Hydropower 2016/17. Estimation of runoff Water balance Mathematical modelling. Rodrigo Proença de Oliveira

Transcrição

1 Hydropower 2016/17 Estimation of runoff Water balance Mathematical modelling Rodrigo Proença de Oliveira

2 Water cycle Land component Precipitação Evaporação Transpiração Escoamento superficial Zona não saturada Zona saturada Infiltração Recarga Escoamento sub-superficial Natural conditions: E x -R = 0 Evaporação Escoamento subterrâneo Evaporação P = H + E + S p + S s + S u S = S p + S s + S u P = H + E + S

3 Water cycle Esc = Prec ET - S Annual analysis S ~ 0 Esc = Prec ET Monthly or daily analysis Esc = Prec ET S Hourly analysis (rainfall event) ET ~ 0 S = Inf Inf pode ser calculado com modelos simplificados Esc = Prec Inf

4 Annual water balance Precipitation Precipitação Real evapotranspiration Evapotranspiração real Runoff Escoamento Gerês: P = 2500 mm; ETR = 800 mm; H = = 1700 mm Alentejo interior: P = 500 mm; ETR = 400 mm; H = = 100 mm Hydropower Proença de Oliveira 2016

5 Estimation of annual average runoff and annual average stream flow

6 Runoff maps Assume a watershed with 200 km 2 marked in the map. What is the average annual runoff generated in the watershed and the annual flow volume in hm 3? H = 150 mm Flow volume = 0.15 x 200 x 10 6 = 30 hm 3

7 Using a nearby stream flow gage (hydrometric station) record Hydropower Proença de Oliveira 2016 Flow depends on the watershed characteristics: Area; Precipitation pattern; Topography; Watershed shape and river network characteristics; Soil type; Land use. If we assume that all properties except the area are similar, i.e. the average specific flow (or runoff) is equal in both watersheds, then Q???? B EH A Specific flow (m 3 /s/km 2 ) = Avg discharge / Area of the watershed Runoff (mm) = Flow volume / Area of the watershed AvgFlow B = AvgFlow A x A B / A A

8 Keller, Wundt e Langbein formulas Keller (1906): Wundt (1937): H Langbein (1949): b 1 P Keller eq. for central Europe : 2 H b P 2 H b 3 a 1 H 0,942 P a 2 (P 2 P0) 405 H Runoff D Flow deficit, i.e. loss to evapotranspiration. D = P H H (mm) The parameters a 1, a 2, b 1, b 2 and b 3 are dependent on temperature. D P (mm)

9 Turc formula Turc (1951; 1954/55) Data from Europa, América, África e Java D L 2 P 0,9 2 P L T 2 P 2 L 0,1 3 0,05 T lim P D L T in ºC and P in mm

10 Quintela regional curves for Portugal

11 Exercise Estimate the annual runoff (in mm and dam 3 ) generated in a watershed in continental Portugal, where soils have low infiltration capacity, the average annual temperature is 12ºC and the average annual precipitation is 850 mm. Use Quintela s regional formulas and the Turc method. The area of the watershed is 280 km 2.

12 Hydrologic modeling Input variables: Precipitation Potential evapotranspiration Model parameters Output variables HYDROLOGIC MODEL Streamflow Real evapotranspiration Infiltration Why modeling: To study processes; To complete or to validate data; To evaluate situations which cannot be studied in the field. Modeling steps: Calibration; Validation; Application.

13 Modeling steps CALIBRAÇÃO Conjunto de observações 1 Parâmetros do modelo Valores dos parametros Conjunto de observações 1 Variáveis de entrada MODELO Variáveis de saída VALIDAÇÃO Conjunto de observações 2 Valores dos parametros Parâmetros do modelo Variáveis de entrada MODELO Variáveis de saída Resultados 2 Conjunto de observações 2 APLICAÇÃO Conjunto de observações 3 Valores dos parametros Parâmetros do modelo Variáveis de entrada MODELO Variáveis de saída Resultados 3

14 Hydrologic modeling Types of models Physical models Mathematical models Types of mathematical models Empiric vs conceptual Event vs continuous Lumped vs distributed Deterministic vs stochastic Examples of hydrological models: Thorthwaite-Matter (conceptual, continuous, lumped) Stanford Watershed Model (Linsley, 1960) (conceptual, continuous, lumped) MIKE11 and MIKE-SHE (DHI) (conceptual, continuous, distributed) SWAT (conceptual, continuous pseudo-distributed HEC-HMS (ex HEC1) (conceptual, event, lumped)

15 Hydrologic modeling Continuous model vs event model: Escoamento Caudal Evento 1 Evento 2 Evento 3 Evento 4 Simulação contínua Tempo Lumped model vs distributed model: Simulação de eventos Novas condições iniciais Novas condições iniciais Novas condições iniciais

16 Thornthwaite-Mather water balance

17 Thornthwaite Mather model Hmax P H ETP ETR X O,5 x X O,5 x X Com atraso temporal Q A single parameter: H max Original sugestion =150 mm, For instance, it requires a soil depth of 5 m and porosity of 0,3 m. Smaller values are expected in PT. H t disp = min ETP t P t H t 1 H max ; min(h t 1, H max ) Não é necessário calcular se P t ETP t se P t ETP t H disp Water available for evapo transpiration; it depends on the water available in the soil (H t-1 ) and on the difference bewteen ETP - P; ETR t = ቐ ETP disp t se ETP t P t + H t disp disp P t + H t se ETP t P t + H t Real evapotranspiration during timestep t. H max H t = ቊ H t 1 + P t ETR t se P t ETR t H max H t 1 se P t ETR t H max H t 1 Water available in the soil at time t X t = P t ETR t H t H t 1 Q t = 0, 5 X t + 0, 5 X t 1 Hydropower Proença de Oliveira 2016 Instead of 0,5 one can use another parameter and calibrate it. Q t = α X t + (1 α) X t 1

18 Thornthwaite Mather model H t disp = min ETP t P t H t 1 H max ; min(h t 1, H max ) Não é necessário calcular Alternative formulation se P t ETP t se P t ETP t A part of ETP is satisfied by precipitation; The rest of ETP, namely ETP-P is satisfied by the water available in the soil, if possible; The water available in the soil for evapotranspiration, Hdisp, cannot be larger than the soil maximum capacity Hmax nor than the soil initial storage; L é a perda potencial de água no solo; diferença (<0) entre a precipitação e a ETP acumulada desde o início do período seco período tal que (P-ETP)<0 até ao passo de cálculo i. Quanto maior for L maior é a dificuldade de extrair água do solo. L i = ቊ L i 1 + P i ETP i se L i < 0 0 se L i 0 Hydropower Proença de Oliveira 2016 min H i 1 + P i ETP i ; H max H i = ቐ L i H max e Hmax se P i ETP i se P i < ETP i

19 Excel setup Data External computation Parameter to calibrate Hmax P T ETP ETR L H X Q Qobs Monthly values: 12 x Number of years Compairison

20 Modelo Thornthwaite Mather: Calibration

21 Exercise The monthly hydrologic balance of a given watershed shows that for a particular month the precipitation and potential evapotranspiration is 100 mm and 80 mm, respectively. Assuming that the water available for infiltration and runoff is evenly split between these two flow components, compute for that particular month the real evapotranspiration and the infiltration.

22 Exercise The table shows the results of an application of the Thornthwaite-Matter model to a given watershed. Compute the missing values, explaining your reasoning. Mês Prec (mm) ETP (mm) Hsolo inicial (mm) ETR (mm) Q (mm) 1 60 A B C D