beluco

1. Renewable Energy 33 (2008) 2157–2165
A dimensionless index evaluating the time complementarity between
solar and hydraulic energies
Alexandre Belucoa,Ã, Paulo Kroeff de Souzaa
, Arno Krenzingerb
a
Instituto de Pesquisas Hidra´ulicas, Universidade Federal do Rio Grande do Sul, Porto Alegre, RS, Brazil
b
Escola de Engenharia, Universidade Federal do Rio Grande do Sul, Porto Alegre, RS, Brazil
Received 24 September 2007; accepted 8 January 2008
Available online 21 April 2008
Abstract
The power plants based on renewable sources face various acceptance difficulties mainly due to high initial costs and low overall
efficiencies. A way to improve performance of these systems is to utilize more than one type of source of energy chosen to provide some
degree of complementarity. An interesting, albeit improbable, combination is obtained using hydroelectric and photovoltaic energy,
taking advantage of the complementarity between these two types of sources coupled to reservoir and/or battery storage. This paper
discusses energy complementarity in time and proposes a numerical dimensionless index, evaluating this energy complementarity
between two types of energy sources, in the same or in different locations, or between two sources of the same type in different locations.
In the end, the results of the application of this index to the solar and water availabilities over the state of Rio Grande do Sul, in southern
Brazil, is presented in the form of maps.
r 2008 Elsevier Ltd. All rights reserved.
Keywords: Renewable resources; Energetic complementarity; Hybrid energy systems; Solar energy; Micro-hydropower
1. Introduction
The power plants based on renewable sources face
various acceptance difficulties mainly due to high initial
costs and low overall efficiencies. A way to improve
performance of these systems is to utilize more than one
type of source of energy chosen to provide some degree of
complementarity. For quite some time, fossil fuel-based
generators were considered a necessary support to the
operation of renewable source plants, but only in the last
few years the use of more than one type of renewable
source in the same energy system, such as wind and solar,
have been seriously contemplated. An interesting, albeit
improbable, combination is obtained using hydroelectric
and photovoltaic energy, taking advantage of the com-
plementarity between these two types of sources coupled to
reservoir and/or battery storage.
This paper is dedicated to the complementarity between
energy sources. The term complementarity should be taken
as the ability of working in a complementary way. The
expressions energy complementarity and time complemen-
tarity between energy sources refer to the ability of two (or
more) energy sources to present complementary availabil-
ity between them. This complementarity may occur in time,
in space or both, and may occur between sources of the
same or of different types.
This paper discusses the concept of energy complemen-
tarity and proposes a numerical dimensionless index,
evaluating this energy complementarity between two types
of energy sources, in the same or in different locations, or
between two sources of the same type in different locations.
In the end, the results of the application of this index to the
solar and water availabilities over the state of Rio Grande
do Sul, in southern Brazil, is presented in the form of maps.
2. Types of complementarity
Space complementarity may exist when the energy
availabilities of one or more types of sources complement
themselves over a certain region. An example [1] is the
complementarity between solar and wind sources over the
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doi:10.1016/j.renene.2008.01.019
ÃCorresponding author. Tel.: +55 51 3308 6407; fax: +55 51 3308 7291.
E-mail address: albeluco@iph.ufrgs.br (A. Beluco).

2. territory of Great Britain which is scarcely explored due to
the small amounts of available energy.
Time complementarity may exist when the energy
availability of two or more types of sources present periods
of availability which are complementary over time in the
same region.
Complementarity may also exist when the availability of
energy of only one type of source is considered over a vast
region and over time. As an example, the availability of
hydraulic energy over the Brazilian territory may be
mentioned and which is one of the main reasons that led
to the interconnection of the south–southeast and the
north–northeast electrical energy supply systems. This is an
example of complementarity in time and space.
The next section establishes what shall be considered the
perfect complementarity. The two subsequent sections
propose the numerical dimensionless index evaluating this
energy complementarity in time and evaluate the comple-
mentarity of hydraulic and solar energy availabilities over
the territory of the state of Rio Grande do Sul, in the south
of Brazil, based on this index.
3. Energy complementarity in time
Different energy availabilities may be considered per-
fectly complementary if the variation of the availability
values presents equal periodicity and their respective
maximum and minimum values occur in time intervals
half a period apart (out of phase). Furthermore, the
average values of the availabilities should be the same as
well as the relation between the respective maximum and
minimum values of availability of the two sources.
The values of energy supplied by generators in a hybrid
system may also be considered complementary in time even
when the values of availability are not completely comple-
mentary. So, the availabilities may present an imperfect
complementarity and the generators may be sized to supply
energy values that have the same average values along the
period. Obviously this is possible only if the available
energy values are greater than the energy demand.
Fig. 1 presents two sinusoidal curves, showing a comple-
mentary instance, which will be considered perfect for the
purposes of the present work. The two curves present
hypothetic availabilities of two sources of energy expressed
in terms of energy or power along a year.
Both curves present periods of 1 year, average values
equal to 1, maximum values equal to 1.2 and minimum
values equal to 0.8. The minimum of the first curve occurs
at 0.75 of the year whereas the one of the second curve is at
0.25 of the year or 0.5 year out of phase.
The complementarity between these curves may be con-
sidered perfect since the minima and the maxima are 0.5 year
out of phase, the difference between the maximum and the
minimum is 0.4 in both cases and the average values are equal.
The functions depicted above may represent energy
availabilities of two sources or the energy or power
supplied by two generators. These functions will be used
for the setup of a complementarity index but they do not
adequately describe, in detail, for example, the behavior of
solar sources since these present daily variations, which
have an effect in the detailed behavior of hybrid systems.
The need to evaluate how much two availability
functions, which are not perfectly complementary, differ
from the situation depicted in Fig. 1, considered as a
reference, naturally leads to the creation of numerical
dimensionless indexes considering the characteristics men-
tioned above. Indexes varying from 0 to 1 are suggested to
evaluate the complementarity between, for instance,
hydraulic and solar energy availabilities.
4. Complementarity index
The complementarity index necessarily involves time and
is elaborated to express the degree of complementarity
between two energy sources. It is defined according to
Eq. (1) and includes the evaluation of three components:
the phase difference between the energy availability values
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Nomenclature
k time-complementarity index
kt partial time-complementarity index
ke partial energy-complementarity index
ka partial index of amplitude-complementarity
a1 function used to obtain ka
a2 function used to obtain ka
Dh day number of the occurrence of the maximum
value of hydraulic energy availability
dh day number of the occurrence of the minimum
value of hydraulic energy availability
Ds day number of the occurrence of the maximum
value of solar energy availability
ds day number of the occurrence of the minimum
value of solar energy availability
Eh total hydraulic energy available along a year
Es total solar energy available along a year
Edh max maximum value of daily hydraulic energy
supply
Edh min minimum value of daily hydraulic energy
supply
Eds max maximum value of daily solar energy supply
Eds min minimum value of daily solar energy supply
dh difference between maximum and minimum
values of hydraulic energy availability
ds difference between maximum and minimum
values of solar energy availability
A. Beluco et al. / Renewable Energy 33 (2008) 2157–21652158

3. of the two sources, the relationship between the two
average availability values and the relationship between the
amplitudes of variation of the availability functions.
k ¼ ktkeka. (1)
In this equation kt is the partial time-complementarity
index, ke is the partial energy-complementarity index
describing the complementarity between the average values
of energy availability and ka is the partial index of
amplitude-complementarity taking care of the relation
between amplitudes of the variation of the energy
availability of the sources. These partial indexes will be
discussed in the following sub-sections.
4.1. Partial time-complementarity index
The partial time-complementarity index, kt, is defined by
Eq. (2) and evaluates the time interval between the
minimum values of availability of the two sources of
energy. If this interval is exactly half the period, the index
will be equal to one. If the interval is null that is, if the
availability minima coincide, the index will be equal to
zero. Intermediate values are linearly related.
kt ¼
dh À dsj j
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
Dh À dhj j Ds À dsj j
p (2)
where Dh is the number of the day of maximum value of
hydraulic energy availability, dh is the number of the day of
minimum value of hydraulic energy availability, Ds is the
number of the day of maximum value of solar energy
availability and ds is the number of the day of minimum
value of solar energy availability. This expression may be
rewritten as Eq. (3) supposing that the respective (DÀd)
differences are equal to half a year that is more practical
for estimates.
kt ¼
dh À dsj j
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
180 Â 180
p ¼
dh À dsj j
180
. (3)
4.2. Partial energy-complementarity index
The partial energy-complementarity index, ke, is defined
by Eq. (4). It evaluates the relation between the average
values of the availability functions. If the average values
are equal the index should equal to one. If those values are
different the index should be smaller and tend to zero as
differences increase. Intermediate values of difference are
linearly related to the index.
ke ¼ 1 À
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
Eh À Es
Eh þ Es
2
s
(4)
where Eh is the total of the hydraulic energy over the
year and Es is the total solar energy over the same
period.
Alternatively, an expression for ke may be developed
from a coefficient e as defined by (5). This coefficient varies
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minimum availability values are
0.5 year out of phase
the minimum availability of one source coincides
with the maximum availability of the other
the maximum availability of one source coincides
with the minimum availability of the other
the average values of the variations
of avaliabilities are equal
the amplitudes of the variations of
energy availabilities are equal
1.2
1
0.8
0.6
0.4
0.2
energyavailabilityofsecondsource
0
energyavailabilityofsecondsource
1.2
1
0.8
0.6
0.4
0.2
0
0
0.25 0.5 0.75 1
year
0 0.25 0.5 0.75 1
year
Fig. 1. Mathematical functions characterizing perfectly complementary energy availabilities along a year.
A. Beluco et al. / Renewable Energy 33 (2008) 2157–2165 2159

4. between 0 and 2, being equal to 1 when energies Eh and Es
are equal. When Eh is much bigger than Es, e tends to 2
whereas if Eh is much smaller than Es, e tends to zero.
e ¼
2
1 þ ðEh=EsÞ
. (5)
The index ke, however, should be ke ¼ 0 if e ¼ 0 or e ¼ 2
and ke ¼ 1 when e ¼ 1. This is obtained by the following
equation, which is equivalent to (4).
ke ¼ 1 À
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1 À eð Þ2
q
. (6)
4.3. Partial amplitude-complementarity index
The partial amplitude-complementarity index, ka,
is defined by Eq. (7) and evaluates the relation between
the values of the differences of the maxima to the
minima of the two energy availability functions. If those
differences are equal the index shall be equal to 1.
Otherwise the index shall fall from 1, tending to 0 as
depicted in Fig. 2.
ka ¼
1 À
ðdh À dsÞ2
ð1 À dsÞ2
for dhpds
ð1 À dsÞ2
ð1 À dsÞ2
þ ðdh À dsÞ2
for dhpds:
8
:
(7)
This index is obtained from a suitable manipulation between
the dh and ds, differences between the respective maximum and
minimum values of the energy availabilities. These differences
are obtained from the following Eq. (8), where Edmax is the
maximum daily energy availability value in a year, Edmin is the
minimum daily energy availability value in a year and Edc is
the year average daily energy consumption.
d ¼ 1 þ
Ed max À Ed min
Edc
. (8)
This index was created to include the difference be-
tween the maximum and the minimum energy availa-
bility of the sources in the complementarity evaluation.
If one of the sources has no available energy along the period
of interest, it is impossible to consider it for complementarity
purposes. If the two sources have the same difference between
maximum and minimum availability, they are ideally com-
plementary and the index should be equal to 1. In the
intermediate cases where the differences are unequal, the index
should express it by values between 0 and 1 for complemen-
tarity is less than ideal.
The ds difference is always greater than 1 and may be
considered constant over a quite extensive area since it
represents the availability of solar radiation.
The dh difference presents a minimum value of 1, in which
case the complementarity index should be null. On the other
hand, dh may present rather large values as compared to ds
and in these cases, the index should decay from the
maximum value as the dh value increases. This behavior of
the index as a function of dh for ds ¼ 2 is depicted in Fig. 2.
For the purpose of the development of the expres-
sions for the ka index, described in the next few paragraphs,
we also consider the value ds ¼ 2. The resulting curve
shall be continuous and smooth, it shall present a
zero slope for dh ¼ ds, and it shall be very nearly symmetrical
in the proximity of its peak. It is also desirable to obtain an
expression for the quick calculation of the ka index.
There is no obvious mathematical expression for a
function with those characteristics (which can be seen in
Fig. 2). The development of an expression for the part of
the curve to the right of the maximum can be based on
the Agnesi curve, adapted so that its maximum value is 1
and corresponds to abscissa equal to ds, which leads to
the expression.
y2 ¼
1
1 þ dh À dsð Þ2
. (9)
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0 1 2 3 4 5 6 7 8
0
0.2
0.4
0.6
0.8
1
delta h
partialamplitude-complementariryindex
Fig. 2. Behavior of ka index, as a function of dh, for ds ¼ 2.
0 1 2 3 4 5 6 7 8
0
0.2
0.4
0.6
0.8
1
delta h
y1ey2
Fig. 3. Superposition of the functions, y1 in lower line and y2 in upper
line.
A. Beluco et al. / Renewable Energy 33 (2008) 2157–21652160

5. The Agnesi curve presents the desired symmetry
characteristics with respect to its maximum as can be seen
in Fig. 3 (dotted line) for the abscissa dh equal to ds. The
final form for the right-hand side of the Fig. 2 function is
obtained by slightly modifying Eq. (9) to smooth the slopes
near the maximum to ease its connection to the expression
to be used for the left part of the curve.
y2 ¼
1 À dsð Þ2
1 À dsð Þ2
þ dh À dsð Þ2
. (10)
For the left part of the curve (as seen in Fig. 2) a
quadratic function seems adequate in view of the three
contour conditions (Fig. 3, solid line). The y1 function,
with dh as the independent variable, centered in the value of
ds, is
y1 ¼ 1 À
dh À dsð Þ2
1 À dsð Þ2
. (11)
Fig. 3 shows both functions, y1 in solid line and y2 in
dotted line. As it can be seen in Fig. 3, the set obtained by
connecting the first half of y1 with the right part of y2 yields
the curve shown in Fig. 2.
Fig. 4 shows the appearance and the smoothness of the
ka index curves for different values of ds.
5. Time-complementarity for hydroelectric and solar energy
availabilities in Rio Grande do Sul
This chapter presents the calculation of the complemen-
tarity indexes from precipitation and solar radiation data,
and describes the elaboration of complementarity maps
from the calculated indexes leading to the presentation of
the results over the territory of the state of Rio Grande do
Sul in southern Brazil.
5.1. Calculation of the indexes, from precipitation and
incident solar radiation data
In a real situation, the calculation of the indexes may be
carried out through functions adjusted to the monthly
average data by the least-squares method. Fig. 5 shows
monthly average precipitation data and monthly average of
daily incident solar radiation data over a flat horizontal
surface as supplied by a weather station in the state of Rio
Grande do Sul. The same graph shows the least-squares
adjusted curve (in the line) over the supplied data.
The adjusted solar energy availability curve in, Fig. 5, is
quite similar to the idealized curve of daily availability
shown in Fig. 1. The situation is different for the water
availability, a second lesser peak appearing near the
position of the valley of the idealized curve.
The monthly average intensity of precipitation does not
adequately represent the water availability. However, in
smaller river basins flow variations present small phase
lag with respect to precipitation variations and also are
closely related the amplitudes of the variations. The water
availability curve is lower in the January–May interval. If
January is used, and being the minimum solar availability
in July, the partial time-complementarity index is equal to
1.00. The partial energy-complementarity index and the
partial index of amplitude-complementarity evaluations
are not possible using these numbers. However, an
expedited evaluation is made to allow the elaboration of
the maps that follow.
The determination of the indexes from river flow data
may be made in the same way, using adjusted curves over
the monthly averaged data. The use of daily data for water
and solar availability would certainly produce better
results!
The value of ds used for this work is 1.1496. The value
for dh may vary considerably as a function of the water
availability in the plant area and the installed capacity of
the hydroelectric generator but actual values will seldom be
outside those considered in Fig. 2. Moreover, considering
its definition, dh will never be less than 1, which
corresponds to a situation where the hydroelectric gen-
erator turns out always the same power, the corresponding
flow presenting a short recurrence time, which implies a
high frequency.
5.2. Elaboration of complementarity maps
For just a visualization of wide areas of application of
the results of this work, the partial time-complementary
index, the partial index of amplitude-complementarity
and the complementarity index itself were calculated for
the state of Rio Grande do Sul from a base of monthly
data published by Fundac-a˜ o Estadual de Pesquisas
Agropecua´ rias [2,3]. Data on water availability (monthly
precipitation) and solar availability (monthly solar radia-
tion incident on a horizontal surface) were considered.
Results are shown in Figs. 6–8, respectively. This last map
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0 1 2 3 4 5 6 7 8
0
0.2
0.4
0.6
0.8
1
delta h
partialamplitude-complementariryindex
Fig. 4. ka index curves for ds values of 1,5, 2,5 e 5.
A. Beluco et al. / Renewable Energy 33 (2008) 2157–2165 2161

6. was elaborated under the supposition that the energy-
complementarity index is equal to 1 allover the state. The
maps show in the dots some of the main cities of the state.
The data interpolation net was obtained through the
Kriging method using a commercial software resulting in a
1200-line  1200-column matrix. In all three maps iso-lines
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0
40
80
120
160
Jan Fev Mar Abr Mai Jun Jul Ago Set Out Nov Dez
Months
Months
Jan Fev Mar Abr Mai Jun Jul Ago Set Out Nov Dez
Precipitation[mm/month]
0
175
350
525
700
RadiationSolar[MJ/m2
month]
Fig. 5. Monthly average precipitation data and monthly average of daily incident solar radiation data from the Fundac-a˜ o Estadual de Pesquisas
Agropecua´ rias (FEPAGRO) weather station, in Taquari, RS. Least-squares adjusted curves are in the line over the supplied data.
Fig. 6. Time complementarity between hydraulic and solar energy availability, calculated using data on monthly precipitation and monthly solar radiation
incident on a horizontal surface, in the state of Rio Grande do Sul. The different values of complementarity appear in shades of gray, white corresponding
to no complementarity and black to full complementarity.
A. Beluco et al. / Renewable Energy 33 (2008) 2157–21652162

7. were superimposed on the image generated. In Fig. 6, iso-
lines were drawn in steps of 0.20 for values of kt from 0.20
to 1.00. In similar manner, iso-lines for Fig. 7 were drawn
in steps of 0.10 for values of ka from 0.60 to 1.00. Finally,
the iso-lines of k in Fig. 8 were drawn in steps of 0.20 for
values varying from 0.20 to 1.00.
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Fig. 7. Complementarity between the amplitudes of variation of the hydraulic and solar availabilities, calculated using data on monthly precipitation and
monthly solar radiation incident on a horizontal surface, in the state of Rio Grande do Sul. The different values of complementarity appear in shades of
gray, white corresponding to no complementarity and black to full complementarity.
Fig. 8. Overall complementarity between the hydraulic and solar energy availabilities, calculated using data on monthly precipitation and monthly solar
radiation incident on a horizontal surface, in the state of Rio Grande do Sul. The different values of complementarity appear in shades of gray, white
corresponding to no complementarity and black to full complementarity.
A. Beluco et al. / Renewable Energy 33 (2008) 2157–2165 2163

8. 5.3. The complementarity in Rio Grande do Sul
As can be appreciated in Fig. 6, about 58% of the area of
the state has a kt greater than 0.60, corresponding to more
than 72 days of phase difference between the minima of the
two availability curves, the best values occurring from the
southeast to the northwest border. It can also be seen that
nearly 50% of the state area present kt values greater than
0.80, that is, phase differences of near 50% of the cycle of
the hydraulic and solar energies availability, the extreme
values appearing in the center of the state. On the other
hand, 4.67% of the state area presents k values greater than
70%. It is, however, clearly visible that the most adequate
area from the time-complementarity point of view is
generally not the most adequate area from the amplitude-
complementarity point of view. The final complementarity
index k will consequently show intermediate values in these
areas whereas the best values will be near the northwest
border.
As it will be shown later, the systems based on
availabilities with higher time-complementarity (which
can be evaluated from the indexes proposed in this article)
tend to presenting less consumer demand satisfaction
failures. So, from this point of view, the Fig. 6 map shows
the ‘‘best’’ complementarity areas between the hydraulic
and solar availabilities.
In the same way, as it will be seen later, small differences in
the amplitudes of variation of the hydraulic and solar
availabilities also lead to better performing systems. Fig. 7
map shows the best-valued areas for the amplitude-
complementarity index that are, consequently, the best areas
from this point of view, for consumer demand satisfaction.
In areas where the time-complementarity index is less
satisfactory the complementarity condition can be helped
by the use of water reservoirs with the effect of improving
the phase difference between the minima to near a half-
year, which is the ideal value. Regions with a smaller kt will
require bigger accumulation volumes for the system to
approach the performance levels corresponding to a full
complementarity.
In areas with lower values for this index the generating
systems performance can also be improved by the use of
reservoirs that can help improving the amplitude variation
of the hydraulic availability approaching it to the value
corresponding to a perfect complementarity, which is the
same as the variation of the solar availability. And,
as mentioned above, regions with a smaller index value
will need bigger reservoirs for a given level of system
performance.
It is interesting to note, in these two maps, that the areas
requiring reservoirs, to improve system performance for
the two different reasons, do not coincide: areas exempt
from reservoirs for time complementarity reasons would
require them for amplitude complementarity reasons and
vice versa. But it should be noted that the smaller values of
the amplitude-complementarity index in the map are better
than 50%!
The use of monthly averages to calculate time-comple-
mentarity is somewhat inadequate in that it precludes
a precise determination of cycle the energy availabilities
and, for the amplitude-complementarity index these
averages mask the maxima and minima of the variations.
Nevertheless, the depicted maps allow spotting areas to
be initially investigated to take advantage of the com-
plementarities. Less expedite results may be obtained,
for example, using flows determined by regionalization
studies.
For the time-complementarity index, the semi-periods of
the hydraulic and solar availabilities were taken as half a
year, as suggested in Eq. (3), and the months corresponding
to the minima of availabilities were defined. The use of, at
least, daily flow data taken from time-series over decades is
recommended for more accurate calculations involving this
index. Radiation data, however, are pretty regular.
For the amplitude-complementarity index, precipitation
data do not provide a good evaluation for water
availability since flow, in a given measurement section of
a river, is dependent upon several other factors. However,
since the relationship between the maxima and the minima
of precipitation approach very well the relationship
between the maxima and minima of flow in smaller basins,
which is precisely the field for the application for most of
the systems aimed at by this work, the evaluation thus
obtained is reasonable.
The calculation of these indexes based on data on the
energy made available by the contemplated conversion
equipment (maximum, average and minimum power made
available by hydroelectric and photovoltaic generators
along a year) yields an evaluation for the use of com-
plementarity in the operation of a system. The elaboration
of the third map, the one for the overall complementarity
between the chosen availabilities, required the acceptance
of a supposition on the complementarity of average values
of energy.
A precise and reliable evaluation of complementarity in
a given place should be based on flow data across a given
river section and on incident solar radiation data taken
daily. The insight on the hybrid system performance gained
through computer simulations and experimental studies
allow the evaluation of the effects of the complementarity
on the system parameters and may justify deeper and more
comprehensive studies for the characterization of the
complementarity.
The Brazilian National Electric Energy Agency, ANEEL,
centralizes data from pluviometric, fluvial and meteorologi-
cal stations of the whole country, which can be used for the
identification of complementarity. However, only a few
stations present long and complete time-series of data on
solar radiation or flow in rivers and only in special and
recent cases are daily flow data available. Moreover, series
of data for rivers in smaller basins have to be obtained by
the application of transposition models on larger basins
data. Finally, available data are not always verified for
consistency.
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A. Beluco et al. / Renewable Energy 33 (2008) 2157–21652164

9. 6. Conclusions
The concept of energy-complementarity was discussed
and a numerical non-dimensional index to evaluate the
complementarity between energy sources, in a given place
and over time, was proposed. In the end, some results, in
map form, are presented concerning the application of this
index to identify complementarity between hydraulic and
solar sources of energy along the territory of the state of
Rio Grande do Sul in southern Brazil.
References
[1] McVeigh JC. Energia solar. Lisboa, Portugal: Cetop; 1977. p. 238.
[2] FEPAGRO (Fundac-a˜ o Estadual de Pesquisas Agropecua´ rias). Atlas
agroclima´ tico do Estado do Rio Grande do Sul, Porto Alegre, 3v,
1989.
[3] FEPAGRO (Fundac-a˜ o Estadual de Pesquisas Agropecua´ rias).
Se´ ries de dados utilizadas para preparac-a˜ o do ‘A´ tlas agroclima´ tico
do Estado do Rio Grande do Sul’, Personally obtained, unpublished
data, 2000.
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