Among the processes contributing to the global CO2 budget, net uptake by the land surface bears the largest uncertainty. Therefore, the land sink is often estimated as the residual from the other terms that are known with greater certainty. On average over the last decades, the difference between modeled land surface uptake and this residual is negative, thus suggesting that the different modeling approaches miss an important part in land–atmosphere exchange. Based on experience with atmospheric modeling at high resolution, it is argued that this discrepancy is likely due to missed mesoscale (thermally or dynamically forced) circulations in complex terrain. Noting that more than 50% of the land surface qualifies as complex terrain, the contribution of mesoscale circulations is hypothesized to alleviate at least partly the uncertainty in the modeled land surface uptake. While atmospheric models at coarse resolution (e.g., for numerical weather prediction; also climate simulations) use a parameterization to account for momentum exchange due to subgrid-scale topography, no such additional exchange is presently taken into account for energy or mass. It is thus suggested that a corresponding parameterization should be developed in order to reduce the uncertainties in the global carbon budget.

The incorporation of mesoscale circulations would increase the accuracy of global (or regional) atmospheric carbon budget models—A finding that calls for more much-needed research.

Anthropogenic activities, such as combustion of fossil fuels plus cement production and land use changes, result in large CO2 emissions into Earth's atmosphere. The corresponding CO2 emission values for the year 2011 are 9.5 ± 0.5 and 0.9 ± 0.5 PgC yr−1, respectively (Le Quéré et al. 2013). About half of the manmade CO2 remaining in the atmosphere (the so-called airborne fraction) contributes to a steady increase in atmospheric CO2 concentration that strongly supports global warming (Peters et al. 2012). The rest is absorbed approximately in equal shares by the oceans and the land surface (Le Quéré et al. 2009, 2013; Raupach 2011). Whether oceans and land ecosystems will continue to substantially take up CO2, without which warming would proceed at double speed (Raupach 2011), is the topic of controversial discussions (Le Quéré 2010; Ballantyne et al. 2012). Current estimates of the terrestrial and oceanic sinks are associated with considerable uncertainties [35% and 20%, respectively, according to Le Quéré (2010), or 100% and 30%, respectively, according to Ciais et al. (2010)]. Together with the uncertainties of the other carbon budget components (in particular those of land use changes), this yields a residual (unexplained) carbon flux that is of similar magnitude as the oceanic or terrestrial sinks (Le Quéré et al. 2009; Raupach 2011).

The land surface exchange of CO2 with vegetation and soils bears by far the largest uncertainty in understanding the global carbon budget. This component is therefore often estimated as the residual from the others (e.g., Le Quéré et al. 2009, 2013; Peters et al. 2012). The comparison between CO2 land exchange estimated by the residual approach and the model-based bottom-up approach shows a considerable disagreement of up to ±2.1 PgC yr−1 (Le Quéré et al. 2009). On average, the residual approach implies a 0.7 PgC yr−1 more negative net land–atmosphere exchange (i.e., a larger sink) than global inversion estimates (Gurney and Eckels 2011; Le Quéré et al. 2009). Reducing these uncertainties is key to making more reliable projections of future climate change, as well as to monitoring the implementation of climate change mitigation policies (Le Quéré 2010; Raupach 2011).

Here, we argue that our inability to close the land CO2 balance is at least partly due to the fact that the modeling framework, on which the bottom-up estimation of carbon exchange is based, is valid only over flat terrain. Applying these concepts over complex terrain, which covers more than 50%1 of the land surface (Rotach et al. 2008), leads to an underestimation of the net exchange.

This is not only true for CO2, but also applicable to the surface exchange of energy, mass, and momentum. For the latter, developers of numerical weather prediction (NWP) models already in the 1980s introduced additional drag due to subgrid-scale topography in order to realistically reproduce the atmospheric momentum budget (Palmer et al. 1986).

Clearly, other processes, such as heterogeneity of the surface (even if the terrain is flat) or variable weather conditions (e.g., Hurwitz et al. 2004), also contribute to CO2 exchange and—when neglected—to uncertainty in modeling the carbon budget. These are, however, not necessarily systematic. Here we therefore focus on the contribution of complex topography, for which we will discuss the hypothesis that neglecting subgrid-scale contributions leads to a systematic underestimation of (modeled) net CO2 exchange.

ESTIMATING THE GLOBAL LAND CARBON BUDGET.

There are four main approaches to estimate the global land carbon budget (Xiao et al. 2012): (i) inventory based, (ii) ecosystem modeling, (iii) upscaling from “flux tower” measurements, and (iv) atmospheric inversion modeling. All four approaches have in common that they heavily rely on experimental data—that is, ecosystem carbon pool sizes, in situ CO2 concentrations (e.g., Chevallier et al. 2011), surface CO2 fluxes [flux towers from Flux Net work (FLUXNET); Baldocchi 2008], or from satellites (e.g., Chevallier et al. 2005)—and hence on a representative distribution of obser vationa l sites. Generally it is argued that the available sites (e.g., from the FLUXNET) represent the dominant biomes (Chevallier et al. 2005). While this is true (to the degree of affordable infrastructure), the sites are certainly not representative for different topographic terrain types. If it is argued—as we do here—that exchange characteristics between the land surface and the atmosphere are crucially dependent on the degree of complexity of the terrain, CO2 flux sites in truly complex terrain are certainly underrepresented. Figure 1 shows that more than 50% of the flux towers are located in “noncomplex terrain” and only a few remain if we look for sites in truly complex terrain (e.g., Sun et al. 2007; Wohlfahrt et al. 2008; Galvagno et al. 2013). The same is true for mean CO2 concentration observations (used in the atmospheric inversion approach) that are predominantly made over the oceans (Ciais et al. 2010).

Fig. 1.

Geographic locations of active (Aug 2012) FLUXNET towers (a) globally and (b) in Europe. Color coding shows the standard deviation of subgrid-scale topography with respect to a 20 km × 20 km grid. Some 57% of the FLUXNET sites (triangles) worldwide are located in noncomplex (non-HHF) terrain, if “complex” is defined as having a standard deviation in terrain height of greater than 50 m with respect to the 20 km × 20 km grid.

Fig. 1.

Geographic locations of active (Aug 2012) FLUXNET towers (a) globally and (b) in Europe. Color coding shows the standard deviation of subgrid-scale topography with respect to a 20 km × 20 km grid. Some 57% of the FLUXNET sites (triangles) worldwide are located in noncomplex (non-HHF) terrain, if “complex” is defined as having a standard deviation in terrain height of greater than 50 m with respect to the 20 km × 20 km grid.

At least the latter three of the above approaches to estimate land–atmosphere carbon exchange or budgets have furthermore in common that they, in one way or another, take into account the atmospheric boundary layer's efficiency to mix matter from and to the surface. While the FLUXNET community (and thus the upscaling approach) has at least started to address the problem of representativity in complex terrain (Baldocchi et al. 2000; Ciais et al. 2010)—even if “complex” still essentially refers to mildly undulating terrain—the associated upscaling or ecosystem modeling methods and likewise the meteorological component in the atmospheric inversion approach use a theoretical framework that has been developed under the assumption of stationary flow over horizontally homogeneous and flat surfaces (see sidebar on “Atmospheric boundary layer”). For a horizontal model resolution of 1°–2° (corresponding to some 100–200 km in midlatitudes), as is typical for global atmospheric inversion modeling (Ciais et al. 2010), most major terrain features are smoothed out to a degree that the assumption of “flat terrain” might even be defendable (in other words, even major mountain ridges appear as smooth hills at this resolution). If the missed subgrid-scale variability of topography, however, contributes to the exchange between the “complex surface” and the free troposphere—as it is argued below—then parameterizations in coarse-resolution models should take this additional exchange into account.

ATMOSPHERIC BOUNDARY LAYER

The atmospheric boundary layer (ABL) constitutes the lowest layer of the troposphere and thus the interface between Earth's surface and the atmosphere.

Because of friction and buoyancy effects, the flow becomes turbulent. The available radiation energy Q* is distributed into turbulent transport of sensible heat H and “latent heat”—that is, water vapor LvE and ground heat flux G. Momentum loss at the surface through friction is compensated for by turbulent transport of momentum M.

Magnitude and sign of turbulent transport and thus the efficiency of exchange between the surface and the free troposphere are largely determined by ABL stability (i.e., the daily cycle of solar radiation).

Theoretical understanding is provided by so-called similarity theory (Stull 1988) and models generally use local exchange parameterizations [e.g., according to Monin and Obukhov (1954) for the surface layer; i.e., the lowest 10% of the ABL].

Local turbulent exchange means that turbulent transport is proportional to the local gradient of the property to be transported: in the example, the turbulent flux of CO2 is downward since the mean concentration in the atmosphere is larger than that “at the surface”:

 
formula

where KCO2 is an exchange coefficient that is specified according to similarity theory.

Formulations of these relationships are based on the assumption of horizontal homogeneity and flat terrain (HHF).

In summary, if surfaces that are not horizontally homogeneous and flat (non-HHF) systematically contribute to land surface–atmosphere exchange, then the more statistically oriented approaches (inventory based, and data-driven upscaling; Xiao et al. 2012) suffer from a severe underrepresentation of sites in complex terrain and the approaches explicitly taking boundary layer dynamics into account will require a subgrid-scale parameterization in order to adequately represent complex terrain effects on the net surface exchange.

EXCHANGE OVER COMPLEX TOPOGRAPHY.

The near-surface flow over complex topography is intrinsically inhomogeneous through varying dynamical and thermal forcing (Rotach and Zardi 2007). Thermally, this leads to so-called mesoscale circulations (MSCs) as, for example, valley–plain or slope wind systems. On the spatial scale of an entire mountain ridge (several hundreds of kilometers) a “mountain–plain wind circulation” can be introduced, resulting in what is sometimes called “mountain venting.” In principle, numerical models can handle this situation with appropriate surface exchange parameterizations and, most importantly, sufficiently high spatial resolution. Global atmospheric NWP models presently have a horizontal resolution of at most about 16 km, thus leaving considerable terrain variability as “subgrid” over large parts of Earth's land surface. Simulation systems focusing on global climate typically have a (much) coarser resolution owing to the long integration times over many decades or even centuries.

Already in the adolescent days of NWP (when NWP resolution was about that of today's climate simulators), it was realized that turbulent exchange of momentum at the surface alone was not sufficient to realistically simulate the atmosphere's momentum balance (Palmer et al. 1986) and thus an “orographic drag parameterization” was introduced and such an additional parameterization is used in all current global models in one or the other form. The need for such a parameterization became obvious through too-strong simulated average zonal wind, especially in northern midlatitudes.

Noppel and Fiedler (2001) were arguably the first to propose that the subgrid-scale terrain variability not only affects the momentum budget but also the surface–atmosphere exchange of scalars (sensible heat in their case) in complex terrain and, therefore, would call for parameterization in coarse-resolution models. Recent simulations using an idealized valley configuration (Schmidli and Rotunno 2010, 2012) indeed demonstrated that thermal circulations decisively contribute to the heat budget of a valley and its surroundings.

Henne et al. (2004) used an “air mass budget approach” based on limited observational evidence to estimate the pollutant export from an alpine valley during daytime thermal wind conditions. They arrived at a factor of 2.5 enhancement when compared to a flat (average) atmospheric boundary layer (ABL) for a few sample days. In a later study, the same authors (Henne et al. 2005) extended the analysis to yield climatological evidence for enhanced moisture content (“elevated moisture layers”) in the lee of the Alps what they attributed to mountain venting. Based on the assessment of excess moisture in these elevated layers downwind of the Alps, they estimated substantial mountain-induced exchange of up to one-third of the boundary layer air per hour.

The most obvious dynamical process associated with thermal valley flows is convergence (divergence) due to geometrical or local effects, which leads to export (import) of mass (Fig. 2). Clearly, this “geometrical” exchange similarly occurs if the valley flow is dynamically forced (e.g., through large-scale synoptic pressure gradient). Cross-ridge flow (“flow over hills”) experiences a combined effect of redistribution of heat (correspondingly exchange of mass) through the interaction of the drag on the topography with the buoyancy field (Hunt et al. 1988).

Fig. 2.

Moisture flux into/out of the Riviera Valley in southern Switzerland for 2 days during Mesoscale Alpine Project (MAP) Riviera (Rotach et al. 2004). The black dashed line shows the total flux from high-resolution LES; the blue dashed line shows total flux a coarse model would see; and the solid lines show flow convergence–divergence (red), thermal MSC (green), turbulent exchange at the lid (purple). Redrawn from Weigel et al. (2007).

Fig. 2.

Moisture flux into/out of the Riviera Valley in southern Switzerland for 2 days during Mesoscale Alpine Project (MAP) Riviera (Rotach et al. 2004). The black dashed line shows the total flux from high-resolution LES; the blue dashed line shows total flux a coarse model would see; and the solid lines show flow convergence–divergence (red), thermal MSC (green), turbulent exchange at the lid (purple). Redrawn from Weigel et al. (2007).

Weigel et al. (2007) used high-resolution large-eddy simulation (LES; 350-m horizontal mesh size) to simulate these exchange processes for 3 days of a “pure” valley wind situation in an Alpine valley with water vapor as a tracer. In addition, they compared their results to “what a coarse model would see”—that is, a model (resolution) that does not resolve the topography. It should be noted that these are not only model-versus-model comparisons, since the results of the LES corresponded very well with a broad number of observations performed in the valley atmosphere (Chow et al. 2006; Weigel et al. 2006). Results show (Fig. 2) the following:

  • There is considerable exchange of mass (moisture in this case) between the valley atmosphere and the free troposphere that is missed by a model of coarse resolution.

  • The exchange is due to a mixture of dynamical and thermodynamical processes with flow-dependent contributions. This leads to a quite different temporal pattern between the actual (resolved) flux and that produced by a coarse model.

  • The actual (resolved) mass flux can be some 3 times larger than what a coarse-resolution model yields when summed over daytime hours in this case.

Hence, based on the few available case studies it appears that mass exchange between complex surfaces and the free troposphere is substantially altered when compared to HHF terrain as suggested by theoretical and idealized numerical modeling. Numerical models with coarse resolution are prone to miss substantial parts of the exchange in complex terrain.

CARBON EXCHANGE OVER COMPLEX TOPOGRAPHY.

First of all, it should be noted that the “carbon monitoring community” has started to recognize the problem of atmosphere–ecosystem exchange over complex terrain in the last decade or so. First, experimental studies have been conducted to address the impact of, for example, local advection on the total near-surface exchange [e.g., the Advection Experiment (ADVEX); Aubinet et al. 2010]. Here, we treat these local processes as the “surface source (sink) function,” which indeed requires additional experimental and conceptual efforts to represent the “true local flux.” The focus of the following discussion, however, will be on a larger spatial scale—that is, the mesoscale (usually defined as ranging from some 2 to 200 km)—adding another exchange mechanism between the “complex topography” and the free troposphere.

If effective mesoscale exchange of heat, momentum, and mass (water vapor) can be altered by a factor as large as 3 (i.e., >>100% sensitivity) over complex topography as reported above at least for particular atmospheric conditions, this should in principle also apply for other conservative tracers, such as CO2. The relative importance of the mesoscale enhancement, however, is likely to depend on the scalar source–sink characteristics—that is, the near-surface exchange that in turn is also subject to substantial uncertainty over complex terrain (see above). Unlike water vapor, which during the night exhibits a close to zero flux, the nighttime ecosystem–atmosphere exchange of CO2 can be of similar magnitude as compared to daytime, however with an opposite, positive sign (i.e., net emission). Whether the bidirectional flux of CO2 further aggravates the discrepancy between exchange in complex as opposed to HHF topography or possibly leads to compensating effects is largely unknown. Among the few available studies, Sun and De Wekker (2011) showed that the daytime mountain circulation provided an efficient vertical transport of near-surface nocturnal CO2-rich air from the plains. In the sidebar on “Highly idealized CO2 simulation in a valley,” some preliminary numerical simulations using an extremely idealized setup for both the terrain and the meteorological conditions, as well as for the CO2 exchange at the surface, are shown. They seem to confirm our hypothesis that the vertical exchange of a passive tracer like CO2 is altered over complex terrain when compared to a flat reference case.

Therefore, in order to properly simulate the net regional ecosystem–atmosphere exchange of CO2 over complex terrain, MSCs need to be reproduced—either through high-resolution modeling (e.g., Pérez-Landa et al. 2007; Pillai et al. 2011, for some pioneering examples) or, as suggested by Kretschmer et al. (2012), through introducing some “ad hoc correction” into the ABL scheme.

Here we argue that in complex terrain a substantial part of the vertical mixing is due to (thermo) dynamically induced MSCs. To the extent that these MSCs are largely determined by local turbulent surface exchange characteristics, they are certainly influenced by the models' turbulence (i.e., ABL) parameterizations. Until very high spatial resolution (i.e., subkilometer for most regions of complex terrain) can be afforded for CO2 budgeting, a subgrid-scale parameterization taking into account the effect of MSCs—similar to the “orographic drag parameterization” for momentum exchange in coarse-resolution atmospheric models—should be introduced.

Devising such a parameterization will require a combination of experimental and numerical modeling efforts. Long-term (as opposed to episodical; e.g., Sun et al. 2010) observations will be necessary to identify the relative importance of processes and corresponding meteorological conditions. Special emphasis will have to be given to stable (nighttime) stratification owing to the fact that CO2 exchange is also active during the night. Similar to the oro-graphic drag parameterizations (e.g., Stensrud 2012), high-resolution simulations using idealized terrain configurations will then yield an explicit formulation (e.g., Lott and Miller 1997) that can be validated on independent experimental data.

HIGHLY IDEALIZED CO2 SIMULATION IN A VALLEY

To test the present hypothesis concerning CO2 exchange in complex terrain, highly idealized simulations using the Weather Research and Forecasting model with Chemistry (WRF/Chem; Grell et al. 2005) at 1-km horizontal mesh size were performed. The topography corresponds to that used in an intercomparison study for mesoscale atmospheric models (Schmidli et al. 2011). Two idealized ridges of 100-km length and 1500-m height with a peak-to-peak lateral distance of 20 km are placed in a 120 km (east–west) × 200 km (north–south) domain. Thus, between the ridges, a valley (0.5-km half-width of the valley floor) is formed embedded in a plain [see Schmidli et al. (2011) for details]. Atmospheric CO2 concentrations in the valley atmosphere are evaluated in a 20 km × 20 km box between 20 and 40 km from the valley entrance up to ridge height and compared to a reference simulation (a 20 km × 20 km domain) with identical atmospheric forcing, which also corresponds to that used in Schmidli et al. (2011), but with flat terrain.

CO2 is initialized with a uniform background concentration of 380 ppmv throughout the domain. Ecosystem respiration is assumed at a constant rate of 10 µmol m−2 s−1, while gross photosynthesis is modeled at a constant rate of 25 µmol m−2 s−1 between 0600 UTC (corresponding to local time) and 1800 UTC, thus yielding a (extremely simplified) net “source function” Fs between +10 (nighttime) and −15 µmol m−2 s−1 (daytime). This source function is designed to correspond in the order of magnitude to the average (of 10 years) diurnal growing-season net CO2 exchange cycle at a FLUXNET site in an alpine valley (Wohlfahrt et al. 2008).

Results (for the second day of simulation; i.e., after a spinup time of 24 h) indicate that the CO2 concentration in the valley atmosphere shows a larger (as compared to the plain) amplitude and, in particular, an enhanced CO2 enrichment during the second part of the night as a consequence of trapping within the topography owing to local-scale downslope flow. The concentration differences between the respective “surface boxes” and those overlaying (“1.5–3 km”) indicate large differences in vertical exchange between the valley atmosphere and the plain. Because of the temporal asymmetry of the assumed CO2 flux at the surface (larger uptake during daytime than release during the night) over both surfaces, the mean concentrations decrease (dashed lines). Over the complex surface, however, the “atmospheric” concentration is always less than that over the plain, suggesting more effective vertical exchange due to MSCs. For water vapor, vertical exchange between the complex topography and the free troposphere is positive during the day and slightly negative during night (and the coarse-gridded model sees it positive all day long; Fig. 2). For CO2, on the other hand, the MSCs introduce a complicated local flow pattern that gives rise to modified exchange processes in the presence of complex topography.

Fig. SB2-1.

Day 2 of CO2 exchange in an idealized valley simulation. The blue lines show the mean concentration in the valley atmosphere (solid) and above (dashed), while the green lines show the mean CO2 concentration in the same height ranges, but over a plain. The black line shows the extremely idealized CO2 flux at the surface.

Fig. SB2-1.

Day 2 of CO2 exchange in an idealized valley simulation. The blue lines show the mean concentration in the valley atmosphere (solid) and above (dashed), while the green lines show the mean CO2 concentration in the same height ranges, but over a plain. The black line shows the extremely idealized CO2 flux at the surface.

If 10-km resolution is a reasonable target for future regional estimates of the carbon budget (e.g., Pillai et al. 2011), then most of the MSCs will remain sub-grid scale. With more than 50% of the land surface essentially consisting of complex terrain and a contribution to vertical exchange of MSCs comparable in magnitude to that of ABL mixing, it is likely that proper treatment of the former can alleviate substantial parts of the uncertainty associated with the land sink in the global carbon budget.

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Footnotes

1

In fact, the cited reference even puts it to “70% complex terrain.” Since our own estimate based on the number of FLUXNET sites in terrain with a standard deviation in terrain height of greater than 50 m with respect to a 20 km × 20 km grid (see Fig. 1) yields 57%, we use the more conservative “more than 50%.”