Concentration changes of N2O and 222Rn were monitored in the surface layer above a grass sward during the first half of two calm nights. N2O flux on a local or field scale was then estimated from the ratio of the concentration differences between 0.1m and 0.4m height and the directly measured 222Rn flux. This estimate (∼7 g N2O-N ha−1d−1) was between the N2O flux on a larger scale (∼4.5 g N2O-N ha−1d−1), as estimated from changes in the N2O/222Rn ratio over time, and the small scale flux on the grass plot (∼50 g N2O-N ha−1d−1) as measured with closed chambers.
 N2O is a powerful greenhouse gas and causes loss of stratospheric ozone. Total anual emissions into the atmosphere are estimated between 6.7 and 36.6 Tg N [IPCC, 2001]. Potentially the largest single source are agricultural soils. They are also the most uncertain source with estimates ranging from 0.6 to 14.8 Tg N y−1 [IPCC, 2001]. Partly, this uncertainty results from the large spatial variability in N2O fluxes [Ball et al., 1997], and from the lack of a measurement method capable of integrating often the very small N2O fluxes over larger areas.
 The aim of this study was to find a simple method for estimating small trace gas fluxes (<0.4 nmol m−2s−1, or <10 g N2O-N ha−1d−1) on a local or field scale (104–106 m2) under very stable nocturnal conditions. Such conditions generally occur during clear nights when conventional models of atmospheric transport, and therefore micrometeorological measurement techniques, are no longer applicable [Mahrt, 1998]. While very stable conditions are unfavorable from this point of view, they lead to the accumulation of soil-emitted trace gases and strong gradients within the inversion layer close to the ground. This is favorable from an analytical point of view, especially where small fluxes are involved and concentration gradients would be difficult to detect under neutral or unstable conditions.
 During daytime, the atmosphere near the ground is generally unstable. Thus, trace gases are mixed easily by turbulent transport from the ground level into the large volume of the convective boundary layer. The concentration of a trace gas near the ground is a function of height, flux strength within the area influencing the measurement, and the exchange coefficient, which depends mainly on wind speed, atmospheric stability and surface roughness. Fluxes can be estimated by measuring concentration differences between two heights and scaling them with a reference flux that is more amenable to direct measurement. The Bowen ratio method is based on this principle using heat flux as a reference [Monteith and Unsworth, 1990]. Similarly, we might employ 222Rn as a reference flux. We can assume the 222Rn flux to be spatially homogenous over large areas of same soil type. Under this condition, the area influencing the measurement is the same as that of other techniques based on the measurement of vertical concentration profiles [Horst, 1999]. During the daytime, this area extends roughly 100 times the mean measurement height upwind and is of the scale we are interested in, when trying to do field scale measurements.
 After sunset, low wind speed and radiative cooling of the earth's surface can lead to reduced vertical mixing and the development of a shallow and stable boundary inversion layer [Mahrt, 1998]. Concentrations within this layer change appreciably, integrating surface fluxes along the path of a column of air moving over the landscape [Denmead et al., 1996]. This leads to a shift of the entire near ground concentration profile towards higher concentrations. While fluxes near the measurement location are still reflected in the relative concentration differences with height, they are now overlaid on the change in absolute concentrations with time, which are subject to average fluxes on a much larger scale (Figure 1).
 We may take N2O as an example of a soil emitted trace gas. Making the assumption of all gases being transported in the atmosphere with the same efficiency by turbulent processes we can write:
where and are the N2O and 222Rn fluxes from the soil, and Δ and Δ are concentration differences of N2O and 222Rn in the atmosphere.
 Δ and Δ can be derived from concentration changes over time (ΔCt), if a large scale N2O flux estimate is desired. This requires at least two measurements at different times and at one height during an inversion situation (i.e. C(z1,t1) and C(z1,t2) in Figure 1). To reduce measurement errors, we might integrate over longer time periods and do more than two measurements. ΔCt can then be determined as the slope of a linear regression through measured concentrations during the time of steady concentration increase.
 From one two-point profile (ΔCz) of N2O and 222Rn we can theoretically estimate flux on a field scale. Again, to reduce error, we might measure several profiles at the same heights but at different times to derive an average ΔCz. For this purpose it is not necessarily required that concentrations increase over time. If measurements are made alternately between the two heights, we might derive same-time concentration values by interpolating at one height between measurements.
3. Experimental Techniques
 Measurements were carried out in an intensively managed agricultural plane, the Swiss Plateau, between the Alps and the Jura (Seeland). The area is flat, with occasional windbreaks. During the time of the experiment (25–30 August 2000), there were mature arable crops in most of the fields, some of which were already being harvested. One of the few grassland plots in this area was selected as the experimental site. It was 200m long, 11m wide and located between a mature cornfield and a mature vegetable field (Brussels sprouts). A detailed description of the field site can be found in Gut et al.  and Neftel et al. .
 N2O flux from the grassland plot was measured with 4 closed chambers of 0.4 m diameter and 0.16 m height. Measurements were carried out twice daily by closing the chambers with a lid and sampling the headspace at 10-minute intervals over 30min for subsequent analysis by gas chromatography with electron-capture detector (ECD).
 The instrumentation for the 222Rn-tracer technique consisted of two air-sampling inlets in the center of the grassland at 0.1m and 0.4m above the ground. Measurements of atmospheric 222Rn and N2O were made during the first half of the night on 25 and 28 August, sampling alternately at each height over 20min intervals and storing the air in 12 liter Tedlar® bags. Gas samples were analyzed the following day for N2O with a tunable diode laser instrument (TDL) and for 222Rn with an ionization chamber. Meteorological parameters were measured by sonic anemometer 1.2 m above ground; in addition, a hot-sphere anemometer measured wind speed 0.25 m above ground.
 Two days before the measurements started the grass on the experimental plot was cut. Consequently, emissions of N2O as measured with closed chambers were rather high. They fell from around 80 to 30 g N2O-N ha−1d−1 from 25 to 26 August. After a heavy rain in the evening of the 26 August they increased to over 200 g N2O-N ha−1d−1 before declining again to about 50g N2O-N ha−1d−1 on the 28 and 29 August. Radon flux reacted conversely to the rain by decreasing from around 11 before to 2 mBq m−2s−1 after the event. On the 28/29 August, values had increased again to over 8 mBq m−2s−1 and still seemed to increase slightly afterwards (Figure 2)
 During the first night of atmospheric measurements conditions were very stable. The sky was absolutely clear and temperatures at 1.2 m above ground fell by 10°C during the measurement period from 19:20–23:00. The wind speed above the grass at 0.25 m (v0.25) was on average 0.2 m s−1 and friction velocity (u*) was 0.05 m s−1. The second night was slightly less stable. There were occasional clouds, temperatures at 1.2 m only fell by 3°C from 19:30–23:00, and v0.25 and u* were higher (0.37m s−1 and 0.08m s−1).
 Concentration changes in N2O and 222Rn were more strongly expressed during the first night than during the second night. Also, concentration differences between the two measurement heights were larger during the first than during the second night. Compared to the relatively steady increase in N2O over time reflected by correlation coefficients (r) between 0.94 and 0.99, 222Rn concentrations seemed to behave less consistent with values of r between 0.78 and 0.95 (Figure 3). This is likely due to the larger analytical error in the 222Rn measurements (20%) as compared to the N2O measurements (1%).
 Large scale N2O flux estimates based on concentration changes over time were similar for both nights and both heights of measurement (Table 1). On average they were 4.4 g N2O-N ha−1d−1. The error of the individual estimate was on average 26% of its mean. Field scale estimates based on concentration differences with height were about 60% larger and were 7.2 and 6.9 g N2O-N ha−1d−1 during the first and the second night, respectively (Table 2). While the error was 30% of the mean for the more stable first night, it was larger than the mean for the measurement during the less stable second night. The large error is mainly a result of the error associated with the concentration difference in 222Rn (Δ) (Table 2).
Table 1. Increase in N2O and 222Rn concentration over time as measured at different heights (z1=0.1m, z2=0.4m). Together with the measured 222Rn flux these values were used to calculate large scale N2O flux.
N2O measured ppb h−1
222Rn measured Bq m−3h−1
222Rn flux measured mBq m−2s−1
N2O flux calculated g N2O-N ha−1d−1
Note that by mere chance at T=15°C and p=965 mb the units used in the Table convert almost exactly as follows: [1(ppb/h)/1 Bq/(m3h)] × 1 mBq/(m2.s) = 1 g N2O N ha−1d−1.
1. night ΔCt(z1)
2. night ΔCt(z1)
Table 2. Average differences in N2O and 222Rn concentrations with height (0.1m to 0.4m). Together with the measured 222Rn flux these values were used to calculate N2O flux on the local or field scale.
N2O measured ppb m−1
222Rn measured Bq m−3m−1
222Rn flux measured Bq m−2h−1
N2O flux calculated g N2O-N ha−1d−1
1. night ΔCz (t0…tn)
2. night ΔCz (t0…tn)
 Field site and meteorological situation during this experiment represent a case, where traditional micrometeorological techniques would not be applicable. This is mainly because of atmospheric stability during the clear summer nights, large changes in roughness lengths between the relatively small field plots with different vegetation height, and also because of the very small fluxes involved. Nevertheless, such a situation is not untypical in this area and probably in many other parts of the world. Therefore, it seems appropriate to investigate alternative methods for flux measurements under such conditions. Choosing a field plot with relatively large emissions surrounded by fields with lower emissions allowed to qualitatively test a method that is expected to integrate over an intermediate area, incorporating some proportion from both sources.
 The fluxes measured directly on the grassland plot with chambers were relatively large for grassland that has not been fertilized for several months but comparable to other published flux values for intensively managed temperate grassland sites [e.g. Clayton et al., 1997; Dobbie et al., 1999]. They were about 20 times larger than the large scale background fluxes of the surrounding arable fields estimated from the N2O/222Rn concentration changes over time. The large scale fluxes compare well with published N2O flux values for arable crops around harvest time [e.g. Bronson and Mosier, 1993; Smith et al., 1998]. It might be argued that the 222Rn tracing of concentration changes over time is only applicable at a height where the boundary layer is well mixed. However, the course of N2O concentration changes over time was found to be very steady despite the heterogeneity of the terrain and the frequent changes in wind direction. Also, the fluxes derived at the two different heights were very similar, indicating little influence of this factor, at least within the range of heights selected in this experiment.
 Flux measurements on the local scale based on concentration changes with height yielded values between the large grassland fluxes and the much smaller background flux. This method worked well during the first night, but not during the second night when the error of the estimate was larger than its mean. This might have been partly due to the large relative error in the Δ. Also, concentration differences with height were smaller during the second night. While u* and v0.25 were only slightly higher during the second night, the cooling rate was reduced to one third. This might have led to a weaker surface inversion and better mixing of the air near the ground.
 We might assume the N2O flux in the neighboring arable plots to be the same as the large scale background flux. In this case, the estimated influence of the grassland on the local scale measurement would be about 5%. Since there were mostly arable fields in the area but also a few grassland plots, the large scale background flux is likely to be a mixture of both and flux from the arable fields might indeed be smaller. The estimate of 5% is therefore the lower end of our estimate for the contribution of the grassland to our local scale flux estimate. Assuming N2O flux in the neighboring fields to be zero would give us an upper estimate of 12–14%.
 The total area influencing the local scale measurement can only be roughly estimated since no source area model can be applied under these geometrical and atmospheric conditions. Parallel measurement of activities of the short-lived isotope 220Rn (half-life 56 seconds) averaged 350 Bq/m3 at 3 cm and 110 Bq/m3 at 8 cm above ground during the first night yielding a (constant) K-value of 2.3 × 10−5 m2 s−1. Thus, the corresponding estimated vertical transport time between these two levels was about 2 minutes [Lehmann et al., 1999]. Even with the minimal wind speeds of 0.15 m s−1 an average horizontal displacement of 18 m results (clearly more than the 5.5 m half-width of our field) during such a time interval. Obviously, hardly any atoms or molecules emitted within a few meters from our sampling site can reach the detectors because of the extremely slow vertical transport under such stable conditions. The values of 5 to 14% estimated above for the contribution of the grass field appear to be quite reasonable in such a situation.
 Further study needs to be done to enable a more precise description of the source area under similar conditions. However, in a first approximation, we estimate the source area in this case to extend from almost 100 m to 200 m upwind from the sampling inlets. Thus, it seems possible to use this approach to estimate small trace gas fluxes from fields of several hectares in size. This method might therefore enable more spatially integrated measurements of N2O fluxes from agricultural soils and in the long term a reduction of the uncertainty associated with this important source.
 The converse reaction of N2O and 222Rn flux to heavy rain indicates an important limitation of this technique. While N2O flux is likely to increase after rain, if nitrate is not limiting [Dobbie et al., 1999], 222Rn flux decreases as a result of reduced diffusivity of the soil surface [Lehmann et al., 2000]. This may lead to substantial changes in 222Rn soil flux on a time scale in the order of hours and result in strong reductions of nocturnal 222Rn accumulation near the ground [Ussler et al., 1994]. Vegetation intercepting most of the precipitation during a rain event could have a buffering effect on such variaions [Ussler et al., 1994]. The assumption of a constant 222Rn flux could lead to an overestimation of N2O flux during and after rainfall.
 Measurements of small N2O fluxes from soils are possible under stable nocturnal conditions and in inhomogeneous terrain by 222Rn calibration of the near surface concentration profile. The area influencing the measurement can only be roughly estimated but seems to be several times larger than under neutral or unstable atmospheric conditions. At the same time such measurements can give an estimate of the integrated larger scale flux through a different interpretation of the same data.
 This project was supported by the Darwin Trust (University of Edinburgh). The authors thank Christoph Ammann and Pierluigi Calanca for valuable discussions.