APRIL 1998
ZENG AND DICKINSON
537
Effect of Surface Sublayer on Surface Skin Temperature and Fluxes
XUBIN ZENG
AND
ROBERT E. DICKINSON
Institute of Atmospheric Physics, The University of Arizona, Tucson, Arizona
(Manuscript received 15 November 1996, in final form 29 July 1997)
ABSTRACT
The surface sublayer is the layer of air adjacent to the surface where the transfer of momentum and heat by
molecular motion becomes important. Equations are derived to incorporate this surface sublayer (or the variable
ratio of the roughness length for momentum over that for heat, zo /zoh ) over bare soil into a commonly used
formulation for aerodynamic transfer coefficients. Along with the consideration of the laminar layer around
vegetation leaves in the Biosphere–Atmosphere Transfer Scheme (BATS), these equations provide a consistent
approach for the computation of surface fluxes over bare soil or vegetated surface.
Qualitative and quantitative analyses show that the surface sublayer tends to substantially increase the surface
skin temperature for a given sensible heat flux and decrease the heat flux for a given surface versus air temperature
difference. Using a climate model output as the atmospheric forcing data for BATS over a semiarid region, it
is also found that the surface sublayer significantly increases the monthly and July-averaged hourly surface skin
temperature and decreases surface sensible heat and net radiation fluxes.
Comparison with limited observations of zo /zoh also suggests that the same (or different) exchange coefficients
should be used over bare soil and vegetated portions in a grid box for dense canopies (e.g., grassland or forest)
[or sparse canopies (e.g., semiarid regions)].
1. Introduction
The surface sublayer (typically 1023–1021 m in thickness over bare soil) is the layer of air adjacent to the
surface where the transfer of momentum and heat by
molecular motion becomes important. In this sublayer,
the Monin–Obukhov similarity analysis developed for
the surface layer (i.e., the nearly constant flux layer
above the surface sublayer but usually lower than 100
m) is not valid. While only molecular transfer is important for heat in this sublayer, both molecular transfer
and pressure fluctuations (particularly around bluff elements) are important for momentum, and so the net
effect of the surface sublayer on the latter is much less
noticeable. The variations of temperature and humidity
across the sublayer can also be very large (e.g., Hall et
al. 1992). Furthermore, as will be discussed in section
2, these variations are directly related to the concept of
a difference between the roughness length for momentum (zo ) versus that for heat (zoh ).
An understanding of this sublayer (or the ratio of zo /
zoh ) is necessary in order to be able to use surface skin
(or radiative) temperature (Becker and Li 1995) from
satellite remote sensing for the computation of surface
fluxes (Moran et al. 1994), for the validation of climate
Corresponding author address: Dr. Xubin Zeng, Institute of Atmospheric Physics, The University of Arizona, PAS Bldg., #81, Tucson, AZ 85721.
E-mail: xubin@gogo.atmo.arizona.edu
model skin temperature (Jin et al. 1997) and for the
retrieval of soil moisture content (Nemani et al. 1993;
Gillies and Carlson 1995). In addition, Beljaars and Viterbo (1994) and Holtslag and Ek (1996) showed that
the value of zo /zoh is important for the modeling of land
surface fluxes. Brutsaert (1982), Garratt (1992), and
Mahrt (1996) have reviewed prior work on this sublayer
(or zo /zoh ).
Over homogeneous bare soil or vegetated surfaces,
Garratt and Francey (1978) found that ln(zo /zoh ) is about
2. Over heterogeneous surfaces (e.g., sparse canopies),
however, recent studies (e.g., Beljaars and Holtslag
1991; Duynkerke 1992; Hignett 1994; Stewart et al.
1994; Malhi 1996; Verhoef et al. 1997) reported that zo
and zoh could differ by several to over 10 orders of
magnitude. Garratt et al. (1993) interpreted these extremely small values of zoh as possibly a consequence
of measurement errors and of the impact of sparse vegetation cover. Malhi (1996) showed that a significant
cause of the low measured value of zoh over a heterogeneous surface may be the use of radiative surface
temperature, which itself is difficult to define over actual
atmospheric surfaces with complex vegetation (Becker
and Li 1995), as a representative surface temperature.
The impact of sparse canopy on the estimate of ln(zo /
zoh ) was further studied in Blyth and Dolman (1995),
who showed that the value of zoh depends on vegetation
fraction and other environmental conditions. Similarly,
Hignett (1994) and Sun and Mahrt (1995) demonstrated
that zoh is flow dependent.
538
JOURNAL OF CLIMATE
Various approaches have been previously proposed
to incorporate this surface sublayer (or zo /zoh ) into the
surface layer Monin–Obukhov similarity theory. They
include: 1) determining new stability functions as a
function of surface skin temperature directly (Brutsaert
1992; Sun and Mahrt 1995); 2) assuming a flux-gradient
relation in the sublayer (or, alternatively, assuming a
relation between zo /zoh and other surface quantities; see
discussions in section 2) (Zilitinkevich 1970; Brutsaert
1982; Kustas et al. 1989; Garratt 1992; Kohsiek et al.
1993); and 3) adding an extra surface resistance term
(Lhomme et al 1988; Vidal and Perrier 1989; Sauer et
al. 1995). Despite these efforts, no general guidance is
yet available to provide a priori estimates of zoh over
heterogeneous surfaces for the modeling of the coupled
soil–vegetation–atmosphere system.
The current paper attempts to address this issue by
separate treatments of the surface sublayer over bare
soil versus the laminar layer over a canopy. In contrast
to the common emphasis on the use of remotely sensed
surface temperature for the estimation of surface fluxes,
this paper focuses on the inclusion of surface sublayer
in land surface parameterization for weather and climate
models. However, its framework may also be useful for
the assimilation of surface skin temperature from satellite remote sensing in a numerical model.
Section 2 uses the flux-gradient approach to derive
equations that can then be interpreted in terms of the
various approaches summarized above and so provide
a unified treatment for the inclusion of the sublayer in
the computation of surface fluxes over bare soil and
vegetated surface for weather and climate models. Section 3 evaluates the impact of this sublayer on surface
skin temperature and fluxes, the relationship between
our equations and limited observations over homogeneous and heterogeneous surfaces, and the effect of
measurement errors on the estimates of ln(zo /zoh ).
2. Theory
This section derives equations for vegetated surface
with the vegetation fraction cover sv ranging in value
from zero (i.e., bare soil) to unity. Surface fluxes over
bare soil and canopy are computed separately; and both
the surface sublayer over bare soil and laminar boundary
layers within a canopy are considered.
a. Bare soil
Using the Monin–Obukhov similarity theory, the
flux-gradient relation for momentum in the surface layer
(usually a few tens of meters above the ground) can be
written as (e.g., Garratt 1992)
[
]
12
u
z
z
u(z) 5 * ln 2 cm
,
k
zo
L
(1)
where k is the von Kármán constant (0.4), zo is the
VOLUME 11
aerodynamic roughness length for wind with u(zo ) 5 0,
cm is the stability function for momentum (see Garratt
1992), and L is the Monin–Obukhov length defined as
L5
uu 2
*.
kgu
*
(2)
Note that the term cm (zo /L) has been omitted in (1) as
much smaller than other terms. Similarly, the surfacelayer relation for temperature (e.g., Garratt 1992) is
[
]
u
z
z
u (z) 2 u (z oh ) 5 * ln 2 ch
,
k
z oh
L
12
(3)
where ch is the stability function for heat, and zoh is the
roughness length (or, more correctly, surface scaling
length) for heat.
The roughness length zo has a sufficiently clear physical meaning that its value can be estimated from the
vertical scale and other properties of the soil or vegetation (e.g., Garratt 1992). In contrast, the physical significance of zoh is not evident, and its value cannot be
determined from surface features alone. In fact, both zoh
and u(zoh ) are undefined in (3), and choosing one specifies the other. As discussed in Brutsaert (1982) and
Garratt (1992), if we take zoh 5 zo , u(zoh ) can be defined
as the temperature at zo , but its measurement would still
be difficult to make in practice. Alternatively, by identifying u(zoh ) with the surface skin (i.e., radiative) temperature, which is the key parameter in surface energy
balance and can be readily measured from remote sensing, zoh can be determined experimentally from
[
]
12
u
z
z
u (z) 2 ug 5 * ln 2 ch
,
k
z oh
L
(4)
where ug is the surface skin (i.e., radiative) temperature.
As mentioned in the introduction, zo is greater than zoh
over land due to the impact of pressure fluctuations on
momentum transfer (but not on heat transfer). Therefore,
applying (4) to z 5 zo yields
u
z
u (z o ) 5 ug 1 * ln o ,
k
z oh
(5)
where small terms ch (zo /L) and ch (zoh /L) have been
omitted.
As already mentioned, the transfer of heat by molecular motion becomes important in the interfacial sublayer very near the ground. On the basis of dimensional
analysis and interpretation of heat transfer experiments,
Zilitinkevich (1970) suggested a relation between u(zo )
and ug :
1 2
u
u z
u (z o ) 5 ug 1 * a * o
k
n
0.45
,
(6)
APRIL 1998
539
ZENG AND DICKINSON
where a 5 0.13.1 The quantity (u*zo /n) is the roughness
Reynolds number (Re*) (and may be interpreted as the
Reynolds number of the smallest turbulent eddy in the
flow) with the kinematic viscosity of air, n, being about
1.5 3 1025 m 2 s21 . It is seen from (5) and (6) that
ln
1 2
zo
u z
5a * o
z oh
n
.
(7)
gz(u 2 ug )
Rb 5
,
uu 2
u* u* 5 CH u(u 2 ug ) 2
and
(9)
u* u* 5 C9H (z/z o , z/z oh , Rb)u(u 2 ug ),
(10)
where the transfer coefficients for momentum and heat
are, respectively,
and
(11)
C9H 5 k 2 /[ln(z/z o ) 2 cm (z/L)][ln(z/z oh ) 2 ch (z/L)].
(12)
Equations (7)–(10) can be directly used for the computation of surface fluxes through iterations. However,
it is perhaps preferable to use analytical forms of the
transfer coefficients to avoid iterations. In addition, such
forms allow for the correct asymptotic behavior as u →
0 (i.e., requiring heat fluxes to reach finite values as u
→ 0). Such analytical forms have been obtained for a
constant or variable ratio of zo /zoh (Garratt 1992; Mascart
et al. 1995; Uno et al. 1995; Holtslag and Ek 1996).
For the general case with a variable ratio of zo /zoh , (1)
and (3) are combined to give
u*u* 5 CH u[u 2 u(zo )],
[
]
CH u z o
ln
u u ,
u* k z oh * *
(13)
where the aerodynamic exchange coefficient
1
Note that a 5 0.13 3 0.74 5 0.0962 in Deardorff (1974) and
Pielke (1984). The factor 0.74 was introduced by Businger et al.
(1971) partly based on k 5 0.35. With the now generally accepted
value of k close to 0.4, the factor 0.74 should also be dropped.
(15)
which, with the help of (9), can be further rearranged
as
@[
u* u* 5 CH u(u 2 ug )
11
1 2
]
CH
z
ln o .
1/2
kC D
z oh
(16)
Using the Zilitinkevich relation (7), we can obtain from
(16)
@[
u* u* 5 CH u(u 2 ug )
11
1 2
a uz o
k n
]
0.45
CH C 20.275
.
D
(17)
Similarly, moisture flux can be derived as
@[
q* u* 5 CH u(q 2 qg )
11
1 2
a uz o
k n
0.45
]
CH C D20.275 ,
(8)
we can obtain from (1) and (4) that
CD 5 k 2 /[ln(z/z o ) 2 cm (z/L)] 2 ,
With (5), (14) can be rewritten as
0.45
Brutsaert (1982) has suggested separate alternative
equations for ‘‘smooth’’ surfaces, surfaces with ‘‘bluff
elements,’’ and surfaces with ‘‘permeable or randomly
distributed elements.’’ Equation (7) and all those summarized in Table 4.2 of Brutsaert (1982) were developed
primarily from experimental laboratory data with Re*
smaller than 1000. Whether these equations can also be
applied to the surface sublayer in the atmosphere with
a higher Re* has not been tested due to a lack of data.
This issue will be briefly addressed in section 3b. Note
that (7) is applied to only bare soil in our method.
For the computation of surface fluxes in numerical
models, a transfer coefficient formulation is widely
used. Defining the bulk Richardson number Rb as
u*2 5 CD (z/z o , Rb)u 2 ,
CH 5 k 2 /[ln(z/zo ) 2 cm (z/L)][ln(z/zo ) 2 ch (z/L)]. (14)
(18)
where it has been assumed, as is widely accepted, that
the transfer coefficient is the same for temperature and
humidity. The quantity qg is the specific humidity at
surface; various methods have been proposed for its
determination in land surface models. For instance, in
the Biosphere–Atmosphere Transfer Scheme (BATS)
(Dickinson et al. 1993), the term (q 2 qg ) is replaced
by b[q 2 qs (ug )] [where qs (ug ) is the saturated humidity
at surface skin temperature] with the wetness factor b
determined by the maximum realizable upward soil
moisture flux.
Therefore, for the general case with a variable ratio
of zo /zoh , (9), (17), and (18) give the aerodynamic transfer coefficient formulations for the computation of surface momentum, sensible heat, and latent heat fluxes,
respectively, with the transfer coefficients being a function of z/zo and Rb only. For instance, for the National
Center for Atmospheric Research (NCAR) Community
Climate Model (CCM2), these are given as (Louis 1979;
Holtslag and Boville 1993)
CD 5 CN (z/z o ) f D (z/z o , Rb),
CH 5 CN (z/z o ) f H (z/z o , Rb),
and
(19a)
(19b)
where CN is the neutral exchange coefficient and f D and
f H are stability functions.
Note that (17)–(18) were derived with the second
approach discussed in the introduction, but the factors
in square brackets could alternatively be interpreted as
providing an additional stability correction to transfer
coefficients to allow use of surface skin temperature
(i.e., the first approach for flux calculations). In addition,
if the aerodynamic resistance for heat, rah , is introduced,
540
JOURNAL OF CLIMATE
rah 5 1/(CH u),
(20)
then (17) can be rewritten as
u*u* 5 (u 2 ug )/[rah 1 rss ],
(21)
where the additional resistance from the surface sublayer is
rss 5
a
1 2
u* z o
u* k n
0.45
5
1 2
a uz o
uk n
0.45
C D20.275 .
(22)
Furthermore, (18) can be expressed with this additional
resistance (the third approach). In sum, it has been
shown that (17) and (18) provide a unified approach for
the computation of surface fluxes over bare soil.
b. Vegetated surface
For a partially vegetated land surface with a vegetation fraction of sv and bare soil fraction of (1 2 sv ),
surface fluxes can be computed by use of various methods to obtain an effective roughness length, as summarized in Garratt (1992), and then application of (9),
(17), and (18). An alternative and perhaps more realistic
approach is to compute fluxes over vegetated fraction
sv and bare soil fraction (1 2 sv ) separately. Over bare
soil, the above equations (9), (17), and (18) are directly
applied, while over canopy, a one-layer canopy treatment as in BATS (Dickinson et al. 1993) is adopted.
Provided the air within the canopy has negligible heat
capacity, the heat flux from the foliage (u*u*)f and from
the soil (u*u*)g must be balanced by heat flux to the
atmosphere (u*u*)a , that is,
(u * u * ) a 5 (u * u * ) f 1 ( u * u * ) g
where these fluxes are given by
(23)
(u* u* )a 5 sv CH u(u 2 uaf ),
(u* u* )f 5 0.01sv Ild Lsai u*0.5(uaf 2 uf ),
(u* u* )g 5 0.004sv C 1/2
D u(uaf 2 ug ),
(24)
and
VOLUME 11
Likewise, for vegetated surface, the total moisture
flux to the atmosphere is the area-weighted sum of fluxes
over bare soil [computed from (18)] and over canopy
[computed using equations similar to (23)–(26) except
that both the evaporation from wet canopy and transpiration from dry canopy need to be considered (cf.
Dickinson et al. 1993 for detailed discussions)].
Note that our treatments of the surface sublayer over
bare soil [i.e., Eq. (6)] and the laminar boundary layer
past leaves treated as flat plates when the local velocity
is u* [i.e., Eq. (25)] have similar dependence on u*. To
see it clearly, (6) can be written as
(u*u*)soil ; u*0.55[u(zo ) 2 ug ],
while (25) can be written as
(27a)
(u*u*)foliage ; u*0.5[uaf 2 u f ].
(27b)
This functional form was inferred from Gates (1980),
whose review suggests that an exponent of u* as large
as 0.8 might be appropriate in (27b) for a turbulent leaf
boundary layer. Evidently, the canopy surface resistance
can be accounted for over a fully vegetated surface similar to that done in (22) for bare soil. Conversely, a
possible physical model from which the Zilitinkevich
relationship could be derived would be a new laminar
flow of velocity u* past individual surface roughness
elements.
3. Sensitivity tests
Surface temperature and humidity are determined as
part of a land surface model, while the wind, temperature, and humidity at the reference height are provided
by observations or an atmospheric model. This section
discusses sensitivity tests for prescribed sensible heat
fluxes or temperatures (i.e., independent of any specific
atmospheric or land models) and then with the BATS
land model.
(25)
(26)
where Lsai is the sum of leaf and stem (including dead
matter) area indexes, Ild is the inverse square root of the
characteristic plant surface dimension in the direction
of wind flow (5 m21/2 for most of the vegetation types
in BATS), and u, ug , and uf are air, soil, and canopy
surface temperatures, respectively. While it is very difficult to accurately compute the soil flux under the canopy (u*u*)g , it is small relative to other two terms in
(23) so that we have not attempted to improve the simple
bulk formulation (26) from BATS. The canopy air temperature uaf can then be obtained from (23) to (26), and
the sensible heat flux to the atmosphere, that is, (u*u*)a ,
can subsequently be obtained from (24) over vegetated
portion. The area-weighted sum of this term and the
heat flux over bare soil computed from (17) gives the
total heat flux to the atmosphere.
a. Desert summer afternoon
Since the denominator in (17) is always greater than
unity, the sublayer should increase the surface skin versus air temperature differences for a given sensible heat
flux (SH) and decrease SH for a given temperature difference. This impact is shown quantitatively by analyzing the simple case of a typical warm summer afternoon.
The air temperature at z 5 10 m is 310 K, and the wind
speed (u) varies from 1 to 10 m s21 . In addition, the
roughness length (zo ) is assumed to be either 0.01 m (as
used in offline BATS) or 0.05 m (as used for bare soil
for BATS implemented in the NCAR CCM2).
Equation (17) with aerodynamic transfer coefficients
from Holtslag and Boville (1993) is used to analyze the
impact of the surface sublayer on the surface skin temperature for a given value (500 W m22 ) of SH, typical
of arid conditions. These results are summarized in Fig.
1. Figure 1a shows that, in the limit of weak wind and
APRIL 1998
ZENG AND DICKINSON
541
FIG. 1. Results with zo 5 0.01 and 0.05 m for a prescribed sensible heat flux are denoted by
the solid and dotted lines, respectively. (a) The difference in surface temperatures computed with
Eq. (17) (i.e., with the surface sublayer) vs zo /zoh 5 1 (i.e., the standard formulation) as a function
of wind speed. (b) The difference in surface temperatures from (17) vs ln(zo /zoh ) 5 2. (c)
Temperature difference between surface and z 5 zo from (17). (d) Temperature difference between
surface and z 5 10 m from (17). (e) Logarithm of roughness length ratios from (17). (f ) Ratio
of the surface resistance [cf. Eq. (22)] to the air resistance [cf. Eq. (20)].
zo 5 0.05 m, the surface skin temperature from (17)
(i.e., with the surface sublayer) can be at least 10 K
larger than that using the conventional formulation [i.e.,
(17) without the denominator, or assuming zo /zoh 5 1).
Even for the strong wind conditions, the temperature
difference is still 3–6 K.
For a constant ratio of zo /zoh , the sensible heat flux
can be calculated using (16). Figure 1b shows the surface skin temperature difference between (17) and (16)
with ln(zo /zoh ) 5 2 as suggested by Garratt (1992). The
smoother surface (zo 5 0.01 m) given by (16) is hotter
by up to 7 K for weak winds, whereas the rougher
surface (zo ) 5 0.05 m) is cooler by 3 K, almost independent of wind speed. Agreement would evidently be
better for some intermediate roughness length values,
but the point is seen that the more physically based
expression, Eq. (6), implies that the ratio of zo /zoh varies
with environmental conditions [Fig. 1e shows that ln(zo /
zoh ) varies from 1 to 2 for zo 5 0.01 m, and from 2 to
nearly 5 for zo 5 0.05 m].
The difference between surface skin temperature and
temperature at z 5 zo—that is, [ug 2 u(zo )]—is shown
in Fig. 1c. Comparison of Fig. 1c with 1a shows that
their shapes are similar but that the values in Fig. 1c
are 2–3 K larger. In other words, the temperature at z
5 zo predicted using (17) is similar to (but 2–3 K cooler
than) the surface temperature based on the conventional
formulation and quite different from the surface skin
542
JOURNAL OF CLIMATE
VOLUME 11
FIG. 2. (a) The ratio of sensible heat flux (SH) based on the assumption of zo /zoh 5 1 (i.e.,
the standard usage) over that using Eq. (17) (i.e., with the surface sublayer). (b) The ratio of
SH based on the assumption of ln(zo /zoh ) 5 2 over that using (17). Results with zo 5 0.01 and
0.05 m for a prescribed surface vs air temperature difference are denoted by the solid and dotted
lines, respectively.
temperature predicted using (17). Figure 1d shows the
difference between surface temperature obtained from
(17) and the air temperature at z 5 10 m—that is, (ug
2 u). Comparison of this panel with Fig. 1c shows that
the [ug 2 u(zo )] is about 50% of (ug 2 u) for zo 5 0.05
m and about one-third of (ug 2 u) for zo 5 0.01 m.
Figure 1f shows that the surface resistance rss [cf. (22)]
is generally larger than the air resistance rah [cf. (20)]
over rougher surface (zo 5 0.05 m). Even over smoother
surface (zo 5 0.01 m), rss is still 40% of rah .
How the surface sublayer affects sensible heat flux
(SH) for a given value (325 K) of ug (i.e., ug 2 u 5 15
K) is summarized in Fig. 2. Figure 2a shows that the
ratio of the sensible heat flux using the conventional
formulation [i.e., (17) without the denominator] over
that using (17) is about 1.3 and 2 for zo 5 0.01 and
0.05 m, respectively, almost independent of wind. When
ln(zo /zoh ) 5 2 is assumed, Fig. 2b shows that the ratio
of the heat flux using this assumption over that using
(17) can be larger or smaller than unity but varies from
0.75 to 1.4.
b. Summer afternoon over vegetated surface
For a vegetated surface with a vegetation fraction sv ,
different treatments are expected (but have not been
developed yet) for dense canopies (e.g., grassland) and
sparse canopies (e.g., semiarid regions). Roughly speaking, (1 2 sv ) refers to the small spacing between canopies for dense canopies and to unvegetated parts of a
grid area on various spatial scales for sparse canopies.
The exact meaning of sv is unclear, because as a model
APRIL 1998
ZENG AND DICKINSON
543
FIG. 3. (a) The effective roughness length (zoe ) for momentum, and (b) the logarithm of the
roughness length ratios, as a function of vegetation fraction ( sv ). For each sv, 540 different
combinations of environmental conditions prescribed in the text are used. Observational values
from Stewart et al. (1994) are denoted by the star signs in (b).
parameter, it cannot be accurately determined from satellite remote sensing due to the strong impact of viewing
angle and the but indirect relationship between sv and
remotely sensed variables (e.g., Nemani et al. 1993;
Gillies and Carlson 1995; Sellers et al. 1996). Here the
same aerodynamic exchange coefficients are used to
compute the heat flux for the bare soil and vegetated
portions separately [with (17) and BATS formulations
(23)–(26), respectively], which might be reasonable
only for small enough spacing between vegetation and
bare soil. The total surface sensible heat flux is then
obtained by area averaging the individual fluxes. Using
area-weighted averaged values of temperature, wind,
and fluxes, the ratio of effective roughness length for
momentum over that for heat (i.e., the ratio if bare soil
and vegetated portion are treated together) can be ob-
tained from (16), which can then be compared with
limited observations.
For a typical summer afternoon over vegetated surface, the air temperature is 300 K at z 5 10 m, and Ild
and Lsai in (25) are 5 m21/2 and 6, respectively. The wind
speed is taken as 1, 3, 5, 7, 9, or 11 m s21 ; the surface
temperature is 305, 310, or 315 K; the vegetation temperature is 300.3, 302.3, or 304.3 K; the roughness
length of bare soil (zo ) is 0.01 or 0.05 m; and the roughness length of canopy (zof ) is 0.3, 0.6, 0.9, 1.2, or 1.5
m. The results from these 540 different combinations
of parameters for each vegetation fraction sv are then
given in Fig. 3. Limited observations from Stewart et
al. (1994) are also given in the figure. Also shown in
Fig. 3 is the effective roughness length for momentum
(zoe ), which is obtained by assuming that the effective
544
JOURNAL OF CLIMATE
neutral drag coefficient [CN in (19)] is the area-weighted
mean value; that is,
[ln(z/zoe )]22 5 (1 2 sv )[ln(z/zo )]22 1 sv [ln(z/zof )]22 .
(28)
Because zoe depends on sv , zo , and zof only, many of the
plus signs overlap in Fig. 3a. In contrast, each vertical
line in Fig. 3b is not a line but consists of 540 dots.
Figure 3a shows that, just as implied by (28), if zoe is
used for the computation of surface fluxes (without computing fluxes over bare soil and vegetated portions separately), this value will generally vary between surfaces.
Figure 3b shows that, depending upon environmental
conditions and the prescribed surface parameters, the
value of ln(zoe /zoh ) could be close to the observed value
of 2 over homogeneous surfaces (Garratt and Francey
1978) or close to some of the observed values over
heterogeneous surfaces (Stewart et al. 1994). The sensitivity of ln(zoe /zoh ) to various environmental conditions
will be discussed briefly at the end of this section.
However, the maximum value of ln(zoe /zoh ) in Fig. 3b
(i.e., 6.1) is still much smaller than some of the observed
extremely high values (i.e., extremely small zoh ) reported in the literature (e.g., 12 in Stewart et al. 1994;
14 in Hignett 1994; 34 in Malhi 1996). This suggests
that the use of the same exchange coefficients over bare
soil and canopy for both dense and sparse canopies
might be incorrect. With larger spacing (for sparse canopies in comparison with dense canopies), the air may
not be well mixed between bare soil and vegetation
canopy so that different exchange coefficients should
be used. The distinction between this ‘‘mixture’’ and
‘‘tile’’ approach is reviewed in IPCC 1995 (i.e., Dickinson et al. 1996).
Using the same parameters as those used in generating
Fig. 3, we have recomputed ln(zoe /zoh ) by computing
both the exchange coefficients and fluxes separately
over soil and canopy, and the results are summarized
in Fig. 4a. Comparison of Fig. 3b and Fig. 4a shows
that the value of ln(zoe /zoh ) can be larger for averaging
over tiles [i.e., the mosaic or tile approach (Avissar and
Pielke 1989; Koster and Suarez 1992; Seth et al. 1994)].
For instance, the maximum value in Fig. 4a is 15.1 in
comparison with 6.1 in Fig. 3b. Results in Fig. 4a also
become more consistent with observed values (e.g.,
Stewart et al. 1994).
Figure 4b gives ln(zoe /zoh ) as a function of Re* for
cases in Fig. 4a with the vegetation fraction between
0.1 and 0.9. For the given values of Re*, the values of
ln(zoe /zoh ) using (7) and the Brutsaert formulation for
bluff rough elements [i.e., (4.133) in Brutsaert (1982)
or (4.14) in Garratt (1992)] are also shown in Fig. 4b.
The values using the Brutsaert formulation are much
larger than the computed values. In contrast, for Re* ,
10 4 , results from (7) are consistent with computed values but become larger for Re* . 10 4 . Equation (7) is
also more consistent with observations of Stewart et al.
(1994) (see their Fig. 1) than with the Brutsaert for-
VOLUME 11
mulation. Figure 4b also shows that, if (16) with an
effective roughness length for momentum (zoe ) is directly applied to a partially vegetated surface (without
computing fluxes over soil and canopy separately), both
(7) (for Re* . 10 4 ) and the Brutsaert formulation appear
to give unrealistically large values of ln(zoe /zoh ), although (7) is relatively better.
Finally, we use (16) to briefly address the impact of
measurement errors on the estimates of ln(zo /zoh ). The
possibility of such errors is also part of the reason that
we do not emphasize the exact agreement between modeling and observations. Even though quantities in (16)
are ultimately determined by the wind and temperatures,
they may be independently measured in field experiments. The sensitivity of ln(zo /zoh ) to other quantities in
(16) can be expressed as
d ln
1 2
zo
kuC 1/2
kC 1/2
D
D dCH
5
d(u 2 ug ) 1
z oh
u * u*
CH CH
1 0.5 ln
2
kC 1/2
z o dCD
D (u 2 ug )
1
du
z oh CD
u * u*
1 2
kuC 1/2
D (u 2 ug ) d(u u )
* * .
u* u*
u * u*
(29)
For the case of log(Re*) 5 4.2 (close to the maximum
value in Stewart et al. 1994) with the maximum value
(about 10.5) of ln(zo /zoh ) (denoted by the plus sign in
Fig. 4b), the coefficients in (29) can be determined to
obtain
d ln
1z 2 5 21.69d(u 2 u ) 1 3.22 C
dCH
zo
g
oh
H
1 1.53du 2 13.8
d(u* u* )
.
u* u*
1 5.27
dCD
CD
(30)
This means that a warm bias of 2 K in measuring surface
temperature ug or an overestimate of wind speed by 1
m s21 would increase ln(zo /zoh ) by about 3.4 and 1.5,
respectively. Similarly, an underestimate of the sensible
heat flux by 20% would increase ln(zo /zoh ) by 2.8. When
CD is increased by 50% (e.g., due to the consideration
of form drag over heterogeneous surfaces), this would
increase ln(zo /zoh ) by about 2.6. Equation (30) also
shows that the impact of measurement errors of CH on
ln(zo /zoh ) is much smaller than that of the heat flux [i.e.,
the last term in (30)].
c. BATS test
The importance of the surface sublayer can be further
illustrated by using ‘‘realistic’’ atmospheric inputs over
a seasonal cycle. For reasons of availability, we use
output from a climate model to determine these inputs.
One year of hourly output is obtained from the NCAR
APRIL 1998
ZENG AND DICKINSON
545
FIG. 4. (a) The same as Fig. 3b except that different exchange coefficients are used over soil
and canopy, and (b) the logarithm of roughness length ratios in (a) as a function of the logarithm
to the base 10 of the roughness Reynolds number over a vegetated surface with the vegetation
fraction between 0.1 and 0.9. Equation (7) and the Brutsaert formulation for bluff rough surfaces
are denoted by the solid and dotted lines, respectively, in (b). The plus sign in (b) represents the
case on which sensitivity analysis is discussed at the end of section 3b.
CCM2 coupled with BATS (Hahmann et al. 1995) as
the input for our offline BATS sensitivity tests. One grid
box at 23.78N and 08E over Africa is selected to represent the typical semidesert environment. For the BATS
vegetation type of 11 (semidesert) that is prescribed for
this location, the vegetation cover varies from 0 to 0.1
while the bare soil fraction varies from 0.9 to 1 over
the seasonal cycle. The roughness length for momentum
(zo ) is 0.05 m over bare soil and 0.1 m over canopy in
CCM2/BATS. While the laminar layer over canopy is
included, the surface sublayer over bare soil is not considered in the standard BATS. Monthly averaged results
and hourly values averaged in July from the standard
BATS, BATS with the sublayer formulation [i.e., Eq.
(17)], and BATS with the assumption of ln(zo /zoh ) 5 2
are summarized in Figs. 5–7.
Figure 5a shows monthly averaged fluxes from the
standard BATS. Over semiarid and arid regions, the
latent heat flux is small and limited by soil water supply—that is, the latent heat flux (LH) in Fig. 5a simply
reflects the precipitation whose total amount for the year
is 165 mm. Except in winter, the sensible heat flux (SH)
is much larger than LH, and it closely follows the net
radiation flux (Rnet). Figure 5b shows that, in July, LH
is close to zero and Rnet is mainly balanced by SH (and
to a lesser degree by ground heat flux). Figure 5c reflects
the fact that average surface temperature is larger
(smaller) than air temperature in summer (winter), while
546
JOURNAL OF CLIMATE
VOLUME 11
FIG. 5. (a) Monthly averaged latent and sensible heat and net radiation fluxes denoted by the
solid, dotted, and dashed lines, respectively. (b) The same as in (a) except for July-averaged
hourly fluxes. (c) Monthly averaged surface skin temperature and air temperature at the first
model level (about 65 m) denoted by the solid and dotted lines, respectively. (d) The same as
in (c) except for July-averaged hourly temperatures. The standard BATS is used.
Fig. 5d shows that the maximum daytime temperature
difference between surface and the first model level of
CCM2 (about 65 m) is about 10 K, which is smaller by
up to a factor of 2 than values typically observed over
arid/semiarid regions.
Figure 6a shows that neither the use of (17) nor the
assumption of ln(zo /zoh ) 5 2 can significantly affect the
simulation of monthly averaged LH, because LH is limited by soil water supply (from precipitation) only. Figure 6b demonstrates that the use of (17) decreases the
monthly averaged SH by 8 W m22 in summer (about
10% of SH from the standard BATS). Figure 6c, compared with Fig. 6b, shows that the decrease of SH is
largely compensated by a decrease in Rnet (increase in
upward longwave radiation). It is also seen from Figs.
6b,c that there is little difference in fluxes resulting from
the use of (17) versus that with the assumption ln(zo /
zoh ) 5 2 (at most 3 W m22 in summer). Figure 6d shows
that the monthly averaged surface skin temperature with
(17) exceeds that without a sublayer by more than 18K
in summer, but in summer exceeds that with ln(zo /zoh )
5 2 by at most 0.4 K.
Similar to Fig. 6a, Fig. 7a shows that the hourly latent
heat flux (LH) averaged in July differs little between
different simulations. Figures 7b–d show substantial differences implied by the inclusion of a surface sublayer.
The afternoon peak skin temperature is increased by 4
K (Fig. 7d), and the peak sensible heat fluxes are reduced by 50 W m22 (Fig. 7b). This flux reduction is
partially compensated by decreased net radiation flux
(mainly through increased upward longwave radiation)
(28 W m22 ) (Fig. 7c) and partially by increased flux
APRIL 1998
ZENG AND DICKINSON
547
FIG. 6. Monthly averaged (a) latent heat flux difference, (b) sensible heat flux difference, (c)
net radiation flux difference, and (d) surface skin temperature difference. Differences between
BATS with the sublayer formulation [i.e., Eq. (17)] and the standard BATS (i.e., zo /zoh 5 1 over
bare soil) are denoted by solid lines, while those between BATS with the sublayer formulation
and BATS with the assumption of ln(zo /zoh ) 5 2 over bare soil are denoted by dotted lines.
into the soil (22 W m22 ), both a result of the increased
skin temperature. Comparison of the dotted and solid
lines in Fig. 7 shows that the peak changes obtained
with ln(zo /zoh ) 5 2 are only about two-thirds as large.
It can also be found from Figs. 7d and 5d that the peak
temperature difference between surface and the first
model level of CCM2 (about 65 m) increases from about
10 K without the surface sublayer to a perhaps more
reasonable 14 K with (17). The decrease of SH (and the
corresponding increase of surface temperature) due to
the inclusion of the surface sublayer is also consistent
with the observational data analysis of Stewart et al.
(1994).
Note that the peak temperature difference of 4 K in
Fig. 7d is consistent with that in Fig. 1a for the zo 5
0.05 m case, allowing for differences in the sensible
heat flux (SH)—that is, 500 W m22 assumed for the
computation of Fig. 1a versus a peak SH of 400 W m22
found for the standard BATS (see Fig. 5b) and 350 W
m22 for BATS with (17) (see Figs. 5b and 7b). If SH
were 400 W m22 for both the standard BATS and BATS
with (17), the peak temperature difference would be
about 5.5 K. The effect of the reduction of 50 W m22
can be estimated from 0.1 [i.e., (50 W m22 )/(500 W
m22 )] of Fig. 1d to be about 1.5–2 K, hence reducing
the difference to the calculated 4 K. When the surface
sublayer is included in a diurnally varying land model,
the temperature increase is smaller and sensible heat
flux reduction larger than would be expected for a constant net radiation. The temperature increase has a negative feedback from the increases in upward longwave
and midday downward soil heat fluxes. In addition,
since energy requirements largely determine daytime
summer surface skin temperature, the addition of the
548
JOURNAL OF CLIMATE
VOLUME 11
FIG. 7. The same as in Fig. 6 except for July-averaged hourly fluxes or temperatures.
surface sublayer resistance in a climate model should
act to reduce surface air temperature somewhat but usually less than the differences just discussed.
4. Conclusions
The surface sublayer (typically 1023–1021 m over
bare soil) is the layer of air adjacent to the surface where
the transfer of momentum and heat by molecular motion
becomes important. The variations of temperature and
humidity across the sublayer depend on the ratio of the
roughness length for momentum (zo ) over that for heat
(zoh ). By linking these variations to the roughness Reynolds number as suggested by Zilitinkevich (1970), we
have derived equations to incorporate this surface sublayer (or the variable ratio of zo /zoh ) into the surface
layer Monin–Obukhov similarity theory for aerodynamic transfer coefficients over bare soil.
Various approaches have been proposed in the past
to consider this sublayer (or zo /zoh ). Because our derived
equations can be interpreted according to any of these
approaches, they provide a unified approach for the inclusion of the sublayer in the computation of surface
fluxes. In addition, provided transfer coefficient formulations are given as a function of z/zo and the bulk
Richardson number Rb only (e.g., Louis 1979), no iterations are needed in our equations.
The derived equations (9) and (17)–(18) are only applied to bare soil in our formulation, but they are shown
to be consistent with inclusion in a canopy model of
the laminar layer around leaves. Together, they provide
a consistent approach for the computation of surface
fluxes over bare soil or vegetated surface.
For a desert summer afternoon, and given a sensible
heat flux (SH) of 500 W m22 , the temperature difference
between surface and z 5 zo can vary from 4 to 14 K
under various wind and zo conditions. The surface sublayer also increases the calculated surface skin temperature by 3–11 K compared to the conventional formulation with zo /zoh 5 1. For zo 5 0.05 m (as used in the
APRIL 1998
ZENG AND DICKINSON
NCAR CCM2), zo /zoh varies by an order of magnitude
for a typical range of wind conditions. In addition, given
the surface and air temperature, the surface sublayer
significantly reduces SH (by as much as 50% for zo 5
0.05 m).
Over vegetated surface, both the effective roughness
length for momentum (zoe ) and for heat (zoh ) will vary
with the vegetation fraction. With the same aerodynamic
exchange coefficients used to compute fluxes over bare
soil and vegetated portions separately, our formulations
give ln(zoe /zoh ) either close to the observed value of 2
over homogeneous surfaces or to the somewhat larger
values as observed over some heterogeneous surfaces.
By considering soil and canopy surfaces as separate
tiles, our formulations are also able to obtain extremely
high values of ln(zoe /zoh ) observed over other heterogeneous surfaces.
There appears to be no obvious generalization to this
paper’s approach using Eq. (7) with combined surfaces
except through combination of the contributions of the
individual surfaces, which is consistent with the Verhoef
et al. (1997) conclusion that ln(zoe /zoh ) should be avoided
for sparse vegetation. Simple sensitivity analysis also
shows that the value of ln(zoe /zoh ) is quite sensitive to
measurement errors of surface temperature, drag coefficient, and sensible heat flux when ln(zoe /zoh ) is large.
Use of the NCAR CCM2/BATS output as the atmospheric forcing data for BATS over a semiarid region
shows that the surface sublayer increases the monthly
averaged summer surface versus air temperature difference by more than 1 K (peak daytime by 4 K) and
decreases the SH and net radiation (Rnet) by 8 W m22
(peak daytime by 50 W m22 ). In regions of adequate
soil moisture, additional effects on latent heat fluxes
would occur, but the impact on temperature and sensible
heat fluxes would be smaller.
Acknowledgments. This work was supported by
NASA through its EOS IDS Program (429-81-22; 42881-22), NSF under Grant ATM-9419715, and Department of Energy under Grant DE-FG02-91ER61216. R.
Avissar and an anonymous reviewer are thanked for
their helpful comments. M. Sanderson-Rae is thanked
for her editorial assistance. Part of the computations
were carried out on the NCAR computational facility
as sponsored by NSF.
REFERENCES
Avissar, R., and R. A. Pielke, 1989: A parameterization of heterogeneous land surfaces for atmospheric numerical models and its
impact on regional meteorology. Mon. Wea. Rev., 117, 2113–
2136.
Becker, F., and Z. Li, 1995: Surface temperature and emissivity at
various scales: Definition, measurement and related problems.
Remote Sens. Rev., 12, 225–253.
Beljaars, A. C. M., and A. A. M. Holtslag, 1991: Flux parameterization over land surfaces for atmospheric models. J. Appl. Meteor., 30, 327–341.
, and P. Viterbo, 1994: The sensitivity of winter evaporation to
549
the formulation of aerodynamic resistance in the ECMWF model.
Bound.-Layer Meteor., 71, 135–149.
Blyth, E. M., and A. J. Dolman, 1995: The roughness length for heat
of sparse vegetation. J. Appl. Meteor., 34, 583–585.
Brutsaert, W. H., 1982: Evaporation into the Atmosphere—Theory,
History, and Applications. Reidel, 299 pp.
, 1992: Stability correction functions for the mean wind speed
and temperature in the unstable surface layer. Geophys. Res.
Lett., 19, 469–472.
Businger, J. A., J. C. Wyngaard, Y. Izumi, and E. F. Bradley, 1971:
Flux-profile relationships in the atmospheric surface layer. J.
Atmos. Sci., 28, 181–189.
Deardorff, J. W., 1974: Three-dimensional numerical study of the
height and mean structure of a heated planetary boundary layer.
Bound.-Layer Meteor., 7, 81–106.
Dickinson, R. E., A. Henderson-Sellers, and P. J. Kennedy, 1993:
Biosphere–Atmosphere Transfer Scheme (BATS) version 1e as
coupled to the NCAR Community Climate Model. NCAR Tech.
Note NCAR/TN-3871STR, 72 pp. [Available online at http://
www.atmo.arizona.edu/bats/batsmain.html.]
, V. Meleshko, D. A. Randall, E. Sarachik, P. Silva-Dias, and A.
Slingo, 1996: Climate processes. Climate Change 1995: The
Science of Climate Change, J. T. Houghton, L. G. Meira Filho,
B. A. Challander, N. Harris, A. Kattenberg, and K. Maskell,
Eds., Cambridge University Press, 192–227.
Duynkerke, P. G., 1992: The roughness length for heat and other
vegetation parameters for a surface of short grass. J. Appl. Meteor., 31, 579–586.
Garratt, J. R., 1992: The Atmospheric Boundary Layer. Cambridge
University Press, 316 pp.
, and R. J. Francey, 1978: Bulk characteristics of heat transfer
in the unstable, baroclinic atmospheric boundary layer. Bound.Layer Meteor., 15, 399–421.
, B. B. Hicks, and R. A. Valigura, 1993: Comments on ‘‘The
roughness length for heat and other vegetation parameters for a
surface of short grass.’’ J. Appl. Meteor., 32, 1301–1303.
Gates, D. M., 1980: Biophysical Ecology. Springer-Verlag, 611 pp.
Gillies, R. R., and T. N. Carlson, 1995: Thermal remote sensing of
surface soil water content with partial vegetation cover for incorporation into climate models. J. Appl. Meteor., 34, 745–756.
Hahmann, A. N., D. M. Ward, and R. E. Dickinson, 1995: Land
surface temperature and radiative fluxes response of the NCAR
CCM2/BATS to modifications in the optical properties of clouds.
J. Geophys. Res., 100, 23 239–23 252.
Hall, F. G., K. F. Huemmrich, S. J. Goetz, P. J. Sellers, and J. E.
Nickeson, 1992: Satellite remote sensing of surface energy balance: Success, failures, and unresolved issues in FIFE. J. Geophys. Res., 97, 19 061–19 089.
Hignett, P., 1994: Roughness lengths for temperature and momentum
over heterogeneous terrain. Bound.-Layer Meteor., 68, 225–236.
Holtslag, A. A. M., and B. A. Boville, 1993: Local versus nonlocal
boundary layer diffusion in a global climate model. J. Climate,
6, 1825–1842.
, and M. Ek, 1996: Simulation of surface fluxes and boundary
layer development over the pine forest in HAPEX-MOBILHY.
J. Appl. Meteor., 35, 202–213.
Jin, M., R. E. Dickinson, and A. M. Vogelmann, 1997: A comparison
of CCM2/BATS skin temperature and surface-air temperature
with satellite and surface observations. J. Climate, 10, 1505–
1525.
Kohsiek, W., H. A. R. de Bruin, H. The, and B. van den Hurk, 1993:
Estimation of the sensible heat flux of a semi-arid area using
surface radiative temperature measurements. Bound.-Layer Meteor., 63, 213–230.
Koster, R. D., and M. J. Suarez, 1992: Modeling the land surface
boundary in climate models as a composite of independent vegetation stands. J. Geophys. Rev., 97, 2697–2715.
Kustas, W. P., B. J. Choudhury, M. S. Moran, R. J. Reginato, R. D.
Jackson, L. W. Gay, and H. L. Weaver, 1989: Determination of
550
JOURNAL OF CLIMATE
sensible heat flux over sparse canopy using thermal infrared data.
Agric. For. Meteor., 44, 197–216.
Lhomme, J. P., N. Katerji, A. Perrier, and J. M. Bertolini, 1988:
Radiative surface temperature and convective flux calculation
over crop canopies. Bound.-Layer Meteor., 43, 383–392.
Louis, J. F., 1979: A parametric model of vertical eddy fluxes in the
atmosphere. Bound.-Layer Meteor., 17, 187–202.
Mahrt, L., 1996: The bulk aerodynamic formulation over heterogeneous surfaces. Bound.-Layer Meteor., 78, 87–119.
Malhi, Y., 1996: The behavior of the roughness length for temperature
over heterogeneous surfaces. Quart. J. Roy. Meteor. Soc., 122,
1095–1125.
Mascart, P., J. Noilham, and H. Giordani, 1995: A modified parameterization of flux-profile relationships in the surface layer using
different roughness length values for heat and momentum.
Bound.-Layer Meteor., 72, 331–344.
Moran, M. S., W. P. Kustas, A. Vidal, D. I. Stannard, J. H. Blanford,
and W. D. Nichols, 1994: Use of ground-based remotely sensed
data for surface energy balance evaluation of a semiarid rangeland. Water Resour. Res., 30, 1339–1349.
Nemani, R., L. Pierce, S. Running, and S. Goward, 1993: Developing
satellite-derived estimates of surface moisture status. J. Appl.
Meteor., 32, 548–557.
Pielke, R. A., 1984: Mesoscale Meteorological Modeling. Academic
Press, 612 pp.
Sauer, T. J., J. M. Norman, C. B. Tanner, and T. B. Wilson, 1995:
Measurement of heat and vapor transfer coefficients at the soil
VOLUME 11
surface beneath a maize canopy using source plates. Agric. For.
Meteor., 75, 161–189.
Sellers, P. J., S. O. Los, C. J. Tucker, C. O. Justice, D. A. Dazlich,
G. J. Collatz, and D. A. Randall, 1996: A revised land surface
parameterization (SiB2) for atmospheric GCMs. Part II: The
generation of global fields of terrestrial biospherical parameters
from satellite data. J. Climate, 9, 706–737.
Seth, A., F. Giorgi, and R. E. Dickinson, 1994: Simulating fluxes
from heterogeneous land surfaces: Explicit subgrid method employing the Biosphere–Atmosphere Transfer Scheme (BATS). J.
Geophys. Rev., 99, 18 651–18 667.
Stewart, J. B., W. P. Kustas, K. S. Humes, W. D. Nichols, M. S.
Moran, and H. A. R. de Bruin, 1994: Sensible heat flux-radiometric surface temperature relationship for eight semiarid areas.
J. Appl. Meteor., 33, 1110–1117.
Sun, J., and L. Mahrt, 1995: Determination of surface fluxes from
the surface radiative temperature. J. Atmos. Sci., 52, 1096–1106.
Uno, I., X. M. Cai, D. G. Steyn, and S. Emori, 1995: A simple
extension of the Louis method for rough surface layer modeling.
Bound.-Layer Meteor., 76, 395–409.
Verhoef, A., H. A. R. de Bruin, and B. J. J. M. van den Hurk, 1997:
Some practical notes on the parameter kB21 for sparse vegetation.
J. Appl. Meteor., 36, 560–572.
Vidal, A., and A. Perrier, 1989: Analysis of a simplified relation used
to estimate daily evapotranspiration from satellite thermal data.
Int. J. Remote Sens., 10, 1327–1337.
Zilitinkevich, S. S., 1970: Dynamics of the Atmospheric Boundary
Layer. Leningrad Gidrometeor, 291 pp.