Reservoir Yield Vulnerability under Global Change

Transcription

1 Reservoir Yield Vulnerability under Global Change José Nilson Beserra Campos, PhD Ticiana Marinho de Carvalho Studart, Dr Patrícia Freire Chagas, MSc Department of Water Resources and Environmental Engineering Universidade Federal do Ceará, P.O. Box 6018, Fortaleza, Ceará, Brazil, Fax: (+55) There is not a scientific consensus on how the climate changes will modify the hydrological cycle. Climate models still need to be improved in order to better evaluating accurately this changes. Predictions of regional effects in the hydrological cycle vary significantly among different models. Besides that, there is a consensus on global precipitation and evaporation increase. Despite of all these uncertainties, some likely trends in hydrological cycle can be named: An increase on air temperature leads to an increase in evapotranspiration and, as a result, an intensification of the hydrological cycle. For a mean global temperature increase of 2 0 C, potential evapotranspiration increases by up 40% (Hoff, 2001). There are a tendency on increasing the total precipitation over the world. Besides of that, for some regions, a decrease in precipitation is expected, despite of the global trend to a higher precipitation, due to changes in global circulation and atmospheric conditions (Hoff op. cit.). The Northeast of Brazil (NEB) has a semi-arid climate subject to recurrent droughts and one the main concerns of researchers is evaluating the impact of global changes in water availability in the region. In NEB it was created a culture of storing water in surface reservoirs, as much as possible. It is common one reads in drought s historiography that, for solving the drought problem, it would be necessary keeping in reservoirs up to the last drop of water from the intermittent rivers of the Region. Than, the estimation of the impacts of climate in water availability in NEB is strongly related to evaluation of the impacts in reservoirs yield. The present study intends to evaluate the impacts of climate change in the availability of water in Northeast of Brazil, taking as case study the Várzea do Boi river basin. The main focus is on the water yielded by surface reservoirs, which represents the main source for most portion of Ceará State.

2 THE STUDY AREA The study area comprises Várzea do Boi Reservoir s drainage basin, in Tauá municipality, situated in the microregion of Sertões dos Inhamuns.(Figure 1 ). Várzea do Boi reservoir is in upper part of Jaguaribe River Basin, which is the largest intermittent river of the world. The climatic and hydrological conditions in Várzea do Boi reservoir correspond to typical Ceará State s semi-arid condition: highly variable precipitation and run-off patterns, both within-the-year as well as overyear scales, associated to high negative water balance. The mean annual precipitation is around 520mm, mean annual inflow (μ) approximately equal to 42,6 hm³, standard deviation of annual inflows (σ) equal to 66.8 hm³, coefficient of variation of annual inflows (CV) equal to 1.57 and mean annual evaporation during dry season (E v ) equal to 1,438mm. The drainage area (A) is 1,256 km² and the reservoir s capacity (K) is 51.8 hm² (Campos, Vieira and Queiróz, 2000). Figure 1. Várzea do Boi Reservoir s location in Jaguaribe Basin (Ceará State)

3 METHODOLOGY A reservoir woks as a hydrologic transformation system. The water provided in a very irregular manner by Nature is stored and released according to the demand. In that process, the inflows are partitioned in three portions: (1) the evaporation from the lake; (2) the reservoir s spills to downstream and (3) controlled volume, which is named reservoir yield, and represents the system s availability. This third part represents the reservoir yield, or water availability, witch is focus of the present study. The reservoir yield was estimated under two approaches. In the first approach, the yield was estimated solving the reservoir budget equation, in parametric formulation of Campos (1987, 1996), using Monte Carlo simulation. In the second, the yield was computed for an infinite reservoir according to an equation, obtained using also Monte Carlo simulation and the parametric formulation referred (Campos and Ibiapina, 1997; Campos, Ibiapina and Studart, 2001) To introduce the climate change in the study, we analyzed two standards for hydrological modifications in Várzea do Boi river basin. For each standard, it were built scenarios for different values of precipitation, lake evaporation and reservoir inflows. The yield estimations were performed using both procedures: Monte Carlo Simulation and infinite reservoir yield equation. In addition, it was also estimated the global change impact on reservoir yield, for the climate scenario estimated in the Waves Project. ( Chapter Andreas). Standards assumed for hydrological changes Due the uncertainties in the expected hydrological modifications in Várzea do Boi river basin, we studied the impacts of climate change on water availability under two different standards of hydrological modifications in the basin. In each standard, it were built 10 scenarios grouped in an ensemble, named ensemble 1 and ensemble 2 respectively. In ensemble 1, precipitation, evaporation and inflows increases at the same ratio (K X ). In ensemble 2, precipitation and evaporation increases at the same ratio (K X ) and the coefficient of surface run-off increases according to Aguiar (1937) polynomial rule (K R ). This is a kind of optimistic assumption, once the Aguiar s empirical rule is valid for a constant value for evapotranspiration. So, once an increase in evapotranspiration is expected as consequence of global change, it is also expected that the run-off increases a little less than

4 the obtained by Aguiar s formulation. On the other hand, the first ensemble is a kind of pessimistic regarding to reservoir inflow, because some increase in run-off is expected due to the increase in precipitation. The computations to estimate the global change impacts on water availability were performed in the following steps: 1- The initial condition are that in the year 2000, with the data got from the Jaguaribe River Basin Water Management Plan (COGERH 1999). 2- For each ensemble, it were built 10 hydrological scenarios ( K X varying from 1.02 to 1.20) and computed the values of precipitation, evaporation and reservoir inflows. The coefficient of variation was assumed constant and equal to the conditions in the scenario of the year For each scenario, there were estimated the reservoir yield and efficiency, according to two methodologies: a) using Monte Carlo simulation and b) using an empirical formulation for an infinite reservoir (Campos and Ibiapina, 1997; Campos, Studart and Ibiapina, 2001) In addition it was also estimated the impact in the reservoir yield for the global change in precipitation, evaporation and run-off estimated in the Waves project. This estimation was done only by the infinite reservoir procedure. Yield estimation using Monte Carlo simulation The reservoir water budget was solved using Campos (1987; 1996) formulation. The procedure consists in making a parameterization of the budget equation and computes the yield using Monte Carlo simulation. The water budget can be represented by equations 1 and 2, as follows: Z t + 1 = Z t + I t - M - ( 1/2 ).( A t +1 + A t ).E - S t (1) with S t = max ( Z t + I t M. ( 1/2 ).( A t A t ).E v - K; 0 ) (2)

5 where Z t + 1 and Z t storage at the beginning of the (t+1) th and t th years, respectfully; I t inflow into the reservoir during the t th year; M release from the reservoir during year the t th (M is assumed constant from year to year); A t+1 and A t lake area at the beginning of the (t+1) th and t th years; E v - mean evaporation depth during the dry season (E v is assumed constant from year to year); K - reservoir capacity and S t - spill from the reservoir during the t th year The reservoir and lake morphologies are described, respectively, by Z(h)=α.h 3 and A(h)= 3.α.h ². The α value can be estimated from a regression equation between the lake level (h) and the stored volume (Z). Considering Z(h) and A(h), Equation 1 can be rewritten as Equation 3: Z Zt+ 1 = Zt + It 3 23 / 23 / 13 α / t+ 1 t + Z 2 E S t (3) The reservoir budget equation is reduced to the following parametric presentation: f M = Φ (CV, G, f K, f E ) (4) where G is the reservoir reliability (assumed 90%) in this study, f K is the dimensionless capacity ( K/μ ), f E is the dimensionless evaporation factor computed by (3α 1/3 E V ) / μ 1/3 and f M is the dimensionless release in steady state conditions estimated by f M = M/μ. The Equation 4 is solved for synthetic inflows, for an gamma distribution function, using a coefficient of variation of annual inflows equal to The yield from an infinite reservoir To estimate the global impacts on an infinite reservoir yield (theoretically, the maximum yield from a basin controlled by a single reservoir), it was used the equation defined by Campos, Studart and Ibiapina (2001). Assuming reliability (G) of 90%, the authors obtained a general equation for reservoir s efficiency (η M ) on the steady state of the storage process (Equation 5). Only two input parameters are necessary: the coefficient of variation of annual inflows (CV) and the dimensionless factor of evaporation (f E ). This equation is valid for CV ranging from 0.5 to 1.6 and f E ranging from 0.05 to 2.0. In this study the reservoir s efficiency will be estimated for CV=1 to 1.6 and for the various values of f E defined in ensembles 1 and 2.

6 η M = 0.99 exp [-f E / ( CV CV² CV³) (5) The infinite reservoir efficiency (η M ) and the dimensionless factor of release (f M ) are related by η M = 0.95 f M and the reservoir annual release (M) is given by M = 1.05.μ.η M. RESULTS The results obtained are analyzed grouped by hydrological modifications standards (ensembles) and by the methodology used in yield evaluation. Ensemble 1 estimated by Monte Carlo simulations The results (Table 1) show that, in these assumptions, there are a negative trend in water availability and in reservoir efficiency. For example, if the mean precipitation and evaporation increases 4%, the reservoir yield drops from 5.48 hm 3 /year to 5.39 hm 3 /year (approximately 1.7%). Regarding to reservoir s efficiency, it remains constant for a significance of Table 1. Values of annual yield (M) and the reservoir efficiency (η) for a 90% reliability, computed by Monte Carlo Simulations, in ensemble 1 K X μ σ f E M f M η =0.95 f M (hm³/year) (hm³/year) (hm³/year) Note: The reference scenario (year 2000) is shaded. Ensemble 1 with yield estimated by infinite reservoir equation The analysis shows that there are a slight positive trend in reservoir yield. Notice that this yield represents the maximum controllable yield in the basin. So, regarding to maximum regulation capacity, in case of hydrologically balanced changes (ensemble 1), the impact of global change in Várzea do Boi River Basin will be slightly positive.

7 Table 2. Values of annual yield (M) and the reservoir efficiency (η) with 90% of reliability for an infinite reservoir in ensemble 1 K X μ f E M η =0.95 f M (hm³/year) (hm³/year) Note: The reference scenario (actual values) is shaded. Ensemble 2 with yield estimated by Monte Carlo simulations Ensemble 2 embraces the scenarios where precipitation and evaporation increase in the same ratio (K X ) and run-off increases in a rate K R, according to Aguiar s rule (Equation 6): R(mm) = 28.53H 112.9H² H³ H 4 (6) where H is the mean annual precipitation over the basin and R(mm) is the run-off in millimeters, for an unit basin. Using H=0.52m ( mean annual precipitation for Várzea do Boi) one can find the run-off (Rmm) equals to 25.01mm. The ratio of increasing in run-off (K R ), for an increasing K X in precipitation, is performed dividing the unit area run-off for an precipitation K X, H, by the unit area run-off for initial conditions. Then, the runoff in scenario K X is estimated by multiplying the initial run-off by K R. The results are showed in Table 3. Table 3. Values of annual yield (M) and the reservoir efficiency (η) for a 90% reliability, computed by Monte Carlo Simulations, in ensemble 2 K X H R K R μ σ F E M f M η =0.95 f M (m) (mm) (hm³/year) (hm³/year) (hm³/year) ,13 0, ,13 0, ,12 0, ,12 0, ,12 0, ,11 0, ,10 0, ,10 0, ,09 0, ,09 0, ,09 0,08

8 As can be saw in Table 3, there a positive trend in water availability for K X ranging from 1.02 to For instance, when precipitation increasing 4%, the reservoir yield increases 4.7%. That is, in the global change assumptions of ensemble 2, it is expected a reasonable gain in water availability. For values of K X greater than 1.08, the value of reservoir yield decreases and increases in an irregular way. Ensemble 2 with yield estimated by infinite reservoir equation The analysis showed that there are a positive trend in reservoir yield. Regarding to maximum capacity of regulation, in case of hydrologically balanced changes (ensemble 2), the impact of global change in Várzea do Boi River Basin will be positive regarding to water availability. Regarding the efficiency, otherwise, there are a slightly negative trend (Table 4). Table 4. Values of annual yield (M) and the reservoir efficiency (η) for a 90% reliability for an infinite reservoir in ensemble 2. K X K R μ f E M η =0.95 f M (hm³/year) (hm³/year) ,16 0, ,95 0, ,78 0, ,63 0, ,51 0, ,43 0, ,38 0, ,36 0, ,37 0, ,41 0, ,48 0,33 Scenario Waves: According to WAVES Program Climate Group and running the hydrological model named WASA, there will be a decrease in precipitation (-12%), run-off (-32%) and evaporation (-0.1%). The coefficient of variation of annual inflows is almost the same (present 1.21 and future 1.22). In that case, there will be a decrease both on annual yielded and on reservoir efficiency (Table 5) Table 5. Annual yield (M) and efficiency (η) for a infinite reservoir considering WAVES global change (it is assumed G=90%) f E CV M η Reference scenario ,25 0,52 Waves scenario ,87 0,39

9 FINAL COMMENTS The results of this research regarding to impacts of global change in water availability in Várzea do Boi river basin reach the following conclusions: For the WAVES global change scenario, the water availability in assumption of an infinite reservoir, maximum yield in the basin, the reservoir yield drops from hm 3 /year to hm 3 /year ( 49 %), and the reservoir efficiency drops from 52% to 39%. For the hydrologically balanced changes ensemble 1 (precipitation, evaporation and inflows increasing at the same ratio) there are an negative trend in the reservoir yield and efficiency in the actual topology of Várzea do Boi River Basin. On the other hand, in the assumption of infinite reservoir, basin run-off totally controlled, there a slightly positive trend in reservoir yield and a negative trend in reservoir efficiency. For the hydrologically balanced changes ensemble 2 (precipitation and evaporation increasing at the same ratio, and inflows increasing according Aguiar s polynomial rule) there are a positive trend in the reservoir yield for the actual topology of Várzea do Boi River Basin as well as for the totally controlled basin. On the other hand, there are, on both situations decrease in reservoir efficiency. The general conclusion is that, in case of Waves scenario, there are substantial losses in water availability in the basin. On the other hand, if the global change are hydrologically balanced, as prior defined, most of results point out to an increase in water availability in the basin. Only in the pessimistic assumption of evaporation, precipitation and inflows increasing at the same rate, there will be small losses on the reservoir yield. In the case of totally controlled basin and hydrologically balanced changes, the are always gains in the water availability in the basin. ACKNOWLEDGMENTS The authors would like to thank CNPq for supporting the research. REFERENCES AGUIAR, F.G.. Estudo Hidrométrico do Nordeste Brasileiro. Departamento Nacional de Obras Contra as Secas. Boletim Técnico. 36 n. 2 jul./dez Reimpressão. CAMPOS, J.N.B. (1987). A Procedure for Reservoir Sizing on Intermittent Rivers Under High Evaporation Rate. Fort Collins, Colorado State University. PhD thesis.

10 CAMPOS, J.N.B., VIEIRA NETO, J. e QUEIROZ, E.A. (2000). Impacto Cumulativo da pequena açudagem: um estudo de caso do Açude Várzea do Boi, em Tauá, Ce. IN: V Simpósio de Recursos Hídricos do Nordeste, Natal, RN. CAMPOS, J.N.B. (1996). Dimensionamento de Reservatórios: O Método do Diagrama Triangular de Regularização Edições UFC. Fortaleza 1996 CAMPOS, J. N. B.; IBIAPINA, N. G. (1997). Uma Equação para a Máxima Capacidade de Regularização em um Reservatório In. XII Simpósio Brasileiro de Recursos Hídricos, Vitória, ES. Associação Brasileira de Recursos Hídricos. HOFF, H. (2001). Climate Change and Water Avaiability. IN: Lozán, J.L., Graβl H. and Hupter, P. In: Climate ot the 21 st Century: Changes ans Risk. Wissenschaftliche Auswertungen. Hamburg. CAMPOS, J.N.B, STUDART, T.M.C. e NEY G. IBIAPINA (2001). Computing the Yield from an Infinite Reservoir. In: American Geophysical Union 21 th Annual Hydrology Days, Colorado State University, Colorado, USA, April.