Description

Methodical assessment of the differences between the QNSE and MYJ PBL schemes for stable conditions

All materials on our website are shared by users. If you have any questions about copyright issues, please report us to resolve them. We are always happy to assist you.

Related Documents

Share

Transcript

Quarterly Journal of the Royal Meteorological Society
Q. J. R. Meteorol. Soc.
(2015) DOI:10.1002/qj.2503
Methodical assessment of the differences between the QNSE and MYJPBL schemes for stable conditions
Esa-Matti Tastula,
a
* Boris Galperin,
a
Jimy Dudhia,
b
Margaret A. LeMone,
b
Semion Sukoriansky
c
and Timo Vihma
d
a
College of Marine Science, University of South Florida, St. Petersburg, FL, USA
b
National Center for Atmospheric Research, Boulder, CO, USA
c
Department Mechanical Engineering, Ben-Gurion University of the Negev, Beer-Sheva, Israel
d
Finnish Meteorological Institute, Helsinki, Finland
*Correspondence to: E.-M. Tastula, College of Marine Science, University of South Florida, 830 1st Street Southeast, St. Petersburg,FL 33701, USA. E-mail: tastulae@mail.usf.edu
The increasing number of physics parametrization schemes adopted in numerical weatherforecasting models has resulted in a proliferation of intercomparison studies in recent years. Many of these studies concentrated on determining which parametrization yieldsresults closest to observations rather than analyzing the reasons underlying the differences.In this work, we study the performance of two 1.5-order boundary layer parameterizations,the quasi-normal scale elimination (QNSE) and Mellor–Yamada–Janji´c (MYJ) schemes,in the weather research and forecasting model. Our objectives are to isolate the effect of stability functions on the near-surface values and vertical proﬁles of virtual temperature,mixing ratio and wind speed. The results demonstrate that the QNSE stability functions yield better error statistics for 2 m virtual temperature but higher up the errors related toQNSE are slightly larger for virtual temperature and mixing ratio. A surprising ﬁnding isthesensitivityofthemodelresultstothechoiceoftheturbulentPrandtlnumberforneutralstratiﬁcation(
Pr
t0
)
:intheMonin–Obukhovsimilarityfunctionforheat,thechoiceof
Pr
t0
issometimes more important than the functional form of the similarity function itself. Thereis a stability-related dependence to this sensitivity: with increasing near-surface stability,the relative importance of the functional form increases. In near-neutral conditions, QNSEexhibits too strong vertical mixing attributed to the applied turbulent kinetic energy subroutine and the stability functions, including the effect of
Pr
t0
.
Key Words:
stable boundary layer; stability function; NWP system
Received 30 May 2014; Revised 3 December 2014; Accepted 11 December 2014; Published online in Wiley Online Library
1. Introduction
Thepastdecadeofdevelopmentinnumericalweatherforecastinghas witnessed numerous studies in which various physicsparametrizations were compared with observations (e.g. Zhangand Zheng, 2004; Jankov
et al.,
2005; Tastula and Vihma, 2011;Draxl
et al.,
2014). In particular, the studies have been commonfor models that allow the choice of several different physicsconﬁgurations, such as the weather research and forecasting(WRF)model(SkamarockandKlemp,2008).Althoughstudiesof thiskindhavebeenvaluableindeterminingoptimalcombinationsfor model physics options and possible incompatibilities amongschemes,studiesoftheactualphysicswithintheparametrizationsarerare.Yet,understandingtheroleofvariousprocessesandtheirinteraction is an essential prerequisite for model developmentand may shed more light than the outputs from the proverbial‘black-box’ model studies.A planetary boundary layer (PBL) parameterization providesestimates for turbulent ﬂuxes of grid-scale variables. The mostcommon approach is the downgradient one
w
′
φ
′
=−
K
∂φ∂
z
, (1)where the turbulent ﬂux of a quantity
φ
is estimated via thevertical gradient of its mean proﬁle and an exchange coefﬁcient
K
. The
K
-formulation has a large effect on the model results. In1.5-level PBL schemes in the Mellor–Yamada hierarchy such astheMellor–Yamada–Janji´c(MYJ;Janji´c,2001)andquasi-normalscale elimination (QNSE; Sukoriansky
et al.,
2005),
K
takes thefollowing form:
K
=
α
lS
√
TKE, (2)
c
2014 Royal Meteorological Society
E.-M. Tastula
et al.
where
α
is a non-dimensional coefﬁcient,
S
is the inverse of astability function,
l
is a turbulence length scale, and TKE is theturbulence kinetic energy.Close to the surface, parametrizations of turbulent ﬂuxesof momentum, heat and moisture are typically based onthe Monin–Obukhov similarity theory (MOST), which relatesmean proﬁles of meteorological quantities to their respectivesurface ﬂuxes (Monin and Obukhov, 1954). Under the MOSTassumptions, the stability functions in Eq. (2) become non-dimensional gradient functions, also known as similarity functions, which are determined empirically. The validity of these log–linear expressions is supported by direct numericalsimulation (DNS) studies (e.g. Ansorge and Mellado, 2014).A substantial body of literature exists that addresses similarity functions: reviews have been given by e.g. H¨ogstr¨om (1996) andFoken(2006).Thefunctionalformsoftheseempiricalexpressionsdiverge strongly in stable conditions (Grachev
et al.,
2007),whereas unstable conditions feature much closer agreement(Businger
et al.,
1971).Turbulence in stable conditions is structurally complicated.The unsteadiness and intermittency of the stable PBL havebeen major obstacles in the way of gaining even qualitativeadvances (Mahrt, 2014). Low-level jets, terrain slope ﬂows andgravitywaves,oftenfoundinstableconditions,furthercomplicatethe situation. Yet an accurate prediction of the evolving stably stratiﬁed PBLs is essential in many practical applications, such aspredictions related to air pollution (Mahrt, 1999).A widely used formulation of the stability functions in stableconditions was developed by Mellor and Yamada (1982). Thestability functions given therein depend on the Brunt–V¨ais¨al¨afrequency,verticalwindshearandseveralempiricallydeterminedcoefﬁcients. The srcinal Mellor–Yamada 2.5-level model wasfound problematic in several studies and various correctionshave been suggested (e.g. Galperin
et al.,
1988; Helfand andLabraga, 1988; Deleersnijder, 1992). The coefﬁcients were revisedin Janji´c’s (2001) non-singular implementation. A revision of theclosure constants and turbulence length-scale formulation wasalso suggested by Nakanishi and Niino (2009).Analytical expressions for the stability functions srcinating inclose proximity to ﬁrst principles based upon the Navier–Stokesequationshavebeenrare.Therelativelyrecentlydevelopedquasi-normal scale elimination (QNSE) theory of stably stratiﬁedturbulence (Sukoriansky
et al.,
2005, 2006) yields such a set
of analytical functions for the vertical eddy viscosity andeddy diffusivity. Close to the surface in the approximation of the constant ﬂux layer, these functions constitute the MOSTsimilarity functions. Although numerical weather prediction(NWP) systems such as the WRF model have adopted theQNSE-based turbulence parametrization, no previous studieshave assessed the isolated effect of the analytical QNSE stability functions on model simulations. Such comparisons are critical,however,notonlyduetotheusageoftheQNSEstabilityfunctionsin NWP systems to compute near-surface turbulent exchange,but also due to the need for better theoretical understandingof turbulence in stably stratiﬁed conditions. Moreover, such anapproach wouldilluminatethe impactof stability functions uponvertical proﬁles of different variables; an aspect usually missing inintercomparisons of boundary layer schemes. Having explainedthe approach used in this study, it is important to point outthat the lack of understanding of stably stratiﬁed turbulenceis not the only factor limiting predictive stable boundary layer skills: radiative transport, representation of soil/vegetation,local topography/surface heterogeneity and wave–turbulenceinteractions are among other factors that challenge modellers.The purpose of this study is to compare the performance of theQNSE and MYJ models by scrutinizing their stability functions.To accomplish this goal, we have modiﬁed the MYJ PBL andsurface layer codes in the WRF model in such a way that the only signiﬁcant difference between the QNSE and MYJ approaches isthe representation of stability functions (see section 4 for details).
Figure 1.
The inverses of the QNSE and MYJ stability functions
S
M
and
S
H
as afunction of gradient Richardson number.
OthertestsrelatedtoMOSTfunctionsarecarriedoutaswell.TheMYJ model was selected as a reference because it is a widely usedscheme in the WRF model and its code structure is similar to thatof QNSE.The study compares the performance of these stability functionsfromthemodellingperspective.TheoreticaltestsfortheQNSE approach are addressed in Tastula
et al.
(2014). The modelsimulations test the model’s skill in reproducing observations of:(i) near-surface temperature, mixing ratio, and wind speed at 12stations in southeastern Canada in winter; (ii) vertical proﬁlesof virtual temperature, mixing ratio, and wind speed during theCASES97 and CASES99 ﬁeld campaigns in Kansas, USA; (iii)turbulence regimes during CASES99.
2. The QNSE theory
The feature that sets the QNSE theory apart from thetraditional Reynolds-averaged Navier–Stokes (RANS) modelsis the inclusion of waves and turbulence anisotropy. This isenabled by the spectral nature of QNSE, which is based uponsuccessive ensemble-averaging over inﬁnitesimally thin spectralshells yielding scale-dependent horizontal and vertical eddy viscosities and eddy diffusivities that account for the transportprocesses on the eliminated scales. This is not possible for RANSmodelsastheyarebaseduponensemble-averagingovertheentiredomain of ﬂuctuating modes (Ferziger, 1993), a procedure thatlumps all scales together (Sukoriansky
et al.,
2005, 2006; Galperin
and Sukoriansky, 2010; Sukoriansky and Galperin, 2013).The QNSE operates with the inverses of the stability functions,
S
M
=
K
M
/
K
0
and
S
H
=
K
H
/
K
0
, where
K
0
is the eddy viscosity at
Ri
g
=
0,
K
M
and
K
H
are the actual eddy viscosity and eddy diffusivity, respectively, all in the vertical direction. Furthermore,
Ri
g
refers to the gradient Richardson number, and
S
M
and
S
H
andare given in Figure 1 in terms of
Ri
g
evaluated using adjacent gridpoints. Due to the breaking of internal gravity waves accountedfor in the QNSE, the eddy viscosity remains ﬁnite at high valuesof
Ri
g
.
3. Closure of TKE in MYJ and QNSE
A turbulence closure module that uses either the MYJ orQNSE schemes invokes the prognostic equations for TKE; theremaining equations are reduced to algebraic relationships. With
c
2014 Royal Meteorological Society
Q. J. R. Meteorol. Soc.
(2015)
Stability Functions in QNSE and MYJ Models
Table 1
.
Formulations for calculating the inverse of stability functions (
S
), lengthscale (
l
) and
TKE
production/dissipation in the MYJ and QNSE schemes.QNSE MYJ
S S
m,h
(
Ri
loc
)
S
m
,
h
TKE
,
l
,(
∂
u
∂
z
)
2
,
∂
v
∂
z
2
,
∂θ
v
∂
z
l
If
N
2
≥
0,
l
=
1
l
−
1
b
+
l
−
1
s
where
l
b
=
kz
1
+
kz
λ
,
l
s
=
0
.
75
√
TKE N
, and
λ
=
0
.
0063
u
∗
f
Preliminary
l
=
l
0
kz
/
(
kz
+
l
0
)
l
0
=
0
.
1
hpbl
0
zq
d
z
/
hpbl
0
q
d
z q
=
(2
TKE
)
0
.
5
l
adjusted to satisfy an equation for
l
/
q
If
N
2
<
0,
l
as in MYJTKE
TKE
=
TKE
l
,
K
M
∂
V
∂
z
2
,
K
H
N
2
Iterative procedure
TKE
=
TKE
l
,
TKE
,
K
M
∂
V
∂
z
2
,
K
H
N
2
Ri is the gradient Richardson number, k is the von K´arm´an constant, hpbl is theboundary layer height, K
M
is the eddy viscosity, K
H
is the eddy diffusivity, N isthe Brunt-V¨ais¨al¨a frequency, f is the Coriolis parameter, and u
∗
is the frictionvelocity. The subscript loc refers to calculation on the basis differences betweenadjacent model levels.
its three variables, Eq. (2) encapsulates the three differencesbetween the QNSE and MYJ schemes, namely, the effect of the stability functions (
S
), turbulence length scale (
l
) andTKE. The formulations for the length scale in the QNSEscheme do not srcinate from the QNSE theory; rather, thelength scale for stable stratiﬁcation is based on Detering andEtling (1985) and Sukoriansky and Galperin (2008). The TKEproduction/dissipation is a basic implementation of the TKEequation that, nevertheless, employs the QNSE-based eddy viscosity and eddy diffusivity, whereas MYJ uses a PBL-height-based expression for
l
.
In addition to the traditional TKE balanceequation, it also uses an iterative approach to better adjust theturbulent ﬂuxes to their values at the current computational step(Janji´c, 2001). Further details are given in Table 1. The stability functions in MYJ and QNSE are graphed as functions of
Ri
g
inFigure1.TheMYJfunctionsfeatureacriticalRichardsonnumberof 0.505 beyond which the ﬂow becomes laminar. As the goalof the article is to validate the analytical stability functions fromthe QNSE theory, isolating the effect of stability functions is of primary importance. To accomplish this, the QNSE formulationsfor the turbulence length scale and TKE are transferred to theMYJ scheme.As both MYJ and QNSE schemes employ MOST in the surfacelayer, the differences between the schemes in this layer aredictated by the similarity functions. The QNSE-based functionsare compatible with the stability functions used in the boundary layer scheme and are derived from them in the constant ﬂux layer approximation. Since the QNSE theory applies to stably stratiﬁed and weakly unstably stratiﬁed turbulence, its resultscannot be used in strongly unstable conditions. Therefore, theQNSE expressions for the weakly unstable regime are extendedintothestronglyunstableregimeusingPaulson’s(1970)similarity functions. Contrasting with the QNSE approach, the similarity functions in the MYJ surface layer scheme are not based on thestability functions in the MYJ boundary layer scheme. Instead,empirical formulations of Holtslag and De Bruin (1988) are usedin stable conditions and the aforementioned Paulson functionsare invoked in the case of unstable stratiﬁcation.The integrated similarity functions are introduced in the MYJand QNSE surface layer schemes as follows:
Sf
m
=
X
MYJ,QNSE
+
log
z z
o
, (3)
Sf
h
=
Pr
t0
Y
MYJ,QNSE
+
log
z z
T
, (4)where
Sf
m
and
Sf
h
are the integrated similarity functions formomentumandheat,respectively,and
X
and
Y
representdifferent
Table 2
.
Model conﬁgurations used in the experiments.Abbreviation TKE Stability function
l
Sfc layer
Pr
t0
MYJ M M M M 1MYJ Pr072 M M M M 0.72MYJ Pr1 qnse Sf M M M Q 1QNSE Q Q Q Q 0.72MYJ 1 TKE Q M Q M 1MYJ TKE Q M M M 1QNSE Pr1 Q Q Q Q 1Q, QNSE; M, MYJ.
expressions used in the QNSE and MYJ schemes. The roughnesslength is given by
z
o
, the thermal roughness length is
z
T
, and
z
denotes height above the ground level. The theoretically derivedvalue of
Pr
t0
in QNSE is 0.72, while in MYJ it is increased to1 by modifying one of the srcinal Mellor–Yamada constants(Janji´c, 2001).
4. Model, set-up and experiments
The WRF model is a state-of-the-art NWP system used for bothresearch and operational applications. It is a community-basedmodel developed in collaboration among several institutions inthe United States. The WRF software framework (WSF) includesdynamic solvers, physics packages, initialization programs,and the WRF variational data assimilation system. The twodynamics solvers are the advanced research WRF (ARW) and thenonhydrostatic mesoscale model (NMM). The ARW is discussedbelow in more detail, as it is the solver utilized in this study.The ARW solver features fully compressible, Euler non-hydrostatic equations, which are conservative for scalar variables.The top of the model domain is a constant-pressure surface, andthe applied vertical coordinate is based on a terrain-followinghybrid level approach. In the horizontal regime, Arakawa C-grid staggering is used. The time integration part of the modelcurrently uses a second- or third-order Runge–Kutta schemewith a smaller time step for acoustic and gravity wave modes.A full description of the solver is presented in Skamarock andKlemp (2008).To study the issues presented in section 1, seven differenttypes of WRF model experiments were carried out (Table 2)for three different time periods and two different domainset-ups (Table 3). These include experiments with unmodiﬁedQNSE and MYJ schemes, and the MYJ scheme with the QNSEturbulent length-scale and TKE production/dissipation (labelledas MYJ l TKE). The comparison between MYJ l TKE and QNSEis the most important as the only differences between the two isthe representation of the stability functions and MOST functionsin the surface layer. In MYJ l TKE,
Pr
t0
is 1 whereas QNSEuses the analytical result of 0.72 from spectral theory. Next, twoexperiments test the relative signiﬁcance of the functional formof the MOST functions and
Pr
t0
. Experiment MYJ Pr072 uses itsusual Holtslag and de Bruin and Paulson MOST functions, butwith
Pr
t0
equaltotheQNSEvalueof0.72,whereastheexperimentMYJ Pr1 qnse Sf utilizes QNSE-based MOST functions alongwith
Pr
t0
from MYJ. These tests provide important informationabout the impact of the value of
Pr
t0
upon the MOST-basedsurface layer results and predictions in the bulk of the PBL.Experiment MYJ TKE refers to the MYJ scheme using the QNSETKE subroutine. Finally, QNSE Pr1 refers to a QNSE experimentin which
Pr
t0
was assigned the value 1 in both surface andboundary layer schemes.Note that in the QNSE surface layer scheme
z
T
is given aslightly different expression than in MYJ. Other differences arethe computation of saturation mixing ratio at the surface overwater and potential temperature. To isolate the effect of stability functions,weusedtheQNSEexpressionforbothofthesevariablesin MYJ l TKE. For water points, the surface saturation mixingratio in QNSE is related to surface moisture ﬂux and the surface
c
2014 Royal Meteorological Society
Q. J. R. Meteorol. Soc.
(2015)
E.-M. Tastula
et al.
Table 3
.
Case studies.Simulation period HorizontalresolutionVerticallevelsSoutheasternCanada12 Feb 2003 1800 UTC to17 Feb 2003 0000 UTC– 50CASES97 28 Apr 1997 0000 UTC to29 Apr 1997 1800 UTC4 May 1997 0000 UTC to5 May 1997 1800 UTC Parent domain 5610 May 1997 0000 UTC to11 May 1997 1800 UTC30 km20 May 1997 0000 UTC to21 May 1997 1800 UTCCASES99 4 Oct 1999 0000 UTC to8 Oct 1999 0000 UTC7 Oct 1999 0000 UTC to11 Oct 1999 0000 UTC10 Oct 1999 0000 UTC to14 Oct 1999 0000 UTC13 Oct 1999 0000 UTC to17 Oct 1999 0000 UTC Nest 6 km 5616 Oct 1999 0000 UTC to20 Oct 1999 0000 UTC19 Oct 1999 0000 UTC to23 Oct 1999 0000 UTC22 Oct 1999 0000 UTC to26 Oct 1999 0000 UTC25 Oct 1999 0000 UTC to29 Oct 1999 0000 UTC
heat-exchangecoefﬁcient(
K
HS
),whereasMYJusesanexponentialformula based on surface temperature (
T
sfc
) and surface pressure(
P
sfc
).The ability of the MYJ and QNSE schemes to reproduce thenear-surface observations at 12 stations in very cold conditionswas tested in the model runs featuring a cold air outbreak insoutheastern Canada (Figure 2(a)). During the period of thesimulation there was strong steady southsoutheastward ﬂow over the inner domain, with no synoptic-scale fronts presentto complicate the near-surface validation. The srcinal QNSEimplementation in WRF did not include the option for fractionalsea ice. For the case study in question, however, this option wascrucial as the Gulf of St Lawrence was partially covered by seaice during the simulation period. A sea-ice wrapper was thereforeadded for the QNSE surface-layer scheme in the surface drivermodule.VerticalproﬁleswereexaminedinmodelrunsfortheCASES97and CASES99 ﬁeld campaigns in April and May 1997, and 5–29October 1999 (Figure 2(b)). A total of 46 radio soundings wasused to evaluate the model performance in the lowest 1000 mduring stable conditions. The CASES99 turbulence data fromSun
et al.
(2012) were used to validate the relationship betweenturbulencestrengthandwindspeedsinthemodel.Furtherdetailsof the model runs are listed in Table 3.The physics options used in all experiments are the WRFsingle-moment three-class scheme for microphysics (Hong andLim, 2006), the rapid radiative transfer model (RRTM) for long-wave radiation (Mlawer
et al.,
1997), the Dudhia (1989) schemefor short-wave radiation, and the Noah land surface model forland surface (Chen and Dudhia, 2001a, 2001b; Ek
et al.,
2003).The initial and boundary conditions are from the ERA-Interimreanalysis (Dee
et al.,
2011).
5. Results
5.1. Near-surface quantities
The model experiments for southeastern Canada are from 12February 2003 at 1800 UTC to 17 February 2003 at 0000 UTC. Atthe end of the 24 h model spin-up period, a surface low-pressurearea was centred close to 51
◦
N, 60
◦
W and moved slowly eastwardbringing a northerly ﬂow from the Labrador Peninsula to theGulf of St Lawrence region before moving over the Atlantic. Tocheck the validity of the model simulation, surface observationsfrom 12 weather stations (inside the nest in Figure 2(a))were used.Table4providestheerrorstatisticsforthesoutheasternCanadaexperiments. The QNSE yields considerably smaller average bias(
−
0.9K)forthe2mvirtualtemperature(T2)thanMYJ(
−
2.3K).For the MYJ l TKE experiment, the bias is close to that of MYJ(
−
2.2K).TheRMSEalsofeaturesaslightlylowervalueforQNSE(3.4 K) than for MYJ (3.7 K) and MYJ l TKE (3.6 K). The mostsurprising details were found, however, in the comparison of theexperiments MYJ, MYJ Pr072 and MYJ Pr1 qnse Sf. When
Pr
t0
in the surface-layer scheme is set to 0.72 instead of 1 given inthe srcinal MYJ MOST function, both the bias and root meansquareerror(RMSE)ofT2arereducedclosertotheQNSEvalues.The bias drops to
−
1.7 K and the RMSE becomes 3.4 K. On theother hand, curiously, if the value
Pr
t0
= 1 is used in tandemwiththeQNSE-basedsimilarityfunctions(insteadoftheHoltslagand de Bruin and Paulson functions), then the results are almostidentical to those from the MYJ experiment. The correlationcoefﬁcient between observations and model predictions for T2decreases when the Prandtl number is reduced from 1 to 0.72:MYJ, MYJ l TKE and MYJ Pr1 qnse Sf all yield 0.7 whereasMYJ Pr072 and QNSE produce 0.6.The error statistics for the 2 m mixing ratio (MR2) and 10 mwind speed reveal no advantage of QNSE over MYJ: the MR2RMSE and bias in MYJ l TKE (0.21 and 0.07 g kg
−
1
) are close tothose for QNSE (0.20 and 0.09 g kg
−
1
). For W10, QNSE yieldsa slightly smaller bias (2.7 m s
−
1
) than MYJ l TKE (3.1 m s
−
1
).The RMSE is higher for QNSE, however. The similarity betweenMYJ and MYJ Pr1 qnse Sf is also obvious for the MR2 and W10results.
5.2. Vertical proﬁles
The effect of stability functions on the vertical proﬁles of virtualtemperature,mixingratio,andwindspeedisstudiedinthemodelexperiments for CASES97 and CASES99 (Table 3). As our focusis on stably stratiﬁed conditions, only soundings exhibiting stabletemperature proﬁles were selected. The layer bulk Richardsonnumber (
Ri
b
) for the layer 2–150 m was between 0 and 2 in amajority of the proﬁles. In only eight cases was
Ri
b
greater than2. The Coordinated Universal Time (UTC) for the proﬁles usedranges from 0000 UTC to 1230 UTC. For the error analysis, thesounding data were linearly interpolated to model levels.Figure 3 displays the RMSE and bias for the selected variables.The modelled proﬁles for the ﬁrst ﬁve CASES97 and CASES99experiments listed in Table 3 converge at the approximate heightof 800 m. The errors in the virtual temperature proﬁle arecharacterized by slightly negative biases close to the surfaceand positive values higher aloft. The QNSE features higherRMSEs than MYJ l TKE between 30 and 200 m and largerbiases in the layer 10–150 m. Unlike in the southeastern Canadaexperiments, QNSE and MYJ l TKE yield almost identical 2 mvirtual temperature bias. Below 30 m, the errors produced by MYJ Pr072 are larger than those in any of the four otherexperiments. Consistent with Table 4, the differences betweenMYJ and MYJ Pr1 qnse Sf are very small.Both PBL schemes under investigation struggle to accurately reproduce the shapes and heights of the temperature inversions:outofthe46proﬁles,theinversiontopwasplacedatthesamelevelas in observations in 13 (MYJ) and 12 (QNSE) cases. If we countonly the times when the virtual temperature bias was less than orequal to 1 K at that level, the numbers are reduced to seven (MYJ)and ﬁve (QNSE). These failures reﬂect difﬁculties of simulatingstable boundary layers. They stem from such phenomena as low-level jets (LLJ), the interaction of turbulence with internal gravity
c
2014 Royal Meteorological Society
Q. J. R. Meteorol. Soc.
(2015)
Stability Functions in QNSE and MYJ Models
(a)(b)
Figure 2.
Domain set-ups for southeastern Canada experiments (a) and CASES97 and CASES99 experiments (b).
waves, turbulence intermittency and anisotropy (e.g. Mahrt,2014). All these factors are poorly represented in numericalmodels yet they affect the virtual temperature proﬁle.The mixing ratio error proﬁles in Figure 3 feature a very clearseparation between three groups of experiments: (i) MYJ andMYJ Pr1 qnse Sf,(ii)QNSEandMYJ Pr072and(iii)MYJ l TKE.QNSE and MYJ Pr072 show the largest bias and RMSE. It issigniﬁcant that the slight modiﬁcation in the value of
Pr
t0
(from1 to 0.72) in the surface-layer scheme makes the MYJ Pr072experiment fall within the QNSE group. This means that themoisture proﬁle is sensitive to the value of
Pr
t0
used in thesurface-layer scheme much more than the temperature proﬁle.The stability functions applied have a profound effect on themixing ratio bias up to 500 m. Experiment MYJ l TKE yields asmallerbiasthantheQNSEbetween80and500m,butbelowthisthe absolute biases are similar in magnitude. The RMSEs for the
c
2014 Royal Meteorological Society
Q. J. R. Meteorol. Soc.
(2015)

Search

Similar documents

Tags

Related Search

ASSESSMENT OF THE CAUSES AND IMPACT OF FINANCan assessment of the role of the civil societAssessment of the Role of Market Woman in CooAN ASSESSMENT OF THE LEVEL OF COMPLIANCE WITHDiseases Of The Eye And AdnexaThe History Of The Decline And Fall Of The RoHistory of the Crusades and the Latin EastHistorical Theology of the Catholic and ProteHistory of the Highlands and Islands ScotlandThe archaeology of the Himalayas and Tibet

We Need Your Support

Thank you for visiting our website and your interest in our free products and services. We are nonprofit website to share and download documents. To the running of this website, we need your help to support us.

Thanks to everyone for your continued support.

No, Thanks

SAVE OUR EARTH

We need your sign to support Project to invent "SMART AND CONTROLLABLE REFLECTIVE BALLOONS" to cover the Sun and Save Our Earth.

More details...Sign Now!

We are very appreciated for your Prompt Action!

x