EFFECT OF THE EVAPORATION ON THE DESIGN OF THE STORAGE CAPACITY OF ARTIFICIAL RESERVOIRS

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1 EFFECT OF THE EVAPORATION ON THE DESIGN OF THE STORAGE CAPACITY OF ARTIFICIAL RESERVOIRS Ana Rita Álvaro Albuquerque Martins Instituto Superior Técnico, Lisboa, Portugal Abstract April 2016 Due to the temporal irregularity of the river flows in mainland Portugal, it becomes necessary to have artificial reservoirs that adequate the temporal pattern of the inflows to the one of the water demands. The goal of the presented research is to ascertain the effect of the evaporation on the design of the storage capacity of such reservoirs. In order to evaluate this effect, seven case studies were used. The design of the reservoir of each case study utilized the simulation of its exploration on a monthly scale. The water inflows in natural regime to each reservoir applied a regionalization model, through hydrometric data transposition, developed for mainland Portugal. To estimate the evaporation from the reservoir relationships between class A pan evaporation and Thornthwaite potential evapotranspiration were developed and applied. The study showed that the effect of evaporation on the storage capacity of artificial reservoirs can be quite significant, namely in warmer regions and in reservoirs with large water mirrors. Keywords: Storage capacity, artificial reservoirs, simulation algorithms, evaporation, evapotranspiration. 1. Introduction This research addressed the effect of the evaporation on the design of the storage capacity of artificial reservoirs, in order to access its relevance under the climatologic context of mainland Portugal. For that purpose seven case studies were adopted and analyzed based on the simulation of their exploitation at a monthly scale. The simulation utilized the mass equation taking into account at each time step the water inputs and outputs in the system. The water inputs are the inflows to the reservoir and the direct precipitation on its surface and the water outputs are the water demands, the water volumes released downstream and the water losses due to infiltration and evaporation. Prior the application of the simulation algorithm to each case study, it was necessary to evaluate the monthly inflows to the same and to identify a model able of providing the estimates of the monthly evaporation. Regarding the inflows a regionalization model, based on transposition of hydrometric data, was applied. To evaluate the evaporation relationships between evaporation and the potential 1

2 evapotranspiration of Thornthwaite were developed by analyzing twenty weather stations. Moreover, the obtained results were compared with previous ones on the same subject. 2. Artificial reservoirs 2.1. Sizing of storage capacity Artificial reservoirs aim to allow the temporary storage of water in order to adequate the temporal patterns of the natural river inflows and of the water demands, taking into account the reliabilities of the latter. The design of the storage capacity of these reservoirs can be done using different methods, including the simulation method. Notwithstanding the simplicity of its formalism, the simulation method allows considering in the design the different variables which can influence the capacity of the reservoir, either of hydrological nature or related to the demands (independently from their temporal patterns) and to performance indicators of the system (reliability and failures in the supply). The simulation uses the mass equation, applied to consecutive time steps (on a monthly scale), given by: S t+1 = S t + Q t D t E t + P t L t (1) with the restriction: 0 S t+1 C (2) Equation (1) indicates that the volume stored in the reservoir at the end of each time step t + 1, S t+1, is a function of the storage volume at the beginning of the time step t, S t, of the inflows volumes into the reservoir between t and t + 1 from river flows, Q t, and to the precipitation over the reservoir, P t, and from outflow volumes between t and t + 1, related to the demands, D t, and the losses by evaporation, E t, as well as other losses, L t. The design variables may be the storage capacity of the reservoir, C the demands, D, or their reliability, G. Once fixed the values of two of these three variables, the simulation method allows the estimation of the third, whether directly (in the case of the estimation of G by fixing C and D), whether through iterative algorithms (estimation of C, by fixing D and G, and estimation of D, fixing C and G). In the analysis accomplished, the reservoirs were assumed to be full at instant 0, and only uniform demands were considered to be uniform, along with the disregard of P t e L t Previous studies for mainland Portugal More often, reservoirs are created in river sections without flow data which hinders considerably the design of their storage capacities. To overcome this issue, comprehensive research was developed 2

3 for mainland Portugal, in order to enable the preliminary design of those capacities, under the scarcity or even inexistence of hydrometric data (Portela e Quintela, 2000, 2001, 2002, 2005, 2006a,b, and Portela, 2014). Having in mind that, in mainland Portugal, the mean annual flow depth, H, is directly related to the relative temporal variability of the flow regime, those developed the following relationship: C Q = αh β (3) where Q is the mean annual flow volume to the reservoir is a positive coefficient and the exponent is negative. The previous equation is valid for fixed pairs of D Q and G, H being the parameter of the design of the storage capacity. The values of and for different reliabilities, G, and draft, D Q can be found in the previously cited references. These results were confirmed by Silva (2010), not only through the update of the hydrometric data, but also, more importantly, through the use of synthetic series of monthly flows. 3. Case studies The previous studies for mainland Portugal did not take into account the effect of the evaporation in the design of the storage capacity of artificial reservoirs. This effect may not always be negligible due to local climatological factors, as well as to the geometry of the reservoirs and of the area of their water mirrors. As the evaporation from a reservoir depends on the geometrical characteristics of the same, the analysis of its effect on the design of the storage capacity is case dependent. In the studies carried out the seven case studies, provided by CENOR Consulting Engineers, S.A., identified in Table 1, along with some of their characteristics, were considered Table 1. Identification of the case studies: location, purpose, area of the river basin, A b, mean annual flow depth, H, modulus, Qmod, and minimum level of exploitation, Nme. Case studies District 1 Évora Purpose A b (km 2 ) H (mm) Qmod (l/s) Irrigation Nme Viseu Urban supply Bragança Urban supply Bragança Urban supply Viseu Urban supply Guarda Irrigation Viseu Urban supply

4 4. Monthly affluent flows in natural regime The estimation of the monthly inflows at each case study used the regionalization model by transposition of hydrometric data developed by Portela and Quintela (2000, 2001, 2002, 2005, 2006a,b) and Portela (2014). Essentially, the model considers that the relative temporal variability of the flow regime at different temporal scales (year, month or day) is close in river basins with similar mean annual flow depths, H. Accordingly to the previous authors, the available flow series, at a given time scale, in a gauged river section (referenced by 1), with a mean annual flow depth H 1 (mm), can be transposed to an ungauged river section (river basin 2), where an estimation of the mean annual flow depth H 2 (mm) was obtained, close to H 1 (H 1 H 2) by applying the following equation (Portela, 2014): Q 2 1 i,j = Q Qmod 2 i,j (5) Qmod 1 k where Q i,j is to the mean flow volume in month or day j of year i at section k, and Qmod k the modulus at that section (thus, the index k identifies the sections 1 and 2). The model requires that the river basins 1 and 2 have similar geomorphological and occupation conditions, as well as similar mean annual flow depths. Table 2 identifies the rive gauge stations utilized to estimate the monthly inflows at each case study, as well as the period with available flow data that supported the analysis. The schematic location of the case studies and of the previous river gauge stations is presented in Figure 1, according to the identification code also specified in Table 2. Table 2. Case studies, hydrometric stations used on the estimation of the monthly flows, time frames of the flows and characteristics of the flows in those stations and in the case studies. Name Identificacion in Figue 1 Time frame of records Mena annual flow mm Case study Caso / /97 Hydrometric station Albernoa (26J/01H) EH Case study Caso / /90 Hydrometric station Ponte Santa Clara Dão (10K/01H) EH Case study Caso / /97 Hydrometric station Vinhais (Quinta Ranca) (03P/01H) EH Case study Caso / /03 Hydrometric station Ponte Figueira (09O/02H) EH4/ Case study Caso / /04 Hydrometric station Cabriz (07I/04H) EH Case study Caso / /03 Hydrometric station Ponte Figueira (09O/02H) EH4/ Case study Caso / /80 Hydrometric station Pedre Ribeiradio (09H/01H) EH m m 4

5 5. Evaporation from reservoirs The evaporation data is scarce which complicates considerably the issue of estimating the water losses from artificial reservoirs due to that process. To identify alternative procedures to estimate evaporation, several authors have analyzed the dependency between the corrected evaporation in class A pans and the potential evapotranspiration of Thornthwaite. Those authors concluded that the two previous variables show a significant dependency (Klosowski and Galvani, 1997; Amatya et al., 2014) which allows the use of the evapotranspiration to estimate the evaporation. This dependency becomes even more attractive since the calculation of the potential evapotranspiration of Thornthwaite is quite simple because it only depends on the mean monthly temperatures, according to the following equation: a ETP m = { 16N (10T m m ) I, T m > 0 0, T m 0 (6) where ETP m (mm) is the estimated potential evapotranspiration in a given month, m; N m is a correction factor that takes into account number of days and the daytime of that month (Quintela, 1996, p. 7.19); T m (ºC) is the mean daily air temperature of the month m; and α is an exponent related to the heat index I, which depends on the 12 monthly mean temperatures. In order to relate the monthly values of the evaporation and the Thornthwaite evapotranspiration, 21 weather stations with temperature and class A pan evaporation data were analyzed. By simple linear regression analysis, assuming null y-intercept, it was concluded that, for 20 of the 21 weather stations analyzed, the dependency on a monthly scale between the two hydrological variables was significant, associated to considerable correlation coefficients (between 0.88 and 0.97). The weather station where there was not possible to establish any relation presented an irregular and physically unexplainable behavior, quite possible due to measurement errors, and, as such, was excluded from the research. The previous study has revealed that, despite the fact that the linear dependence between the corrected evaporations of class A pans and the potential evapotranspiration of Thornthwaite is statistically significant, the regression lines have a spatially limited application. As such, the generalization, in spatial terms, of these relations is not valid. Thus, in order to estimate the evaporations from the reservoir of each case study, the regression equations, relative to the weather stations which are closest geographically to them, were applied using the previously estimated values of monthly evapotranspiration of Thornthwaite. Hence, for the evaporation of each month, the average of the obtained evaporations was used. In Table 3, the weather stations whose air temperatures were used to calculate the potential evapotranspirations of Thornthwaite, for the different case studies, are identified, as well as the weather stations whose regression equations were applied to obtain the evaporations based on those 5

6 evapotranspirations. In the regression equations ETP m represents the Thornthwaite potential evapotranspiration of in a given month, and EV m the corresponding evaporation. The weather stations of Table 3 are also schematically located in Figure 1 according to the code specified in the table. Table 3. Monthly potential evapotranspiration of Thornthwaite and corresponding monthly evaporations from the reservoirs of the case studies. Weather stations used, general characteristics and simple linear regression equations. Case studies Weather station Monthly potencial evapotranspiration ofthornthwaite Identification in Figure 1 Time frame of records Mean of monthly values Evapotranspiration Figure 1 tion Weather station ( C) (mm) (mm) Air temperature Monthly evaporation from the reservoirs Identification in Regression equation Mean monthly evapora- Amieira (24L/01C) EC8 EV m =1.56 ETP m Case 1 Évora (22J/02) EC1 1970/ / Barragem de Odivelas (24I/03C) EC9 EV m =1.22 ETP m Barragem de Vale do Gaio (24H/02C) EC10 EV m =1.30 ETP m Barragem do Divor (21J/03C) EC11 EV m =1.39 ETP m Case 2 Viseu (10J/01) EC2 1940/ / Case 3 Bragança (03Q/01) EC3 1956/ / Case 4 Folgares (06N/01C) EC4 1981/ / Case 5 Régua (07K/01) EC5 1966/ / Case 6 Case 7 Rio Torto (04N/01C) Barragem de Castelo Burgães (08G/01C) EC6 EC7 1981/ / / / In Figure 1 the location of the case studies, the hydrometric stations used by the regionalization model and the weather stations, considered to estimate both the monthly potential evapotranspiration of Thornthwaite and the corresponding evaporations from the reservoir, are presented. The symbols adopted in the figure to identify the case studies, the hydrometric stations and the climatological stations are presented in Tables 2 and 3, as previously stated. Figure 1. Schematic location of the case studies, river gauge stations considered in the flow transposition model and weather stations used to calculate the monthly potential evapotranspirations of Thornthwaite and the corresponding evaporations from the reservoirs. The symbols used are specified in Tables 2 and 3. 6

7 6. Results The analysis of the consequences of evaporation on the storage capacity of a reservoir in each of the seven case studies was made for three different scenarios: reference scenario or scenario 0 corresponding to the assumption that the evaporation is negligible; scenario 1, in which evaporation from the reservoir is not negligible, yet it is assumed that all of the capacity of the reservoir can be used (null dead volume); and scenario 2, which simultaneously admits the contribution of evaporation from the reservoir and considers the existence of a dead volume, defined by the minimum level of exploitation, Nme. The results from the analysis, expressed as a function of specific storages, C Q, for reliabilities, G, of 80, 90 and 95%, and for draft, D Q, of 20, 40 and 60% are presented in Table 4, which also includes the results relative to the volumetric reliability, G V, albeit it not being used as a performance criteria for the design. Table 4. Specific storages, C Q, and volumetric reliabilities, G V, for different pairs of values of reliability, G, and draft, D Q, in the scenario 0, scenario 1 and scenario 2 Case studie s G D / Q Scenario 0 Scenario 1 Scenario 2 C / Q G V C / Q G V C / Q G V studies C / Q G V C / Q G V C / Q G V (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) Case G D / Q Scenario 0 Scenario 1 Scenario 2 7

8 The fact that, in the previous table, the values of G V are greater that the values of G indicates that some of the failures are partial, i.e. they refer to months where the demand demands were partially satisfied. Table 4 shows that the consideration of the evaporation from each reservoir always leads to an increase of the specific storage, C Q, which is necessary to account for. For scenario 1, except in case 1, the increase has little sensitivity to the increase of the reliability, G, or to the increase of draft, D Q. The exception of case 1 is possibly due to its location in a region with considerably higher air temperature (Figure 1), associated to the geometry of the reservoir, with a large water mirror, resulting in a high volume of evaporated water. The ratio between the specific storage in scenario 1 and scenario 0 ranges from slightly higher than 1 (case studies 4 and 7) to approximately 4 (case study 1), with an average of approximately 1.3. Thus, comparatively to scenario 0, the consideration of the evaporation resulted on an average increase of the specific storage, C Q of 30%. For scenario 2, the increase of the storage capacity relatively to scenario 0, is even more noticeable. Indeed, the ratio between specific storage, C Q, of scenarios 2 and 0 ranges from a minimum of 1.2 to a maximum of 17.2, averaging 2.8, for the seven case studies (an average increase of specific storage of 180%). The effect of the variation of reliability, G, and of draft, D Q, in C Q, is, still, variable and unclear, certainly due to the importance of the dead volume in comparison with the other volumes at stake. Moreover, the results from the different scenarios were compared with those of the previous studies of Silva (2010). The comparison showed that the results from scenario 0 match perfectly the previous ones, with which they are directly comparable, within the confidence intervals (95%) established in those studies. Regarding scenario 1, it was concluded that the previous studies can provide an alternative design criteria, if the upper limits then obtained for the confidence intervals are used. However, despite some results are encompassed by those upper limits, the combination of the evaporation losses with the need to restitute a minimum level of exploitation, each time the level of the reservoir falls below (scenario 2), may result in significant increases in the specific storages,c Q. This last issue clearly indicates that the design of C needs to take into account all the relevant variables, and therefore the equations presented in Silva (2010) cannot be used. Conclusions The presented research highlights the importance of considering evaporation on the design of the storage capacity of reservoirs, being significantly more important for reservoirs located in warmer regions and with larger water mirrors. The consideration of minimum levels of exploitation, below which the water surface can fall down due to evaporation and that need to be reestablished in order to resume the supplies, further increases the 8

9 relevance of the losses due to evaporation. However, the analysis of this issue has to be developed on a case-by-case basis, because the water volumes lost are strictly dependent on the characteristics (climatologic and geometrical) of the reservoirs. Moreover, the research showed that, for mainland Portugal, it is also possible to relate the class A pan evaporation, and, consequently, the evaporation from artificial reservoirs with the potential evapotranspiration which constitutes am added value in a number of problems related to water resources and infrastructures, even more so due to the simplicity of the calculation of that evapotranspiration, which depends on widely available hydrological data (monthly air temperatures). To conclude, it should be stressed the consistency between the results obtained for scenario 0 and those of previous studies, overtly reinforcing the fact that the mean annual flow depth, H, represents a parameter that encompass in itself much of the information regarding the relative temporal variability of the river flow regime in mainland Portugal. Bibliography Amatya, D.M., Harrison, C.A., Trettin, C.C., Comparison of potencial evapotranspiration (PET) using three methods for a grass reference and a natural forest in coastal plain of South Carolina, Proccedings of the 2014 South Carolina Water Resources Conference, Columbia U.S.A, Klosowski, E.S., Galvani, E., Estimativas de evapotranspiração potencial para a região de Maringá: Estudo comprativo entre os métodos do tanque classe A, Thornthwaite, Camargo e Penman simplificado, Revista UNIMAR, nº. 19(4), Brasil, Portela, M.M., Da regionalização de informação hidrométrica ao dimensionamento de albufeiras e à análise de incertezas, Lição correspondente ao Sumário a que se refere a alínea c) do Artigo 5º do Decreto-Lei n.º 239/2007, de 19 de Junho. IST, Lisboa, Portugal, Portela, M.M., Quintela, A.C., A altura do escoamento anual médio numa bacia hidrográfica como parâmetro de regionalização de informação hidrométrica, In: 1º Congresso sobre Aproveitamento e Gestão de Recursos Hídricos em Países de Idioma Português, pp , Rio de Janeiro, Brasil, Portela, M.M., Quintela, A.C., A altura do escoamento anual médio como parâmetro de regionalização de informação hidrométrica, Tecnologia da Água, Vol 4 (2), pp , Elsevier Información Professional, S.A., ISSN , Portugal (invited paper), Portela, M.M., Quintela, A.C., Assessment of the stream flow characteristics under unavailability of discharge data: the mean annual flow depth over the watershed as a regionalization parameter. The Portuguese case, In: EGS XXXVII General Assembly, European Geophysical Society, Nice, France,

10 Portela, M.M., Quintela, A.C., Estimação de séries de caudais médios diários na ausência de informação hidrométrica. In: VII Simpósio de Hidráulica e Recursos Hídricos dos Países de Língua Oficial Portuguesa (7º SILUSBA), Évora, Portugal, Portela, M.M., Quintela, A.C., Estimação em Portugal Continental de escoamentos e de capacidade úteis de albufeiras de regularização na ausência de informação, Recursos Hídricos, Vol. 27 (2), pp. 7-18, Número Temático: Hidrologia e Modelação Hidrológica, 2006a. Portela, M.M., Quintela, A.C., Preliminary design of the storage capacity of reservoirs based on a flow regionalization parameter, In: BALWOIS 2006, International Conference on Water Observations and Information Systems for Decision Support, Ohrid, 2006b. Quintela, A.C., Hidrologia e Recursos Hídricos, Instituto Superior Técnico, Folhas de apoio à disciplina de Hidrologia e Recursos Hídricos. Associação de estudantes do Instituto Superior Técnico, Lisboa, Silva, A.T.C.F., Design of the storage capacity of artificial reservoirs, Dissertação de Mestrado em Engenharia Civil, Instituto Superior Técnico, Lisboa,