Jacob Svensson Boundary Layer Parametrization in Numerical Weather Prediction Models –

Boundary Layer Parametrization in Numerical Weather Prediction
Models –
Jacob Svensson
Boundary Layer Parametrization in
Numerical Weather Prediction
Models
Jacob Svensson
c
Jacob
Svensson, Stockholm 2015
ISBN 978-91-7649-194-2
Printed in Sweden by E-print AB, Stockholm 2015
Distributor: Department of Meteorology, Stockholm University
Abstract
Numerical weather prediction (NWP) and climate models have shown to have
a challenge to correctly simulate stable boundary layers and diurnal cycles.
This aim of this study is to evaluate, describe and give suggestions for improvements of the descriptions of stable boundary layers in operational NWP
models. Two papers are included. Paper I focuses on the description of the
surface and the interactions between the surface and the boundary layer in
R
COAMPS
, a regional NWP model. The soil parametrization showed to be
of great importance to the structure of the boundary layer. Moreover, it showed
also that a low frequency of radiation calculations caused a bias in received solar energy at the surface.
In paper II, the focus is on the formulation of the turbulent transport in stable boundary layers. There, an implementation of a diffusion parametrization
based on the amount of turbulent kinetic energy (TKE) is tested in a single
column model (SCM) version of the global NWP model Integrated Forecast
System (IFS). The TKE parametrization turned out to behave similarly as the
currently operational diffusion parametrization in convective regimes and neutral regimes, but showed to be less diffusive in weakly stable and stable conditions. The formulations of diffusion also turned out to be very dependent
on the length scale formulation. If the turbulence and the gradients of wind
temperature and wind are weak, the magnitude of turbulence can enter an oscillating mode. This oscillation can be avoided with the use of a lower limit of
the length scale.
List of Papers
The following papers, referred to in the text by their Roman numerals, are
included in this thesis.
PAPER I: Svensson, J. (2015): Sensitivity tests with COAMPS in stable
boundary layers over the CASES 99 area. Internal report.
PAPER II: Svensson, J., Sandu, I., Bazile, E., Svensson, G. (2015): Evaluation of a TKE based diffusion parametrization in ECMWF IFS
model. Manuscript, intended for submission to Boundary-Layer
Meteorology.
I have done most analysis in Paper I. The model was set up by Iulia Ibanescu
and the simulations were done together with Bishma Tyagi.
In the second paper, I have done the simulations, analysis and text writing. Eric Bazile has worked with the development of TKE parametrization in
ARPEGE and has together with Irina Sandu implemented it in IFS. Eric, Irina
and Gunilla have all contributed with ideas and suggestions for the paper.
Contents
Abstract
v
List of Papers
vii
1
Introduction
11
2
The atmospheric boundary layer
2.1 Radiative heat fluxes . . . . . . . . . . . . . . . . . . . . . .
2.2 Turbulence, stratification and stability . . . . . . . . . . . . .
2.3 Diurnal cycle . . . . . . . . . . . . . . . . . . . . . . . . . .
13
13
14
16
3
The boundary layer in NWP models
3.1 Soil energy budget . . . . . . . . . . . . . . . . . . . . . . .
3.2 Surface layer fluxes . . . . . . . . . . . . . . . . . . . . . . .
3.3 The outer layer turbulence parametrization . . . . . . . . . . .
18
19
19
19
4
Connection between turbulent diffusion and large scale circulation 21
5
Evaluate parametrizations with observations
23
6
Summary of results
25
7
Outlook
27
Sammanfattning
Acknowledgements
xxviii
xxix
1. Introduction
The atmospheric boundary layer (ABL), which typically extends from just tens
of meters during stable stratification up to several thousand meters on a convective day, is the part of the atmosphere where turbulence is present because of
the surface. The ABL is where we spend most of our life and where a large part
of the ecosystem is located. It is where we feel the atmosphere, where we experience cold clear nights or the heat during sunny days, where the wind through
down trees or whirls up dust and where the amount of humidity determines if
the ground is dried or morning dew is formed. It is where the meteorological quantities has largest impact on humanity and the society. Therefore, it is
of great importance that we both understand the processes that determines the
structure of the ABL and are able to predict them, both in a weather forecast
time range as well as in modelling of a future climate scenario.
Turbulence, radiation, convection and other important physical processes
in the ABL occurs on spatial scales than are smaller than what numerical
weather prediction (NWP) models and climate models can resolve. Therefore, they need to be parametrized as functions of the resolved variables. These
parametrizations are simplifications of the reality. Much work has been done to
resolve a realistic boundary layer in convective and neutral stratification. Stable stratifications suppress turbulent motions and fluxes are weak. Gradients of
wind and temperature can be stronger. The weak and sometimes intermittent
fluxes makes them hard to describe in NWP models.
During the last ten years, GEWEX (Global Energy and Water Cycle Experiment) Atmospheric Boundary Layer Study (GABLS) has been a framework
for evaluations and improvements of modelling of boundary layer processes
(Holtslag et al. 2013). The study has pointed out that there is a need for a
better understanding and representation of stable atmospheric boundary layers
(SBL), of diurnal cycles and the transition between neutral or unstable and stable conditions. A number of test cases with different level of idealization, have
been designed to evaluate and compare the performance of parametrizations
for different aspects of the boundary layer processes.
In this thesis, the performance of the parametrization of different processes that has an effect on the evolution of the ABL is investigated. Paper
I, focuses on the description of the surface and the interactions between the
R
surface and the boundary layer in COAMPS
(Hodur 1997), a regional NWP
11
model developed by US Naval Research Laboratory (NRL). Based on a study
R
by Steeneveld et al. (2006), it was identified that COAMPS
, together with
other NWP models, showed deviations from observed values in simulations of
the CASES99 (Hodur 1997) measurement campaign. In Paper I, these deviations are further investigated through an analysis of surface fluxes and study of
the sensitivity for changes in the surface energy budget.
Paper II, moves the focus slightly aloft, to the formulations of the turbulent transports in stable boundary layers. GABLS test cases are used to evaluate an implementation of a diffusion parametrization based on the amount
of turbulent kinetic energy (TKE) in a single column model (SCM) version
of the global NWP model Integrated Forecast System (IFS). IFS is a world
leading global model that is developed and operationally run by the European
center for Medium Range Weather Forecast (ECMWF 2014) in Reading UK.
Data from the IFS model is commonly used by weather services in Europe,
the Swedish met services SMHI and Swedish Armed Forces Weather Service
included, as well as in other parts of the world. ECMWF main task is to produce detailed NWP data for up to 2 weeks ahead but also produce ensemble
forecasts for seasonal climate tendencies up to a year ahead.
12
2. The atmospheric boundary
layer
At the earth’s surface, interaction and exchange processes with the atmosphere
takes place. This interaction is of great importance for the entire biosphere.
Without redistribution of heat from the earth’s surface in the tropics via the
atmosphere to northerly latitudes, the tropics would be too hot and the polar
regions too warm to be inhabitable. Without an exchange of water no precipitation would occur, and all vegetation would wilt.
Different processes drive this redistribution of heat. The heated surface
transfers heat to the atmosphere via long wave radiation and through turbulent
diffusion of sensible and latent heat. The large scale weather systems then
transports and redistributes heat over latitudes.
The structure of the ABL is dependent on its surroundings and the structure
inside it. Above the boundary layer, in the free atmosphere, the large scale dynamics determines the wind, temperature, humidity, stability, vertical motions.
In the ABL, the magnitude of turbulence, the stability and surface conditions
determines the structure. At the surface, the turbulent interaction with the ABL
as well as net radiation budget and soil fluxes of heat and moisture defines the
properties. As the boundary layer structure is dependent on the surface conditions, and the surface conditions on the boundary layer structure, the coupled
system is highly non linear.
2.1
Radiative heat fluxes
Long wave (LW) radiation is emitted according to Stefan Boltzmann’s law:
LW = εσ T 4
(2.1)
where ε is an emissivity coefficient normally close to 1, σ Stefan-Boltzmann’s
constant and T the temperature in Kelvin. Part of the LW radiation emitted
from the Earth’s surface is absorbed in the atmosphere, and re-emitted both
upwards to space and downwards to the surface and a part is directly transferred to space and cool the entire globe. The atmospheric absorption of LW
radiation from the surface in the atmosphere is dependent on the amount of
13
greenhouse gases as water vapour, carbon dioxide and methane and cloudiness. Low and meddle high clouds effectively reflect incoming solar radiation
in daytime and effectively absorbs and re-emits LW radiation, which which
counteract surface cooling in night time. Thus clouds reduces difference between night and day and so cloudy nights are warmer than clear nights and
cloudy days in wintertime are warmer than clear days.
2.2
Turbulence, stratification and stability
The redistribution of heat is also driven by turbulent transport. Turbulence in
the atmosphere acts as a counterforce to gradients. The stronger the mixing is,
the weaker the gradients become. ABL with much turbulence get well mixed
and show very weak gradients, compared to a boundary with weak turbulence
that could maintain strong gradients. The magnitude of turbulence in the ABL
is dependent on the wind shear and stratification.
Turbulence increases with increased wind shear, for example when the
winds in the free atmosphere is strong, and increases with high surface roughness. Hills, tall buildings or an uneven canopy of a forest gives large roughness,
whilst new ice, calm seas or grasslands give low roughness.
Turbulence can either be generated or destructed by buoyancy; In unstable
layers, the warmer (lighter) air is located below colder (heavier) air. Thus a
redistribution of air masses will occur which creates turbulence and mixes the
warm and cold air. In stable layers, cold (heavy) air is located below warmer
(lighter) air and does not spontaneously create turbulence, instead it suppresses
vertical motions and limits turbulence. The vertical temperature distribution as
well as the surface temperature is thus an important factor for the stability of
the boundary layer.
Potential temperature θ , can be used to compare buoyancy between air
parcels in the vertical dimension, as it is conserved under adiabatic vertical
motions. If density variations due to differences in humidity (and cloud water)
are taken into account the virtual potential temperature θv is a better choice.
Note that this variable is not similar to the equivalent potential temperature θe
(e.g. Holton 2004) which is a conserved variable in condensation and evaporation, and is useful for analysis of the trajectory of an air parcel. With the use
of potential temperature, the stratification can be defined as:
Unstable if
∂θ
< 0;
∂z
neutral if
∂θ
= 0;
∂z
and stable if
∂θ
> 0. (2.2)
∂z
Typical shapes of atmospheric profiles in these conditions is shown in Fig. 2.1.
14
z
a)
z
Stable
z
b)
Neutral
θ
θ
c)
Unstable
θ
Figure 2.1: Examples of vertical potential temperature profiles in the boundary
layer for a) stable surface conditions, b) neutral conditions and c) unstable surface
conditions.
Richardson gradient number RiG is a measure of the local stability in a
vertical section of the atmosphere. It is the ratio of buoyancy and wind shear
production, written as:
RiG =
g ∂ θv
θv ∂ z
2
∂U ∂z (2.3)
In unstable conditions RiG < 0, in neutral conditions RiG = 0 and in stable conditions RiG > 0. If RiG is used as a measure of the stability, stability decreases
with increasing winds. If the wind shear is very small, RiG becomes very
large. If turbulence is present and if RiG increases, the turbulence destruction
will be larger than shear production and turbulence will decay after a certain
point, called the critical RiG number. On the other hand, if no turbulence is
present and the shear increases, the RiG will be closer to 0 and turbulence will
be created. The exact value of this point has been a question for research in
many years. Recent analysis of field measurements have shown that there is
a critical limit in the wind shear between the intermittent, very stable regime,
and the weakly stable turbulent regime (Sun et al. 2011). Van Hooijdonk et al.
(2014) proposed a new dimensionless group, shear capacity, which relates the
required wind shear for turbulence for a certain surface heat flux to the actual
wind shear.
As noted in a poem in Richardson (1922, pp 66), turbulence in the boundary layer continuously cascades to smaller and smaller scales and then dissipates. This dissipation sets an upper limit of the amount of turbulence. On
the other hand, without a turbulence production by shear or buoyancy that are
larger than or equal to the dissipation rate, the turbulence would vanish.
15
2000
Free Atmosphere
Entrainment
Zone
Cloud Layer
Capping Inversion
Height (m)
Entrainment Zone
1000
Residual Layer
Convective
Mixed Layer
Convective
Mixed Layer
Surface Layer
Noon
Surface Layer
Sunset
S1
Midnight
S2
Local Time
Sunrise
S3
Noon
S4
S5
S6
Figure 2.2: The boundary layer structure during a diurnal cycle. The day is
convective with clouds at the inversion top, during the night the surface cools
and create a stable layer. In the morning, the solar heating recreates a convective boundary layer. Figure by NikNaks, based on Stull 1988) [CC BY-SA 3.0
(http://creativecommons.org/licenses/by-sa/3.0)], via Wikimedia Commons.
The amount of turbulence can be expressed with the turbulent kinetic energy (TKE, described in Paper II). The prognostic equation for TKE evaluates
the temporal evolution of turbulence dependent on buoyancy production or destruction, the shear generation, diffusion of turbulence, pressure distribution,
dissipation and advection. As seen in Sec. 3.3 and the second paper, TKE can
be used as in the formulation of turbulent fluxes.
2.3
Diurnal cycle
The diurnal cycle, caused by the solar heating during daytime and the radiative
cooling during day time, largely impacts the time evolution of the ABL. The
strength of the diurnal cycle varies with the time of the year, the latitude, the
cloudiness, the surface and the weather condition. The diurnal cycle is strong
when the difference is large between the surface energy budget in daytime and
night time. This is the case in the suptropical deserts or in clear periods in sub
polar regions during spring and autumn. The diurnal cycle is weak in winter
time at high latitudes when the incoming solar radiation is weak, during cloudy
nights or over the sea, when the surface temperature is almost similar during
day and night.
Figure 2.2 shows a schematic profile of the boundary layer during a diurnal
cycle. In daytime, if the solar radiation is strong enough to heat the ground so
16
that the surface temperature will get warmer than the air aloft, θsur f > θair , and
start to rise convectively. The air continues upwards until its kinetic energy is
destructed by negative buoyancy. This causes a deep mixing of the boundary
layer. Similarly, if it is very windy, the large eddies caused by wind shear mix
a deep layer.
If then the surface starts too cool, by negative surface radiation budget, the
temperature at the surface will be colder than the air aloft and the lowest part of
the boundary layer transits to stable stratification where turbulence is destructed by negative buoyancy. The air aloft, which gets decoupled and does not
feel the surface below, is called the residual layer and is still almost neutrally
stratified. When the residual layer gets decoupled, the wind just above the surface inversion still has a ageostrophic component towards the lower pressure
caused by friction. This ageostrophic wind accelerates the air and creates a
low level jet (LLJ).
If the turbulence ceases in the stable layer close to surface, the turbulence
in the residual layer will not be fed by turbulence from below and thus slowly
dissipate. The stable boundary layer remains until turbulence is recreated, either by strong winds or solar heating of the surface next morning.
As showed by Svensson and Lindvall (2015) and also pointed out by Holtslag et al. (2013), climate models and NWP models struggles to correctly simulate realistic diurnal cycles, especially when turbulence is weak. The rapid
transition between stability regimes during nights and mornings is a great challenge for models, as it demands realistic description of not only the ABL turbulence, but also the representation of radiation, soil and surface. Thus, a
deeper investigation of how a model behaves in the transition regimes reveals
much information of the behaviour and characteristics of a boundary layer
parametrization. In this study, several of the test cases that are used for model
evaluation involves transitions between stability regimes.
17
3. The boundary layer in NWP
models
NWP models are very important components in the weather forecasting process, especially on time ranges longer than a couple of hours. Models numerically solve equations that describe the time evolution of basic state variables in
the atmosphere as temperature, wind and content of water in different forms.
Typical contemporary resolutions are around 2.5 km and 15 km for regional
and global NWP models, respectively. The processes that occurs on smaller
scale than approximately 5-7 times this distance, as for example convection
and turbulence, are not fully resolved and needs to be parametrized as functions of the resolved mean state variables.
If turbulence is assumed to be horizontally homogeneous, the basic equations of wind and temperature in each grid point can be expressed as (freely
after e.g. Stull 1988; Holton 2004):
Du
1 ∂p
∂ u0 w0
=
+ f v−
∂t
ρ0 ∂ x
∂z
∂ u0 w0
Dv
1 ∂p
=
− f u−
∂t
ρ0 ∂ y
∂z
(3.1)
∂ θ 0 w0
1
D θvl
=
Q − vl
∂t
ρ cp
∂z
where p is pressure, f is the Coriolis force and Q is the diabatic heating. The
terms including u0 w0 , v0 w0 and θ 0 w0 defines the convergence or divergence of
turbulent momentum respective heat transport. At the lowest model level,
the surface flux parametrization provides the values of turbulent fluxes from
below, while fluxes from above is determined by the outer layer turbulence
parametrization. The turbulence parametrization for these terms are described
more in Sec. 3.2 and 3.3. The diabatic heating term Q defines the response
to physical processes that causes heating and includes radiation heating and
latent heat release.
As stated in previous chapters, the characteristics of the boundary layer is
dependent both on its surroundings and the structure of the physical processes
in the ABL itself. To get realistic values of the quantities in the boundary
18
layers, it is therefore important the the properties in the free atmosphere, and
the lower boundary, the surface, and the physical processes in the boundary
layer is well simulated and physically reasonable.
3.1
Soil energy budget
The representation of the ground in NWP models have different complexity.
R
uses a two layer force-restore model, i.e. a surface layer with a
COAMPS
specified soil heat capacity and a deep soil layer with fixed values during a
model cycle (Fig 2, Paper I). The change of temperature is based on a residual
of an energy budget equation and the soil heat capacity.
More complex schemes, as the one used in IFS, uses multiple soil layers.
It has a infinitesimal surface layer that is in energy balance and a vegetation
layer. Several previous reports have shown the importance of the the soil representation on surface conditions (e.g. Viterbo et al. 1999; Holtslag et al. 2013).
The results in Paper I also highlights the importance of the parametrization of
the soil and vegetation layer for the ABL development.
3.2
Surface layer fluxes
The surface is the very lowest part of the boundary layer, where interchanges
between the ground and the atmosphere takes place. In NWP models it is
often assumed to be the layer between the soil and the first vertical model level
where the prognostic equations for mean quantities (Eq. 3.1) are solved.
The descriptions of turbulent transports from the surface to the first model
layer in NWP models are usually based on similarity theory (e.g. Stull 1988;
ECMWF 2014), which relates the gradient of a variable in the surface layer
to the surface flux. In Paper I, Appendix A, a description of the surface layer
R
fluxes in COAMPS
are found. It has been pointed out that experiments that
are used to evaluate the Monin-Obukhov similarity often are affected by selfcorrelation (Baas et al. 2006). In very stable conditions, especially when turbulence is intermittent, several recent reports have shown that Monin-Obukhov
similarity breaks down. (e.g. Baklanov et al. 2011; Mahrt et al. 2012; Sorbjan
2010).
3.3
The outer layer turbulence parametrization
The parametrizations for the surface layer described above are usually only
used for the fluxes between the surface and the first model layer. Between the
model layer, usually another approach is used to parametrize turbulence. Many
19
NWP models today use a flux parametrization that includes both a component
from turbulent diffusion and a mas flux component which simulates the transport by convection. In IFS, this concept is called Eddie Diffusivity Mass Flux,
EDMF (ECMWF 2014).
In Paper II, two different concepts of diffusion formulations are tested and
compared to variants of these. The first concept, called a 1st order closure,
relates the vertical turbulence transport of the quantity χ to a length scale l, the
wind shear ∂U/∂ z, and a stability dependent function F according to:
2
w0 χ 0 = Fχ l1st
|∂U| ∂ χ
∂z ∂z
(3.2)
The second approach uses a prognostic TKE to relate the fluxes to the gradients
according to:
√
∂χ
w0 χ 0 = c lTKE T KE
(3.3)
∂z
In both expression, the length scale l1st or lT KE has a large influence. The
length scale is related to the largest vertical size of the turbulent eddies, and
thus is an estimate of the diffusion efficiency. In Paper II also the influence of
the diffusion and length scale formulation is further investigated.
With the formulation of length scale, the stability parameter, constants
and relationship between heat and momentum flux (Prandtl number), different characteristics of the diffusion parametrization can be achieved. If the
scheme gives large fluxes at weak gradients, the strong mixing will keep weak
gradients and spread deviations from the mean state over a larger altitude and
opposite for weak mixing at similar gradients. If momentum is more efficiently mixed than temperature, the model will have small gradients of wind
but stronger temperature gradients, and thus keep a larger RiG value.
20
4. Connection between turbulent
diffusion and large scale
circulation
As argued in Sec. 2 and Sec. 3 the large scale weather influences the characteristics of the boundary layer. Similarly, the boundary layer processes inluences
the large-scale circulation.
In Eq. 3.1, the parametrized physics in the boundary layer have an influence on the mean state variables, either through diabatic heating or turbulent
processes. Through the hydrostatic equation and the continuity equation this
modifies gradients of heat and pressure, which causes indirect effects on the
large-scale flow. For example, convection rapidly redistributes mass vertically
and transports heat and humidity from the surface to upper layers, changing
the local temperature and moisture content but also the horizontal temperature
and pressure gradients.
Due to the surface stress, the wind speed in the boundary layer is lower
than what is required for the Coriolis force to balance the pressure gradient
force. The flow thus has a component towards the lower pressure. In a cyclonic motion, this leads to a convergence in the low pressure center, and for a
anticyclonic motion a divergence in the high pressure center. This convergence
and divergence counteracts the baroclinic developments (called spin down) and
thus weakens the cyclone strength (e.g. Holton 2004, for Ekman pumping and
spin down). Beare (2007) calculated the influence of different processes and
found that the Ekman pumping causes the dominant transport of negative momentum that that reduces the activity of cyclones.
The operational diffusion parametrization in the IFS uses an enhanced mixing close to the surface (ECMWF 2014). Sandu et al. (2013) showed that the
skill of the forecast decreased when the enhanced diffusion parametrization
in the IFS model was exchanged to a parametrization that is less diffusive in
stable condition close to the surface. They discuss different possible processes
for the connections to the large-scale circulations, and the conclusion is that
the linking process is most likely the Ekman pumping. This is linked to findings by (Svensson and Holtslag 2009), who showed that enhanced diffusion
decreases the angle between surface stress and geostrophic wind and increases
21
the cross isobaric mass flux and gives stronger Ekman pumping. In the idealized test case GABLS1, the enhanced diffusion parametrization gives too
weak gradients of temperature and wind close to the surface (see e.g. Cuxart
et al. 2006), and smaller angle between surface wind and geostrophic wind
and larger cross isobaric flux (Svensson and Holtslag 2009), compared to less
diffusive parametrizations, observations and large eddy simulations (LES).
Diffusion could also interact with large-scale flow in other ways than through
Ekman pumping. Entrainment in the stratocumulus layer modifies the cloud
fraction and changes the radiation balance (Lock et al. 2000). As turbulence
weakens gradients, it also erodes local wind extremes as LLJ (Cuxart et al.
2006) or possibly even upper level jet streaks when similar parametrization
also is used for turbulence above the boundary layer. The properties of the upper level jet wind is crucial for baroclinic developments (see e.g. Holton 2004,
Ch. 6). Thus, the description of turbulence at the boundaries of jet streaks could
potentially influence the level of baroclinicity.
In Paper II, an evaluation of cross isobaric flow is done for the test cases
GABLS1 and GABLS4, and a calculation for the wind turning at the surface
is done. Here, as well as in Svensson and Holtslag (2009), the more diffusive
schemes had a larger cross isobaric mass flux and smaller wind turning at the
surface.
22
5. Evaluate parametrizations with
observations
To verify that a NWP model is realistic, it is necessary to evaluate simulations
to observations. Although, turbulence and turbulent fluxes are complicated
to measure, and are not observed by the regular meteorological observation
network, e.g. Lindvall et al. (2012) compared simulations to a number of observation sites through the network FLUXNET. For special test cases, physical
parametrizations of turbulence and other boundary layer processes can be evaluated with data from special turbulence measurements campaigns.
In this thesis, observations are used from three sites equipped with towers
for measurements of mean values and turbulent quantities at different levels.
Observations of radiation, surface fluxes, temperature and wind are also available in close vicinity of the towers. This give extensive datasets that can be
used for evaluation of models and simulations.
It is not always straight forward to isolate the impact of certain processes
when simulations are compared to observations, as real cases often are effected of multiple processes acting on many scales. First, both advection and
other large-scale forcing are needed to be correctly described for the observation area. If, as in Paper I, a 3-D model is used, the model in itself supplies
advection and large-scale dynamics and these parameters are complicated to
control. In Paper II, when a 1-D model is used, the advection and large scale
dynamics need to be prescribed, either using model data from a external 3-D
simulation or using data from measurements. Secondly, the surface parameters
and initialization values needs to appropriately chosen. It is not necessary that
minimal biases in the surface variables in a model gives the least bias in the
boundary layer.
In this thesis, measurements from three sites are used. CASES-99 was an
extensive field campaign in the grasslands of Kansas in October 1999 (Poulos
et al. 2002). The terrain is flat, the soil is dry which gives horizontal homogeneity. Data from CASES-99 is more extensively described in Paper I, and is
also used for the parametrization comparison project DICE (Best et al. 2015)
in Paper II. Data from the Cabauw tower in the Netherlands is used for the
experiment GABLS3 (Bosveld et al. 2014) in Paper II and data from Dome C
at Antarctica in GABLS4, although the observational dataset in GABLS4 is
23
not available yet for comparison.
To isolate processes in SCM simulations, more idealized simulations can
be used. As the reality seldom behaves idealized, it is at times more suitable to
use LES as a reference. The test case GABLS 1 (Cuxart et al. 2006), in Paper
II, only prescribes a cooling surface temperature, a constant surface roughness
and a constant geostrophic wind. That simulation is ideal to recognize the
basic behaviour of a certain diffusion parametrization.
24
6. Summary of results
In Paper I, the sensitivity of the boundary layer to surface parameters were inR
NWP model. Through analysis of each comvestigated using the COAMPS
ponent of the parametrized fluxes at the surface, it was found that:
• The largest deviation between simulations and observations occurred for
the soil heat flux. The soil heat flux, is determined from the gradient
between the deep soil temperature and the surface temperature.
• The model could not reproduce a diurnal cycle that was as strong as in
the observations.
• Changes in the deep soil temperature dramatically changed the surface
temperature and thereby the structure of the boundary layer. Integrated
over time, it acts as a source or sink of heat to the atmosphere depending
on the value used. A too low value will slowly cool the atmosphere and
a too high value will slowly heat the atmosphere.
• The deep soil temperature and moisture is set to the surface values at the
initialization, which highlights the importance of time of initialization.
• The deep soil temperature could be used to either raise or lower the daily
temperature curve, but as long as the value was kept constant, there was
no change in the diurnal cycle.
• The results from the simulations are dependent on the frequency of radiation calculation. By default settings, the values from the radiation
calculations are only updated once an hour.
To allow for a more realistic diurnal cycle, the model would benefit from an
implementation of a vegetation layer, which allows more rapid cooling and
lower temperatures at night time and higher temperatures during the day. The
model would also benefit from a more detailed and complex soil parametrization with more vertical structure. More frequent calculations would increase
the computational time but is necessary for the timing of the diurnal cycle over
land.
25
In Paper II, an implementation of a TKE based diffusion scheme is evaluated in a SCM version of the IFS model. Four test cases are simulated, GABLS
1, GABLS 3, DICE and GABLS 4. The simulations with TKE are compared to
the first order scheme used operationally, to a less diffusive first order scheme
and the TKE based schemes with different length scale formulations. In unstable and neutral conditions, the different parametrizations behaved similarly,
especially when the mass flux scheme is activated. In weakly stable and very
stable conditions, the parametrizations diverged more and the following features appeared:
• The new TKE scheme is less diffusive than the previous first order scheme
and the formulation of mixing length scale strongly affect the level of
diffusivity.
• Turbulence diminishes when stability becomes too strong. If turbulence
has vanished, the model creates too sharp wind gradients before turbulence is rapidly re-created. Then turbulence start to diminish again. This
leads to an unrealistic oscillation.
• The unrealistic oscillation is avoided with a minimum length scale that
enhances fluxes when turbulence is weak and prohibits too strong gradients to evolve. This enhancement can be detrimental in situations when
very weak turbulence is realistic.
• The integrated cross isobaric flow and difference between surface wind
direction and geostrophic wind direction follows the level of diffusivity,
i.e. a diffusive scheme has a larger cross isobaric flux and smaller angle
compared to less diffusive schemes. In GABLS1, though, the evaluated
TKE scheme had the same vale of vertically integrated cross isobaric
flux as the operational scheme. The reason for this is slightly stronger
momentum diffusion close to the surface and weaker momentum diffusion aloft in the TKE scheme compared to the operational scheme. The
equality in vertically integrated cross isobaric flux might be an indication
that the new implementation has potential for a more realistic structure
of stable boundary layers compared to the operational scheme without
deteriorating the skill of the large scale forecast.
26
7. Outlook
The results in this thesis indicate that there are more work to be done in the repR
resentation of boundary layers in NWP models. For COAMPS
, a more complex soil parametrization, an implementation of a vegetation layer and more
R
frequent radiation calculations are desirable. COAMPS
is mostly used in
applications over oceans since it is the US Navy model. However inland ABL
development is important for coastal flows as e.g. sea breeze and coastal jets.
In the IFS model, the implementation of the TKE based diffusion parametrization is promising, but more tests are needed. It is necessary to revisit the
length scale formulation. The proposed minimum length scale of 10 m in
the Bougeault & Lacarrère (Bougeault and Lacarrere 1989) formulation might
introduce undesirable strong diffusion close to the surface when turbulence is
expected to be very weak and above the surface inversion and erode LLJ. Further, all SCM simulations presented here are for cases with clear skies and no
precipitation. The performance in cloudy conditions and in precipitation also
needs to be evaluated. This could be done by SCM experiments developed
within the GEWEX Cloud System Study (GCSS), such as ASTEX (van der
Dussen et al. 2013) or BOMEX (Siebesma et al. 2003).
Before the TKE implementation is ready for operational use most importantly are test in 3-D. It is not until then its effect on the large-scale circulation
for all possible locations and weather conditions can be evaluated.
Although 3-D simulations are crucial for determining the behaviour of a
parametrization in a NWP model, SCM simulations are still an effective way
of analysing the basic behaviour of a parametrization or a physical process
and its interactions with other parametrizations. Moreover, the influence of the
diffusion scheme on both low level jets and jet streams in the upper troposphere
are not well documented in literature, and the potential influence on the largescale circulation are also of interest. This could be done with a combination of
SCM simulations and 3-D simulations.
Further, the concept of Total Turbulent Energy (Zilitinkevich et al. 2008;
Angevine et al. 2010) has a physically attractive framework and might be a step
towards a numerically stable but less diffusive TKE parametrization. When a
TKE parametrization already is implemented, an implementation and testing
of a TTE formulation can be achieved within a reasonable amount of work as
test cases for SCM are already available.
27
Sammanfattning
Det har visat sig att det är en stor utmaning för numeriska väderprognosmodeller (NWP-modeller) att simulera stabilt skiktade atmosfäriska gränsskikt och
gränsskiktets dygnscykel på ett korrekt sätt. Syftet med denna studien är att
utvärdera, beskriva och ge förslag på förbattringar av beskrivningen av gränsskiktet i NWP-modeller. Studien innehåller två artiklar. Den första fokuserar på
beskrivningen av markytan och interaktionen mellan marken och gränsskiktet
R
i den regionala NWP-modellen COAMPS
. Det visade sig att beskrivningen
av markytan har en signifikant inverkan på gränsskiktets struktur. Det framkom också att strålningsberäkningarna endast görs en gång i timmen vilket
bland annat orsakar en bias i inkommande solinstrålning vid markytan.
Den andra artikeln fokuserar på beskrivningen av den turbulenta transporten i stabila skiktade gränsskikt. En implemenering av en diffusionsparametrisering som bygger på turbulent kinetisk energy (TKE) testas i en endimensionell version av NWP-modellen Integrated Forecast System (IFS), utvecklat
vid European Center for Medium Range Weather Forecasts (ECMWF). Den
TKE-baserade diffussionsparametriseringen är likvärdetigt med den nuvarande operationella parametriseringen i neutrala och konvektiva gränsskikt, men
är mindre diffusivt i stabila gränsskikt. Diffusionens intensitet är beroende på
den turbulenta längdskalan. Vidare kan turbulensen i TKE-formuleringen hamna i ett oscillerande läge om turbulensen är svag samtidigt som temperatur- och
vindgradienten är kraftig. Denna oscillation kan förhindras om längdskalans
minsta tillåtna värde begränsas.
Acknowledgements
First I would like to thank my main supervisor Gunilla Svensson for inspiration, ideas, enthusiasm and encouragement. Thanks go also to my co-supervisor
Michael Tjernström, both for sharing memories from the Air Force and for inspiration for experimental science.
I am also thankful to my employer, the Swedish Armed Forces, for the
opportunity to study full time at the university and ty my colleagues in the
Weather Service for inspiration and support.
I also want to give thanks to my co workers during the experiments with
COAMPS, Bhishma Tyagi and Iulia Ibanescu. For the experiments with IFS, I
would like to thank Irina Sandu at ECMWF, for the idea of the project and the
opportunity to work with and learn more of the IFS model and, together with
Eric Bazile at Metéo France, for support and advises during the experiments.
At MISU I would like to thank Marcus Löfverström for all lunch chats,
Henrik Carlson for interesting discussions, Jenny Lindvall for support in the
Boundary-Layer Meteorology, Wing Leung for refreshing runs around Norra
Djurgården, the innebandy players for all nice games, the technical and administartive personell for support and fika-chats. To my room mates during the last
year, Lena Frey, Waheed Iqbal and Etienne Pauthenet, thanks for nice support
and interesting discussions. Thanks to all other colleagues that make MISU to
what it is.
Finally I would give my deepest acknowledgements to my family; my parents, my brother and my sisters for support and joy. Finally, my wife, Svetlana,
thank you for being my inspiration, my joy and my best friend and being who
you are.
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