Hydrology, environment and water resources 2015 / 2016

Hydrology, environment and water resources 2015 / 2016 Flood risk analysis Rodrigo Proença de Oliveira

Flood cost IST: Hydrology, environment and water resources 2015/16 Rodrigo Proença de Oliveira, 2015 17-11-2015 2

Spatial distribution IST: Hydrology, environment and water resources 2015/16 Rodrigo Proença de Oliveira, 2015 17-11-2015 3

Flood losses IST: Hydrology, environment and water resources 2015/16 Rodrigo Proença de Oliveira, 2015 17-11-2015 4 99 vitimas por ano

Lisbon area, November 1967 110 mm / 5 hours: 700 deaths and 1000 loss their homes IST: Hydrology, environment and water resources 2015/16 Rodrigo Proença de Oliveira, 2015 17-11-2015 5

Lisbon area, November 1983 10 deaths e 200 families lost their homes IST: Hydrology, environment and water resources 2015/16 Rodrigo Proença de Oliveira, 2015 17-11-2015 6

Madeira, February 2010 42 deaths IST: Hydrology, environment and water resources 2015/16 Rodrigo Proença de Oliveira, 2015 17-11-2015 7

Madeira, February 2010 IST: Hydrology, environment and water resources 2015/16 Rodrigo Proença de Oliveira, 2015 17-11-2015 8

Madeira, February 2010 IST: Hydrology, environment and water resources 2015/16 Rodrigo Proença de Oliveira, 2015 17-11-2015 9

Madeira, February 2010 IST: Hydrology, environment and water resources 2015/16 Rodrigo Proença de Oliveira, 2015 17-11-2015 10 EARAM study (IST) results

Lower Tagus flood, April 2013 IST: Hydrology, environment and water resources 2015/16 Rodrigo Proença de Oliveira, 2015 17-11-2015 11

New Orleans, 2005 (Katrina hurricains) 1000 deaths, one million lost their homes IST: Hydrology, environment and water resources 2015/16 Rodrigo Proença de Oliveira, 2015 17-11-2015 12

Flood control (flood risk reduction) IST: Hydrology, environment and water resources 2015/16 Rodrigo Proença de Oliveira, 2015 17-11-2015 13 Clearance of flood prone areas / Deslocação de pessoas e bens de áreas com uma probabilidade elevada de ocorrência de inundações; River works to increase the cross-section area / Melhoramento das secções dos cursos de água para aumento da sua capacidade de vazão; Building of dikes to increase the cross-section area / Construções de diques para aumento da secção de vazão; Use of reservoirs for flood atenuation / Atribuição de um volume de encaixe de cheias para atenuação do hidrograma de cheia; Caudal afluente, Qa Caudal efluente, Qe

Dikes in lower Tejo IST: Hydrology, environment and water resources 2015/16 Rodrigo Proença de Oliveira, 2015 17-11-2015 14

Mississipi 1927 130,000 homes lost; 700,000 people were displaced. 246 deaths; million 350 dollars of Property damage (5 billion dollars today) IST: Hydrology, environment and water resources 2015/16 Rodrigo Proença de Oliveira, 2015 15

Flood control act of 1928 and the Room for the river project and the 2011 flood event IST: Hydrology, environment and water resources 2015/16 Rodrigo Proença de Oliveira, 2015 16 2011: No deaths 21.000 homes and business impacted 2,8 billions USD losses Scenario without the MRTSystem 1,5 billions of homes and business impacted 238 billions USD losses

Holanda, Rhine IST: Hydrology, environment and water resources 2015/16 Rodrigo Proença de Oliveira, 2015 17-11-2015 17

Projecto Room for the river (Holanda) IST: Hydrology, environment and water resources 2015/16 Rodrigo Proença de Oliveira, 2015 18 Dar espaço ao rio Reno / Room for the river; Objectivos / Objectives: Reduzir o risco de cheias; Melhorar a qualidade da água. Metas / Targets: Até 2015: Assegurar uma capacidade de escoamento de 16 000 m3/s; Até 2020: Reduzir os níveis máximos de cheia em 70 cm.

Projecto Room for the river (Holanda) Medidas / Actions: Remoção de obstáculos / removal of flow obstacules; Rebaixamento e alargamento do leito / channel dredging ; Afastamento de diques / Dikes removals ; Custo: Remoção de polders / Polders removal; 2.1 biliões de euros. Melhoria do dique (casos pontuais) / Dikes improvement; IST: Hydrology, environment and water resources 2015/16 Rodrigo Proença de Oliveira, 2015 17-11-2015 19

IST: Hydrology, environment and water resources 2015/16 Rodrigo Proença de Oliveira, 2015 Exemplo: Room for the river (Holanda) Plano base: 2015 20

Flood analysis

Factors influencing flood risk Factor Watershed area / Área Watershed shape / Forma Watershed orography / Relevo River network / Rede hidrográfica Influences Time for flow accumulation (concentration time ands isochrones) Tempo para acumulação do escoamento (tempo de concentração / isócronas) Soils / Solos Soil cover / Coberto vegetal Soil use / Uso da superficie Infiltration Infiltração Precipitation temporal distribution / Distribuição temporal da precipitação Temperature / Temperatura Less important Menos importante IST: Hydrology, environment and water resources 2015/16 Rodrigo Proença de Oliveira, 2015 17-11-2015 22

Flood hydrograph Precipitação, P Intercepção, retenção e infiltração Interception, retention and infiltration Precipitação útil Net precipitation Discharge Q Caudal, Q Escoamento total Total flow Escoamento directo Direct flow Escoamento de base Base flow Tempo de ascenção Rising time Tempo de decrescimento Decreasing time Tempo, t Time, t IST: Hydrology, environment and water resources 2015/16 Rodrigo Proença de Oliveira, 2015 17-11-2015 23

Main parameters or variables that are usually estimated Discharge Peak discharge Caudal de ponta It depends on the purpose of the analysis: Flood volume Volume de cheia Preliminary risk assessment / Avaliação preliminar do risco de cheia Spillways design / Dimensionamento de descarregadores Bridge design / Dimensionamento de pontes Dikes design / Dimensionamento de diques Storm water drains design / Dimensionamento de colectores Time Flood peak / Caudal máxim (ponta de cheia) Design of flood attenuation storage volume / Dimensionamento de volumes de encaixe de cheia Flood damage evaluation studies / Avaliação da duração da cheia e dos prejuizos causados Flood peak / Caudal máxim (ponta de cheia) Flood volume / Volume de cheia IST: Hydrology, environment and water resources 2015/16 Rodrigo Proença de Oliveira, 2015 17-11-2015 24

Water balance simplification IST: Hydrology, environment and water resources 2015/16 Rodrigo Proença de Oliveira, 2015 17-11-2015 25 Precipitação Precipitação P = H + E + S p + S s + S u + E x R Evapotranspiração For a short time interval / Para um intervalo de tempo curto: Evaporação Intercepção E = 0 (evapotranspiration) S u = 0 (aquíier contribution) Retenção Infiltração Escoamento superficial (directo) Evaporação E x R = 0 (export-import) Logo, H = P - S p - S s Recarga Escoamento intermédio Escoamento de base Se S u <> 0 Considered in a simplified way Considerado de forma simplificada Logo, H = P - S p - S s + S u Considered in a simplified way Considerado de forma simplificada

Opções para pequenas bacias hidrográficas Assumptions for small watersheds analysis IST: Hydrology, environment and water resources 2015/16 Rodrigo Proença de Oliveira, 2015 17-11-2015 26 Possible assumptions on hydrological fluxes during a flood / Possíveis simplificações na análise dos fluxos hidrológicos durante uma cheia: Evaporation and evapotranspiration: Often ignored/ Evaporação + evapotranspiração: São frequemente desprezadas na análise de situação de cheia Retention, interception and infiltration ( losses ): A simple model is used / Retenção, intercepção, infiltração ( perdas ) / Assume-se um modelo simples: Loss models: Constant infiltration / Taxa constante; Initial loss + Constant infiltration / Volume inicial + taxa constante; Precipitação, P Intermediate flow: Often ignored / Escoamento intermédio Frequentemente desprezado; Base flow: Often ignored or estimated using a simple model independent from infiltration estimate. / Escoamento de base: Por vezes ignorado ou calculado com base num modelo simples e independente da infiltração. Precipitação, P

Isochrones and time of concentration

Isochrones Consider a rainfall event with a duration equal to the double of the time of concentration Chuvada com uma duração da precipitação útil igual ao dobro do tempo de concentração da bacia hidrográfica Time Tempo Areas contributing to flow Áreas que contribuem para o escoamento Ponto mais afastado 0 0 1/3 x tc A 2/3 x tc A + B tc A + B + C B C 4/3 x tc A + B + C 5/3 x tc A + B + C 2 x tc A + B + C A Isócrona 2/3 x tc Isócrona 1/3 x tc 7/3 x tc B + C 8/3 x tc C 3 x tc 0 IST: Hydrology, environment and water resources 2015/16 Rodrigo Proença de Oliveira, 2015 17-11-2015 28

Time of concentration Precipitation, P Interception, infiltration Discharge, Q Net precipitation Time of concentration Assuming the precipitation falls uniformly over the whole watershed (valid for small watersheds) Assumindo que a precipitação se distribui de forma uniforme em toda a bacia hidrográfica (válido em pequenas bacias). Total flow Net precipitation, Pu Direct flow Base flow Discharge, Q Direct flow Time of concentration Rising time Falling time Time, t Tempo, t IST: Hydrology, environment and water resources 2015/16 Rodrigo Proença de Oliveira, 2015 17-11-2015 29

Time of concentration IST: Hydrology, environment and water resources 2015/16 Rodrigo Proença de Oliveira, 2015 17-11-2015 30 Travel time from the most distant point to the watershed outflow section / Tempo de percurso de uma gota de água entre o ponto cinematicamente mais afastado da secção da bacia e a secção definidora da bacia; We assume it is an intrinsic characteristic of the watershed; Propriedade intrínseca da bacia hidrográfica / Assume-se que é independente da precipitação, dependendo apenas das condições de escoamento desde o ponto mais afastado até à secção final; Depends on the watershed characteristics / Na prática assume-se que depende das características da bacia hidrográfica: Watershed area / Área da bacia (A); Length of the main watercourse / Comprimento do curso de água principal (L); Watershed average heigth / Altura média da bacia (hm); Slope of the main watercourse /Declive médio do curso de água principal (dm); Altitude difference along the main watercourse /Diferença de cotas do talvegue do curso de água principal (H);

Time of concentration estimation methods IST: Hydrology, environment and water resources 2015/16 Rodrigo Proença de Oliveira, 2015 17-11-2015 31 Analysis of observed hyetographs and hydrographs / Análise dos hietogramas e hidrogramas observados; Cinematic computation based on distance travelled and water velocity estimation / Cálculo cinemático: Cálculo do tempo de escoamento do ponto cinematicamente mais afastado até à secção de referência, aplicando por exemplo a fórmula de Manning-Strickler tendo em conta as condições de escoamento ao longo das encostas e nos cursos de água de ordem crescente; Empirical formulas (for small watersheds) / Fórmulas empíricas (para pequenas bacias hidrográficas): Giandotti: Temez: t c Kirpich (segundo Chow): t c 4 A 1,5 L 0,8 h L 0,3 0,25 d m m 0,76 t c L 0,95 H 1,155 0,385 t c (h) Time of concentration A (km 2 ) 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) Altitude difference along main river

Exercise A net precipitation with intensity I A, I B, I C and I D occurred in each of the areas of the represented watershed. The following table presents such distribution with I 0 representing a reference intensity and t c the time of concentration of the watershed. Determine the direct flow hydrograph resulting from such precipitation in I 0 xa 0 units. Em cada uma das zonas da bacia hidrográfica representada ocorreu precipitação útil de acordo com as intensidades I A, I B, I C e I D que se apresentam no quadro seguinte, onde I 0 representa uma intensidade de referência e t c, o tempo de concentração da bacia hidrográfica. Determine o hidrograma do caudal do escoamento directo resultante de tal precipitação, em unidades de I 0 A 0. t/(t c /4) (-) 0-1 1-2 2-3 3-4 4-5 I A /I 0 (-) 0.0 0.0 0.0 0.5 0.0 I B /I 0 (-) 0.0 0.0 0.5 0.5 0.0 I C /I 0 (-) 0.0 0.5 0.5 0.0 0.0 I D /I 0 (-) 1.0 0.5 0.0 0.0 0.0 IST: Hydrology, environment and water resources 2015/16 Rodrigo Proença de Oliveira, 2015 17-11-2015 32

Exercise IST: Hydrology, environment and water resources 2015/16 Rodrigo Proença de Oliveira, 2015 17-11-2015 33 In particular river basin, with 290 km 2, in prolonged periods without rainfall, the flow rate in the reference section follows the following law / Em determinada bacia hidrográfica, com 290 km 2, em períodos prolongados sem precipitação, o caudal na secção de referência segue com bastante aproximação uma lei de esgotamento do tipo. Q Q 0 e k(t t 0 ) Knowing that at 9 am of March 4 and March 13 the flow rate at the outlet of this basin was respectively 10.9 and 7.3 m 3 /s and assuming that no precipitation occurred between these two dates, estimate the volume of water that has passed through the outlet from the latter date until full depletion of the basin. Express this volume in water height evenly distributed over the basin / Sabendo que nessa bacia hidrográfica, às 9 horas de 4 de Março e de 13 de Março o caudal era respectivamente de 10,9 e 7,3 m 3 /s e admitindo que não ocorreu precipitação, estime o volume de água que passou na secção de referência desde a última data até ao total esgotamento da bacia. Exprima esse volume em altura de água uniformemente distribuída sobre a bacia.

Empirical formulas for peak discharge estimation

Empirical formulas Iskowski (1886) Q K m P A Not a function of the return period Q Peak flow (m 3 /s) K Coeficient dependent on soil type, land cover and orography m Coeficient dependent on the area of the watershed P Average annual precipitation (m) A Watershed area (km 2 ) Giandotti Q A h t c Q Peak flow (m 3 /s) A Watershed area (km 2 ) Tc Time of concentration Coeficient dependent on the area of the watershed h Precipitation (mm) Soil Conservation Service Q Mockus Q 0,277 k A h t c 0,6 t c 0,277 k Assumes a critical precipitation duration of t p 2 A h t c Q Peak flow (m 3 /s) A Watershed area (km 2 ) h Event precipitation (mm) k Peak factor in the range of 1 and 0,5 t p Peak time = 0,5 D + 0,6 T c D Duration of precipitation Meyer α Q C A Q Peak discharge; (m 3 /s) C Coeficient dependent on the watershed characteristics and return period; a Coeficient dependent on the watershed characteristics (0.4 < a < 0.8) A Watershed area (km 2 ) IST: Hydrology, environment and water resources 2015/16 Rodrigo Proença de Oliveira, 2015 17-11-2015 35

Rational formula Precipitation rate, i Q C i A P a t n Peak discharge Q = C i A A Q f C i A f 2 n C Coeficient dependent on the watershed characteristics and return period / Coeficiente dependente das características da bacia (tipo de solo e uso do solo) e do período de retorno: C smaller for permeable soils and LU and larger watersheds / C menor para solos e uso de solos mais permeáveis; bacias maiores; C greater for impervious soils and LU and higher return periods / C maior para solos e uso 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-uniform precipitation events / Factor de majoração para considerar distribuições não uniformes da precipitação; n Exponent of the rain depth-duration-frequency curve / Expoente da curva de possibilidade udométrica; IST: Hydrology, environment and water resources 2015/16 Rodrigo Proença de Oliveira, 2015 17-11-2015 36

Linear reservoirs Inflow, I Storage, S ds dt = I O Outflow, O Linear reservoirs: O = k S ds dt = I k S if I = 0 then S = S o e k t Storage, S Outflow, O S t Delay or lag Inflow, I Attenuation Storage, S Outflow, O IST: Hydrology, environment and water resources 2015/16 Rodrigo Proença de Oliveira, 2015 17-11-2015 37

Factor C Chow et al, 1988 Department of Water Affairs and Forestry, Africa do Sul IST: Hydrology, environment and water resources 2015/16 Rodrigo Proença de Oliveira, 2015 17-11-2015 38

What is the critical precipitation duration? IST: Hydrology, environment and water resources 2015/16 Rodrigo Proença de Oliveira, 2015 17-11-2015 39 Assuming that the precipitation falls uniformly over the whole watershed (valid for small watersheds): A small increase of the precipitation duration leads to an increase in the area of the watershed contributing to the flow at the outlet; When the duration is higher than the time of concentration there is an instant where the whole watershed contributes to the flow at the outlet; An increase of the duration of the precipitation event leads to a reduction in the average precipitation rate for a given probability (return period); Therefore, precipitation events with durations close to the time of concentrations are the ones that lead to higher peak flows.

Exercise IST: Hydrology, environment and water resources 2015/16 Rodrigo Proença de Oliveira, 2015 17-11-2015 40 Use the rational formula to determine the peak flow associated with a return period of 100 years from a watershed with 80 km 2 and a time of concentration of 2.5 h. Assume that 15% of the precipitation is lost to infiltration and there is a peak flow attenuation through the watershed of 20%. Assume the following precipitation-duration curve, with P in mm and 0,45 t in min: P 4 t Utilize a fórmula racional para estimar o caudal de ponta de cheia associado a um periodo de retorno de 100 anos, gerado numa bacia hidrográfica com 80 km 2 de área e 2,5 h de tempo de concentração. Assuma que 15% da precipitação é perdida por infilitração e que há uma atenuação do caudal de ponta de cheia de 20%. Assuma que a linha de possibilidade udométrica para esse período de 0,45 retorno, com P em mm e t em min, é C = 0.8 x 0.85 = 0,68 D = t c = 2,5 h = 150 min P = 4 x 150 0.45 = 38 mm i = P / D = 15 mm/h P 4 Q = C x i x A = 0,68 x 15 x 10-3 / 3600 x 80 x 10 6 = 230 m 3 /s t

Exercise IST: Hydrology, environment and water resources 2015/16 Rodrigo Proença de Oliveira, 2015 17-11-2015 41 Use the Temez formula and the rational formula to determine the peak flow for T = 100 years of a rural watershed with 80 km 2, where the main river has 8 km and an average slope 0f 0.005. Assume the following precipitation-duration curve for T=100 years, with P in mm 0,45 and t in min, is: P 4 t

Exercise IST: Hydrology, environment and water resources 2015/16 Rodrigo Proença de Oliveira, 2015 17-11-2015 42 Compute the design flow of an infra-structure whose functionality should not be affected more 10 times in a century. The watershed of the infrastructure has an area of 40 km 2 and its main water course flows along 4 km with an average steepness of 0.002. Use the Temez equation and the rational formula with correcting factor, assuming a C coeficient of 0,5. The watershed lies within a region with the following Precipitation Depth- Duration-Frequency curve (P in mm and D in min). D (h) T=10 T=50 T=100 T=500 a n a n a n a n 0,5 h 6 h 37.837 0.398 50.233 0.368 55.673 0.360 67.615 0.344 6 h 48 h 33.867 0.473 41.092 0.501 44.068 0.509 51.207 0.523

Exercise IST: Hydrology, environment and water resources 2015/16 Rodrigo Proença de Oliveira, 2015 17-11-2015 43 During a rainfall event, the flow capacity of a spillway, estimated in 120 m 3 /s, was almost exceeded. The watershed of that spillway na área of 60 km 2 and its main waterscourse flows along 10 km, with an average steepness of 0.0008. The watershed lies within a region with the following IDF curve (i em mm/h e D em min). Compute the order of magnitude of the return period of the rainfall event, using the rational formula and the Kirpich formula. Assume a C coeficient of 0,5. t (min) T=10 T=50 T=100 T=500 a b a b a b a b 5 min 30 min 567-0,665 742-0,652 815-0,649 987-0,643 30 min 6 h 445-0,602 668-0.632 765-0.640 992-0.656 6 h 48 h 293-0,527 317-0.499 329-0.491 361-0.477

Exercise A linear reservoir with a constant k = 15x10-6 s-1, has at a certain moment a volume of water V0 = 10 5 m3. From that moment onwards the inflow is represented by the hydrograph presented in the table is below, Determine the hydrograph of the reservoir outflow (Q) from the starting time up to 18 h later and plot the two hydrographs (I and Q). Um reservatório linear, com uma constante k=15x10-6 s -1, apresenta em determinado instante um volume de água V 0 =10 5 m 3. Sabendo que a partir desse instante foi alimentado de acordo com o hidrograma que se apresenta no quadro que se encontra abaixo, determine o hidrograma do caudal saído do reservatório (Q) desde o instante inicial até 18 h depois e represente graficamente os dois hidrogramas (I e Q). t (h) 0 1 2 3 4 5 6 7 I (m 3 /s) 0 14 20 30 46 28 12 0 IST: Hydrology, environment and water resources 2015/16 Rodrigo Proença de Oliveira, 2015 17-11-2015 44

Unit hydrograph

The concept of unit hydrograph Provides the relationship between the flood hydrograph and the originating precipitation / Relaciona a resposta da bacia (hidrograma de cheia) com a precipitação que lhe deu origem; We assume it is an intrinsic characteristic of the watershed / It is the hydrograph produced by a unit net precipitation that fall during a certain duration; Assume-se que é uma propriedade íntriseca da bacia, independente da precipitação / É o hidrograma resultante de uma chuvada de um valor unitário de precipitação útil e com uma determinada duração; Each unit hydrograph is associated with a given duration / Está associado a uma determinada duração da chuvada. Precipitação, P Caudal, Q IST: Hydrology, environment and water resources 2015/16 Rodrigo Proença de Oliveira, 2015 17-11-2015 46 1

How to apply the unit hydrograph (Additivity and proportionalities principles) IST: Hydrology, environment and water resources 2015/16 Rodrigo Proença de Oliveira, 2015 17-11-2015 47 Net precipitation (mm) Precipitação útil (mm) Net precipitation (mm) Precipitação útil (mm) 1 1 dt dt dt dt q, u / umax q, u / umax 2 2 Unit hydrograph for a duration dt Unit hydrograph for a duration dt Hidrograma unitário para uma duração dt 1 Hidrograma unitário para uma duração dt 1 0 1 2 3 4 5 6 7 8 Tempo / dt 0 1 2 3 4 5 6 7 8 Tempo / dt

Application of the unit hydrograph IST: Hydrology, environment and water resources 2015/16 Rodrigo Proença de Oliveira, 2015 48 17-11-2015 0. 8 4 4 7 3 4 4 3 6 2 4 3 3 4 2 5 1 4 2 3 3 2 4 1 4 1 3 2 2 3 1 3 1 2 2 1 2 1 1 1 q Pu u q Pu u Pu u q Pu u Pu u Pu u q Pu u Pu u Pu u Pu u q Pu u Pu u Pu u q Pu u Pu u q Pu u q 4 3 2 1,,, Pu Pu Pu Pu 0,,,,, 0 5 4 3 2 1 0 u u u u u u 0 1 2 3 4 5 6 7 8

Unit hydrograph characteristics IST: Hydrology, environment and water resources 2015/16 Rodrigo Proença de Oliveira, 2015 17-11-2015 49 mm Precipitation of 1 unit ocurring in t Corresponds to a precipitation intensity of 1/t Tc (m 3 /s)/mm t min Unit hydrograph for a duration of t When discretized in t intervals, it has Tc/T values that are different from 0. The volume of the unit hydrograoh is equal to 1 x A, where A is the watershed area. min

Synthetic unit hydrographs

How to estimate a unit hydrograph IST: Hydrology, environment and water resources 2015/16 Rodrigo Proença de Oliveira, 2015 17-11-2015 51 The UH can be estimated from / O hidrograma unitário pode ser estimado: Observed records from previous precipitation events (hyetographs and hydrographs) / A partir de registos observados de precipitação (hietograma) e de caudal (hidrograma) de um evento de cheia; From watershed characteristics using synthetic unit hydrographs proposed by different authors / A partir das características da bacia Hidrograma unitário sintético. Different authors have proposed synthetic unit hydrographs / Vários autores avançaram com várias propostas de hidrogramas unitários sintéticos: Giandotti Clark; Snyder; Soil Conservation Service; 1 1 Precipitação útil (mm) u / umax 0 1 2 3 4 5 6 7 8 Tempo / dt. ta / dt (D + tc) / dt D = dt

Giandotti unit hydrograph IST: Hydrology, environment and water resources 2015/16 Rodrigo Proença de Oliveira, 2015 17-11-2015 52 Hidrograma de Giandotti Q Q max Q med Q med ψ P A t Qmax ρ Q med tt γ t c t t ρ 1 ρ a t c (γ 1) ρ ρ b t c t A (km 2 ) (-) (-) (-) (-) ]0, 300] 10 4.0 0.50 1.25 ]300, 500] 8 4.0 0.50 1.00 ]500, 1000] 8 4.5 0.40 0.71 ]1000, 8000] 6 5.0 0.30 0.36 ]8000, 20000] 6 5.5 0.25 0.27 ]20000, 70000] 6 6.0 0.20 0.20 Quintela aconselha que se adopte para A < 500 km 2 = 6.5 = 4.0 = 0.50 O que corresponde a C = = 0.81 t a t c t b t t t

Snyder unit hydrograph IST: Hydrology, environment and water resources 2015/16 Rodrigo Proença de Oliveira, 2015 17-11-2015 53 Parâmetros: Lag (h), Tp Peak Coeficient, Cp Caudal Lag, Tp Up Tempo U T p A p C 2,72 T c p p 0,5 T 0, 75T c Mais informação em HEC-HMS Technical Reference Manual, Cap. 6

Clark unit hydrograph Parameters: Time of concentrarion (h), Tc Storage coeficient (h), R Diagrama tempo-área Reservatório fictício Área t c Tempo de escoamento para a secção de refência More information in HEC-HMS Technical Reference Manual, Cap. 6 IST: Hydrology, environment and water resources 2015/16 Rodrigo Proença de Oliveira, 2015 17-11-2015 54

SCS unit hydrograph IST: Hydrology, environment and water resources 2015/16 Rodrigo Proença de Oliveira, 2015 17-11-2015 55 Parameters: Lag (h), Tlag Caudal D Lag, T lag U p U 2. 08 T p D 2 A T p T lag p Tempo T 0, 6 lag T c See more in HEC-HMS Technical Reference Manual, Cap. 6

Precipitação útil (mm) SCS triangular unit hydrograph 2 1 0 t a t 0.6 5 3 b t a t c D 2 1.2 1 0.8 u 0.208 max A t a t c t t D? a b u / umax 0.6 0.4 0.2 0 0 1 2 3 Tempo / t a t a t b 17-11-2015 IST: Hydrology, environment and water resources 2015/16 Rodrigo Proença de Oliveira, 2015 56

Exercise A continuous and constant net precipitation of 60 mm/h over a given watershed generates the following hydrograph of direct flow. Please estimate: Time of concentration of the watershed. Area of the watershed. Unit hydrograph of the water for 0.25 h. Em determinada bacia hidrográfica, em resultado de uma precipitação útil com grande duração e intensidade constante de 60 mm/h, obteve-se o hidrograma do escoamento directo indicado no quadro. Determine a área da bacia hidrográfica. Determine o hidrograma unitário para a duração de 0.25 h. t (h) 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 Q d (m 3 /s) 0 60 150 280 320 340 350 350 IST: Hydrology, environment and water resources 2015/16 Rodrigo Proença de Oliveira, 2015 17-11-2015 57

Exercise A precipitation event with a duration of 1,5 h and net precipitation amounts of 5 mm, 10 mm and 3 mm in 3 successive 0.5h time periods over a given watershed, generates the following hydrograph of direct flow. Please estimate: Time of concentration of the watershed. Unit hydrograph of the water for 0.5 h. Area of the watershed. Em determinada bacia hidrográfica, em resultado de precipitação útil que de 30 min em 30 min foi 5 mm, 10 mm e 3 mm, obteve-se o seguinte hidrograma do escoamento directo. Determine o tempo de concentração da bacia. Determine o hidrograma unitário para a duração de 0,5 h. Calcule a área da bacia, em km 2. t (h) 0,0 0,5 1,0 1,5 2,0 2,5 3,0 Q d (m 3 /s) 0 15 70 99 44 6 0 IST: Hydrology, environment and water resources 2015/16 Rodrigo Proença de Oliveira, 2015 17-11-2015 58

Exercise A precipitation event with a duration of 0,5 h and net precipitation amounts of 15 mm and 5 mm in 2 successive 0,25h time periods, generates the following hydrograph of direct flow. Please estimate the unit hydrograph of the water for 0.5 h. Em determinada bacia hidrográfica, em resultado de uma precipitação útil de 15 mm em 15 min e de 5 mm nos 15 min seguintes, obteve-se o seguinte hidrograma do escoamento directo. Determine o hidrograma unitário para a duração de 30 min. t (h) 0.00 0.25 0.50 0.75 1.00 1.25 1.50 Q d (m 3 /s) 0 150 275 225 125 25 0 IST: Hydrology, environment and water resources 2015/16 Rodrigo Proença de Oliveira, 2015 17-11-2015 59

Exercise The table presents the unit hydrograph of a given watershed for unit hyetograph with a duration of 0,5h. Please estimate: Time of concentration of the watershed. Area of the watershed. The direct hydrograph generated by an event with a net precipitation of 20 mm, 30 mm e 12 mm, in 3 successive intervals of 30 min. Unit hydrograph of the water for 1 h. Apresenta-se no quadro seguinte o hidrograma unitário de determinada bacia hidrográfica para a precipitação útil com a duração de 0.5 h. Determine o tempo de concentração da bacia hidrográfica. Determine a área da bacia hidrográfica. Calcule o hidrograma do escoamento directo que resultaria na secção de referência dessa bacia hidrográfica de uma precipitação útil de 20 mm, 30 mm e 12 mm, em intervalos sucessivos de 30 min. Calcule o HU para uma duração de 1 hora. t (h) 0.0 0.5 1.0 1.5 2.0 2.5 u (m 3 /s/mm) 0 15 34 17 9 0 IST: Hydrology, environment and water resources 2015/16 Rodrigo Proença de Oliveira, 2015 17-11-2015 60

Design hyetograph

What is the critical precipitation duration? IST: Hydrology, environment and water resources 2015/16 Rodrigo Proença de Oliveira, 2015 17-11-2015 62 Assuming that the precipitation falls uniformly over the whole watershed (valid for small watersheds): A small increase of the precipitation duration leads to an increase in the area of the watershed contributing to the flow at the outlet; When the duration is higher than the time of concentration there is an instant where the whole watershed contributes to the flow at the outlet; An increase of the duration of the precipitation event leads to a reduction in the average precipitation rate for a given probability (return period); Therefore, precipitation events with durations close to the time of concentrations are the ones that lead to higher peak flows.

Design hyetograph: How to arrange the precipitation blocks? Hietogramas com o mesmo volume útil What is the precipitation distribution patterns that leads to the highest peak flow? Qual é a distribuição temporal que conduz ao maior caudal de ponta? Precipitação útil (mm) Precipitação útil (mm) Precipitação útil (mm) Precipitação útil (mm) Tempo (h) Tempo (h) Tempo (h) Tempo (h) Caudal, Q Caudal, Q Caudal, Q Caudal, Q All hyetographs have the same total ammount of precipitation and this is the same as the flood volume of all hydrographs. Only the time distribution changes. Tempo (h) Tempo (h) Tempo (h) Tempo (h) Hidrogramas com o mesmo volume de cheia Q 1 =Pu 1 u 1 Q 2 =Pu 2 u 1 +Pu 1 u 2 Q 3 =Pu 3 u 1 +Pu 2 u 2 +Pu 1 u 3. To maximize a given Q i : Multiply the largest u by the largest Pu; Multiply the 2 nd largest u by the 2 nd largest Pu;. IST: Hydrology, environment and water resources 2015/16 Rodrigo Proença de Oliveira, 2015 17-11-2015 63

Maximization of the flood peak 1 Precipitação útil (mm) 0 1 2 3 4 5 6 7 8 u / umax dt 2 dt 3 dt... D k dt P a 1 P P... 12 123 a a dt 2 3 n proj i1 i1 n dt dt n P 2 P 3... P P P n u Ordem u P Pu 0 0 1 u1 (5) P7 Pu7 2 u2 (2) P6 Pu6 3 u3 (1) P4 Pu4 4 u4 (3) P3 Pu3 5 u5 (4) P1 Pu1 6 u6 (6) P2 Pu2 7 u7 (7) P5 Pu5 8 0 12 123 P k 1 P P a D i 12 n Precipitação útil (mm) 0 1 2 3 4 5 6 7 8 1 0 1 2 3 4 5 6 7 8 The u / umax graphs are simetric around its maximum value / Gráficos simétricos em torno do seu máximo 0 1 2 3 4 5 6 7 8 IST: Hydrology, environment and water resources 2015/16 Rodrigo Proença de Oliveira, 2015 17-11-2015 64

Exercise IST: Hydrology, environment and water resources 2015/16 Rodrigo Proença de Oliveira, 2015 17-11-2015 65 The unit hydrograph of a given watershed is indicated in the table. Assuming a 0.5 rainfall depth-duration-frequency curve for T=100 years equal to P 5 t, with P in mm and t in min, please compute: The hyetograph that maximizes the peak flow; The peak flow of resulting hyetograh; The peak flow that would result from a precipitation event with a uniform precipitation rate. O hidrograma unitário de determinada bacia hidrográfica encontra-se representado no seguinte quadro. Desprezando as perdas da precipitação e sabendo que a linha de possibilidade udométrica para o período 0.5 de retorno de 100 a na região é P 5 t com P em mm e t em min, determine: a distribuição temporal da precipitação que maximiza o caudal de ponta de cheia para esse período de retorno, o referido caudal máximo de ponta de cheia, o caudal de ponta de cheia que resultaria de uma precipitação com distribuição temporal uniforme. t (h) 0.0 0.5 1.0 1.5 2.0 2.5 3.0 u (m 3 /s/mm) 0 10 30 25 12 6 0

Transformation of the unit hydrograph

Unit hydrograph transformation IST: Hydrology, environment and water resources 2015/16 Rodrigo Proença de Oliveira, 2015 17-11-2015 67 One unit of net precipitation during dt produces the UH for dt. Precipitação unitária com uma duração de dt e hidrograma unitário para uma duração de dt. u One can compute the flood hydrograph produces by a rainfall event discretized in dt. O hidrograma resultante de um hietograma com um intervalo de cálculo dt pode ser calculado a partir de umhidrograma unitário para uma duração de dt. What should we do when the precipitation is discretized in a time interval distinct from dt? O que fazer quando o intervalode de cálculo é diferente de dt?? 0 1 2 3 4 5 Q 0 1 2 3 4 5 6 7 8

Estimation of unit hydrograph for a dt2 distinct from dt1 IST: Hydrology, environment and water resources 2015/16 Rodrigo Proença de Oliveira, 2015 17-11-2015 68 (1) (2) Curva S Hydrograph from a continuous long with an intensity of 1/dt1 Hidrograma resultante de uma precipitação constante com intensidade 1/dt1 UHs for dt1 Hidrogramas unitários para uma precipitação unitária de duração dt1 HU for dt1 Sum of various HU S curve for a precipitation intensity of 1/dt1 Multiplication by dt1/dt2 (3) Curva S Hydrograph from a continuous long with an intensity of 1/dt2 Hidrograma resultante de uma precipitação constante com intensidade 1/dt2 UHs for dt2 Hidrogramas unitários para uma precipitação unitária de duração dt2 S curve for a precipitation intensity of 1/dt2 S curve movement (translation) by dt2 and subtraction of the two S curves HU for dt2

S-curve shift and HU computation IST: Hydrology, environment and water resources 2015/16 Rodrigo Proença de Oliveira, 2015 17-11-2015 69 S curve for i=1/dt2 Ordinates of the UH for dt2 S curve for i=1/dt2 translated by dt2 dt2

Estimation of unit hydrograph for a dt2 distinct from dt1 IST: Hydrology, environment and water resources 2015/16 Rodrigo Proença de Oliveira, 2015 17-11-2015 70 Tempo Hidrogramas unitários para dt1 desfasado de dt1 Curva S Curva S' Tempo Curva S Curva S HU dt2 i=1/dt1 i=1/dt2 i=1/dt2 desfas. dt2 0.000 0 0.00 0.00 0.0 0.00 0 0.143 1 0 0.58 0.42 0.2 0.75 0.00 0.75 0.286 1 1 0 1.75 1.25 0.4 2.25 0.75 1.50 0.429 2 1 1 0 3.50 2.50 0.6 3.65 2.25 1.40 0.571 1 2 1 1 0 HU for dt1 4.90 3.50 0.8 4.55 3.65 0.90 0.714 1 1 2 1 1 0 Multiplication 5.95 4.25 by 1.0 5.00 4.55 0.45 0.857 1 1 1 2 1 1 0 dt1/dt2 6.65 4.75 1.2 5.00 5.00 0.00 1.000 0 1 1 1 2 1 1 0 7.00 5.00 1.4 5.00 5.00 0.00 1.143 0 0 1 1 1 2 1 1 0 7.00 5.00 1.6 5.00 5.00 0.00 1.286 0 0 1 1 1 2 1 1 0 7.00 5.00 1.8 5.00 5.00 0.00 1.429 0 0 1 1 1 2 1 1 0 7.00 5.00 2.0 5.00 5.00 0.00 1.571 0 0 1 1 1 2 1 1 0 7.00 5.00 Change 2.2 of 5.00 5.00 0.00 1.714 0 0 1 1 1 2 1 1 0 7.00 5.00 2.4 5.00 5.00 0.00 discretization interval 1.857 0 0 1 1 1 2 1 1 0 7.00 5.00 2.6 5.00 5.00 0.00 2.000 0 0 1 1 1 2 1 1 0 7.00 5.00 2.8 5.00 5.00 0.00 2.143 0 0 1 1 1 2 1 1 0 7.00 5.00 3.0 5.00 5.00 0.00 2.286 0 0 1 1 1 2 1 1 0 7.00 5.00 3.2 5.00 5.00 0.00 2.429 0 0 1 1 1 2 1 1 0 Sum 7.00 5.00 3.4 5.00 5.00 0.00 2.571 0 0 1 1 1 2 1 1 0 7.00 5.00 3.6 Translation 5.00 5.00 by 0.00 2.714 0 0 1 1 1 2 1 1 0 7.00 5.00 2.857 0 0 1 1 1 2 1 1 0 7.00 5.00 dt2 3.000 0 0 1 1 1 2 1 1 0 7.00 5.00 3.143 0 0 1 1 1 2 1 1 0 7.00 5.00 3.286 0 0 1 1 1 2 1 1 0 7.00 5.00 3.429 0 0 1 1 1 2 1 1 0 7.00 5.00 3.571 0 0 1 1 1 2 1 1 7.00 5.00

Exercise Consider the S curve of a given watershed represented in the table. Determine: Time of concentration of the watershed Area of the watershed Unit hydrograph for a duration of 0,5h O hidrograma em S de determinada bacia hidrográfica encontra-se representado no seguinte quadro. Com base nesse hidrograma determine: o tempo de concentração da bacia hidrográfica; a área da bacia hidrográfica; o respectivo hidrograma unitário para a duração de 0,5 h. t (h) 0,0 0,5 1,0 1,5 2,0 2,5 S (m 3 /s/mm) 0 2 10 20 36 36 IST: Hydrology, environment and water resources 2015/16 Rodrigo Proença de Oliveira, 2015 17-11-2015 71

Exercise The following direct flow hydrograph was generated from a long, continuous, uniform precipitation event with a net rate of 600 mm/h. Determine the unit hydrograph for 0.3 h. Em determinada bacia hidrográfica, em resultado de uma precipitação útil com grande duração e intensidade constante de 60 mm/h, obteve-se o hidrograma do escoamento directo indicado no quadro. Determine o hidrograma unitário para a duração de 0.3 h. t (h) 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 Q d (m 3 /s) 0 60 150 280 320 340 350 350 IST: Hydrology, environment and water resources 2015/16 Rodrigo Proença de Oliveira, 2015 17-11-2015 72

Exercise The following table shows the unit hydrograph of a given watershed for a 0,5h duration. Determine the unit hydrograph for 20 min. Apresenta-se no quadro seguinte o hidrograma unitário de determinada bacia hidrográfica para a precipitação útil com a duração de 0.5 h. Calcule o HU para uma duração de 20 min t (h) 0.0 0.5 1.0 1.5 2.0 2.5 u (m 3 /s/mm) 0 15 34 17 9 0 IST: Hydrology, environment and water resources 2015/16 Rodrigo Proença de Oliveira, 2015 17-11-2015 73

Flood attenuation in reservoirs

IST: Hydrology, environment and water resources 2015/16 Rodrigo Proença de Oliveira, 2015 Reservoir storage zones 17-11-2015 75 Inflow Afluências Evaporation Evaporação NMC NPA Nme Flood storage volume / pool Volume de encaixe de cheias Net/useful storage Volume útil Dead storage / Volume morto Uptake/abstraction Captação Discharge Descarga Energy Energia H Turbined flow Volume turbinado NMC Maximum design storage level / Nível de maxima cheia NPA Full storage level or top of conservation pool / Nível de pleno armazenamento Nme Minimum operation level / Nível minimo de exploração

Sizing of the flood control storage zone IST: Hydrology, environment and water resources 2015/16 Rodrigo Proença de Oliveira, 2015 76 Inflow Qafluente NMC NPA Flood storage pool Encaixe de cheias Descarga Outflow Net storage pool Qefluente Volume útil Nme Volume morto Dead storage pool Tempo Tempo Peak reduction Redução do pico da cheia Controled flood volume Volume encaixado

Inflow and outflow discharge IST: Hydrology, environment and water resources 2015/16 Rodrigo Proença de Oliveira, 2015 17-11-2015 77 Inflow from the watershed, obtained from the flood analysis. In a reservoir the outflow is a function of the store volume and of the outflow control devices. For example: Qe 3 2 i _ cal c b 2 g Hi

Outflow discharge computation IST: Hydrology, environment and water resources 2015/16 Rodrigo Proença de Oliveira, 2015 17-11-2015 78 H 2 3 Qa c b g H max 2 3 b Qe 3 2 i _ cal c b 2 g Hi V i1 V i Qai Qai 2 1 Qei Qei 2 1 dt Valores inicialmente arbitrários H i Vi A alb i Tempo(h) Qai Vi Hi Qei atrib Qei calc Abs(Qei_atrib-Qei_calc) 0 0 0 0 0 0 0 0 1 dt Qai 1 x x x x x 2 2dt Qai 2 x x x x x 3 3dt Qai 3 x x x x x 4 4dt Qai 4 x x x x x 5 5dt Qai 5 x x x x x Goal seek: Abs(..)=0

Outflow discharge computation IST: Hydrology, environment and water resources 2015/16 Rodrigo Proença de Oliveira, 2015 17-11-2015 79 For each time step: arbitrar Qe i1 V i1 Qai Vi V i H 1 i1 Aalb ˆe Qai 2 1 Q i c b 2 g H 1 i 3 2 1 Qei Qei 2 1 dt Qe i Qe i Qe ˆ 1 N i1 Qe ˆ 1 i1 0,01?? Stop S We need to automate this computation!

Goal seek global via VB IST: Hydrology, environment and water resources 2015/16 Rodrigo Proença de Oliveira, 2015 17-11-2015 80 Col Abs( ) Col Qei_atrib Goal seek aplica-se de t=1 a.

Mathematical modelling

Existing mathematical models HEC Hydrological Engineering Center (USACE). Análise de registos históricos Hydrologic model: Input: Hietogram; Output: Hidrogram; e.g.: HEC-HMS (ex HEC1); Modelação hidrológica Hydraulic model: Input: Hidrogram; Output: h, U, flooded areas; e.g.: HEC-RAS (ex HEC2); Modelação hidráulica IST: Hydrology, environment and water resources 2015/16 Rodrigo Proença de Oliveira, 2015 17-11-2015 82

Hydrologic model IST: Hydrology, environment and water resources 2015/16 Rodrigo Proença de Oliveira, 2015 17-11-2015 83

Hydraulic model IST: Hydrology, environment and water resources 2015/16 Rodrigo Proença de Oliveira, 2015 17-11-2015 84

Hydraulic model - results 4115.34 Geom: novasseccoes_testecoordinates Flow: steady1 4078.38 4024.89 4009.73 4000.74 Legend WS Max WS Ground Bank Sta Novas seccoes_apresntacaonov2003 Plan: Plan 06 13/11/2003 4:52:18 PM Geom: novasseccoes_testecoordinates Flow: steady1 Legend WS PF 1 WS PF 2 WS PF 3 1748.12* 1699.07* 1650.01* Ground Bank Sta 1797.17* Ground 1846.23* 1600.96* 1551.90* 1502.85* Novas seccoes_apresntacaonov2003 Plan: Plan 06 13/11/2003 4:52:18 PM Geom: novasseccoes_testecoordinates Flow: steady1 Legend WS PF 1 WS PF 2 WS PF 3 1453.8* Ground Bank Sta Ground 1404.74* 1748.12* 1699.07* 1650.01* 1600.96* 1355.69* 1179.97 1208.53 1306.63* 1134.45 1257.58* 1404.74* 1086.27* 1179.97 1355.69* 1208.53 1306.63* 1257.58* Novas seccoes Plan: Plan 06 10/10/2003 3:17:13 PM 1134.45 1038.10* 1086.27* 989.934* 941.763* 893.591* 845.419* 797.247* 749.076* 700.904* 652.732* 604.560* 556.389* 508.217* 460.045* 411.873* 363.702* IST: Hydrology, environment and water resources 2015/16 Rodrigo Proença de Oliveira, 2015 17-11-2015 85