Dalton medal 2018 went to Gaby Katul

Gaby Katul (GS) is one of the most prominent hydrologists around the world (if this statement can have a meaning): his production is extremely high both in quality and quantity and for any is a lighthouse to follow. His production is especially directed to study turbulence and eco-hydrology. Therefore there is no doubt that his Dalton medal, received this week at EGU general assembly is well deserved. I could not be in Wien this year. However, I asked Gaby if he can send to me his presentation that all the present qualified as outstanding.

Please clicking on the above figure access and enjoy it.

Monday's discussion on evapotranspiration - Part I - The vapor budget

Last Monday at lunch, I and my students discussed about evapotranspiration. I already talk about it in various comments here. However, the starting point was the impression, coming from one of my student that the topic of transpiration is still in its infancy. I agree with him and I offered my synthesis.

1. In hydrology we use Dalton’s law (here, slide 21) or the derived equations named Penman-Monteith and Priestley Taylor (forgetting all the empirical formulas).
2. Dalton’s law  puts together, diffusive vapor flux, vapor storage and turbulent transport.
3. We should have a water vapor budget equation instead, written for some control volume where all the stuff is at its right place.

There is no difficult to recognize that control volume is limited in our case by the open atmosphere and the surfaces that are emitting vapor as consequence of  their thermodynamics. There is also no difficult to recognize that such limiting surfaces can be very complicate, as those of a canopy, for instance, which is also varying in shape and form with time. Out of these surfaces comes a vapor flux which is dependent on the thermodynamics and physiology existing below them, the holes in number and distribution through which the vapor is emitted, the water availability (and dynamics) in the storage below the surface and, last but not least, the vapor content in the control volume which, as in Dalton’s law commands the driving force.

It is not easy actually to account well for all of these factors. We can, maybe, for a single leaf. It is more complicate for the canopy of a single tree. It is even more difficult for a forest. Unless some goddess  acts to simplify the vapor budget, over the  billions of details, and reduces all to some tretable statistics (we can call this statistics the Holy Grail of evapotranspiration - or the whole Hydrology itself) 

Assume we can deal with it, and  we have the fluxes right. Then the vapor budget seems cristalline simple to obtain, the variation of vapor in the control volume is given by the incoming vapor flux, minus the outcoming vapor flux, minus, in case, the vapor condensation. The good old mass conservation. Unfortunately, also the output flux is not that easy to estimate, because the transport agent is atmospheric turbulence, which is affected by the non-linearities of Navier-Stokes (NSeq) equations, and its interactions  with the complex boundary represented by the terrain/vegetation surfaces. All of this involves a myriads of spatio-temporal scales and degrees of freedom which are not easy to simplify. 

Therefore, literature treats the evaporation as a flux, forgets the real mechanics of fluxes and simplifies turbulence according to similarity theory, essentially due to Prandtl work at the beginning of the last century with the additions of Monin-Obukhov theory.  However, in real cases, the hypotheses of similarity theory are easily broken and the velocities distributions are rarely those expected. All of this makes largely unreliable the transport theory applied in a pedestrian way (as we do). See References below and here a quite informed lecture to get a deeper view.

Summarizing,  the transport is complicate because turbulence interacting with complex surfaces is complicate (probably would be better to say "complex"). Numerically is a problem whose solution is still open (a full branch of science, indeed), and we do not know how to model the rustling of leaves (“… and the icy cool of the far, far north, with rustling cedars and pines). 
In fact, the models we use for what we usually call potential evapotranspiration, are an extreme simplification of the wishlist.

Finally, the above picture forgets the role of air and soil temperature (thermodynamics). We were thinking, in fact, only to the mass budget and the momentum budget (the latter is what NSeq is),  but there is no doubt that evaporation and transpiration are commanded also, and in many ways, by the energy budget. Turbulence itself is modified by temperature gradients, but also water vapor tension which concurs to establish the quantity of water vapor ready to be transported at vapor emitting surfaces. A good news is that energy is conserved as well, but this conservation includes the phase of the matter transported (the so-called latent heat). So necessarily, in relevant hydrological cases, we have to solve besides the mass and momentun conservation, the energy conservation itself.

Looking for simplified versions of mass, momentum and energy budget, would require a major rethinking of all the derivations and new impulse to proper measurements that, however, some authors already started (e.g., for instance Schymansky, Or and coworkers,  here).

References

• Albertson, J. D., Katul, G. G., & Wiber, P. (2001). Relative importance of local and regional controls on coupled water, carbon, and energy fluxes. Advances in Water Resources, 24, 1103–1118.
• Böhm, M., Finnigan, J. J., Raupach, M. R., & Hughes, D. (2012). Turbulence Structure Within and Above a Canopy of Bluff Elements. Boundary-Layer Meteorology, 146(3), 393–419. http://doi.org/10.1007/s10546-012-9770-1
• Denmead, O. T., & Bradley, E. F. (2017). On Scalar Transport in Plant Canopies. Irrigation Science, 8, 131–149.
• Dwyer, M. J., Patton, E. G., & Shaw, R. H. (1997). Turbulence kinetic energy budgets from a large-eddy simulation of airflow above and within a forest canopy. Boundary-Layer Meteorology, 84, 23–43.
• Finnigan, J. J. (2000). Turbulence in plant canopies. Annual Review of Fluid. Mechanics, 32, 519–571.
• Hollinger, D. Y., Kelliher, F. M., Schulze, S.-D., & Köstner, B. M. M. (1994). Coupling of tree transpiration  to atmospheric turbulence. Nature, 371, 60–62.
• Katul, G., Geron, C. D., Hsieh, C.-I., Vidakovic, B., & Guenther, A. B. (1998). Active turbulence and scalar transort near the forest-atmosphere interface. Journal of Applied Meteorology and Climatology, 1533–1546.
• Katul, G. G., Mahrt, L., Poggi, D., & Sanz, C. (2004). ONE- and TWO-Equation Models for Canopy Turbulence. Boundary-Layer Meteorology, 113(1), 81–109. http://doi.org/10.1023/B:BOUN.0000037333.48760.e5
• Katul, G. G., Cava, D., Siquera, M., & Poggi, D. (2013). Scalar Turbulence within the Canopy Sublayer. In J. G. Venditti, J. L. Best, M. Church, & R. J. Hardy (Eds.), Coherent Flow Structures at Earths Surface (pp. 73–95). John Wiley and Sons.
• Raupach, M. R., & Thom, A. S. (1981). Turbulence in and above plant canopies. Annual Review of Fluid. Mechanics, 13, 97–129.
• Raupach, M. R., Finnigan, J. J., & Brunet, Y. (1996). Coherent eddied and turbulence in vegetation canopies: the myxing -layer analogy. Boundary-Layer Meteorology, 78, 351–382.
• Schymanski, S. J., Or, D., & Zwieniecki, M. (2013). Stomatal Control and Leaf Thermal and Hydraulic Capacitances under Rapid Environmental Fluctuations. PLoS ONE, 8(1), e54231–16. http://doi.org/10.1371/journal.pone.0054231
• Schymanski, S. J., & Or, D. (2017). Leaf-scale experiments reveal an important omission in the Penman–Monteith equation. Hydrology and Earth System Sciences, 21(2), 685–706. http://doi.org/10.5194/hess-21-685-2017
• Staebler, R. M., Akingunola, A., Zhang, J., McLinden, C., Kharol, S. K., Pabla, B., et al. (2017). The effects of forest canopy shading and turbulence on boundary layer ozone. Nature Communications, 8, 1–14. http://doi.org/10.1038/ncomms15243
• Pan, Y., Chamecki, M., & Isard, S. A. (2014). Large-eddy simulation of turbulence and particle dispersion inside the canopy roughness sublayer. Journal of Fluid Mechanics, 753, 499–534. http://doi.org/10.1017/jfm.2014.379

WRF and LES

Dino Zardi sent to me and some other colleagues, a small synthesis WRF and LES which you can find below

Introduction to Large-Eddy Simulations (LES) with the Weather Research and Forecasting (WRF) model,

By Lorenzo Giovannini

The Weather Research and Forecasting model (WRF, Skamarock et al., 2008) is a numerical weather prediction model used for both operational and research applications at scales ranging from regional to large-eddy simulations (LES). Several planetary boundary layer (PBL) parameterization choices are available in WRF, which are intended for use in cases in which the horizontal grid resolution does not enable the representation of three-dimensional turbulence (resolution coarser than 1 km). For simulations requiring higher resolution to capture evolving three-dimensional turbulence or flows in complex terrain, a LES is more appropriate. LESs explicitly resolve large turbulent eddies, whereassome portion of the turbulence (below the filter imposed by the computational grid) must still be modeled using a sub-grid scale (SGS) model. There are different options in WRF to model SGS turbulence. In the first option eddy viscosity coefficients are determined using a 3D Smagorinsky turbulence closure from deformation and stability, whereas in the second option a prognostic equation for turbulent kinetic energy (TKE) is used, and eddy viscosity coefficients are based on TKE. Finally, another approach to model SGS stresses in WRF is the nonlinear backscatter and anisotropy (NBA) model of Kosović (1997), (see Skamarock et al., 2008 and Kirkil et al. 2012 for further details). 

WRF (in LES mode) calculates horizontal and vertical diffusion in physical space.

Several issues arise when performing LES simulations, and in particular LES simulations nested in mesoscale domains, for which the flow contains essentially no resolved turbulence. To this regard several authors provided recommendations that should be followed. As discussed in Mirocha et al. (2010), the aspect ratio, or ratio of the horizontal grid size to the vertical grid size, can strongly impact the accuracy of an LES. They found that aspect ratios between 2 and 4 are ideal for neutral boundary layer flows over a flat plate, but the authors pointed out that different results may be expected in situations with more complex terrain. Then it must be remarked that the grid spacing used in the LES domain must be << than the energy-containing eddies, to resolve large eddies. This recommendation may be a constraint in stable atmospheric boundary layer (ABL), when the expected large eddies are of the order of 10 m. Finally, one of the most important issues arising when coupling an LES with a mesoscale model is the spin-up of turbulence at inflow boundaries, as it is discussed also below.

Moeng et al. (2007) pointed out that WRF can be a reliable tool to perform real-world LES. In fact WRF uses real world terrain and land use data as well as real atmospheric conditions. In order to test the performance of the two-way nesting capability for LES in WRF, the authors performed LES-within LES simulations, where one LES was nested within the other. Promising results were obtained with the alteration of the SGS stress model, the careful selection of the nest size, and the use of a relaxation zone close to nest edges. A similar investigation was carried out by Mirocha et al. (2013), who in particular analyzed errors arising at nest interfaces by changes in mesh spacing from a coarser domain to a finer domain, using different SGS models. They found significant discrepancies in many parameters between the nested simulation and a single-domain simulation, concluding that extensive buffer zones, whose extension depends on the SGS model used, are required for equilibration of flow parameters on nested domains. Moreover the authors stated that vertical nesting, which is not present inthe current WRF release, would likely improve the results. Both Moeng et al. (2007) and Mirocha et al. (2013) pointed out that nesting an LES inside a mesoscale model would pose a much bigger challenge than nesting a finer LES within a coarser LES, due to the different ways to treat turbulent motions and due to turbulence spin-up problems when prescribing an inflow into the LES domain from the mesoscale model, whose flow is laminar by construction.

This problem was analyzed in detail by Mirocha et al. (2014), who highlighted that, despite mechanisms for downscaling from mesoscale to LES are present in several models (including WRF), little information exists regarding conditions under which this approach is appropriate. In particular the authors compared the development of turbulence between LES nested within mesoscale domains and non-nested LES. They found that, under relatively weak forcing conditions, turbulence generally develops too slowly in LES nested within mesoscale domains. Moreover they found that nesting a fine LES domain within a coarse LES gave better results than nesting it directly within the mesoscale model, as turbulence can begin to develop in the coarser LES.

Applications of nested LES within mesoscale domains using WRF in real test cases are provided byLiu et al. (2011) and Talbot et al. (2012). Liu et al. (2011) tested WRF-LES in a nested mesoscale-LES configuration for wind power applications down to a resolution of ~100 m. Four coarse domains were run with mesoscale model settings and continuous data assimilation, while two finer mesh domains were run with LES model settings. The model results, compared with wind farm anemometer measurements, were found to capture many intra-farm wind features and microscale flows. Talbot et al. (2013) tested the skills of WRF-LES in nested real-world simulations using six nested domains, with a resolution of 50 m in the inner domain. The three largest domains were run with mesoscale model settings, while the three inner domains were run with LES model settings. The performance of the model was rather poor in simulating wind speed and direction, while better results were found with respect to air temperature. Several sensitivity tests highlighted that the most important controls on model results were the meteorological forcing data, which are downscaled by WRF and significantly impact also the smaller domains. In particular the errors in wind speed and direction in the mesoscale simulations were largely passed on to all LESs, which were unable to correct them. On the other hand it was found that the mesoscale horizontal turbulence closure and the LES SGS model had a relatively small impact on results. Finally increased resolution improved the ability of the model to capture surface variability, but did not improve regionally averaged results or bulk atmospheric boundary layer properties.

Kirkil G, Mirocha J, Bou-Zeid E, Chow FK, Kosović B. 2012. Implementation and evaluation of dynamic subfilter-scale stress models for large-eddy simulation using WRF. Monthly Weather Review140: 266-284.

Kosović B. 1997. Subgrid-scale modeling for the large-eddy simulation of high-Reynolds-number boundary layers. J. Fluid Mech. 336: 151-182.

Liu Y, Warner T, Liu Y, Vincent C, Wu W, Mahoney B, Swerdlin S, Parks K, Boehnert J. 2011. Simultaneous nested modeling from the synoptic scale to the LES scale for wind energy applications.Journal of Wind Engineering and Industrial Aerodynamics 99: 308-319.

Mirocha JD, Lundquist K, Kosović B. 2010. Implementation of a non-linear subfilter turbulence stress model for large-eddy simulation in the advanced research WRF model. Monthly Weather Review 138:4212-4228.

Mirocha JD, Kirkil G, Bou-Zeid E, Chow FK, Kosović B. 2013. Transition and equilibrium of neutral atmospheric boundary layer flow in one-way nested large-eddy simulations using the Weather Research and Forecasting model, Monthly Weather Review 141: 918-940.

Mirocha JD, Kosović B, Kirkil G. 2014. Resolved turbulence characteristics in large-eddy simulations nested within mesoscale simulations using the Weather Research and Forecasting model. Monthly Weather Review 142: 806-831.

Moeng C-H, Dudhia J, Klemp J, Sullivan P. 2007. Examining two-way grid nesting for large eddy simulation of the PBL using the WRF model. Monthly Weather Review 135: 2295-2311.

Skamarock WC, Klemp JB, Dudhia J, Gill DO, Barker DM, Duda MG, Huang X-Y, Wang W, Powers JG. 2008. A description of the advanced research WRF version 3. NCAR Technical Note TN-475+STR, 125.

Talbot C, Bou-Zeid E, Smith J. 2012. Nested mesoscale large-eddy simulations with WRF: performance in real test cases. Journal of Hydrometeorology 13: 1421-1441.

Turbulence

Want to start with turbulence ? Start first with fluid dynamics:

• George Batchelor [Old, but classics]
• An Introduction to Fluid Dynamics ( I have the feeling to be able to do better in some parts - but without trying it how one can say ?)

Some freely available resources:

• Stephan Childress:  Lectures on Fluid Dynamics
• Richard Fitzpatrick: Fluid Mechanics

Regarding Turbulence itself, I would start from on-line resources, and the first reading could easily be:

• J. M. McDonough - Introductory lectures on Turbulence

which could continue continue with some selected topics by

• James C. McWilliams - Lectures on Turbulences

If I have to choose just other three references, I would select (in brackets [ ] Shalizi's -see below-comments, in  ( ) my comments) :

• George Batchelor [Old, but classics]
  • The Theory of Homogeneous Turbulence (obsolete mathematics but a clear view of the problem)
• Uriel Frisch, Turbulence: The Legacy of A. N. Kolmogorov [An excellent introduction, very strong on defending Kolmogorov's work from misunderstandings and invalid criticisms.] One paper that summarizes Frisch view is here. 

and a different, but, in my opinion in the long-term the winning perspective:

• V. I. Arnol'd, Topological Methods in Hydrodynamics

Of the latter this paper by David Ruelle can be a complement.

• Jensen, Paladin and Vulpiani, Dynamical systems approach to turbulence is a complementary approach to remind.

Also the old classic book by Tennekes and Lumley  is available, legally or not, on-line, here.

Other stuff  which is intriguing me, are random cascades (and turbulence), a topic that I came to know through the work of Ed Waymire, and that you can come close by reading:

• Peckham, S. and E. Waymire, The simmetry of turbulence, 1996
• Birnir, The Kolmogorov, Obukhov, She, Leveque scaling in turbulence, 2013

Also interesting is the works on rinormalization group and turbulences of which this is a google synthesis.

Finally, you can look at the Cosma Shalizi's bibliography. Huge and overwhelming indeed, it was the starting point of this my own post.