Methods for flux estimates

When an air parcel is transported from Westmaas to Zweth, the mole fraction of CO2 in

that air parcel is affected by processes that occur during transport. Therefore, comparing CO2 mole fractions at Westmaas and Zweth can provide information on the magnitude of

those processes in their footprint. Previous research has shown that observations made during flights upwind and downwind of a source sector of interest can be used to estimate the flux for that sector (Caulton et al., 2014; Karion et al., 2013; Mays et al., 2009; Peischl et al., 2015). The integrated flux of X (FX) over the total sector between the two flight

tracks can be calculated using a mass balance equation:

(1)

where v∙cos(α) is the proportion of the wind velocity parallel to the observed concentration gradient, and ΔXobs is the observed concentration enhancement over a

background value which is integrated over a horizontal (y) and vertical (z) plane where zi is

boundary-layer height adjusted for vertical transport and boundary-layer growth (Peischl et al., 2015). In contrast to these studies we lack a y-dimension as the location of our observational sites is stationary in time, but we do have a longer time series that allows us to apply data selection.

To get a flux estimate from continuous in-situ observations we adapt the previous mass balance equation to the one-box model (Fig. 2.2). The change in concentration [kg m-3] of species X in a box is a function of the inflow Fin and outflow Fout (advection), chemical

reactions (C and L), emission (E) and deposition (D, all fluxes in [kg km-2 hr-1]):

(2)

where Δt is the time difference between two measurements of X in hours and h the boundary layer height in km. We adopt a Lagrangian approach in which this box moves with the wind from an upwind to a downwind site and advection becomes zero. Since CO2

is chemically inert only emission (both fossil fuel emissions Eff and biogenic respiration Ebio)

and deposition (photosynthesis An) remain, resulting in the following equation:

(3)

where ΔXobs is equal to the concentration at Zweth measured at time t+Δt minus the

concentration at Westmaas measured at time t. With a distance of 20.15 km between the sites the time difference Δt for wind parallel to the gradient is typically between 0.5 and

INTERPRETING CONTINUOUS IN-SITU OBSERVATIONS

33 1.5 hours. Note that we round off Δt to full hours since we binned our observations (approx. 1 per second) into hourly concentrations.

Figure 2.2: Representation of a one-box model. Source: Jacob (1999)

We define a footprint from which the fluxes are observed at Zweth when the wind is coming from Westmaas. We need to identify this area of influence in order to compare the flux estimates made with Eq. 3 with those given by emission databases for the same area. We define the footprint as the area covered by a Gaussian plume at neutral stability (to represent dominant wind speed and mixing conditions) from the downwind to the upwind site (i.e. it has a triangular shape). The total area of the footprint between Westmaas and Zweth is about 44 km2 (see Table 2.2) following:

(4)

where F (0.32) and f (0.78) are empirical stability parameters, x is the travel distance in m and σy is the standard deviation of the Gaussian plume in the horizontal direction in m. We

multiply by 3 to get the 3σ width of the normal distribution.

To estimate the fossil fuel flux we need to approximate the biogenic fluxes in the footprints and account for their contribution to the CO2 concentration gradient. This is

done based on observations in the Netherlands of annual cycles of the net ecosystem exchange (NEE = Ebio - An) (Hendriks et al., 2007), from which we determine monthly mean

NEE. An average daily cycle for May is determined based on the work of Jacobs et al. (2003) and scaled according to the monthly mean NEE. This gives us an average daily cycle per month (Appendix A), which will be used to calculate the total biogenic flux. Both the Hendriks et al. and Jacobs et al. studies used NEE observations over well-watered/wet grassland, which match with the agricultural land use in our study area.

Note that the mass balance approach assumes the emissions to be well-mixed throughout the boundary layer by the time it reaches the downwind site and that h is taken as a constant during transport. We use a monthly value of h based on measurements at the nearby Cabauw site (Royal Netherlands Meteorological Institute (KNMI), 2007) and assume this value to be maximal and relatively constant during the afternoon (see Appendix A). These assumptions on constant h and neutral stability are

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only valid during well-mixed afternoon conditions. Therefore we select only 12-16h UTC data from our time series that correspond to a wind speed of at least 3 m s-1.

Although this process of using an up- and downwind observational site to constrain urban emissions seems rather straightforward, Turnbull et al. (2015) have identified several difficulties related to this strategy for Indianapolis. First, the mole fraction is heterogeneous in space and time. Spatial heterogeneity implies that the upwind observation is not necessarily representative for the mole fraction of the entire ‘background’ air parcel moving over the city. This is especially relevant if the wind direction is not exactly parallel to the concentration gradient. The issue of temporal heterogeneity is addressed by accounting for the travel time between the up- and downwind site. Note, however, that the gradient then becomes:

(5)

where time lag τ between the observations at the upwind and downwind site is:

(6)

and x is the distance between the sites, v the wind speed and α the wind direction relative to the gradient. The time lag is zero when the wind blows perpendicular to the gradient (so the gradient consists of measurements taken simultaneously at both sites). The value of Δt in Eq. 3 is independent of the wind direction, but merely a function of wind speed and travel distance.

Second, other sources and sinks affect the mole fraction during transport, which makes it difficult to extract the impact of fossil fuel emissions from the total signal. We have previously discussed the biogenic sources and sinks, but Turnbull et al. (2015) also mention the importance of entrainment when the free-tropospheric concentration significantly differs from the boundary-layer background concentration. However, estimating entrainment requires an estimate of the free-tropospheric mole fractions. Additionally, mixing and entrainment of CO2 can be highly variable as those processes

depend on atmospheric conditions and the land surface (Vilà-Guerau de Arellano et al., 2004). Therefore, similar to Turnbull et al. (2015) we assumed entrainment did not affect the mole fraction during transport. During the afternoon hours we selected here, this assumption is supported by a typically quite constant boundary layer height h (Vilà- Guerau de Arellano et al., 2004).

Finally, the distinction has to be made between in-city and remote observational sites. Kort et al. (2013) argue that in-city observational sites are continuously affected by local emissions. Therefore, they are better suitable for constraining urban fluxes than remote sites, even though they are only sensitive to a small part of the entire urban area. In contrast, remote sites only detect urban emissions at certain wind directions and even

INTERPRETING CONTINUOUS IN-SITU OBSERVATIONS

35 then the signal is diluted by other fluxes, i.e. the urban air is mixed with other air masses. Turnbull et al. (2015) also found an occasional and diluted signal at a 130m-tower 24 km downwind of the centre of Indianapolis. In contrast, our downwind site is at only 7 km from the city centre and within an urbanized area, so we consider it to be semi-urban rather than remote. However, the sampling height is only 10 m. Therefore, we will explore the use of such sites for monitoring urban fluxes. We expect that the effect of dilution is limited while at the same time we are able to detect urban signals for most wind directions. We will go more in-depth in the discussion.