Hydrology, environment and water resources 2016 / Flood risk analysis

Transcrição

1 Hydrology, environment and water resorces 06 / 07 Flood risk analysis

2 Workplan IST: Hydrology, environment and water resorces 06/7 Rodrigo Proença de Oliveira, Week : Part and : Comptation of the rainfall depth-dration-freqency crve Estimation of the annal maximm daily precipitation vales for a set of retrn periods. Estimation of the annal maximm precipitation vales for different drations and for a set of retrn periods. Determination of the rainfall depth-dration-freqency crves. Comptation of the time of concentration; Comptation of peak flow sing the rational formla (with and withot the majoration factor) Week : Part.: Determination of the flood hydrograph Comptation of a niform hyetograph for T = 00 years; Estimation of the nit hydrograph for D = tc/6. Comptation of the flood hydrograph for a niform precipitation. Week : Parts. and.: Determination of the flood hydrograph Comptation of a non-niform hyetograph for T = 00 years; Estimation of the nit hydrograph for D = tc/5. Comptation of the flood hydrograph for a non-niform precipitation. Comparison of reslts.

3 Part Comptation of the rainfall depth dration - freqency crve

4 Comptation steps IST: Hydrology, environment and water resorces 06/7 Rodrigo Proença de Oliveira, Part a) Get the daily maximm precipitation time series recorded at the gage nearest to the watershed with at least 5 years of data (preferably with more that 0) / Consltar o SNIRH e obter a série de valores da precipitação diária máxima anal do posto mais próximo da bacia hidrográfica em análise com mais de 5 anos de anos o de preferência mais de 0 anos; Identify best pdf to describe the variability of the daily maximm precipitation time series / Identificar a fnção de distribição de probabilidade qe melhor se ajsta à série de precipitação diária máxima anal; Compte the daily maximm precipitation vales for different time series (0, 50, 00 and 000 years) / Calclar o valor da precipitação diária máxima para diferentes períodos de retorno (0, 50, 00 e 000 anos); Part b) Read from the map the ratio between Pmx_xhors and Pmx_day / Obter os valores dos ratios entre a precipitação diária máxima (denom.) e a precipitação máxima para drações sb-diárias e 4 horas para T=00 anos; Read from the map the ratio between Pmx_xmin and Pmx_hor / Obter os valores dos ratios entre a precipitação horária máxima (denom.) e a precipitação máxima para drações inferiores à hora; Estimate Pmx for different drations (Pmx_xmin and Pmx_xhors ) / Calclar os valores da precipitação máxima para drações sb-diárias e 4 horas para T=00 e 000 anos; Estimate the rainfall depth-dration-freqency crves for T= 00 e 000 years / Estimar as crvas de possibilidade dométrica para T=00 e 000 anos.

5 Probability distribtion fnction fit IST: Hydrology, environment and water resorces 06/7 Rodrigo Proença de Oliveira, P, X (mm) Z F(x) T (anos) T F(x) Z x x 0 x x 0 x x 00 x x 00 x x 000 x x

6 Comptation of vales assming different pdfs x(i) Valores de precipitação ordenados por ordem crescente; F(x): Probabilidade de não excedência de acordo com Weibll o Gringorten. Z: Normal redzida: X: F(x) Z X (mm) Ano P (mm) Y = Ln P Ordem P (mm) i/(n+) Norm.Red. Normal LNorm Gmbel Pearson III x y x() /(n+) z x x x x x y x() /(n+) z x x x x x y x() /(n+) z x x x x.... n xn yn n x(n) n/(n+) zn x x x x Normal F x F p x p F Log-normal Gmbel Pearson III X X X Log-Pearson III p p p X S z ExpY X K X G S X p X p X KP X F Z S Y N Red p K G S X Z p F x p 6 p ExpY KLP S 0,577 ln ln F( x) Y Graf: X i p n Graf: Y i 0,44 p n 0, k = γ 6 K p = z p + z p k + z p 6z k z p k + z p k 4 + k5 Cannot be sed if G<0; Use this one K p = γ + z p γ 6 γ 6 γ

7 Smmary table T 0 anos 50 anos 00 anos 000 anos Maximm annal daily precipitation (mm) Normal Log Normal P, X (mm) Gmbel Pearson Log Pearson Fnção Adoptada IST: Hydrology, environment and water resorces 06/7 Rodrigo Proença de Oliveira, Z F(x) T (anos)

8 IST: Hydrology, environment and water resorces 06/7 Rodrigo Proença de Oliveira, T=00 anos Relação P mx_x horas /P mx_diária fonte: INAG, 00, Análise dos fenómenos extremos de precipitação intensa em Portgal Continental P mx_h /P mx_d P mx_6h /P mx_d

9 Precipitação (mm) Rainfall depth-dration-freqency crves IST: Hydrology, environment and water resorces 06/7 Rodrigo Proença de Oliveira, Precipitação (mm) Annal maximm precipitation (mm) D (h) T=0 y T=00 y T=000 y x x x 6 x x x x x x 4 x x x 48 x x x 000 P (mm) Valores de precipitação estimados assmindo ma determinada fdp, seleccionada por m processo de ajstamento a ma amostra de valores máximos anais de precipitação para a dração D D D D D 4 T T T Dração y = x 0.47 R² = y = x 0.47 R² = Dração (horas) Dração (horas)

10 Part Evalation of the flood peak sing the rational formla

11 Time of concentration Precipitation, P Interception, infiltration Discharge, Q Net precipitation Time of concentration Assming the precipitation falls niformly over the whole watershed (valid for small watersheds) Assmindo qe a precipitação se distribi de forma niforme em toda a bacia hidrográfica (válido em peqenas bacias). Total flow Net precipitation, Direct flow Base flow Discharge, Q Direct flow Time of concentration Rising time Falling time Time, t Tempo, t IST: Hydrology, environment and water resorces 06/7 Rodrigo Proença de Oliveira,

12 Time of concentration estimation methods IST: Hydrology, environment and water resorces 06/7 Rodrigo Proença de Oliveira, Analysis of observed hyetographs and hydrographs / Análise dos hietogramas e hidrogramas observados; Cinematic comptation based on distance travelled and water velocity estimation / Cálclo cinemático: Cálclo do tempo de escoamento do ponto cinematicamente mais afastado até à secção de referência, aplicando por exemplo a fórmla de Manning-Strickler tendo em conta as condições de escoamento ao longo das encostas e nos crsos de ága de ordem crescente; Empirical formlas (for small watersheds) / Fórmlas empíricas (para peqenas bacias hidrográficas): Giandotti: Temez: t c Kirpich (segndo Chow): t c 4 A,5 L 0,8 h L 0, 0,5 d m m 0,76 t c L 0,95 H,55 0,85 t c (h) Time of concentration A (km ) Area of watershed L (km) Length of main river h m (m) Avg heigth of watersh d m (-) Avg slope of main river H (m) Altitde difference along main river

13 Rational formla Precipitation rate, i Q C i A P a t n Peak discharge Q = C i A A Q f C i A f n C Coeficient dependent on the watershed characteristics and retrn period / Coeficiente dependente das características da bacia (tipo de solo e so do solo) e do período de retorno: C smaller for permeable soils and LU and larger watersheds / C menor para solos e so de solos mais permeáveis; bacias maiores; C greater for impervios soils and LU and higher retrn periods / C maior para solos e so de solos menos permeáveis; maiores períodos de retorno; i Precipitation intensity / Intensidade de precipitação; A Watershed area / Área da bacia; f - Majoration coeficient to consider non-niform precipitation events / Factor de majoração para considerar distribições não niformes da precipitação; n Exponent of the rain depth-dration-freqency crve / Expoente da crva de possibilidade dométrica; IST: Hydrology, environment and water resorces 06/7 Rodrigo Proença de Oliveira,

14 Part. Determination of the flood hydrograph

15 The concept of nit hydrograph IST: Hydrology, environment and water resorces 06/7 Rodrigo Proença de Oliveira, Provides the relationship between the flood hydrograph and the originating precipitation / Relaciona a resposta da bacia (hidrograma de cheia) com a precipitação qe lhe de origem; We assme it is an intrinsic characteristic of the watershed / It is the hydrograph prodced by a nit net precipitation that fall dring a certain dration; Assme-se qe é ma propriedade íntriseca da bacia, independente da precipitação / É o hidrograma resltante de ma chvada de m valor nitário de precipitação útil e com ma determinada dração; Each nit hydrograph is associated with a given dration / Está associado a ma determinada dração da chvada. Precipitação, P Cadal, Q

16 How to apply the nit hydrograph (Additivity and proportionalities principles) IST: Hydrology, environment and water resorces 06/7 Rodrigo Proença de Oliveira, Net precipitation (mm) Precipitação útil (mm) Net precipitation (mm) Precipitação útil (mm) dt dt dt dt q, / max q, / max Unit hydrograph for a dration dt Unit hydrograph for a dration dt Hidrograma nitário para ma dração dt Hidrograma nitário para ma dração dt Tempo / dt Tempo / dt

17 Application of the nit hydrograph IST: Hydrology, environment and water resorces 06/7 Rodrigo Proença de Oliveira, q q q q q q q q 4,,, 0,,,,,

18 Unit hydrograph characteristics IST: Hydrology, environment and water resorces 06/7 Rodrigo Proença de Oliveira, mm Precipitation of nit ocrring in Dt Corresponds to a precipitation intensity of /Dt Tc (m /s)/mm Dt min Unit hydrograph for a dration of Dt When discretized in Dt intervals, it has Tc/DT vales that are different from 0. The volme of the nit hydrograoh is eqal to x A, where A is the watershed area. min

19 Definition of the synthetic nit hydrograph IST: Hydrology, environment and water resorces 06/7 Rodrigo Proença de Oliveira, Warning: Check dt defined in the assignement. Atenção: Verifiqem o dt definido no annciado Precipitação útil (mm) / max D = t c / 6 D = T c 6 D + T c = 7 t = 7D T a = 7 D + T c UH volme = mm x Abacia max c max D t 0,00 A ( m m ) 0,00 A D t 0 = 0 = max = max = 4 5 max c m s mm mm 4 = 5 max 5 = 5 max Tempo / dt ta / dt 6 = 5 max 7 = 0 (D + tc) / dt

20 Comptation of the flood hydrograph Unit hydrograph Ordenada do hidrograma nitário Net precipitation ocrring between time 0 and time Precipitação ocorrida no intervalo entre o instante 0 e o instante Instante t (h) (m/s/mm) (mm) Q (m/s) dt q *dt q *dt q 4 4*dt 4 4 q4 5 5*dt 5 5 q5 6 6*dt 6 6 q6 7 7*dt 7 7 q7 8 8*dt q8 9 9*dt 0 0 q9 0 0*dt 0 0 q0 *dt 0 0 q *dt 0 0 q q q q q4 Precipitação útil (mm) dt dt Q, 4 Hidrograma nitário para ma dração dt 4 Nota: Na Parte do trabalho = = =./in Part == Tempo / dt IST: Hydrology, environment and water resorces 06/7 Rodrigo --06 Proença de Oliveira, 06 0

21 Comptation of the flood volme IST: Hydrology, environment and water resorces 06/7 Rodrigo Proença de Oliveira, Cadal, Q Método dos trapézios n Qi Vol i Q i t i t i Tempo, t

22 Parts. and Part. Determination of the flood hydrograph Reslt compairison

23 What is the critical precipitation dration? IST: Hydrology, environment and water resorces 06/7 Rodrigo Proença de Oliveira, Assming that the precipitation falls niformly over the whole watershed (valid for small watersheds): A small increase of the precipitation dration leads to an increase in the area of the watershed contribting to the flow at the otlet; When the dration is higher than the time of concentration there is an instant where the whole watershed contribtes to the flow at the otlet; An increase of the dration of the precipitation event leads to a redction in the average precipitation rate for a given probability (retrn period); Therefore, precipitation events with drations close to the time of concentrations are the ones that lead to higher peak flows.

24 Design hyetograph: How to arrange the precipitation blocks? Hietogramas com o mesmo volme útil What is the precipitation distribtion patterns that leads to the highest peak flow? Qal é a distribição temporal qe condz ao maior cadal de ponta? Precipitação útil (mm) Precipitação útil (mm) Precipitação útil (mm) Precipitação útil (mm) Tempo (h) Tempo (h) Tempo (h) Tempo (h) Cadal, Q Cadal, Q Cadal, Q Cadal, Q All hyetographs have the same total ammont of precipitation and this is the same as the flood volme of all hydrographs. Only the time distribtion changes. Tempo (h) Tempo (h) Tempo (h) Tempo (h) Hidrogramas com o mesmo volme de cheia Q = Q = + Q = + +. To maximize a given Q i : Mltiply the largest by the largest ; Mltiply the nd largest by the nd largest ;. IST: Hydrology, environment and water resorces 06/7 Rodrigo Proença de Oliveira,

25 Maximization of the flood peak Precipitação útil (mm) / max dt dt dt... D k dt P a P P... a a dt n proj i i n dt dt n P P... P P P n Ordem P 0 0 (5) P7 7 () P6 6 () P () P 5 5 (4) P 6 6 (6) P 7 7 (7) P P k P P a D i n Precipitação útil (mm) The / max graphs are simetric arond its maximm vale / Gráficos simétricos em torno do se máximo IST: Hydrology, environment and water resorces 06/7 Rodrigo Proença de Oliveira,

26 Unit hydrograph transformation IST: Hydrology, environment and water resorces 06/7 Rodrigo Proença de Oliveira, One nit of net precipitation dring dt prodces the UH for dt. Precipitação nitária com ma dração de dt e hidrograma nitário para ma dração de dt. One can compte the flood hydrograph prodces by a rainfall event discretized in dt. O hidrograma resltante de m hietograma com m intervalo de cálclo dt pode ser calclado a partir de mhidrograma nitário para ma dração de dt. What shold we do when the precipitation is discretized in a time interval distinct from dt? O qe fazer qando o intervalode de cálclo é diferente de dt?? Q

27 Estimation of nit hydrograph for a dt distinct from dt IST: Hydrology, environment and water resorces 06/7 Rodrigo Proença de Oliveira, () () Crva S Hydrograph from a continos long with an intensity of /dt Hidrograma resltante de ma precipitação constante com intensidade /dt UHs for dt Hidrogramas nitários para ma precipitação nitária de dração dt HU for dt Sm of varios HU S crve for a precipitation intensity of /dt Mltiplication by dt/dt () Crva S Hydrograph from a continos long with an intensity of /dt Hidrograma resltante de ma precipitação constante com intensidade /dt UHs for dt Hidrogramas nitários para ma precipitação nitária de dração dt S crve for a precipitation intensity of /dt S crve movement (translation) by dt and sbtraction of the two S crves HU for dt

28 S-crve shift and HU comptation IST: Hydrology, environment and water resorces 06/7 Rodrigo Proença de Oliveira, S crve for i=/dt Ordinates of the UH for dt S crve for i=/dt translated by dt dt

29 Estimation of nit hydrograph for a dt distinct from dt IST: Hydrology, environment and water resorces 06/7 Rodrigo Proença de Oliveira, Tempo Hidrogramas nitários para dt desfasado de dt Crva S Crva S' Tempo Crva S Crva S HU dt i=/dt i=/dt i=/dt desfas. dt HU for dt Mltiplication by dt/dt Change. of discretization interval Sm Translation by dt