Hydrological Sciences
Journal — des Sciences Hydrologiques, 31,1, 3/1986
An evaluation of Thornthwaite's water balance
technique in predicting stream runoff in Costa
Rica
JULIO C, CALVO
Departamento de Ingenieria
Forestal,
Institute
Tecnologico
de Costa
Rica,
Apartado 159, Cartago, Costa Rica
ABSTRACT
The Thornthwaite water balance technique is
used to predict monthly stream runoff from Rio Macho
basin in Costa Rica. The method was tested by comparing
observed and predicted runoff over a 15 water-year period.
The study shows that this method provides mean annual and
monthly estimates in close agreement with measured values.
Generally these mean estimated values fall between the 90%
confidence intervals for the measured runoff. These
results indicate that the Thornthwaite method can be
satisfactorily applied to estimate mean monthly streamflow in the uplands of Costa Rica.
Que vaut la technique
du bilan hydrologique
de Thornthwaite pour prévoir
les débits des rivières
au Costa
Rica?
RESUME
La technique du bilan hydrologique de Thornthwaite est celle utilisée pour prévoir les débits du
bassin du fleuve Macho au Costa Rica. Cette technique a
ete employee pour comparer les valeurs estimées a celles
mesurées au long de 15 années hydrologiques.
L'étude
démontre que la technique qui, consiste a procéder a des
estimations des moyennes mensuelles et annuelles donne
des résultats très proche des valeurs mesurées. En terme
general, les valeurs moyennes estimées se trouvent pour
90% a l'intérieur de l'intervalle de confiance des valeurs
mesurées, les résultats indiquent que la méthode de
Thornthwaite peut être appliquée avec succès pour
1'estimations des débits moyens mensuels au Costa Rica.
INTRODUCTION
The reliable assessment of river flow characteristics is basic for
the development of water resources. For a few small basins there
exist streamgauging records of sufficient length to make an accurate
assessment of the water yield characteristics. However, a vast
majority of small basins have either no streamflow records or only a
few years of records. On the other hand, most catchments have
representative meteorological records , or records which can be
estimated from nearby meteorological stations.
This report evaluates the utility of the Thornthwaite method in
predicting water yields in one gauged basin in the uplands of Costa
Rica.
51
52
Julio C.Calvo
DESCRIPTION OF THE STUDY BASIN
The Rio Macho basin used in this study lies in the Talamancas
mountain chain and comprises the southernmost drainage basin of the
Reventazon River, Costa Rica. The basin is gauged by the Costa Rican
Electricity Institute (ICE) and drains an area of 47.4 km2.
Elevations in the basin range from 1960 to 2840 m a.s.l. The
basin is well defined and is dominated by a dendritic drainage
pattern. Calcareous sandstone is widely distributed in the study
area and igneous intrusions of variable depth are frequently found
in this formation. Soils are young and shallow, with textures
ranging from sand to clay and with a high content of organic matter.
Most of the soils are classified as Inceptisols (Brenes, 1976;
Calvo, 1982; Otarola, 1976). A great percentage of the study area
is covered by dense rainforest dominated by oaks (Quercus spp),
typical of areas with diurnal fog cover. The only agricultural areas
of any extent are found in the upper part of the basin (Calvo, 1982;
Mojica, 1967).
The climate in the study area is strongly influenced by the
Intertropical Convergence Zone (ITCZ), trade winds and the local
topographic conditions. It has been shown that precipitation
increases with elevation and that five seasons characterize the
precipitation pattern in this area:
(a) A dry season that extends from January to the first part of
May, when the area is under the influence of northern surface winds
caused by the Bermuda high pressure cell.
(b) The first
wet season which extends from the middle of May to
June, when the ITCZ is active in the area.
(c) A season of alternating
wet and dry periods,
extending from
the end of June into August, when the area is under the influence of
the southern surface winds.
(d) A long wet season lasting from August to October, when the
ITCZ is again active in the area.
(e) A storm season lasting from the beginning of November to the
end of December, during which cyclonic storms occur due to the
collision of cooler northern winds with the ITCZ.
The monthly mean temperature is fairly constant through the year
as a result of the intense radiation at this latitude. Colder and
warmer temperatures are associated with cloudiness of the study area.
Clear skies during the dry season favour outgoing radiation.
Conversely, cloud cover during the wet season suppresses outgoing
radiation (Dohrenwend, 1972; Mojica, 1967, 1971).
METHOD
Thornthwaite (1948) proposed an empirical method to estimate the
potential évapotranspiration from mean temperature data. The method
was modified by Thornthwaite & Mather (1955) to make it more useful
over a wide range of soils and vegetations.
The method uses air temperature as an index of the energy
available for évapotranspiration, assuming that air temperature is
correlated with the integrated effects of net radiation and other
controls of évapotranspiration, and that available energy is shared
Thornethwaite's water balance technique for runoff in Costa Rica
53
in fixed proportions between heating the atmosphere and évapotranspiration.
The empirical equation developed by Thornthwaite which relates the
évapotranspiration to mean air temperature is:
PE = 1.6 (10 T / I ) a
where PE is the monthly potential évapotranspiration, T is the
monthly mean air temperature (°C), I is a heat index for the station
which is the sum of 12 monthly heat indices i given by i =
(Ta/5) "5 , and a is a cubic function of I. Both a and I can be
found from tables, e.g. Thornthwaite & Mather (1957).
This method of computing the monthly water balance was revised
and summarized by Thornthwaite & Mather (1957). In order to
determine the water balance at a site it is necessary to have the
following specific information:
(a) latitude,
(b) mean monthly air temperature,
(c) mean monthly precipitation,
(d) necessary conversion and computation tables,
(e) information on the water-holding capacity of the depth of
soil for which the balance is to be computed.
Black (1981) wrote a computer program in APL of the water balance
as originally developed and described by Thornwaite & Mather (1957).
The program was used in this study to compute ail water balances and
was run at the Syracuse University Computer Center.
The Rio Macho basin was used to check the accuracy of the Thornthwaite method for predicting water yields. Measured monthly and
annual streamflow values were compared with streamflows computed
according to the Thornthwaite method. The following considerations
made possible this comparison:
(a) The study basin, with its steep slopes and sharp ridges,
met the requirementsof an independenthydrological unit, with water
gains and losses taking place within the sharply defined boundaries
and the residual streamflow passing out through the outfall of the
basin via the main drainage channel,
(b) The underlying homogeneous plutonic rocks and calcareous
sandstone are water-tight and losses to deep seepage are negligible.
The evaluation of the Thornthwaite water balance technique
involves determining the nature and extent of the relationship
between measured and computed streamflow. The mean monthly and mean
annual streamflow estimation error in per cent were determined. The
latter was defined as 100 times the difference between the mean
measured streamflow and computed streamflow values divided by the
mean measured streamflow values. Correlation coefficients of
measured and computed streamflow were determined by linear regression analysis. Graphs of measured streamflow and computed
streamflow provided a visual idea of the goodness of fit of the
estimation. Finally 90% confidence intervals were calculated for
the measured streamflow in order to evaluate the significance of the
estimations.
54
Julio C. Calvo
DESCRIPTION OF DATA
Meteorological
data
Three raingauges operated by ICI were used in the study. Figure 1
illustrates their location within the study area. Precipitation
values for the basin were obtained by the Thiessen method. Fortunately, the available raingauges provide an adequate coverage of
elevation and topography.
83°45*
— |
-—
_J
_ —
_ l —
-
•
. 9045.
h9°40'
•
LEGEND
Ç) Raingauges
A
11 4.
-
1
£x Water sèves
-
-
J
recorder
'
0 0
° .. .50° . . .°
EHBTLH
iOOO
Interamerican Highway
Fig. 1
2000
j-^—=]
3OO0
p
4O00 M . t r e ,
q
SCALE
Rio Macho basin location map, Costa Rica.
Using the mean elevation of the Rio Macho basin, which is 2344 m
a.m.s.l., and the thermogradient determined by Mojica (1967) which
o
s
is 0.5 C/100 m for this section of the Reventazon basin, the
monthly temperature values were estimated from the Cachi thermometer,
Thornethwaite's water balance technique for runoff in Costa Rica
55
located 15 km north of the basin, at an elevation of 1018 m a.m.s.l.
Water-holding
capacity
The estimated soil depth within the basin is between 500 and 1000 mm
with fine textured surface horizons. According to the Oficina de
Planificacion del Sector Agropecuario (OPSA, 1979), the waterholding capacity for this area ranges from 100 mm to more than 200 mm.
In view of this uncertainty, the program was run with three different
water-holding capacities (300 mm, 200 mm and 100 mm) to observe if
the water balances are sensitive to variations in this factor. Since
no difference was observed in the outputs, the selected water-holding
capacity was 200 mm, which was considered representative for the
general terrain conditions of the study area.
Streamflow
data
The monthly measured streamflow data used to check the accuracy of
the Thornthwaite method were taken from the Hydrological Bulletins
of the Costa Rican Electricity Institute (ICE).
DISCUSSION AND RESULTS
Values have been computed by utilizing the above-mentioned data.
These values give the magnitude of the various water balance
parameters of the Rio Macho basin in water years (May-April), from
1964 to 1978.
Figure 2 compares the monthly computed and measured data of the
historical streamflow records. It can be seen that, in general, the
computed monthly stream runoff agrees with the measured monthly
stream runoff. However, in a number of years the estimated high and
low flows do not compare very well with the measured values. For
example, the water years 1966, 1970 and 1974 show peak discrepancies.
These anomalies are attributed in part to the fact that the method
assumes that the basin receives uniform precipitation in both time
and space, and that the rainfall data are representative of what
actually occurred. Therefore the method cannot handle the
occurrences of convective type storms on the basin. Convective
precipitation is of very short duration, but high intensity, and may
extend over only small areas.
A statistical comparison of the estimated and the measured
streamflow is summarized in Table 1, This shows the mean monthly and
mean annual estimated and measured streamflows, the correlation
coefficient between measured and estimated streamflows, the mean
monthly and annual percentage error of estimation and the 90%
confidence interval for the mean streamflow. Table 2 shows the
complete output from a run of the averages of 15 years of data for
the Rio Macho basin.
The months of June, December, January, March and April showed the
highest correlation coefficients between measured and computed
streamflow. These correlations agree with the graphs which show,
for the same months, a good visual approximation of the estimated
peaks with the measured peaks. These months also had the highest
56
Julio C.Calvo
mm
o
<
LU
CE
0
! " '1964 • '• -"n-
)965
Î J '
' ' •' ' ' ' • i9S7
• • • • • •
I9SS
mm
mm
o
<
LU
CE
s-
1975
1978
1977
WATER YEARS (APRIL TO MAY)
Fig. 2
Comparison of measured and computed mean monthly streamflow for Rio
Macho basin, Costa Rica, 1964-1978,
Thornethwaite's water balance technique for runoff in Costa Rica
57
Table 1 Comparison of Thornthwaite water balance and actual streamflow on Rio Macho basin,
Costa Rica
Month
May
June
July
Aug.
Sept.
Oct.
Nov.
Dec.
Jan.
Feb.
March
April
Year
Measured streamflow
(mm)
„
X*
St
128.8
229.0
228.7
306.6
307.6
300.4
219.5
246.5
131.6
86.8
62.8
82.4
2330.9
90% Confidence interval §
_
_.
X + t.05S/Vn
X - 1 . 0 5 SA/rî
75.49
78.78
70.79
71.07
76.42
73.96
52.35
191.69
59.26
37.22
21.34
89.88
489.1
162.9
264.6
260.7
338.7
342.1
333.8
243.1
333.2
158.4
103.6
72.4
123.0
94.67
193.3
196.6
274.5
273.1
267.0
195.8
159.8
104.8
70.0
53.1
41.8
2552.06
2109.7
Estimated
streamflow (mm)
-_
X*
St
% error of
estimation
Corr.
coeff.
131.4
199.2
209.0
261.8
274.8
280.7
230.4
178.0
117.8
69.4
40.9
44.0
45.18
51.88
48.59
37.43
42.83
38.08
40.96
71.31
46.58
29,74
20.67
43.18
2.01
13.01
-8.61
-14.61
-10.66
-6.55
4.96
-27.78
-10.48
-20.04
-34.87
-46.60
0.4027
0.7228
0.6315
0.4901
0.3701
0.4465
0.4742
0.8704
0.7444
0.5759
0.7248
0.7645
2038.3
288.24
-12.55
0.5144
*Average
tStandard deviation
§90% confidence intervais for measured streamflow.
Table 2
Mean water balance (mm) for the Rio Macho basin, Costa Rica, 1964-1978 (latitude: 10°N;
soil storage capacity: 200 mm)
Component*
Month:
May June
July
Aug.
Sept.
Oct.
Nov.
Dec.
Jan.
Feb.
March
April
Year
TDEGC
PPTMM
MROMM
HEATI
UNPET
CORFA
POTET
PMPET
STRGE
ACTET
SURPL
WATRO
TROMM
14
291
128
5
2
31
60
232
200
60
232
136
136
14
273
229
5
2
29
54
219
200
54
219
210
210
14
369
306
5
2
30
54
315
200
54
315
262
262
13
339
308
4
2
30
52
287
200
52
287
275
275
14
339
300
5
2
28
52
287
200
52
287
281
281
14
236
220
5
2
31
55
181
200
55
181
231
231
13
179
246
4
2
31
54
125
200
54
125
178
178
13
110
132
4
2
32
52
58
200
52
58
118
118
13
68
87
4
2
32
53
15
200
53
15
66
66
13
62
63
4
2
33
56
6
200
56
6
36
36
14
108
83
5
2
32
61
47
200
61
47
41
41
13.6
2697.0
2331.0
55.0
14
326
229
5
2
31
58
267
200
58
267
202
202
661.3
2035.6
661.3
2035.6
2035.1
2035.1
*The abbreviations used for the 1 3 components of the water budget are as follows:
Input data
TDEGC
temperature (°C), required
PPTMM
precipitation (mm), required
MROMM
measured stream-runoff (mm), if desired
Calculation of potential évapotranspiration
HEATI
heat index
UNPET
unadjusted potential évapotranspiration
CORFA
monthly correction factors
POTET
adjusted potential évapotranspiration
Calculation of storage and actual evaporation
PMPET
precipitation minus potential évapotranspiration
STRGE
soil storage (mm)
ACTET
'actual' évapotranspiration as limited by storage
Calculation of runoff
SURPL
surplus
WATRO
water runoff (if SURPL available, STRGE is full and TDEGC > - 1 )
TROMM
total predicted stream-runoff (mm)
percentage error of estimation. Because of these two reasons, the
correlation coefficient alone apparently cannot be considered an
accurate indicator of a satisfactory estimation.
58
Julio C.Calvo
On a monthly and annual basis, the method provides conservative
estimated values. It is important to point out that the months
associated with the dry season (November-April) showed the most
conservative estimations, and at the same time they match very well
with the pattern of measured values (Fig.2)
The fact that the method provides conservative estimated values
and that in some cases, the fit of high and low flows does not
compare very well, leads to a consideration of some of the weaknesses of the method, for example:
(a) There are imperfections in the structure of the method due
to simplification of the processes of basin behaviour. For example,
the method assumes that approximately 50% of the surplus water that
is available for runoff in any month actually runs off and the rest
of the surplus is detained in the subsoil, groundwater, lakes and
channels of the basin and is available for runoff during the next
month. This proportion should be evaluated for the basin emphasizing
the depth and texture of the soil, the physiography and the land use
of the basin. Additionally, Dunne & Leopold (1978) state that the
proportion of water surplus detained will be less than 50% for
catchments of only a few square kilometres.
(b) Another possible source of error is the analysis of rainfall
input since the raingauges do not measure fog interception. In this
geographical area, horizontal interception is an important component
of the hydrological cycle which could add a substantial amount of
water to the soil or conserve it by precluding surficial evaporation
throughout the year.
(c) Finally, the model is valid for situations in which data
from a large number of years are analysed and rainfall is fairly
evenly distributed throughout the year. However, another weakness
of this model occurs when data from a single year are analysed. In
these instances, there are greater discrepancies between observed
and measured stream runoff,
In order to correct the déficiences of the model suggested above,
basic research needs to be conducted to determine the proportion of
water surplus detained by the basin. With more accurate data
regarding the percentage of water surplus available for runoff, the
Thornthwaite model can then be tested using values other than the
currently assumed value of 50%. The monthly fog drip, referred to
in (b) above, can also be assessed by basic research so that the
estimation of rainfall input will be more accurate. The final
limitation of the model, described by (c) above, requires that there
be an adequately long time-frame to provide substantial data for
analysis. In the author's opinion, data for a minimum period of
10 years are necessary. Nevertheless, it has to be pointed out that
conducting this additional research for every basin could entail
great cost and additional difficulties in application.
Despite the déficiences mentioned above, the Thornthwaite method
has produced relatively good results in this study. Generally, it
yielded an estimated mean of monthly and annual streamflow which
was in close agreement with measured mean values. Moreover, this
study has affirmed that most of the mean estimated values fall
between the 90% confidence intervals for the measured streamflow,
which assures 90% confidence of being accurate. These results
indicate that this method is suitable for predicting monthly and
Thornethwaite's water balance technique for runoff in Costa Rica
59
annual stream runoff for ungauged basins for projects of domestic
water supply, irrigation or the production of hydroelectric power
in Costa Rica.
Since it was not possible to find a generally accepted criterion
by which a method of estimating the water balance and streamflow can
be judged acceptable or unacceptable, it is considered that this
judgement must depend upon the application to be made of the results.
Nevertheless, in comparing the results of this study with those
shown by Thornthwaite & Mather (1955) in the James River basin and
Great Valley of Virginia, and those obtained by Van Hylckama (1958)
in the Delaware Valley, it has been concluded that the Thornthwaite
method provides acceptable results.
Although the Thornthwaite method was derived from North-American
conditions and its utility for tropical basins has been questioned,
the applicability of the method of the estimation of monthly streamflow in the uplands of Costa Rica has been demonstrated in this study,
RECOMMENDATIONS
This study has suggested ways in which the Thornthwaite method may
be improved. Among these are:
(a) Use of long term average climatic data since this provides
the best picture of the seasonal march of rainfall, temperature,
soil moisture and runoff.
(b) Special attention to be paid to the determination of monthly
precipitation and temperature for the basin in order to achieve
acceptable results.
(c) Additional basic research could provide more accurate data
regarding water surplus detention and fog drip which could substantially improve the model,
(d) The assumption of 50% of water surplus currently used by the
Thornthwaite model needs to be re-evaluated.
(e) Before applying the Thornthwaite method to ungauged basins
it is suggested that the method be evaluated in a nearby representative gauged basin in order to judge the accuracy of the estimations.
ACKNOWLEDGEMENTS
The author is grateful to Dr A.Eschner, Dr
P.Black and Dr L.Herrington, Professors of the State College of
Environmental Science and Forestry, Syracuse, for their assistance
and s ugge s t i ons.
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The Thornthwaite
Water Balance
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Lie. Thesis, Universidad de Costa Rica, Escuela de Historia y
60
Julio C. Calvo
Geografia, San José, Costa Rica.
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de Asociaciones
de Subgrapos de Suelos de Costa
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Centerton, New Jersey.
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and Tables
for
Computing Potential
Evapotranspiration
and the Water
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Received
14 May 1985;
accepted
10 October
1985.