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 NOAA Technical Report ERL 407-PMEL 32 
 
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 *>*r c sO«'' 
 
 A Regional Surface Wind Model 
 for Mountainous Coastal Areas 
 
 James E. Overland 
 Matthew H. Hitchman 
 Young June Han 
 
 June 1979 
 
 U. S. DEPARTMENT OF COMMERCE 
 National Oceanic and Atmospheric Administration 
 Environmental Research Laboratories 
 
-sSgagjv 
 
 NOAA Technical Report ERL 407-PMEL 32 
 
 A Regional Surface Wind Model 
 for Mountainous Coastal Areas 
 
 James E. Overland 
 Matthew H. Hitchman 
 Young June Han 
 
 Pacific Marine Environmental Laboratory 
 Seattle, Washington 
 
 June 1979 
 
 U. S. DEPARTMENT OF COMMERCE 
 Juanita M. Kreps, Secretary 
 
 National Oceanic and Atmospheric Administration 
 
 a. 
 
 <S Richard A. Frank, Administrator 
 
 o 
 
 Environmental Research Laboratories 
 
 Boulder, Colorado 
 Wilmot N. Hess, Director 
 
NOTICE 
 
 Mention of a commercial company or product does not constitute an 
 endorsement by NOAA Environmental Research Laboratories. Use 
 for publicity or advertising purposes of information from this publica- 
 tion concerning proprietary products or the tests of such products is 
 not authorized. 
 
 
 
 (Order by SD Stock No. 003-017-00461-9) 
 
 
 For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402 
 
 
CONTENTS 
 
 Abstract 1 
 
 1. INTRODUCTION 1 
 
 2. THE MODEL 2 
 
 3. DETAILS OF THE MODEL 3 
 
 3.1 Finite Difference Form 3 
 
 3.2 Boundary Conditions 3 
 
 3.3 Flooding 4 
 
 3.4 Entrainment 4 
 
 3.5 Initialization 4 
 
 4. SIMPLE EXPERIMENTS 4 
 
 4.1 Onshore Flow with Flat Topography 5 
 
 4.2 Offshore Flow with Flat Topography 6 
 
 4.3 Modification of Flow by a Coastal Mountain 7 
 
 5. SIMULATION FOR PUGET SOUND /STRAIT OF JUAN DE FUCA 9 
 
 5.1 Regional Description 9 
 
 5.2 Data Sources 9 
 
 5.3 Model Simulations 11 
 
 5.3.1 Cyclonic Storm System 13 
 
 5.3.2 Interior High Pressure 13 
 
 5.3.3 Offshore High Pressure 26 
 
 6. ACKNOWLEDGMENTS 32 
 
 7. REFERENCES 32 
 
 APPENDIX: Derivation of Boundary Layer Equations 33 
 
 in 
 

 Digitized by the Internet Archive 
 
 in 2013 
 
 http://archive.org/details/regionalsurfacewOOover 
 
A REGIONAL SURFACE WIND MODEL 
 FOR MOUNTAINOUS COASTAL AREAS 
 
 James E. Overland, Matthew H. Hitchman, 
 and Young June Han 
 
 ABSTRACT. A mesoscale numerical model of the planetary boundary layer (PBL) was 
 modified for application to mountainous regions along the northwestern coast of the con- 
 tiguous United States and the southern coast of Alaska. The model treats the PBL as a one- 
 layer primitive equation system solving for boundary layer height, potential temperature, 
 and the two components of horizontal velocity. Input parameters are the large-scale geo- 
 strophic wind pattern and the stability of the air mass. Experiments with a cross-section ver- 
 sion of the model were performed to assess its response to variable terrain, differential heat- 
 ing, and differential roughness at the coast for a domain containing both a flat coastal plain 
 and low coastal mountains. The complete model was applied to three quite dissimilar mete- 
 orological situations for the Puget Sound/Strait of Juan de Fuca system in northwestern 
 Washington state. The model is specifically useful in suggesting the relative roles of inertia 
 and topography. 
 
 1. INTRODUCTION 
 
 A major limitation of coastal marine mete- 
 orology is the inadequate specification of the local 
 wind field at the spatial resolution necessary to re- 
 solve wind drift, local waves, and vessel or oil- 
 spill leeway. Typically, this is due to the difficulty 
 in estimating nearshore wind fields directly from 
 large-scale synoptic patterns or from widely 
 scattered and often unrepresentative wind meas- 
 urements. Near the coastline, topography and dis- 
 continuities in surface roughness and heating give 
 rise to significant mesoscale variations. Strong 
 ageostrophic winds exist in the passes of the south- 
 eastern Alaskan coast and are attributed to chan- 
 neling around islands. The open coast is also sub- 
 ject to anomalous winds caused by high coastal 
 mountains. Of particular importance are winds 
 blowing off the land, called katabatic winds, 
 forced by the contrast of warm ocean tempera- 
 tures and cold temperatures 50-100 km inland. 
 Farther south, in the Puget Sound basin in Wash- 
 ington, forecasters are aware of a quiet zone of re- 
 duced winds in the lee of the Olympic Mountains. 
 This zone changes location as a function of the off- 
 shore wind direction. Sea breeze circulation is an 
 
 additional example of coastal wind modification. 
 
 This report documents the combined use of a 
 numerical meteorological model and a field meas- 
 urement program to explore regional wind pat- 
 terns. Within the context of its formulation, the 
 model can be used to assess how changes in large- 
 scale flow, surface parameters, and assumed dy- 
 namics affect the wind pattern in a limited region. 
 A major goal is the ability to infer local winds and 
 small-scale spatial variations in wind fields from 
 the large-scale flow pattern for locations where 
 long-term observations are not practical. 
 
 We have chosen to adapt the mesoscale 
 numerical model of the planetary boundary layer 
 (PBL) proposed by Lavoie (1972, 1974; see also 
 Keyser and Anthes, 1977). Lavoie treats the PBL, 
 typically 0.5 to 2.0 km deep, as a one-layer, verti- 
 cally integrated primitive equation model. The 
 model solves for boundary layer height, potential 
 temperature, and the two components of hori- 
 zontal velocity, throughout a limited region. 
 Large-scale geostrophic wind, surface elevation, 
 temperature, and the stability of the air in the 
 layer above the PBL are specified as boundary 
 conditions. Air temperature and PBL height are 
 specified along the inflow boundaries. The local 
 response is calculated by specifying smooth initial 
 
 "Contribution No. 366 from the NOAA/ERL Pacific Marine Environmental Laboratory. 
 
Free 
 Atmosphere 
 
 Inversion 
 Layer 
 
 — Transition 
 Layer 
 
 Planetary 
 
 Boundary 
 
 Layer 
 
 Surface 
 Layer 
 
 50 m 
 
 Figure 1. — Model-defined parameters of height, velocity, and 
 potential temperature. 
 
 values of wind, temperature, and PBL height, and 
 then time-stepping the equations of continuity, 
 momentum, and heat conservation until a state of 
 equilibrium is obtained. The system allows esti- 
 mation of mesoscale wind variations caused by 
 contrasts in heating and roughness of land and 
 water, modification of the down-wind environ- 
 ment by advection, and channeling by topog- 
 raphy for a given static large-scale pressure pat- 
 tern. Since the model considers only one layer, 
 processes that depend upon vertical structure can- 
 not be directly resolved. For example, questions 
 remain on the adequacy of the model to represent 
 sea breeze circulation without explicitly resolving 
 return flow aloft. However, the model is well 
 suited to estimating wind patterns in mountainous 
 regions with strong orographic control. 
 
 The Puget Sound/Strait of Juan de Fuca re- 
 gion in northwestern Washington was chosen for 
 a test basin because there was a fairly comprehen- 
 sive data set available for comparison. Since the 
 model is quickly dominated by complex topog- 
 raphy, several cases with simple geometry, based 
 on a topography similar to that of western Ore- 
 gon, are included in Section 4 to build confidence 
 in interpreting more complicated results. The 
 question of the type and quality of large-scale 
 pressure field input is also addressed by compari- 
 son of prepared sea level pressure analysis with 
 computer-generated objective analysis from the 
 National Meteorological Center. 
 
 2. THE MODEL 
 
 The atmosphere is represented by four layers 
 defined by changes in the lapse rate of potential 
 temperature, as shown in fig. 1. The layer in con- 
 
 tact with the surface is a constant stress or surface 
 layer assumed to be represented by a logarithmic 
 velocity profile. The upper limit of this layer is 
 taken to be 50 m. Above the surface layer is the 
 planetary boundary layer (PBL), represented by 
 vertically integrated values of velocity and poten- 
 tial temperature. The PBL is capped by a density 
 discontinuity, which parameterizes the restoring 
 force of an inversion layer of stable air above the 
 PBL. The PBL is the only layer that is explicitly 
 modeled. The model specifies four dependent vari- 
 ables: the PBL height, h, identified with the inver- 
 sion base in unstable or neutral stratification; the 
 PBL potential temperature, 6; and the two compo- 
 nents of the vertically integrated wind velocity 
 within the PBL, u and v, represented here by the 
 vector v. The governing equations for conserva- 
 tion of mass, momentum, and heat result from 
 vertically integrating the primitive equations for 
 the PBL, treating the lower atmosphere as a Bous- 
 sinesq system. Interactions with the surface layer 
 and upper atmosphere are parameterized. The re- 
 sulting equations (see appendix) reduce to 
 
 dh 
 
 ~ + V(h-D)v =£, 
 
 (1) 
 
 d(h-D)v 
 
 dt 
 
 + V(h-D)vv + (h-D)fkxv 
 
 = -(h 
 
 _ DfFi+ g (h-D)A6 vh 
 
 ! g{h 'R )2 V6 +Ev + -Cd\v\v, (2) 
 
 20 o 
 
 d(h-D)6 
 
 dt 
 
 + y(h-D)vd 
 
 = E0+-Ch\v\ (d-6 5 ). 
 
 (3) 
 
 The right side of the mass conservation equa- 
 tion (1) represents the recruitment of mass into the 
 PBL through entrainment of the overlying fluid at 
 rate E. The height of the top of the surface layer 
 above sea level is indicated by D, so that h-D is the 
 local PBL thickness. The thickness of the surface 
 layer is 6. In the momentum equation (2), the sec- 
 ond term is inertia; / is the Coriolis parameter; g is 
 gravity; 6 is a reference temperature; v + is the ve- 
 locity at the base of the inversion layer (entrained 
 into the PBL at rate £), and Co is the surface drag 
 parameter. The temperature increase between the 
 PBL and the inversion layer is Ad. The air stability 
 associated with the inversion is thus modeled as a 
 jump condition in density. F, represents the uni- 
 
form pressure gradient associated with the back- 
 ground large-scale flow (the major input to the 
 model), while the next two terms consider pres- 
 sure gradients induced by the local variations in 
 PBL height and temperature. In the absence of 
 mesoscale variation, (2) reduces to a geostrophic 
 balance modified by surface drag. The right-hand 
 side of the heat equation (3) indicates that the PBL 
 can be warmed by entrainment at the top of the 
 PBL (6+ being the temperature at the base of the 
 inversion) or by surface heating proportional to 
 the difference between the PBL air temperature, 6, 
 and the surface temperature, d 5 . 
 
 The wind velocity v is an average for the en- 
 tire PBL. Since almost all wind shear is confined to 
 the surface layer, the model wind can be taken as 
 nearly equal to the wind at 50 m elevation. At this 
 level the wind speed is approximately 15% greater 
 than the wind measured at the normal anemom- 
 eter height of 10 m. Corrected for height in this 
 manner, the model winds should correspond to 
 30-min averaged anemometer winds, which are 
 not unduly influenced by surface features smaller 
 than the mesh length of the model for a well-mixed 
 PBL. 
 
 
 
 Figure 2. — Staggered mesh for primary variables. Mesh loca- 
 tions specify the following variables: x — temperature (9) and 
 PBL height (h); o — v component of velocity; • — u compo- 
 nent of velocity. 
 
 3. DETAILS OF THE MODEL 
 3.1 Finite Difference Form 
 
 The chosen grid is a single Richardson lattice 
 (fig. 2) in which the u and v components are 
 staggered relative to the height field and each 
 other. This approach is optimal for gravity waves. 
 This lattice also eliminates over-specification of 
 boundary conditions, a difficulty with Lavoie's 
 original formulation. The flux form of the advec- 
 tive terms maintains conservation of scaler quanti- 
 ties. Upstream values, rather than centrally aver- 
 aged values, for advected quantities are chosen to 
 maintain the transportive property, which guar- 
 antees one-way flow of information. 
 
 3.2 Boundary Conditions 
 
 Specification of boundary conditions for 
 limited-area integrations of the primitive equa- 
 tions is a formidable task. One advantage of the 
 present approach is that constant values on the 
 boundaries can be specified, with the integration 
 run until all the ringing of the time-dependent 
 modes is frictionally damped. 
 
 For domain sizes on the order of several hun- 
 dred kilometers it is important to emphasize the 
 gravitationally controlled circulation, which re- 
 quires specification of either boundary layer 
 height or inflow velocity. Along inflow bound- 
 aries over the ocean, we have chosen to specify 
 constant PBL height, hi, and air temperature, 6,. 
 These values are held fixed for all time. Inflow 
 boundaries over land specify the PBL height and 
 temperature as 
 
 h = hi + aD, a = 0.5, 
 
 (4) 
 
 subject to a minimum PBL height. This minimum 
 was set at 300 m. After the h values are set by (4), 
 they are smoothed twice to remove the influence 
 of rapid variations in the ground elevation D. The 
 model needs to be rerun on a case-by-case basis, 
 adjusting the constant a to minimize the influence 
 of the open boundary on the height field at inte- 
 rior points. The authors are currently experiment- 
 ing with setting the PBL height along inflow 
 boundaries from the results of a one-dimensional 
 model. At outflow boundaries we follow Lavoie 
 by setting the PBL height and potential tempera- 
 ture at their upstream values. 
 
 Specifying the momentum flux through the 
 open boundaries for the non-linear advection 
 terms in the momentum equations must be done 
 with care, because advection in a limited domain 
 
is significant. Several options for inflow velocities 
 were investigated, including specifying the 
 laterally homogeneous solution for the given geo- 
 strophic wind and drag coefficient. This proved 
 unsatisfactory because the imbalance between the 
 boundary values and the internal values influ- 
 enced by orography caused severe geostrophic ad- 
 justment problems throughout the model domain 
 and resulted in large deviations in the height field. 
 Our final choice is to assume zero gradient condi- 
 tions on the velocity components at the inflow 
 boundary. This assumption results in determina- 
 tion of the values at the first interior point by the 
 local dynamic balance. This decision is consistent 
 with the limited data input available and the desire 
 to resolve orographic control interior to the 
 model. Since upstream differencing is used for mo- 
 mentum advection, only minor difficulties are en- 
 countered at outflow boundaries. 
 
 3.3 Flooding 
 
 In our initial application to mountainous re- 
 gions we will assume that an oceanic PBL height 
 can be specified a priori and, for the time interval 
 necessary for a parcel to flow through the domain 
 of the model, that no significant modification is 
 contributed directly through entrainment, i.e., Eis 
 set to zero. Entrainment can be added to this type 
 of model (Stull, 1976, for example), but represents 
 a major complication and is of secondary impor- 
 tance relative to the influence of large topographic 
 features. ' 
 
 3.5 Initialization 
 
 The values of parameters and input condi- 
 tions in table 1 are used in subsequent model runs. 
 
 The background large-scale pressure 
 gradient, F„ is calculated to balance the specified 
 geostrophic wind, v g . The PBL height is initialized 
 by hi and velocities are initialized by 70% of the 
 geostrophic wind. 
 
 In the presence of high mountains or low 
 mean velocities, the top of the marine inversion 
 layer may actually intersect the topography. For 
 the vertically integrated model, this is equivalent 
 to forming an island. 
 
 In the cases studied by Lavoie it was not nec- 
 essary to resolve this feature, but it must be re- 
 solved for such cases as those of Puget Sound and 
 the high Alaskan coastal mountains. In the present 
 model flooding is accomplished by selectively re- 
 moving a grid point if the PBL depth falls below a 
 preset value, and adding points if the surrounding 
 PBL heights are great enough to increase the PBL 
 depth above a minimum. Since adding or drop- 
 ping points creates new internal boundary condi- 
 tions, flooding increases the relaxation time to 
 steady state by a factor of three. 
 
 4. SIMPLE EXPERIMENTS 
 
 In the sections to follow, complex topog- 
 raphy dominates the flow field through the over- 
 lapping influence of several mountains and the 
 contrasts between land and water. These all con- 
 tribute to local modification of the wind field. To 
 aid in interpretation of more complex results, we 
 first describe several experiments with simple 
 topography, isolating particular physical pro- 
 cesses. The examples use a one-dimensional ver- 
 sion of the model (i.e., north-south derivatives are 
 set to zero) with the parameters given in table 1. 
 The experiments consider either a flat topography 
 with a land/ocean discontinuity or a mountain 
 barrier 700 m in elevation located adjacent to the 
 
 3.4 Entrainment 
 
 Even in the absence of mountains, determina- 
 tion of the PBL height is a complex problem. For 
 unstable boundary layers the height cannot be ex- 
 plicitly determined, but is governed by a rate 
 equation that considers free and forced convec- 
 tion, large-scale subsidence, shear instabilities, 
 and solar radiation. The importance of entrain- 
 ment is problem-dependent and we can suppose 
 that it is more significant in the Gulf of Alaska in 
 winter, for example, with cold air outbreaks over 
 warm water, than in Puget Sound. 
 
 Table 1. — Input parameters 
 
 Parameter 
 
 Value 
 
 g 
 
 980.6 cm sec" 2 
 
 f 
 
 1.08 x looser' 
 
 Co (water) 
 
 1.5 x 10"' 
 
 Ch (water) 
 
 1.5 X 10"' 
 
 Co (land) 
 
 9.0 X 10"' 
 
 Ch (land) 
 
 7.0 x 10"' 
 
 A0 
 
 3.0 K 
 
 do 
 
 281 K 
 
 lv 
 
 600 m 
 
 Ax 
 
 3 km 
 
 v x 
 
 13ms"' 
 
 E 
 
 
 
coastline. The model is assumed to run from west 
 to east, with the ocean to the west. While the latter 
 topography is fictional, it is roughly comparable 
 to a slice through the Coast Range in Oregon. The 
 total domain is large (300 km) to reduce the influ- 
 ence of the inflow or outflow boundaries. The grid 
 mesh is 3 km. While most of the conclusions in 
 this section can be derived from analytic solutions 
 or scale analysis, we take the numerical approach 
 consistent with development of the two-dimen- 
 sional model. 
 
 4.1 Onshore Flow with 
 Flat Topography 
 
 line. Clearly, in the absence of heating and moun- 
 tains, inertia dominates onshore flow, resulting in 
 almost no modification of the marine wind until it 
 reaches the coastline. 
 
 The third example (fig. 4) is a sea breeze with 
 a background geostrophic wind of 3.0 m s" 1 from 
 290°. The land temperature is 291 K, 10 K 
 warmer than the ocean. The temperature equi- 
 librates to 90% of the temperature contrast 
 100 km inland from the coast. There is little varia- 
 tion in direction except for a delayed frictional 
 turning inland. The wind speed is maximum at the 
 coastline in response to pressure gradient induced 
 by the land-water temperature difference. Conti- 
 nuity in this model requires a lowering of the PBL 
 
 Figure 3a shows the simplest case of onshore 
 flow for a flat coastline. Geostrophic wind ap- 
 proaches from the left (270°) at 13.0 m s" 1 with a 
 boundary layer height of 600 m and no contrast 
 between the temperatures over land and water. 
 Seaward, the horizontally homogeneous solution 
 matches the analytical solution for a momentum 
 integral (Brown, 1974) with the boundary layer 
 wind 0.96 of geostrophic and an inflow angle of 
 17°. Coastal influence begins near the shoreline 
 and, inland, results in a PBL height increase of 
 260 m and a reduction in wind speed to 9.0 m s" 1 . 
 One measure of the relaxation distance for the 
 flow to return to a near geostrophic-frictional bal- 
 ance is given by the ratio of the magnitude of the 
 inertia terms (udu/dx, etc.) to the large-scale pres- 
 sure gradient force (fv g ). This ratio is given as the 
 top curve in fig. 3a; it is largest just landward of 
 the coast and is 0.1 at a distance of 100 km inland. 
 Near the outflow boundary the solution again fits 
 Brown's solution for the increased drag coefficient 
 over land. For mass continuity in a one-dimen- 
 sional model with no entrainment, the product of 
 the u component of velocity and the PBL depth 
 must be constant throughout the model domain. 
 In the example of fig. 3a, conservation is satisfied 
 to better than 0.2%. 
 
 The importance of momentum advection is 
 further illustrated by contrasting 3a with 3b. In 
 fig. 3b, the same conditions are specified as in 3a, 
 except that the momentum advection terms are set 
 to zero, leaving large-scale and locally induced 
 pressure gradients and friction as the only forces. 
 The seaward extent of coastal influence is much 
 greater. The main feature, induced by the rise in 
 the PBL height, is a coastal jet of 14.5 m s" 1 from 
 226°, nearly a 65° change from the offshore direc- 
 tion. Another important feature is a nearly com- 
 plete frictional equilibrium landward of the coast- 
 
 E 800 
 600 
 
 
 
 
 PBL Height 
 
 
 
 
 
 
 - 
 
 - 
 
 Water - 
 
 / Land 
 
 - 
 
 1 1 1 1 1 1 
 
 1 1 1 
 
 1 1 ! 1 1 1 
 
 30 60 90 120 150 180 210 240 270 
 Distance (km) 
 
 «, 290 
 
 0) 
 
 £,250 
 
 
 
 ~° 210 
 _ 13.0 
 
 'en 
 
 E 
 9.0 
 
 800 
 
 600 
 
 Wind Direction 
 
 Wind Speed 
 
 30 60 90 120 150 180 210 240 270 
 Distance (km) 
 
 Figure 3. — (a) Onshore flow with flat coastline; (b) same case 
 with acceleration terms set to zero. 
 
height in the vicinity of the coast as a result of the 
 increased velocity; the resulting slope of the PBL 
 height influences the winds 40 km seaward of the 
 coast. An interesting feature is the double peak in 
 the magnitude of the inertia terms. 
 
 4.2 Offshore Flow with 
 Flat Topography 
 
 Figure 5 shows an offshore wind for the same 
 parameters as in 3a. There is acceleration across 
 the coastline with a maximum 6 km offshore. Ac- 
 celeration terms still account for 20% of the mag- 
 
 Inertia/Pressure 
 2.0 1— Gradient Force 
 
 60 90 120 150 180 210 240 270 
 Distance (km) 
 
 Figure 4. — Sea breeze circulation with a flat coastline. 
 
 .2 2.0 
 
 Inertia/Pressure 
 Gradient Force 
 
 nitude of the geostrophic term at the limit of the 
 model, 180 km seaward of the coast. Velocities 
 over land are in frictional equilibrium but they 
 gradually increase offshore to a super-geostrophic 
 magnitude of 14.6 m s" 1 at a distance of 110 km 
 from the coast. A gradual decline is indicated near 
 the limit of the model domain. For an overwater 
 drag coefficient of 1.5 x 10" 3 , the boundary layer 
 has only begun to equilibrate with surface friction 
 within the. model domain. One can project that 
 coastal influences of offshore flow extend seaward 
 at least 300 to 500 km. This length scale is further 
 substantiated by the land breeze case shown in 
 fig. 6, in which the ocean is 10 K warmer than the 
 land. The air temperature increases only 3 K over 
 a distance of 180 km. The contribution of the land 
 breeze increase over the background flow is of 
 order 1 m s" 1 , compared with the sea breeze- 
 induced increase of 3 m s~\ The length scale for 
 thermal equilibrium of a coastal temperature dis- 
 continuity is well beyond the domain of the model 
 even for modest advective velocities on the order 
 of 4 m s"" 1 . 
 
 Inertia/Pressure 
 Gradient Force 
 
 Water 
 
 II 
 
 30 60 90 120 150 180 210 240 270 300 
 Distance (km) 
 
 Figure 6. — Land breeze circulation with flat coastline. 
 
 30 60 90 120 150 180 210 240 270 300 
 Distance (km) 
 
 Figure 5. — Offshore wind with flat coastline. 
 
4.3 Modification of Flow 
 By a Coastal Mountain 
 
 Figures 7a, 7b, and 7c show the case of a 
 coastal mountain, with onshore flow for three 
 options of offshore PBL height and no tempera- 
 ture contrast. Even for moderate terrain the results 
 are qualitatively very dissimilar to the flat coastal 
 plain. All three cases show similar patterns of a 
 coastal influence zone that extends from 50 to 
 100 km offshore. The offshore transition is not 
 gradual, but is marked by a sharp front at the sea- 
 ward limit as seen in the PBL height and magni- 
 tude of the advective terms. Within this "offshore 
 coastal zone" the winds are reduced by as much as 
 40% with a minimum approximately 20 to 40 km 
 offshore. The winds veer to the southwest as they 
 approach the coastline and accelerate on the lee 
 
 1600 
 1200 
 
 800 
 
 400 
 
 
 
 Wind Speed 
 PBL Height 
 
 Land Elevation 
 
 l l l l I l I l I I 
 
 30 60 90 120 150 180 210 240 270 300 
 Distance (km) 
 
 16.0 
 
 12.0 
 
 8.0 
 
 Wind Direction 
 Wind Speed 
 
 2000 
 
 PBL Height s> 
 
 
 1600 
 
 ^s' 
 
 - \ 
 
 1200 
 
 
 f\ 
 
 800 
 
 
 400 
 
 Land Elevation ~ 
 
 ] l I I i i i I l I I 
 
 A 
 
 
 
 / 1 i i i i i i 
 
 30 60 90 120 150 180 210 240 270 300 
 Distance (km) 
 
 16.0 
 
 _ Wind Direction 
 Wind Speed 
 
 12.01- 
 8.0 
 
 2400 
 
 ~PBL Height 
 
 ^N 
 
 2000 
 
 
 - \ - 
 
 1600 
 
 - ' 
 
 \y 
 
 1200 
 
 
 - 
 
 800 
 
 
 r\ 
 
 400 
 
 - Land Elevation - 
 
 II I I I I I I I I I 
 
 -A - 
 
 
 
 \ i i i i i i i 
 
 30 60 90 120 150 180 210 240 270 300 
 Distance (km) 
 
 Figure 7. — Onshore flow with coastal mountain. Offshore PBL height equals (a) 500 m, (b) 900 m, and (c) 1500 m. 
 
8.0 
 o 
 « 4.0 
 
 0.0 
 290 
 280 
 
 S 1 250 
 
 Inertia/Pressure 
 Gradient Force 
 
 Temperature 
 
 Wind Direction 
 
 6.0- 
 
 " 2.0 
 
 1200 
 
 800 
 
 400 
 
 
 
 Wind Speed 
 
 PBL Height 
 
 Land Elevation 
 
 
 
 I l l l l I 
 
 30 60 90 120 150 180 210 240 270 300 
 Distance (km) 
 
 Figure 8. — Sea breeze circulation with coastal mountain. 
 
 B 3.0 
 
 CD 
 
 "" 0.0 
 1 280 
 S 1 200 
 
 "D 
 
 16.0 
 T 12.0- 
 E 8.0 
 
 Inertia/Pressure 
 Gradient Force 
 
 /\ 
 
 Wind Direction 
 
 Wind Speed 
 
 1600 
 
 1200 
 
 800 
 
 400 
 
 
 PBL Height 
 
 - Land Elevation 
 
 
 
 i l l i 
 
 J L 
 
 30 60 90 120 150 180 210 240 270 300 
 Distance (km) 
 
 Figure 9. — Offshore flow with coastal mountain. 
 
 side of the mountain. They then recover to a near- 
 frictional balance within 40 km of the lee side PBL 
 minimum. Figure 8 shows the influence of the 
 presence of the mountain on sea breeze circulation 
 (10 K temperature contrast between land and sea). 
 In this formulation the mountain acts as an effec- 
 tive barrier to development and emphasizes the 
 importance of low-level valleys in the mountain 
 range for the development of sea breeze circula- 
 tion. In addition to temperature contrasts, flows 
 
 8.0 
 4.0- 
 0.0 
 286 
 
 Inertia/Pressure 
 Gradient Force 
 
 278 
 
 Temperature 
 
 30 60 90 120 150 180 210 240 270 300 
 Distance (km) 
 
 Figure 10. — Land breeze with coastal mountain. 
 
 through valleys would be enhanced by the high 
 pressure developed on the windward side of the 
 ridge. Figures 9 and 10 show offshore flow and 
 land breeze for a low coastal mountain. Unlike the 
 onshore flow case with constant friction on the lee 
 side of the mountain, , a pronounced minimum in 
 the PBL height does not occur when there is a re- 
 duction in friction on the leeward side of the 
 mountain. This case strongly contrasts with the 
 offshore flow case for flat topography in that there 
 is virtually no variation in velocity seaward of the 
 coastline. In the land breeze case, the temperature 
 contrast reinforces the down-slope flow, resulting 
 in a maximum wind speed of 9 m s -1 at the coast, 
 reducing to 4 m s" 1 at 20 km offshore. 
 
 Several important qualitative results can be 
 inferred from the one-dimensional model runs. 
 First, the length scale for frictional and thermody- 
 namic equilibrium over water is several hundreds 
 of kilometers; this is consistent with wintertime 
 observations of outbreaks of cold continental air 
 over the Atlantic Ocean along the northeastern 
 coast of the United States. Second, in the vicinity 
 of discontinuities, advective effects dominate. 
 Third, the presence of even modest orography 
 modifies the offshore flow pattern. One can antici- 
 pate that alongshore variations in topography are 
 also important. Finally, except for certain special 
 cases, observations made right at the coast should 
 be, at best, only qualitatively similar to the off- 
 shore flow field. 
 
5. SIMULATION FOR PUGET 
 SOUND/STRAIT OF JUAN 
 DE FUCA 
 
 A matter of primary importance is determin- 
 ing the transport mechanism of any petroleum 
 spilled into the waters of Puget Sound or south- 
 eastern Alaska. Since winds have a sizable effect 
 on surface drift, direct measurements of winds 
 over the water are being made as part of coastal 
 assessment programs. A goal of the regional mete- 
 orological model is to extend the usefulness of 
 these observational data sets and to enhance the 
 understanding of the mesoscale atmospheric 
 response. 
 
 We have selected for modeling three gener- 
 alized examples of meteorological flow conditions 
 for the Puget Sound system. Midwinter is charac- 
 terized by a series of cyclonic storms (Section 
 5.3.1) with strong winds from the southwest 
 carrying warm moist air inland over western 
 Washington. Another frequent winter case is the 
 lull between storms, with high pressure to the east 
 of the region (Section 5.3.2) causing strong 
 easterly winds along the axis of the Strait of Juan 
 de Fuca with relatively light winds elsewhere. In 
 the summer months, anticyclonic flow around a 
 well-developed semi-permanent high pressure cell 
 to the west of the region (Section 5.3.3) causes pre- 
 vailing northwest winds offshore along the west- 
 ern coasts of Washington and Vancouver Island. 
 
 5.1 Regional Description 
 
 The area investigated includes western Wash- 
 ington, the southern end of Vancouver Island, and 
 southwestern British Columbia. Major features 
 are the offshore ocean, Puget Sound, and the 
 Straits of Juan de Fuca and Georgia (fig. 11). This 
 region spans the coordinates 121 °W to 126 °W and 
 46 d N to 56 °N. Topographic data for the model 
 were obtained from a master tape at the National 
 Center for Atmospheric Research (NCAR). The 
 mesh is a grid of 5 minutes latitude and longitude, 
 with an average elevation computed for each 
 square. The NCAR elevation data were smoothed 
 in both directions (Shuman, 1957). Figure 12 pre- 
 sents a view of the smoothed topographic grid as 
 seen from the southwest. 
 
 The Cascade Mountains form a north-south 
 barrier to the east ranging from a low elevation of 
 916 m at Snoqualmie Pass to a high of 4392 m at 
 
 Mt. Rainier, with an average height of 1800 m. 
 The Olympic Mountains in the center of the re- 
 gion rise gradually from the south and west to 
 2428 m at the summit of Mt. Olympus, with an 
 average height of 1600 m, descending rapidly to 
 the north and east. A significant area of higher ele- 
 vation to the south is the Willapa Hills, 300 to 
 600 m high, between the Columbia River and the 
 Chehalis River Valley. Vancouver Island is pri- 
 marily mountainous, with heights averaging 
 900 m, reaching 1200 m in several locations. 
 
 This topography establishes one main low- 
 level north-south passageway, extending from the 
 Columbia River Valley through Puget Sound, and 
 two low-level east-west passageways, the Strait of 
 Juan de Fuca and the Grays Harbor Inlet/Chehalis 
 River Valley area. 
 
 5.2 Data Sources 
 
 We obtained a set of data that adequately 
 represent the regional wind field during the period 
 November 1976 through January 1977. This set in- 
 cludes data from routine meteorological station 
 reports and from an array of recording anemom- 
 eters at strategic locations. Figure 13 and table 2 
 provide station locations, sources, and National 
 Weather Service (NWS) station symbols. Teletype 
 data for NWS offices and Coast Guard stations 
 were obtained from the Ocean Services Unit of the 
 Seattle Weather Service Forecast Office. The 
 Weather Service offices and ships from the North- 
 east Pacific typically report every 6 h. The Coast 
 Guard stations usually report every 3 h, but most 
 do not report during the night. Three MRI Model 
 7092 Anemometers set out by the authors yielded 
 strip charts, which were converted to 1-h averages 
 and plotted every 6 h. Data from three vector- 
 averaging anemometers in the Strait of Juan de 
 Fuca were provided by the MESA Puget Sound 
 project (Holbrook and Halpern, 1978). It should 
 be noted that stations 10-17 in table 1 a. 2 well in- 
 land; thus, local microtopography affects the air 
 movement there more than at the shore stations, 
 and makes them less indicative of the general 
 flow. Station wind reports were mapped every 6 h 
 from 0000 Greenwich Mean Time (GMT) on 27 
 November 1976 to 1800 GMT on 26 January 1977. 
 From these regional maps, examples of typical 
 weather events were selected. 
 
 For each case selected, large-scale synoptic 
 pressure maps centered on western Washington 
 were prepared from North Pacific synoptic charts. 
 In addition, objective sea level pressure analyses 
 
125° 
 
 124° 
 
 123° 
 
 122° 
 
 125° 
 
 124° 
 
 123° 
 
 122° W 
 
 Figure 11.— The Puget Sound/Strait of Juan de Fuca region. 
 
 
 10 
 
Table 2. — Stations used on local wind maps 
 
 Number 
 
 Station Location 
 
 Source 
 
 Symbol 
 
 1 
 
 Transient Ships 
 
 W 
 
 
 2 
 
 Columbia River 
 
 
 
 
 Weather Ship 
 
 W 
 
 NNCR 
 
 3 
 
 Astoria 
 
 w 
 
 AST-791 
 
 4 
 
 Willapa Bay 
 
 c 
 
 89S 
 
 5 
 
 Cape Shoalwater 
 
 A 
 
 
 6 
 
 Westport 
 
 c 
 
 84S 
 
 7 
 
 La Push 
 
 c 
 
 87S 
 
 8 
 
 Quillayute 
 
 w 
 
 UIL-797 
 
 9 
 
 Cape Flattery 
 
 c 
 
 93S 
 
 10 
 
 NorthPoint 
 
 w 
 
 105 
 
 11 
 
 Snider 
 
 w 
 
 109 
 
 12 
 
 South Olympic 
 
 w 
 
 138 
 
 13 
 
 Dayton 
 
 w 
 
 253 
 
 14 
 
 Wolf Point 
 
 w 
 
 572 
 
 15 
 
 Round Mountain 
 
 w 
 
 743 
 
 16 
 
 Lester 
 
 w 
 
 450 
 
 17 
 
 Little Mountain 
 
 w 
 
 432 
 
 18 
 
 Buoy 3 
 
 H 
 
 
 19 
 
 Buoy 4 
 
 H 
 
 
 20 
 
 Buoy 2 
 
 H 
 
 
 21 
 
 Port Angeles 
 
 C 
 
 NOW 
 
 22 
 
 New Dungeness 
 
 c 
 
 96S 
 
 23 
 
 Point Wilson 
 
 c 
 
 53S 
 
 24 
 
 Point Wilson 
 
 A 
 
 
 25 
 
 Smith Island 
 
 
 
 26 
 
 Friday Harbor 
 
 C 
 
 S19 
 
 27 
 
 Victoria 
 
 w 
 
 VI-200 
 
 28 
 
 Patricia Bay 
 
 w 
 
 YJ-799 
 
 29 
 
 Cassidy Airport 
 
 w 
 
 CD-890 
 
 30 
 
 Comax 
 
 w 
 
 QQ-893 
 
 31 
 
 Vancouver 
 
 w 
 
 VR-892 
 
 32 
 
 Abbotsford 
 
 w 
 
 XX-108 
 
 33 
 
 Point No Point 
 
 c 
 
 97S 
 
 34 
 
 West Point 
 
 c 
 
 43S 
 
 35 
 
 West Point 
 
 A 
 
 
 36 
 
 Alki Point 
 
 c 
 
 91S 
 
 37 
 
 Sea-Tac Airport 
 
 w 
 
 SEA-793 
 
 38 
 
 Point Robinson 
 
 c 
 
 99S 
 
 KEY 
 
 C Coast Guard station report 
 
 A PMEL land-based anemometers 
 
 H PMEL buoy-placed anemometers 
 
 W National Weather Service station report 
 
 on the Limited Area Fine Mesh Model (LFM) grid 
 were obtained for the region from the National 
 Meteorological Center. We will compare the ob- 
 jective analyses on the 160-km mesh to the hand- 
 drawn charts to determine whether LFM input is 
 adequate for the regional model. Upper-air sound- 
 ing data were available from Quillayute station on 
 the Washington coast; weather ship Papa, located 
 at 50 °N, 145 °W; Sea-Tac airport, south of 
 Seattle; and Portage Bay in Seattle. The pressure 
 analysis maps show pressure in millibars, written 
 out to the units place on isobars and to the tenths 
 place at stations. In the latter the first two digits 
 are deleted; e.g., 236 = 1023.6 mbar. Wind is given 
 on these maps as barbs (one full barb = 10 kn). 
 On the local wind maps, direction and speed to- 
 
 Figure 12. — Topographic grid used in the computations as 
 viewed from the southwest. 
 
 gether are given at stations; e.g., 2813 — wind 
 from 280°, speed 13 kn. 
 
 5.3 Model Simulations 
 
 Two basic regimes describe the general 
 weather characteristics of Decembers in western 
 Washington. As is typical of the latitude, a succes- 
 sion of frontal passages from the west, varying in 
 number and intensity, dominates, producing 
 strong winds from the southwest. Between storms, 
 high pressure builds up near the area, often in the 
 continental interior, bringing clear skies and rela- 
 tively low winds lasting for several days to a week 
 or more. The fall and winter of 1976 were unusual 
 in that a persistently recurring ridge of high pres- 
 sure (500 mbar) over the Northeast Pacific, fre- 
 quently extending almost to the pole, allowed 
 only an occasional weakened frontal passage 
 through the area. Surface high pressure associated 
 with the 500-mbar pattern, but displaced eastward 
 over the continent, dominated the Puget Sound 
 Basin. 
 
 We selected examples from the data set de- 
 scribed above to model both of the basic winter 
 regimes, the typical midwinter case (cyclonic 
 storm system) and the frequent lull between win- 
 ter storms (interior high pressure). In addition, we 
 chose to use data from the same winter set to 
 model the typical summer case (offshore high 
 pressure), since, in all respects except temperature, 
 the example selected is representative of the sum- 
 mer pattern. 
 
 11 
 
125° 
 
 124° 
 
 123° 
 
 122° 
 
 48° 
 
 47° — 
 
 Fraser River Valley 
 
 - 50° 
 
 49° 
 
 48° 
 
 47° 
 N 
 
 125° 
 
 124° 
 
 123° 
 
 122°W 
 
 Figure 13. — Locations of anemometer stations that collected data for December 1976-January 1977. 
 
 12 
 
5.3.1 Cyclonic storm system 
 
 The front that approached the coast at 0000 
 GMT, 8 December 1976 (fig. 14), turned into a 
 cold front of respectable energy as the high re- 
 treated far to the south. The even isobars and 
 southwesterly geostrophic flow before this front 
 are typical before the passage of a cold front. 
 From the local wind vectors (fig. 15), one first 
 notices that the flow is channeled by the Olympic 
 and Cascade Mountains. Winds over Puget Sound 
 are stronger and more southerly than offshore. A 
 region of light winds is evident in the lee of the 
 Olympic Mountains. There is also general steerage 
 of the flow along the axis of the Strait of Georgia, 
 more than a 90° deflection from the geostrophic 
 wind. The temperature sounding at 1605 GMT on 
 7 December at Sea-Tac shows a relatively moist, 
 deep, well-mixed PBL with near-neutral stability 
 (fig. 16). This is illustrated further by the fact that 
 the 850-mbar flow is very similar to the surface 
 flow on the LFM maps (see figs. 17a and 17b). The 
 hand-drawn and LFM surface maps agree well. 
 Figures 18 and 19 for 0000 GMT, 15 December, 
 show an additional example of strong winds from 
 the southwest. 
 
 The corresponding storm situation of 8 De- 
 cember 1976 is simulated by a model run for PBL 
 heights of 1800 m and 900 m (figs. 20a and 20b). 
 Geostrophic wind is 14.7 m s" 1 from 251°. The 
 overall wind pattern for a PBL height of 1800 m is 
 much smoother than that suggested by observa- 
 tions. The pattern for the lower height, however, 
 is about as detailed as the observed pattern. An 
 eddy has formed at the east end of the Strait of 
 Juan de Fuca near Port Angeles in each simulation. 
 The PBL height deviations show a gentle rise over 
 the windward side of the mountains with a pro- 
 nounced lee wave trough on the downwind side of 
 the Olympics and Vancouver Island. With a low 
 inversion height, increased winds flow through 
 the low point in the mountains of Vancouver Is- 
 land and spill out over the inland waters. Ob- 
 served winds in the east end of the Strait of Juan 
 de Fuca are less intense and more westerly than 
 either model run suggests. It may be that the posi- 
 tion of the eddy and the magnitude of the pressure 
 gradient that develops along the axis of the Strait 
 of Juan de Fuca are very sensitive to the volume of 
 air channeled through Puget Sound, which de- 
 pends in turn on the orientation of the offshore 
 flow. Inflow along the southern boundary is not 
 handled satisfactorily by arbitrary specification of 
 inversion height, especially at the land-water in- 
 terface. However, this does not appear to unduly 
 influence the flow in the central basin. 
 
 In the previous section it was noted that 
 
 inertia plays a dominant role in mesoscale circula- 
 tions. The main difference between the two model 
 runs lies in whether the flow goes over the moun- 
 tain or around it. Since observations resemble 
 more the case with a lower inversion, perhaps the 
 effective cross-sectional height of the mountains is 
 higher than the model-assumed average eleva- 
 tions; the light stable stratification of the PBL 
 shown in the Sea-Tac sounding may contribute to 
 increased channeling. 
 
 5.3.2 Interior high pressure 
 
 A good example of interior high pressure oc- 
 curred at 0000 GMT on 1 December 1976. For 
 several days before and after this time, high pres- 
 sure prevailed over southeastern British 
 Columbia, extending north and south over the 
 interior plateau (fig. 21). In areas of flat topog- 
 raphy, widely spaced isobars would suggest a 
 weak flow outward from the high pressure center 
 westward over the area. However, the local wind 
 shown in fig. 22 reveals a complex pattern with 
 easterly winds at the coast and calm or light 
 northerly winds in Puget Sound. A very interest- 
 ing feature is seen in the Strait of Juan de Fuca. In 
 sharp contrast to the weak and variable winds 
 elsewhere on the inland waters, there is a strong 
 flow out the Strait, reaching 20 kn at Cape 
 Flattery. This isolated jet was reported by Reed 
 (1931) but is not specifically mentioned in more re- 
 cent literature. Associated with these low-level 
 wind vectors are temperature soundings over the 
 area that reveal a strongly stratified regime 
 throughout the planetary boundary layer. The 
 Sea-Tac sounding at 1610 GMT on 30 November 
 1976 is shown in fig. 23. Lines of constant poten- 
 tial temperature are also shown, indicating stable 
 stratification throughout the boundary layer. 
 
 In the objective analyses from the National 
 Meteorological Center, the absence of horizontal 
 air flow seen at 850 mbar in fig. 24a for 1 Decem- 
 ber, 0000 GMT, contrasts with the surface pattern 
 (fig. 24b), which shows a light pressure gradient 
 east-west through the region in agreement with the 
 hand-drawn map. The spacing on the surface LFM 
 map is 1 mbar, approximately equivalent to the 
 10-geopotential meter spacing of the 850-mbar 
 LFM map. The decoupling of the 850-mbar and 
 surface layer is consistent with the strong vertical 
 stratification observed at Sea-Tac. Stability re- 
 stricts the flow to regions below the mountain tops 
 where the air is accelerated along the east-west 
 pressure gradient out through the Strait of Juan de 
 Fuca and west through the Cowlitz Valley south of 
 the Olympic Mountains. The winds are stronger 
 in the strait than along the southern Washington 
 
 13 
 
Figure 14. — Sea level pressure chart, 8 December 1976, 0000 GMT. 
 
 14 
 
Figure 15.— Local wind observations, 8 December 1976, 0000 GMT. 
 
 15 
 
3042 
 
 
 N. I 
 
 I I 
 \ \ 
 
 \ * '•• 
 
 I I 
 
 i 
 
 E 
 
 
 
 x \ 
 
 
 
 r 1483 
 
 — \ 
 
 
 "\ > 
 
 
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 sz 
 
 
 
 \ 
 
 •• \<s> 
 
 
 
 
 
 V 
 
 
 
 
 
 
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 \ Nfe 
 
 
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 \ 
 
 
 
 
 
 X 
 
 \ \ 
 
 \ \ 
 
 - 
 
 153 
 
 
 
 I 
 
 I \ 
 
 
 i 
 
 700 
 750 
 
 800 -. 
 
 E 
 850 - 
 
 900 a 
 a. 
 
 950 
 
 1000 
 1018 
 
 -15 -10 
 
 10 15 
 
 Figure 16. — Temperature sounding (••••)/ dew point ( ), 
 
 and potential temperature ( ) at Sea-Tac for 1605 
 
 GMT, 7 December 1976. 
 
 a b 
 
 Figure 17.— Objective analysis of (a) 850-mbar heights and (b) sea level pressure on 8 December 1976, 0000 GMT. 
 
 16 
 
Figure 18. — Second example of strong onshore flow from southwest, 15 December 1976, 1800 GMT. 
 
 17 
 
Figure 19. — Local wind observations for fig. 18. 
 
 18 
 
w, 
 
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 10ms" 
 
 Figure 20.— Velocity vector plots of model winds for southwest flow. Offshore PBL height equals (a) 1800 m and (b) 900 m. 
 
 coast because the down-gradient acceleration is 
 uninhibited by surface friction. Another curious 
 feature is that the winds in Puget Sound proper 
 flow south, in the opposite direction to those in- 
 ferred from the surface geostrophic wind. A sec- 
 ond example of winds under the high pressure re- 
 gime is seen in figs. 25 and 26, where high pressure 
 has built up rather rapidly between frontal pass- 
 ages. The local stations again reflect the widely 
 spaced isobars with easterly winds on the coast, 
 calm in the sound, and acceleration along the 
 Strait of Juan de Fuca. 
 
 Figure 27a shows the wind pattern generated 
 by the model corresponding to the case of 1 De- 
 cember 1976. Although the boundary layer is not 
 well mixed as assumed in Section 2, we believe 
 that we can simulate the forced channeling for the 
 east wind case by assuming a very shallow PBL in 
 the model, capped by very strong stability. Input 
 parameters are summarized in table 3. The model 
 
 was initialized by a geostrophic wind of 4.8 m s" 1 
 from 144° and a low PBL height of 0.6 km as rep- 
 resentative of stable conditions throughout the 
 lower troposphere. The major features are light 
 winds in the central basin, weak easterly flow 
 along the coast, and accelerating easterly flow 
 down-gradient through the Strait of Juan de Fuca, 
 
 Table 3. — Model input parameters 1 
 
 Wind 
 
 Date 
 
 Geostrophic 
 
 Wind 
 
 hi 
 
 Ad 
 
 T a 
 
 Type 
 
 (1977) 
 
 Speed 
 
 (m/s) 
 
 Direction 
 
 (km) 
 
 (K) 
 
 (K) 
 
 E 
 
 1 Dec 00Z 
 
 4.8 
 
 144° 
 
 0.6 
 
 9.8 
 
 273.0 
 
 SW, 
 
 8 Dec 00Z 
 
 14.7 
 
 260° 
 
 1.8 
 
 7.0 
 
 289.5 
 
 sw 2 
 
 8 Dec 00Z 
 
 14.7 
 
 260° 
 
 0.9 
 
 7.0 
 
 289.5 
 
 NW 
 
 9 Dec 12Z 
 
 16.2 
 
 321° 
 
 1.0 
 
 5.2 
 
 280.1 
 
 'The influence of temperature in the form of land-water tem- 
 perature differences was neglected in all Puget Sound cases. 
 Thus, it was not necessary to carry the heat equation in the 
 calculations. 
 
 19 
 
Figure 21. — Sea level pressure analysis, 1 December 1976, 0000 GMT. 
 
 20 
 
Figure 22.— Local wind observations, 1 December 1976, 0000 GMT. 
 
 21 
 
3149 
 
 E 
 
 ~ 1720 
 
 I 
 
 - 
 
 I I 
 
 I 
 
 i § i 
 
 - 
 
 
 
 \1 
 
 V<s> \ 
 
 
 - 
 
 v2» 
 
 
 I X 1 
 
 - 
 
 ( 
 
 V 
 
 
 
 
 ^ ( 
 
 
 
 >^ 
 
 
 
 
 v > 
 
 - 
 
 \ 
 
 
 
 \/f 
 
 
 - -> 
 
 [ I 
 
 i 
 
 \ 1 
 
 
 700 
 
 750 
 
 800 ~ 
 
 E 
 850 - 
 
 900 S 
 
 IX 
 
 950 
 
 1000 
 1029 
 
 -15 -10 -5 5 10 
 
 Figure 23. — Temperature sounding (• • • •), dew point ( ), 
 
 and potential temperature ( ) at Sea-Tac for 1610 
 
 GMT and wind at Portage Bay for 2015 GMT, 30 November 
 1976. 
 
 a b 
 
 Figure 24. — Objective analysis of (a) 850-mbar heights and (b) sea level pressure on 1 December 1976, 0000 GMT. 
 
 22 
 
Figure 25.— High pressure to the northeast of Puget Sound, 21 December 1976, 1800 GMT. 
 
 23 
 
Figure 26. — Local wind observations for pressure field shown in fig. 25. 
 
 24 
 
10 m s~ 1 
 Figure 27a . — Velocity vector plot of model run for east wind case . 
 
 similar to the conditions shown in figs. 22 and 26. 
 As the flow in all channels is out of the Puget 
 Sound basin, this case could not be run to steady 
 state. In the prototype the outflowing air is re- 
 placed by subsidence associated with the synoptic 
 high pressure. Subsidence is not included in the 
 model to balance the falling PBL height; fig. 27a is 
 the model-estimated wind field when the interior 
 PBL height has reached 400 m after 4 h and is fall- 
 ing at a constant velocity. To increase the resolu- 
 
 tion in the main area of interest, the Strait of Juan 
 de Fuca, the grid length was reduced to one-half of 
 its previous value in the north-south direction, 
 and the domain was also reduced to see whether 
 the model could be sectionalized (fig. 27b). Good 
 agreement is obtained in the strait. Contrary to 
 the inference from observations, at the east end of 
 the Strait of Juan de Fuca a more geostrophic flow 
 occurs if the southern end of Puget Sound is not 
 included in the model domain. 
 
 25 
 
10 ms -1 
 
 Figure 27b.— Velocity vector plot of model run for east wind case with increased north-south resolution. 
 
 5.3.3 Offshore high pressure 
 
 The front depicted in fig. 25 was the weakest 
 of four crossing the region in December 1976. For 
 a day following the 8 December front and a day 
 following the 22 December front, a cell of high 
 pressure existed off the coast of Oregon and 
 Northern California and brought strong north- 
 westerly winds through Washington as part of an 
 anticyclonic circulation. Except for temperature 
 effects, this pattern is typical of summertime con- 
 ditions in the region. The hand-drawn pressure 
 map of 1800 GMT, 23 December 1976, shows a 
 relatively uniform pressure gradient from offshore 
 inland to Vancouver, B.C. (fig. 28). The local ane- 
 mometer readings (fig. 29) reveal the effect of 
 topography on a northwesterly geostrophic wind. 
 Strong channeling is indicated in the Strait of Juan 
 de Fuca with variable winds in the lee of the 
 Olympic Mountains. It is interesting that for this 
 
 case and for 1200 GMT, 9 December 1976 (figs. 30 
 and 31), there is a southerly flow in lower Puget 
 Sound in the lee of the Olympics, but only at the 
 surface. Figure 32 shows the wind sounding for 
 1400 GMT, 9 December, at McChord Air Force 
 Base, and the Quillayute temperature sounding. 
 The LFM maps (figs. 33a and 33b) concur with the 
 hand analysis in showing a northwesterly geo- 
 strophic flow. 
 
 Figure 34 shows the model velocity field for 
 northwest winds. Channeling is indicated in the 
 Strait of Juan de Fuca and especially in the Strait 
 of Georgia. Height deviations are less intense than 
 for the southwest wind case, although the velocity 
 field indicates that the lee wave eddy is still a 
 major feature. A southerly tendency is indicated 
 in the lower Puget Sound trough where the flow is 
 parallel to the pressure gradient below the ridge 
 crests. 
 
 26 
 
Figure 28.— Sea level pressure chart, 23 December 1976, 0800 GMT. 
 
 27 
 
125° 
 
 124° 
 
 123° 
 
 122° 
 
 50° 
 
 49° 
 
 48° 
 
 47° 
 
 50° 
 
 49° 
 
 48° 
 
 47° 
 N 
 
 3212 
 
 125° 
 
 124° 
 
 123° 
 
 122°W 
 
 Figure 29. — Local wind observations, 23 December 1976, 1800 GMT. 
 
 28 
 
Figure 30.— Sea level pressure chart, 9 December 1976, 1200 GMT. 
 
 29 
 
Figure 31.— Local wind observations, 9 December 1976, 1200 GMT. 
 
 30 
 
3000 
 
 — 1475 
 
 165 
 
 
 _A 
 
 i i 
 
 l 
 
 i 
 
 i 
 
 \ 
 
 ^^ 
 
 
 
 _ 
 
 \ 
 
 v\ 
 
 
 
 
 ^ 
 
 V 
 
 \<s> 
 
 
 
 _\ 
 
 \ <s> 
 
 V 
 
 *• x sS 
 
 X 
 
 - 
 
 ^ 
 
 
 : 
 
 
 
 ^ 
 
 
 I 
 \ 
 \ 
 
 
 - 
 
 - / 
 
 
 K 
 
 
 - 
 
 - y 
 
 i i 
 
 i 
 
 i 
 
 IX 
 
 700 
 
 750 
 
 - 800 
 
 900 £ 
 
 Q_ 
 
 950 
 
 1000 
 1015 
 
 -10 
 
 10 
 
 Figure 32. — Temperature sounding (....), dew point ( ), 
 
 and potential temperature ( ) at Quillayute (Washing- 
 ton coast) for 1200 GMT and wind at McChord Air Force 
 Base (Puget Sound) for 1400 GMT, 9 December 1976. 
 
 a b 
 
 Figure 33. — Objective analysis of (a) 850-mbar heights and (b) sea level pressure on 9 December 1976, 1200 GMT. 
 
 31 
 
7. REFERENCES 
 
 Brown, R. A. (1974): A simple momentum integral 
 
 model. /. Geophys. Res. 79:4076-4079. 
 Holbrook, J. R., and D. Halpern (1978): Variability of 
 
 near-surface currents and winds in the western Strait 
 
 of Juan de Fuca. Pacific Marine Environmental 
 
 Laboratory, Seattle, Washington. Unpublished 
 
 manuscript. 
 Keyser, D., and Anthes, R. (1977): The applicability of 
 
 a mixed-layer model of the planetary boundary layer 
 
 to real-data forecasting. Mon. Wea. Rev. 105:1351- 
 
 1371. 
 Lavoie, R. (1972): A mesoscale numerical model of 
 
 lake-effect storms. /. Atmos. Sci. 29:1025-1040. 
 Lavoie, R. (1974): A numerical model of tradewind 
 
 weather on Oahu. Mon. Wea. Rev. 102:630-637. 
 Ogura, Y., and N. W. Phillips (1962): Scale analysis of 
 
 deep and shallow convection in the atmosphere. /. 
 
 Atmos. Sci. 19:173-179. 
 Reed, J. (1931): Gap winds of the Strait of Juan de Fuca. 
 
 Mon. Wea. Rev. 59:373-376. 
 Shuman, F. G. (1957): Numerical methods in weather 
 
 prediction, II: smoothing and filtering. Mon. Wea. 
 
 Rev. 85:357-361. 
 Stull, R. B. (1976): Mixed-layer depth model based 
 
 upon turbulent energetics. /. Atmos. Sci. 33:1268- 
 
 1278. 
 
 10ms" 1 
 
 Figure 34. — Velocity vector plot of model winds for northwest 
 flow. 
 
 6. ACKNOWLEDGMENTS 
 
 This study was supported jointly by the 
 Marine Ecosystems Analysis (MESA) Puget Sound 
 Project and the Outer Continental Shelf Environ- 
 mental Assessment Program (OCSEAP) to assist 
 in providing wind field information for oil spill 
 trajectory calculations, and by the Marine Ser- 
 vices Program at the Pacific Marine Environ- 
 mental Laboratory (PMEL), which aids National 
 Weather Service marine prediction along the west 
 coast and the Gulf of Alaska. 
 
 We wish to thank Robert Anderson and his 
 colleagues at the Seattle National Weather Service 
 Forecast Office for their collaboration in the field 
 program and in compiling the routine observation 
 data sets, and Jim Holbrook of PMEL for making 
 available his anemometer observations and dis- 
 cussing their implications. 
 
 32 
 
APPENDIX: Derivation of Boundary Layer Equations 
 
 We shall write the equations of motion for 
 deviation from a steady reference state. If the ref- 
 erence state changes only very little with height, it 
 is possible to use the Boussinesq approximation, 
 but with potential temperature as the thermal 
 variable (Ogura and Phillips, 1962). 
 
 The momentum equation is 
 
 dv _ _ 
 Jt +V '* V 
 
 W -r- + fkxv + CpOoVir 
 oz 
 
 dz 
 
 (v'w') 
 
 (Al) 
 
 where 
 
 «&■ 
 
 R/c p . 
 
 The hydrostatic equation is 
 
 - p "dz 
 
 = -g- 
 
 The equation of continuity is 
 dw 
 
 V«u + 
 
 dz 
 
 0. 
 
 (A2) 
 
 (A3) 
 
 The first law of thermodynamics is approximated 
 by 
 
 dd , _ _ fl , 86 d ,— 
 
 — + v-ve + w— = - - (w 
 
 at dz dz 
 
 '). 
 
 (A4) 
 
 In these equations v is Reynolds' averaged hori- 
 zontal velocity vector, v ' is the deviation ve- 
 locity, 6 is potential temperature, and 6 is the 
 potential temperature of the reference state (con- 
 stant). The other terms are defined in the usual 
 meteorological sense. 
 
 We simplify the hydrostatic equation (A2) in 
 the following way: 
 
 c ^=_1= .I (i±"\ 
 
 where 0"'= 6 - d . 
 
 If we define t such that 
 
 - p dz d ' 
 
 dir" g 6' 
 
 - p ~di ' Wo do 
 
 then 
 
 where -k" = tt-ttq. 
 
 Since 7T is a function of z only, we can rewrite eq. 
 (Al) 
 
 — + u-Vu + w — 
 3f 3z 
 
 + fkxv + CpdoVir ' 
 d 
 
 (A6) 
 
 dw 
 
 {v'w'). 
 
 We shall use eqs. (A3), (A4), (A5), and (A6) for 
 describing the flow field in the well-mixed layer. 
 
 We now integrate (A4) and (A6) through the 
 mixed layer. The basic equations then become 
 
 dv , r 
 
 — + v-W + fkxv + 
 
 dt 
 
 -pvo 
 
 h -o / -" 
 
 : - {v'w' h- v'w ' s )/(h-D), 
 
 ^ + v.ve = -(w 7 i 
 
 at 
 
 dz 
 (A7) 
 
 w'6 s ')/(h-D). 
 
 (A8) 
 
 In addition, the mass continuity equation, by defi- 
 nition, can be written 
 
 ^+V(h-D)v=E 
 
 (A9) 
 
 where E is the net entrainment rate at which the 
 well-mixed layer gains mass from the free at- 
 mosphere. 
 
 Using the hydrostatic equation, we evaluate 
 the vertically integrated pressure gradient force: 
 
 Cpdo 
 
 f Vir" dz = - c p doVir H 
 
 D 
 
 + | (H-fi)v0 H "-f (B h "-8")Vh 
 
 + | Vi(h-D)V6" (A10) 
 
 vo 
 
 where subscript H denotes the top of the model 
 atmosphere. 
 
 For the convenience of finite differencing, eq. 
 (A8) is written in a flux form: 
 
 dt 
 
 (h-D)d + V.(h-D)v6-6E 
 
 = -(w'd'h + (W'd')s 
 
 (All) 
 
 33 
 
In deriving the equation, eq. (A9) was used. The where Av = v + '-v- and Ad = 6+ - 6-. 
 
 momentum equation (A7) was also put in flux 
 
 form. The flux form of (A9) with the substitution of 
 
 Integrating eq. (Al) and (A4) across the jump (A10), equations (A9) and (All), and entrainment 
 
 between the PBL and inversion layer using Leib- relations (A12) and (A13) form a closed set of 
 
 nitz' rule, we obtain relations equations, (1), (2), and (3) in the text, given that 
 
 the entrainment rate can be parameterized in 
 
 (v'w')h = -EAv (A12) terms of the mixed layer variables. 
 
 and (w'6') h = -EA6 (A13) 
 
 34 
 
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