Apr 15, 1989 - speed first decreases but then increases over the MIZ. This suggests ... if not the details of its vertical structure, it is not appropriate to the study ...
JOURNAL
OF GEOPHYSICAL
RESEARCH,
VOL. 94, NO. C4, PAGES 4959-4970, APRIL 15, 1989
A Numerical Model of the Atmospheric Boundary Layer Over a Marginal Ice Zone LAKSHMI
H.
KANTHA
1 AND GEORGE L. MELLOR
Atmospheric and Oceanic SciencesProgram, Princeton University, Princeton, New Jersey A two-dimensional, multilevel model for simulating changes in the atmospheric boundary layer across a marginal ice zone is described and applied to off-ice, on-ice, and along-ice edge wind conditions. The model incorporates a second-momentclosure for parameterizing the intensification and suppression of turbulent mixing in the boundary layer due to stratification effects. For off-ice winds, as the atmospheric boundary layer passes from cold smooth ice onto warm open water, the onset of intense convection raisesthe inversion. Over the transition zone of rough rafted ice with open leads, the shear stresson the ice cover increasessignificantlybefore dropping down to the downstream values over water. Such nonmonotonic surface stresscould be the cause of divergence of sea ice near the ice edge in a marginal ice zone. These results are in agreement with the one-layer model simulations of off-ice winds by Overland et al. (1983). For on-ice wind conditions, as the warm flow in the boundary layer encounters the cold ice conditions, the resulting stable stratification could rapidly suppressthe turbulence in the boundary layer, leading to the development of a shallow inversion and an associatedjet. When the wind is predominantly along the ice edge, the temperature contrast between the open water and the ice could produce a thermal front at the ice edge in the boundary layer with strong associatedturbulence. More observations are needed to verify these model predictions. Nevertheless, these model results suggest that it is important to account for the changes in the characteristics of the atmospheric boundary layer across the marginal ice zone in our attempts to understand the behavior of the ice cover in these regions.
1.
dimensional
INTRODUCTION
The interactions between the atmosphere, the ocean, and the ice cover are particularly strong in a marginal ice zone (MIZ). It is therefore preferable to study the coupled system as a whole rather than each medium in isolation, in order to
further our understanding of this important part of our environment. The complexity of the interactions between the atmosphere and the ocean, especially when mediated by the ice cover, makes such a study rather difficult. One promising approach is through process studies using a numerical model of the coupled system that accounts for the dynamic and thermodynamic interactions between all three media. Unfortunately, it will be a while before reliable coupled models, tested against observations, can be used routinely for this purpose. One of the principal problems is, of course, the dearth of suitable data sets that can be used for a meaningful verification of the capabilities of such models. Despite the increasedattention being paid to the Arctic and the Antarctic in recent years, through multinational efforts such as the Marginal Ice Zone experiments (MIZEX), our empirical data base is still rather scanty. Simultaneous observations of the characteristics of all three media, essential to the successof a coupled model, are very few. Nevertheless, the necessity of studying the coupled system has been increasingly recognized in recent years. Efforts are now underway to develop and test coupled atmosphereice-ocean models for these regions. As part of one such effort, we have developed a coupled ice-ocean model and an atmospheric boundary layer model and are testing both models before coupling them to each other. Two•Nowat Institutefor NavalOceanography, StennisSpaceCenter, Mississippi.
Copyright 1989 by the American Geophysical Union.
the MIZ
of both these models
have simulated
and showed
that most of the observed
variations
in
the atmospheric boundary layer (ABL) over the Bering Sea MIZ made in 1981 can be attributed to the increased roughness over the MIZ and the increased heat flux over the open ocean. He found that the heat flux in the MIZ
itself and cloud
processesdid not alter the results significantly. He also used a single-layer or slab model for this study. His results emphasize the importance of ice surface roughness variations on ice drift in a MIZ.
While a slab model can capture the essence of the boundary layer modificationsover a MIZ during off-ice conditions, if not the details of its vertical structure, it is not appropriate to the study of more general cases including on-ice wind conditions.
Paper number 89JC00076. 0148-0227/89/89J C-00076505.00
versions
flows in a marginal ice zone. The results of the ice-ocean model will be reported elsewhere [Kantha and Mellor, 1989; Mellor and Kantha, 1989]. In this paper we will present the results of the application of the two-dimensional atmospheric boundary layer model to off-ice, on-ice, and alongice edge wind conditions in a MIZ. The modifications of the atmospheric boundary layer by a MIZ under off-ice wind conditions have been simulated by Overland et al. [1983] using a single-layer, two-dimensional model of the boundary layer. This study demonstrates the strong influence of the changes in the roughness of and the heat transfer from the underlying surface on the structure of the boundary layer. It shows that as the wind flows off the smoothice and onto open water over a rough MIZ, the wind speed first decreases but then increases over the MIZ. This suggestsan atmospheric mechanism for ice edge convergence and divergence, which might act in concert with the oceanic drag mechanism suggestedby McPhee [1983]. Reynolds [1984] made a more detailed study that included the effects of clouds, surface heat flux, and radiative cooling in
This has led to the increased
use of a multilevel
model over the MIZ [Bennett and Hunkins, 1986; Overland, 4959
4960
KANTHA
AND MELLOR:
ATMOSPHERIC
BOUNDARY
LAYER
MODEL
1988]. Overland [1988] has used a multilevel, oneconsidered to be dry and the perfect gas relation p = pRT, dimensional model to test the sensitivity of the geostrophic where p is the pressure, R is the gas constant, p is the drag coefficient to various atmospheric parameters over a density, and T is the temperature, is used to reduce the MIZ. This study complemented his earlier comprehensive governing equations for ensemble mean quantities to review [Overland, 1985] of the drag coefficient estimates and Ow
measurements over sea ice. Bennett and Hunkins [1986] have used a linear, two-dimensional, multilevel model to simulate
on-ice
wind
conditions
over the Weddell
Sea MIZ
corresponding to the observations of Andreas et al. [1984]. However, there appear to have been no model studies of along-ice edge wind conditions in a MIZ, a situation that could also lead to significant modifications of the atmospheric boundary layer structure (J. Overland; personal communication, 1988). A multilevel model is essential for
V ß V + --= 0V --+V.VV+w--+f
0V
Ot
characteristics
of the ice surface in a MIZ
and their conse-
quent influence on the drag felt by the atmosphericboundary layer. The surface drag coefficient has been found to be correlated
rather
well
with
ice concentration
and with the
roughness and size of ice floes. It appears therefore that the most important factors in the evolution of the atmospheric boundary layer over a MIZ are the strong variations in the ice surface roughness and the strongdisparity in the heat transfersfrom the ice surfaceand the ocean to the atmosphere. We therefore concentrate on these features in our multilevel atmospheric boundary layer model and ignore the liquid water vapor thermodynamicsfor the time being. While the atmosphere is dry and therefore somewhat simplified, the turbulent mixing processesthat are essential for accounting for the changes of roughness and heat flux on the structure of the boundary layer are parameterized using second-moment closure. The model is twodimensional and ignores the variations along the ice edge, thus assuming that the scale of variations along the ice edge is larger than that across the ice edge. The paper is organized as follows. Section 2 deals with a description of the boundary layer model, and Section 3 discusses the relevant
numerical
details.
Section 4 details the
results of its application to off-ice, on-ice, and along-ice edge wind conditions. Section 5 contains concluding remarks. 2.
THE NUMERICAL
MODEL
The numerical model for the atmosphericboundary layer is similar to the ocean model described by Blumberg and Mellor [1983] and Oey e! al. [1985]. Many of the numerical details of the ocean model are given by Blumberg and Mellor [1987]. The atmospheric model also uses second-moment closure for parameterizing vertical mixing. The governing equations and the method of solution are similar. The model is based on fully nonlinear hydrodynamic equations of motion for conservation of mass, momentum, and enthalpy; it simplified, however, by the use of incompressible,hydrostatic, and Boussinesqapproximations. The atmosphereis
(1)
19 x
Oz
V
Vrr
= -•oo
+ Oz KM Otr
+ F (2)
19o
O-• = -g •'
such studies.
There are few observations of the atmospheric boundary layer over sea ice, but the situation is improving steadily. The various large-scale international data collection efforts such as the Marginal Ice Zone experiments have improved our knowledge of the ice edge processesin general and the behavior of the atmospheric boundary layer in particular. For example, field observations reported by Anderson [1987], Guest and Davidson [1987] and Kellner et al. [1987] over the Greenland Sea MIZ during the 1983 MIZEX have again emphasized the strong variations in the roughness
0
•+V. Ot
VI9=--
=
Oz
K•/
(3) +Fo
c.o0
(4)
(6)
Equation (3) is the hydrostatic approximation, while equations (5) and (6) define a potential temperature O and a pressure term •. The quantity f is the Coriolis vector, V is the horizontal velocity vector, and V is the horizontal gradientoperator. The quantity y is the ratio of specificheats
at constant pressureCpandconstantvolumeCv,whileR = Cp -Cv. The subscript0 denotesa referencestate.The quantity g is the gravitational acceleration; z is the vertical coordinate, and w is the vertical velocity. The quantitiesK• and K, denote vertical eddy diffusivitiesfor turbulent mixing of momentum and heat. The horizontal diffusion terms
F•,y andF o are givenby
Fx=• 2A•• +• A• • +•
(7)
Fy=• 2A•
+• A• • +•
(8)
+• An
(9)
Fo=• A,•
where the quantitiesA• and An denote horizontal diffusivities. The vertical eddy coefficientsK• and Kn are calculated kom
KM,H= qlSM,H
(10)
where S• and Sn are stability functions,prescribedfrom the level 2• model of the Mellor-Yamada second-moment closure hierarchy [Me#or and Yamada, 1982]:
SM [6AiA2GM]+ SH [1 - 3A2(4A• + B2)GH]= A2
(11)
S• [1+ 6A•GM-9A•A2Gn] - Sn [3Al(4A1 + 3A2)Gn] = A• (1 - 3C1)
G•=•
•
+ • 12 g 00
G.=
0ooz
(12)
(13)
KANTHA
AND MELLOR:
ATMOSPHERIC
The turbulence velocity q and length scale I are given by equations
(q2)+V. Vq 2+w•=-0z 0zqlSq•
(q2)
+ 2(Ps+ Pb- e) + Fq
(15)
(q2/) +V. V(q2/) +w• (q2/) =• qlS1 • (q2/) + Ell(Ps + E3Pb) - le l + E2 •
+ Ft
(16)
where
e-
q3 Btl
(17)
BOUNDARY
LAYER
MODEL
4961
also, the entrainment rate at the inversion needs to be parameterized from data, thus introducing empiricism into the formulation, although at a strong inversion the model results appear to be rather insensitive to this prescription [Overland et al., 1983]. The assumption of a well-mixed, homogeneous boundary layer, although often invoked in both the oceanic and atmospheric mixed layer models, is an approximation whose degree of validity depends on the flow conditions being simulated. Thus, for example, while it may be adequate for a convective mixing such as that encountered by the boundary layer as it flows off the ice onto warm open water, it is a poor approximation for the opposite situation, where a warm layer flows off the ocean onto cold ice surface and mixing may be inhibited by strong stable stratification. Both situations occur in a MIZ, and the present model is equally applicable to both on-ice and off-ice conditions.
The above equations have been recast in sigma coordinates, so that the number of levels in the vertical is indepenes=Km • + • (18) dent of the topography of the underlying surface. However this feature is not essential to the current application to a g 0© MIZ. (Sigma coordinates are useful, however, in simulating flow over topography.) The mass and momentum conservation equations are integrated in the vertical, and the resulting The symbols Ps and P•, denote shear and buoyancy external mode equations are solved at smaller steps dictated production of turbulence kinetic energy, and e denotes its by the speedsof propagationof barotropic disturbances.The viscous dissipation; I is the turbulence length scale, a meainternal mode equations are solved at larger time steps sure of the scale of the energy-containing eddies that condictated by baroclinic modes. The interested reader is retribute to the cascade process. ferred to Blumberg and Me#or [1987] for relevant details. The symbolsFq and F t, denotehorizontalmixingterms We note here that in the application of the above atmowith expressions similarto thatof Fo exceptthatq2andq2l spheric boundary layer model to a MIZ, we orient the y axis replace ©; L is a measure of the distance from a solid
Pb= - KH(90Oz
(19)
surface.The constants k, Al, A2, B•, B2, Ci, El, E2, E3, Sq and St are 0.4, 0.92, 0.74, 16.6, 10.1, 0.08, 1.8, 1.33, 1.0, 0.2, and 0.2, respectively, and are assumed to be universal constants applicable to all turbulent flows. The reader is refered to Me#or and Yamada [1982], Markatos [1986], and Rodi [1987] for recent reviews of second-moment closure of turbulence.
It is also necessary to impose realizability conditions on G•u, Gr•, and I such that GH --
