Intermittent turbulence and oscillations in the stable boundary layer over land

As the title of this thesis indicates, our main subject of interest is: "Intermittent turbulence and oscillation in the stable boundary layer over land". As such, this theme connects the different chapters. Here, intermittent turbulence is defined as a sequence of events were 'burst' of increased turbulence activity are followed by relatively quiet periods with low turbulence levels. This intermittent turbulence affects the mean structure of the SBL, in a sense that it may cause alternations on the nocturnal evolution of wind speed and temperature. In this way the time series of these quantities may show an oscillatory-type of behavior, referring to the title. Intermittency is commonly observed, especially in conditions of strong stratification. As such, several observed examples of this intermittent behavior are given in this thesis (chapter 3 and 4). Despite of the fact that it is ubiquitous relatively is known about intermittency: e.g. what physical mechanism causes intermittency? What are its typical statistical characteristics (e.g. regarding time-scales and amplitudes of the turbulent events)? Under what conditions can we expect intermittency to occur?

From a number of studies with atmospheric column models (e.g. Welch et al., 1986; Lin, 1990, Revelle, 1993; Vukelic and Cuxart, 2000) it appears that an intermittent behavior of turbulence is found in some specific parameter ranges. However, from these studies no general picture explaining the essential physics behind this behavior is available. Furthermore, some of these studies (e.g. Lin, 1990, Revelle, 1993) indicate that different regimes are simulated upon varying the pressure gradient: besides the intermittent regime two non-intermittent regimes emerge. From an observational point of view also, the existence of non-intermittent regimes (e.g. the continuous turbulent regime) is well known. On the other hand, it is not clear what external conditions cause the stable boundary layer to end up in one regime or another.

The large number of unanswered questions, about the intermittency phenomenon in particular and stable boundary layer dynamics in general, largely motivated the present work. In relation to the problems posed above, the following research questions are addressed in this thesis:

1. - What is the physical essence of this intermittent behaviour?

   - Is it possible to simulate both intermittent and non-intermittent regimes with a simple model?

2. - What external forcing parameters control the transitions between the different regimes?

   - Can we predict the occurrence of intermittent and non-intermittent regimes?

3. - What regimes are actually observed in the field? Under which conditions do they occur?

The present work consists of three parts: the first part is a numerical study (chapter 2), the second part an analytical study (chapter 3) and the third part is an observational study (chapter 4).

The study focuses on an intermittency mechanism first qualitatively described by Turner (1973) and Businger (1973): on clear nights over land in presence of weak winds, strong surface radiation may built up a strong surface inversion, such that turbulence is suppressed effectively. This causes the atmosphere to decouple from the underlying surface. Soon, however, due to the reduced friction, the air in the lower atmosphere will be accelerated by the omnipresent pressure force, until shear is strong enough to break through the stratification. Because of this mixing, shear is reduced largely and soon a new stratification is built up by surface cooling. Thus, the situation has returned to its 'initial' state and the mechanism starts over again, causing intermittent bursts of turbulence.

In chapter 2 it is shown that the essence of this intermittency mechanism can be captured by a 1D bulk model consisting of three coupled nonlinear differential equations. According to the authors, the bulk model considers the essential elements of the SBL: surface cooling by longwave radiation, supply of mechanical energy by the synoptic pressure gradient, and the limiting effect of stratification on mixing efficiency. In the simplified model structure only direct interaction of the lower atmosphere (first tens of meters) with the vegetation surface was considered, with no interaction with the air aloft. Consequently, this type of assumptions may limit the generality of the results.

It appears that this bulk model is able to mimic the intermittent behavior described above. Surprisingly (in view of model simplicity), model simulations predict both intermittent and non-intermittent SBL to occur for different external forcings, confirming the results of others with more detailed model configurations (e.g. Lin, 1990, Revelle, 1993). It appears that three regimes occur (two non-intermittent and one intermittent) when the pressure gradient is varied.

Model results show that intermittent turbulence is most likely to occur over land surfaces with low vegetation under clear sky conditions in presence of a low synoptical pressure gradient. The results indicate that the existence of a vegetation layer has a strong influence on intermittency dynamics: due to its small heat capacity, the vegetation temperature is able to respond quickly to rapid changing conditions. This, in turn, affects the stability of the lower atmosphere, causing an important feedback mechanism (see also: chapter 4). In addition it is found that intermittent behavior in SBL models occurs for various first-order closure schemes with different stability functions (as in Derbyshire, 1999). On the other hand we find that 'broad tail' stability functions that allow turbulent transport beyond the critical Richardson number effectively suppress intermittent/oscillatory behavior. Currently, these types of broad tail stability functions are often used in numerical weather prediction to prevent excessive SBL cooling in very stable conditions. Furthermore it is noted that, strictly speaking, time-averaged flux-profile relationships will not be valid in intermittent flows. In those conditions, average flux-profile relations cannot be unique due to their nonlinear nature.

The advantage of using a simplified SBL model, as proposed in chapter 2, is that it allows an analytical study of the system. Such analytical study is presented in chapter 3, were the governing equations of the bulk model are studied from a system dynamics point of view. In this way the transition between the different flow regimes is identified as a Hopf bifurcation. At the Hopf bifurcation point the stability of the equilibrium solution of the system changes such that a stable non-oscillatory solution alters in an unstable oscillatory solution (or vice versa). This property is used to derive a dimensionless parameter (denoted as, which is a function of external forcing parameters such as the pressure gradient and the radiative forcing, and of local parameters such as the aerodynamic roughness, heat capacity and bulk conductivity of the vegetation layer. With this dimensionless parameter the equilibrium behavior of the system (i.e. intermittent or non-intermittent) can be predicted exactly. As such this parameter is proposed as a classification tool to predict SBL regimes. The proposed classification parameter provides different information than classical parameters such as z/L and Ri. The main difference lies in the fact that theconsiders the stability of the system as a whole, including feed-backs from the turbulence-, soil heat flux-, and the radiation scheme, whereas z/L and Ri are scaling parameters for turbulence only. Becausehas a rather complicated structure, a less exact but simpler stability criterion is also derived, based on a fixed shear criterion for instability (Derbyshire, 1999). This, more practical criterion allows a clear physical interpretation. It is found that the main cause of instability is the positive feedback between stratification and mixing which occurs under strong stratified conditions. Furthermore it is shown that the heat exchange due to longwave radiation (outside the atmospheric window region) and by the soil heat flux imply strong negative feedbacks counteracting instability. According to the simplified criterion, theparameter can be approximated by two dimensionless groups: a bulk Richardson number and a so-called partitioning parameter. The latter is interpreted as the ratio of the summed radiative and soil heat exchange coefficient compared to the exchange coefficient for turbulent heat transport (or, alternatively, the ratio of fluxes). As such, this partitioning parameter represents the competition between the positive and negative feed-backs described above.

In chapter 4 SBL classification is studied from an observational point of view. In this chapter observations of the extensive CASES99 field experiment are presented (CASES: Cooperative Atmospheric Surface-Exchange Study). This field experiment, carried out by various groups from the U.S. and Europe, was specially designed to quantify the physical characteristics of the stable boundary layer over land, with a variety of observational tools. It took place in Kansas (U.S.) over a relatively flat area with dry, open prairie-grass, and lasted for a whole month (Oct. 1999), under various meteorological conditions. This makes the experiment very suitable for studying the different SBL regimes in relation to external forcings.

In chapter 4, first a classification of stable boundary layer regimes is presented based on time-series observations of near surface turbulence during CASES99. It is found that the different nights can be divided in three subclasses: a turbulent regime, an intermittent regime and a radiative regime. The existence of these three regimes is in agreement with the theoretical findings of chapter 2 and 3.

Secondly, this classification based on flux time series is compared with the theoretical predictions using(based on external parameters). To this end, for the CASES99 nights, thisis evaluated from a detailed analysis of the available data. Such evaluation from real data is not a trivial task, due to the number of assumptions in the equations on whichis based (e.g. the estimation of an effective value for the pressure gradient). The comparison between the theoretical predictions and the actual observed time-series shows generally good agreement. Also, the results are robust and discriminative in a qualitative sense. As such, it is e.g. shown that intermittent turbulence often occurs in clear sky conditions with a moderately weak (effective) pressure gradient. Similarly, in clear sky conditions, radiative and continuous turbulent regimes occur during conditions of very weak pressure gradients and strong pressure gradients respectively. This robustness is explained from the main ingredients of the mechanism described in chapter 2. On the other hand, the quantitative features of the theoreticalclassification are rather sensitive to (often uncertain) local parameter estimations, such as the bulk heat conductance of the vegetation layer. Due to this sensitivity, the relative value offor a certain night compared to other nights at the same location, provides more information about the SBL regime to be expected than a singlevalue by itself.

As a practical test case also the simplified criterion of chapter 3 is applied to the CASES99 data set. The approximate parameter shows less discriminative than the originalparameter: although the extreme cases are predicted correctly, more subtle cases showed to be less decisive or even incorrect. This is probably caused by the neglection of important feed-backs between wind shear and stratification in the momentum and heat budget equations. Thus apart from its clear conceptual value (chapter 4) its practical value is limited to more extreme cases.

Generally, we reflect that the analytical approach in this thesis, using a truncated set of equations, has clear advantages: e.g. internal relations between various processes can be made explicit, and equilibrium system behaviour can be expressed a priori in terms of the external forcing parameters. As such, this type of system analysis provides a fruitful way for continuation of the present research on SBL dynamics. Additionally, there is a need for detailed studies on the instability mechanisms that may generate intermittent bursts, using more complex model configurations with higher resolution and less strict assumptions. Such models are useful in simulating individual bursting events selected from observational case-studies. Also, as a continuation of the present observational work, it is interesting to test the proposed classification under different climatological conditions. In this observational respect, there is also a need for long-term measurement campaigns providing an accurate statistical climatology/characterization about the typical time-scales and amplitudes of the intermittent bursts under different conditions. Regarding practical applications, it is shown that the equilibrium solutions presented in the thesis provide a useful starting point for parameterization studies. Because, especially with stable boundary layers, many practical problems are a consequence of its scientific counterparts, future theoretical progress may directly benefit practical applications.