Simulating CO2 concentrations with a mixed-layer model on time-scales larger than a day

Modelling the CO2mixing ratio with a mixed-layer model during dayand night-time conditions Thirza van Laar January 2014 Internship at Universitat Politecnica de Catalunya (UPC) Advisor: David Pino (UPC) Supervisor: Jordi Vila (Wageningen University) Abstract Previous research on the temporal evolution of CO2concentrations focused either on short, local time-scales, or on larger regional time-scales. On these different time-scales the importance of dynamical processes for the CO2concentration can differ as well. To study this shift of significance, a model is needed that is able to capture all relevant processes for both short and long time-scales. The purpose of this paper is to extend a mixed-layer model in order to make it suitable for longer time-scales. A mixed-layer model is only valid for convective day-time conditions and can only simulate the convective boundary layer during several hours. By including the theory of Nappo & van Dop (1994) the model will also be suitable for simulating night-time conditions of the mixing ratio of CO2, and as a consequence also longer simulations can be done with it. The results of this extended model are compared with observations of 2426 September 2003 to assess the accuracy. This shows that the mixing ratio of CO2is well captured during the first day and night, but after the transition of night to day the mixing ratio is too low. This is due to incorrect morning conditions (especially the boundary-layer depth), which emphasizes that when modelling the concentration of a chemical compound accurately, first the dynamical characteristics should be correct. 1 Introduction In the context of global warming, it is important to be able to understand the evolution of carbon dioxide (CO2) concentrations in the atmospheric boundary layer (ABL) and the factors that influence this evolution (Houghton, 1993; Cox et al., 2000). It is already clear that next to processes at the surface, such as respiration and photosynthesis (Jacobs & de Bruin, 1992; Kim & Verma, 1 1990), also processes related to boundary layer dynamics have a large effect on the variability of CO2concentrations. Culf et al. (1997), as well as de Arellano et al. (2004) showed that during morning hours the CO2budget is more influenced by entrainment than by the surface flux. Casso-Torralba et al. (2008) assessed the importance of advection. With the help of a mixed-layer model, Pino et al. (2012) and Pino et al. (2013) studied how uncertainties in boundary layer dynamical variables influence the mixing ratio of CO2. All in all, diurnal variability of CO2concentrations on local scales is quite well understood. However, not only local spatial scales are of interest, but larger regional scales are that as well (Bakwin et al., 2004). Increasing spatial scales automatically implies also increasing the time-scale of the processes involved (Stull, 2009). Certain dynamical processes are important on small time-scales, but they may loose their significance if the time-scale increases (Williams et al., 2011). Entrainment and storage are usually ignored on time-scales larger than a day (Helliker et al., 2004); on shorter time-scales it is common to neglect advection (Yi et al., 2004). To study this shift in the importance of dynamical processes on CO2concentrations during the transition from local to regional scales, a model which is capable of capturing all dynamical processes involved, on increasing temporal scales, must be used. An example of such a model is the mixed-layer (MXL) model (Tennekes, 1973), which solves boundary layer dynamics together with atmospheric chemistry at low computational costs. However, this model is only valid for day-time conditions since it is based on the assumption of a convective, well-mixed boundary layer. It can therefore only be used for simulations up to several hours. Because of this limitation of the MXL model, the purpose of this paper is to extend the model in such a way that it can also capture the evolution of CO2concentrations during stable conditions. By including the proposed algorithm of Nappo & van Dop (1994) for a scalar (in our case CO2) for nighttime conditions the simplicity of the model is kept. Nappo & van Dop (1994) show that their parameterization is mass conserving and gives realistic results for a scalar, when tested with a simple one-dimensional model. After including their method, the extended model is suitable for longer simulations for the mixing ratio of CO2and we can increase the time-scale from hours to days. To assess the accuracy of the model, the results will be compared with observations, taken at Cabauw (The Netherlands) during three days: 24-26 September, 2003. In the next section the theory for both the convective and the stable boundary layer on which the model is based will be described. Followed in section 3 by an analysis of the observations. In section 4 the settings of the model are given with which the results of section 5 are achieved. All this is summarized in the last section, where also the conclusions and an outlook to further research is given. 2 2 Theory In this section the mixed-layer model is briefly described. It will be used to model the boundary layer variables during the day, in convective conditions. Next to the mixed-layer model, also the model used for the temporal evolution of the CO2mixing ratio during the night, when a stable layer has developed, is described in more detail. Finally, the methods for the transitions between these two different models are explained as well. 2.1 Convective Boundary Layer Daytime conditions will be simulated by using zeroth-order mixed-layer theory (Tennekes, 1973; Tennekes & Driedonks, 1981; Driedonks, 1982). More recently models based on this theory has been used for example by de Arellano et al. (2004) to study the role of entrainment in the evolution and distribution of CO2in the boundary layer, and by Ouwersloot et al. (2012) to study the role of large scale atmospheric dynamics on the evolution of chemical species concentrations over a boreal forest. During the day the boundary layer is assumed to be well mixed up to the thermal inversion due to turbulent mixing. This creates a vertically homogeneous profile of the mixing ratio of a conserved scalar in the boundary layer. The mixing ratio vertical profile of a conserved scalar shows a jump at the height of the inversion and above this height, in the free troposphere, the scalar mixing ratio follows a linear profile. 2.2 Stable Boundary Layer During the night, radiative cooling at the surface produces a stable boundary layer (SBL), due to thermal stratification. Consequently, turbulence intensity is lower than during the day because it is only produced by mechanical mixing due to wind speed, producing less mixing during the night (Stull, 2009). In this situation mixed-layer theory is no longer valid. Due to the negative sensible heat flux and the consequential absence of vertical turbulent motions, it is assumed that there is no entrainment of CO2at the top of the boundary layer. Since the surface flux of CO2is positive during night time, mixing ratios are assumed to decrease linearly with height in the stable boundary layer. To describe the boundary layer profile of CO2during night-time conditions in the model, the method described by Nappo & van Dop (1994) for the stable boundary layer is followed. It is important to note that this method doesn’t analyse the atmospheric dynamics during the night, but only the scalar concentration. As in their theory we assume a constant nocturnal boundary-layer depth (zi) and due to the absence of entrainment also a constant mixing ratio 3 of CO2at this height. Therefore, the CO2mixing ratio at a given height and time is represented by: CO2(z, t) = CO2,0(t)1−z zi+CO2,ziz zi(1) where CO2,0is the mixing ratio at the surface, zthe height and CO2,zithe mixing ratio of CO2at the boundary layer height. Different than Nappo & van Dop (1994), who dealt with a general atmospheric compound, we assume for our case that both the deposition flux and the source term of CO2(vdand qvin their equation 19) are zero. Therefore, CO2,0is given by: CO2,0(t) = CO2,zi+2hw0CO0 2|si zi (t−t0),(2) where the averaged surface flux of CO2,hw0CO0 2|si, is: hw0CO0 2|si= [Zt t0 w0CO0 2|sdt]/(t−t0).(3) 2.3 Transitions between day and night To apply the equations of the previous subsections we assume that the transitions between day and night will occur when the sensible heat flux changes sign. The sensible heat flux is used for this since it is closely related to temperature and thereby to stability, regardless of the moisture conditions of the surface. Because the stable boundary layer is shallower than the convective boundary layer (CBL), the profile of the CBL at the end of the day can be used as initial profile for the SBL. We assume a constant nocturnal boundary-layer depth and prescribe it by using the observations. Below that height the stable boundary layer develops. Above this height a residual layer is formed which remains unchanged during the night and has the same characteristics as the former CBL (Stull, 2009). The transition from night to day is not as straightforward. The model should conserve the mass of CO2, and the linearly decreasing profile must be converted into a vertically homogeneous one. On top of these restrictions there is also a residual layer left from the previous night. Ouwersloot et al. (2012) showed an example of how to deal with a residual layer in the mixed-layer model. However, if we would apply their same method, new initial values for the thermodynamical variables should be prescribed since they are not simulated during the night. To avoid this and to have a model that runs continuously, the residual layer is instantaneously incorporated in the mixed layer during the early morning. The height of the SBL is changed to the final height of the CBL of the previous day. The jump in the mixing ratio of 4 CO2at the boundary layer height and the CO2mixing ratio in the boundary layer itself are determined by guaranteeing mass conservation of CO2. The gained mass of CO2during the night is evenly distributed over the new, higher boundary-layer depth. 3 Observations By using observations we describe the evolution of the boundary layer dynamics and the CO2mixing ratio during the period of 24-26 September 2003, with a special interest in the nights. The day of 25 September has already been studied by Casso-Torralba et al. (2008) and Pino et al. (2012). Observations are from the Cabauw site (The Netherlands), which is surrounded by an open field mostly covered with short grass. Beljaars & Bosveld (1997) and Vermeulen et al. (2011) described the measurement site in detail. Along the 213-m meteorological tower of this site the vertical profiles of temperature, humidity, wind and CO2are measured, as well as the fluxes of momentum, CO2, sensible and latent heat. The CO2mixing ratio is measured at 20, 60, 120 and 200 m, the flux of CO2is measured at 5, 60, 100 and 180 m. 3.1 Temporal evolutions Figure 1 shows the temporal evolution at all available measurement heights of potential temperature, wind speed and the CO2mixing ratio for both nights of interest. For the same period, Figure 2 shows the temporal evolution of the flux of CO2, the sensible and latent heat flux at 5, 60, 100 and 180 m. The potential temperature decreases in the lower layers (up to 40/80 m for night 1/2, Figs. 1-a,b), and this cooling produces a stable layer. This is confirmed by the negative sensible heat fluxes, which can be observed in Figures 2-a,b. The time of the minimum sensible heat flux differs between the two nights. Steeneveld et al. (2005) found a coupling between the heat fluxes and wind speed, and we can find it here as well. The wind speeds are shown in Figs. 1-c,d. In the first night wind speed increases gradually to a maximum at the end of the night, also the fluxes have their largest magnitude at the end of the night. In the second night the maximum wind speed is found at the beginning of the night. This can explain the sudden variations of the fluxes during the second night at 21 UTC. Because of respiration by the soil and by vegetation, CO2mixing ratio increases during the night (Figs. 1-e,f). At the end of both nights the mixing ratio of CO2at 20 m reaches a value of approximately 440 ppm. This represents an increase of 60 ppm and 50 ppm for the first and second night respectively. The time of the maximum CO2mixing ratio for the two lowest levels coincides 5 with the largest observed CO2fluxes at the surface (Figs. 2-e,f). By analysing observations taken during the first night (Figs. 1-a,c,e) it is noticed that there is a decoupling between 40 and 80 m. Above 80 m the temperature does not increase anymore, staying fairly constant. In the tendency of wind speed and CO2for this night (Figs. 1-a,e) the same decoupling is seen, from which can be deduced that the stable boundary-layer depth must be in the range of 40-80 m for the first night. For the second night (Figs. 1-b,d,f), this decoupling is observed between 80 and 140 m. Thus the stable boundary layer becomes not as shallow in the second night as in the first night. Unfortunately there is no continuous data of night-time boundary-layer depths available to verify this. 3.2 Radiosondes Figure 3 shows three vertical profiles of potential temperature (θ) as observed by radiosondes on 24 and 25 September at 12 UTC and on 25 September at 00 UTC. The radiosondes are launched at De Bilt, approximately 40 km away from Cabauw. The well-mixed profiles for potential temperature during the day are clearly visible. Unfortunately the sounding of 26 September at 00 UTC did not record data below 200 m. The launch on 25 September at 00 UTC shows the linearly increasing profile of potential temperature during the night. It can also be seen that the boundary-layer depth is located at least lower than 100 m for this night. 3.3 Budget analysis By using the observations shown in Figures 1,2, the budget analysis method can be applied (Betts, 1992; Betts & Ball, 1994; de Arellano et al., 2004). With this method the contribution of advection, vertical flux divergence and storage for a scalar can be assessed. Notice that radiative cooling is not included, and since this is an important process influencing temperature during the night, the method cannot be applied for this variable during the night. Due to the relative homogeneous surface conditions at Cabauw, the horizontal flux divergence is omitted for this study. Next to this and following de Arellano et al. (2004) and Casso-Torralba et al. (2008) the vertical advection is omitted as well. The budget for a scalar Sthen reads: ∂S ∂t +u∂S ∂x +v∂S ∂y +∂w0S0 ∂z ≈0 (4) In this equation the first term represents the storage term (or tendency term) and is expressed as the rate of change of the scalar in time. The second and third terms are the horizontal advection. Finally, the last term represents the 6 divergence of the scalar flux which accounts for the vertical transport of the scalar. The storage term is determined by using the average value of observations at 60 and 20 m. These heights are different than for example in the study of Casso-Torralba et al. (2008). This is because we analyse the stable boundary layer instead of the convective boundary layer and the heights of the observations have to be in the boundary layer (Betts, 1992). The same holds for the determination of the divergence of the CO2flux. For this, the observations at 60 and 5 m are used, so that both are very likely to be inside the nocturnal boundary layer. Unfortunately, there is no data available from the same heights as for the storage term. The horizontal advection is assumed to be the residual term of the equation when storage and divergence are known. The result for the CO2budget for both nights is shown in Fig. 4. During both nights storage is a positive term, as could already be deduced by the increasing mixing ratios in Figs. 1-e,f. Note that due to the sign convention used here, negative advection means air rich(er) in CO2. The storage of CO2 at the end of both nights has comparable magnitude (4 ppm/hour). This is supported by Figs. 1-e,f, showing that the CO2mixing ratio at the surface at the end of both nights reaches approximately the same value (440 ppm). However, although the total storage of both nights is comparable, this is not the case for the divergence of the CO2flux and advection. In the first night the divergence of the CO2flux is close to zero, whereas in the second night it reaches a value of -1.5 ppm/hour. At the same time the advection is less negative (so less advection of CO2), leading to comparable storage terms for both nights. 4 Model settings Table 1 shows the initial settings used for the simulation. They are based on the observations shown in the previous section. Note that we assume that there is no advection. The prescribed fluxes of sensible heat, latent heat and CO2 follow a sinusoidal function during both day and night and are fitted by using the observations of the fluxes at 5 m, as illustrated in Fig. 5. The magnitude of their maxima and minima can be found in Table 2. The simulation starts at 8 UTC in the morning of 24 Sep and ends at 16 UTC on 26 Sep. The start and end times of the nights (moments of transition) are shown in Table 3. 7 21 00 03 06 280 290 (a) θ[K] 24-25 Sep 21 00 03 06 0 5 10 15 (c) Wind speed [m/s] 21 00 03 06 350 400 450 (e) CO2[ppm] Time (UTC) 21 00 03 06 280 290 (b) θ[K] 25-26 Sep 2 m 10 m 20 m 40 m 80 m 140 m 200 m 21 00 03 06 0 5 10 15 Wind speed [m/s] (d) 10 m 20 m 40 m 80 m 140 m 200 m 21 00 03 06 350 400 450 (f) Time (UTC) CO2[ppm] 20 m 60 m 120 m 200 m Figure 1: Temporal evolution of the observed potential temperature (a,b), wind speed (c,d) CO2mixing ratio (e,f), at all available measurement heights for the nights of 24-25 and 25-26 September 2003. 8 21 00 03 06 −50 0 50 w′θ′[W m−2] 24-25 Sep (a) 5 m 60 m 100 m 180 m 21 00 03 06 0 50 100 w′q′[W m−2] (c) 21 00 03 06 −0.5 0 0.5 1 w′CO′ 2[ppm m s−1] (e) Time (UTC) 21 00 03 06 −50 0 50 (b) 25-26 Sep 21 00 03 06 0 50 100 (d) 21 00 03 06 −0.5 0 0.5 (f) Time (UTC) Figure 2: Temporal evolution of the observed fluxes of sensible heat (a,b), latent heat (c,d) and CO2(e,f) for the nights of 24-25 and 25-26 September 2003. 9 mixing ratios are comparable for both nights, although during the first night advection plays a more important role than during the second night. Unfortunately there is only one radiosonde launched during night-time available (00 UTC, 25 Sep), it shows that the potential temperature profile linearly increases with height. During the first day the model correctly reproduces the atmospheric dynamics. This leads also to correct CO2mixing ratios. Also the CO2mixing ratios during the first night are well represented, confirming the theory of Nappo & van Dop (1994). However, due to an oversimplification of the nightday transition, the morning value of the boundary-layer depth for the second day is incorrect. This leads to an overestimation of the boundary-layer depth and therefore too low mixing ratios for CO2during the rest of the simulated period. We can conclude that, although several assumptions were made, the CO2 mixing ratios of the first night are well reproduced by the model. 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