Effect of the Evapotranspiration of Thornthwaite and of Penman-Monteith in the Estimation… DOI: http://dx.doi.org/10.5772/intechopen.88441

#### Figure 3.

the data provided: precipitation, P; mean, average maximum and average minimum air temperatures, Tmed, Tmax and Tmin, respectively; air relative humidity, HR; number of sunshine hours, I; and wind velocity, v. In Figure 2, the corresponding mean monthly values are represented. The recording periods of Table 1 refer to

Climatological stations. General features and mean monthly values of precipitation, P; mean, average maximum and average minimum air temperature,Tmed,Tmax and Tmin, respectively; air relative humidity,

Figure 2 shows that from the north to the south of Mainland Portugal, the precipitation decreases and the temperature and the sunshine hours increase.

Based on the records of Table 1, the potential evapotranspirations of Thornthwaite (EVP) and Penman-Monteith (EV0) were computed, as well as the surface flows that they predict according to the Thornthwaite-Mather water balance

In Figure 3, the Thornthwaite (EVP) and Penman-Monteith (EV0) monthly potential evapotranspirations are compared for each of the 16 climatologic stations. Each diagram contains the representation of the straight line from the linear regression analysis between EVP and EV0, its equation, and the respective correlation coefficient. There is also a second dashed straight line representing the equality between the two evapotranspirations under consideration. The scale of the axes is always the same in order to allow the comparison between those evapotranspirations and among the results from the different climatological stations. Figure 3

hydrological years, which in Portugal start on October 1.

Mean monthly values of P,Tmed,Tmax,Tmin, HR, I, and v, according to Table 1.

HR; number of sunny hours, I; and wind velocity 2 m above the ground, v.

Current Practice in Fluvial Geomorphology - Dynamics and Diversity

4. Results

98

Table 1.

Figure 2.

model—Eqs. (3) and (4).

clearly highlights two relevant conclusions:

Monthly potential evapotranspiration of Thornthwaite, EVP, and of Penman-Monteith, EV0. Linear regression line (continuous line), equation, and correlation coefficient, r. Line representing the equality between monthly EVP and EV0 (dashed line).


The first conclusion anticipates that the application of Thornthwaite-Mather water balance model would yield rather distinct estimates of the surface runoff when based upon on EVP or on EV0.

In the previous scope, Figure 4 shows the comparison between monthly streamflows (expressed in water depth) from the water balance model based on the monthly potential evapotranspiration of Thornthwaite (HP) and of Penman-Monteith (H0). Such results were obtained assuming a maximum useable water capacity of the soil (Smax) of 150 mm that allegedly corresponds to the average conditions prevalent in Mainland Portugal, though, in fact, the values of Smax are expected to be slightly higher in the southern than in the northern parts of the country.

The results from the linear regression analysis between HP and H0 are represented in each graph by a continuous straight line, its equation, and the corresponding correlation coefficient, r. The graph also includes a dashed straight line representing the equality between HP and H0. The scale of the axes is always the same in order to allow the comparison between the two surface runoffs and among the different climatological stations.

It is important to emphasize that, for most of the climatological stations, the high values shown in Figure 4 for the linear correlation coefficient indicate a statistically significant dependency between monthly streamflows evaluated on the basis of Thornthwaite (HP) and Penman-Monteith (H0) evapotranspiration. As the potential evapotranspiration of Thornthwaite (EVP) is always lower than the potential evapotranspiration of Penman-Monteith (EV0), its derived monthly streamflows (HP) are sometimes higher, although only slightly, than those provided by the Penman-Monteith data (H0).

However, significant differences between potential evapotranspirations, as those shown in Figure 3, may not necessarily lead to substantial differences between surface runoff evaluated based on those evapotranspirations. This is the case of the climatologic stations of Bragança (03Q/01), Mirandela (05T/01), Vila Real (06K/01), Régua (07K/01), Viseu (10J/01), Coimbra-Bencanta (12G/06), Alcobaça/E. Fruticultura (16D/06), Ota (19D/01), and Sassoeiros (21B/03), where the monthly surface runoffs obtained by the water balance model considering either EVP or EV0 are very close, regardless of the differences between evapotranspirations.

This highly interesting, and innovative observation can be explained by the fact that the largest differences between monthly values of EVP and EV0 occur in the dry semester—from April to September—during which the water excess (or superavit) and, consequently, the surface runoff are no longer controlled by the evapotranspiration. They are a consequence, instead, of the combined effect of low or even nonexisting rainfall and groundwater storage.

This effect results in an actual evapotranspiration that is rather unrelated to the potential one since it is limited not by the "potentiality" of the soil and plants to transfer water to the atmosphere, but, instead, by the scarcity of water that inhibits that "potentiality." Under these circumstances, the actual evapotranspirations derived considering either EVP or EV0 become very close even when these potential evapotranspirations are quite different.

Figure 5 intends to demonstrate the previous conclusion, based on the climatological stations of Vila Real (06K/01), Alcobaça/E. Fruticultura (16D/06), and Viseu (10J/01) chosen as examples.

However, even during this season, the differences between the monthly mean

Monthly flows predicted by the monthly Thornthwaite-Mather water balance model applied to the monthly evapotranspirations of Thornthwaite (HP) and of Penman-Monteith (H0). Linear regression line (continuous line), equation, and correlation coefficient, r. Line representing the equality between monthly HP and H0 (dashed line).

Effect of the Evapotranspiration of Thornthwaite and of Penman-Monteith in the Estimation…

DOI: http://dx.doi.org/10.5772/intechopen.88441

It is also important to stress that the month-by-month variability of the EVP series is larger than the one of the EV0 series (higher standard deviations). Despite this fact, the within-the-year variability of the flow series obtained from both evapotranspirations is very similar, meaning that the water balance model applied to ETP or ET0 yields to monthly streamflows that are very similar, either in value or

surface runoffs HP and H0 are very small.

Figure 4.

101

in what concerns their statistical characteristics.

For each of the stations adopted as examples and for each month, Figure 5 shows the monthly averages and the standard deviations of the series of EVP and of EV0 and of the surface runoffs predicted by applying the Thornthwaite-Mather water balance model to those evapotranspirations (HP and H0, respectively).

The previous figure shows that, on average, the monthly values of EVP are always lower than those of EV0, the differences being larger in the summer period.

## Effect of the Evapotranspiration of Thornthwaite and of Penman-Monteith in the Estimation… DOI: http://dx.doi.org/10.5772/intechopen.88441

#### Figure 4.

In the previous scope, Figure 4 shows the comparison between monthly streamflows (expressed in water depth) from the water balance model based on the monthly potential evapotranspiration of Thornthwaite (HP) and of Penman-Monteith (H0). Such results were obtained assuming a maximum useable water capacity of the soil (Smax) of 150 mm that allegedly corresponds to the average conditions prevalent in Mainland Portugal, though, in fact, the values of Smax are expected to be slightly higher in the southern than in the northern parts of the

Current Practice in Fluvial Geomorphology - Dynamics and Diversity

The results from the linear regression analysis between HP and H0 are represented in each graph by a continuous straight line, its equation, and the corresponding correlation coefficient, r. The graph also includes a dashed straight line representing the equality between HP and H0. The scale of the axes is always the same in order to allow the comparison between the two surface runoffs and

It is important to emphasize that, for most of the climatological stations, the high values shown in Figure 4 for the linear correlation coefficient indicate a statistically significant dependency between monthly streamflows evaluated on the basis of Thornthwaite (HP) and Penman-Monteith (H0) evapotranspiration. As the potential evapotranspiration of Thornthwaite (EVP) is always lower than the potential evapotranspiration of Penman-Monteith (EV0), its derived monthly streamflows (HP) are sometimes higher, although only slightly, than those provided by the

However, significant differences between potential evapotranspirations, as those shown in Figure 3, may not necessarily lead to substantial differences between surface runoff evaluated based on those evapotranspirations. This is the case of the climatologic stations of Bragança (03Q/01), Mirandela (05T/01), Vila Real (06K/01), Régua (07K/01), Viseu (10J/01), Coimbra-Bencanta (12G/06), Alcobaça/E. Fruticultura (16D/06), Ota (19D/01), and Sassoeiros (21B/03), where the monthly surface runoffs obtained by the water balance model considering either EVP or EV0 are very close, regardless of the differences between

This highly interesting, and innovative observation can be explained by the fact that the largest differences between monthly values of EVP and EV0 occur in the dry semester—from April to September—during which the water excess (or superavit) and, consequently, the surface runoff are no longer controlled by the evapotranspiration. They are a consequence, instead, of the combined effect of low

This effect results in an actual evapotranspiration that is rather unrelated to the potential one since it is limited not by the "potentiality" of the soil and plants to transfer water to the atmosphere, but, instead, by the scarcity of water that inhibits that "potentiality." Under these circumstances, the actual evapotranspirations derived considering either EVP or EV0 become very close even when these poten-

Figure 5 intends to demonstrate the previous conclusion, based on the climatological stations of Vila Real (06K/01), Alcobaça/E. Fruticultura (16D/06), and Viseu

For each of the stations adopted as examples and for each month, Figure 5 shows the monthly averages and the standard deviations of the series of EVP and of EV0 and of the surface runoffs predicted by applying the Thornthwaite-Mather water balance model to those evapotranspirations (HP and H0, respectively). The previous figure shows that, on average, the monthly values of EVP are always lower than those of EV0, the differences being larger in the summer period.

among the different climatological stations.

or even nonexisting rainfall and groundwater storage.

tial evapotranspirations are quite different.

(10J/01) chosen as examples.

100

Penman-Monteith data (H0).

evapotranspirations.

country.

Monthly flows predicted by the monthly Thornthwaite-Mather water balance model applied to the monthly evapotranspirations of Thornthwaite (HP) and of Penman-Monteith (H0). Linear regression line (continuous line), equation, and correlation coefficient, r. Line representing the equality between monthly HP and H0 (dashed line).

However, even during this season, the differences between the monthly mean surface runoffs HP and H0 are very small.

It is also important to stress that the month-by-month variability of the EVP series is larger than the one of the EV0 series (higher standard deviations). Despite this fact, the within-the-year variability of the flow series obtained from both evapotranspirations is very similar, meaning that the water balance model applied to ETP or ET0 yields to monthly streamflows that are very similar, either in value or in what concerns their statistical characteristics.

Through regression analysis techniques, it is also possible to derive the monthly Penman-Monteith potential evapotranspiration from the Thornthwaite one and then to apply the Thornthwaite water balance model or another model to estimate the surface runoff, like the Temez model. By this way, the overestimation of surface runoff that may result from the direct use of EVP, particularly in dryer regions, will

Effect of the Evapotranspiration of Thornthwaite and of Penman-Monteith in the Estimation…

This work is funded by the Coordenação de Aperfeiçoamento de Pessoal de Nível

\*, João Santos<sup>2</sup> and Ticiana Marinho de Carvalho Studart<sup>3</sup>

Superior (CAPES), Brazil, finance code 001, as for the third author.

The authors declare that they have no conflict of interest.

1 Civil Engineering Research and Innovation for Sustainability (CERIS), Instituto Superior Técnico/Lisbon University (IST/UL), Lisbon, Portugal

\*Address all correspondence to: maria.manuela.portela@ist.utl.pt

3 Department of Hydraulics and Environmental Engineering, Federal University of

© 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

2 Department of Engineering, ESTIG, Beja, Portugal

be corrected.

Acknowledgements

DOI: http://dx.doi.org/10.5772/intechopen.88441

Conflict of interest

Author details

103

Maria Manuela Portela<sup>1</sup>

Ceará, Fortaleza, Ceará, Brazil

provided the original work is properly cited.

#### Figure 5.

Averages and standard deviation of the monthly series of EVP, EV0, HP, and H0 in some of the climatologic stations of Table 1.

### 5. Conclusions

The main conclusions of this study are as follows:


According to the previous results, one may conclude that, despite its poor data requirements, the potential evapotranspiration of Thornthwaite combined with the simplest water balance model provides a feasible and accurate approach (i) to fill in the gaps of monthly flow series, (ii) to increase the spans of such series, and (iii) to estimate monthly flows at ungauged catchments.

Effect of the Evapotranspiration of Thornthwaite and of Penman-Monteith in the Estimation… DOI: http://dx.doi.org/10.5772/intechopen.88441

Through regression analysis techniques, it is also possible to derive the monthly Penman-Monteith potential evapotranspiration from the Thornthwaite one and then to apply the Thornthwaite water balance model or another model to estimate the surface runoff, like the Temez model. By this way, the overestimation of surface runoff that may result from the direct use of EVP, particularly in dryer regions, will be corrected.
