Boundary Layer Observations over Heterogeneous Land Surface for
Determination of Regional Surface Flux and Entrainment Flux
Tetsuya HIYAMA
Hydrospheric Atmospheric Research Center (HyARC), Nagoya University
e-mail: hiyama@ihas.nagoya-u.ac.jp
TEL: +81-52-789-3478,

FAX: +81-52-789-3436

1. Introduction
Data set of temporal variations of heat and water vapor fluxes (sensible and latent heat fluxes)
is necessary to predict precipitation activity over land surface. Behavior of atmospheric boundarylayer (ABL) also affects for the precipitation activity through the land-surface processes (exchange
processes of sensible and latent heat fluxes) and through the interaction with cloud-layer. Inadditions, vegetation and/or land-use change will have impacts for the change of ABL structure.
Therefore it is necessary to monitor the surface (vegetation) condition, (regional) surface fluxes,ABL structures, and entrainment processes.
LAPS/CREST project focuses on the interaction of land surface processes with precipitation
processes. It will carry out ABL observations using with “Flux Tower & Meteorological Observation
System”, “Wind (& Temperature) Profiler”, “Microwave Water Vapor Radiometer”, and “DopplerSodar (Acoustic Wind Profiler)”. Thus in this extended abstract, we will review how to estimate
regional surface fluxes and how to evaluate entrainment processes from the one-dimensional profilesof wind speed, temperature, and humidity within the ABL.

2. Estimation of Regional Surface Fluxes
Convective boundary layer (CBL) is generally divided into three layers, i.e., surface sub-layer(SL), mixed layer (ML), and entrainment layer (EL) in turn from above the surface to the freeatmosphere. If we have cloud in the entrainment layer partly or completely, EL is also defined as
cloud-layer (CL). For the estimation of regional surface fluxes from one-dimensional profiles, wecan apply three approaches described below.

2.1. Temporal Scalar Budget Approach
In the absence of subsidence, the conservation equation for a given scalar is classically written as(Lhomme et al., 1997)

hdCm
dh= F0 + (C f − Cm )dtdt(1)

where h is the CBL depth, Cm the scalar concentration of the well-mixed layer, t the time, F0 thesurface flux, Cf the scalar concentration in the undisturbed atmosphere (free atmosphere or justabove the capping inversion). By integrating (1) between an initial time t1, when Cm = Cm1, Cf = Cf1,and h = h1, and a time t2 (Cm2, Cf2, h2), one obtains the integral form of the CBL budget(McNaughton and Spriggs, 1986)
t2

h2

t1

h1

I 0 = ∫ F0 (t )dt = h2 C m 2 − h1C m1 − ∫ C f (h)dh(2)where I0 is the cumulative surface flux between t1 and t2. With some parameterization, one can use(2) to evaluate the time-integrated flux of sensible heat and latent heat from mean profile
measurements.

2.2. Mixed Layer (Bulk) Similarity Approach
In the steady state ABL, the ratio of inversion flux (entrainment flux; He) to the surface flux (H0),
He/H0, is strongly related to zi/L (Brutsaert and Sugita, 1991). This means that at least in the case of
sensible heat, the incorporation of the entrainment flux He would lead to redundancy and it cantherefore be omitted from the analysis. In the light of these considerations, a bulk similarity to theouter region (i.e., mixed layer) can be written as follows⎡ ⎛ z −d ⎞z − d ⎞⎤⎟⎟ − C ⎛⎜ i
H 0 = (θ 0 − θ m )ku* ρc p ⎢ln⎜⎜ i
⎟⎥
zL
⎝
⎠⎦
0h⎝
⎠
⎣

(3a)

⎡ ⎛z −d⎞⎛ z − d ⎞⎤⎟⎟ − D⎜ ilE 0 = (q 0 − q m )lku* ρ ⎢ln⎜⎜ i⎟⎥⎝ L ⎠⎦⎣ ⎝ z 0v ⎠(3b)

andwhere H0 and lE0 are the surface sensible and latent heat fluxes, θ0 and q0 the surface potential
temperature and specific humidity, θm and qm the characteristic potential temperature and specifichumidity in the well-mixed layer, k = 0.4 von Karman’s constant, u* the friction velocity, ρ thedensity of the air, cp the specific heat at constant pressure, l the latent heat for vaporization, zi theinversion height (height of the mixed layer), d the zero-plane displacement height, z0h and z0v thescalar roughness lengths for sensible and latent heats, L the Obukhov length, and C and D are thesimilarity functions, which are generally accepted to depend on zi/L only (Brutsaert and Sugita,
1991). There are several proposals for the similarity function C = C ((zi – d) / L) and D = D ((zi – d) /L). We should evaluate the C and D functions for different ABL conditions but with no subsidence
and no horizontal flux divergence.

2.3. Surface Sub-layer (Monin-Obukhov) Similarity Approach
If we could get mean profiles only within the surface sub-layer, the following Monin-Obukhov
similarity theory could be applied for the determination of surface fluxes.

⎡ ⎛ z−d ⎞z − d ⎞⎤⎟⎟ − Ψh ⎛⎜H 0 = (θ 0 − θ s )ku* ρc p ⎢ln⎜⎜⎟⎥⎝ L ⎠⎦⎣ ⎝ z0 h ⎠(4a)⎡ ⎛z−d⎞⎛ z − d ⎞⎤⎟⎟ − Ψv ⎜lE 0 = (q 0 − q s )lku* ρ ⎢ln⎜⎜⎟⎥⎝ L ⎠⎦⎣ ⎝ z 0v ⎠(4b)

andWhere θs and qs are the potential temperature and specific humidity within the surface sub-layer, z
the height above the ground, and Ψh and Ψv are the stability function of temperature and humidity
profiles. This approach should be out of application if the surface is statistically inhomogeneous (e.g.,Brutsaert, 1998). For the application of (3) and (4), surface parameter z0h, z0v, and d are necessary.
There is possibility to combine the bulk similarity approach with the Monin-Obukhov similarity
approach. We have already proposed the combined similarity approach (CSA) for the evaluation ofmomentum flux using soundings of wind speed (Hiyama et al., 1999). If we succeeded to combine
two approaches for the temperature and humidity profiles, surface parameters z0h and z0v could beomitted from the equation. The consideration of this possibility is one of the research topics in thisLAPS/CREST.

3. Importance of Entrainment processes for Derivations of Surface Fluxes
If we can apply three-dimensional approach and assume no horizontal eddy flux divergences,mass and heat budgets within the convective boundary layer are derived as follows (Betts and Ball,1994).

ρ w'ξ 0 ' = −1 pt ∂ξ1 pt ⎛ ∂ξ∂ξ ⎞1 pt ∂ξdp − ∫ ⎜⎜ u+ v ⎟⎟dp − ∫ w dp + ρ w'ξ t '∫pp
g 0 ∂tg 0 ⎝ ∂xg p0 ∂p∂y ⎠(5)

Where ξ is scalar variables, w the vertical wind speed, g the acceleration of gravity, p the airpressure, u and v are the longitudinal (x axis) and latitudinal (y axis) wind components. Subscript 0
and t indicate surface and top of the ABL, respectively. Left-hand side of (5) is the surface flux
density. Fourth term in the right-hand side of (5) is the eddy flux density at pt. We can also refer tothe non-surface terms in right-hand side of (5) as the budget contributions from local change (term 1),
horizontal advection (term 2), and vertical advection (term 3).
Entrainment parameter (AR) is convenient parameter for the estimation of heat and water vapor
fluxes on the boundary of ML and EL. AR is defined as follows (Betts, 1992).

H e = − AR

1 + (0.07 β 0 )
H0
1 + (0.07 β e )(6a)andlEe =Heβe(6b)AR is an empirical constant (Stull, 1988), He and lEe are the entrainment flux of sensible heat andlatent heat, β0 the surface Bowen ratio, and βe the inversion-level (entrainment) Bowen ratio.
Equation (6) assumes that the entrainment virtual heat flux density is a constant fraction (-AR) of thesurface virtual heat flux density. The value for β e is possible to estimate from soundings
immediately above the ABL, using a layer in which ∂θ/∂q is relatively constant (Betts and Ball,1994). Barr and Strong (1996) pointed out importance of vertical wind speed (vertical advection;
third term of right-hand side in equation (5)) for the estimation of surface fluxes and AR.
Grant (2001) implied that AR is changeable in different kinds of cloud (Cu, Cb, Sc, St, etc.).
Thus the determination of AR in different cloud conditions is necessary for the derivation of heat andwater vapor fluxes on the surface as well as entrainment fluxes.

4. Summary
We reviewed methods how to estimate regional surface fluxes using mean profiles within theABL. We also suggested importance of entrainment parameter (AR) and vertical wind speed (verticaladvection) for the estimation of surface fluxes. If we can assume no meso-scale horizontal advection
and no horizontal flux divergences, the regional surface fluxes could be estimated with the mean
profiles measured with “Wind (& Temperature) Profiler” and “Microwave Water Vapor Radiometer”.
Those precise time-series of profiles will be capable for the detection of meso-scale disturbance, thus
we have great opportunity for the evaluations of cloud-capped boundary layer processes (e.g.
entrainment process) for various kinds of cloud type as well as precipitation process andland-atmosphere processes.

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