more similar to one another than measurements made at 6 m and 18 m spacings. The smooth curve shown corresponds to the following function:

                   S= a₁{1- 0.5[1 + cos(a₂h)]exp(- a₃h)}+ a₄ ,                                                   (1)

where S is semivariance, h is lag, and a_l, ..., a₄ are empirical constants determined by nonlinear regression.

Given a semivariogram, estimates for the variable at unsampled locations can be obtained through kriging (Journel and Huijbregts, 1978). Kriging was used to provide estimated rates at sampled locations for comparison to the measured rates. The measured rate at the location to be estimated was temporarily deleted from the data set. Then the estimated rate was obtained as a weighted average of the rates at the 14 locations nearest to the location where the rate was to be estimated, with weights based upon the semivariogram model. If the measured rate at the location where the rate is to be estimated is not deleted from the data set, then kriging will predict a rate equal to the measured rate (Journel and Huijbregts, 1978). The process of temporary deletion of a measurement at a location in order to obtain by kriging a meaningful prediction of the rate at that location is often referred to as jackknifing (Vieira et al., 1983). The jackknifed rates of denitrification for each of the 31 groups of soil cores are shown in Figure 10.2 plotted against the rates measured at the same locations. The slope of the line of best fit (0.58) through the points in Figure 10.2 differs significantly from 0 at the p < 0.01 level. Kriging appears to provide meaningful estimates for the rates of denitrification along the transect, and the autocorrelation of denitrification rate suggested by Figure 10.1 is probably not illusory.

Figure 10.2  Denitrification rates predicted using kriging plotted against the actually measured rates

Although meaningful estimates of denitrification rates can be obtained with kriging, ideally one would wish the line of best fit (Figure 10.2) to have a slope of one with the points clustered tightly about it, which is not the case with the jackknifed estimates shown. Observed correlations suggested that cokriging using water content variables might be employed to improve the kriged estimates. Variables useful for cokriging must exhibit spatial autocorrelation before they can be used to improve the estimates for another variable with which they are correlated. Both NO₃^-concentration and CO₂-evolution rates had semivariograms so flat as to suggest very little spatial autocorrelation for these variables, Water fraction (g H₂O/g sample) did exhibit strong spatial autocorrelation. Using this model of the semivariogram (Figure 10.3), jackknifed water fractions agreed with measured water fractions more closely than did jackknifed and measured denitrification rates. The slope (0.71) of the regression line of best fit for jackknifed vs. measured water fractions differed significantly from 0 at the p < 0.0001 level.

Cokriging is rarely worth the extra analytical effort unless the variable of interest has been undersampled in comparison with correlated variables

Figure 10.3 Semivariogram for water fraction. The spherical model shown by the smooth curve was fit by nonlinear regression after deletion of the points at lags of 14, 16, and 18 m, as explained in the text

(Journel and Huijbregts, 1978). Because soil water contents can be measured easily and inexpensively, we determined whether cokriging would outperform kriging in predicting denitrification rates when many more measurements of water fraction are available than of denitrification. If the use of soil water contents for cokriging substantially improves the quality of the estimates, then it may be possible to develop an optimal combination of water content and denitrification measurements that maximizes the accuracy of the predictions that may be obtained for a given investment of resources. Kriging and cokriging were used to generate predicted values for the sampling locations; cokriging outperformed kriging on these data sets with undersampled denitrification rates.

The cokriging procedure using jackknifing required temporary deletion .of both the denitrification rate and the water fraction measured at the location where a denitrification rate was to be estimated. Thus, the water fraction actually measured at the location of interest was ignored in predicting the denitrification rate. This suggested the possibility of using the water fraction at the location where denitrification was to be estimated to obtain a prediction independent of the kriged estimate. Rates of denitrification are shown plotted against water fractions in Figure 10.4. Five of the locations along the transect were much drier than the others (Figure 10.4). At the 26 locations with water fractions greater than 0.2, the correlation between denitrification rate and water fraction appeared reasonably good. However, the data from the five drier locations did not cluster about the same regression line with the rest of the data. The response of denitrification rate to increasing water fraction was modelled as shown by the two intersecting lines in Figure 10.4. The shape of the model shown in Figure 10.5 is in agreement with the results of Nömmik (1956), who found that significant denitrification did not occur until a certain moisture level was reached in the soil.

Figure 10.4 Plot of denitrification rate against water fraction. The bilinear model shown was fit by nonlinear regression

The cokriged and nonlinear regression estimates were combined using the following formula:

where Z is a predicted denitrification rate, S is the variance of a prediction, and subscripts r and c indicate regression and cokriging, respectively. This formula was derived from one in Granger and Newbold (1977) under the assumption that cokriging and the regression model give independent predictions. Cokriging provides an expected variance for each estimate, and this was used for S_c. The mean sum of squares left unexplained by the regression model was used for S_r. The predicted denitrification rates obtained from the combined estimator were the best of all the estimates produced during this study and left an unexplained sum of squares of only 41 out of 121. For comparison, the unexpected sum of squares left by cokriging and the regression model were 75 and 59, respectively. By using an optimal combination of the rates of denitrification predicted by cokriging and from a bilinear regression model of the effects of soil water contents on denitrification rates, it was possible to explain nearly two-thirds of the variation in the rates of denitrification along the transect.

Spatial variation in denitrification rates did not appear to be entirely random but appeared to contain a component that could be reduced by such techniques as kriging. In addition, much of the variability of denitrification was found to be associated with the variability of soil moisture, a quantity much more easily measured or remotely sensed than denitrification rates. The great disadvantage of both kriging and cokriging is that these techniques require at least one actual measurement of the variable to be estimated within the region for which the variable is to be estimated (Journel and Huijbregts, 1978). Although the data requirements of kriging and cokriging render these techniques unsuitable for use in estimating the rates of denitrification over truly large areas, such as continents, they are likely to prove ideally suited for estimating rates over areas of about 1 ha.

RATES AND PATHWAYS OF N₂O PRODUCTION

In the second example we consider a study of spatial and temporal variability in the rates and pathways of N₂O production. In this study, field and laboratory flux measurements were used to develop a simple model of N₂O production from grassland soils (Mosier and Parton, 1985; Mosier et al., submitted). The objective of this study was to develop a model that could be used to estimate fluxes over large areas, accounting for spatial and interannual variability, without requiring intensive data from each site modelled. The model partitions N₂O production into components resulting from nitrification and denitrification. Parameters allowing this partitioning were developed from experiments in which N₂O flux was measured with and without C₂H₂, and by relating N₂O flux to moisture and NO₃^- production.

Our current model is shown in Equation (3). Production of N₂O from nitrification and denitrification are represented separately as functions of temperature (M_t ), soil water (M_d, M_n ),NO₃, and NH₄. M_d and M_n are the effects of relative water content (actual available water/maximum available water) on denitrification and nitrification, respectively (Figure 10.5). S is an integrated parameter that allows the model to be fit for sites with varying textures and N availabilities.
                                                     

Parameters were estimated for two sites that represented much of the range of variability in soils and vegetation encountered in the shortgrass ecosystem (Schimel et al., 1985).

The full model was not readily applicable to the target scale of study. A simplified version of the model was developed that did not include separate terms for NO₃^- and NH₄⁺ , because these variables require intensive time series data that are not usually available over large areas and are difficult to model with sufficient accuracy for use in the N₂O model. The simplified model uses an empirical multiplier related to the nitrogen availability of a given site and is otherwise the same. While the simplified model does not fit the data as well as the full model, it is much more suitable for coarse-scale applications.

The N₂O model was linked to soil temperature and water flow models driven by time series weather data from 1950 to 1984 to simulate interannual variability. Two sites were simulated, a mid slope and a swale. Difference in mean plant production and soil texture were used to simulate the differences between the sites studied. Daily soil water and temperature were used as input into the simplified model to simulate interannual and intersite variations in N₂O production rates. Good agreement was obtained between observed and simulated results for those years when N₂O flux observations were made (Figure 10.6a, b).

Figure 10.5 The effect of soil NH₄⁺ level on nitrification (a), the effect of relative water content on nitrification (M_n) and denitrification (M_d) (b), and the impact of soil temperature on nitrification and denitrification (c)

Figure 10.6 (a) Simulated and observed N₂O production for an unfertilized swale soil; (b) predicted and observed N₂O production for an unfertilized midslope soil

Table 10.1 Simulated annual N₂O loss (g N ha^-1 y^-l ) for two soil types with and without N fertilizer (from Mosier et al., submitted)

Results showed that mean simulated annual N₂O loss ranged from 82 g N ha^-l y ^-l  for the midslope to 161 g N ha ^-l y ^-l  for the swale (Table 10.1). The variation between years is relatively small, with N₂O flux ranging from a minimum of 73 g N ha ^-l y ^-l to a maximum of 100 g N ha^-l y ^-l for the midslope site (Table 10.1). As expected, N₂O production was highest during the wet years and lowest during dry years. Flux rates were highest in 1979, when the precipitation was 40 cm, and lowest in 1964, when precipitation was 10 cm. A reference point for the importance of N₂O flux rates to a site's N budget is the amount of N deposited in rainfall. Wetfall atmospheric N deposition has been observed at the shortgrass steppe site for the last six years by the National Atmospheric Deposition Program, with the total N deposited ranging from 2.0 k g N ha^-l y ^-l  to 3.3 kg N ha^-l y ^-l  with 60% of the N as NH₄⁺ .The simulated N₂O loss from the two sites ranged from 5.1 to 8.7% for the swale and from 2.4 to 4.8% of atmospheric-N inputs for the midslope. Measured losses of N from the system account for less than 20% of the annual inputs, and suggests that N may be accumulating in the system.

The fractions of N₂O produced by nitrification (N_F) were calculated with the full model for N-amended treatments at both swale and midslope sites. The average fraction of the total N₂O loss produced by nitrification was 85% for the swale site and the percentage ranged from 93% in a very wet year (59 cm annual rainfall) to 70% during a very dry year (10 to 11 cm annual rainfall). Higher nitrification N₂O losses during wet years result from the greater number of large rainfall events during wet years. This results in an increase in the length of time when soil water contents are at intermediate levels, while the number of days when the soil water content is near field capacity (conditions needed for denitrification) are only slightly increased. The increase in the time period with intermediate water content greatly enhances nitrification because nitrification rates stay high until the relative water content drops below 0.4 (see Figure 10.5b), while denitrification rates drop very rapidly as water content drops below field capacity (see Figure 10.5b). The higher fraction of N₂O produced by denitrification during the dry year is caused by a drop in the number of days with intermediate soil water content, rather than in the number of rainfall events, each of which is followed by more or less the same period of time at field capacity. Thus, N₂O production by denitrification is less temporally variable than is N₂O production by nitrification.

Differences in N₂O production seasonally and between sites were closely coupled to mineral-N dynamics. Soil NO₃^-concentration, nitrification, and mineralization rates all peaked in June, along with the N₂O production rate (Figure 10.6) (Schimel, 1982; Schimel et al., 1985; Schimel and Parton, 1986). These data suggest that nitrification is the dominant vector for N₂O production in the shortgrass steppe, further suggesting that patterns of temperature and water availability have their effect on N₂O production by controlling N mineralization and nitrification. The formation of anaerobic microsites during wet periods is of secondary importance in the soils studied. While the difference in texture suggested that the difference in N₂O production between midslope and swale was due to porosity-related differences in water relations, the above argument suggests that differences in inorganic N turnover rate may be more significant. The swale has a significantly higher in situ N mineralization rate than did the midslope (55 vs 41 kg N ha^-1 y^-l ; Schimel et al., 1985), which may contribute to the higher N₂O fluxes observed.

The sites chosen in this study were chosen to represent the range of variability in soil and vegetation properties found in the shortgrass steppe. Previous quantitative studies showed only two quantitatively separable major landscape units, "uplands and swales," based on either soil or vegetation analysis (Anderson, 1983; Yonker et al., submitted). The processes leading to the strong differentiation between these landscape units are discussed in Schimel et al. (1985). Techniques such as those proposed in the first part of this paper, applied to each landscape unit, would further improve the precision of such an estimate.

AMMONIA PRODUCTION FROM CATTLE URINE

Production of NH₃⁰ from wild and domestic animal urine is significant to the global NH₃⁰ budget (Crutzen, 1983). In this example, we describe a study of NH₃⁰ release from cattle urine that considered the correlated spatial distributions of cattle-urine deposition and soil properties that control NH₃⁰ volatilization.

Flux of NH₃⁰ from simulated urine patches on several soils (adjacent to those used in N₂O studies described above) was monitored by direct collection of NH₃⁰ and by mass balance using ¹⁵N (Schimel et al., 1986). Urine was applied at several times of the year to characterize the effects of temperature and moisture on NH₃⁰ flux. Total urine deposition was determined by monthly urine collection from catheterized, free-ranging cattle. Behavioural observations of uncatheterized free-ranging cattle were used to calculate spatial partitioning of urine, assuming that each urination represented an equal

Table 10.2 Spatial and seasonal variations in the deposition and subsequent volatilization of urine N (adapted from Schimel et al., 1986)

portion of the total urine produced during a collection interval (Senft, 1983). These field studies were supplemented with extensive laboratory studies on moisture and water loss rate effects. Flux rates varied with soil type and time of year and the proportions of deposition lost as NH₃⁰ shown in Table 10.2 were used in all subsequent calculations. NH₃⁰ emission rates were low in swale soils, which had high rates of immobilization, low pHs and greater plant uptake. Emission rates were higher in upslope soils, which had the opposite properties. Interestingly, NH₃⁰ emissions were high whereN₂O emissions were low and vice versa.

Cattle deposition of urine was not uniform with respect to the soil properties identified as important in flux studies. Results from studies on cattle grazing and urine deposition behaviour, stratified by season and landscape position, showed deposition to occur disproportionately in areas of low potential loss (Table 10.2) (Senft, 1983; Stillwell, 1983). The product of the seasonally and spatially stratified deposition and volatilization data, assuming a pasture divided 70:30 between uplands and swales, yields an ecosystem-level estimate of loss of only 110 g N ha^-1 y^-1. Emission of NH₃⁰ from pastures composed entirely of upland soils and at the same stocking rate would be 760 g N ha^-1 y^-l, a significantly higher value. A similar calculation for N₂O emission, using the rates presented above, results in an estimated ecosystem-level flux of 104 g N ha^-1 y^-l. N₂O emission from an upland pasture would be 80 g N ha^-1 y^-l. Any ecosystem or landscape in which N is transferred between areas of low and high emission potential will require careful study, particularly if either rates of transport or of emission are modified by anthropogenic activity.

CONCLUSIONS

Spatial heterogeneity is high for measurements of gas flux from terrestrial ecosystems. Both fine (as in the first example) and coarse grained (as in the last two examples) variability must be considered in computing estimates of gas fluxes from large areas. While no single class of techniques will resolve problems of measuring gas fluxes across all levels of scale, certain commonalities are evident in the several examples presented in this paper. First, identification of variables which are easy to measure or obtain from regional data sources and which are predictors of gas flux rates is critical. These predictor variables may be used in either statistical or simulation models to obtain spatially or temporally integrated estimates of gas flux rates. The variables chosen must be measurable in some way at the desired scale. In the study of N₂O flux modelling, variables which improved the fit of the model (NO₃^-,NH₄+ ) were dropped from the model because they were difficult to measure or model at the chosen scale. Instead, an empirical variable, estimable from soil texture and organic matter content was substituted. Second, choice of appropriate predictor variables must be guided by thorough knowledge of the processes governing the emission rate. Without such mechanistic knowledge at a level of scale below the scale of integration, choice of predictor variables becomes empirical and extrapolation out of the original universe of study becomes problematic. Thus, successful attempts to estimate flux rates over large areas must be based on careful intensive studies to guide choice of predictor variables. Operating at multiple 'levels of resolution' becomes particularly important when controls over gas fluxes behave nonlinearly, as was the case for the effect of water on denitrification (example 1), and on the denitrification/nitrification ratio (example 2). While coarse-scale models need not, and usually must not, include detailed mechanism, oversimplification can lead to serious error when nonlinear functions are encountered.

The approaches presented here are not new but, rather, are rooted in systems analysis and are consistent with recent developments in hierarchy theory (O'Neill, 1988). Our purpose here is to give concrete examples of studies which take advantage of multiple scales of investigation and to illustrate by example techniques for extrapolating small-scale studies of gas flux to larger spatial domains.

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