Atmospheric Sciences

surface layer

A simple model of convection to study the atmospheric surface layer

A simple model of convection to study the atmospheric surface layer

Since being immortalised in Hollywood film, “the butterfly effect” has become a commonplace concept, despite its obscure origins. Its name derives from an object known as the Lorenz attractor, which has the form of a pair of butterfly wings (Fig. 1). It is a portrait of chaos, the underlying principle hindering long-term weather prediction: just a small change in initial conditions leads to vastly different outcomes in the long run.

Figure 1: The Lorenz attractor.

The three-equation system that gives rise to the Lorenz attractor is often referred to as a simple model of atmospheric convection, yet amongst the atmospheric science community, attention is rarely paid to the original fluid flow that the Lorenz equations describe. Consisting of a fluid layer heated from below and cooled from above, Rayleigh-Bénard convection (Fig. 2) is a hallmark flow beloved by fluid dynamicists and mathematicians alike for its analytical tractability, yet rich behaviour. It is often cited as being of immediate relevance for many geophysical and astrophysical flows [1]. The success of turbulent Rayleigh-Bénard convection in leading to our understanding of chaos, as exemplified by the Lorenz attractor, suggests the enticing possibility of gaining other key conceptual insights into the behaviour of the Earth’s atmosphere through the use of this simple convective system.


Figure 2: Schematic of Rayleigh-Bénard convection.

In a recent study [2] we explored this potential by investigating to what extent turbulent Rayleigh-Bénard convection serves as an analogue of the daytime atmospheric boundary layer, also known as the convective boundary layer (CBL). In particular, we investigated whether statistical properties in the surface layer develop with height in a similar way in both systems. The surface layer is typically just a few tens of metres thick, but due to the strong turbulent mixing that takes place there, it is of primary importance for the development of the boundary layer. The surface boundary conditions of Rayleigh-Bénard convection and the CBL are the same, which might lead one to think that surface-layer properties should behave similarly in both cases. However, differences in the upper boundary conditions between the two systems modify the large-scale circulations that appear in both systems and this may have an impact in the surface layer.

Indeed, despite the much-heralded relevance of Rayleigh-Bénard convection to geophysical flows, we find that its cooled upper plate modifies the large-scale structures in such a way that it substantially alters the behaviour of near-surface properties compared to the CBL. In particular, the downdrafts in Rayleigh-Bénard convection are considerably stronger than in the CBL and their impingement into the surface layer changes how velocity and temperature statistics develop with height.

However, we also find that just an incremental change to the upper boundary condition of Rayleigh-Bénard convection is needed to closely match surface-layer statistics in the CBL. If instead of being cooled, the upper plate is made adiabatic, i.e. no heat is allowed to escape (Fig. 3), the influence of the strong, cold downdrafts is removed, resulting in surface-layer similarity between this modified version of Rayleigh-Bénard convection and the CBL. Rayleigh-Bénard convection with an adiabatic top lid has the advantage that it is a simpler experimental set-up than the CBL and provides a longer statistically steady state, allowing for greater statistical convergence to be achieved through long-time averaging.

Figure 3: Schematic of the modifed version of Rayleigh-Bénard convection with an adiabatic top lid.

In the long term, the classical Rayleigh-Bénard system will continue to serve as a paradigm for studies of natural convection, though we are increasingly beginning to see that its practical application to geophysical and astrophysical [3] flows may not be as straightforward as past literature seems to suggest.


[1] A. Pandey, J. Scheel, and J. Schumacher.  Turbulent superstructures in Rayleigh-Bénard convection.Nature Communications, 9:2118, 2018.

[2] K.  Fodor,  JP  Mellado,  and  M.  Wilczek.   On the  Role  of  Large-Scale Updrafts and Downdrafts in Deviations From Monin-Obukhov Similarity Theory  in  Free  Convection. Boundary-Layer Meteorology,  2019.

[3] F. Wilczynski, D. Hughes, S. Van Loo, W. Arter, and F. Militello.  Stability  of  scrape-off  layer  plasma:  a  modified  Rayleigh-Bénard  problem. Physics of Plasmas, 26:022510, 2019.

Edited by Dasaraden Mauree

 Bettina DialloKatherine Fodor is a PhD. candidate at the Max Planck Institute for Meteorology in Hamburg, Germany. She uses very high resolution computer simulations to study turbulence in the atmosphere. In particular, her research concerns interactions between large-scale structures and small-scale turbulence. You can find her on Twitter @FodorKatherine where, in addition to science, she also tweets about cycling.”



How can we use meteorological models to improve building energy simulations?

How can we use meteorological models to improve building energy simulations?

Climate change is calling for various and multiple approaches in the adaptation of cities and mitigation of the coming changes. Because buildings (residential and commercial) are responsible of about 40% of energy consumption, it is necessary to build more energy efficient ones, to decrease their contribution to greenhouse gas emissions.

But what is the relation with the atmosphere. It is two folds: firstly, in a previous post, I have already described what is the impact of the buildings / obstacles on the air flow and on the air temperature. Secondly, the fact that the climate or surrounding environment is influenced, there will be a significant change in the energy consumption of these buildings.  Currently, building energy simulation tool are using data usually gathered outside of the city and hence not representative of the local context. Thus it is crucial to be able to have necessary tools that capture both the dynamics of the atmosphere and also those of a building to design better and more sustainable urban areas.

In the present work, we have brought these two disciplines together by developing a multi-scale model. On the one side, a meteorological model, the Canopy Interface Model (CIM), was developed to obtain high resolution vertical profile of wind speed, direction and air temperature. On the other hand, an energy modelling tool, CitySim, is used to evaluate the energy use of the buildings as well as the irradiation reaching the buildings.

With this coupling methodology setup we have applied it on the EPFL campus, in Switzerland.  We have compared the modelling results with data collected on the EPFL campus for the year 2015. The results show that the coupling lead to a computation of the meteorological variables that are in very good agreement. However, we noted that for the wind speed at 2m, there is still some underestimation of the wind speed. One of the reason for this is that the wind speed close to the ground is very low and there is a higher variability at this height.

Comparison of the wind speed (left) and air temperature (right) at 2m (top) and 12m (bottom).

We intend to improve this by developing new parameterization in the future for the wind speed in an urban context by using data currently being acquired in the framework of the MoTUS project. One surprising result from this part of the study, is the appearance inside of an urban setup of a phenomena call Cold Air Pools which is very typical of valleys. The reason for this is the lack of irradiation reaching the surface inside of dense urban parts.

Furthermore, we have seen some interesting behaviour in the campus for some particular buildings such as the Rolex Learning Center. Buildings with different forms and configuration, reacted very differently with the local and standard dataset. We designed a series of additional simulation using multiple building configuration and conducted a sensitivity analysis in order to define which parameters between the wind speed and the air temperature had a more significant impact on the heating demand (see Figure 1). We showed that the impact of a reduction of 1°C was more important than a reduction of 1m s-1.

Figure 1. Heating demand of the five selected urban configurations (black dots), as function of the variation by +1°C (red dots) and -1°C (blue dots) of the air temperature, and by +1.5 m s-1 (violet dots) and -1.5 m s-1 (orange dots).

Finally, we also analysed the energy consumption of the whole EPFL campus. When using standard data, the difference between the simulated and measured demand was around 15%. If localized weather data was used, the difference was decreased to 8%. We have thus been able to reduce the uncertainty of the data by 2. The use of local data can hence improve the estimation of building energy use and will hence be quite important when building become more and more efficient.

Reference / datasets

The paper (Mauree et al., Multi-scale modelling to evaluate building energy consumption at the neighbourhood scale, PLOS One, 2017) can be accessed here and data needed to reproduce the experiment are also available on Zenodo.