Transport and dispersion of passive tracers in the fine resolution simulation over the Cadarache

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Surface energy exchanges

The earth receives and reflects solar radiation (mainly shortwave), emits longwave radiation from the surface and receives longwave radiation from the atmosphere. The net energy from radiation is the energy source for turbulent and conductive fluxes in the boundary layer, generally causing instability during the day and stability at night. The soil cover and vegetation influence all these processes.

Radiation balance

At the earth’s surface, most energy comes from the sun in as shortwave radiation. Here albedo reflects part of the radiation to space. Another way of energy loss is the surface-emission of longwave radiation. Wien’s displacement law (eq. 1.9) determines the predominant wavelength, peak wavelength, at which a body emits radiation according to its surface temperature. According to the Stephan-Boltzmann relationship (eq. 1.10), all things with a temperature above zero Kelvin emit radiation. Applying it gives small or short wavelengths for the sun (effective emitting surface at ~6000K) and long wavelengths for the earth (around 288 K) and eq. 1.10 gives the total amount of radiated energy.
In both eq. 1.9 and eq. 1.10, temperatures are in Kelvin. Where c is a constant of 2897 K μm, F is the flux density, is the Stephan-Boltzmann constant of 5.67 × 10−8 Wm−2K−4 and is the emissivity of the surface ( =1 signifies a perfect black body). For the net energy available to the earth’s surface, we use the radiation balance (eq. 1.11), where ↑ indicates outgoing and ↓ incoming fluxes for shortwave (SW) and longwave (LW).
The net radiation, ∗, determines energy availability for the surface heat fluxes. For clear-sky daytime conditions, solar radiation ( ↓) enters the atmosphere, and the surface albedo reflects a fraction ( ↑). Not all shortwave radiation arrives directly from the sun, the atmosphere scatters and reflects a part of the shortwaves and these indirect sources of shortwave radiation are called diffuse radiation and are largest during partially thinly clouded skies (Page, 2012). Surfaces emit ↑ towards space, while the in-between air and clouds emit both down ↓ and upwards.
Clouds and air moisture play a significant role in determining the magnitude of the radiation fluxes. Clouds have a high albedo and reflect a substantial fraction of ↓ to space. Where liquid water clouds reflect most radiation, ice clouds are more transparent (Ebert & Curry, 1992). However, the situation is more complicated due to mixed-phase clouds (Sun & Shine, 1994). Additionally, clouds replace the earth’s surface as active black body emitters because of their opacity. Regarding LW radiation, greenhouse gases, such as water vapor, absorb it better than most gases and increase atmospheric temperatures, creating a larger ↓ flux and increasing the surface net radiation and the earth’s surface temperature.

Non-radiative surface energy fluxes

Surface fluxes are non-radiative fluxes of energy with their origin at the surface. In the surface energy balance, we consider two vertical turbulent fluxes, latent heat ( ) and sensible heat ( ), suplemented with a conductivity-based soil heat flux ( ). describes the evaporation at the surface, which consists of the moisture mass flux (E) and the energy required for evaporation (Lv = 2501 103 eq. 1.12 describes the surface energy balance, its left-hand side contains the net radiative energy and soil heat flux, and the right-hand side terms are the turbulent fluxes. Generally, non-radiative fluxes are negative when they transport energy away from the surface. However, in this thesis, I use the following sign convention: upwards equals positive. During the day, the balance typically has positive values, while they are usually negative at night. Effectively, ∗ supplies energy to the surface and is adjusted by the soil heat flux and storage, leaving the remaining energy for turbulent fluxes. Sometimes eq. 1.12 is supplemented with a storage or intake term, which considers the energy storage of vegetation and energy uptake by photosynthesis.
Where is the thermal conductivity in W m−1 K−1, the exact conductivity depends on the soil moisture content and the type of soil. The usual evolution of G is opposite to the ∗ evolution, with a slight delay due to heat capacity, as the top layer of the soil heats before it starts heating up the atmosphere and lower soil layers. This temperature difference proceeds slowly increasing the time shift at deeper layers.
Description of averaged turbulent fluxes generally happens with use of covariances of ′ and appropriate physical quantity ′, density, and possible conversion constants such as Lv or Cp. We can approximate the transported amount (of energy) as described by the covariances by using the vertical gradients of the mean quantity (scalars like heat, momentum, moisture or 2). The gradients of heat and moisture are used for and respectively. Approximations of these turbulent fluxes, according to K-theory (Moene and Dam, 2014), look like:
In eq. 1.14, eq. 1.15 and eq. 1.16 is the turbulent exchange coefficient in m2 s −1, where the subscript h stands for heat, subscript e for water, and subscript m for momentum. is the heat capacity of dry air at constant pressure in J K−1kg−1. is called sensible heat flux as it changes atmospheric temperature, whereas indicates moisture transport caused by surface evaporation and potentially phase changes at higher altitudes. It represents energy for water phase changes but does not directly change the temperature, which changes available energy at the surface. Nonetheless, condensation in clouds does release energy at altitude. Eq. 1.16 is the transport mechanism of momentum, it is related to turbulence thus partly determines the magnitude of the other turbulent fluxes. In contrast with the two energy fluxes, the momentum flux is usually negative, transporting wind towards the surface where it is zero due to friction with the surface.

Bowen ratio

The ratio of over is called the Bowen-ratio, given in eq. 1.17. This ratio is indicative of the typical dryness of a surface area and is a component for soil evaporation calculations. Generally, the Bowen ratio is positive (at least during the daytime), and values above 1 indicate relatively dry areas from semi-arid landscapes at 2-6 to deserts with values above 10. While grasslands and temperate forests generally have ratios of 0.4 to 0.8, tropical oceans are below 0.1, indicating that, at these surfaces, more energy goes to evaporation than heating of air.

Land cover and soil effects

As mentioned above, different surface covers have different Bowen ratios. Land cover and soil type contribute in several ways to the difference, and I will address some of them.
The soil cover is crucial because it directly influences the system’s available energy. Vegetation, in turn, can enhance water infiltration and evaporation. Certain soil types have more water available for evaporation than others do. For example, clay can contain plenty of water, but it clings firmly to this water. On the other hand, sand contains less water but has no strong binding (Tuller & Or, 2005). At the surface evaporated water is replaced by groundwater through capillarity or with the next rain (or flood). Thus, precise evaporation calculations require knowledge on soil cover, available water, and vegetation.
Evaporation is not the only process through which soils lose water. Plants need water just like any other living organism. They extract water from the ground through their roots and transpire with their leaves, whereas evaporation occurs in the skin layer, the net loss of water is referred to as evapotranspiration. To be more specific, different types of plants have different rooting depths and place the bulk of their root system at varying soil depths, drawing water from different depths. Generally, large plants have deeper rooting depths than small plants. The plants transport the absorbed moisture from their roots to their leaves to replenish the water evaporated through air exchange (transpiration) at the stomata. The combined amount of water released by the surface and plants is called evapotranspiration (Katul et al., 2012). In short, plants enlarge the latent heat flux over land at the expense of sensible heat flux.
Surface covers influence not only the surface exchange rates but also radiative parameters and hinder airflow. From the windless conditions at the surface, in idealized views wind increases with a quasi-logarithmic profile to geostrophic values at high levels, influencing the vertical transports. Besides surface friction, additional flow blocking comes from vegetation, enlarging the area with reduced wind speeds. Most vegetation density decreases with height, and wind can pick up. However, forests are an exception since they have their densest part several meters above ground (the canopy), creating a wind speed peak between the surface and the vegetation bulk. This peak makes low-level winds harder to represent (Kaimal & Finnigan, 1994). Further, vegetation density of forests can create flow sheltering, which leads to different temperatures at the soil surface in the forest than outside the forest due to reduced vertical mixing. Altogether, soil and cover thereof are vital parts of the land surface interaction. Most surfaces have vegetation and their flows are relatively close to the surface, making it essential to know how soil covers influence local flows.
Governing equations of atmospheric flows
To simplify the calculations of atmospheric variables, I describe the atmosphere as a fluid and assume that no mass is lost. Further, I apply several conservation principles in fluid mechanics and thermodynamics, resulting in the momentum, mass and enthalpy equations and a generalized equation applicable to most scalars. I write equations in the Eulerian form, describing them as observed from a fixed point. The conservation of mass, also known as the continuity equation (eq. 1.18), describes the mass at a location.
Here and in the coming equations, a subscript “i” denotes Einstein’s summation notation, “j” covers a twin summation independent of “i”. eq. 1.18 is considered equal zero because of the assumption of constant mass in the atmosphere. Next to the mass equation, I have the momentum equation (Stull, 2009), eq. 1.19, and averaged it looks like:
With δi3the Kronecker delta, set for the vertical and = 2 sin ( ) the Coriolis parameter, where is the rotation of the earth (7.29 × 10−5 −1) and the latitude. 3 is the Levi-Civita symbol, and is kinematic viscosity. Describing the momentum equation terms from left to right, the first term on the left-hand side represents momentum storage. The second term shows the advection of momentum by wind. On the right-hand side, the first term describes gravity forces. The second term is the effect of apparent forces, the Coriolis force. The third term concerns the effect of pressure-gradient forces. The fourth term is the influence of molecular viscosity on motion. Lastly, the fifth term is the Reynolds’ stress effect on motions. Altogether, eq. 1.19 has some simplification options for easier calculations of idealized cases. Other scalars such as moisture, heat, or gases concentrations follow a basic conservation equation depicted in eq. 1.20:
Note that can act both as source or sink and can be composed of several terms.
In the heat equation, potential temperature often proxies for heat and writes like:
Where W signifies the mass of water vapor created from phase change per unit volume per unit time, thus negative for water vapor loss due to condensation. ∗ represents the net heat source related to radiation divergence, meaning the change in net radiation with height, mainly through either increasing LW upwelling by the atmosphere emission or reducing SW downwelling through scattering and absorption in the atmosphere.


Boundary layers

The planetary boundary layer (PBL) is part of the troposphere and directly interacts with the earth’s surface. This section describes the different regimes and sections of boundary layers and a few typical flows relevant to valley winds, concluding with topography and complex terrain influence.
I will use the terminology for heights, as is common in aviation, meaning that the vertical distance of surface above mean sea level (amsl) is called elevation, a height means the distance above ground level, and altitude is the combination of the two, expressed in meters amsl. A small note is made on the word PBL height. In literature, it can be used for the altitude of the PBL top and the length of the PBL column. Duine & De Wekker (2020) propose to use PBL depth for the length of the PBL column and PBL height for the altitude of the PBL top.

Boundary-layer lifecycle

In contrast with the higher atmosphere layers, PBLs have a distinct daily cycle with highly varying depths, e.g., from a few 100 m (estimations) at night to more than 2 km at mid-latitudes during the day.

Daily cycle

The boundary layer is coupled with the solar cycle through surface heating. After sunrise, the sun starts to heat the surface and creates a convective boundary layer (CBL). Here, convection results from the instability due to a heated surface and colder air above, generally capped with a temperature inversion limiting growth. Growth of the CBL occurs at its top and arises through the entrainment and encroachment growth processes. Entrainment is the process of compensating air movements when an air parcel overshoots the equilibrium height at the CBL top and enters the layer above the CBL, mixing the layers and heightening the inversion. Encroachment is the process by which the CBL growth originates solely from surface heat flux, thus only causing growth in a CBL without an inversion. Entrainment is generally the faster process for CBL growth. At sunset, when the energy input for convective mixing stops, under clear-sky conditions, a nocturnal or stable boundary layer (SBL) starts around sunset. Under cloudy or windy conditions, it remains more neutral. The layer between the top of the newly formed SBL and the top of the former CBL is called the residual layer and is initially neutral.
Regardless of the time, the bottom 10 % of a PBL is called the surface layer. Figure 1.4 shows a typical, mostly clear-sky day with all different components of a PBL.

Convective boundary layer

After sunrise, solar irradiation starts to heat the surface creating turbulent eddies due to instability and slowly increasing the CBL. At first, turbulence slowly integrates the SBL and then the residual layer by engulfing those layers with warm air parcels from the surface. Later, the fully formed CBL can nibble the free atmosphere (see Figure 1.4). In the free atmosphere, potential temperature increases, and the air is drier. Substantial gradients separate the free atmosphere and the CBL, suppressing fast CBL growth. During the overshoot period of entrainment, the thermals cause diffusion and mixing processes of the CBL with the air in the inversion layer, increasing the temperature and decreasing the moisture content. Altogether, in a CBL, surface fluxes bring both heat and moisture into the CBL through the surface heat flux and evaporation. At the same time, entrainment from the free atmosphere incorporates warm dry air, heating and drying the CBL. Leading to moistening of the CBL in the morning while the afternoon often dries, as more free-atmosphere entrainment occurs. Since in the morning the moist residual layer is entrained before, it reaches the free atmosphere in the afternoon.

Nocturnal boundary layer

The nocturnal boundary layer (NBL) starts when the solar radiation can no longer create convection and ends after sunrise when irradiation again creates convective turbulence. A nocturnal boundary layer cools from the ground and generally has less turbulence than a CBL since it lacks thermal convection created by solar irradiation. Because of cooling ground and reduced vertical mixing, the layer becomes stable. A different way of creating an SBL is by advection of warm air over a cold surface; however, I will not focus on this SBL type. Section 1.2.2 details the typical size and profiles, and 1.2.4 describes dominant processes in an SBL. Favorable conditions for SBL development are clear skies for radiative cooling and wind speeds low enough not to displace the cooled air but fast enough to create mechanical turbulence.
The previous sections already mentioned several profile structures because those are important for the SBL formation or CBL growth. I will describe the profiles and depths of mature stages in the PBL, starting with the CBL and then the SBL.
Figure 1.5: Typical vertical profiles of a mature convective boundary layer for temperature, wind, moisture, and other variables (or pollutants). Figure originates from Stull (2009) and reprinted with permission from Springer.
Figure 1.5 shows typical profiles of the CBL for different variables. PBL depths at mid-latitude reach 1-2 km maximum, peaking around noon or in the afternoon. In some desert areas, maximum CBL depths of 5 km can occur (Xu et al., 2018). Later in the day, turbulent eddies are still created but no longer reach the maximum height, leaving a neutral residual layer with less turbulence. In the residual layer, the air is well-mixed, similar to the recently decayed CBL, and values resemble the CBL since it was part of it.
Figure 1.6: Typical profiles of the stable boundary layer of the mean (a) absolute temperature, (b) potential temperature, (c) wind speed, and (d) specific humidity. Figure originates from Stull (2009) and reprinted with permission from Springer.
In contrast to the CBL, Figure 1.6 shows the profiles of a mature SBL, which has its deepest stability at the surface and gradually becomes more neutral towards the neutral residual layer, having maximum depths around 200-400 m. It is classified as a temperature inversion when the stability is strong enough to increase T with height (Figure 1.6a). In that case, the SBL is synonymous with the nocturnal inversion.
Momentum has the same quasi-logarithmic profile near the surface as during the CBL, however, due to the reduced amount of vertical turbulent transport the wind speed near the surface is generally lower than during daytime. Sometimes, decoupling from the surface drag can lead to a small peak in the wind speed at the height where the wind would return to geostrophic values (Figure 1.6c). This peak is called a low-level jet.
Moisture in the SBL (Figure 1.6d) has a similar profile to (and ) with a low near the surface in case of condensation, and a slow increase towards the residual layer, again decreasing towards the free atmosphere. However, the surface can continue to evaporate after precipitation or with dry air above. Note that when relative humidity is high enough, cooling can generate a fog layer close to the surface.
In contrast to the CBL, the SBL does not have an inversion cap, however for pollutant or dispersion calculations it is required to have an estimate of the PBL thickness ℎ. The determination of ℎ is therefore difficult. Several methods exist to estimate the layer depth. The most accessible options are to look for a particular condition with height, e.g., when stability becomes neutral or to consider the height of an LLJ. However, these methods are uncertain because the SBL often does not exactly meet these conditions but only approaches them, making them difficult to use. Stull, 2009 describes several other options and methods in detail.
Lastly, I point out the difference between the turbulence in the CBL and SBL. While buoyancy is the driving factor in the CBL, it is a sink of turbulence in the SBL. The SBL turbulence is produced through wind shear only (Stull, 2009). At night, turbulence is often patchy and intermittent, meaning that mixing happens locally and sporadically. Still, when averaging over long enough periods (hours) reliable values of fluxes, representative for larger areas can be obtained. In the SBL, turbulence is relatively independent of surface processes, and a surface forcing needs 7 – 30 h to influence the upper part, compared with 10 – 15 min across the CBL (Stull, 2009).

The surface layer

As mentioned before, the surface layer is either defined as the lowest 10 % of the PBL, or the layer where turbulent fluxes do not significantly vary with height, or the location where the log profile of wind is valid. It is here that, the vegetation influences the different fluxes. At the bottom of the surface layer, the exchange between the soil and atmosphere occurs in the microlayer, where molecular diffusion is a more effective transport mechanism than turbulence, with a depth of a few mm to centimeters.

Table of contents :

1 Understanding the structure of the stable boundary layer flow in valleys and its simulation
1.1 Atmosphere: basics, scales, and formulas.
Different scales of the atmosphere
Atmospheric stability
Surface energy exchanges
Governing equations of atmospheric flows
1.2 Boundary layers
Boundary-layer lifecycle
Vertical profile and depth
The surface layer
Processes and evolution of the nocturnal and stable boundary layer
1.3 Effects of topography on air flow
Thermally-induced slope flows
Valley flows
Classification of different types of valley flow systems
Froude Number
Various origins of valley flows
Measurement campaigns on stable boundary layer flows
1.4 Weather simulation strategies
The Weather Research Forecasting model
Known uncertainties with WRF
Fine resolution runs
2 Presentation and analysis of field campaigns in the Cadarache region
2.1 Site description and typical winds
Typical weather conditions
Relevant field campaigns in Southern France
2.2 KASCADE field campaigns and major findings
Instrumentation layout of the KASCADEs
KASCADE-2013: the vertical structure over Cadarache Valley
KASCADE-2017: spatial investigation of the Cadarache Valley
KASCADE Intensive observation periods
2.3 Supplementary analyses of KASCADE data
Determining typical stable situations in the CV
KAS13 filters applied on KAS17
Length scale statistics of KAS17
SODAR wind profiles during IOPs and their typical patterns
2.4 Existing calculation methods for the local valley winds
WRF simulations
Nowcasting with GBA threshold values
Artificial Neural Network
2.5 Chapter summary
3 Land cover in simulation: creation, evaluation, and illustration with two cases in the Durance Valley
3.1 Summary of the article
3.2 Article
3.3 Additional analyses of KAS13-IOP16
3.3.1 Daytime metrics
3.3.2 Nighttime metrics
3.4 Eleven-day simulation analyses
3.4.1 Period description
3.4.2 Complete simulation analysis
3.4.3 Day- and Nighttime metrics
3.5 Conclusions
4 Evaluation of a fine-resolution simulations over the Cadarache and neighboring valleys
4.1 Introduction
4.2 Summary of the article
4.3 Article
4.4 Additional analyses
4.4.1 Structures and flows within the CV
4.4.2 Analyses of wind outside of the CV
4.5 Summary of Chapter 4
5 Transport and dispersion of passive tracers in the fine resolution simulation over the Cadarache
Valley and neighboring valleys
5.1 Background on tracers
What are tracers
Numerical tracer release in weather models
5.2 Tracer set-up
Magnitude of tracer releases
5.3 Results
Cadarache valley tracers
Durance Valley
Abéou Valley
Verdon Valley
5.4 Discussion
5.5 Conclusion and prospects
General Conclusion and prospects


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