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A FIRST INVESTIGATION OF TEMPORAL ALBEDO
DEVELOPMENT OVER A MAIZE PLOT
Robert Beyer
May 1, 2007
INTRODUCTION
Albedo, also known as shortwave reflectivity, is defined as the ratio of incoming
radiation to reflected radiation for a given waveband—in this case global irradiation. Many
courses present the concept of albedo, primarily, as a function of the optical characteristics for a
given material. Very little, if any, discussion is explicitly directed toward the temporal aspect of
albedo and its implications. It is well understood that an agricultural plot changes throughout the
four seasons of the year; however, while albedo may remain relatively constant during the offfarming season, the growing season of maize, from pre-emergence to tasseling or senescence, is
a distinct period where land change is a gradual process. Although albedo is a simple concept, it
is nonetheless very robust in its implications to many biogeophysical and biogeochemical
processes. In particular, although it is not in the scope of this paper, this author is interested in
how dynamic albedo plays part in the energy balance partitioning; furthermore, how albedo
changes can alter climate patterns over all spatial and temporal scales.
The purpose of this investigation is to examine how albedo changes, as a function of
time, throughout a portion of a growing season. To meet this end, shortwave radiation data will
be analyzed, via a few simple biophysical models, at time scales from the whole data set period
(day of year 113 to 230) down to hours. The resolved quantitative results will then be compared
to another data set from two other growing seasons and locations, as well as, a few theoretical
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models. The initial hypothesis is that albedo will change from values for soil to that of maize as
presented by Campbell and Norman—0.08-0.13 to 0.18-0.22, respectively.
SITE, INSTRUMENTATION, AND DATA
Discussion of following is important given the nature of the cursory analysis of the
provided data. While it is believed that this analysis will elucidate certain behaviors and patterns
that pertain to the goal of this paper, it would be no less than fair to state that an unfamiliarity
with the site, instrument, and how the data was collected—as well as other environmental
observations—may raise questions to the validity of this analysis. However, the following
analysis is based an experiment that was conducted by the United States Department of
Agriculture—specifically, the National Soil Tilth Laboratory; to this end, there is high
confidence that the data provided has integrity worthy of the professionalism found at this
research facility.
The maize field site was located in Ames, Iowa, at 42.0°N and 94.7°W and data was
collected during the 2005 growing season from April 23 until August 18 (day of year 113 to
230). It should be noted that partial data was collected on the days before and after this period,
but not included in this investigation. The site information provided indicates that the corn was
planted in 30-inch rows running from North to South. Neither plant separation, within rows, nor
plant density was supplied.
Shortwave and longwave radiation was collected by a Kipp and Zonen CNR1 net
radiometer. The CNR1 is configured with four sensors, 2 pyranometers and 2 pyrgeometers,
which account for shortwave and longwave radiation, respectively, in the incoming and outgoing
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direction. For the purposes of this paper, we are concerned with the pyranometers, CM3, used in
this assembly. The pyranometers have a full hemispherical view and are sensitive to a selected
spectral range of 0.305 to 2.800 µm. It should be noted, that these pyranometers are designed
such that they read direct and diffuse shortwave radiation. Although the placement of the
radiometer, relative to the surface, was not specified, it will be assumed that it was positioned
and wired in accordance to manufacture’s specifications to the best of the technician’s ability at
that time.
The data set that was acquired by the assembly described above shows data points at time
averaged 15-minute intervals throughout the collection period. This temporal resolution permits
the description of longer and shorter anomalous events that may have an effect upon the
radiation data. There are two data streams utilized, from this data set, in this analysis they are;
the downwelling and upwelling solar radiation.
As mentioned above, the analysis of data will be compared against the results from
research conducted by Jacobs and Van Pul in 1985 and 1986. A more complete description of
the background of their data will be provided later in the discussion. In addition, a comparison
of incoming radiation will be compared against a biophysical model derived from information in
the text by Campbell and Norman. For accuracy’s sake, the models use inputs based on Ames’
geographical location of 42.0° N 93.6° W and 230 for the day of the year. In an attempt to
evaluate a more accurate value for incoming solar radiation, a real time total solar irradiance
value of 1328.4113 W/m2 was obtained from the SOURCE satellite data from the Laboratory for
Atmospheric and Space Physics’ website. Atmospheric transmission (τ) values of 0.4 and 0.7 for
cloudy days and clear days, respectively, were chosen to represent ends of the τ continuum. It
should be noted that the models were generated by using MATLAB and Microsoft Excel due a
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developing skill set to write programs for the former. However, MATLAB was still utilized
because it was the least cumbersome method to resolve values that required tedious iterations.
METHOD
The focal point of this investigation is albedo and is calculated as:
(1)
Where: ρ is the albedo as prescribed by Campbell and Norman (also known as α in many
climate text)
Su is the upwelling shortwave solar radiation
Sd is the downwelling shortwave solar radiation
The comparison against the results of Jacobs and Van Pul require the calculation of the
daily main albedo. To this end, to maintain an equal comparison required an average based on
the slope of the regression line between incoming and outgoing radiation as discussed in Jacobs,
1990. Hence, the mean was resolved statistically and not arithmetically, as might be expected.
To meet this requirement, Excel was implemented to generate the equation for the linear
regression line and the slope was recorded for each day.
The model used to generate an incoming solar radiation time series graph utilized the
solar beam equation, as well as other components to this equation, as offered by Campbell and
Norman as:
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[W/m2]
(2)
Where: Sb is the incoming solar flux incident upon the surface at a given angle, Ψ
Sp is the solar irradiance normal to the surface
Ψ is the zenith angle of the sun as a function of time and location
[W/m2]
(3)
Where: Sp is the solar irradiance normal to the surface
Spo is the solar constant, which will be defined as mentioned above
τ is the atmospheric transmittance
m is the air mass number
(4)
Where: Ψ is the zenith angle of the sun
is the latitude of the location
δ is the solar declination as a function of the day of year
t is the time of day
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t0 is the time of solar noon
**Note, all angles were converted to radian value for use in Excel and MATLAB
The above formulas were the heart of the model. Other equations pertaining to the above
can be referenced in An Introduction to Biophysics by Norman and Campbell.
RESULTS AND DISCUSSION
Figure 1 is the result from Jacobs and Van Pul’s research. The important aspects of this
graph are the 1985 and 1986 lines representing the evolution of mean daily albedo. This graph
illustrates that two seasons worth of data indicate an increase in albedo as the maize crop
matures, with regard to the period analyzed for comparison.
Fig 1. The evolution of mean daily albedo as described by Jacobs and Van Pul
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Figure 2 is the analysis of data for day of year (doy) 113 through 230 in the method
described by Jacobs and Van Pul. This permits a more fair comparison between the two data
sets—three seasons. The values for albedo do not match directly; however, this could be due to
numerous factors. In particular, Jacobs and Van Pul conducted their research in a different
location (51°58’N, 5°42’E) with different soils and may have not used the same maize crop or
oriented the rows from North to South. Again, as stated above, the data set used for figure 2 was
also lacking in crop density data or the specific position of the pyranometers. Lastly, only
shortwave flux density values where incoming exceeded outgoing and both were positive were
used. This was intentionally done to remove possible erroneous values. In selecting these data,
any instrumentation error values were discarded and represented as gaps in the graph of figure 2.
This leaves much to be desired in the way of a true comparison. Despite these disparities, there
is a trend of increasing albedo between both data sets. Furthermore and perhaps rather
significantly, figure 2 illustrates expected approximated albedo values for soil to maize of 0.08 0.13 to 0.18-0.22, respectively, for the growth period examined.
Fig 2. Evolution of Mean Daily Albedo for 2005(in the same method as Jacobs and Van Pul)
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To get a truer sense of the development of albedo throughout the season and removing
much of the noise observed in figure 2, six days throughout the period were selected, where the
incoming shortwave radiation exhibited clear sky behavior, for plotting of albedo on at an hourly
resolution—figure 3. Again, the data set used had data points for every 15 minutes. The upcurving behavior of the graphs is due to the zenith angles throughout the day. As the zenith
angle approaches 90 degrees, the reflection of solar energy increases greatly. This graph
illustrates an interesting trend in the development of albedo through the period; however, it is
difficult to distinguish and requires higher resolution.
Fig 3. Albedo plotted hourly for six clear sky days throughout the growth period examined.
Figure 4 is the same as figure 3; however, higher resolution was obtained by selecting the
period from 1100 to 1400 hours. It is now possible to see the results of the albedo calculations
for the data set. Interestingly, if this pattern is indicative of agricultural fields, the albedo is as
the beginning of the period is as one might expect from soils. While the albedo values for soils
are at the upper end of what Campbell and Norman offer in their text, the fact remains that there
is a trend to be observed. The albedo increase to a high value, on July 4th, of approximately 0.19,
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roughly in the middle of the period, then decrease to a value of approximately 0.17 by the end of
the period, when the crop canopy has matured but not senesced.
Figure 4. High resolution of figure 3 during a 3-hour time frame depicting the behavior of albedo
development during crop canopy development
Figure 5 illustrates the comparison between observed and modeled values for incoming
shortwave solar radiation. It can be observed that the modeled values, pink and yellow,
underestimate the observed. Speculation lends itself to the fact that the pyranometers read
diffuse, as well as, direct radiation. As such, the model should fall short of the true value for
incoming radiation. The other aspect to consider is the modeling side of the comparison. While
values for τ and m can be adjusted to make the model look like the observed, there is no
component in any of the equations used that address diffuse radiation. The model only considers
the sun angle, time of day, doy, and location. One could anticipate that the τ value should be
lower, since August 18th observed values indicate clear skies.
A closer look at the models also indicates a subtle phase shift to the left for modeled
values. This is problematic. Again, speculation, given the minimal education for this subject
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matter, may indicate atmospheric effects caused by daytime heating or wind. Hourly values are
all adjust to standard time; hence, a computational error for solar noon is not being considered.
It is possible that the instrument was not level—perhaps a bias toward the sun setting side of the
horizon.
Figure 5. Incoming shortwave radiation observed and modeled for August 18th, doy 230
CONCLUSION
Contrary to the initial hypothesis, the albedo did not increase throughout the time frame
under investigation. It increased to a maximum and then subsided to a lower value by the time
of full canopy development. This was only discovered by comparing separate days throughout
the growing period. However, the results of this investigation agree—despite the lack of more
specific information about the experiments—with a lower albedo for a crop canopy of a
particular plant species (Norman, 1998). It will require more investigation to understand why
this is true. Evidently, a crop canopy acts as a trap for solar radiation.
The modeling data should illustrate that great care must be taken when considering their
use. Many factors need to be accounted for and extrapolation may not be accurate enough to
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serve the desired purpose. This may be of particular importance to climate modeling where the
aggregation of errors could invalidate findings—as an example pertaining to the interest of this
investigation. Again, understanding the phase shift and investigating what might have happened
if diffuse radiation were accounted for may elucidate the differences. However, this is for
another study.
Works Cited
Jacobs, A.F.G. and W.A.J. Van Pul. (1990). Seasonal Changes in the Albedo of a Maize Crop. in
Agricultural and Forest Meteorology. vol. 49 pg 351-360. Elsevier Science, Amsterdam.
Campbell, Gaylon S. and John M. Norman. (1998). An Introduction to Environmental
Biophysics. 2nd Ed. Springer Science. NY, NY.