180 M.D. Novak et al. Agricultural and Forest Meteorology 102 2000 173–186
bly because of the greater effort required to manually separate all the clumps of baled straw at the higher
rates. The R
i
function can be represented by the empirical equation,
R
i
= 3.01R
− 0.104
i
− 2.07,
R
i
1R, 24
which is shown in Fig. 3. Note that this applies for fresh straw, which was appropriate since the field ex-
periments lasted 3–5 days for each application rate. Hares 1988 also measured transmissivities of straw
that had been in the field for about 1 year and found large reductions compared to the fresh values Hares
and Novak, 1992, in agreement with the field obser- vations of Wagner-Riddle et al. 1996. Eq. 24 was
used to calculate in Eq. 5 for all i≥3. For i=2 the measured τ =0.76 was used.
Mulch element reflectivity, α
m
, was measured directly by pasting fresh dry barley straw onto a
0.4 m×0.4 m wooden board so that the area was com- pletely covered with straw without any gaps. Solar
radiation fluxes incident to and reflected from the board were measured outdoors around midday on a
clear day 16 October 1996 with the board placed in two orientations, yielding solar-beam angles of 0
and 70
◦
relative to the direction normal to the board. The measurements were done with a single model
CM5 Kipp Zonen solarimeter, which was manu- ally rotated between facing away from and facing the
Fig. 3. Clumping index determined from measured transmissivities vs residue-area index for the barley-straw mulch. Also shown is
the fitted nonlinear regression given by Eq. 24.
board, the latter with the radiometer 0.1 m away from the centre of the board. The solarimeter signal was
monitored directly with a voltmeter. The effects of the background grassed area with measured reflectivity
of 0.25 and the shadow of the solarimeter on the board, both of which were partially in the view of the
solarimeter when it faced the board, were accounted for using standard view factor theory Kreith, 1973
similar to the corrections for τ described above. The α
m
so-measured was 0.46±0.04, which we used in the radiation model for the mulch plots consisting of
pure barley straw. However, for the application rates with clover and weed residues mixed in with the bar-
ley straw, the α
m
was determined by matching mod- elled and measured R
n,1
for the 5 t ha
− 1
mulch during 12:00–13:00 hours PST on 26 September 1993, a
clear day. This α
m
was used for all other times and mulch application rates with the mixed mulch Table
1. The measured α
m
were similar to those of other residue types, e.g., α
m
= 0.46±0.06 for a flail-chopped
corn residue TS90 and α
m
= 0.31 for a sugar-cane
residue Bussière and Cellier, 1994. A value of α
s
= 0.1 moist soil was estimated based
on previous field measurements Hares and Novak, 1992. It was assumed that a
= 0.6, the oceanic value
Idso, 1980, because the site is located within 500 m of the ocean and west-northwest winds prevailed for
most of the study. Because of the variation of the ratio of h to application rate, the effective layer depth for
the 10 t ha
− 1
mulch is actually slightly greater 0.33 than the 0.3 nominally assumed Table 1.
4. Results and discussion
4.1. Comparison with field measurements Diurnal variations of modelled and measured hourly
average R
n,1
for the indicated day in each of the 2, 5, 10, and 15 t ha
− 1
mulch application rate experimen- tal periods are shown in Fig. 4. Agreement between
the model and measurements for all application rates is generally excellent, especially during daytime
and the first half of the night 19:00–24:00 hours PST. Discrepancies, however, are clearly found from
0:00–8:00 hours PST on 11 September 15 t ha
− 1
, 22 September 2 t ha
− 1
, and to a lesser extent on 26
M.D. Novak et al. Agricultural and Forest Meteorology 102 2000 173–186 181
Fig. 4. Diurnal variations on the indicated days in 1993 of measured symbols and modelled solid curves hourly average net radiation
flux density above straw mulches applied at rates of 2, 5, 10, and 15 t ha
− 1
.
September 5 t ha
− 1
. The most likely explanation for these is measurement error due to moisture condensa-
tion on the upper dome of the net radiometer, which we suspect occurred often during the experiments.
The moisture has an emissivity close to 1 and con- sequently the net radiometer overestimates R
n,1
. On 11, 22, and 26 September RH90 was measured at
the climate station during 0:00–6:00 hours PST, but otherwise RH80. During 29 August, RH80
all day which is consistent with the condensation ex- planation. Another possibility, which we feel is less
likely, is a greater cloud cover at night compared with daytime. The C used in the model is based on day-
time measurements of S
and so would then be too low at night, which would cause the model to under-
estimate R
n,1
= L
n,1
. Despite these discrepancies, good agreement is found between measurements and
calculations when all available data from the four mulch application rates are compared on 1:1 plots
Fig. 5. Table 3 reports the linear regression statistics intercept forced through 0 for these 1:1 plots which
show that the r
2
values are all above 0.93. Figs. 6 and 7 present comparisons similar to those in
Figs. 4 and 5, respectively, but between modelled and
Fig. 5. Plots of all available modelled vs measured hourly average net radiation flux density above straw mulches applied at rates of
2, 5, 10, and 15 t ha
− 1
during 1993. Also shown are the 1:1 lines.
measured hourly average S
′ d,N −1
+ S
′′ d,N −1
+ L
d,N −1
. The 1:1 regression statistics are also reported in Ta-
ble 3. Agreement between the model and measure- ments is excellent for all mulch application rates at
night and for the 10 and 15 t ha
− 1
application rates during daytime. But agreement is occasionally poor
during the daytime for the 2 and 5 t ha
− 1
applica- tion rates. This is mainly attributed to the spatial het-
erogeneity of the transmitted shortwave flux beneath these thin canopies. Based on the wheat curve in Gre-
gory 1982, the estimated cover of the soil surface for the barley-straw mulch is 64 and 92 for the 2
and 5 t ha
− 1
mulches, respectively, so that it is ex- pected that the full above-mulch solar radiation flux
would occasionally penetrate to near the bottom of the mulch as solar elevation and azimuth change during
the day. Tram systems have been generally used to overcome this heterogeneity problem by greater spa-
tial sampling when measuring radiation fluxes within forests. Black et al. 1991 found that the more open
the forest canopy, the longer the pathway of the tram should be in order to obtain good spatial averaging.
Because a mulch is much denser than a forest, the to- tal downward radiation flux under the thick mulches
was adequately smooth standard error of estimation
10 W m
− 2
even without spatial averaging which in practice could be done with a line solarimeter but this
182 M.D. Novak et al. Agricultural and Forest Meteorology 102 2000 173–186
Table 3 Statistics associated with the linear regression intercept forced through 0 between modelled and measured net radiation flux density above
the mulch, R
n,1
, and total downward radiation flux density at 0.6 cm above the soil surface within the mulch, S
′ d,N −1
+ S
′′ d,N −1
+ L
d,N −1
, for straw application rates of 2, 5, 10, and 15 t ha
− 1
during 1993 Rate t ha
− 1
r
2
Slope Standard error W m
− 2
Range W m
− 2
Number of hours R
n,1
2 0.96
0.98 30
− 91–407
112 5
0.99 1.02
16 −
75–279 86
10 0.99
1.09 17
− 78–331
89 15
0.94 0.96
32 −
76–274 73
S
′ d,N −1
+ S
′′ d,N −1
+ L
d,N −1
2 0.88
0.99 50
297–782 112
5 0.87
0.96 25
334–532 86
10 0.98
0.99 6.0
369–492 89
15 0.97
1.00 5.4
357–456 73
was not so for the thin mulches standard error of es- timation in the range 20–50 W m
− 2
. 4.2. Model sensitivity analysis
Inputs to the model include variables S , T
a
, e
a
, T
u,i
, T
d,i
, and T
s
, all given as functions of t in the pe- riod of interest and parameters R
i
, α
m
, and α
s
. Outputs of the model consist of various radiation flux
Fig. 6. Diurnal variations on the indicated days in 1993 of mea- sured symbols and modelled solid curves hourly average total
downward radiation flux density at 0.6 cm above the soil surface within straw mulches applied at rates of 2, 5, 10, and 15 t ha
− 1
.
densities of interest. Here, we consider the sensitivity of R
n,i
because of its importance in energy balance modelling at the top i=1, or above the mulch, mid-
dle i=N+22, and bottom i=N+1, or at the soil surface of the mulch to changes in S
, T
u,i
, ε
ac
, α
m
, α
s
, and . The fractional sensitivity, f
p
, of R
n,i
to a fractional change in an input variable or parameter p
is defined as McNaughton and Spriggs, 1986 f
p
= R
t
1
t
p∂R
n,i
∂p dt
R
t
1
t
R
n,i
dt ,
25
Fig. 7. Plots of all available modelled vs measured hourly average total downward radiation flux density at 0.6 cm above the soil
surface within straw mulches applied at rates of 2, 5, 10, and 15 t ha
− 1
during 1993. Also shown are the 1:1 lines.
M.D. Novak et al. Agricultural and Forest Meteorology 102 2000 173–186 183
where t and t
1
are the initial and final times of the period of interest. Because the partial derivative
and integrals in Eq. 25 cannot easily be computed analytically, the partial derivative was replaced by
a finite-difference approximation, 1R
n,i
1p , with
1 p=0.1p, and the integrals were replaced by sums
over the hourly calculated values. For the variables that vary with t and in addition for R
i
and T
u,i
that also vary with i, i=1. . . N, p is a factor that multiplies each of them, with p=1 corresponding to
the base case. Fractional sensitivities were calculated for daytime
6:00–19:00 hours PST and nighttime 19:00–6:00 hours PST averages during 28–31 August 1993, with
the 10 t ha
− 1
mulch Table 4. Sensitivities for the other mulch application rates not shown are qualita-
tively similar. The average daytime R
n,i
is sensitive to S
and ε
ac
, especially in the upper part of the mulch. This was also reported by Tuzet et al. 1993, who
used evapotranspiration rate as the output for their model sensitivity analysis. Daytime R
n,i
is also sen- sitive to , especially in the lower part of the mulch.
T
u,i
, α
m
, and α
s
have little effect except for α
m
at the top of the mulch. Nighttime average R
n,i
is very sensitive to ε
ac
and , especially at the mulch top for the former and at the mulch bottom for the latter.
Changes in the other inputs have little effect. Although R
n,i
is insensitive to T
u,i
, it is of interest to know how large the error is if it is assumed that
T
u,i
= T
d,i
. Additional model calculations show that daytime average R
n,1
is 6 higher when this assump-
Table 4 Fractional sensitivity of the daytime and nighttime averages of net
radiation flux density at the top, middle, and bottom of the 10 t ha
− 1
straw mulch to input variables solar irradiance, S , upper-surface
element temperature, T
u,i
, and atmospheric clear-sky emissivity, ε
ac
and input parameters element shortwave reflectivity, α
m
, soil shortwave reflectivity, α
s
, and clumping index, during 28–31August 1993
Daytime Nighttime
Top Middle
Bottom Top
Middle Bottom
S 1.7
1.2 0.91
− 0.007
− 0.004
− 0.003
T
u,i
− 0.059
− 0.005
0.000 −
0.022 0.033
0.000 ε
ac
1.7 0.92
0.62 −
4.3 −
2.0 −
1.4 α
m
− 0.68
− 0.025
0.25 0.002
0.000 −
0.001 α
s
− 0.001
− 0.006
− 0.08
0.000 0.000
0.000
− 1.1
− 1.9
− 2.7
− 0.12
− 1.3
− 1.8
tion is made. For hourly R
n,1
, the maximum differ- ence is 10. During nighttime, the difference is small
5. Within the mulch, the effects on R
n,i
decrease, becoming negligible at the soil surface. Therefore, al-
though not as important as S , ε
ac
, α
m
, and , measur- ing T
u,i
should be considered if a 10 error is deemed significant.
4.3. Modelled vertical profiles of radiation A major application of the radiation model is to
determine the vertical profiles of the components of the radiation balance within the mulch. Fig. 8 shows
modelled vertical profiles of R
n
, S
d
= S
′ d
+ S
′′ d
, S
u
= S
′ u
+ S
′′ u
, L
d
, and L
u
within the 10 t ha
− 1
straw mulch during 12:00–13:00 hours PST on 29 August 1993.
The largest component at the mulch top is S
d
, which attenuates quickly with decreasing z in the top 13
of the mulch, indicating strong interception of short- wave radiation. A fraction of the intercepted solar ra-
diation is reflected upward as shortwave radiation and the rest is absorbed, and in steady state, re-emitted
as longwave radiation, resulting in R
n
≈ S
d
2 near the canopy top. The albedo of the mulch is 0.27, consid-
erably less than α
m
= 0.46, in agreement with other
studies Tanner et al., 1987. In the lower part of the
Fig. 8. Modelled vertical profiles of downward and upward short- wave, S
d
and S
u
, respectively, and longwave, L
d
and L
u
, respec- tively, radiation flux densities and net radiation flux density, R
n
, within the 10 t ha
− 1
straw mulch during 12:00–13:00 hours PST on 29 August 1993.
184 M.D. Novak et al. Agricultural and Forest Meteorology 102 2000 173–186
mulch, S
d
decreases slowly due to the high degree of clumping of the mulch elements. R
n
decreases even more slowly because the net longwave increases and
S
u
decreases. The shift from loss to gain for the long- wave balance occurs near the middle of the mulch,
which is explained by the vertical profiles of T
u
and T
d
≈T
a
, with the former increasing with z through- out the mulch and the latter reaching a maximum near
zh=23 Novak et al., 2000b. S
d
and R
n
are signifi- cantly large at the soil surface below the mulch which
has implications for the energy balance there Novak et al., 2000b.
Fig. 9 shows modelled vertical profiles within the 10 t ha
− 1
straw mulch during 0:00–1:00 hours PST on 29 August 1993. During nighttime only the longwave
components are nonzero. Although T
u,1
T
a
, R
n
above the mulch is negative because the atmospheric emis-
sivity is much less than that of the residue elements. As zh decreases the sky view factor decreases and R
n
therefore increases slowly. However, R
n
is still nega- tive at the soil surface.
In conservation tillage practices, the degree of clumping among residue elements may change from
one situation to another TS90. The model was used to investigate the impact of clumping on the mulch
radiation balance. In principle, a complete assessment of this impact requires that the effects of changing
Fig. 9. Modelled vertical profiles of downward and upward long- wave radiation flux densities, L
d
and L
u
, respectively, and net ra- diation flux density, R
n
, within the 10 t ha
− 1
straw mulch during 0:00–1:00 hours PST on 29 August 1993.
on the vertical profiles of T
u
and T
d
be known, either from measurements or calculations with a full
energy balance model of the mulch. These effects are not considered here but, as shown by the sensitivity
analysis, they should be small compared to those associated with directly. Fig. 10 shows vertical
profiles of S
n
within the 10 t ha
− 1
straw mulch dur- ing 12:00–13:00 hours PST on 29 August 1993 for
different assumed values of . Except for the =0 case maximum clumping
there is little effect of on S
n
at the top of the mulch in spite of the sensitivity of R
n
indicated in Table 4. For =0, the shortwave radiation reaching
the underlying soil surface is a maximum. A large evaporation rate from soil would be expected in this
case if the soil was wet, so that this element arrange- ment is not efficient for conserving soil moisture but
may be good for warming the soil at high latitudes where low soil temperatures in early spring are a
problem. Both the =1 random distribution and =
3.5 most uniform distribution cases virtually eliminate shortwave radiation at the underlying soil
surface and so are effective for water conservation. According to the actual measured transmissivities,
the mulch elements are clumped to a moderate degree and so an intermediate radiation distribution exists.
Fig. 10. Modelled vertical profiles of net shortwave radiation flux density calculated with the indicated clumping indices within the
10 t ha
− 1
straw mulch during 12:00–13:00 hours PST on 29 August 1993. The transmissivities corresponding to the actual mulch
and =0, 1, and 3.5 were calculated with Eqs. 24, 2, 3, and 4, respectively.
M.D. Novak et al. Agricultural and Forest Meteorology 102 2000 173–186 185
Clumping might explain the 150–200 W m
− 2
under- estimate of evaporation under a sugar-cane mulch by
the model presented in Bussière and Cellier 1994. Their model assumed that the mulch elements were
distributed randomly in each layer. Clearly, clumping greatly alters radiation distribution patterns within a
mulch, which can, therefore, be modified according to different applications.
5. Summary and conclusions
